integral of cot^2(ax)

Lösung

\int cot^{2} (a x) d x

- x - \frac{1}{a} cot (a x) + C

Schritte zur Lösung

\int cot^{2} (a x) d x

Umschreiben mit Hilfe von Trigonometrie-Identitäten

= \int - 1 + csc^{2} (a x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int 1 d x + \int csc^{2} (a x) d x

\int 1 d x = x

\int csc^{2} (a x) d x = - \frac{1}{a} cot (a x)

= - x - \frac{1}{a} cot (a x)

Füge eine Konstante zur Lösung hinzu

= - x - \frac{1}{a} cot (a x) + C

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