Integration by parts Definition and 438 Threads

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...

Homework Statement I don't know why, but the partials are really confusing me here. I need to integrate the following expression in a derivation: I = \int_0^\delta v(x,y)\frac{\partial{u(x,y)}}{\partial{y}}\,dy \qquad(1)Homework Equations I am supposed to integrate by parts here. \int...

Homework Statement integral of x^2ln(x)dx Homework Equations The Attempt at a Solution u=ln(x) du= 1/x dv=x2dx x^3/3 integral x^2ln(x)dx = ln(x)x^3/3-intergral(x^3/3)(1/x)

hello, i am stuck on how to do this I know how to do it for an indefinite integral, but it gets confusing for a definite integral. from my knowledge, when doing a definite integral, you have to change the upper and lower limit. but when it comes to integration by parts for a definite integral...

Homework Statement \intx^2tan^{-1}xdx The Attempt at a Solution \int{x^2tan^{-1}xdx} \int{x^2tan^{-1}xdx} = \frac{x^3}{3}tan^{-1}x-{\frac{1}{3}}\int \frac {x^3}{1+x^2}dx let {}u=1+x^2, \frac{du}{2}=xdx \frac{x^3}{3}tan^{-1}x- \frac{1}{6}\int (1-1/u)...

Homework Statement \int t sin(2t) dt Homework Equations Integration by parts formula: \intudv = uv - \intvdu The Attempt at a Solution I chose t to be u so, u=t du=dt dv=sin(2t)dt v=(sin)^2 (hope that's right. I used double angle formula to change sin(2t) into 2sint...

Homework Statement Is this true or false? \int_V {\vec \nabla \Phi \bullet {\bf{E'}} \cdot {d^3}x} = \vec \nabla \Phi \bullet {\bf{E'}} - \int_V {\Phi \cdot \vec \nabla \bullet {\bf{E'}} \cdot {d^3}x}

Homework Statement Hello. I am doing some problems on integration by parts and got stuck on the following problems. Any help would be appreciated. i. \int \arcsin x dx ii. \int_{0}^{1} x \ln (9+x^2) dx iii. \int x^2 \arctan x\, dx Homework Equations u\,du=uv-v\,du The Attempt at a...

[PLAIN]http://img25.imageshack.us/img25/8933/lastscante.jpg I am new to integration by parts and am not sure what boundries to use when eveluating v on the bottom right.

Homework Statement The definite integral of from 0 to 1 of ∫ (r3)dr/sqrt(4+r2)Homework Equations ∫udv = uv - ∫vdu ∫du/sqrt(a2 - u2) = arcsin(u/a) + C ∫du/(asqrt(a2 - u2)) = (1/a)arcsec(u/a) + C The Attempt at a Solution I made u = (4+r2)-1/2 because I thought it easier to get it's...

Homework Statement Integrate: \sqrt{x}e^\sqrt{x}Homework Equations See aboveThe Attempt at a Solution Well I started off first by taking t=sqrt(x) but that didn't get me very far. So then I decided to make x equal to t^2 which sort of worked. After hours of struggle I decided to have a look at...

is the following formula of integration by parts \int_{-\infty}^{\infty}dxf(x)D^{n}g(x) = (-1)^{n} \int_{-\infty}^{\infty}dxg(x)D^{n}f (x) valid for real or non-integer n? the problem i see here is the term (-1)^{n} , which may be not so well defined for non-integer 'n'

Homework Statement Homework Equations The Attempt at a Solution I tried this problem and couldn't figure it out so I went and got the solution. However, I don't understand step 6 of the solution. I'm not sure how (n-1)\int\sin^{n-2}x(1-\sin^2x)dx=(n-1)\int\sin^{n-2}dx-(n-1)\int\sin^nx dx

Homework Statement dy/dx = e^ysin^2x/ysecx Stewart 6e 10.3 # 8 Homework Equations The Attempt at a Solution ydy/e^y = sin^2xdx/secx e^-ydy = sec^-1xsin^2xdx Integration by parts u = e^-y du = -e^-y dv = ydy v = y^2/2 ∫udv = e^-yy^2/2 + ∫y^2/2e^-y = y^2/2e^y +...

Homework Statement find the integral of cot^(-1)of (5x) Homework Equations Integration by parts The Attempt at a Solution u = x du = dx dv = cot ^ (-1) v = ? and then i would plug into equation [uv- integral of vdu ]

Homework Statement My homework problem is the double integral of y/1+xy dxdy. It is a definite double integral and both integrands have the values of a = 0 and b = 1. Homework Equations Integration by parts: uv - int(vdu) The Attempt at a Solution My first step of the double integral is I...

Homework Statement Calculate: \integral \frac{1}{(x^2+1)(x+1)} Homework Equations \integral f(x) g'(x) = f(x) g(x) - \integral f'(x) g(x) + C The Attempt at a Solution I've tried using both 1/(x+1) and 1/(x^2 + 1) as dv, but both end up in another integral I can't solve, one...

Homework Statement Given characteristic functions f and g on the intervals [1,4] and [2,5] respectively. The derivatives of f and g exist almost everywhere. The integration by parts formula says \intf(x)g'(x)dx=f(3)g(3)-f(0)g(0)-\intf'(x)g(x)dx. Both integrals are 0 but f(3)g(3)-f(0)g(0) is...

Homework Statement Indefinite Integral (x^3)(e^x) Homework Equations The Attempt at a Solution I know I need to substitute t=x^2 t^(3/2)e^sqrt(t) U=e^sqrt(t) du=e^sqrt(t) dt dv=t^(3/2) V= (5/2)t^(5/2) Because it has an exponential function, I know I need to use the...

Homework Statement Hi This is something i don't remember what I'm supposed to do. So anyway here goes. For example if my function was xe^yx and i wanted to integrate with respect to dx then i do an integration by parts with these variables: u = x dv = e^yx now my question...

Homework Statement Evaluate integral of e2ysin(2y)dy using integration by parts.Homework Equations integral udv = uv - integral vdu The Attempt at a Solution I tried applying the above equation several times, but the integral and derivative of both e2y and sin(2y) will always have a y in...

Homework Statement a. integral of x arcsec(x) dx b. integral of sin(root x) dx *Instruction says that I should use substitution before integration by parts. c. integral of 2x^3 cos(x^2) dx *Instruction says that I should use substitution before integration by parts. Homework...

We know the formula is \inline{\int udv=uv-\int vdu} but when you say that for example, dv=e^x dx, then why when you integrate to get v, you don't include the integration constant? For this integral: \int xe^{x}dx dv = e^x dx v = e^x + C?

Homework Statement \int arctan(4t) Homework Equations I know what the answer is to the problem but when i look at the solution i have no idea how they get from one step to the next. The Attempt at a Solution once we integrate by parts we get 1/4 U arctan(U) - 1/4 \int U/1+U^2...

Homework Statement integral of ln(2x +1) Homework Equations I know this is an easy problem but i can not seem to figure out what to substitute for my U and my dV. I was thinking on making my U= 2x+ 1. but then my problem is what would my dV be? ln U? lnx? the ln is throwing me off a bit...

Homework Statement If g(1)=3, g(5)=8 and the integral from 1 to 5 of g(x)dx=-9. Then, evaluate the integral from 1 to 5 of xg'(x)dx. 2. Homework Equations and attempt at solution I used integration by parts to get =xg(x)-(integral of)g(x)dx from 1 to 5. Then substituting in, I get...

Homework Statement Integrating 1/xlnx by parts... Homework Equations Find the integral of 1/xlnx The question asks to solve by substitution, which I can do and results in ln(ln(x)) + c It then asks to compute using integration by parts, and then to explain how it can be true (because...

Homework Statement [/b] http://i324.photobucket.com/albums/k327/ProtoGirlEXE/Capture1.jpg The attempt at a solution[/b] http://i324.photobucket.com/albums/k327/ProtoGirlEXE/100_0635.jpg Answer I got: http://i324.photobucket.com/albums/k327/ProtoGirlEXE/Capture2.jpg I thought my...

Homework Statement Integrate the following by parts twice \int_{a}^{b}\frac{d}{dr}(r\frac{dT(r)}{dr})\psi(r)dr and show that it can be written as -\lambda^2\bar{T} , where \bar{T}=\int_{a}^{b}r\psi(r)T(r)dr and the function \psi satisfies the following equation...

Just working through a problem Acheson's book (From Calculus to Chaos) if anyone knows it.. eq 8.6 in this book.. As he's working through the problem he makes the step of this: m\int_{t_{1} }^{t_{2}} \left( \dot{y}_{\scriptscriptstyle A }\dot{\eta} - g\eta \right)\,dt (1) to...

Integration by parts - Exponential distribution Homework Statement Solve the following definite integral: \int^{\infty}_{0} \frac{1}{\lambda} x e^{-\frac{x}{\lambda}} dx I'm asked to solve this integral. The solution is \lambda, although I'm not sure how this was done. Homework...

Homework Statement Hi all! I seem to be having trouble doing integration by parts. I seem to have a pretty clear picture of the steps I need to do but something seems to always trick me. Usually I would ask my prof but she is away for a week. I use the formula: uv - ∫vdu = given...

\[\int e^x(x+1)\ln x \ dx \] Not sure how to approach this. Would I have to multiply it out first?

The past few examples in my review book demonstrated u-substitution to integrate trig functions. The example I'm on suddenly shows integration by parts. The book doesn't explain why this method is used over u-sub. \intsec3x dx In what situation am I supposed to use one method over the other?

Homework Statement Evaluate the double integral. Homework Equations integral by part: uv - integral of v*du The Attempt at a Solution I wrote out my works. And I am just stuck at the x integration... Please click on the links to see the pictures. I don't want to resize it which may...

Homework Statement Hi there. I'm confused about this exercise. It asks me to solve the integral using integration by parts. And the integral is: \displaystyle\int_{}^{}3x\cos(\displaystyle\frac{x}{2})dx The Attempt at a Solution What I did: u=3x du=3dx dv=cos(\displaystyle\frac{x}{2})...

Homework Statement Evaluate the indefinite integral. ∫(x + 3)/(x^2+6x) dx Homework Equations This is an online homework prob. that covers sections integration by parts and substitution in indefinite integrals. it looks to me that it fits into the formula ∫udv=uv-∫vdu if you change...

Homework Statement Gosh I've been asking a lot of questions lately...anyways... I tried this question two separate times and couldn't manage to figure out where i went wrong... \int e^{-x}cos2x dx Homework Equations uv - \int v du = \int u dvdx The Attempt at a Solution let u = e^{-x}...

Homework Statement find ⌠cotx using integration by parts with using u= 1/sinx and dv= cosx Homework Equations cotx=cosx/sinx The Attempt at a Solution u= 1/sinx and dv= cosx dx du = -cotxcscx dx v= sinx ⌠udv = 1 + ⌠sinx cotx cscx sinx and cscx cancel out. ⌠cotx = 1 +...

So, in my class we are learning how to use the tabular method to solve an integration by parts problem... but what happens if the two parts of the integral continuously repeat? The example I have in mind is \int e^x sin(x) dx. I know how to solve this using repeated integration by parts...

Homework Statement By integrating by parts , show that \int \frac{1}{1-x^2}dx=\frac{x}{1-x^2}-\int \frac{2x^2}{(1-x^2)^2}dx Homework Equations The Attempt at a Solution I don see which is u and v.

How do I integrate the following: \int_0^\infty r e^{-ar} \sin{(Kr)} dr i tried writing r e^{-ar} = -\frac{d}{da} e^{-ar} and using integration by parts but i couldn't get anywhere. any ideas?

Homework Statement ∫e^-x cos(2x)dx Homework Equations I'm trying integration by parts and I set u=e^-x and dv=cos(2x) The Attempt at a Solution I got to where ∫udv= (e^-x)(1/2 sin(2x))+1/2∫sin(2x)e^-x I am trying to run through a second time and I'm a little stuck

Homework Statement the question : integrate the following : integration of d(y/x) = integration of(c cos x/x^2) dx , where c is a constant Homework Equations integration of d(y/x) = integration of(c cos x/x^2) dx y/x = c integration of (c cos x/x^2) dx (*) = c(x^-2...

Homework Statement Can anyone tell me which one is right (LIPET or LIATE)? Also, in trig, which one come first? sin,cos or tan? thxHomework Equations The Attempt at a Solution

Homework Statement Find \int^{1}_{0} (x^{2} - 3x + 1)e^{x} dxHomework Equations Let f =(x^{2} - 3x + 1) [tex g = e^{x}[/tex] f' = 2x - 3 \int (g) dx = e^{x} The Attempt at a Solution We are going to have to use intergation by parts twice as the degree of the first function (f) is 2...

Hi, Can you tell me if I am on the right track with this problem. Thanks in advance. Homework Statement Evaluate the integral using integration by parts Homework Equations ln(2x + 1)dx The Attempt at a Solution ln(2x + 1)dx = ln(2x + 1) * 1dx Let U = ln(2x + 1)...

\int_0^{infinity} \ e^{-s*t}*t*cos(t) dt I tried integration by parts with u=t*cost and dv=e^(-s*t) but that didn't get anywhere. I then tried: \L{t^n*g(t)}=(-1)^n d/ds[\int_0^{infinity} \ e^{-s*t}*cos(t) dt but again nothing was working. This is a Laplace Transformation where ft=t cos(t)

Integration By Parts? Homework Statement int.arctan(2x)dx Homework Equations Integration By Parts The Attempt at a Solution In the attached image is the original problem with the ansewer I came up with using integration by parts and then a v=sub. later in the problem I did not...