integral of 6x^5-4x^4-9x^2

Lösung

\int 6 x^{5} - 4 x^{4} - 9 x^{2} d x

x^{6} - \frac{4 x ^{5}}{5} - 3 x^{3} + C

Schritte zur Lösung

\int 6 x^{5} - 4 x^{4} - 9 x^{2} 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 6 x^{5} d x - \int 4 x^{4} d x - \int 9 x^{2} d x

\int 6 x^{5} d x = x^{6}

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

\int 9 x^{2} d x = 3 x^{3}

= x^{6} - \frac{4 x ^{5}}{5} - 3 x^{3}

Füge eine Konstante zur Lösung hinzu

= x^{6} - \frac{4 x ^{5}}{5} - 3 x^{3} + C

\int (2 x^{3} - 9 x^{2} + 5 x) e^{- x} d x

\int \frac{x}{2 ( x ^{2} + 1 )} d x

\frac{d}{d x} (\frac{e ^{x} + e ^{- x}}{x ^{3}})

y^{3} - (14 x + 8) + 3 x y^{2} \frac{d y}{d x} = 0

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