What is the integral of (x-6)^2(x+8) ?

The integral of (x-6)^2(x+8) is (x^4)/3-(x^4}{12}-4x^3+\frac{8x^3)/3-30x^2+288x+C

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integral of (x-6)^2(x+8)

\int (x - 6)^{2} (x + 8) d x

\frac{x ^{4}}{3} - \frac{x ^{4}}{12} - 4 x^{3} + \frac{8 x ^{3}}{3} - 30 x^{2} + 288 x + C

Solution steps

\int (x - 6)^{2} (x + 8) d x

Apply Integration By Parts

: (x + 8) (\frac{x ^{3}}{3} - 6 x^{2} + 36 x) - \int \frac{x ^{3}}{3} - 6 x^{2} + 36 x d x

= (x + 8) (\frac{x ^{3}}{3} - 6 x^{2} + 36 x) - \int \frac{x ^{3}}{3} - 6 x^{2} + 36 x d x

\int \frac{x ^{3}}{3} - 6 x^{2} + 36 x d x = \frac{x ^{4}}{12} - 2 x^{3} + 18 x^{2}

= (x + 8) (\frac{x ^{3}}{3} - 6 x^{2} + 36 x) - (\frac{x ^{4}}{12} - 2 x^{3} + 18 x^{2})

Simplify

(x + 8) (\frac{x ^{3}}{3} - 6 x^{2} + 36 x) - (\frac{x ^{4}}{12} - 2 x^{3} + 18 x^{2}) : \frac{x ^{4}}{3} - \frac{x ^{4}}{12} - 4 x^{3} + \frac{8 x ^{3}}{3} - 30 x^{2} + 288 x

= \frac{x ^{4}}{3} - \frac{x ^{4}}{12} - 4 x^{3} + \frac{8 x ^{3}}{3} - 30 x^{2} + 288 x

Add a constant to the solution

= \frac{x ^{4}}{3} - \frac{x ^{4}}{12} - 4 x^{3} + \frac{8 x ^{3}}{3} - 30 x^{2} + 288 x + C

\frac{\partial}{\partial x} (y - ln (x y))

\frac{d ^{2}}{d x ^{2}} ((14 t^{2} + 6)^{0.5})

10 x^{^{''}} + 1000 x = 0

\frac{d}{d x} (\frac{4 π x ^{3}}{3})

(e^{x} + e^{- x})^{^{'}}

What is the integral of (x-6)^2(x+8) ?
The integral of (x-6)^2(x+8) is (x^4)/3-(x^4}{12}-4x^3+\frac{8x^3)/3-30x^2+288x+C