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Beliebt Rechnen >

integral of 2arctan(x)

Lösung

\int 2 arctan (x) d x

Lösung

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

Schritte zur Lösung

\int 2 arctan (x) d x

Entferne die Konstante:

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

= 2 \cdot \int arctan (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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