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Beliebt Rechnen >

integral of xcos^3(x)

Lösung

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

Lösung

x sin (x) - \frac{1}{3} x sin^{3} (x) + \frac{2}{3} cos (x) + \frac{1}{9} cos^{3} (x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int sin (x) - \frac{1}{3} sin^{3} (x) d x = - \frac{2}{3} cos (x) - \frac{1}{9} cos^{3} (x)

= x (sin (x) - \frac{1}{3} sin^{3} (x)) - (- \frac{2}{3} cos (x) - \frac{1}{9} cos^{3} (x))

Vereinfache

x (sin (x) - \frac{1}{3} sin^{3} (x)) - (- \frac{2}{3} cos (x) - \frac{1}{9} cos^{3} (x)) : x sin (x) - \frac{1}{3} x sin^{3} (x) + \frac{2}{3} cos (x) + \frac{1}{9} cos^{3} (x)

= x sin (x) - \frac{1}{3} x sin^{3} (x) + \frac{2}{3} cos (x) + \frac{1}{9} cos^{3} (x)

Füge eine Konstante zur Lösung hinzu

= x sin (x) - \frac{1}{3} x sin^{3} (x) + \frac{2}{3} cos (x) + \frac{1}{9} cos^{3} (x) + C

Graph

Beliebte Beispiele

limit as x approaches 0 of (ln(1+1/x))/x

x \to 0 lim (\frac{ln ( 1 + \frac{1}{x} )}{x})

derivative of x/((1-2x^2))

\frac{d}{d x} (\frac{x}{( 1 - 2 x ) ^{2}})

integral of (cos(x))^5sin(x)

\int (cos (x))^{5} sin (x) d x

integral of (x^2+2x)^5(2x+2)

\int (x^{2} + 2 x)^{5} (2 x + 2) d x

derivative of x^5e^{-x}

\frac{d}{d x} (x^{5} e^{- x})