What is expand (x^2-2)^3xdx ?

The solution to expand (x^2-2)^3xdx is x^7dx-6x^5dx+12x^3dx-8xdx

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expand (x^2-2)^3xdx

expand

(x^{2} - 2)^{3} x d x

x^{7} d x - 6 x^{5} d x + 12 x^{3} d x - 8 x d x

Solution steps

(x^{2} - 2)^{3} x d x

(x^{2} - 2)^{3} = x^{6} - 6 x^{4} + 12 x^{2} - 8

= x (x^{6} - 6 x^{4} + 12 x^{2} - 8) d x

= x (x^{6} - 6 x^{4} + 12 x^{2} - 8) d x

Distribute parentheses

= x d x x^{6} + x d x (- 6 x^{4}) + x d x \cdot 12 x^{2} + x d x (- 8)

Apply minus-plus rules

+ (- a) = - a

= x^{6} x d x - 6 x^{4} x d x + 12 x^{2} x d x - 8 x d x

Simplify

x^{6} x d x - 6 x^{4} x d x + 12 x^{2} x d x - 8 x d x : x^{7} d x - 6 x^{5} d x + 12 x^{3} d x - 8 x d x

= x^{7} d x - 6 x^{5} d x + 12 x^{3} d x - 8 x d x

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

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

\frac{1}{( t + 1 ) ^{4}}

(3 + 4 t^{4} + 2 e^{- 4 t}) u (t)

y^{2} (e^{2 x} + c)

What is expand (x^2-2)^3xdx ?
The solution to expand (x^2-2)^3xdx is x^7dx-6x^5dx+12x^3dx-8xdx