Question

Integrate the function: $xsec^2x$

Answer 1

The correct answer is: $=x\,tanx+log|cosx|+C$
Let $I=∫xsec^2x dx$
Taking $x$ as first function and $sec^2 x$ as second function and integrating by parts,we
obtain
$I=x∫sec^2x dx-∫[{{\frac{d}{dx} x}∫sec^2x\, dx}]dx$
$=x\,tanx-∫1\,.tanx. dx$
$=x\,tanx+log|cosx|+C$