Question

Evaluate :
$\int e^x\left[\frac{1+\text{x log x}}{x}\right]dx$

Answer 1

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

$=\int \frac{e^x}{x}dx+\int e^{x}logxdx$

$x=logx$ $\Rightarrow dx=\frac{1}{x}dx$

$dV=e^{x}dx$ $\Rightarrow V=e^x$

$=\int \frac{e^x}{x}dx+e^{x}logx-\int \frac{e^x}{x}dx+c$

$=e^{x}logx+c$

Where C is the constant of integration.