Question

$I=\frac{-x\sec x}{x\sin x+\cos x}+\tan x+C=\frac{\sin x-x\cos x}{x\sin x+\cos x}+C$

Answer 1

$\frac{-xsecx}{xsinx+cosx}+tanx+c$

$\Rightarrow \frac{-x\left(\frac{1}{cosx}\right)}{xsinx+cosx}+\frac{sinx}{cosx}+c$

$\Rightarrow \frac{\frac{-x}{cosx}\times cosx+sinx(xsinx+cosx)}{cosx(xsinx+cosx)}+c$

$\Rightarrow \frac{-x+xsi{n}^{2}x+sinxcosx}{cosx(xsinx+cosx)}+c$