integral of x^2arctan(3x)

Lösung

\int x^{2} arctan (3 x) d x

\frac{1}{3} x^{3} arctan (3 x) - \frac{1}{162} (9 x^{2} + 1 - ln 9 x^{2} + 1) + C

Schritte zur Lösung

\int x^{2} arctan (3 x) d x

Wende die partielle Integration an

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

\int \frac{x ^{3}}{9 x ^{2} + 1} d x = \frac{1}{162} (9 x^{2} + 1 - ln 9 x^{2} + 1)

= \frac{1}{3} x^{3} arctan (3 x) - \frac{1}{162} (9 x^{2} + 1 - ln 9 x^{2} + 1)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} arctan (3 x) - \frac{1}{162} (9 x^{2} + 1 - ln 9 x^{2} + 1) + C

\frac{\partial}{\partial x} (4 x + 5)

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