# Integrate : $\int \cos^3 x \sin ^2 x dx$

$(a)\;\tan ^2 x +\cot ^2 x +c \qquad(b)\;\cos^2 x - \sin ^2 x +c \qquad(c)\;\frac{(\cos x)^3}{3}+\frac{(\cos x )^5}{5}+c \qquad (d)\;\frac{(\sin x)^3}{3}+\frac{(\sin x )^5}{5}+c$

Suppose $\cos x =t$
=> $cosin x dx=dt$
=> $+ \cos x dx.dt$
=> $\int (1-t^2)t^2 dt$
=> $\int (t^2-t^4) dt$
=> $\large\frac{t^3}{3} -\frac{t^5}{5} +c$
=>$\large\frac{(\sin x)^3}{3}+\frac{(\sin x )^5}{5}+c$
Hence d is the correct answer.