What is expand (x^2+1)^2(2x)dx ?

The solution to expand (x^2+1)^2(2x)dx is 2x^5dx+4x^3dx+2xdx

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expand (x^2+1)^2(2x)dx

expand

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

2 x^{5} d x + 4 x^{3} d x + 2 x d x

Solution steps

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

Remove parentheses:

(a) = a

= (x^{2} + 1)^{2} \cdot 2 x d x

(x^{2} + 1)^{2} = x^{4} + 2 x^{2} + 1

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

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

Distribute parentheses

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

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

Simplify

2 x^{4} x d x + 2 \cdot 2 x^{2} x d x + 2 \cdot 1 \cdot x d x : 2 x^{5} d x + 4 x^{3} d x + 2 x d x

= 2 x^{5} d x + 4 x^{3} d x + 2 x d x

(- 8 t^{3} + 68 t^{2} - 204 t + 207) \cdot (- 1, + 2)

\frac{( a y + b x ) ( x a + y b )}{( a y - b x ) ( x a - y b )}

\frac{4 x}{ln ( 10 ) ( x ^{2} + 1 )}

\frac{d}{d x} ((z) (4 z^{3} + 3 x z^{2} - x y z - 2 x y^{2} + 7))

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

What is expand (x^2+1)^2(2x)dx ?
The solution to expand (x^2+1)^2(2x)dx is 2x^5dx+4x^3dx+2xdx