integral of x^2arcsin(x^3)

Lösung

\int x^{2} arcsin (x^{3}) d x

\frac{1}{3} x^{3} arcsin (x^{3}) + \frac{1}{3} 1 - x^{6} + C

Schritte zur Lösung

\int x^{2} arcsin (x^{3}) d x

Wende die partielle Integration an

= \frac{1}{3} x^{3} arcsin (x^{3}) - \int \frac{x ^{5}}{1 - x ^{6}} d x

\int \frac{x ^{5}}{1 - x ^{6}} d x = - \frac{1}{3} 1 - x^{6}

= \frac{1}{3} x^{3} arcsin (x^{3}) - (- \frac{1}{3} 1 - x^{6})

Vereinfache

= \frac{1}{3} x^{3} arcsin (x^{3}) + \frac{1}{3} 1 - x^{6}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} arcsin (x^{3}) + \frac{1}{3} 1 - x^{6} + C

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