What is expand (x^2+5)^32xdx ?

The solution to expand (x^2+5)^32xdx is 2x^7dx+30x^5dx+150x^3dx+250xdx

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expand (x^2+5)^32xdx

expand

(x^{2} + 5)^{3} 2 x d x

2 x^{7} d x + 30 x^{5} d x + 150 x^{3} d x + 250 x d x

Solution steps

(x^{2} + 5)^{3} \cdot 2 x d x

(x^{2} + 5)^{3} = x^{6} + 15 x^{4} + 75 x^{2} + 125

= 2 x (x^{6} + 15 x^{4} + 75 x^{2} + 125) d x

= 2 x (x^{6} + 15 x^{4} + 75 x^{2} + 125) d x

Distribute parentheses

= 2 x d x x^{6} + 2 x d x \cdot 15 x^{4} + 2 x d x \cdot 75 x^{2} + 2 x d x \cdot 125

= 2 x^{6} x d x + 2 \cdot 15 x^{4} x d x + 2 \cdot 75 x^{2} x d x + 2 \cdot 125 x d x

Simplify

2 x^{6} x d x + 2 \cdot 15 x^{4} x d x + 2 \cdot 75 x^{2} x d x + 2 \cdot 125 x d x : 2 x^{7} d x + 30 x^{5} d x + 150 x^{3} d x + 250 x d x

= 2 x^{7} d x + 30 x^{5} d x + 150 x^{3} d x + 250 x d x

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What is expand (x^2+5)^32xdx ?
The solution to expand (x^2+5)^32xdx is 2x^7dx+30x^5dx+150x^3dx+250xdx