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

Lösung

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

- 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

\int \frac{4}{x ^{2} + 5} d x

\int π d x

\int x sin (2 x - 1) d x

\int 21 x^{2} - 12 x - 5 d x

\int \frac{x ^{2}}{x + 6} d x