integral of (3x+2)^2

Lösung

\int (3 x + 2)^{2} d x

3 x^{3} + 6 x^{2} + 4 x + C

Schritte zur Lösung

\int (3 x + 2)^{2} d x

Multipliziere aus

(3 x + 2)^{2} : 9 x^{2} + 12 x + 4

= \int 9 x^{2} + 12 x + 4 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 9 x^{2} d x + \int 12 x d x + \int 4 d x

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

\int 12 x d x = 6 x^{2}

\int 4 d x = 4 x

= 3 x^{3} + 6 x^{2} + 4 x

Füge eine Konstante zur Lösung hinzu

= 3 x^{3} + 6 x^{2} + 4 x + C

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

a re a y = 4 x - x^{2}, y = - 6 x

x \to 8 lim (x^{2} - 64)

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

\int x x^{2} - 1 d x