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Beliebt Rechnen >

integral of xarctan^2(x)

Lösung

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

Lösung

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

(\partial ^2)/(\partial x\partial y)(xy+8/x+8/y)

\frac{\partial ^{2}}{\partial x \partial y} (x y + \frac{8}{x} + \frac{8}{y})

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\int 28 tan^{6} (x) d x

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