integral of (sin(2x)+5tan^2(x)csc^2(x))

Lösung

\int (sin (2 x) + 5 tan^{2} (x) csc^{2} (x)) d x

- \frac{1}{2} cos (2 x) + 5 tan (x) + C

Schritte zur Lösung

\int sin (2 x) + 5 tan^{2} (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 sin (2 x) d x + \int 5 tan^{2} (x) csc^{2} (x) d x

\int sin (2 x) d x = - \frac{1}{2} cos (2 x)

\int 5 tan^{2} (x) csc^{2} (x) d x = 5 tan (x)

= - \frac{1}{2} cos (2 x) + 5 tan (x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{2} cos (2 x) + 5 tan (x) + C

\int \frac{sin ( x ) + cos ( x )}{sin ( 2 x )} d x

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