$\int\left(x^x\right)^x\left(2 x \log _e x+x\right) d x$ is equal to
Answer & explanation
Correct answer: option 2
Let
$I=\int\left(x^x\right)^x\left(2 x \log _e x+x\right) d x=\int x^{x^2}\left(2 x \log _e x+x\right) d x$
$\Rightarrow I=\int 1 \cdot d\left(x^{x^2}\right)=x^{x^2}+C=\left(x^x\right)^x+C$