integral of 9(3x-2)^2

Lösung

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

9 (3 x^{3} - 6 x^{2} + 4 x) + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 9 \cdot \int (3 x - 2)^{2} d x

Multipliziere aus

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

= 9 \cdot \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

= 9 (\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

= 9 (3 x^{3} - 6 x^{2} + 4 x)

Füge eine Konstante zur Lösung hinzu

= 9 (3 x^{3} - 6 x^{2} + 4 x) + C

x \to c lim (3 f (x))

d er i v a t i v e f (x) = \frac{3}{x + 5}

x \to 2 lim (\frac{x + 7 - 3 4 x + 19}{x - 2})

\int 2 x csc (2 x) cot (2 x) d x

\int x^{x} d x