integral of (2x+5)^2

Lösung

\int (2 x + 5)^{2} d x

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

Schritte zur Lösung

\int (2 x + 5)^{2} d x

Multipliziere aus

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

= \int 4 x^{2} + 20 x + 25 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 4 x^{2} d x + \int 20 x d x + \int 25 d x

\int 4 x^{2} d x = \frac{4 x ^{3}}{3}

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

\int 25 d x = 25 x

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

Füge eine Konstante zur Lösung hinzu

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

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