integral of 10(5x-2)^2

Lösung

\int 10 (5 x - 2)^{2} d x

10 (\frac{25 x ^{3}}{3} - 10 x^{2} + 4 x) + C

Schritte zur Lösung

\int 10 (5 x - 2)^{2} d x

Entferne die Konstante:

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

= 10 \cdot \int (5 x - 2)^{2} d x

Multipliziere aus

(5 x - 2)^{2} : 25 x^{2} - 20 x + 4

= 10 \cdot \int 25 x^{2} - 20 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

= 10 (\int 25 x^{2} d x - \int 20 x d x + \int 4 d x)

\int 25 x^{2} d x = \frac{25 x ^{3}}{3}

\int 20 x d x = 10 x^{2}

\int 4 d x = 4 x

= 10 (\frac{25 x ^{3}}{3} - 10 x^{2} + 4 x)

Füge eine Konstante zur Lösung hinzu

= 10 (\frac{25 x ^{3}}{3} - 10 x^{2} + 4 x) + C

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