If $\int e^x(1+x). \sec^2(xe^x)dx-f(x)+constant$ then $f(x)=$

Question

\[\begin {array} {1 1} (1)\;\cos (x e^x) & \quad (2)\;\sin (x e^x) \\ (3)\;2 \tan ^{-1} (x) & \quad (4)\;\tan (x e^x) \end {array}\]