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Beliebt Rechnen >

integral of cos(x)(6sin^2(x)-1)

Lösung

\int cos (x) (6 sin^{2} (x) - 1) d x

Lösung

- sin (x) cos (2 x) + C

Schritte zur Lösung

\int cos (x) (6 sin^{2} (x) - 1) d x

Multipliziere aus

cos (x) (6 sin^{2} (x) - 1) : 6 sin^{2} (x) cos (x) - cos (x)

= \int 6 sin^{2} (x) cos (x) - cos (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 6 sin^{2} (x) cos (x) d x - \int cos (x) d x

\int 6 sin^{2} (x) cos (x) d x = 2 sin^{3} (x)

\int cos (x) d x = sin (x)

= 2 sin^{3} (x) - sin (x)

Vereinfache

2 sin^{3} (x) - sin (x) : - sin (x) cos (2 x)

= - sin (x) cos (2 x)

Füge eine Konstante zur Lösung hinzu

= - sin (x) cos (2 x) + C

Graph

Beliebte Beispiele

integral of (x^2-x-6)/(x^3+x)

\int \frac{x ^{2} - x - 6}{x ^{3} + x} d x

integral of (x^2+3x^{13})^5

\int (x^{2} + 3 x^{13})^{5} d x

integral of sin(x)-x^4

\int sin (x) - x^{4} d x

integral of 1-u^2

\int 1 - u^{2} d u

integral of csc^2(x)sqrt(1-3cot(x))

\int csc^{2} (x) 1 - 3 cot (x) d x