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Beliebt Rechnen >

integral of (x^3+5)^2

Lösung

\int (x^{3} + 5)^{2} d x

Lösung

\frac{x ^{7}}{7} + \frac{5 x ^{4}}{2} + 25 x + C

Schritte zur Lösung

\int (x^{3} + 5)^{2} d x

Multipliziere aus

(x^{3} + 5)^{2} : x^{6} + 10 x^{3} + 25

= \int x^{6} + 10 x^{3} + 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 x^{6} d x + \int 10 x^{3} d x + \int 25 d x

\int x^{6} d x = \frac{x ^{7}}{7}

\int 10 x^{3} d x = \frac{5 x ^{4}}{2}

\int 25 d x = 25 x

= \frac{x ^{7}}{7} + \frac{5 x ^{4}}{2} + 25 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{7}}{7} + \frac{5 x ^{4}}{2} + 25 x + C

Graph

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