Integrate Definition and 642 Threads

How do I integrate ∫x3dx/x+1?

[HELP] How to integrate ∫ 1/(1-cosx)^2 dx ?? Hi all, A very fundamental question here, but I cannot find solution from calculus books. Anyone know how to integrate ∫ 1/(1-cosx)^2 dx ?? Thanks.

∫x(dx)^2=? and what is the difference between dx^2 and (dx)^2?

Do we get function for velocity or do we get the function for the total change in velocity?

I have found that while these two should be the same, mathematica does not evaluate them equally. Integrate[(a + b el + c el^2) DiracDelta[u], {u, 0, 1}, {el, e1, e2}] Integrate[ Integrate[(a + b el + c el^2) DiracDelta[u], {el, e1, e2}], {u, 0, 1}] I believe the second one is correct...

Would be very grateful if someone helped me on this. $\displaystyle\int_0^\infty \frac{dx}{1+x^3}$

I have tried the substitutions I know og, but I just can't solve it. It would be great if someone helped me on this one.

How would you Integrate a Sigma Sum?

this may seem simple, but try doing this yourself. I've tried sustituting t=e^x , e^-x. but the problem lies after that. do it and see it for yourself.

Homework Statement Use both substitution and integration by parts to solve: ∫x3ex2dx 2. The attempt at a solution ∫x3ex2dx ∫ex2x3dx (1/2x)ex2x3-∫(1/2x)ex23x2dx (1/2)ex2x2-(3/2)∫ex2xdx (ex2x2/2)-(3/2)∫eux(du/2x) (ex2x2/2)-(3/2)(1/2)∫eudu (ex2x2/2)-(3/4)eu + C...

Homework Statement Find the potential inside and outside a uniformly charged solid sphere of radius R and total charge q. Homework Equations V(r) = -∫E dl The Attempt at a Solution I just have a question about finding the potential inside the sphere. Why integrate from infinity...

how to solve this without expanding the numerator. $\displaystyle \int\frac{(x-1)^3}{x^2}dx$

Homework Statement ∫\frac{Cos(x)}{x} dx Homework Equations Taylor series expansion for Cos(x) The Attempt at a Solution I have used Taylor series to find the product of (1/x) * (cos[x]). After integration i get In[x] - x^2/8 + x^4/96 + x^6/4320+... I don't know what to do...

Hi, I don't know how to calculate the following integral of an even function limit{n goes to ∞} int_{-∞}^{∞}frac{sqrt(n)}{(x^2+1)^n}=? Can this calculus be done by complex integral? I was thinking for a few days and no answer so far : ( Thanks!

I do not understand the following integral: \int^{\infty}_{0}2e^{2+jωt}dt = \frac{j2e^{2}}{\omega} Why is it not ∞? Here are my steps: Let u = 2+jωt, du = jωdt, dt = \frac{1}{jω}du = -\frac{j}{ω}du \int^{\infty}_{0}2e^{2+jωt}dt = -\frac{2j}{ω}\int^{\infty}_{2}2e^{u}du =...

I was doing a question using u substitution and at one point,I got sqrt(u-2). How do I integrate it further? Can I integrate is straight away with sqrt(u-2)(2/3) as answer or do I have to use trigonometric substitution? How to do if it's trigonometric?

How do I integrate sqrt(x/2-x)dx?

Dear Valued Member of the forum i am from Bangladesh, we want to build a site. here to i want to how to integrate ms word 2010 eq editor with my website. so , anyone pls help me, how to add this editor, ?

Homework Statement ∫ Sinx cos x dx Homework Equations The Attempt at a Solution If you integrate it using substitution, you get -cos2(x)/2but if you use double angle formula to rewrite the problem, it will be ∫1/2 sin(2x), and integrate it, you get -cos(2x)/4. isn't it weird?

Homework Statement Integrate ∫dx/(sin(x)+a), where a is a constant.Homework Equations The Attempt at a Solution I have been working on this for a while, and for some reason I can't figure it out. The attempt that seemed the most promising to me was to multiply top and bottom by (sin(x)-a)...

1. Homework Statement [/b] \int _{C} Re z^{2} dz clock wise around the boundary of a square that has vertices of 0, i, 1+i, 1.Homework Equations \int_{c} f(z) dz = \int \stackrel{b}{ _{a}} f[z(t)] \stackrel{\cdot}{z(t)}dtThe Attempt at a Solution Since it is piece-wise continuous I know I need...

How to integrate below? $$\int \sqrt{\frac{r^{2}-x^{2}+x^{2}}{r^{2}-x^{2}}} dx$$ neither if u = r^2 - x^2 nor u = x^2 will get the result.

Homework Statement Integrate (8-16x)/(8x^2-4x+1) dx Q Homework Equations I separate it first 8/(8x^2-4x+1)dx -16x/(8x^2-4x+1)dx Then I have no idea what to do next. The Attempt at a Solution none ;(

Homework Statement integrate 2t^(2)/(1+t^2)^(2) Homework Equations trig sub 1+tan^2(x)= sec^2(x) The Attempt at a Solution the attempted solution is attached.

Homework Statement \int_0^1\frac{\sin(\pi x)}{1-x}dxHomework Equations \int \frac{\sin (\pi x)}{1-x}=Si(\pi-\pi x)The Attempt at a Solution I was stuck on the above integral while solving an exercise, I found out earlier on Wolfram that this integral doesn't probably have an elementary...

Hi, I'm working on an independent research project - and am trying to integrate this (with respect to x between some arbitrary m and infinite). http://www.wolframalpha.com/input/?i=+x+%3D%28t%2B2%29%2F%281%2Be%5E%28t-r%29%29%2C+y%3D%28e%5E%28-t%5E2%2F2%29%29%2Fsqrt%282*pi%29 If you graph this...

I want to integrate (1-k^2 cos(x)^2)^(-3/2) with lower limit 0 and upper limit pi/2, where x is the variable and k is the constant.

Hello MHB, I got stuck on integrate this function $$\int \frac{\sin^3(\sqrt{x})}{\sqrt{x}}dx$$ my first thinking was rewrite it as $$\int \frac{\sin^2(\sqrt{x})\sin(\sqrt{x})}{\sqrt{x}}dx$$ then use the identity $$\cos^2(x)+\sin^2(x)=1 \ \therefore \sin^2x=1- \cos^2(x)$$ $$\int...

Homework Statement (Everything here is frequency dependant, but I have left off the v from all the variables to minimise chance of typos - hopefully that is ok but please let me know if not and I will try and retype!) The equation of radiative transfer is dI/dτ = -I + S We guess...

Hi, I never really understood this fundamental concept of integration of rings to find the electric field for say a flat disk. In my book to find the electric field on a point charge on the axis of a disk a distance z away they just integrate all the rings of charge to the end of the disk. If it...

Hey everyone, I need to do the following integral. I just need a little help getting this started, I'm not sure where I need to go. Here is the problem: \int_{0}^{1-v} du \int_{0}^{\frac{1}{2}} dv \frac{1}{1+u^2-v^2} I think I have the boundaries for the integral set up correctly, {0≤v≤1/2...

Every time I try to do a simple definite integral simbolically such as: Integrate[R/P - c1/(T^2), {P,P1,P2}] it takes about 2 minutes then gives a long conditional expression. Basically it assumes that P1 and P2 are general numbers with complex parts and negative and such. HOW do I tell...

Consider example 4 in the attachment. Why did they integrate from 1 to ∞ instead of e to ∞?

Homework Statement How do I integrate this easily? \frac{2}{T}\int^{T/2}_{0}sin(120\pi t)cos(120\pi n t) Homework Equations The Attempt at a Solution I used Wolfram Alpha to integrate this, but are there ways to use substitution or another trick instead?

I am trying to integrate $$ \int_0^{\nu}\frac{d\theta}{(1 + e\cos\theta)^2} $$ where $0<e<1$. I tried using Residue Theory but that was messy and didn't come up as needed. The highlights of that were: $\cos z = \frac{z + \frac{1}{z}}{2}$ Denominator became $z + 2ze^2 + 2z^2e^2 + 2e^2 + 4z^2 +...

see image http://i.imgur.com/OCj7Q5f.jpg

Homework Statement How can I integrate this? I already tried substitution u=x-1 and partial fractions. ∫[dx]/[(1-X^2)√((x^2)-3x+2)] Homework Equations The Attempt at a Solution

I hope this isn't too simple for the maths forum. I'm trying to find the length of the locus described by the bottom of a garage door as it is raised. It's all fairly straightforward until I have to integrate a function of the form √ (sin2θ + k cos2θ) k does not depend on θ. I tried...

Homework Statement Integrate \frac{xe^{2x}}{(1+2x)^2} with respect to x Didn't get anywhere with integration by parts or substitution using u=xe^(2x) A push in the right direction would be much appreciated.

Integrate e^[a*sqrt(b^2+x^2)] * e^c*x I can integrate the first part alone, i.e. ∫ea*√(b2+x2) and the result is [√(b2+x2)/a - 1/a2] ea*√(b2+x2). For the full integral, i.e. ∫ea*√(b2+x2) * ec*x I tried using integration by parts but it does not work since the exponent of the first e is not...

I've been reading in my engineering textbooks and came across a frequent equation manipulation that involves multiplying/bringing the dx term of dy/dx to the other side of the equation, and then integrate both sides. I don't know what technique this is and I can't find it in my Stewart's...

I have a LARGE function that I must integrate over 2 variables, {x,y} both from 0 to 1. The Function looks like : F[x_,y_] = A[q] G[x,y] + B[q] G2[x,y] + (...) Where (...) MAY be 100's of terms long, if not thousands. But the fact is each term is separable, in SOME way to a function of...

Homework Statement Integrate √(x2(x+3)) from -3 to 0. 0 ∫√(x2(x+3)) dx -32. The attempt at a solution Here is what I did: √(x2(x+3)) = x√(x+3) Let u=x+3, du=dx, x=u-3 Insert the bounds and change the bounds to: 0 to 3. x√(x+3)= (u-3)√(u) = u3/2-3u1/2 Thus we have: 3 ∫(u3/2-3u1/2) du 0...

Prove that $$\int_0^{\pi/2} (\log \sin x )^2 dx = \frac{1}{24} \left(\pi ^3+12 \pi \log^2(2)\right)$$

\displaystyle\int sin^22tcos^2t\ dt This was part (b) to a question, the previous part of the question was to integrate \displaystyle\int sin^22tcost\ dt which I managed to do by expressing sin^22t as 4(sin^2t - sin^4t) I tried a similar method for the integrand above, but didn't...

Consider a forcefree mass point in one-dimensional space. (a) Calculate the action S for the actual path of the mass point in the time interval [0, T] and for the boundary conditions x(0) = 0 and x(T) = d. I said the Lagrangian was just equal to L=1/2mv^2. I'm not sure if my reasoning for...

Homework Statement Evaluate $$\int_ \ \sqrt[2]{9-x^{2}} \, \mathrm{d} x.$$ Homework Equations U substitution Integration by parts The Attempt at a Solution My teacher said it wasn't possible "by hand", but Wolframalpha provided a step-by-step solution. I'm clueless as to how wolfram came...

Homework Statement Integrate ettdt using integration by parts.2. The attempt at a solution Seems like a very easy problem; however, I just started learning integration by parts-- didn't understand this. So the book's method: u=t...

Homework Statement Integrate \sqrt{x-x^2} The attempt I did a trig substitution, letting cos(\theta)=\frac{x}{sqrt(x)} and after some manipulation ended up with -2\int \ |sin(\theta)cos(\theta)|sin(\theta)cos(\theta) d\theta which I have no idea how to integrate. If I make a...