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Beliebt Rechnen >

integral of 2xarcsin(x^2)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int x arcsin (x^{2}) d x

Wende die partielle Integration an

= 2 (\frac{1}{2} x^{2} arcsin (x^{2}) - \int \frac{x ^{3}}{1 - x ^{4}} d x)

\int \frac{x ^{3}}{1 - x ^{4}} d x = - \frac{1}{2} 1 - x^{4}

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

Vereinfache

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

= x^{2} arcsin (x^{2}) + 1 - x^{4}

Füge eine Konstante zur Lösung hinzu

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

Graph

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