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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{x ^{16}}{8} + \frac{3 x ^{14}}{2} + \frac{27 x ^{12}}{4} + \frac{27 x ^{10}}{2} + \frac{81 x ^{8}}{8} + C

Schritte zur Lösung

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

Multipliziere aus

(- 2 x^{3} - 3 x) (- x^{4} - 3 x^{2})^{3} : 2 x^{15} + 21 x^{13} + 81 x^{11} + 135 x^{9} + 81 x^{7}

= \int 2 x^{15} + 21 x^{13} + 81 x^{11} + 135 x^{9} + 81 x^{7} 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 2 x^{15} d x + \int 21 x^{13} d x + \int 81 x^{11} d x + \int 135 x^{9} d x + \int 81 x^{7} d x

\int 2 x^{15} d x = \frac{x ^{16}}{8}

\int 21 x^{13} d x = \frac{3 x ^{14}}{2}

\int 81 x^{11} d x = \frac{27 x ^{12}}{4}

\int 135 x^{9} d x = \frac{27 x ^{10}}{2}

\int 81 x^{7} d x = \frac{81 x ^{8}}{8}

= \frac{x ^{16}}{8} + \frac{3 x ^{14}}{2} + \frac{27 x ^{12}}{4} + \frac{27 x ^{10}}{2} + \frac{81 x ^{8}}{8}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{16}}{8} + \frac{3 x ^{14}}{2} + \frac{27 x ^{12}}{4} + \frac{27 x ^{10}}{2} + \frac{81 x ^{8}}{8} + C

Graph

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