If $\int e^x(1+x) \sec ^2\left(x e^x\right) d x=f(x)+$ Constant, then $f(x)$ is equal to

$\cos \left(x e^x\right)$ $\sin \left(x e^x\right)$ $2 \tan ^{-1} x$ $\tan \left(x e^x\right)$

$\tan \left(x e^x\right)$

We have, $\int e^x(1+x) \sec ^2\left(x e^x\right) d x$ $=\int \sec ^2\left(x e^x\right) d\left(x e^x\right)=\tan \left(x e^x\right)+C$ ∴   $f(x)=\tan \left(x e^x\right)$