integral of (x^8-2x^4)^3(x^7-x^3)

Lösung

\int (x^{8} - 2 x^{4})^{3} (x^{7} - x^{3}) d x

\frac{x ^{32}}{32} - \frac{x ^{28}}{4} + \frac{3 x ^{24}}{4} - x^{20} + \frac{x ^{16}}{2} + C

Schritte zur Lösung

\int (x^{8} - 2 x^{4})^{3} (x^{7} - x^{3}) d x

Multipliziere aus

(x^{8} - 2 x^{4})^{3} (x^{7} - x^{3}) : x^{31} - 7 x^{27} + 18 x^{23} - 20 x^{19} + 8 x^{15}

= \int x^{31} - 7 x^{27} + 18 x^{23} - 20 x^{19} + 8 x^{15} 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^{31} d x - \int 7 x^{27} d x + \int 18 x^{23} d x - \int 20 x^{19} d x + \int 8 x^{15} d x

\int x^{31} d x = \frac{x ^{32}}{32}

\int 7 x^{27} d x = \frac{x ^{28}}{4}

\int 18 x^{23} d x = \frac{3 x ^{24}}{4}

\int 20 x^{19} d x = x^{20}

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

= \frac{x ^{32}}{32} - \frac{x ^{28}}{4} + \frac{3 x ^{24}}{4} - x^{20} + \frac{x ^{16}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{32}}{32} - \frac{x ^{28}}{4} + \frac{3 x ^{24}}{4} - x^{20} + \frac{x ^{16}}{2} + C

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