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Beliebt Rechnen >

integral of (arccos(x))^3

Lösung

\int (arccos (x))^{3} d x

Lösung

x arccos^{3} (x) - 3 (arccos^{2} (x) 1 - x^{2} - 2 (- x arccos (x) + 1 - x^{2})) + C

Schritte zur Lösung

\int (arccos (x))^{3} d x

Vereinfache

= \int arccos^{3} (x) d x

Wende die partielle Integration an

= x arccos^{3} (x) - \int - \frac{3 x arccos ^{2} ( x )}{1 - x ^{2}} d x

\int - \frac{3 x arccos ^{2} ( x )}{1 - x ^{2}} d x = 3 (arccos^{2} (x) 1 - x^{2} - 2 (- x arccos (x) + 1 - x^{2}))

= x arccos^{3} (x) - 3 (arccos^{2} (x) 1 - x^{2} - 2 (- x arccos (x) + 1 - x^{2}))

Füge eine Konstante zur Lösung hinzu

= x arccos^{3} (x) - 3 (arccos^{2} (x) 1 - x^{2} - 2 (- x arccos (x) + 1 - x^{2})) + C

Graph

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