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Beliebt Rechnen >

integral of arcsin(x)*x

Lösung

\int arcsin (x) \cdot x d x

Lösung

\frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x))) + C

Schritte zur Lösung

\int arcsin (x) x d x

Wende die partielle Integration an

= \frac{1}{2} x^{2} arcsin (x) - \int \frac{x ^{2}}{2 1 - x ^{2}} d x

\int \frac{x ^{2}}{2 1 - x ^{2}} d x = \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))

= \frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x)))

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} arcsin (x) - \frac{1}{4} (arcsin (x) - \frac{1}{2} sin (2 arcsin (x))) + C

Graph

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