# Partial Fraction Integrals

• November 11th 2009, 06:12 AM
Kevlar
Partial Fraction Integrals
Hey i've got 3 integrals i need to solve which are the following.

$\int \frac{x^2-2}{(x+1)(x-2)}$
$\int \frac{x-1}{(x+1)(x-2)^2}$
$\int \frac{1}{(x+1)(x^2+2x+2)}$

For every other example i've done, before I convert the fraction to something I can integrate the question tells me what form to put the equation in.

So my question is how do i know what form do i have to put the fraction in before i integrate i.e.

$\int \frac{x^2-2}{(x+1)(x-2)} = \int \frac{A}{x+1} +\int \frac{Bx+C}{x-2}$

or would it be something like

$\int \frac{x^2-2}{(x+1)(x-2)} = \int A + \int \frac{Bx+C}{x+1} + \int\frac{D}{x-2}$
• November 11th 2009, 06:58 AM
Amer
Quote:

Originally Posted by Kevlar
Hey i've got 3 integrals i need to solve which are the following.

$\int \frac{x^2-2}{(x+1)(x-2)}$
$\int \frac{x-1}{(x+1)(x-2)^2}$
$\int \frac{1}{(x+1)(x^2+2x+2)}$

For every other example i've done, before I convert the fraction to something I can integrate the question tells me what form to put the equation in.

So my question is how do i know what form do i have to put the fraction in before i integrate i.e.

$\int \frac{x^2-2}{(x+1)(x-2)} = \int \frac{A}{x+1} +\int \frac{Bx+C}{x-2}$

or would it be something like

$\int \frac{x^2-2}{(x+1)(x-2)} = \int A + \int \frac{Bx+C}{x+1} + \int\frac{D}{x-2}$

$\int \frac{x^2-2}{(x+1)(x-2)} dx$

$\int \frac{x^2-4 +2 }{(x+1)(x-2)} dx$

$\int \frac{(x-2)(x+2)}{(x+1)(x-2)} dx + \int \frac{2}{(x+1)(x-2)} dx$

$\int \frac{(x+1)}{(x+1)} + \frac{1}{(x+1)} dx + \int \frac{2}{(x+1)(x-2)} dx$

$\frac{2}{(x+1)(x-2)} = \frac{A}{x+1} + \frac{B}{x-2}$

find A and B I think A=-2/3 and B=2/3