integral of x(x+5)

Lösung

\int x (x + 5) d x

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

Schritte zur Lösung

\int x (x + 5) d x

Multipliziere aus

x (x + 5) : x^{2} + 5 x

= \int x^{2} + 5 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^{2} d x + \int 5 x d x

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

\int 5 x d x = \frac{5 x ^{2}}{2}

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

Füge eine Konstante zur Lösung hinzu

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

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

in v erse l a pl a ce \frac{10}{s} (\frac{1}{10 s + 1})

d er i v a t i v e x^{2} + e^{x}

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

\frac{\partial}{\partial x} (\frac{x - y}{x + 2 y})