Question

Evaluate: $\int e^x\left(\begin{array}{c}\frac{x-1}{x^2}\end{array}\right)dx$.

Answer 1

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

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

$I=\int e^x(\frac{1}{x}-\frac{1}{x^2})$

Using the property, we get:

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

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