Question

Evaluate:
$\int e^x(\frac{1}{x}-\frac{1}{x^2})dx$

Answer 1

As we know that,

$\int e^x(f\left(x\right)+f^{\prime }\left(x\right))dx=e^{x}f\left(x\right)+c$

Therefore,

$\int e^x(\frac{1}{x}+\left(\frac{-1}{x^2}\right))dx$

$=e^x\left(\frac{1}{x}\right)+c(\because \frac{d}{dx}\left(\frac{1}{x}\right)=\frac{-1}{x^2})$