Evaluate the following integrals: ∫ x cos 3 x 2 sin x 2 dx

Question

Philoid · Accepted Answer

Let cosx² = t

Then d(cosx²) = dt

Since d(xⁿ) = nxⁿ⁻¹ and d(cos x) = -sinx dx

dt = 2x (-sin x²) = -2x sin x² dx

x sin x²dx =

hence ∫ x cos³ x² sin x² dx =

=