Calculus 2 Help: How to Integrate 2/((x^2)-1)

[ashleyk]

Hi, I have calculus 2 in college right now and am drawing a complete blank and need to get my homework done. If I wanted to take the integral of 2/((x^2)-1)...what would I do or where would I start? Thanks!

 

[ircdan]

Use partial fractions.

 

[HallsofIvy]

First, that 2 in front shouldn't bother you. Just do the integral without the 2, then multiply by 2.
$$\frac{1}{x^2- 1}= \frac{1}{(x-1)(x+1)}$$
and that can be expanded by "partial fractions":
$$\frac{1}{x^2-1}= \frac{A}{x-1}+ \frac{B}{x+1}$$
To find A and B, multiply both sides of that by x²-1 then let x= 1 and -1 in turn.

To integrate the resulting fractions, look up the integral of $\frac{1}{x}$.