Integration by parts Definition and 438 Threads

Homework Statement In preparation for an exam next week, I'm solving some of the end-of-chapter questions. There are 30 questions. I've solved a few on my own, but here's one I'm getting stuck on. Question 2) \int x5^x dx, problem here is I don't know how to deal with 5^x. The correct...

Homework Statement I can find on Wikipedia the "formula" for integration by parts for the case where there is a multi-variable integrand, but I would like to know what substitutions to make in order to show my steps. Homework Equations For multiple variables we have...

Integration by Parts HELP! Hey, I am working on some calculus and I am having some trouble with the last few integration by parts problems. I got the first couple, and i grasp the concept of integration by parts but for some reason I just can't figure these 3. Any help would be greatly...

Integration by parts HELP! Hey, I am working on some calculus and I am having some trouble with the last few integration by parts problems. I got the first couple, and i grasp the concept of integration by parts but for some reason I just can't figure these 3. Any help would be greatly...

Ok. I have a definite integral of e^sqroot(x) dx from x=0 to x=1. I would use u=sqroot(x) and du=1/2*sqroot(x), but I'm confused what I would set v=?

[SOLVED] integration by parts question Homework Statement This is part of a larger problem but I'm just not sure if I have the right answer. edit: this is integral of ln(x-7)dx i just can't seem to figure out how to make it in latex Homework Equations The Attempt at a Solution...

Homework Statement Got an exam later today on this, just looking for some practice. I know this is kinda reverse of what the forum is intended for, but I'd like to ask for people to post some problems that I can solve via Integration by Parts. Just like 5 or so. Homework Equations...

[SOLVED] integration by parts question Homework Statement I think my first problem is at integration by parts, but let me know if you see a different error in my work. Edit: I shoud mention that this is Calculus 2 and we just learned first order differential equations today. So I don't...

I was sick and missed class:rolleyes: ∫ sin^2x dx = x/2 – sin2x/4 + C (I see that there is a trig identity in the answer as sin2x = 2sinxcosx) What I tried (copying the example in the book) u = sinx du = sinxcosx dx (why is du not cosx?) v = -cos x dv = sinx dx (why is this...

Homework Statement Hi, I have a test coming up soon so I was doing some questions from the textbook when I stumbled upon this one and I'm stuck after like 5 tries. Here is the question: \intcos^2(x)dx Solve. Homework Equations the question then states we should solve using this...

the answer to \int\frac{1}{x}(dx) is lnx +c. but if you do it with integration by parts, you end up with \int\frac{1}{x}(dx) = 1 + \int\frac{1}{x}(dx) which comes to 0=1. why does this happen?

The teacher kinda skipped over this and expects us to know how to do it. Being I can't understand what he is saying, I'm kinda lost, so I missed how to do the whole u, du thing. Homework Statement Solve \int{ 8x^{3}\ln\!\left(x\right) \, dx} using Integration by Parts. Homework...

Homework Statement Integrate x^2 e^x^3 dx Homework Equations I = uv - integral of u'v The Attempt at a Solution I don't know where to begin this question at all and have been stuck on it for the past half hour. Any help would be really appreciated. :(

Homework Statement I have tried this question a number of times, but to no avail. Could somebody please help with the first couple of lines, thank you. \int_0^x2cte^{-ct^2}dt where c is a postive constant Homework Equations The Attempt at a Solution Let u=t and let dv=2ce^{-ct^2}dt

Homework Statement \int e^{2x}sin(e^x)dx Homework Equations Can I make the substitution: w = e^x ; dw = e^x dx Making a "new / simpler" problem: \int w sin(w) The Attempt at a Solution Using integration by parts on the "new" problem: u = w ; dw = du dv =...

[SOLVED] Integration by parts Homework Statement I've been staring at this for 30 minutes and can't figure out what's wrong. I end up with 1/xi instead of xi. The book says, \int_{-\infty}^{+\infty}te^{-t^2/2}\sin(\xi t)dt=\int_{-\infty}^{+\infty}e^{-t^2/2}\xi \cos(\xi t)dt The...

little help? simple question... Homework Statement Integrate: xlnx dx use integration by parts Homework Equations The Attempt at a Solution let u = x du = dx dv = ln x v = ??

how would one integrate by parts the following: \int sin^2xdx thanks!

Be used to prove that a constant coefficiant can be taken out the integral? such as 2x just being 2 multiplied by the integral of x? \int{2x} = 2\int{x} Also, what is the integral of 0? Is it 0 or "c"? I'm mainly asking because I recently got dropped with a Fourier series homework and its...

Homework Statement I'm studying from Zee's QFT in a nutshell. On page 21, I don't understand how he uses integration by parts to get from Eq (14) to Eq (15), ie from Z = \int D \varphi e^{i \int d^4 x \{ \frac{1}{2}[(\partial \varphi)^2 - m^2 \varphi^2] + J\varphi \}} to Z = \int D \varphi...

I am either making the same mistake repeatedly, or I can't factor! I did this \int\ln(2x-3)dx first by parts and then using the formula \int\ln u du=u\ln u-u+C By parts I got: u=\ln(2x-3) dv=dx so =x\ln(2x-3)-\int\frac{2x}{2x-3}dx and by long division: =x\ln(2x-3)\int...

Is this the correct way to use the Tabular Method for \int x^2e^{-5x}dx repeated diff: x^2 2x 2 repeated Integration: e^{-5x} -\frac{1}{5}e^{-5x} \frac{1}{25}e^{-5x}...

[SOLVED] Integration by parts help. Homework Statement I'm working on ym Math assignment, and we are currently doing Integration by parts. I haven't had too much trouble except with the last 3. Ill only post the first of those 3 for now. I need to find \intarctan(1/x)dx Homework...

Homework Statement integrate: (x^3) e^(3x^2) dx Homework Equations uv- integral vdu The Attempt at a Solution i've tried this many times on paper and can't get the right answer. I'm starting to get really frustrated. Please help...

How would you go about doing this: \int64x^2cos(4x)dx The question specifically asks to integrate it by parts, so I integrated it that way a couple of times and came out with some long mess of sines and cosines, but it's not the right answer. Thanks.

Homework Statement Can anybody help me integrate x^3 e^{x^2} The Attempt at a Solution I can't see how to do it by substitution or integration by parts.

Hi. When evaluating an integral such as: \int {x^4 e^x dx} Is integrating by parts 4 times the best method, or is there a more efficient way? Thanks in advance, Dan.

[SOLVED] Integration By Parts and Substitution Short background; Took Calc 1 my senior year in high school. Got As all 4 quarters and found it quite easy. Freshman year comes around and I sign up for Calc 2. Turns out the only teacher teaching Calculus 2 for my fall and spring semester is a...

\int\sec^{5}{x}dx i need a hint on this problem, my teacher told us that we prob. can't solve it with the method we've just learned. I'm not sure where to look in the book, I've looked through it but i don't know what is the best method. hint? pleasezz and i'll post all my work :D i...

Picture. I don't know where I've gone wrong :-[ Any advice on how to tackle Integration by Parts? What should I subst. with what? Thanks! http://img528.imageshack.us/img528/9348/ibpkz5.jpg

Homework Statement Hi, I'm trying to solve http://img204.imageshack.us/img204/7199/untitledke0.png in terms of I(n-2) but I'm not exactly sure where to start/what to do :rolleyes:

integration problem :( Homework Statement int from 1 to 1/4 of [cos(pi*sqrt(t))] / sqrt(t) dt Homework Equations The Attempt at a Solution I tried using integration by parts used u = cos pi (sqrt(t)) and dv = sqrt(t), but got a really messy number as int of vdu so I tried u =...

intergrate (ln(x))^2 so i set u=(lnx)^2...which makes du=2lnx(1/x) then i set dv=dx...which makes v=x according to the formula for integration by parts i have x(lnx)^2- integral x(2lnx)(1/x) simplifying it i get x(ln)^2-2intergral lnx and here is where i am stuck...what i the...

Homework Statement Hi, I'm trying to evaluate the integration of (e^x)cos3x dx, by using integration by parts. I've already done a couple of similar questions on integration by parts but this one seems to puzzle me. Homework Equations The answer is supposed to be (e^x/10)*(cos3x +...

Hi, J(m,n) = \int_0^{\frac{\pi}{2}} \cos^m \theta \sin^n \theta d\theta First of all I had to evaluate the following ( I don't know what the correct answers are but here are my calculations: J(0,0) = [\theta]_0^{\frac{{\pi}{2}}}=\frac{\pi}{2} J(0,1) = [-\cos...

Hello there. I feel like this isn't the right answer, but I'd like some verification as to where exactly I went wrong! 1. Homework Statement is \int_{0}^{pi}x^2cos x dx 3. The Attempt at a Solution went something like this: u=x^2 dv=cos x dx du=2x dx v=\int_{0}^{pi}cos x dx= sin x...

Homework Statement ∫ ln(x^2+14x+24) Homework Equations Integration by parts: ∫ udv = uv - ∫ vdu The Attempt at a Solution I chose u = ln(x^2+14x+24) and dv = dx therefore du = 2x+14/x^2+14x+24 and v = x Then once I substitute, I get: ∫...

Homework Statement indefinite integral dx/((e^x)(sqrt(1-e(-2x)))) using integration by parts evaluate the integral. Homework Equations integral u*dv = u*v- integral v*du The Attempt at a Solution To be completely and entirely honest i am not even sure where to start with this...

Homework Statement integrate arctan(1/x) Homework Equations The Attempt at a Solution z=arctan(1/x) dx=-dz(x^2-1) now its the integral of z(x^2-1)dz let u =X^2-1 du=2x dv=-udu v=-u^2/2 integral=(x^2-1)(-u^2/2) - int (-u^2)(2x) this is where i got stuck but i...

im having a bit of trouble, can anyone help me integrate arctan(1/x) using integration by parts? thanks

Homework Statement Use integration by parts to evaluate the integral: ∫ 1 ÷ (16 + x2) dx Homework Equations ∫ u dv = uv - ∫ v u' du The Attempt at a Solution That's the problem, I don't know how to start. How would I divide up 1/(16 + x2) into two? So there would be a value for u...

Hey y'all. I'm new to the forum, and have a problem that I've been working on all night long. I'm having issues previewing the Latex, so bear with me. I'll post the work I've done so far if the problem code shows up. Thanks. \int{\sin^{\frac{3}{2}}2\theta\cos^{3}2\theta} d\theta Now, the...

Homework Statement Hi, I've been having trouble solving the following problem, please help me. Question: (integration from 1 to 4) e^(x^(1/2))dx Homework Equations The Attempt at a Solution So far, i have done the following: u = e^(x^(1/2)) du =...

Hi, I have been working on this problem for the longest time and have just run in circles with it. I am thinking the answer is obvious but for some reason I am missing it. I need to find \int \frac{ln(x)}{x^2} dx I know that I need to use integration by parts and have tried a number of...

i know this is integration by parts so here is the problem I am currently confused on how the get an answer r e^r/2 dr I know I the formula is int udv= uv - int du v what i am not getting is what to use for this one. I figured e^r/2 = v and du = r so u= r^2/2 and what...

integral of (e^(2x))(cos3x)dx I get 1/2e^(2x)sin2x - 3/2integral(e^(2x)cos3xdx) what do i do next?

"Evaluate the integral [0,1] x^3/sqrt[x^2 + 1] by integration by parts" I know I have to use the integration by parts equation, but I don't know what to make u and what to make dv..

integral y(1+y^2)^1/2 dy can someone help me with this? Thanks.

Problem: \int\frac{dx}{a^2-x^2} My Work: \frac{1}{a^2-x^2} =\frac{1}{(a+x)(a-x)}=\frac{A}{a+x}+\frac{B}{a-x}} 1=A(a-x)+B(a+x) If x=a, then 1=2Ba so B=\frac{1}{2a} Thus 1=A(a-x)+\frac{1}{2a}(a+x) if x=0, then 1=Aa+\frac{1}{2} so A=\frac{1}{2a} SO \int\frac{dx}{a^2-x^2}...

Hi all, I am having problems with the integral: \int e^{(ax)} cos(bx) dx I have got to \frac{e^{ax} sin(bx)}{b} - \int \frac{a e^{ax} sin(bx)}{b} dx After this I can only see myself going around in circles. Any help would be appreciated. :smile: Cheers, The Bob (2004 ©)