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Beliebt Rechnen >

integral of arcsin(x)arccos(x)

Lösung

\int arcsin (x) arccos (x) d x

Lösung

x arccos (x) arcsin (x) + arccos (x) 1 - x^{2} - arcsin (x) 1 - x^{2} + 2 x + C

Schritte zur Lösung

\int arcsin (x) arccos (x) d x

Wende die partielle Integration an

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

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

= arccos (x) (x arcsin (x) + 1 - x^{2}) - (arcsin (x) 1 - x^{2} - 2 x)

Vereinfache

arccos (x) (x arcsin (x) + 1 - x^{2}) - (arcsin (x) 1 - x^{2} - 2 x) : x arccos (x) arcsin (x) + arccos (x) 1 - x^{2} - arcsin (x) 1 - x^{2} + 2 x

= x arccos (x) arcsin (x) + arccos (x) 1 - x^{2} - arcsin (x) 1 - x^{2} + 2 x

Füge eine Konstante zur Lösung hinzu

= x arccos (x) arcsin (x) + arccos (x) 1 - x^{2} - arcsin (x) 1 - x^{2} + 2 x + C

Graph

Beliebte Beispiele

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