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Beliebt Rechnen >

integral of-cos^4(x)

Lösung

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

Lösung

- cos^{3} (x) sin (x) - \frac{3}{8} x + \frac{3}{32} sin (4 x) + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d 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)))) : - cos^{3} (x) sin (x) - \frac{3}{8} x + \frac{3}{32} sin (4 x)

= - cos^{3} (x) sin (x) - \frac{3}{8} x + \frac{3}{32} sin (4 x)

Füge eine Konstante zur Lösung hinzu

= - cos^{3} (x) sin (x) - \frac{3}{8} x + \frac{3}{32} sin (4 x) + C

Graph

Beliebte Beispiele

tangent f(x)=6x^2-4x+5

t an g e n t f (x) = 6 x^{2} - 4 x + 5

integral of (2\sqrt[3]{x^5})/3

\int \frac{2 3 x ^{5}}{3} d x

limit as x approaches 1-of sqrt(3-3x)

x \to 1 - lim (3 - 3 x)

integral of 5/(x^2+36)

\int \frac{5}{x ^{2} + 36} d x

integral of 2^{-x}

\int 2^{- x} d x