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Beliebt Rechnen >

integral of cos(x)(1+4sin^2(x))

Lösung

\int cos (x) (1 + 4 sin^{2} (x)) d x

Lösung

sin (x) + \frac{4 sin ^{3} ( x )}{3} + C

Schritte zur Lösung

\int cos (x) (1 + 4 sin^{2} (x)) d x

Wende U-Substitution an

= \int 1 + 4 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 4 u^{2} d u

\int 1 d u = u

\int 4 u^{2} d u = \frac{4 u ^{3}}{3}

= u + \frac{4 u ^{3}}{3}

Setze in

u = sin (x)

ein

= sin (x) + \frac{4 sin ^{3} ( x )}{3}

Füge eine Konstante zur Lösung hinzu

= sin (x) + \frac{4 sin ^{3} ( x )}{3} + C

Graph

Beliebte Beispiele

derivative of \sqrt[3]{1-x^2}

\frac{d}{d x} (3 1 - x^{2})

tangent f(x)=sqrt(x),\at x=25

t an g e n t f (x) = x, at x = 25

derivative of-4/((x-4^2))

\frac{d}{d x} (- \frac{4}{( x - 4 ) ^{2}})

integral of (2x+4)/(x^2+4x+13)

\int \frac{2 x + 4}{x ^{2} + 4 x + 13} d x

sum from n=0 to infinity of 1400700

n = 0 \sum \infty 1400700