What is the integral of x^2(x^3+8)^3 ?

The integral of x^2(x^3+8)^3 is (x^{12}}{12}+\frac{8x^9)/3+32x^6+(512x^3)/3+C

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integral of x^2(x^3+8)^3

\int x^{2} (x^{3} + 8)^{3} d x

\frac{x ^{12}}{12} + \frac{8 x ^{9}}{3} + 32 x^{6} + \frac{512 x ^{3}}{3} + C

Solution steps

\int x^{2} (x^{3} + 8)^{3} d x

Expand

x^{2} (x^{3} + 8)^{3} : x^{11} + 24 x^{8} + 192 x^{5} + 512 x^{2}

= \int x^{11} + 24 x^{8} + 192 x^{5} + 512 x^{2} 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^{11} d x + \int 24 x^{8} d x + \int 192 x^{5} d x + \int 512 x^{2} d x

\int x^{11} d x = \frac{x ^{12}}{12}

\int 24 x^{8} d x = \frac{8 x ^{9}}{3}

\int 192 x^{5} d x = 32 x^{6}

\int 512 x^{2} d x = \frac{512 x ^{3}}{3}

= \frac{x ^{12}}{12} + \frac{8 x ^{9}}{3} + 32 x^{6} + \frac{512 x ^{3}}{3}

Add a constant to the solution

= \frac{x ^{12}}{12} + \frac{8 x ^{9}}{3} + 32 x^{6} + \frac{512 x ^{3}}{3} + C

x^{2} y^{^{'}} + x (x + 2) y = e^{x}

x = 2 y, x = y^{2} - 8

x^{a} (1 - x)^{b}

t \to \infty lim (ln (t))

x \to 0 lim (\frac{5}{1 + x})

What is the integral of x^2(x^3+8)^3 ?
The integral of x^2(x^3+8)^3 is (x^{12}}{12}+\frac{8x^9)/3+32x^6+(512x^3)/3+C