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Beliebt Rechnen >

integral of 3arcsin(3x)

Lösung

\int 3 arcsin (3 x) d x

Lösung

3 x arcsin (3 x) + 1 - 9 x^{2} + C

Schritte zur Lösung

\int 3 arcsin (3 x) d x

Entferne die Konstante:

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

= 3 \cdot \int arcsin (3 x) d x

Wende die partielle Integration an

= 3 (x arcsin (3 x) - \int \frac{3 x}{1 - 9 x ^{2}} d x)

\int \frac{3 x}{1 - 9 x ^{2}} d x = - \frac{1}{3} 1 - 9 x^{2}

= 3 (x arcsin (3 x) - (- \frac{1}{3} 1 - 9 x^{2}))

Vereinfache

3 (x arcsin (3 x) - (- \frac{1}{3} 1 - 9 x^{2})) : 3 x arcsin (3 x) + 1 - 9 x^{2}

= 3 x arcsin (3 x) + 1 - 9 x^{2}

Füge eine Konstante zur Lösung hinzu

= 3 x arcsin (3 x) + 1 - 9 x^{2} + C

Graph

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