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Beliebt Rechnen >

integral of x^2rctan(x)

Lösung

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

Lösung

d (\frac{1}{3} x^{3} arctan (x) - \frac{1}{6} (x^{2} + 1 - ln x^{2} + 1)) + C

Schritte zur Lösung

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

Entferne die Konstante:

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

= d \cdot \int x^{2} arctan (x) d x

Wende die partielle Integration an

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

\int \frac{x ^{3}}{3 ( x ^{2} + 1 )} d x = \frac{1}{6} (x^{2} + 1 - ln x^{2} + 1)

= d (\frac{1}{3} x^{3} arctan (x) - \frac{1}{6} (x^{2} + 1 - ln x^{2} + 1))

Füge eine Konstante zur Lösung hinzu

= d (\frac{1}{3} x^{3} arctan (x) - \frac{1}{6} (x^{2} + 1 - ln x^{2} + 1)) + C

Graph

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\int \frac{tan ( x )}{1 - cos ( x )} d x

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