integral of x(x+2)

Lösung

\int x (x + 2) d x

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

Schritte zur Lösung

\int x (x + 2) d x

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\int_{0}^{1} 6^{3 x} d x

\int \frac{x ^{2} - 49}{x ^{3}} d x

\frac{\partial}{\partial x} (4 x y e^{x})

x \to 2 lim (3 x^{4} + 2 x^{2} - x + 1)

x \to - 8 lim (x^{3})