Integrate this using partial fraction

**charikaar** · December 6th 2009, 11:55 AM

how do i integrate this

$\frac{1}{(3x^2-1)^2(1-x^2)}$

I have to split this into partial fraction but I don't know how

$\frac{1}{(3x^2-1)^2(1-x^2)} =\frac{Ax+B}{(1-x^2)} + \frac{Cx+D}{(3x^2-1)^2}?$

**Chris L T521** · December 6th 2009, 11:59 AM

Originally Posted by charikaar

how do i integrate this

$\frac{1}{(3x^2-1)^2(1-x^2)}$

I have to split this into partial fraction but I don't know how

$\frac{1}{(3x^2-1)^2(1-x^2)} =\frac{Ax+B}{(1-x^2)} + \frac{Cx+D}{(3x^2-1)^2}?$

Note that $3x^2-1=\left(\sqrt{3}x-1\right)\left(\sqrt{3}x+1\right)$ and $1-x^2=\left(1-x\right)\left(1+x\right)$ .

So we have $\frac{1}{\left[(\sqrt{3}x+1)(\sqrt{3}x-1)\right]^2(1+x)(1-x)}=\frac{A}{\sqrt{3}x-1}+\frac{B}{(\sqrt{3}x-1)^2}+\frac{C}{\sqrt{3}x+1}$ $+\frac{D}{(\sqrt{3}x+1)^2}+\frac{E}{1+x}+\frac{F}{ 1-x}$

This is going to get quite messy...feel free to post back when you get stuck!

Thread: Integrate this using partial fraction

LinkBack

Thread Tools

Display

Integrate this using partial fraction

Similar Math Help Forum Discussions

Partial fractions integrate

please help improper fraction into partial fraction

partial fraction from improper fraction

Integrate this using partial fraction

Partial Fraction and integrate

Search Tags