What is the integral of (6+x^9)^5x^8 ?

The integral of (6+x^9)^5x^8 is 864x^9+360x^{18}+80x^{27}+10x^{36}+(2x^{45})/3+(x^{54})/(54)+C

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integral of (6+x^9)^5x^8

\int (6 + x^{9})^{5} x^{8} d x

864 x^{9} + 360 x^{18} + 80 x^{27} + 10 x^{36} + \frac{2 x ^{45}}{3} + \frac{x ^{54}}{54} + C

Solution steps

\int (6 + x^{9})^{5} x^{8} d x

Expand

(6 + x^{9})^{5} x^{8} : 7776 x^{8} + 6480 x^{17} + 2160 x^{26} + 360 x^{35} + 30 x^{44} + x^{53}

= \int 7776 x^{8} + 6480 x^{17} + 2160 x^{26} + 360 x^{35} + 30 x^{44} + x^{53} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 7776 x^{8} d x + \int 6480 x^{17} d x + \int 2160 x^{26} d x + \int 360 x^{35} d x + \int 30 x^{44} d x + \int x^{53} d x

\int 7776 x^{8} d x = 864 x^{9}

\int 6480 x^{17} d x = 360 x^{18}

\int 2160 x^{26} d x = 80 x^{27}

\int 360 x^{35} d x = 10 x^{36}

\int 30 x^{44} d x = \frac{2 x ^{45}}{3}

\int x^{53} d x = \frac{x ^{54}}{54}

= 864 x^{9} + 360 x^{18} + 80 x^{27} + 10 x^{36} + \frac{2 x ^{45}}{3} + \frac{x ^{54}}{54}

Add a constant to the solution

= 864 x^{9} + 360 x^{18} + 80 x^{27} + 10 x^{36} + \frac{2 x ^{45}}{3} + \frac{x ^{54}}{54} + C

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What is the integral of (6+x^9)^5x^8 ?
The integral of (6+x^9)^5x^8 is 864x^9+360x^{18}+80x^{27}+10x^{36}+(2x^{45})/3+(x^{54})/(54)+C