writing sin^{3}a.cos^{3}a = sin^{3}a.cos^{2}a.cosa= sin^{3}a.(1-sin^{2}a).cosaput sin a as then cos a da = dt integral(t^{3}(1-t^{2}).dt= integral of t^{3}- t^{5} dt= t^{4}/4-t^{6}/6 + c where t = sina