Question

$\int \frac{e^{x}}{x}\left(x\,log\,x+1\right)dx$ is equal to

• A. $\frac{e^{x}}{x}+C$
• B. $xe^x\, log \,| x | +C$
• C. $e^x\, log | x | +C$
• D. $x(e^x +log \,|x|) + C$

Answer 1

Answer: (C)

$e^x\, log | x | +C$

Answer 2

$\int \frac{e^{x}}{x}(x \log x+1) d x$
$=\int \underset{II}{e^{x}} \underset{I}{\log} x d x+\int \frac{e^{x}}{x} d x$
$=e^{x} \log x-\int \frac{e^{x}}{x} d x+\int \frac{e^{x}}{x} d x+C$
$=e^{x} \log x+C$