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Beliebt Rechnen >

integral of (1-cos(x))^2

Lösung

\int (1 - cos (x))^{2} d x

Lösung

\frac{3}{2} x + \frac{1}{4} sin (2 x) - 2 sin (x) + C

Schritte zur Lösung

\int (1 - cos (x))^{2} d x

Multipliziere aus

(1 - cos (x))^{2} : 1 - 2 cos (x) + cos^{2} (x)

= \int 1 - 2 cos (x) + cos^{2} (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 1 d x - \int 2 cos (x) d x + \int cos^{2} (x) d x

\int 1 d x = x

\int 2 cos (x) d x = 2 sin (x)

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

= x - 2 sin (x) + \frac{1}{2} (x + \frac{1}{2} sin (2 x))

Vereinfache

x - 2 sin (x) + \frac{1}{2} (x + \frac{1}{2} sin (2 x)) : \frac{3}{2} x + \frac{1}{4} sin (2 x) - 2 sin (x)

= \frac{3}{2} x + \frac{1}{4} sin (2 x) - 2 sin (x)

Füge eine Konstante zur Lösung hinzu

= \frac{3}{2} x + \frac{1}{4} sin (2 x) - 2 sin (x) + C

Graph

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

integral of (7x^2)e^{x^3+1}

\int (7 x^{2}) e^{x^{3} + 1} d x

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\int e^{- 2 y} y d y

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