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Beliebt Rechnen >

integral of (cot(x)+csc(x))/(sin(x))

Lösung

\int \frac{cot ( x ) + csc ( x )}{sin ( x )} d x

Lösung

- csc (x) - cot (x) + C

Schritte zur Lösung

\int \frac{cot ( x ) + csc ( x )}{sin ( x )} d x

Multipliziere aus

\frac{cot ( x ) + csc ( x )}{sin ( x )} : \frac{cot ( x )}{sin ( x )} + \frac{csc ( x )}{sin ( x )}

= \int \frac{cot ( x )}{sin ( x )} + \frac{csc ( x )}{sin ( 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 \frac{cot ( x )}{sin ( x )} d x + \int \frac{csc ( x )}{sin ( x )} d x

\int \frac{cot ( x )}{sin ( x )} d x = - csc (x)

\int \frac{csc ( x )}{sin ( x )} d x = - cot (x)

= - csc (x) - cot (x)

Füge eine Konstante zur Lösung hinzu

= - csc (x) - cot (x) + C

Graph

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