What is the integral of (x-8)^2(x+9) ?

The integral of (x-8)^2(x+9) is (x^4)/3-(x^4}{12}-5x^3+\frac{8x^3)/3-40x^2+576x+C

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integral of (x-8)^2(x+9)

\int (x - 8)^{2} (x + 9) d x

\frac{x ^{4}}{3} - \frac{x ^{4}}{12} - 5 x^{3} + \frac{8 x ^{3}}{3} - 40 x^{2} + 576 x + C

Solution steps

\int (x - 8)^{2} (x + 9) d x

Apply Integration By Parts

= (x + 9) (\frac{x ^{3}}{3} - 8 x^{2} + 64 x) - \int \frac{x ^{3}}{3} - 8 x^{2} + 64 x d x

\int \frac{x ^{3}}{3} - 8 x^{2} + 64 x d x = \frac{x ^{4}}{12} - \frac{8 x ^{3}}{3} + 32 x^{2}

= (x + 9) (\frac{x ^{3}}{3} - 8 x^{2} + 64 x) - (\frac{x ^{4}}{12} - \frac{8 x ^{3}}{3} + 32 x^{2})

Simplify

(x + 9) (\frac{x ^{3}}{3} - 8 x^{2} + 64 x) - (\frac{x ^{4}}{12} - \frac{8 x ^{3}}{3} + 32 x^{2}) : \frac{x ^{4}}{3} - \frac{x ^{4}}{12} - 5 x^{3} + \frac{8 x ^{3}}{3} - 40 x^{2} + 576 x

= \frac{x ^{4}}{3} - \frac{x ^{4}}{12} - 5 x^{3} + \frac{8 x ^{3}}{3} - 40 x^{2} + 576 x

Add a constant to the solution

= \frac{x ^{4}}{3} - \frac{x ^{4}}{12} - 5 x^{3} + \frac{8 x ^{3}}{3} - 40 x^{2} + 576 x + C

What is the integral of (x-8)^2(x+9) ?
The integral of (x-8)^2(x+9) is (x^4)/3-(x^4}{12}-5x^3+\frac{8x^3)/3-40x^2+576x+C