Partial fractions Definition and 298 Threads

\Sigma_{n=1}^{ \infty} \frac{1}{(3n-2)(3n+1)} I simplified it to partial fractions to (1/3) / (3n-2) - (1/3) / (3n+1) Now what?

Homework Statement F(X)=[tex]\int[/\frac{1}{1+t^3} Homework Equations The Attempt at a Solution I have tried different substitutions to find fog where g(t) = ? But am getting stuck

Homework Statement Actually i want to ask something actually very easy... i just don't know the meaning of some words in different questions... firstly... multiplication of A and B means A*B right? how about multiplication of A by B means A*B or A/B?? secondly... division of A by B means...

Homework Statement Evaluate the integral: integral (-17e^x-36)/(e^(2x)+5e^x+6 dx Homework Equations partial fractions The Attempt at a Solution Basically, what i did was factored the bottom into (e^x+2) and (e^x+3) because when i expand that, it equals the bottom. From there, i...

Homework Statement I am supposed to evaluate the integral using partial fractions. \int \frac{1}{(x+5)^2(x-1)} dx 2. The attempt at a solution So after doing all the work, I get (-1/36)ln|x+5| - (13/6)ln|x+5| + (1/36)ln|x-1| But the answer in the book appears as (-1/36)ln|x+5| -...

Homework Statement 1/((x^2-1)^2) Homework Equations The Attempt at a Solution so i get (Ax+B)/(x^2-1) + (Cx+D)/((x^2-1)^2) then i multiply both sides by ((x^2-1)^2) then i get 1=(Ax+B)(x^2-1)+ (Cx+D) then i multiply it out Ax^3+Bx^2 -Ax +Cx +D =1 then i equate...

Homework Statement (3x^2-4)/(x^3-4x-6) Homework Equations I guess integration by parts... But how do i set this up? The Attempt at a Solution The numerator is exponentially lower than the denominator, so no long division. The denominator seems not to factor out into anything...

Homework Statement \int\frac{e^x}{(e^x-2)(e^2x +1)} it should be e to the power of 2x Homework Equations Using substitution u=e^x, and then using partial fractions The Attempt at a Solution I have done this problem two separate ways. One with substitution and then partial...

Homework Statement Solve the integral x/x^2+4x+13 Homework Equations I think that you would use partial fractions but I'm not really sure. I know that you need to complete the square on the denominator. The Attempt at a Solution The completed square would be (x+2)^2+9. I don't...

Homework Statement Integrate x^3 + 49 / x^2 + 5x + 4 Homework Equations The Attempt at a Solution Since the numerator has an x cubed, but the denominator only has an x squared, I know I need to divide the numerator by something. I'm not sure what, but maybe the...

Homework Statement The problem asks to evaluate the integral using partial fractions, but I just cannot find out which trick to get this one to work. the equation is \int\frac{x^3+x^2+2x+1}{(x^2+1)(x^2+2)} The Attempt at a Solution I have tried setting it up as a partial fraction...

Homework Statement integrate (4x^2 + 3x + 6)/x^2 (x+2) dx Homework Equations don't have sorry.. The Attempt at a Solution firstly = A/x + B/x^2 + C /x+2 , = A(x^2)(x+2) + B(x)(x+2) + C(x)(x^2) equating with the 4x^2 + 3x + 6,then i integrate it,but my ans turn out to be...

I've been working with Laplace Transforms and integration ALOT lately. Many times I windup having to use partial fractions to solve the problem and frankly my algebra skills just aren't up to the task. Take this fraction for example; I know 3 ways to do it... 1 of the ways doesn't work unless...

\frac{s-1}{s(s-2)^2} How can I expand this fraction? \frac{A}{s} + \frac{B}{(s-2)} + \frac{C}{(s-2)^2} right? This gives me the equation As^3 - 6As^2 + 12As - 8A Bs^3 - 4Bs^2 + 4Bs + Cs^2 - 2Cs = s-1 so that (1) A + B =0 (2)- 6A - 4B + C = 0 (3) 12A + 4B - 2C = 1 (4)...

\int e^{ax}cosbx This one is driving me insane. So I used e^ax as u and cosbx dx as dv. And then I did it again using e^ax as u and sinbx as dv which left me with \int e^{ax}cosbx = \frac{1}{b}e^{ax}sinbx + \frac{a}{b^{2}}e^{ax}cosbx - \frac{a^{2}}{b^{2}}\int e^{ax}cosbxdx I have no...

Homework Statement How does one integrate e.g. \frac{1+x}{(2+x)^{3/2}} by partial fractions? The Attempt at a Solution I have no idea about this. I've never seen this technique applied with fractional powers before.

Homework Statement Derive a formula for the antiderivative of sec x using the identity that sec x= cos x/ (1-sin^2x). Use a substitution for sin x and then partial fractions. Then multiply the solution by (1+sin x)/ (1+sin x) to obtain the more familiar formula for the antiderivative...

This is probably a "basic" question, but I can't seem to remember how to do partial fractions problems where there is only a 1 in the numerator. For example (just making this up), let's say I have: 1/s(s+4)(s+5) So what I'd do is 1/s(s+4)(s+5) = A/s + B/(s+4) + C/(s+5) as one would expect...

I'm trying to solve this integral but I'm not sure if I'm on the right track. My question is: can this integral be solved by partial fractions decomposition? I solved the problem that way but I'm not sure if it is the right answer. thanks! ∫1-x+2x^2-x^3 ÷ x(x^2+1)^2

Homework Statement \int\frac{dx}{x(1+ln x)} Homework Equations Partial Fractions? Maybe I am solving this wrong... The Attempt at a Solution \frac{A}{X} + \frac{B}{1+ln x} = 1 A(1+lnx) + Bx =1 A + Alnx + Bx =1 This doesn't seem to work out properly. I have been having a...

Homework Statement \int {\frac{{2s + 2}} {{(s^2 + 1)(s - 1)^3 }}ds} The Attempt at a Solution This is a long one...First, I split the integrand into partial fractions and find the coefficients: \begin{gathered} \frac{{2s + 2}} {{(s^2 + 1)(s - 1)^3 }} = \frac{{As + B}}...

Homework Statement \int {\frac{{2s + 2}} {{(s^2 + 1)(s - 1)^3 }}ds} The Attempt at a Solution This is a long one...First, I split the integrand into partial fractions and find the coefficients: \begin{gathered} \frac{{2s + 2}} {{(s^2 + 1)(s - 1)^3 }} = \frac{{As + B}}...

Homework Statement Hi everyone, here is a new partial fractions question I just cannot understand: \int\frac{x^{3}}{x^{3}+1}dx Homework Equations Partial Fractions, difference of perfect cubes, polynomial long division The Attempt at a Solution \int\frac{x^{3}}{x^{3}+1} dx...

Homework Statement \[ \int {\frac{{e^t dt}} {{e^{2t} + 3e^t + 2}}} \] I'm not quite sure how to start this one...Any hints? I tried bringing e^t down to the denominator and multiplying it out which still didn't help. I can't see a way to factor the denominator or split this into a...

Homework Statement \int1/(s^{2}(s-1)^{2}) ds Homework Equations Partial Fractions The Attempt at a Solution = \frac{A}{s^{2}}+\frac{B}{s-1}+\frac{C}{(s-1)^{2}} Setting numerators equal to each other: 1 = A(s-1)(s-1)^{2} + Bs^{2}(s-1)^{2}+Cs^{2}(s-1)...

Homework Statement ∫(2t)/(t-3)^2 the integral is 2 to 0 ok does it = A/ t-3 + B/(t-3)^2 I'm not sure if you break up (t-3)^2

Homework Statement ∫1/ x^3-1 dx, ok how would i do this Homework Equations ∫dx/ x^2+a^2= 1/a tan^-1 (x/a) +c i tried to simplify x^3-1 = (x+1)(x-1)(x+1)

Homework Statement ∫ 10/(x-1)(x^2+9) would i change this into 10/ (x-1) (x+3) (x+3) then= A/ x-1 + B/ X+3 + C/ x+3

got an exam coming up in a few days and half way through my question i ran into a partial fractions question instead of having the standard (1/(y+c)(y+d))= A/(y+c) + B(y+d) and multiplying out i had a double root so (1/(y+c)(y+c)) does this change the way i go about the question and are there...

.. oy, I'm just not sure how to find 3 constants! Here is my problem: 5x^2-4/(x-2)(x+2)(x-1) = A/(x-2)+B/(x+2)+C/(x-1) .. i got a bit of it done, but it's all wrong OH! and what am i supposed to do if the numerator of the first equation does not have any sort of variable with it?? my...

For a rational function, (x^2+1)/(x^2-1) = (x^2+1)/[(x+1)(x-1)], if we were to split it into partial fractions so that (x^2+1)/(x^2-1) = A/(x+1) + B/(x-1) = [A(x-1) + B(x+1)]/(x^2-1)...solving for A and B get us A = -1 and B = 1. This would mean that (x^2+1)/(x^2-1) = 2/(x^2-1)...which doesn't...

I'm a little mixed up on the integration for partial fraction decomposition. I basically have x/ x(x^2 + 1) I'm wondering for the (x^2 + 1) part, am I to put Ax + B over it because it is a raised power, or since the outside bracket is not squared, it is to only have one variable over it.

Homework Statement we have 4/((s^2) + 4)(s-1)(s+3) Homework Equations The Attempt at a Solution dividing it up do we get: A/((s^2) + 4) + B/(s-1) + C/(s+3) = 4 or is it (As + B)/((s^2) + 4) + C/(s-1) + D/(s+3) = 4

Homework Statement [e^(-2s)] / (s^2+s-2) Find the inverse Laplace transform. Homework Equations The Attempt at a Solution I know that I can factor the denominator into (s+2)(s-1). Then I tried to use partial fractions to split up the denominator, but I don't know how to do that...

Telescoping Method & Partial Fractions...PLEASE HELP! Homework Statement Find the sum of the series from n=1 to infinity... 2/(4n^2-1) Homework Equations The Attempt at a Solution I want to use the telescoping method... 2/(4n^2) = 2/[(2n-2) * (2n+1)] I am following an...

Hello all, I've got an exam tomorrow so any quick responses would be appreciated. I'm following the Boas section on Laurent series... Anyway, here's my problem: In an example Boas starts with f(z) = 12/(z(2-z)(1+z), and then using partial fractions arrives at f(z) = (4/z)(1/(1+z) +...

(t+1) dx/dt = x^2 + 1 (t > -1), x(0) = pi/4 I have attempted to work this by placing like terms on either side and then integrating. 1/(x^2 + 1) dx = 1/(t + 1) dt arctan x = ln |t + 1| + C x = tan (ln |t + 1|) + C pi/4 = tan(ln |0 + 1|) + C pi/4 = C x = tan (ln |t + 1|)...

Homework Statement Solve y"+4y'=sin 3t subject to y(0)=y'(0)=0 using Laplace Transform The Attempt at a Solution So I got: s^2Y(s)-sy(0)-y'(0)+4[sY(s)-y(0)]=\frac{3}{s^2+9} \Rightarrow Y(s)=\frac{3}{(s^2+9)(s^2+4)} Now it looks like two irreducible quadratics, which I...

[SOLVED] Partial Fractions 1. Evaluate: \int \frac{dx}{x^{2} -1} Attempt: \int \frac{dx}{x^{2} -1} = \int \frac{dx}{(x+1)(x-1)} = \frac{A}{(x+1)} + \frac{B}{(x-1)} = \frac{Ax - A + Bx + B}{(x+1)(x-1)} Where do I got from here? Thanks

Homework Statement Evaluate the indefinite integral. int (6 x + 7)/(x^2 + 1) dx ` The Attempt at a Solution A/(x + 1) + B/(x - 1) 6x + 7 = A(x - 1) + B(x + 1) 6x + 7 = (A + B)x + (-A + B) A + B = 6 -A + B = 7 A + (7 + A) = 6 2A = -1. A = -.5 B = 3.5 So the...

[SOLVED] integration by partial fractions Homework Statement \int((2x^2-1)/(4x-1)(x^2+1))dx Homework Equations A1/ax+b + A2/(ax+b)^2 + ... + An/(ax+b)^n The Attempt at a Solution (2x^2-1)/(4x-1)(x^2+1) = A/4x-1 + Bx+C/x^2+1 2x^2-1/x^2+1 = A + Bx+C(4x-1)/x^2+1 set x =...

Integrate using partial fractions: (int) (x^3)/(x^2 -1) dx I have put into the form (int) (x^3)/((x-1)(x+1)) dx I thought partial fractions had this property: 'Partial fractions can only be done if the degree of the numerator is strictly less than the degree of the denominator.'...

Homework Statement Integration of 1/(x^2-5x+6) Homework Equations The Attempt at a Solution I know i cannot do ln|x^2-5x+6| I've tried some form of substitution or intergration by parts, and they don't work. Should I factor the bottom?

Homework Statement The problem is from Stewart, Appendix G, A58, no.45. Suppose that F, G, and Q are polynomials, and: F(x)/Q(x) = G(x)/Q(x) for all x except when Q(x) = 0. Prove that F(x) = G(x) for all x. [Hint: Use Continuity] The Attempt at a Solution I thought the statement was...

Hi! There's this one problem that I'm having troubles with. I've tried using the decomposition method, but I've ended up getting a messy answer. If someone can give me tips or the solution to the problem, I'll appreciate it. Here's the problem: solve the integral of 1/ y^2-1 dx.

Homework Statement http://books.google.com/books?id=qFNZIUQ_MYUC&pg=PA142&lpg=PA142&dq=loren+larsen+%224.3+23%22&source=web&ots=YKlIl_yPb3&sig=MC2QCtuBii9za-vd4FkAJadZ_dI I am working on 4.3.23b) I can get that \sum_{i=1}^n \frac{g(x_i)}{f'(x_i)}\frac{1}{x-x_i} = g(x)/f(x) but I do not...

Check out the link to see the problem and my work. Can anyone see where I made an error? I can't seem to figure out where I went wrong. https://www.physicsforums.com/attachment.php?attachmentid=11519&stc=1&d=1194912644"

Evaluate the integral of x^2-x/(x^2-1)^2 from 0 to 1. * I know that I have to use partial fractions in order to make the integral integratable. My attempt at partial fractions: A/(x-1) + (B/(x+1)) + (Cx+D/(x^2-1)^2) Is this setup right? (Once I have it set up correctly, I know how...

Homework Statement I am given 9/[(s-1)(s-1)(s-4)] as part of a Laplace Transform. I'm supposed to decompose into partial fractions. Homework Equations So 9/[(s-1)(s-1)(s-4)]= D/(s-1)+E/(s-1)+F/(s-4) The Attempt at a Solution To simplify: 9= D(s-1)(s-4)+ E(s-1)(s-4)+ F(s-1)^2...

Arc Length, Irreducible quadratic factors i'm having a hard time seeing this method, and i have to use this method on one of the problems I'm doing to find it's Arc Length. L=\int_{\sqrt{2}}^{\sqrt{1+e^{2}}}\frac{v^{2}dv}{v^{2}-1}} the book suggests to first divide then use a...