Integration by parts Definition and 434 Threads

Homework Statement I'm going to cut from the initial part of the problem, which I am confident is good to go, and cut straight to the antiderivatives. Homework Equations All antiderivatives are to be integrated on the interval from 0 to π/18 (I1) = -1/9 cos 9x - (I2) (-2/27 * cos3(9x)) + (I3)...

Homework Statement Evaluate ∫e-θcos2θ dθ Homework Equations Integration by parts formula ∫udv = uv -∫vdu The Attempt at a Solution So in calc II we just started integration by parts and I'm doing one of the assignment problems. I know I need to do the integration by parts twice, but I've hit...

$$\int x^2\cos(mx)\,dx$$ When integrating this by parts, the $x^2$ will become the $u$ and the $\cos(mx)\,dx$ will become $dv$. How is the $\cos(mx)$ integrated if there are two variables?

$\int x\ \cot^2\left({x}\right) dx $ $u=x$ $dv=\cot^2\left({x}\right) dx $ $du=\frac{x^2}{2}$ $v=\frac{-\cos\left({x}\right)+x\sin\left({x}\right)}{\sin\left({x}\right)}$

Hi guys! I am reading the book "Gravity" by Hartle. I came across this scary-looking integral. The author does integration by parts and I don't get how he does it. Could someone guide me please? Relevant equations: ∫u dv = uv - ∫v du

In Jackson's 'classical electrodynamics' he re-expresses a volume integral of a vector in terms of a moment like divergence: \begin{align}\int \mathbf{J} d^3 x = - \int \mathbf{x} ( \boldsymbol{\nabla} \cdot \mathbf{J} ) d^3 x\end{align} He calls this change "integration by parts". If this...

Greetings :) Well I wanted to seek help if my solution is on the right path, given as follows: 1) $$ \int cos ^2x dx $$ So my solution follows like this: u = cos^2x du = 1/2 (1+cos(2x)) v = x [math]dv = dx$$ but I've stuck when its in the $$u.v - \int v.du$$...

Homework Statement $$ \int x^{3}cos(x^{2})dx$$ The attempt at a solution OK, so I am aware that there is a way in which to do this problem where you do a substitution (let $$u=x^{2}$$ to do a substitution before you integrate by parts), and I was able to get the answer right using this method...

Homework Statement I have been trying to evaluate an integral that has come up in the process of me solving a different problem, but am completely stuck. As I have confirmed with Wolfram Alpha that the integral once solved yields the correct solution to my problem. However, I am trying to...

Homework Statement I am working through some maths to deepen my understanding of a topic we have learned about. However I am not sure what the author has done and I have copied below the chunk I am stuck on. I would be extremely grateful if someone could just briefly explain what is going on...

Homework Statement Which one is correct? ##\int (3x+2) (2x+1)^{\frac{1}{2}} dx = \frac{1}{3} (3x+2)(2x+1)^{\frac{3}{2}} - \frac{1}{15} (2x+1)^{\frac{5}{2}} + C## or ##\int (3x+2) (2x+1)^{\frac{1}{2}} dx = \frac{1}{3} (3x+2)(2x+1)^{\frac{3}{2}} - \frac{1}{5} (2x+1)^{\frac{5}{2}} + C## ...

Homework Statement Find <r> and <r2> for an electron in the ground state of hydrogen. Express in terms of Bohr radius. Homework Equations We know the relevant wave functions are: R_{10} = \frac{c_0}{a}e^{r/a}Y^0_0 and Y^0_0 = \frac{1}{\sqrt{4\pi}} The Attempt at a Solution As I...

Hi there, I am reading Chapter 9 of Jackson Classic Electrodynamics 3rd edition, and I don't see why this equality is true, it says "integrating by parts", but I still don't know... any help? http://imageshack.com/a/img673/9201/4WYcXs.png

I have a question why everyone says ∫uv' dx=uv-∫u'v dx why don't they replace v' with v and v with ∫vdx and say ∫uv dx=u∫vdx-∫(u'∫vdx) dx i think this form is a lot simpler because you can just plug in and calculate, the other form forces you to think backwards and is unnecessarily complicated.

It is common that we replace \int u(x)v'(x)dx by \int udv where both u and v are continuous functions of x. My question is, must we ensure that u can be written as a function of v before applying this? The above substitution method is involved in the proof of integration by parts but I cannot...

∫(x2 + 7x) cosx dx If I make v = (x2 + 7x) and du = cosx dx I get ((x2 + 7x) sinx)/2 If I make v = cosx and du = (x2 + 7x) dx I get ((x3/3 + 7x2/2) cosx)/2 using the form X=Y-X to X=Y/2 Neither are correct, what did I do wrong?

Homework Statement I stuck on, when the question as for integration by parts method. Need advice

Homework Statement Hello! I am having some trouble solving this integral by parts. I hope someone can help me. ##\int \cos(x)cos(kx) dx## It is need for a Fourier seriesHomework Equations I am using this definition: ##\int f(x)g(x) dx = f(x)G(x)-\int f'(x)G(x) dx## since its an even...

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Homework Statement Evaluate the integral. (Use C for the constant of integration.) ∫te ^ (-9t) dtHomework Equations ∫udv = uv - ∫vdu u=t dv= e ^ (-9t) dt du=dt v=(-1/9) e ^(-9t) The Attempt at a Solution = -1/9 te^(-9t) - ∫-1/9 e ^(-9t) dt Second Integral...

Im supposed to use integration by parts for this problem but i understand how to. $$\int \ \frac{xe^{2x}}{(1+2x)^2},dx$$

Homework Statement Why can't you do integration-by-parts directly on the middle expression in equation 1.29--pull out the time derivative over onto x, note that \displaystyle \frac{\partial x}{\partial t} = 0, and conclude that \displaystyle \frac{d \langle x \rangle }{dt} = 0Homework Equations...

Say I have a function, f(x) = x sec (f(x)) [this is just an example function, the actual problem is more complicated] g(x) = x f(x), then using integration by parts, I can write I = a∫bg(x) dx = a∫bx f(x) dx = (f(x) \frac{x^{2}}{2})|^{b}_{a}- \frac{1}{2}a∫b\frac{d f(x)}{dx} x2 dx...

From the logarithmic integral representation of the Dilogarithm, $$\text{Li}_2(x)$$, $$|x| \le 1$$, prove the reflection formula for the Dilogarithm. Dilogarithm definition:$$\text{Li}_2(x) = -\int_0^1\frac{\log(1-xt)}{t}\, dt = \sum_{k=1}^{\infty}\frac{x^k}{k^2}$$Dilogarithm reflection...

This isn't really a homework question, more just something I noticed while evaluating an integral and was curious about: At this stage, I was able to simplify the expression before solving for the integral algebraically (since the second iteration yielded the original integral the right...

When you have a fraction, how do you know when to use iteration by parts, or use substituion, pick a u, solve for a value of x (like x=u-2) and then plug in those values?

Homework Statement Let f be continuous on an interval I containing 0, and define f1(x) = ∫f(t)dt, f2(x) = ∫f1(t)dt, and in general, fn(x) = ∫fn-1(t)dt for n≥2. Show that fn+1(x) = ∫[(x-t)n/n!]f(t)dt for every n≥0. ALL INTEGRALS DEFINED FROM 0 to x (I can't format :( ) Homework...

Homework Statement Homework Equations N/A The Attempt at a Solution I can't even begin the attempt because I don't know how you could use intergration by parts for this sum in the first place. Can you help me out?

Homework Statement I want to integrate \int_{0}^{a} xsin\frac{\pi x}{a}sin\frac{\pi x}{a}dxHomework Equations I have the orthogonality relation: \int_{0}^{a} sin\frac{n\pi x}{a}sin\frac{m\pi x}{a}dx = \begin{cases} \frac{a}{2} &\mbox{if } n = m; \\ 0 & \mbox{otherwise.} \end{cases} and...

Homework Statement Evaluate the integral. Homework Equations \int e^{2x} sin(3x) dx The Attempt at a Solution I began by using integration by parts. u = sin(3x) v = \frac {e^{2x}} {2} du = 3 cos(3x) dv = e^{2x} dx but I get stuck after that because the...

Hi all ! I'm new here :) So I'm facing some confusions here regarding integration by parts. While surfing through the internet to study more about this topic, I've came across two formulas which are used in solving problems related to integration by parts. They are 1. uv - ∫uv'dx 2. uv -...

Homework Statement First make a substitution and then use integration by parts to evaluate the integral. ∫x^{7}cos(x^{4})dx Homework Equations Equation for Substitution: ∫f(g(x))g'(x)dx = ∫f(u)du Equation for Integration by Parts: ∫udv = uv - ∫vdu The Attempt at a Solution So...

Homework Statement Use integration by parts to evaluate the integral. ∫5x ln(4x)dx Homework Equations ∫udv = uv - ∫vdu The Attempt at a Solution So here's my solution: But the computer is telling me I'm wrong :( We haven't learned how to integrate lnx yet, so the...

Homework Statement ∫((z^3)(e^z ))dzHomework Equations I just tried u dv - ∫v duThe Attempt at a Solution u = z^3 dv = e^z du = 3z^2 v = e^z = z^3e^z - ∫(3e^z (z^2)) dz I got this far but after that if I try integration by parts again, it gets too confusing.

Homework Statement ∫cosx(lnsinx)dx Homework Equations The Attempt at a Solution u=lnsinx dv=cosxdx du=cosx/sinx dx v=sinx =(lnsinx)(sinx)-∫(sinx)(cosx/sinx)dx =(lnsinx)(sinx)-(sinx)+C I thought that I did this correctly, but my teacher said that u should...

How would you integrate this: ## \int x df(x) ## In general, how is this solved: ## \int 1df(x) ## Can you use integration by parts? I tried, but kept getting 0 since I let ## 1 = u## but then ##du = 0## for later purposes. Also, if ## df(x) = u ## then I am still stumped on how to take the...

Homework Statement Can anyone help me integrating (cosecx)^3 without using integration by parts? Homework Equations The Attempt at a Solution i couldn't get a clue how to do it,i used fundamental identity but always ended up like [∫(cosecx) dx] + [(∫(cotx)^2 . (cosecx) dx]...

Here are the questions: I have posted a link there to this thread so the OP can see my work.

Homework Statement ∫x*cos(x^2) dx I tried using integration by parts, but the integral of cos(x^2) is very long, and I couldn't get it completely with my knowledge at the moment, so is there an easier way to solve this problem?

Hi guys, Stuck on an integration by parts question...Not going to post the question as I want to work it out myself, but as I'm a bit of a novice on diff/integration I'm stuck on what we do at a certain step of the process...anyway.. I know integration by parts we end up using ∫udv = uv -...

Integration by parts By repeatedly integrating by parts show that for $ n >1 $, $$ \int \frac{\ln^{n}(1-x)}{x} \ dx = \ln x \ln^{n}(1-x) + \sum_{k=1}^{n} (-1)^{k-1} \frac{n!}{(n-k)!} \text{Li}_{k+1}(1-x) \ln^{n-k} (1-x) + C$$ where $\text{Li}_{n}(x)$ is the polylogarithm function of order $n$.

Homework Statement Find the general solution of the equation (\zeta - \eta)^2 \frac{\partial^2 u(\zeta,\eta)}{\partial\zeta \, \partial\eta}=0, where ##\zeta## and ##\eta## are independent variables. Homework Equations The Attempt at a Solution I set ##X = \partial u/\partial\eta## so that...

Homework Statement Show in detail that: \sigma_{x}^{2} = \int_{-\infty}^{\infty} (x -\bar{x})^{2} \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x-X)^{2}}{2\sigma^{2}}} = \sigma^{2} where, G_{X,\sigma}(x) = \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x-X)^{2}}{2\sigma^{2}}} Homework Equations \int u...

I'm following this example where it is asked to integrate \int \ln{x} dx using integration by parts. I don't understand how it's legal to set v=x since the only x in the equation is the argument of ln and that's already accounted for by u.

Homework Statement I'm doing an integration by parts problem. After setting up [∫udv = uv - ∫vdu], I come across this situation. How is this algebraic manipulation accomplished? From: \int\frac{x^{3}}{1+x^{2}}dx To: \int x - \frac{x}{1+x^{2}}dx

Hi, I am trying to chew through the proof of reciprocity in MRI. At some point I come across to the following expression: \Phi_{M}=\oint\vec{dl}\cdot\left[\frac{\mu_{0}}{4\pi}\int{d^{3}r'}\frac{\vec{\nabla'}\times\vec{M}(\vec{r'})}{\left|\vec{r}-\vec{r'}\right|}\right] Now it says that...

Homework Statement Calculate the following integral with partial integration: \int\frac{1 - x}{(x^2 + 2x + 3)^2}dx The Attempt at a Solution I guess you need to write the integral in easier chunks but I still fail every time.

Hello I am working on this integral. \[\int ln(3x+1)dx\] I choose u=ln(3x+1) and v'=1. It got me to: \[x\cdot ln(3x+1)-\int \frac{3x}{3x+1}dx\] What should I do from here ? Some substitution ? The x up there bothers me...no easier way ? Thank! I also need to solve: \[\int (ln(x))^{2}dx\]...

how would i go about solving these problems? \begin{align*}\displaystyle \int\frac{xe^x}{(1+x)^2}dx\end{align*} \begin{align*}\int\frac{(1-x)dx}{\sqrt{1-x^2}}\end{align*} this is my solution to prob 2...

any idea how to solve this? \begin{align*}\displaystyle \int x^3e^{x^{2}}\,dx\end{align*}