# Math Help - substitution sin and cos

1. ## substitution sin and cos

Hi

I have the answer in the textbook for this one but I am hoping someone can explain it to me.

integral sign (sin x/ (1+ cos^2 x) dx =
integral sign ((sin x cos x)/(1+cos^2 x)dx

why was cos x "added" to the numerator - it wasn't "added" to the denominator - it just seems to come out of no where.

Any enlightenment would be appreciated.

2. I don't know, but here is how you could integrate it. By making a u-sub.

$\int\frac{sin(x)}{1+cos^{2}(x)}dx$

Let $u=cos(x), \;\ -du=sin(x)dx$

Now, can you finish?.