integral of x^3cos(x/2)

Lösung

\int x^{3} cos (\frac{x}{2}) d x

2 x^{3} sin (\frac{x}{2}) - 6 (- 2 x^{2} cos (\frac{x}{2}) + 16 (\frac{1}{2} x sin (\frac{x}{2}) + cos (\frac{x}{2}))) + C

Schritte zur Lösung

\int x^{3} cos (\frac{x}{2}) d x

Wende die partielle Integration an

= 2 x^{3} sin (\frac{x}{2}) - \int 6 x^{2} sin (\frac{x}{2}) d x

\int 6 x^{2} sin (\frac{x}{2}) d x = 6 (- 2 x^{2} cos (\frac{x}{2}) + 16 (\frac{1}{2} x sin (\frac{x}{2}) + cos (\frac{x}{2})))

= 2 x^{3} sin (\frac{x}{2}) - 6 (- 2 x^{2} cos (\frac{x}{2}) + 16 (\frac{1}{2} x sin (\frac{x}{2}) + cos (\frac{x}{2})))

Füge eine Konstante zur Lösung hinzu

= 2 x^{3} sin (\frac{x}{2}) - 6 (- 2 x^{2} cos (\frac{x}{2}) + 16 (\frac{1}{2} x sin (\frac{x}{2}) + cos (\frac{x}{2}))) + C

- 9 x^{2} y + y^{^{'}} = 9 x^{2}

\int cos (t^{5}) d t

\frac{\partial}{\partial y} (4 y^{3} cos (2 x))

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