Integration by parts Definition and 438 Threads

I'm doing a problem where I'm supposed to use integration by parts. I have: Integral ln(x+3)dx u=ln(x+3) dv=dx du=1/(x+3) v=x integral ln(x+3) = xln(x+3) - integral x/(x+3) That's as far as I've gotten. I know that I should be able to find the integral of x/(x+3)...

Why is it that when I do integration by parts on cyclic functions such as (sinx)e^(inx), I get a trivial answer like C=C, C is a constant Have I done something wrong or are there other methods of doing those integrals?

hello could someone give me a pointer here. this integral ∫ln(x + c)dx my guess is, by integration by parts (ab)' = a'b + ab' ∫ba = ab - ∫b'a so here a = ln(c + x) b = c + x a' = 1/(c + x) b' = 1 ab = (c + x)*ln(c + x) and ∫b'a = ∫ ((c + x)/(hc + x)) dx = ∫dx = x...

hi..im new to this topic..can someone check to see if this is right? \int (xe^-^x)dx = \int udV = uV - \int Vdu =x(-e^-^x)- \int -e^-^x =-xe^-^x-e^-^x+C thanks

Hello I am teaching myself Quantum Mechanics from Griffiths. I have run into a mathematical problem which I need help with. As I have found no convincing answer, I am posting all the details here. Ref :Section 1.5 (Momentum) in "Introduction to Quantum Mechanics (2nd Edition)" by David J...

First off, I hope these images show up - I don't have time to figure out this latex stuff atm, so it's easier just to throw the formulae together in openoffice. I'm working on the Laplace Transform for http://home.directus.net/jrc748/f.gif Which is obviously...

I'm kind of lost on where to go next with this integration by parts problem. I have to integrate e^xcos(x)dx. I've gotten as far as one step of integration by parts, but I can't understand how this will help. It seems I'll just be going in circles. I have: e^xsin(x) - int(e^xsin(x))dx...

Okay, so here is the problem I have, which I am getting tripped up on for some reason: a) Use integration by parts to show that \int_{a}^{b} f(x) dx = bf(b) - af(a) - \int_{a}^{b} xf'(x) dx this was pretty easy, just regular old integration by parts with limits of integration. b) Use the...

Integration by parts :( hi I have been trying this question for quite a while now and am unsure of what to do. Any help would be apprectiated. Integral x^13 cos(x^7) dx I know you have to use integration of parts. Here is what i have done so far: let U=x^3 dU =13x^12 dx dV=cos(x^7)...

Does the integral of x(ln x)^4 = x^2/x(ln x)^4 - x^2(ln x)^3 + 3/2 x^2 (ln x)^2 - 3/2 x^2(ln x) + 3/2 x +C ? Or did I do something completely wrong? Sorry I didn't show my work, it would probably take me 30 mins to type it up here.

integration by parts?? just trying to figure out this integral int(x^2 (1+x^3)^4 dx) when i integrate by substitution i get anti deriv... 1/15 (1+x^3)^5 which is not the same (but close when u plug in values of x) to 1/15*x^15 +1/3*x^12 + 2/3*x^9 + 2/3*x^6 + 1/3*x^3 am i going about...

I've got a simple, at least it seems so; \int \sqrt{9-x^2}dx I MUST solve it "by parts" (withtout trigonometric substitutions), but I'm stuck. If i choose u = (9-x^2)^(1/2), du = -x/((9-x^2)^(1/2)), dv = dx, v = x. I then have; x\sqrt{9-x^2} + \int \frac{x^2dx}{\sqrt{9-x^2}}...

this no homework, but nevertheless can someone hint me how this integration by parts works? \int {d^4 } x\frac{{\partial L}}{{\partial \left( {\partial _\mu \phi } \right)}}\partial _\mu (\delta \phi ) = {\rm{ }} - \int {d^4 } x\partial _\mu \left( {\frac{{\partial L}}{{\partial (\partial...

Ok guys, this is my first post. Please go easy...:redface: This question is from Morris Kline's Calculus: An Intuitive and Physical Approach and unfortunately there aren't solutions for all questions (really annoying). I'm not even sure if this counts as a contradiction but anyway: Let...

Hi, I'm a bit confused as to what I should assign u and dv in this integration by parts: ln(1+x^2)dx I remember a general rule called the "LIPATE" rule... which is basically Logarithms, inverse trigs, poly, algebra, trig, then exponentials... Now... would I assign u = ln(1+x^2)? and...

Integration by parts... I just started Calc. II and though I struggle a bit, it's fascinating. I have been fooling with a problem lately...one of those standard problems that professors like to assign, and it usually appears in calculus texts: Have ya'll ever done integration by parts with...

Show that x \frac{d(\delta (x))}{dx} = -\delta (x) where \delta (x) is a Dirac delta function. My work: Let f(x) be a arbitrary function. Using integration by parts: \int_{-\infty}^{+\infty}f(x)\left (x \frac{d(\delta (x))}{dx}\right)dx = xf(x)\delta (x)\vert _{-\infty}^{+\infty} -...

My professor gave me the following formula for integration by parts in my multivariable calculus class. He said that we wouldn't find it in our book, and he didn't provide a proof. I have tried to work through it, but I am still left with one question: Why is it necessary that the curve is...

It's not homework, but i think it can make someone think a little. \int\frac{dx}{x} Take it by parts. If you'll be as careless as me you can make a discovery :smile:

Integration by parts HELP ! Ok to be honest with all of you reading this post, i just don't understand how integration by parts work. Can someone please explain how it works? I have looked on the internet for help reading through all the notes but i still do not understand. So please somone...

Can anyone outline, and this is a rather large request, the step by step integration by parts for <C>? This is not a homework question but more something i need to be able to do on tuesday for my final, and have been trying to do for two days.

show that INT x sec^2x dx = pi/4 - ln2/2 (between pi/4 and 0) pls help i don't know where to start i know it is integration by parts - just don't know how i should rearrange it. thanks

hi guys just doing some revision and I am stuck on this question *integral sign* x^2 . exponential ^ -3x . dx I know i have to use integration by parts, but i just can't seem to get it out any ideas? thanx

If f(0)=g(0)=0, show that \int _0 ^a f(x) g ^{\prime \prime} (x) \: dx = f(a) g^{\prime} (a) - f^{\prime} (a) g (a) + \int _0 ^a f ^{\prime \prime} (x) g (x) \: dx I know I need to use integration by parts, but I'm having a hard time figuring out the right choice of u and dv. What I do...

I forgot a little detail in the integration by parts formula Is it \int u \,dv = uv + or - \int v \,du I don't remember if its plus or minus...

Greetings all, here goes... The integral of (xe^(x))/((x+1)^(2)) Thanks

i'm trying to complete my notets from my calculus II class. my professor showed us how to do the following integral using integration by parts but I'm not following his reasoning could some one fill me in on what I'm missing. thanks in advance. \int^{\pi}_03x\sin\frac{x}{2}\\{dx} let \...

ok i`m really struggling with the concept. I've been asked to find the indefinite integral of; \int \frac{x^2}{(2+ x^3)} dx so before i beg for the answer could someone confirm that i`ve got the right rule to solve this; \int u(x) v'(x) = [ u(x) v(x)] - \int v(x) u'(x) if this...

I'm having a tough time trying to do integration by parts with one of my limits being infinity. My Integral looks like: \int_0^\infty x^z e^{-x} dx with z = \frac{-1}{\pi} Now if I let u = e^{-x} and dv = x^z dx, I will have: du = -e^{-x} dx and v = \frac{1}{z + 1} x^{z + 1} and...

I've got a function \int e^{-x}sinx dx From what I know, only functions which has one or more products with a finite number of successive differentials can be evaluated using integration by parts. Because for \int v du in our choice of du, we want to cut down on the number of times we have...

I am usually alright once I figure out how to split up the integral into u: du: v: dv: so i can simply do uv-\int v*du but I keep messing up on there I will post some examples if I can find them and if someone could help me that would be great \int (ln(x))^2

Hi, I've actually got a problem here. How do I evaluate \int e^x^3 x^2 dx I have problem when doing integration by parts of finding \int v du since if I integrate v du, i'll get another expression which i have to integrate by parts again, and this goes on and on ! (its meant to...

i will use "\int" as integral signs, cause latex seems to be down. uv - \int v*du \int 8x^2cos(2x)*dx u = 8x^2 du = 16x*dx dx = 1/16 dv = cos(2x) v = 1/2sin(2x) plug in what i found for the formula 8x^2*1/2*sin(2x) - \int 1/2*sin(2x)*16x take out the 1/2, because it's a...

Ok so I was attempting to solve an integration by parts problem and somewhere along the line I got stuck. Here's the problem: \int^{\infty}_{2} {x^2 e^{-x} - 2xe^{-x} After using integration by parts twice I came up with this: 2xe^{-x} - x^{2}e^{-x} + 2e^{-x} \vert^{\infty}_{2} But...

\int 4x cos(2x) using integration by parts... u=4x du= 4 dv=cos(2x) v=cos(x)sin(x) using the formula uv - \intv*du... 4x*cos(x)sin(x) - \intcos(x)sin(x)*4x hmm i can't seem to finish this problem, can someone help? and am i doing it correctly so far?

hi, i would like help on a problem i am currently stuck on. \int(e^x)/(1+e^(2x))dx <-- it's suppose to be \int (e^x)/(1+e^(2x))dx using integration by parts, here's what i done: u=e^x du=e^x dv=(1+e^(2x)) v = (need to use anti-differentiation, which i don't remeber...) can i...

I'm real stuck with this problem of mine in The Calculus 7 by Leithold \int arctan \sqrt{x} dx Since there is no elementary formula for integration of an inverse trigo function, we cannot manipulate the integrand in such a way as to integrate easily with one step of Integration by...

Hi can anyone help me solve this integral, I'm having trouble with this one? the integral is: int(sin^{8}x.dx)->upper limit=pi ->lower limit=0. Q) Evaluate the integral exactly using integration by parts to get a reduction formulae for int(sin^{n}x.dx)