# Integration by substitution

1. Oct 20, 2006

### sapiental

evaluat the indefinite integral ((sin(x))/(1+cos^2(x)))dx

I let

u = 1 + cos^2(x)

then du = -sin^2(x)dx

I rewrite the integral to

integral (du)/sqrt(u)

can I set it up like this? should I change u to something else?

I also tried it like this by rewriting the original equation to:

indefinite integral ((sin(x))/(1+cos(x)cos(x)))dx

u = cos(x)

du = -sin(x)dx

then

- integral (du)/(1+(u^2))

Also, can somebody give me directions on how to format equations in this message board to make my questions somewhat clearer.

Thanks alot!

I actually tried to evaluate it using one of my methods and arrived at the following result:

2((1+cos^2)^(1/2))+C

2. Oct 20, 2006