integral of x*arccot(x)

Lösung

\int x \cdot arccot (x) d x

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

Schritte zur Lösung

\int x arccot (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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