integral of x-y^3+y^2sin(x)

Lösung

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

- y^{3} x + \frac{x ^{2}}{2} - y^{2} cos (x) + C

Schritte zur Lösung

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

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int y^{3} d x = y^{3} x

\int x d x = \frac{x ^{2}}{2}

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

= - y^{3} x + \frac{x ^{2}}{2} - y^{2} cos (x)

Füge eine Konstante zur Lösung hinzu

= - y^{3} x + \frac{x ^{2}}{2} - y^{2} cos (x) + C

ma c l a u r in (1 + x)^{- \frac{2}{5}}

\int e^{- k x} cos (w x) d x

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

\int csc (\frac{x - π}{2}) cot (\frac{x - π}{2}) d x

x \to 0 lim (x^{8} cos (\frac{6}{x}))