Question

Calculo 2
∫√sen2x.cos2xdx

Answer 1

$\int \left (\sqrt{sen(2x)}*cos(2x) \right) dx$

substituiçao

$U = sen(2x)\\\\dU=2cos(2x)dx\to \frac{dU}{2}=cos(2x)dx$

temos
$\int \sqrt{U} * \frac{dU}{2} \\\\ = \frac{1}{2}\int \sqrt{U} = \frac{1}{2}* \frac{2 \sqrt[2]{U^3} }{3} +C=\boxed{\boxed{ \frac{1}{3}* \sqrt{sen^3(2x)} +C}}$