Answer to Question #103230 in Calculus for Patrick Kariuki

Question

Integrate sin³x dx using reduction method

Answer 1

$\int sin^3x dx=\int sin^2 x\cdot sinx dx=\\ replace\\ cos x=t\\ d(cosx)=dt\\ -sinxdx=dt\\ sin^2x=1-cos^2x\\ =-\int(1-t^2)dt=-(t-\frac{t^3}{3}+C)=\\ =-(cosx-\frac{cos^3x}{3}+C)$