What is the integral of (x+4)^2(x-6)^5(x-9)^3 ?

The integral of (x+4)^2(x-6)^5(x-9)^3 is

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integral of (x+4)^2(x-6)^5(x-9)^3

\int (x + 4)^{2} (x - 6)^{5} (x - 9)^{3} d x

\frac{x ^{11}}{11} - \frac{49 x ^{10}}{10} + \frac{973 x ^{9}}{9} - \frac{9507 x ^{8}}{8} + \frac{37566 x ^{7}}{7} + 17460 x^{6} - \frac{1614816 x ^{5}}{5} + 1184868 x^{4} + 2169504 x^{3} - 30233088 x^{2} + 90699264 x + C

Solution steps

\int (x + 4)^{2} (x - 6)^{5} (x - 9)^{3} d x

Expand

(x + 4)^{2} (x - 6)^{5} (x - 9)^{3} : x^{10} - 49 x^{9} + 973 x^{8} - 9507 x^{7} + 37566 x^{6} + 104760 x^{5} - 1614816 x^{4} + 4739472 x^{3} + 6508512 x^{2} - 60466176 x + 90699264

= \int x^{10} - 49 x^{9} + 973 x^{8} - 9507 x^{7} + 37566 x^{6} + 104760 x^{5} - 1614816 x^{4} + 4739472 x^{3} + 6508512 x^{2} - 60466176 x + 90699264 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 x^{10} d x - \int 49 x^{9} d x + \int 973 x^{8} d x - \int 9507 x^{7} d x + \int 37566 x^{6} d x + \int 104760 x^{5} d x - \int 1614816 x^{4} d x + \int 4739472 x^{3} d x + \int 6508512 x^{2} d x - \int 60466176 x d x + \int 90699264 d x

\int x^{10} d x = \frac{x ^{11}}{11}

\int 49 x^{9} d x = \frac{49 x ^{10}}{10}

\int 973 x^{8} d x = \frac{973 x ^{9}}{9}

\int 9507 x^{7} d x = \frac{9507 x ^{8}}{8}

\int 37566 x^{6} d x = \frac{37566 x ^{7}}{7}

\int 104760 x^{5} d x = 17460 x^{6}

\int 1614816 x^{4} d x = \frac{1614816 x ^{5}}{5}

\int 4739472 x^{3} d x = 1184868 x^{4}

\int 6508512 x^{2} d x = 2169504 x^{3}

\int 60466176 x d x = 30233088 x^{2}

\int 90699264 d x = 90699264 x

= \frac{x ^{11}}{11} - \frac{49 x ^{10}}{10} + \frac{973 x ^{9}}{9} - \frac{9507 x ^{8}}{8} + \frac{37566 x ^{7}}{7} + 17460 x^{6} - \frac{1614816 x ^{5}}{5} + 1184868 x^{4} + 2169504 x^{3} - 30233088 x^{2} + 90699264 x

Add a constant to the solution

= \frac{x ^{11}}{11} - \frac{49 x ^{10}}{10} + \frac{973 x ^{9}}{9} - \frac{9507 x ^{8}}{8} + \frac{37566 x ^{7}}{7} + 17460 x^{6} - \frac{1614816 x ^{5}}{5} + 1184868 x^{4} + 2169504 x^{3} - 30233088 x^{2} + 90699264 x + C

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What is the integral of (x+4)^2(x-6)^5(x-9)^3 ?
The integral of (x+4)^2(x-6)^5(x-9)^3 is