Question

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

Answer 1

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

Using $\int e^x\left[f\right(x)+f^{\prime }(x\left)\right].dx=e^{x}f\left(x\right)+C$

Here,

$f\left(x\right)=\frac{1}{x}\Rightarrow f^{\prime }=-\frac{1}{x^2}$

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

$=\frac{e^x}{x}+C$

Where $C$ is constant of integration