integral of x*arctan(2x)

Lösung

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

\frac{1}{2} x^{2} arctan (2 x) - \frac{1}{8} (- arctan (2 x) + 2 x) + C

Schritte zur Lösung

\int x arctan (2 x) d x

Wende die partielle Integration an

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

\int \frac{x ^{2}}{4 x ^{2} + 1} d x = \frac{1}{8} (- arctan (2 x) + 2 x)

= \frac{1}{2} x^{2} arctan (2 x) - \frac{1}{8} (- arctan (2 x) + 2 x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} arctan (2 x) - \frac{1}{8} (- arctan (2 x) + 2 x) + C

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