integral of (x^7+2)^2

Lösung

\int (x^{7} + 2)^{2} d x

\frac{x ^{15}}{15} + \frac{x ^{8}}{2} + 4 x + C

Schritte zur Lösung

\int (x^{7} + 2)^{2} d x

Multipliziere aus

(x^{7} + 2)^{2} : x^{14} + 4 x^{7} + 4

= \int x^{14} + 4 x^{7} + 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 x^{14} d x + \int 4 x^{7} d x + \int 4 d x

\int x^{14} d x = \frac{x ^{15}}{15}

\int 4 x^{7} d x = \frac{x ^{8}}{2}

\int 4 d x = 4 x

= \frac{x ^{15}}{15} + \frac{x ^{8}}{2} + 4 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{15}}{15} + \frac{x ^{8}}{2} + 4 x + C

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