Integrate Sin2x Cos3x dx

Integrate Sin²x Cos³x .dx

$I = \int \sin^{2} x \cos^{3} x ⅆ x$

Let

$\sin x = t ∴ \cos x d x = d t$

$∴ I = \int \sin^{2} x (1 - \sin^{2} x) \cos x ⅆ x = \int t^{2} (1 - t^{2}) ⅆ t = \int t^{2} ⅆ t - \int t^{4} ⅆ t = \frac{t^{3}}{3} - \frac{t^{5}}{5} + C = \frac{1}{3} \sin^{3} x - \frac{1}{5} \sin^{5} x + C$

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Integrate Sin2x Cos3x .dx

Integrate Sin²x Cos³x .dx