Integration by parts Definition and 434 Threads

greetings . it's known that if g(x), f(x) are two functions ,and f(x) is sufficiently differentiable , then by repeated integration by parts one gets : \int f(x)g(x)dx=f(x)\int g(x)dx -f^{'}(x)\int\int g(x)dx^{2}+f^{''}(x)\int \int \int g(x)dx^{3} - ...

Homework Statement Find the integral of 3x* (2x-5)^6*dx, let u= 2x -5. Homework Equations Im not sure if i am meant to use integration by parts or not?? I was able to do previous questions of the topic just using u sub to get rid of the first x variable. The Attempt at a Solution...

Homework Statement \int_{1}^{2} x^2 e^{x} dx Homework Equations Integrating by parts. Writing out chain rule, integrating both sides and rearranging gives ∫f(x)g'(x) dx = f(x)g(x) - ∫f'(x)g(x) dx The Attempt at a Solution \int_{1}^{2} x^2 e^{x} dx = \left[x^2...

Homework Statement Evaluate the integral. Integral = x f(x) dx from 0 to 1 when f(1) = 6, f'(1) = 7. Answer choices: A. 11/6 + 1/6 integral from 0 to 1 x^3f''(x)dx B. 11/12 - 1/6 integral from 0 to 1 x^3f''(x)dx C. 11/3 + 1/2 integral from 0 to 1 x^2f'(x)dx D. 11/3 - 1/2 integral from 0 to 1...

I found this interesting but different way to solve integration by parts problems on the internet: http://imageshack.us/photo/my-images/854/integration20by20parts2.jpg/ It seems to work well for me when doing most textbook problems, except when the integrand contains a natural logarithm. I just...

I'm confused. I was making up some of my own problems involving higher powers of x to integrate. For example: \displaystyle\int x^5 e^{5x}dx I set about going about finding \frac{dy}{dx} up to \frac{d^6y}{dx^6}. u=x^5 \frac{du}{dx}=5x^4 \frac{d^2u}{dx^2}=20x^3 \frac{d^3u}{dx^3}=60x^2...

Homework Statement Here are two instances where the negative sign just changes for no reason. The one's all the way on the right. Why? I don't understand what is going on here. For the second one, it should + cos x

Homework Statement ∫ x2 sin x Homework Equations uv - ∫ v duThe Attempt at a Solution u = x2 du = 2x dv = sin x v = -cos x step 1. x2 - cos x - ∫ -cos x 2x I think -cos x * 2x becomes -2x cos x so now we have step 2. x2 - cos x - ∫ -2x cos x which means I have to integrate by parts...

Homework Statement In this video from which there is a screen shot above the author went from x/2 to 2x and all he said was half is two quarters. right a half is two quarters it is not 2. I just want to make sure that he made a mistake because I've been seeing some real bizarre things in...

Homework Statement integrate .5e^(t/50)*sin(t) Homework Equations integration by parts uv-∫vduThe Attempt at a Solution I am currently in differential equations and I remember from cal II that I have to keep using the equation above until the integral loops around, then set it equal to...

Homework Statement Integrate By Parts (i.e. not using formulas) ∫e3xcos(2x)dx The Attempt at a Solution I keep going around in circles, I know at some point I should be able to subtract the original integral across the = and then divide out the coefficient and that's the final...

Hello. I'm attempting to integrat ∫ln(x+x^2)dx Our professor gave us the hint of x(1+x) I believe u= ln(x+x^2) and du=1+2x/x+x^2 I am not sure what dv should be Any help would be greatly appreciated! Thanks

Homework Statement Hi, I'm doing fouier transforms and I'm not sure how to integrate (2-x)cos(nPi/2)x, (1,2). Anyone able to help me out? Even the indefinite integral would be fine. Homework Equations The Attempt at a Solution I guess u would be (2-x) and dv would be cos(nPi/2)x dx. I'm not...

Substitution method with Integration by Parts? Homework Statement Evaluate the integral... ∫x^3[e^(-x^2)]dx Homework Equations ∫udv=uv-∫vdu The Attempt at a Solution I first tried using integration by parts setting u and dv equal to anything and everything. This seemed to make...

∫xax u=x du=dx dv=axdx v=ax/lna = xax - ∫axdx/lna is my solution right? my problem now is how to integrate the expression xax - ∫axdx/lna please help..

Homework Statement Calculate the following integral exactly (no approximations) by the method of integration by parts: ∫0t SinIntegral[x] dx Homework Equations the following hints are given: D[SinIntegral[x], x] = Sinc[x]; and SinIntegral[0] = 0 The Attempt at a Solution...

Homework Statement Use integration by parts to derive the formula: \int (a^2 - x^2)^n dx = \frac{x(a^2-x^2)^n}{2n+1} + \frac{2a^2n}{2n+1}\int \frac{(a^2 - x^2)^n}{(a^2 - x^2)} dx + C Homework Equations Integration by parts general formula ∫udv = uv - ∫vdu The Attempt at a...

Hi, I'm wondering how to integrate 4xe^(4x). I got: 4[1/4xe^(4x)-1/16e^(4x)+c] ? which reduces to xe^(4x)-1/4e^(4x)+c Is this the correct integral? Thanks.

Homework Statement Solve integral \int^{1}_0(1-x)\frac{d}{dx}\frac{\sin Cx}{C}dx Homework Equations \int udv=uv-\int vdu The Attempt at a Solution u=1-x dv=\frac{d}{dx}\frac{\sin Cx}{C}dx What is v? How to integrate \frac{d}{dx}\frac{\sin Cx}{C}dx?

Homework Statement I am doing self-study. I am on problem 5.6 #27 in the Stewart text 3rd E. I don't understand why the integration limits changed after the given substitution. The given substitution was: x=θ^2 dx=2θdθ Homework Equations Please see attachment. The Attempt at...

Homework Statement \int_0^\infty{ \frac{1}{x} e^{-x}} Homework Equations Integration by parts \int{u dv} = uv - \int{v du} The Attempt at a Solution u = \frac{1}{x} du = \frac{1}{x^2} dx v = -e^{-x} dv = e^{-x} dx -\frac{1}{x} e^{-x} - \int_0^\infty{-e^{-x}...

I'm watching the video series on Quantum Mechanics taught by Leonard Susskind, (from Stanford). On Lecture #3, Dr. Susskind says that integration by parts is: ∫FG' = -∫GF' However from what I know integral by parts to be, there i missing a +FG on the righthand side, or something... since I...

Homework Statement For ordinary 1D diffusion show that the mean value of the square of the position is equal to 2Dt Homework Equations \left\langle {x^2 \left( t \right)} \right\rangle \equiv \int\limits_0^\infty {x^2 p\left( {x,t} \right)dx} \frac{\partial }{{\partial t}}p\left(...

Homework Statement ∫▒〖(2x-1)e^(-x) 〗 dx I don't want to butcher this but I know you use integration by parts, I just don't know how to do this one in particular because i is one of the simple ones I was told. Please Help

Homework Statement problem: \int2arctanx dx 2\intarctan dx u=arctanx du=1/(1+x2) v=x dv=dx xarctanx-\intx/(1+x2) integrate by parts a second time... u=x du=dx v=arctanx dv=1/1+x2 xarctanx-\intarctanx My final answer I get it 2xarctanx-2xarctanx+2/x2+1 which is...

What is the difference? I was pretty bored last night so I got onto Yahoo Answers and answered a few calculus questions. It was a simple integration by parts question: \intxsin(x) dx I solved as: u = x du = dx dv = sin(x) dx v = -cos(x) uv - \intvdu -xcos(x) + \intcos(x)dx =...

Here I used integration by parts to try to solve an integral (I got it wrong, it seems), I know this has no "simple" solution, but, can anyone explain me exactly what did I do wrong? Here is what I did...

Homework Statement Hi There is a step in my book, which I can't follow. It is the following \int_0^1 {w\left( {\frac{{d^2 u}}{{dx^2 }} - u + x} \right)dx} = \int_0^1 {\left( { - \frac{{dw}}{{dx}}\frac{{du}}{{dx}} - wu + xw} \right)dx} + \left[ {w\frac{{du}}{{dx}}} \right]_0^1 I...

Homework Statement Find the solution to: y' = x.y.cos(x^2)Homework Equations Integration by Parts method.The Attempt at a Solution Step 1 (dy/dx).(1/y) = x.cos(x2) (1/y) dy = x.cos(x2) dx Step 2 Integrate both sides. ln|y| = integratal of [ x.cos(x2) dx ] Step 3 Using integration by...

Somebody could explain me, how of the second line arrive to the third one? in my book says that is integration by parts, please helpppp :eek:

The attempt at a solution \begin{equation*} \begin{split} \ -\ i\int\psi^* \frac{\partial{\psi}}{\partial x}= \\ -i(\psi^*\psi\ - \int\psi \frac{\partial\psi^*}{\partial x})\space\ (?) \end{split} \end{equation*} I thought \psi^*\psi\ = \ constant\neq\ 0. However, it vanishes in...

I'm just curious about the proofs of Integration by Parts & the Change of Variables formula as given in this book on page 357. I think there are a lot of typo's so I've uploaded my rewrite of them but I am unsure of how correct my rewrites are. If someone could point out the errors & why I...

Basically I have answered a question using the integration by parts formulae to work out the centre of gravity inside a fan blade using :- v.du/dx = v.u - u. dv/dx with the integral limits of 0 ==> 20 when v = x then dv/dx =1 when du/dx = 0.3 sinx then u = 0.3cos x and sub this into...

Homework Statement Take the integral of the following: 1. ln(2x+1) 2. arctan4x 3. ecosxsin2x evaluated from 0 to pi The Attempt at a Solution 1. took the derivative of ln(2x+1) and integrated dx. my solution was: xln(2x +1) + x + [(2x + 1)-2]/2 + C The books answer was...

Homework Statement \int xarcsin2xdx 2. The attempt at a solution Can someone explain to me what is happening at step 2? I understand how the integration by parts was done, but where does the (1/8) or (2x) come from?

Homework Statement \int\sqrt{4+9x^{2}}dx Homework Equations Pythagorean Identities? The Attempt at a Solution I find it sort of cumbersome to use the special formatting here, so I hope it is okay that I just photocopied my work on paper. You can see how far I made it, but...

1. How to solve integral of (1/(t2-t))dt 2. to be solved without using laplace transforms 3. integral of( uv)= u*(integral of v) -integral of ((u')*(integral of v)) ... right? integral of (1/t^2-t) = integral of (1/t)*(1/t-1)dt = (1/t-1)*(log t) - integral((-1/(t-1)2*logt ...i don't...

Homework Statement integrate (x*2e^x)/(2e^x-1)2 from x=0 to infinity Homework Equations The Attempt at a Solution let t=2e^x-1 => x=ln((t+1)/2) dt = 2e^x dx Thus equation is now integrate (ln((t+1)/2))/t^2 dt from t=1 to infinity Then let u = (t+1)/2 => 2du=dt Equation now...

I am assuming that the solution was arrived at through integration by parts, however I am not able to completely work through it. First given: cB= XB/Vm the next step shows the solution to dcB given as: dcB=(1-dlnVm/dlnxB)(dxB/Vm)

Homework Statement i)Use integration by parts to express: I(n) = ∫ sin^n (x) dx in terms of I(n-2). ii) Hence show that ∫(π/2 for top, π/4 for bottom) 1/[sin^4 (x)] dx = 4/3 Homework Equations Reduction Formula and Trig Identity [sin²(x) + cos²(x) = 1] π = pi The Attempt at a...

Homework Statement i have to create a general formula for integral of (x^n * e^x) dx using whatever method i deem appropriate. (the only way i could think of is by parts) Homework Equations int(x^n * e^x)dx int(uv')dx=uv-int(vu')dx The Attempt at a Solution i used integration by...

Homework Statement ∫ x * e^-x dx Homework Equations Integration by parts: Just wondering if below is correct. Not brilliant with Integration by parts and not sure if my +ve and -ve signs are correct. Some help to say if i am correct or where i have gone wrong would be brilliant...

[b]1. The problem statement, all variables and given/known Homework Statement \int \frac{sinx}{x}dx Homework Equations The Attempt at a Solution Which method should work here? I tried integration by parts and it looks too much. Is there a way to solve it without approximating it with the...

Homework Statement I had this integral on my physics homework and for the life of me couldn't solve it. I ended up using Maple..well wolframalpha.com because Maple's output sucks. Anyway here is the problem. \int_{0}^{\infty} x e^{-2 \alpha x}dx Homework Equations \int u dv = uv - \int v...

I would like to solve the following integral but I am unsure of the best way to solve it: \int_{0}^{H}xsin(\frac{w}{x})cos(\frac{x}{w})cosh(\frac{H}{w})dx Is it possible to use integration by parts?? Thanks in advance

Hi All, This is not a homework question, I am just trying to be come quicker at integrating by parts, when performing Laplace Transforms. My textbook gives a basic example for performing the Laplace Transform of the variable t, to the transformed variable of s for the equation...

the expression to integrate is: \int x^{3}e^{x^{2}}dx and in the spirit of "LIATE" I set my u and dv as the following: dv=e^{x^{2}}dx u=x^{3} however, doing this that I integrate dv=e^{x^{2}}dx in order to get v...and unless I'm missing something, this does not seem like an easy...

problem is to integrate the following by parts: \int x\sec^{2}xdx my feeling is convert the secant term to cosine by: sec^{2}x=cos^{-2}x\Rightarrow\int\sec^{2}xdx=\int\cos^{-2}xdx then: u=\cos^{-2}x\implies du=2\sin x(\cos^{-3}x) and also: dv=xdx\implies v=\frac{x^{2}}{2}...

problem is solve the following integral by parts: \int\ln(2x+3)dx I used substitution: u=ln(2x+3) \Rightarrow du=\frac{2}{2x+3}dx and for dv: dv=dx \Rightarrow v=x however, once I plug all these into my integration by parts formula, I get: x\ln(2x+3)-\int\frac{2x}{2x+3}dx and this new...

Hi -- I want to integrate this integral and ask if my work is correct or not. \int^\infty_0 dx x^{\alpha-1} e^{-x} (a+bx)^{-\alpha} ---------- I want to integrate it by parts, so I have (a+bx)^{-\alpha} = v -b\alpha(a+bx)^{-\alpha-1}dx = dv x^{\alpha-1} e^{-x} dx = du...