Message received. {lnx} en. Related Symbolab blog posts. . Type in any integral to get the solution, steps and graphFree antiderivative calculator - solve integrals with all the steps. In particular, according to the prime number theorem, it is a very good approximation to the prime-counting function, which is defined. Follow edited Feb 5, 2013 at 1:21. But this makes it clear that, yes, u-substitution will work over here. Answer link. Then du = 1 / (1 + x2)dx and v = x. using integration by parts. I know that ∫ dx x ln(x) = ln(ln x) + C ∫ d x x ln ( x) = ln ( ln x) + C. The first one is quite lame, that ln can only deal with a non-zero positive domain (as long as we are sticking to the real numbers). That special log property: , 100 integrals: math for fun,In this case we take #u(x) = (lnx)^2# and #v(x) = x#, so that: #int (lnx)^2dx = x(lnx)^2-int 2xlnx(1/x)dx= x(lnx)^2-2int lnxdx# We solve this last integral again by parts: #int lnx = xlnx - int x*(1/x)dx = xlnx -int dx = xlnx -x+C#. Calculate limits, integrals, derivatives and series step-by-step. Using integration by parts to find the integral of ln xIntroduction to integral of sin(lnx) In calculus, the integral is a fundamental concept that assigns numbers to functions to define displacement, area, volume, and all those functions that contain a combination of tiny elements. Related Symbolab blog posts. But since y = ln(x) y = ln ( x), we have ey =eln(x) = x e y = e ln ( x) = x and so our original. eln ( x) d dxln(x) = 1. f(x)g ′ (x) = f(x)g(x) − ∫ f ′ (x)g(x) Now we are supposed to assign f(x) to the part that gets easier when we differentiate it, and g ′ (x) to something that gets easier once we integrate it. In mathematical form, the integral of cos (lnx) is: ∫ cos ( ln x) d x = 1 2 [ x sin ( ln x) + x cos ( ln x)] + c. ln (abslnx)+C We have the integral: int1/ (xlnx)dx Use substitution. Here the first function is ln x ln x and the second function is x x. So I think setting ln2(x) to be f(x) would be easier, since differentiating it would get us 2lnx x. Type in any integral to get the solution, steps and graph. You can also get a better visual and understanding of the function and area under the curve using our graphing tool. Let: #u = ln(x+1)# #du = 1/(x+1)dx# #dv = 1dx# #v = x# #uv - intvdu#. Since the original function involves lnx, we are justified in assuming that x>0 and writing: int x^(-lnx) dx =lnx+C. Answer link. This gives you ∫∞ 0ln(x)e − x dx = ∫0 1ln(ln1 u)( − du) = ∫1 0ln(ln1 u)du This answer now shows the answer is − γ. Keep in mind: ln( x−−√) = ln(x) 2. My Notebook, the Symbolab way. Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series. Simplify. using integration by parts. Step 5. You can find out more about the function here. You can also use the change of variable formula setting. Related Symbolab blog posts. Using integration by parts. Login. This calculus video tutorial explains how to find the integral of lnx/x^2 using integration by parts. Solve problems from Pre. This is a common integral: ∫ 1 u du = ln(|u|) +C. In question 2 is it possible to rewrite the equation to lnx * lnx instead of (lnx)^2 and integrate by parts? The problem I'm having when I try to use that method is that after I integrate lnx for the first time and substitute it back into the equation I get: ∫lnx * lnx dx = x(lnx)^2 - x - ∫(xlnx-x)/xHere's a classic integration problem involving a lnx and an x in the denominator. . en. I use the form: #int u dv = uv-intvdu#. Here, PV denotes Cauchy principal value of the integral, and the function has a singularity at . We rewrite the integral as ln (x) times 1dx, then choose f (x) = ln. I tried integrating this by parts but I end up getting integral that doesn't converge, which is this $$ int_0^pi dfrac{x^2cos (x)}{sin(x)} dx$$ So can anyone help me on this one? calculus; integration; definite-integrals; improper-integrals; Share. Advanced Math Solutions – Integral Calculator, common functions. Integral of under root tan x can be written as: ∫ √ (tan x) Let’s find the integral of under root tan x with respect to x. Differentiate with respect to x. #int u v' = uv - int u' v# #I = int ln x / x dx# #= int d/dx(ln x) ln x dx# #= ln x ln x - int ln x d/dx(ln x) dx# #= ln^2 x - int ln x/x dx# #implies I = ln^2 x - I + C#Secondly, I have attempted to find the n n th integral of ln(x) ln ( x) and this is what I found. 26), is defined for real as. They state that there is no easier closed form solution, but that with the exponential integral and imaginary numbers it will only be equivalent to the actual integral in a. Tap for more steps. In summary, the author is trying to find a solution for the homework statement ei (1,-1ln (x)). " Which is nothing but, integration by parts. The formula for the integral of x sin x is given by, ∫xsinx dx = −x cos x + sin x + C, where C is the integration constant. Step 3. integral-calculator int lnx. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. I want to know if it can be solved by any other nice/elegant method. ∫ x ln x dx =Ei(2 ln x) + C. Related Symbolab blog posts. Learning Outcomes. Simplify. Then, ∫ log(log(x))dx = x log(log(x)) − ∫ 1 log(x) dx = x log(log(x)) − li(x) + C ∫ log ( log ( x)) d x = x log ( log ( x)) − ∫ 1 log ( x) d x = x log ( log ( x)) − li ( x) + C. I nverse L ogarithm A lgebraic T rig E xponential. Related Symbolab blog posts. Advanced Math Solutions – Integral Calculator, the complete guide. > <. Cite. It is often used to find the area underneath the graph of a function and the x-axis. 1 Answer. Functions. . en. In this section, we will calculate the definite integration of log x with different limits. Keep integrating by parts until you see a pattern. By the definition of the fundamental theorems of definite integrals, we can compute the definite integration of tan x between any two intervals. The first integral, we use u -substitution: Let u ≡ ln(x), hence du = 1 x dx. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. en. Method 2. There is no integral rule or shortcut that directly gets us to the integral of ln(x). . The Integral Calculator lets you calculate integrals and antiderivatives of functions online — for free! Our calculator allows you to check your solutions to calculus exercises. (And, of course, verified by differentiating the answer. There are other solutions: Both of the solution presented below use Integration by Parts. integral \int 1/ln x. I The derivative and properties. pt. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. The definite integral of x is used when the integration has to be performed between two specified limits. etc. int ln(x^{2}) dx. . 1. nomadreid said: I have seen two justifications for the absolute value sign in ln|x| as the antiderivative of 1/xm, but neither one seems sufficient. So that implies du = dx / x, and v = x. The formula of integral of ln contains integral sign, coefficient of integration and the function as ln(x). . Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series. Calculus 1 Final Exam Review: how to do the integral of ln(x), the natural logarithm function, by using integration by parts that you will learn in Calculus 2. Membros do canal podem escolher questões para esta playlist. To integrate by parts, let u= ln x, dv= ln x dx. Related Symbolab. Formula Integral. Indefinite integration of $ln(1+x^2)arctan x$ 4. near Piacenza (Italy) Sep 6, 2011. In the formula ∫ udv = ∫ ∫ u tan = ln tan. If \(x>0\) and \(y=\ln x\), then \(e^y=x. Why is the hyperbolic area of a horocycle non-convergent when the area of an ideal triangle is not?[int frac{ln{x}}{{x}^{2}} , dx] +. ∫arctanxdx = xarctanx − ∫ x 1 + x2 dx. Related Symbolab blog posts. The Integration by Parts formula gives. Then we have by integration by parts: ∫ udv = uv − ∫ vdu. Both types of integrals are tied together by the fundamental theorem of calculus. So consider the second function as 1 1. I = ∫xsin(lnx) 1 x dx. Like with lower powers of ln(x), such as ln^2. Find $int{arctan x},mathrm dx$ without substitution. Set up the integral to solve. Your integration by parts in the beginning is correct. This calculus video tutorial explains how to find the integral of (lnx)^2 using integration by parts. Type in any integral to get the solution, steps and graph. Let u = ln(x), dv 1 2dx, u = ln ( x), d v = 1 2 d x, so we have v = x 2, du = 1 xdx v = x 2, d u = 1 x d x. ( x) = ∫ 1 x d t t. To do so, we use integration by parts. substitute. If you are studying maths, then you should learn the formula for Integration By Parts (IBP), and practice how to use it: # intu(dv)/dxdx = uv - intv(du)/dxdx #, or less formally # intudv=uv-intvdu # I was taught to remember the less. ∫ + ∞ 0 e − xlog(x)dx = Γ ′ (1) = Γ(1)ψ(1) = − γ follows from differentiation under the integral sign, as shown by Felix. Solve problems from Pre. en. The formula is given below. u = e − x. We rewrite the integral as ln (x) times 1dx, then choose f (x) = ln (x) and g' (x) = 1. i. integral of arctan(ln(x), 1/ln(x)) area between ln(x) and x-axis from x = 0 to 1; integrate x ln(x) integrate x^lnx ; Riemann surface 1/4 z^2 (2 log(z)-1) Integration by parts: ∫ln (x)dx. Organic Chemistry Tutor - Playlists:. At this stage, I was forced to focus on solving the arctangent integral that is trailing on the end up there. For x > 1, this is just the area under the curve y = 1 t from 1 to x. ∫x 11 t dt = − ∫1 x1 t dt, so in this case it is the negative of the area under the. This calculus video tutorial explains how to find the integral of lnx/x using the u-substitution integration technique. Sorted by: 12. . The function ln x is also known as the natural log of x. For math, science, nutrition, history, geography, engineering, mathematics, linguistics, sports, finance, music…The integral of xlnx is equal to (x 2 /2) lnx - x 2 /4 + C, where C is the constant of integration. Anyway, to integrate ln (x), we use Integration by Parts (have you covered Integration by Parts yet?), i. And dv = dx ⇒ v = x. etc. ∫lnxdx = xlnx − x + C = x(lnx − 1) + C. While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful. To find the integration of lnx, we will use the integration by parts formula. calculus-calculator int lnxdx. Tap for more steps. In this video I will teach you how to integrate ln(x^2). . 3 Answers. en. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Solve problems from Pre. I would start with a u-substitution and separate the integral. what is the integration of tan x ? Q. The value of the integral of x can be computed using the power rule, (int x^{n}dx = frac{x^{n+1}}{n+1} + C), with n = 1. But the derivative of ln(x) is 1 x, so f (x) = g'(x). Then we have by integration by parts: ∫ udv = uv − ∫ vdu. Integration by parts formula: ? u d v = u v-? v d u. In mathematical form, the integral of lnx^2 is: $∫(ln x)^2dx = x(ln x)^2 - 2xln x+2x+c$improper integral of ln(x) from 0 to 1, two ways, Check out Oon Han, , Mimi Meow, Feynman. integral-calculator. List of integrals of logarithmic functions. We can then apply Integration By Parts: Let {u = lnx ⇒ du dx = 1 x dv dx = 1 x2 ⇒ v = − 1 x. If we allow more generality, we find an interesting paradox. Repeat as needed to reduce the exponent to zero, and one sees that the limit is zero. Calculus Introduction to Integration Integrals of Exponential Functions. 0. Save to Notebook! Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. The antiderivative of a function is basically the function's integral. Type in any integral to get the solution, steps and graph. \) Differentiating both sides of this equation results in the equation \(e^y\frac{dy}{dx}=1. integral int ln x dx. Notice that ln1 = 0. = lim t → 0 + ( 1 2 x 2 ln x − 1 4 x 2 ) | t 2 Evaluate ∫ x ln x d x using integration by parts with u. Integration is the basic operation in integral calculus. Using ln(e) = 1: = ∫ ln(x) + x x dx. Furthermore, the function y = 1 t > 0 for x > 0. Extended Keyboard. 718 281 828 459. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. en. (x\ln (x)) \int e^x\cos (x)dx Integration can be used to find areas, volumes, central points and many useful things. Hence, the required integral is ∫ ln x d x = x ln x-x + C where C is a constant of integration . So, we want to integrate this: We then let u = ln (x), and dv = dx. . Suggest Corrections. Let u = x and. Integrate functions involving logarithmic functions. We see that on the right side. Example. Calculus 1 Final Exam Review: The Integral Calculator solves an indefinite integral of a function. . Related Symbolab blog posts. Advanced Math Solutions – Integral Calculator, the complete guide. The integration of ln x is an antiderivative of the ln x function which is equal to xln x-x. Let u = ln(x), dv 1 2dx, u = ln ( x), d v = 1 2 d x, so we have v = x 2, du = 1 xdx v = x 2, d u = 1 x d x. In mathematics, the logarithmic integral function or integral logarithm li ( x) is a special function. Integral of ln(x)/x - How to integrate it step by step using the substitution method!👋 Follow @integralsforyou on Instagram for a daily integral 😉📸 @integ. Integral of ln(x) via integration by parts (DI method)![Learn Calculus FAST] Check out the following playlists👉Limits: answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. This calculus video tutorial explains how to find the integral of lnx using integration by parts. Other topics of video are:Integration of e^(ln(x))Integration of exp(ln(x))Integr. Step 2. Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series. 1. int ln (lnx) dx = xln (lnx) - int 1/lnx dx Using integration by parts with u = ln (lnx) and dv = dx, we get. Let u=ln (x) so that du=1/x dx and dv=1/sqrt (x) dx=x^ {-1/2} dx so that v=2x^ {1/2}=2sqrt (x). How to integrate ln(2x) by using the integration by parts methodThe integration technique involved here is to realize that ln(2x)dx is the same as ln(2x) tim. Integral of ln (x)/ (x+1) from 1 ot 0. 🏼 - Integral of ln(1+x^2) - How to integrate it step by step using integration by parts!🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Trouble integrating in an efficient way. integral-calculator. ln (x) dx = u dv. However, because when t is 0, the Ei function is undefined at 0, you must make it the sum of two integrals approaching 0. Created by Sal Khan. Integration by parts is not necessary. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Advanced Math Solutions – Integral Calculator, integration by parts, Part II. intlnxdx=x (lnx-1)+"c" To find an antiderivative of lnx, we must find intlnxdx. So the integration of lnx is equal to ∫ln (x)= xlnx-x+C and this is derived using the integration by parts formula. Answer link. 🏼 - Integral of x*ln(x) - How to integrate it step by step using integration by parts!🔍 𝐀𝐫𝐞 𝐲𝐨𝐮 𝐥𝐨𝐨𝐤𝐢𝐧𝐠 𝐟𝐨𝐫 𝐚. Trigonometric integral. Choose u = cos log x and dv = dx. . The formula of cos (lnx) integral contains integral sign, coefficient of integration and the function as sine. We would like to show you a description here but the site won’t allow us. Put u=lnx and v=1. Let u=lnx so that du=1/xdx. This page lists some of the most common antiderivatives. Related Symbolab blog posts. Keep in mind: ln( x−−√) = ln(x) 2. You can also help support my channel by becoming a memberyour math problems using our free math solver with step-by-step solutions. 7. Related Symbolab blog posts. In order to use sin(lnx)dx in dv, we'll need to be able to integrate dv. The first definition I found is that. The solution is shown here (sometimes Wolfram Alpha has trouble computing integrals with lnx properly, so I gave the backwards check). Related Symbolab blog posts. Integral of ln(x)/x - How to integrate it step by step using the substitution method!👋 Follow @integralsforyou on Instagram for a daily integral 😉📸 @integ. en. integral-calculator. I = ∫xsin(lnx) 1 x dx. Type in any integral to get the solution, steps and graph. $$ ∫ \ln(x)\,dx\,, $$ but integration by parts requires two. . This video shows how to find the antiderivative of the natural log of x using integration by parts. The integral of x ln x is of the form. Share. Related Symbolab blog posts. Solve problems from Pre. In this video, we will find out integral of exponential of natural log of x. So. We can do integration by parts, however, letting: {u = (lnx)2 =⇒ du = 2lnx x dx dv = 1 xdx =⇒ v = lnx. Natural log of x is u-- we set that equal to natural log of x-. We know the antiderivative of ln ( x) is x ln ( x) - x, and so the definite integral is calculated as. Integral(ln(x)) = xln(x) - Integral(x1/x) Awesome. Logarithmic integral function. To find an antiderivative of lnx, we must find ∫lnxdx. If you can use the chain rule and the fact that the derivative of ex is ex and the fact that ln(x) is differentiable, then we have: d dxx = 1. In either case it does not mean. en. We will be using integration by parts in order to take the integral of ln x. Postagens de blog relacionadas ao Symbolab. Related Symbolab blog posts. This typically suggests making u=lnx to complete the substitution!Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. Integration goes the other way: the integral (or antiderivative) of 1/x should be a function whose derivative is 1/x. In my view, writing the antiderivative as $ln|x|$ is a neat way of summarising two results in one, but it carries a serious risk of disguising what is really going on. Similar questions. Advanced Math Solutions – Ordinary Differential Equations Calculator, Exact Differential Equations. ∫lnxdx = xlnx −∫dx = xlnx −x = x(lnx − 1) Answer link. Let us study more about the integration of. Related Symbolab blog posts. Symbolab is the best integral calculator solving indefinite integrals, definite integrals, improper integrals, double integrals, triple integrals, multiple integrals, antiderivatives, and more. The indefinite integral cannot be expressed in terms of elementary functions. The suggestion is made to consider improper integrals, and the conversation then delves into the process of solving the integral using integration by parts. . You don't. The logarithmic integral defined in this way is implemented in the Wolfram Language as LogIntegral [ x ]. Evaluate each of the integrals R 1 0 f (x) dx, R 1 0 g(x) dx, and R 1 0 h(x) dx exactly using the First FTC. Quanto: Again very impressive. Compute answers using Wolfram's breakthrough technology &. Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. 2) I Definition as an integral. Advanced Math Solutions – Integral Calculator, the complete guide. (b) The integral of y = x nis Z x dx = x(n+1) (n +1), for n 6= −1. (y = ln (5x^4)) Before taking the derivative, we will expand this expression. Save to Notebook! Free integral calculator - solve indefinite, definite and multiple integrals with all the steps. 1. However, I often use integration by parts and I wonder what is wrong here, and what should I do to avoid it (here it's plainly wrong, but what if the mistake was more subtle?). Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. This article will cover topics like integration of log x, Definition, Integral of Ln x Formula, Integration of Log x Proof, Definite Integral of ln x, Integral of Ln x From 0 to 1, solved Examples, and FAQs. The first and most vital step is to be able to write our integral in this form: This integral is good to go!Advanced Math Solutions – Integral Calculator, the basics. Tap for more steps. ∫ u d v = u v − ∫ v d u. what is integration of x sin inverse x. Entonces, dejaremos dv = 1 dx. int frac{ln(x)}{x}dx. Both of these are fairly simple integrals: I = xln(1 + x) − x + ln(1 +x) +C. 19: Axes for plotting the functions in Activity. This video shows how to find the antiderivative of the natural log of x using integration by parts. Let u = lnx. where c and d can be arbitrary (possibly different) real numbers. Answer link. Type in any integral to get the solution, steps and graph. If taking the definite integral of ln(x), you don't need the C. We have. Approximating an Integral by Expanding it's Integrand. I = ∫ln x ⋅ 1dx – – – (i) I = ∫ ln x ⋅ 1 d x – – – ( i) Integration of lnx. Type in any integral to get the solution, steps and graph. 7182. en. Integration by Parts Sqrt x ln x. Answer link. Separating the summed integrals: = ∫ ln(x) x dx +∫dx. The solution is shown here (sometimes Wolfram Alpha has trouble computing integrals with lnx properly, so I gave the backwards check). Advanced Math Solutions –. Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step Free Pre-Algebra, Algebra, Trigonometry, Calculus, Geometry, Statistics and Chemistry calculators step-by-step evaluating the indefinite integral of lnx (the natural log of x) 1. But how to prove this? Before proving the derivative of ln x to be 1/x, let us prove this roughly by using its graph. int lnx /x^3 dx = (-lnx)/(2x^2 ) - 1/(4x^2) + C You should learn the IBP formula: int u(dv)/dxdx=uv - int v (du)/dxdx So essentially we are looking for one function that simplifies when it is differentiated, and one that simplifies when integrated (or at least is integrable). We have now reached. What patterns do you observe? Figure 5. ∫udv = uv − ∫vdu. I'm assuming that we have ∫lnx2 dx. It is used to transform the integral of a. This order of priority can help you decide. ∫0 −∞tnetdt = (−1)n∫∞ 0 tne−pdp = (−1)nn! should your tn should be p on the right hand side after the −1). In other words, the derivative of the natural logarithm of x is 1/x. Step 2. As we just saw, this is ln (x). Type in any integral to get the solution, steps and graph. Free Online Integral Calculator allows you to solve. Evaluate the indefinite integral: integral of ((ln x)^3)/(x) dx. The Fundamental Theorem of Calculus allows a definite integral to be evaluated using the anti-derivative. So my preference, if I have an integral giving $ln(hbox{something})$, is to work out whether the "something" is negative or positive, and put in a minus sign, or not, as. The derivative of ln ( x) is 1 x : d d x [ ln ( x)] = 1 x. The logarithmic integral (in the "American" convention; Abramowitz and Stegun 1972; Edwards 2001, p. Follow edited Jun 16, 2016 at 11:47. Making necessary. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things. 56]} you can see that your function at zero continues indefinitely towards #-oo#. Let u = lnx ⇒ du = 1 x dx. The formula of antiderivative of ln x 2 contains integral sign, coefficient of integration and the function as sine. Type in any integral to get the solution, free steps and graph. The antiderivative of ln x is the integral of the natural logarithmic function and is given by x ln x - x + C. Related Symbolab blog posts. Calculate limits, integrals, derivatives and series step-by-step. We’ve covered quite a few integration techniques, some are straightforward, some are more challenging, but finding. Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin. 1: (a) When x > 1, the natural logarithm is the area under the curve y = 1 / t from 1 to x. Hence, the required integral is ∫ ln x = x ln x-x + C,where C is a constant. Advanced Math Solutions – Ordinary Differential Equations Calculator, Exact Differential Equations. Type in any integral to get the solution, steps and graph. All common integration techniques and even special functions are supported. calculus-calculator int frac{1}{lnx}dx. . where C is the constant of integration. Can the following integral integrated by parts? $$intln x;sin^{-1} x, operatorname d!x$$ Stack Exchange Network. The trick is to write $ln(x)$ as $1⋅ln(x)$ and then apply integration by parts by integrating the $1$ and differentiating the logarithm:Proof. − ln(tan x) cos x + ∫ 1 tan x 1 cos2 x ⋅cos xdx = − ln(tan x) cos x + ∫ csc xdx. Evaluate the integral using techniques from the section on trigonometric integrals. substitute u=ln (x), v=x, and du= (1/x)dx. Let's rewrite this integral. Type in any integral to get the solution, steps and graph. High School Math Solutions –. csss. Integral of sin(lnx)/lnx Integral by Feynman's Technique Supreme IntegralCheck out more math tutorials: Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series.