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Beliebt Rechnen >

integral of (arctan(2x))

Lösung

\int (arctan (2 x)) d x

Lösung

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

Schritte zur Lösung

\int arctan (2 x) d x

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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