Question

Evaluate ∫Cosec^2(e^x)e^x dx​

Answer 1

Step-by-step explanation:

We have,

$\int \cosec^{2} ( {e}^{x} ) {e}^{x}dx$

$let \: \: {e}^{x} = t \\ = > {e}^{x} dx = dt$

So,

$\int \cosec^{2} (t) dt$

$= - \cot(t) + c$

$= - \cot( {e}^{x} ) + c$