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Beliebt Rechnen >

integral of (7x^3-7)^4x^2

Lösung

\int (7 x^{3} - 7)^{4} x^{2} d x

Lösung

\frac{2401 x ^{15}}{15} - \frac{2401 x ^{12}}{3} + \frac{4802 x ^{9}}{3} - \frac{4802 x ^{6}}{3} + \frac{2401 x ^{3}}{3} + C

Schritte zur Lösung

\int (7 x^{3} - 7)^{4} x^{2} d x

Multipliziere aus

(7 x^{3} - 7)^{4} x^{2} : 2401 x^{14} - 9604 x^{11} + 14406 x^{8} - 9604 x^{5} + 2401 x^{2}

= \int 2401 x^{14} - 9604 x^{11} + 14406 x^{8} - 9604 x^{5} + 2401 x^{2} 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 2401 x^{14} d x - \int 9604 x^{11} d x + \int 14406 x^{8} d x - \int 9604 x^{5} d x + \int 2401 x^{2} d x

\int 2401 x^{14} d x = \frac{2401 x ^{15}}{15}

\int 9604 x^{11} d x = \frac{2401 x ^{12}}{3}

\int 14406 x^{8} d x = \frac{4802 x ^{9}}{3}

\int 9604 x^{5} d x = \frac{4802 x ^{6}}{3}

\int 2401 x^{2} d x = \frac{2401 x ^{3}}{3}

= \frac{2401 x ^{15}}{15} - \frac{2401 x ^{12}}{3} + \frac{4802 x ^{9}}{3} - \frac{4802 x ^{6}}{3} + \frac{2401 x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= \frac{2401 x ^{15}}{15} - \frac{2401 x ^{12}}{3} + \frac{4802 x ^{9}}{3} - \frac{4802 x ^{6}}{3} + \frac{2401 x ^{3}}{3} + C

Graph

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