Question

Integrate the following function with respect to $x$
$\frac{{\sec }^{3}x}{\csc x}$

Answer 1

According to question,

$\int \frac{se{c}^{3}x}{cosecx}dx$

$\Rightarrow$ $\int se{c}^{2}x.tanxdx$

Let, $tanx=t$

$\Rightarrow$ $se{c}^{2}x.dx=dt$

$\Rightarrow$ $\int t.dt$

$\Rightarrow$ $\frac{t^2}{2}+C$

$\Rightarrow$ $\frac{ta{n}^{2}x}{2}+C$