Question

Solve : $\int \frac{e^x}{x}(1+x\log x)dx$

Answer 1

We have,

$I=\int \frac{e^x}{x}(1+x\log x)dx$

$I=\int \frac{e^x}{x}dx+\int e^x\log xdx$

$I=\int \frac{e^x}{x}dx+e^x\log x-\int \frac{e^x}{x}dx$

$I=e^x\log x+C$

Hence, this is the answer.