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Beliebt Rechnen >

integral of ((tan(x))/(cos(x))-csc^2(x))

Lösung

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

Lösung

sec (x) + cot (x) + C

Schritte zur Lösung

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

\int \frac{tan ( x )}{cos ( x )} d x = sec (x)

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

= sec (x) - (- cot (x))

Vereinfache

= sec (x) + cot (x)

Füge eine Konstante zur Lösung hinzu

= sec (x) + cot (x) + C

Graph

Beliebte Beispiele

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\int \frac{1}{4 ^{x} - 4} d x

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integral of (sin(3x))^3

\int (sin (3 x))^{3} d x