Evaluate the following integrals : ∫ sin5x cos x dx

1.	Evaluate the following integrals : ∫ sin5x cos x dx
Answer» Assume, sinx = t d(sinx) = dt cosx dx = dt ∴ Substituting t and dt in given equation we get ⇒ \(\int\)t⁵dt ⇒ \(\frac{t^6}{6}\) + c But, t = sinx ⇒ \(\frac{sin^6x}{6}\) + c

Answer»

Assume,

sinx = t

d(sinx) = dt

cosx dx = dt

∴ Substituting t and dt in given equation we get

⇒ \(\int\)t⁵dt

⇒ \(\frac{t^6}{6}\) + c

But,

t = sinx

⇒ \(\frac{sin^6x}{6}\) + c

Discussion