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Beliebt Rechnen >

integral of cos(x)(9+5sin^2(x))

Lösung

\int cos (x) (9 + 5 sin^{2} (x)) d x

Lösung

9 sin (x) + \frac{5 sin ^{3} ( x )}{3} + C

Schritte zur Lösung

\int cos (x) (9 + 5 sin^{2} (x)) d x

Wende U-Substitution an

= \int 9 + 5 u^{2} d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 9 d u + \int 5 u^{2} d u

\int 9 d u = 9 u

\int 5 u^{2} d u = \frac{5 u ^{3}}{3}

= 9 u + \frac{5 u ^{3}}{3}

Setze in

u = sin (x)

ein

= 9 sin (x) + \frac{5 sin ^{3} ( x )}{3}

Füge eine Konstante zur Lösung hinzu

= 9 sin (x) + \frac{5 sin ^{3} ( x )}{3} + C

Graph

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