Integration by parts Definition and 434 Threads

I found this passage in a book: http://img8.imageshack.us/img8/1452/75717730.jpg where Φ(x) is the c.d.f. of the normal distribution. However, using integration by parts I also get this term which is not included in the passage: [ e^{itx} \phi(x) ]^{+ \infty}_{- \infty} where i is the...

When faced with an integral which contains the product of two functions, must you always default to integration by parts? Is there no alternative method? Perhaps, one intended for more complex functions? Thank you.

I am stuck with 2 questions. 1. http://132.239.150.164/math/img/math_967.5_fabcf8ac5b3f2459050993af33426844.png[/URL] 2. http://132.239.150.164/math/img/math_972_41ec111060693034ac0775fd52778392.png[/URL] Homework Equations...

Homework Statement Solve for indefinite integral of (7x^3)/sqr(4+x^2)(dx) Homework Equations I just can't seem to find the right solution. The Attempt at a Solution First of all, we can just factor the 7 out of the integral for now since it is only a constant. the inverse square...

Integration by parts and substitution help! Homework Statement ∫0 -1 e ^√x+1 Homework Equations The Attempt at a Solution

i'm having troubles to integrate \int\frac{sin x}{x} dx could anyone help me with hints? i tried using integration by parts, but i see it as a never ending chain, sin will change to cos... and x^-1 will become -x^-2 and so on

Homework Statement Let In=the integral from 0 to pi/2 of sinnxdx show that (I2n+1)/(I2n)=(2n+1)/(2n+2) Homework Equations integral from 0 to pi/2 of sin2n=(2n-1)pi/4n The Attempt at a Solution I can't write down all that I've done because it's just too ridiculous. I've tried lots...

Homework Statement I am actually looking for the expectation of x for the wavefunction that is \Psi (x) = \sqrt{\frac{2}{L}}Sin(\frac{\pi x}{L}) for 0 < x < L. To do this I need to find the solution to this integral: f = \int_0 ^L \! \Psi^* x \Psi \, dx = \int_0^L \...

"Creative" integration by parts Homework Statement Evaluate I=\int_{0}^{Inf}e^{-kw^{2}t}cos(wx)dw in the following way. Determine (partial derivative) dI/dx, then integrate by parts. Homework Equations \int udV = uv - \int vdU The Attempt at a Solution So I have to figure out...

Homework Statement int dx / (x (ln 3)^3) can someone tell me how to start this problem what's my u and dv ??

1. The problem is this: The antiderivative from 0 to 1 of (e^x)*sin(Nx)dx I tried integrating by parts several times and I'm just not sure if what I'm doing was correct. I keep hitting a dead end. I'm not sure if I'm supposed to IBP twice or substitute sin(Nx) for something else. Help...

Homework Statement \int(sin(x)^{-1}), dx Homework Equations *By Parts Formula: f(x)g(x) - \int(g(x) f'(x)) dx Also for d/dx sin(x)^{-1} I used 1/sqrt(1-x^{2}) The Attempt at a Solution Just started learning this method, I tried letting f(x) = sin(x)^{-1} and g(x) = dx but nothing really...

Hello everyone Let's say I want to do this integral: \int_{}^{}f(x)g(x)\,dx We use this formula \int f(x)g'(x)\, dx=f(x)g(x)-\int f'(x)g(x)\, dx I don't understand the utility of this equation, since we want to find \int_{}^{}f(x)g(x)\,dx and not \int f(x)g'(x)\, dx Please...

integration by parts! MIDTERM...really quick question...please help! Homework Statement \int arctan4t dt Homework Equations The Attempt at a Solution ive been attempting this all day. the answer is t arctan4t-1/8 ln(1+16t^2)+C i get this asnwer up until the 1/8... a...

integration by parts! MIDTERM...really quick question...please help! Homework Statement Evaluate the two following integrals: \int xcos5x dx and \int ln(2x+1) dx Homework Equations The Attempt at a Solution ok, for the first one, the answer is 1/5 x sin5x +...

Homework Statement \int x*(ln(x))^4dx = 4ln|x|^3-12ln|x| Homework Equations The Attempt at a Solution I did chart method u...dv...+/- ------------------------ x...ln|x|^4...+ 1...(4ln|x|^3)/x.. - 0...12ln|x|...+ ......-

http://usera.ImageCave.com/kamranonline/369529f005b9d646328ba8de471139.gif Attempt to the solution. I took u=\sqrt{t} and from there i went upto : 2\intu^2Sin(u^{2})dx dunno wat to do next. Havn't been taught integration by parts yet.

Homework Statement integrate ln(x+1) dx (integrate by part) Homework Equations integrate e^-2x sin3x dx The Attempt at a Solution 1st,i make u=x+1 ,so du/dx =1 du=dx..while i use /dv =/ln(x+1) dx and after integrating my v=1/(x+1) so subtitute into uv -/vdu but my ans turn out to...

hello, i'm a self learner currently learning Fourier series. Anyway, I'm having some problem with a question regarding the inner product of two complex functions. This is defined by an integral from negative infi to positive infi of the multiplication of one function and the complex...

Homework Statement How can i find the integral of \int e^{-x^{3}}dx Homework Equations The Attempt at a Solution I tried using integration by parts, but it doesn't seem to give a nice way to solve either.

Homework Statement Integrate the following equation for average energy from -infinity to infinity \int(c*x^4)*(e^(-c*x^4)/KT)dx Homework Equations c, K, T are constants \int(e^(-c*x^4/KT)) = (KT/c)^(1/4)*(2\Gamma(5/4)) The Attempt at a Solution I tried using integration by parts...

Homework Statement Show using integration by parts that: \int x^3 e^x^2 dx = e^x^2 ( \frac{ x^2 -1}{ 2 }) Homework Equations The Attempt at a Solution Integration by parts obviously. \int u dv = uv - \int v du Let u = x^3 and dv = e^x^2 dx \int x^3 e^x^2...

having difficulty integrating the following equation by parts to determine if its symmetric: d4 u / dx4 + K d2 u / dx2 + 6 = 0 0< x < 1 Can someone help with this?

Homework Statement 1/(u²(a+bu)²) a and b are constants u is the variable Homework Equations The Attempt at a Solution i know I am suppose to use substition by parts but i don't know what to use. thanks for help in advance

Integrating Natural Log Function using "Integration by Parts" Method Homework Statement The problem says to integrate ln(2x+1)dx Homework Equations I used u=ln(2x+1); du = 2dx/(2x+1); dv=dx; v=x The Attempt at a Solution So, I integrated it using that (above) 'dictionary' and I...

Homework Statement Estimate \int_{0}^{10} f(x) g'(x) dx for f(x) = x^{2} and g has the values in the following table. \begin{array}{l | c|c|c|c|c|c |} \hline \hline g&0&2&4&6&8&10\\ \hline g(x)&2.3&3.1&4.1&5.5&5.9&6.1\\ \hline \end{array}...

Hello, The problem I'm working on is X225x. I know you have u = x2 and du = 2x however if dv= 25x then what is v? I know if dv were say e2x than v would be 1/2e2x but for this problem would v simply be 1/5*25x? Thank you

Homework Statement Integrate \int{\frac{lnx}{x^4}dx} Homework Equations The Attempt at a Solution I get this: u = ln x, du = \frac{1}{x} dv=x^4, v=\frac{x^5}{5}dx \frac{(lnx)x^5}{5}-\int{\frac{x^5}{5}*\frac{1}{x}dx} = \frac{(lnx)x^5}{5}-\frac{6x^6}{5}dx} Am I doing this right?

Homework Statement \int {\frac{{\cos ydy}} {{\sin ^2 y + \sin y - 6}} } The Attempt at a Solution \int {\frac{{\cos ydy}} {{\sin ^2 y + \sin y - 6}} = } \int {\frac{{\cos ydy}} {{(\sin y - 2)(\sin y + 3)}}} Now I attempt to split this into partial fractions: \begin{gathered}...

b_{n} = \frac{1}{\pi}\int^{\pi}_{-\pi}sin\theta sin n\theta d \theta let u = sin \theta, \ du = cos \theta d \theta dv = sin n \theta d \theta, \ v = -\frac{1}{n}cosn \theta = \left[-\frac{1}{n} sin \theta cos n \theta \right|^{\pi}_{-\pi} + \frac{1}{n} \int^{\pi}_{-\pi} cos...

Integrate the function. (3x)/(3x-2) I am spose to use integration by parts but i don't know how to integrate 1/(3x-2). anybody help??

Homework Statement \intln(7x+9)dx Homework Equations derivative of ln is 1/x The Attempt at a Solution Well I am just learning IBP so i set u=7x+9 dv=lndx but I am stuck there. How do you know which to make ur u is there a way or is it trial and error Can i split the integral as: ∫ln(7x)+∫9

Homework Statement ∫e^x+e^x Homework Equations ∫u dv= uv- ∫v du The Attempt at a Solution u= x+e^x du= e^x so it would be e^u integral = e^u = e^(e^x) +c is that correct, i know the answer is but what i just did

Homework Statement ∫x sin^2 x dx Homework Equations integration by parts ∫u dv= uv-∫ v du The Attempt at a Solution u=x dv=1-cos2x v= 1/2 sin 2x du=dx is that correct i substituted sin^2 x= 1-cos2x Am I allowed to do that.

Hi all, I'm working on an ODE and ran into this integration by parts. My calculus is terrible. Can someone help? e^{2t}x = \int e^{2t}cos(t) \ dt = \frac{1}{2}cos(t) \ e^{2t} + \frac{1}{2}\int e^{2t}sin(t)\ dt = \frac{1}{2}cos(t)\ e^{2t} + \frac{1}{2}\left(-e^{2t}cos(t) + 2\int cos(t)\...

Homework Statement ∫ (theta)^3 *cos(theta)^2 Homework Equations integration by parts ∫u dv= uv- ∫v du The Attempt at a Solution u=theta^3 dv=cos(theta)^2 du=3theta^2 v=sin(theta)^2 here's the problem do i use cos(theta)^2 equal...

Homework Statement ∫ln (2x+1) dx Homework Equations ∫u dv=uv- ∫ v du integration by parts The Attempt at a Solution u= ln (2x+1) dv=dx du=? v=x ok did i choose the right u and how do i derive it, do i have to use the chain rule π²³ ∞ 0° ~ µ ∑ Ω √ ∫ ≤ ≥ ± # … θ φ...

Homework Statement #1. Use Integration by parts to evaluate the integral \int 2x \ln(2x) dx #2. Use Integration by parts to evaluate the integral \int (\ln(3x))^{2} dx #3. Use Integration by parts to evaluate the integral \int x e^{4x} dx #4. Evaluate the indefinite integral. \int \sin(3x)...

Hi, I am trying to integrate (x^5)/7680 . exp (-x/2) dx between 0 and 1. I've had various attempts at this and this is what i have done so far... Taken the 1/7680 outside the integration Using integation by parts I have assigned u=x^5 and dv/dx = exp(-x/2). when i integrate exp(-x/2) i...

I actually have two here, so I will just list both: Homework Statement \int\frac{x}{x^{2}+4x+4}dx Homework Equations None The Attempt at a Solution I tried this one twice. I honestly have no idea how to do it, and I used integration by parts. The first time, I reduced it down...

Homework Statement Use integration by parts to find: y=... if dy=arcsinh(x) dx Homework Equations int(v.du)=uv-int(u.dv) The Attempt at a Solution I understand how to perform integration by parts. My problem here is, what are my 'v' and 'du'?

Hi Can anyone help me with this integration. I will use I to symbol the integer sign Limits between 1 and 0 Ie^-x.Sinxdx I understand I have to integrate by parts and get the following answer, ignoring the limits for the time being. Ie^-x.Sinx = e^-x.Cosx I -Cosx.e^-x dx then i...

Use integration by parts to express: I (n) = ∫(sin)^n (x) dx in terms of I (n-2) Let u = sinn-1 x du = (n-1)sinn-2 x cos x dx v = - cos x dv = sinx dx so integration by parts give: ∫〖sin〗^n x dx= -cos⁡〖x 〖sin〗^(n-1) x+(n-1) ∫〖sin〗^(n-2) 〗 x cos^2⁡〖x dx〗 Since cos2x = 1 –...

I need to integrate 2\int_0^1cosh(\pi x)cosnx Not asking anyone to do it for me, just what method to use? Thanks alot.

Hello, This is not a question regarding a homework problem, but a step in class the professor did not show how to calculate. Homework Statement I am taking a course on Viscous Flow, and for Rayleigh flow after applying the similiarity solution : \eta=(y/(2*\sqrt{\gamma*t})) The...

[SOLVED] Integration by parts 1. Evaluate \int e^{x}sinxdx [Hint: Integrate by parts twice.] I can't seem to get an answer, but by integrating, the process is redundant (repeats itself). Thanks Work: \int e^{x}sinxdx Let u = sin x, therefore du = cosxdx Let dv = e^{x}dx...

I need SERIOUS HELP...integration by parts! Homework Statement Integrate: x^3*e^x Homework Equations The Attempt at a Solution I have the answer in my book but I am not understanding why you have to repeat the integration 3 times... 1.) dv = e^x dx v = e^x u = x^3 du =...

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...