Question

Encontre a integral indefinida ds função: f (x)= 3 cos x/ 7 sin^2 x

Answer 1

$\int \frac{3cos(x)}{7sen^2(x)} dx =\boxed{\boxed{\frac{3}{7} \int \frac{cos(x)}{sen^2(x)} dx }}$

fazendo a substituição  

$\boxed{u = sen(x)}\\\\ \frac{du}{dx}= cos(x)\to \boxed{du=cos(x) . dx}\\\\\ \frac{3}{7} \int \frac{du}{u^2} \\\\= \frac{3}{7} \int u^{-2} du \\\\= \frac{3}{7}* \left( \frac{u^{-2+1}}{-2+1} \right)+C\\\\ = \frac{3}{7} \left( \frac{u^{-1}}{-1} \right) +C\\\\ = \frac{3}{7}* \frac{-1}{u} +C = \boxed{\boxed{\frac{-3}{7} * \frac{1}{sen(x)} +C }}$