integral of x^4-2x^2-4x

Lösung

\int x^{4} - 2 x^{2} - 4 x d x

\frac{x ^{5}}{5} - \frac{2 x ^{3}}{3} - 2 x^{2} + C

Schritte zur Lösung

\int x^{4} - 2 x^{2} - 4 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 x^{4} d x - \int 2 x^{2} d x - \int 4 x d x

\int x^{4} d x = \frac{x ^{5}}{5}

\int 2 x^{2} d x = \frac{2 x ^{3}}{3}

\int 4 x d x = 2 x^{2}

= \frac{x ^{5}}{5} - \frac{2 x ^{3}}{3} - 2 x^{2}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} - \frac{2 x ^{3}}{3} - 2 x^{2} + C

e x p an d \frac{e ^{x} - 2}{( 1 - e ^{- x} ) ^{2}}

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

\frac{\partial}{\partial x} (\frac{1}{2 y})

\int - x e^{- x^{2}} d x

t an g e n t f (x) = x^{2} + x, at x = - 2