integral of x(2x-3)

Lösung

\int x (2 x - 3) d x

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

Schritte zur Lösung

\int x (2 x - 3) d x

Multipliziere aus

x (2 x - 3) : 2 x^{2} - 3 x

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial}{\partial x} (x^{3} - 6 x y + y^{3} - 2)

\frac{d}{d t} (+ 6 t)

\int_{4}^{10} \frac{1}{36 + ( x - 4 ) ^{2}} d x

\frac{d}{d x} (6 x - 6 e^{x})

\frac{d}{d x} (9 + x)