Hi i have this question but see what to do. My best guess is that u = 1 + sin^2x and perhaps that is an identity im not quite seeing?
$\displaystyle \int cos(x)(1+sin^2(x)) dx$
Thanks again!
You're on the right track.
Note that if you let $\displaystyle u = \sin{x}$ then $\displaystyle \frac{du}{dx} = \cos{x}$.
So the integral becomes
$\displaystyle \int{\cos{x}(1 + \sin^2{x})\,dx} = \int{(1 + u^2)\,\frac{du}{dx}\,dx}$
$\displaystyle = \int{1 + u^2\,du}$
$\displaystyle = u + \frac{1}{3}u^3 + C$
$\displaystyle = \sin{x} + \frac{1}{3}\sin^3{x} + C$.