\int((1-sin^2(x))^2*cos(x))dx=\int(1-t^2)^2dt=\int(1-2t^2+t^4)dt=\int1dt-\int 2t^2dt+\int t^4dt=t-2\frac{t^3}{3}+\frac{t^5}{5}=\sin(x)-\frac{2\sin^3(x)}{3}+\frac{\sin^5(x)}{5}