integral of x^3cos(x)

Lösung

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

x^{3} sin (x) - 3 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

= x^{3} sin (x) - 3 (- x^{2} cos (x) + 2 (x sin (x) + cos (x)))

Füge eine Konstante zur Lösung hinzu

= x^{3} sin (x) - 3 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + C

\int_{- 2}^{- 1} (2 x^{2}) - (2 x + 6) d x

\frac{\partial}{\partial x} (x^{6} e^{x y})

\frac{d ^{2}}{d x ^{2}} ((4 x^{2} + 9)^{6})

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

\frac{\partial}{\partial x} (e^{x} + x cos (y))