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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende U-Substitution an

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

\int 5 d u = 5 u

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

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

Setze in

u = sin (x)

ein

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral from 0 to 1 of (\sqrt[3]{1+7x})

\int_{0}^{1} (3 1 + 7 x) d x

integral of x^2-9x+3

\int x^{2} - 9 x + 3 d x

sum from n=1 to infinity of 9/(6+9^n)

n = 1 \sum \infty \frac{9}{6 + 9 ^{n}}

integral of 1/(1-9x^2)

\int \frac{1}{1 - 9 x ^{2}} d x

integral of 2cos(x^2)

\int 2 cos (x^{2}) d x