Question

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

Answer 1

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

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

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

$=\frac{1}{x}\int e^{x}dx$$-$$\int \frac{d}{dx}\frac{1}{x}$$\int e^{x}dx)dx$$-$$\int e^x\frac{1}{x^2}dx$

$=\frac{1}{x}{e}^x$$-$$\int \frac{-1}{x^2}{e}^{x}dx$$-$$\int e^x\frac{1}{x^2}dx$

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