integral of (5x^2+2)^2

Lösung

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

5 x^{5} + \frac{20 x ^{3}}{3} + 4 x + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int 25 x^{4} d x = 5 x^{5}

\int 20 x^{2} d x = \frac{20 x ^{3}}{3}

\int 4 d x = 4 x

= 5 x^{5} + \frac{20 x ^{3}}{3} + 4 x

Füge eine Konstante zur Lösung hinzu

= 5 x^{5} + \frac{20 x ^{3}}{3} + 4 x + C

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