Question

Find the integral of the given function w.r.t - x

$y=e^{2x}+\frac{1}{x^2}$

• A. $\frac{2}{e^{2x}}-\frac{1}{x}+c$
• B. $\frac{e^x}{2}-\frac{1}{x}+c$
• C. $\frac{e^{2x}}{2}-\frac{1}{x}+c$
• D. $e^{2x}-\frac{1}{x}+c$

Answer 1

The correct option is C

$\frac{e^{2x}}{2}-\frac{1}{x}+c$

$y=e^{2x}+\frac{1}{x^2}$

Integration both side w.r.t. 'x',

$I=\int y.dx=\int ⟮e^{2x}+\frac{1}{x^2}⟯dx=\frac{e^{2x}}{2}+\frac{x^{-2+1}}{-2+1}+c[\because \int e^{ax}=\frac{e^{ax}}{a}+c]$

$I=\frac{e^{2x}}{2}-\frac{1}{x}+c$