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Beliebt Rechnen >

integral of (cos(6x)-csc^2(x))

Lösung

\int (cos (6 x) - csc^{2} (x)) d x

Lösung

\frac{1}{6} sin (6 x) + cot (x) + C

Schritte zur Lösung

\int cos (6 x) - csc^{2} (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 cos (6 x) d x - \int csc^{2} (x) d x

\int cos (6 x) d x = \frac{1}{6} sin (6 x)

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

= \frac{1}{6} sin (6 x) - (- cot (x))

Vereinfache

= \frac{1}{6} sin (6 x) + cot (x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{6} sin (6 x) + cot (x) + C

Graph

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