Question

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

Answer 1

$\int \frac{e^x}{x}(1+x\ln x)dx$

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

We know that $\int e^x\left(f\right(x)+f(x\left)\right)dx=e^{x}f\left(x\right)+c$

$=\frac{e^x}{x}+c$ because $\frac{d\left(\ln x\right)}{dx}=\frac{1}{x}$