What is expand 3x(1-x^2)^3dx ?

The solution to expand 3x(1-x^2)^3dx is 3xdx-9x^3dx+9x^5dx-3x^7dx

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expand 3x(1-x^2)^3dx

expand

3 x (1 - x^{2})^{3} d x

3 x d x - 9 x^{3} d x + 9 x^{5} d x - 3 x^{7} d x

Solution steps

3 x (1 - x^{2})^{3} d x

(1 - x^{2})^{3} = 1 - 3 x^{2} + 3 x^{4} - x^{6}

= 3 x (- x^{6} + 3 x^{4} - 3 x^{2} + 1) d x

Distribute parentheses

= 3 x d x \cdot 1 + 3 x d x (- 3 x^{2}) + 3 x d x \cdot 3 x^{4} + 3 x d x (- x^{6})

Apply minus-plus rules

+ (- a) = - a

= 3 \cdot 1 \cdot x d x - 3 \cdot 3 x^{2} x d x + 3 \cdot 3 x^{4} x d x - 3 x^{6} x d x

Simplify

3 \cdot 1 \cdot x d x - 3 \cdot 3 x^{2} x d x + 3 \cdot 3 x^{4} x d x - 3 x^{6} x d x : 3 x d x - 9 x^{3} d x + 9 x^{5} d x - 3 x^{7} d x

= 3 x d x - 9 x^{3} d x + 9 x^{5} d x - 3 x^{7} d x

(x^{2} + 1)^{2} x e^{2 x}

(x ∣ 4) (x - 4)

e^{i (wt - k x)}

- \frac{3 ( 1 - 5 ^{9375} )}{4}

e^{x} (tan (x) - x)

What is expand 3x(1-x^2)^3dx ?
The solution to expand 3x(1-x^2)^3dx is 3xdx-9x^3dx+9x^5dx-3x^7dx