Question

Evaluate $\int \frac{e^{2x}}{1+e^x}dx$

Answer 1

$l=\int \frac{e^{2x}}{1+e^x}dx$

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

Let $(1+e^x)=t$

$e^x=(t-1)$

$e^{x}dx=dt$

$l=\int \frac{(t-1)}{t}dt$

$\int (1-\frac{1}{t})dt$

$=(t-logt)+c$

$=e^x-log{e}^x+c$

$=e^x-x+c$