about indefinite integrals...

Question

who can solve this problem for me please...
please list all the steps to the solution, thanks

∫sin^3(πx)cos(πx) dx


thankssssss

Answer 1

Use substitution
u=sin(πx), du=πcos(πx) dx, then
∫sin^3(πx)cos(πx) dx
=∫u³(1/π) du
=u^4/(4π)+c
=1/(4π) * sin^4(πx)+c

Answer 2

用代換的方法比較快...