integral of (5x^7+2)^3x^6

Lösung

\int (5 x^{7} + 2)^{3} x^{6} d x

\frac{125 x ^{28}}{28} + \frac{50 x ^{21}}{7} + \frac{30 x ^{14}}{7} + \frac{8 x ^{7}}{7} + C

Schritte zur Lösung

\int (5 x^{7} + 2)^{3} x^{6} d x

Multipliziere aus

(5 x^{7} + 2)^{3} x^{6} : 125 x^{27} + 150 x^{20} + 60 x^{13} + 8 x^{6}

= \int 125 x^{27} + 150 x^{20} + 60 x^{13} + 8 x^{6} 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 125 x^{27} d x + \int 150 x^{20} d x + \int 60 x^{13} d x + \int 8 x^{6} d x

\int 125 x^{27} d x = \frac{125 x ^{28}}{28}

\int 150 x^{20} d x = \frac{50 x ^{21}}{7}

\int 60 x^{13} d x = \frac{30 x ^{14}}{7}

\int 8 x^{6} d x = \frac{8 x ^{7}}{7}

= \frac{125 x ^{28}}{28} + \frac{50 x ^{21}}{7} + \frac{30 x ^{14}}{7} + \frac{8 x ^{7}}{7}

Füge eine Konstante zur Lösung hinzu

= \frac{125 x ^{28}}{28} + \frac{50 x ^{21}}{7} + \frac{30 x ^{14}}{7} + \frac{8 x ^{7}}{7} + C

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