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Beliebt Rechnen >

integral of [12+csc(x)(sin(x)+csc(x))]

Lösung

\int [12 + csc (x) (sin (x) + csc (x))] d x

Lösung

- cot (x) + 13 x + C

Schritte zur Lösung

\int 12 + csc (x) (sin (x) + csc (x)) d x

Multipliziere aus

csc (x) (sin (x) + csc (x)) : csc (x) sin (x) + csc^{2} (x)

= \int 12 + csc (x) sin (x) + csc^{2} (x) d x

Vereinfache

12 + csc (x) sin (x) + csc^{2} (x) : csc^{2} (x) + 13

= \int csc^{2} (x) + 13 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 csc^{2} (x) d x + \int 13 d x

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

\int 13 d x = 13 x

= - cot (x) + 13 x

Füge eine Konstante zur Lösung hinzu

= - cot (x) + 13 x + C

Graph

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