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Beliebt Rechnen >

integral of sin^2(x)cos(x)ln(sin(x))

Lösung

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

Lösung

\frac{1}{3} sin^{3} (x) ln (sin (x)) - \frac{1}{9} sin^{3} (x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{1}{3} sin^{3} (x) cot (x) d x = \frac{1}{9} sin^{3} (x)

= \frac{1}{3} sin^{3} (x) ln (sin (x)) - \frac{1}{9} sin^{3} (x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} sin^{3} (x) ln (sin (x)) - \frac{1}{9} sin^{3} (x) + C

Graph

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