Question

Integrate :-
${\int }^{}\frac{1}{e^x-1}dx$

Answer 1

$\int \frac{dx}{e^x-1}=\int \frac{e^x}{e^x-1}dx-\int 1dx$

put $e^x$

$e^{x}dx=dx\int \frac{dt}{t-1}-\int 1dx$

$=ln|t-1|-x+c$

put $t=e^x$

$=ln|e^x-1|-x+c$