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Beliebt Rechnen >

integral of (5+4x^2)^2

Lösung

\int (5 + 4 x^{2})^{2} d x

Lösung

25 x + \frac{40 x ^{3}}{3} + \frac{16 x ^{5}}{5} + C

Schritte zur Lösung

\int (5 + 4 x^{2})^{2} d x

Multipliziere aus

(5 + 4 x^{2})^{2} : 25 + 40 x^{2} + 16 x^{4}

= \int 25 + 40 x^{2} + 16 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 25 d x + \int 40 x^{2} d x + \int 16 x^{4} d x

\int 25 d x = 25 x

\int 40 x^{2} d x = \frac{40 x ^{3}}{3}

\int 16 x^{4} d x = \frac{16 x ^{5}}{5}

= 25 x + \frac{40 x ^{3}}{3} + \frac{16 x ^{5}}{5}

Füge eine Konstante zur Lösung hinzu

= 25 x + \frac{40 x ^{3}}{3} + \frac{16 x ^{5}}{5} + C

Graph

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