# Homework Help: 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 sqrt(du)/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!

2. Oct 20, 2006

### neutrino

That's not right. The derivative of $$\cos^2{x}$$ is NOT $$-\sin^2{x}$$.

Yes you can. The final integral is pretty straightforward.

neutrino's right - you can't differentiate $$\cos^2{x}$$ as $$-\sin^2{x}$$. If it helps, think of $$\cos^2{x}$$ as $$cos{x} * cos{x}$$. You can then use the chain rule.