integral of xsin^3(x)

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{d}{d x} (x^{3} - 4 x)

\frac{d ^{3}}{d x ^{3}} (\frac{7}{x ^{2}})

\frac{\partial}{\partial x} (a^{x})

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

t an g e n t \frac{- 6 x}{( x ^{2} + 1 )}