# Thread: [SOLVED] Integration by Substitution 2

1. ## [SOLVED] Integration by Substitution 2

Integrate

cos(x) / (sin(x)sqrtof(sin^2(x)+1))dx

2. Originally Posted by vinson24
Integrate

cos(x) / (sin(x)sqrtof(sin^2(x)+1))dx
do a substitution. let $u^2 = \sin^2 x + 1$, then your integral becomes $\int \frac 1{u^2 - 1}~du$ .........do you see how to get to this?

(Note that the substitution is $u^{\color{red}2}$ and not just $u$)

now, i suppose you can finish up

3. yes thank you much

4. Another approach: put $u=\csc x+\sqrt{\csc^2 x+1}.$