Integrating sin^5(x)cos(x) (in slow logical steps)

Step 1: Make a substitution for u=Sin(x) differentiate that function to show du/dx =Cos(x)Step 2: Rearrange for dx to show dx=1/Cos(x) du and replace the dx in your original integral to show (integral symbol) Sin^5(x)duStep 4: Substitute in your Sin(x)=u to get u^5Step 5: Integrate u^5 to get (u^6)/6 + CStep 6: Substitute your u=Sin(x) back in to get (Sin^6(x))/6 + C