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Beliebt Rechnen >

integral of ((1-cos^3(x))sin(x))

Lösung

\int ((1 - cos^{3} (x)) sin (x)) d x

Lösung

- cos (x) + \frac{1}{4} cos^{4} (x) + C

Schritte zur Lösung

\int (1 - cos^{3} (x)) sin (x) d x

Multipliziere aus

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

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

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

\int cos^{3} (x) sin (x) d x = - \frac{cos ^{4} ( x )}{4}

= - cos (x) - (- \frac{cos ^{4} ( x )}{4})

Vereinfache

- cos (x) - (- \frac{cos ^{4} ( x )}{4}) : - cos (x) + \frac{1}{4} cos^{4} (x)

= - cos (x) + \frac{1}{4} cos^{4} (x)

Füge eine Konstante zur Lösung hinzu

= - cos (x) + \frac{1}{4} cos^{4} (x) + C

Graph

Beliebte Beispiele

integral of (sin^9(x))cos(x)

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

limit as x approaches 0 of (sin(6x))/x

x \to 0 lim (\frac{sin ( 6 x )}{x})

integral of λe^{-λx}

\int λ e^{- λ x} d x

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\int 2 sin (2 t) d t

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z \to 1 lim (\frac{z - 1}{z ^{2} - 1})