If ∫Sin xCos x (1+cos x)  dx=f(x)+c ⇒ f(x)=

cosx=t⇒−sinx dx= dt              ∫−1t(1+t) dt=∫(1t+1−1t) dt                                    =log|1+tt|+c                                    =log|1+cosxcosx|+c