Question

Integrate the following w.r.t. $x$
$e^{2x}+\frac{1}{x^2}$.

Answer 1

$y=e^{2x}+\frac{1}{x^2}$
Integrating both sides w.r.t. $x$, we get
$I=\int ydx=\int (e^{2x}+\frac{1}{x^2})dx$
$=\frac{e^{2x}}{2}+\frac{x^{-2+1}}{-2+1}+c[\because \int e^{ax}=\frac{e^{ax}}{a}+c]$
$=\frac{e^{2x}}{2}-\frac{1}{x}+c$.