Question

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

Answer 1

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

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

$=e^x.ln\left(x\right)+c$