integration of sin ³A.cos ³A in required steps.

writing sin³a.cos³a = sin³a.cos²a.cosa

= sin³a.(1-sin²a).cosa

put sin a as then cos a da = dt 

integral(t³(1-t²).dt

= integral of t³- t⁵ dt

= t⁴/4-t⁶/6 + c where t = sina