Integration by parts Definition and 438 Threads

Homework Statement Use the method of separation of variables or an integrating factor to find a particular solution of the differential equation that satisfies the given initial condition. y'=x-y+2 ; y(0)=4 2. The attempt at a solution I've used an integrating factor of e^{x} to...

I want to start out by saying that this is not a homework problem, this is something I'm trying to figure out for thesis work. If that should go in the homework problem section, I will gladly post there. A certain mass model I'm working with (Bissant & Gerhard) has a particularly gross form...

Homework Statement Hi, I attached the question.Just integral trouble. Homework Equations The Attempt at a Solution

Homework Statement \int_4^5 \frac{dx}{(3x)(ln(x))(ln^3(ln(x)))} \, Homework Equations I'll probably need to use u-substitution as well as integration by parts for this problem. The Attempt at a Solution \int_4^5 \frac{dx}{(3x)(ln(x))(ln^3(ln(x)))} \, 1. Factor out 1/3 for...

Here is the question: Here is a link to the question: Integration by parts question? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

I'm looking at this problem here. (Exam practice, move to homework if you want...) First part is easy, but it's the second part that I can't quite figure out. I'm trying to get from ∫xe2x cos(2x)dx to this answer: ¼e2x(x cos(2x) + x sin(2x) - ½sin(2x))+C

I've come across this funny problem while messing around with integration by parts. Probably made a mistake somewhere. In the integration of parts expression, it's possible to expand it further. Plugging the second expression into the first, we get I don't think...

Homework Statement Find \int (2x^4\ln3x)\ dx Homework Equations The Attempt at a Solution I let u = ln3x and dv/dx = x4 and I've managed to solve it and get an answer of: x^5(\frac{2}{5}\ln(3x) - \frac{1}{45} + c) Which is really close to the answer from wolfram alpha but the...

Hi, Homework Statement I have already evaluated the integral 1/sqrt(x)exp(-ix) using The Residue Theorem and now I was looking for another method. So I thought of applying integration by parts and I got this attached formula. Now I am wondering how to evaluate this series. My first...

In a Griffith's book (page 15-16) an author derives a momentum operator. In the derivation he states that he used a integration by parts two times. He starts with this equation which i do understand how to get to. $$ \begin{split} \frac{d \langle x \rangle}{dt} = -\frac{i\hbar}{2m}...

Homework Statement |x3sqrt(4-x2)dx Homework Equations uv - | vdu The Attempt at a Solution u = x2 v = -1/3(4-x2)3/2 du = -2xdx dv = x(4-x2)1/2 uv - | vdu x2(1/3)(4-x2)3/2 - | 1/3(4-x2)3/2(2xdx) x2(1/3)(4-x2)3/2 +(1/3)|(4-x2)3/2(2xdx) u = 4 - x2 du = -2xdx...

Homework Statement Integrate by parts.Homework Equations (integral) (x^5 * sqrt(x^3 + 5) dx)The Attempt at a Solution i've tried using simple substitution, not by parts. integral (x^3 * x^2 * sqrt(x^3 + 5) dx u=x^3 + 5 du=3x^2 1/3(integral) (u-5) * u^1/2 du 1/3(u^3/2 - 5u^1/2)...

Homework Statement integrate by parts. Integral: x * 5^xHomework Equations The Attempt at a Solution i got to (1/ln5) * 5^x ;; and I'm not sure how to integrate further.

Homework Statement I don't know how the writer of the book took integral of the first statement and got the second statement? Can anybody clarify on this? Homework Equations Given in the photoThe Attempt at a Solution When I took the integral I just ended up with the exact same statement but...

Here is the question: Here is a link to the question: Calculus integral help? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.

Hey guys, Need you push to proceed further with integration by parts: ∫e3x*3*x2*ydx=y∫e3x*3*x2dx setting u=3*x2-------du=6*x dx dv= e3*xdx--- v= 1/3* e3*x ∫ e3*x*3*x2*ydx=y*(3*x2* 1/3* e3*x-∫6*x*1/3* e3*xdx) =y*(3*x2* 1/3* e3*x-6/3*∫x*e3*xdx)...

Homework Statement I've run into this problem a few times, where I get the right answer, but multiplied by a constant where I would have it divided by the constant or vice versa. "First make a substitution and then use integration by parts to evaluate the integral" ∫cos(√x)dx...

The integration by parts rule in two dimensions is \int_{Ω}\frac{\partial w}{\partial x_{i}} v dΩ = \int_{\Gamma} w v \vec{n} d\Gamma - \int_{Ω} w \frac{\partial v}{\partial x_{i}} dΩ I have two examples in polar coordinates In first example I have \vec{n}=\vec{n_{r}} \int_{\Gamma}...

Recently, a friend of mine asked for help on their calculus homework. The problem was to find \int cos(ln \ x) \ dx. However, I've never gotten around to memorizing the derivatives and integrals of the trig functions. I know that you can do it using integration by parts, with \int cos(ln \...

I am trying to integrate a difficult integrand. \[1/2*\int \sin(\sqrt(3)/2x)*\sec(\sqrt(3)x)\, dx\] I know that it requires to use integrate by parts. Which function do I use to for the differential and integrable?

Homework Statement I do not know how to solve the following indefinite integral. I personally think it is very difficult and would appreciate it had someone can explain it step by step? Homework Equations / The Attempt at a Solution This integral must been solved by mix of...

∫ e^at. sinωt dt This is the second part of an electrical circuit DE problem from our notes (first part not required to solve the above integral) however in-between this integral and the answer our professor only told us that we would get to the answer by using integration by parts twice. I am...

Integration by parts not working for a particular integral When I attempt to use the method of integration by parts on the below integral, I don't get anywhere since I only arrive at the statement a = -b +b -a where a is the integral and b is the boundary term. \int e^{-x}\text{Cos}[k...

Hi all this is my first post hopefully i do it right. Homework Statement integrate ln^2(6x)dx The Attempt at a Solution *integral* ln^2(6x)dx u=ln^2(6x) dv=dx du=(2ln(6x))/x dx v=x xln^2(6x)-*integral*x(2ln(6x))/x dx xln^2(6x)-2*integral*ln(6x) dx u=ln(6x) dv=dx du=1/x...

When integrating by parts the formula is \int{u} dv=uv-\int{v} du I understand where to get the u, and du... but where does one get the v?

Homework Statement ∫x3e5x2 dx Homework Equations uv-∫vdv The Attempt at a Solution I've tried this one a few times, but keep getting answers that are just out there. Could someone, if possible, work out just the beginning.

Homework Statement Consider the following integral: I=\int^{\pi/4}_{0}cos(xt^{2})tan^{2}(t)dt I'm trying to compute as many terms as possible of its asymptotic expansion as x\rightarrow\infty. Homework Equations x The Attempt at a Solution Let u=cos(xt^{2}). And...

I was wondering if someone can show me or point me to a worked out example using integration by parts for more than one variable (as used in relation to pde's, for example). While I took pdes and calc 3, its been awhile and I don't know if I ever understood how to work out a concrete example...

Ok I have to integrate -->∫cos(lnx) dx. could I use cos =U, -sinx=du, dv=lnxdx, v = 1/x I know the difference technically, but in this situation it is kinda weird. because the formula f(x)g(x)= uv-∫vdu. I thinking if they were number like 9(3) it would equal 27 so f(g) = f times G? but then...

Homework Statement Are there any sample problems worked out for trig functions of higher powers which are integrated by reduction formula? Like cos^8 or cos^10 or even just cos^6 or maybe?

Homework Statement αh=α-ε+ih ΔαH/Δα= dαH/dα = d/dα x (α-ε+ih) = 1-(dε/dα)

Homework Statement Evaluate the following indefinite integral: ∫(sin(ln16x))/xdx Homework Equations The Attempt at a Solution let u = ln16x therefore du=16/16x=1/x ∫sinudu =-cosu =-cos(ln16x) Why is this showing as the wrong answer?

Homework Statement Hi , I am reading a little on introductory QM , initial chapters on waves. They have given an integral for a wavepacket , assuming at t= 0. Which is: ψ(x,0) = \int A cosk'x dk' (I don't know how to define limits to the integral in Latex upper = k+Δk , lower limit =...

Homework Statement ∫\frac{1}{x^{2}*ln(x)} Homework Equations ∫udv = uv-∫vdu u=ln(x) du = \frac{1}{x}dx dv = x^{2}dx v = \frac{x^{3}}{3} The Attempt at a Solution Using the above formula I got \frac{x^{3}}{3}*ln(x) - \frac{x^{3}}{9} + C Am I doing this correctly or do I...

I understand this integration technique, for the most part. One thing I am curious to know is why, when you do your rudimentary substitution for this particular technique, does dv have to always include dx?

Homework Statement ∫ln(2x+1) Integrate by parts Homework Equations I got xln(2x+1)+\frac{1}2{}ln(2x+1)-x+C The Attempt at a Solution The solution is \frac{1}{2}(2x+1)ln(2x+1)-x+C I know the answers are the same,but it's bugging me that I can't simplify the first answer I got...

I have some problems understanding the intuition behind the integration by parts technique. I don't quite see why you solve for \int u(x)v\prime (x), instead of one of the other parts, what makes it easier to solve for that particular term? And in general when working with integration...

Hello. I'm just trying to understanding something here. I was taught integration by parts by my professor in what looks to be like an untraditional way. From my understanding, the theorem states: ∫udv = uv - ∫vdu We were given an example in class of: ∫exsin(x)dx =∫ex∫sin(x)dx -...

Homework Statement The functional ##I(u,v)=\int_\Omega F(x,y,u,v,u_x,u_y, v_x,v_y)dxdy## The partial variation of a functional is given as ## \displaystyle \delta I =\int_\Omega (\frac{\partial F}{\partial u} \delta u+\frac{\partial F}{\partial u_x} \delta u_x+\frac{\partial...

FOlks, I am self studying a book and I have a question on 1)what the author means by the following comment "Integrating the second term in the last step to transfer differentiation from v to u" 2) Why does he perform integration by parts? I understand how but why? I can see that the...

Homework Statement integral of e^-xsinxdx Homework Equations uv-/vdu The Attempt at a Solution u=e^-x du = -e^-xdx v=sinx dv=cosxdx e^-xsinx-/(-e^-x)sinx =e^-x(sinx+cosx) Wolfram alpha is telling me that the indefinite integral is actually "-1/2e^-x(sinx+cosx)" where did...

Homework Statement Integral, from 0 to 1, y/(e^2y) Homework Equations Use integration by partsThe Attempt at a Solution I need integration by parts. The answer is 1/4-3/5e^-2. But I got 1/2 and it all makes sense to me, so tell me what I got wrong. I put u=e^2y du=2e^2y dv= 1/e^2y dy (did...

Homework Statement Integral, from 4 to 6, 1/(t^2-9) dt Homework Equations please use my approach to solve it, like with cosh and whatnot The Attempt at a Solution Integral, from 4 to 6, 1/(t^2-9) dt so I multiplied the top and bottom by square root of 9. which got me...

The Integration by Parts Theorem states that if f' and g' are continuous, then ∫f'(x)g(x)dx = f(x)g(x) - ∫f(x)g'(x)dx. My question is, are those assumptions necessary? For example, this holds even if only one of the functions has a continuous derivative (say f' is not continuous but g'...

I would think because of this The following problem: At this stage they should use integration by parts: However, maybe integration by parts is only useful when one of the parts is e^x ln or a trigonometric formula.

Homework Statement Homework Equations uv - integral of vdu The Attempt at a Solution They don't seem to be using the integration by parts formula here. I don't understand why why they don't have a value for what z equals. dz = eu. well, what does z equal. I would think it...

Hi, I need to find ∫ln(x+1)/(x^2+1)dx I think it might involve recursive integration by parts, so first I set: u=ln(x+1) dv = 1/(x^2+1)dx du=1/(x+1)dx v=ArcTan(x) ∫ln(x+1)/(x^2+1)dx = ArcTan(x)Ln(x+1) - ∫ArcTan(x)/(x+1)dx Then I integrated by parts again, so...

Use integration by parts to prove the reduction formula: int(sec^n)x dx = (tan(x)*sec^(n-2)*x)/(n-1) + [(n-2)/(n-1)]int(sec^(n-2)*x dx n /= 1 (n does not equal 1) I used "int" in place of the integral sign. This was a problem on the corresponding test from the cal A class I am from...

Homework Statement I have attached a picture including 2 equations: (2.13) and (2.14) I don't understand how they got from (2.13) to (2.14) using integration by parts Homework Equations The Attempt at a Solution For the integral: \int_{\tau_0}^t\sigma(\tau)d\tau=...

calculate : ∫x²e-x3dx by parts please i need details :) thank you very much