# A fairly easy integral

1. Jan 27, 2012

### sckeen1988

1. The Problem comes down to what I think is a fairly simple integral, I just can't figure it out.

int(x^2/(1+x^2)

I know this is x-arctan(x)+c, but cannot figure out how.

I tried subbing in u for x^2, this didn't really help me with a direction to take though.

2. Jan 27, 2012

### genericusrnme

if you ever see a $1+x^2$ you should imediately think to yourself TRIG SUBSTITUTION!

What relation do you know between $sin^2$ and $cos^2$?

I'd start there

3. Jan 27, 2012

### Ray Vickson

First, write f(x) = x^2/(1+x^2) as f(x) = (x^2 + 1 - 1)/(1+x^2) = 1 - 1/(1+x^2), so
int(f(x)) = x - int(1/(1 + x^2)) The expression 1 + x^2 cries out for the substitution x = tan(t).

RGV

4. Jan 27, 2012

### sckeen1988

ANGER!!! I knew I was forgetting something really easy, like adding and subtracting one. Thanks for the help