Question

Integrate the function.
$\int e^x(\frac{1}{x}-\frac{1}{x^2})dx.$

Answer 1

$LetI=\int e^x(\frac{1}{x}-\frac{1}{x^2})dx.Letf\left(x\right)=\frac{1}{x}\Rightarrow f^{\prime }\left(x\right)=-\frac{1}{x^2}\text{Here, given integral is of the form}\int e^x\left[f\right(x)+f^{\prime }(x\left)\right]dx=e^{x}f\left(x\right)\therefore I=\frac{e^x}{x}+C$