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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

= (2 + 7 sin^{2} (x)) sin (x) - \int 7 sin (2 x) sin (x) d x

\int 7 sin (2 x) sin (x) d x = \frac{14}{3} sin^{3} (x)

= (2 + 7 sin^{2} (x)) sin (x) - \frac{14}{3} sin^{3} (x)

Vereinfache

(2 + 7 sin^{2} (x)) sin (x) - \frac{14}{3} sin^{3} (x) : 2 sin (x) + \frac{7}{3} sin^{3} (x)

= 2 sin (x) + \frac{7}{3} sin^{3} (x)

Füge eine Konstante zur Lösung hinzu

= 2 sin (x) + \frac{7}{3} sin^{3} (x) + C

Graph

Beliebte Beispiele

limit as x approaches infinity of (2^{x+1}+3^x)/(2^x+3^{x+1)}

x \to \infty lim (\frac{2 ^{x + 1} + 3 ^{x}}{2 ^{x} + 3 ^{x + 1}})

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x \to 0 + lim (- ln (x))

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\frac{d}{d x} (\frac{e ^{x}}{e ^{x} + 1})

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