integral of (x-2)^2

Lösung

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

\frac{x ^{3}}{3} - 2 x^{2} + 4 x + C

Schritte zur Lösung

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

Multipliziere aus

(x - 2)^{2} : x^{2} - 4 x + 4

= \int x^{2} - 4 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 x^{2} d x - \int 4 x d x + \int 4 d x

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

\int 4 x d x = 2 x^{2}

\int 4 d x = 4 x

= \frac{x ^{3}}{3} - 2 x^{2} + 4 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - 2 x^{2} + 4 x + C

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

x \to 0 + lim (\frac{e ^{- x} - 1}{x})

x \to 0 + lim ((x + e^{x})^{\frac{1}{x}})

a re a y = 4 x^{3}, y = 100 x

\int (4 x + 5)^{4} d x