Question

me ajude!!
Considerando a tabela de integrais imediatas, a integral de:

Answer 1

$\frac{cos(x)}{ sen^{2}(x) } = \frac{cos(x)}{sen(x)}. \frac{1}{sen(x)}$
$\frac{cos(x)}{sen(x)} = cotg(x)$
$\frac{1}{sen(x)} = cossec(x)$
então$\int\limits { \frac{cos(x)}{ sen^{2} (x)} } \, dx$ =
 = $\int\limits {cotg(x).cossec(x)} \, dx$ = -cossec(x) + C

Answer 2

$\displaystyle\sf{\int\dfrac{cos(x)}{sen^2(x)}~dx=\int\dfrac{1}{sen(x)}\cdot\dfrac{cos(x)}{sen(x)}~dx}\\\sf{=\int csc(x)\cdot cotg(x)~dx=-csc(x)+k}$