Question

What is the integretion of sin²x.sinx dx?

Answer 1

\(\int sin^2x \;sin\,x \,dx\)

\(= \int (1 -cos^2x)sin\,x\, dx\)

\(= \int sin \,x\,dx - \int cos^2 x\; sin x \,dx\)

\(= -cos\, x + \frac{cos^3x}{3} +C\)    (By taking cos x = t ⇒ -sin x dx = dt)