integral of arcsinh(2x)

Lösung

\int arcsinh (2 x) d x

x arcsinh (2 x) - \frac{1}{2} 4 x^{2} + 1 + C

Schritte zur Lösung

\int arcsinh (2 x) d x

Wende die partielle Integration an

= x arcsinh (2 x) - \int \frac{2 x}{4 x ^{2} + 1} d x

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

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

Füge eine Konstante zur Lösung hinzu

= x arcsinh (2 x) - \frac{1}{2} 4 x^{2} + 1 + C

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