integral of (2x^3-3)^7x^5

Lösung

\int (2 x^{3} - 3)^{7} x^{5} d x

\frac{128 x ^{27}}{27} - 56 x^{24} + 288 x^{21} - 840 x^{18} + 1512 x^{15} - 1701 x^{12} + 1134 x^{9} - \frac{729 x ^{6}}{2} + C

Schritte zur Lösung

\int (2 x^{3} - 3)^{7} x^{5} d x

Multipliziere aus

(2 x^{3} - 3)^{7} x^{5} : 128 x^{26} - 1344 x^{23} + 6048 x^{20} - 15120 x^{17} + 22680 x^{14} - 20412 x^{11} + 10206 x^{8} - 2187 x^{5}

= \int 128 x^{26} - 1344 x^{23} + 6048 x^{20} - 15120 x^{17} + 22680 x^{14} - 20412 x^{11} + 10206 x^{8} - 2187 x^{5} 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 128 x^{26} d x - \int 1344 x^{23} d x + \int 6048 x^{20} d x - \int 15120 x^{17} d x + \int 22680 x^{14} d x - \int 20412 x^{11} d x + \int 10206 x^{8} d x - \int 2187 x^{5} d x

\int 128 x^{26} d x = \frac{128 x ^{27}}{27}

\int 1344 x^{23} d x = 56 x^{24}

\int 6048 x^{20} d x = 288 x^{21}

\int 15120 x^{17} d x = 840 x^{18}

\int 22680 x^{14} d x = 1512 x^{15}

\int 20412 x^{11} d x = 1701 x^{12}

\int 10206 x^{8} d x = 1134 x^{9}

\int 2187 x^{5} d x = \frac{729 x ^{6}}{2}

= \frac{128 x ^{27}}{27} - 56 x^{24} + 288 x^{21} - 840 x^{18} + 1512 x^{15} - 1701 x^{12} + 1134 x^{9} - \frac{729 x ^{6}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{128 x ^{27}}{27} - 56 x^{24} + 288 x^{21} - 840 x^{18} + 1512 x^{15} - 1701 x^{12} + 1134 x^{9} - \frac{729 x ^{6}}{2} + C

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