What is expand (x^3+8x)^2(3x^2+8)dx ?

The solution to expand (x^3+8x)^2(3x^2+8)dx is 3x^8dx+56x^6dx+320x^4dx+512x^2dx

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expand (x^3+8x)^2(3x^2+8)dx

expand

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

3 x^{8} d x + 56 x^{6} d x + 320 x^{4} d x + 512 x^{2} d x

Solution steps

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

Apply the distributive law:

a (b + c) = ab + a c

a = (x^{3} + 8 x)^{2} d x, b = 3 x^{2}, c = 8

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

= 3 x^{2} (x^{3} + 8 x)^{2} d x + 8 (x^{3} + 8 x)^{2} d x

Simplify

3 x^{2} (x^{3} + 8 x)^{2} d x + 8 (x^{3} + 8 x)^{2} d x : 3 x^{8} d x + 56 x^{6} d x + 320 x^{4} d x + 512 x^{2} d x

= 3 x^{8} d x + 56 x^{6} d x + 320 x^{4} d x + 512 x^{2} d x

(1 + x) y^{'} (x) - 2 y

- \frac{5 π ( x + 2 ) ( x - 2 ) ( 3 x ^{2} - 20 )}{16}

(x + L \cdot cos (T H))^{2}

2 (e^{3 y x} + 3 y e^{3 y x} x) + 2 y x - y^{3}

\frac{x - 2}{( x + 1 ) ( x - 3 )}

What is expand (x^3+8x)^2(3x^2+8)dx ?
The solution to expand (x^3+8x)^2(3x^2+8)dx is 3x^8dx+56x^6dx+320x^4dx+512x^2dx