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Beliebt Rechnen >

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

Lösung

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

Lösung

cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x)) + C

Schritte zur Lösung

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

Vereinfache

(cos^{2} (x))^{2} : cos^{4} (x)

= \int cos^{4} (x) d x

Vereinfache

cos^{4} (x) : cos^{3} (x) cos (x)

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

Wende die partielle Integration an

= cos^{3} (x) sin (x) - \int - 3 cos^{2} (x) sin^{2} (x) d x

\int - 3 cos^{2} (x) sin^{2} (x) d x = - \frac{3}{8} (x - \frac{1}{4} sin (4 x))

= cos^{3} (x) sin (x) - (- \frac{3}{8} (x - \frac{1}{4} sin (4 x)))

Vereinfache

= cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x))

Füge eine Konstante zur Lösung hinzu

= cos^{3} (x) sin (x) + \frac{3}{8} (x - \frac{1}{4} sin (4 x)) + C

Graph

Beliebte Beispiele

integral of x/(cos^2(x))

\int \frac{x}{cos ^{2} ( x )} d x

sum from n=0 to infinity of (2n-1)/(n!)

n = 0 \sum \infty \frac{2 n - 1}{n !}

derivative of-x/4

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

integral of 1/(sqrt(x^2+x))

\int \frac{1}{x ^{2} + x} d x

fläche y=|x|,y=x^2-6

a re a y = ∣ x ∣, y = x^{2} - 6