sin2x=2*sinx*cosx ⇒ sinx*cosx =sin2x/2
sin^2x*cos^2x =(sin2x/2)^2=sin^22x/4
sin^22x=(1-cos4x)/2
[m]∫ sin^2x\cdot cos^2x dx= ∫ \frac{1-cos4x}{8}dx=\frac{1}{8} ∫ (1-cos4x)dx=[/m]
[m]=\frac{1}{8} ∫ dx- \frac{1}{8} ∫ cos4xdx=\frac{1}{8} x-\frac{1}{32}sin4x + C[/m]