integral of xcos(x)sin^2(x)

Lösung

\int x cos (x) sin^{2} (x) d x

\frac{1}{3} x sin^{3} (x) - \frac{1}{3} (- cos (x) + \frac{cos ^{3} ( x )}{3}) + C

Schritte zur Lösung

\int x cos (x) sin^{2} (x) d x

Wende die partielle Integration an

= \frac{1}{3} x sin^{3} (x) - \int \frac{1}{3} sin^{3} (x) d x

\int \frac{1}{3} sin^{3} (x) d x = \frac{1}{3} (- cos (x) + \frac{cos ^{3} ( x )}{3})

= \frac{1}{3} x sin^{3} (x) - \frac{1}{3} (- cos (x) + \frac{cos ^{3} ( x )}{3})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x sin^{3} (x) - \frac{1}{3} (- cos (x) + \frac{cos ^{3} ( x )}{3}) + C

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