# How do you find the integral of int (sin x)/(cos^2x + 1)dx?

$I = - \arctan \left(\cos x\right) + C$
$I = \int \sin \frac{x}{{\cos}^{2} x + 1} \mathrm{dx} = \int \frac{\sin x \mathrm{dx}}{{\cos}^{2} x + 1} = - \int \frac{d \left(\cos x\right)}{{\cos}^{2} x + 1}$
$I = - \arctan \left(\cos x\right) + C$