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Beliebt Rechnen >

integral of cos(x)(1+7sin^2(x))

Lösung

\int cos (x) (1 + 7 sin^{2} (x)) d x

Lösung

sin (x) + \frac{7 sin ^{3} ( x )}{3} + C

Schritte zur Lösung

\int cos (x) (1 + 7 sin^{2} (x)) d x

Wende U-Substitution an

= \int 1 + 7 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 1 d u + \int 7 u^{2} d u

\int 1 d u = u

\int 7 u^{2} d u = \frac{7 u ^{3}}{3}

= u + \frac{7 u ^{3}}{3}

Setze in

u = sin (x)

ein

= sin (x) + \frac{7 sin ^{3} ( x )}{3}

Füge eine Konstante zur Lösung hinzu

= sin (x) + \frac{7 sin ^{3} ( x )}{3} + C

Graph

Beliebte Beispiele

sum from n=0 to infinity of 1/(n^4+6)

n = 0 \sum \infty \frac{1}{n ^{4} + 6}

tangent f(x)=sqrt(x),\at x=5

t an g e n t f (x) = x, at x = 5

f^{''}(t)-f(t)=-8t,f(3)=-8

f^{^{''}} (t) - f (t) = - 8 t, f (3) = - 8

derivative f(x)=(2x-1)/(4x+8)

d er i v a t i v e f (x) = \frac{2 x - 1}{4 x + 8}

maclaurin 1/(1+x^3)

ma c l a u r in \frac{1}{1 + x ^{3}}