integral x*cos^3(x)

Lösung

integral

x \cdot cos^{3} (x)

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

in t e g r a l \frac{1 + x ^{2}}{k}

in t e g r a l (1 - x) e^{x}

in t e g r a l \frac{1}{( x ^{2} - 2 x )}

in t e g r a l x (a^{2} - x^{2})^{\frac{1}{2}}

in t e g r a l \frac{1}{( x ( x ^{4} + 1 ) )}