What is expand dx[sqrt(x)(5x^4-7x^2-3)] ?

The solution to expand dx[sqrt(x)(5x^4-7x^2-3)] is 5x^4sqrt(x)dx-7x^2sqrt(x)dx-3sqrt(x)dx

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expand dx[sqrt(x)(5x^4-7x^2-3)]

expand

d x [x (5 x^{4} - 7 x^{2} - 3)]

5 x^{4} x d x - 7 x^{2} x d x - 3 x d x

Solution steps

d x (x (5 x^{4} - 7 x^{2} - 3))

Remove parentheses:

(a) = a

= d x x (5 x^{4} - 7 x^{2} - 3)

= x d x (5 x^{4} - 7 x^{2} - 3)

Distribute parentheses

= d x x \cdot 5 x^{4} + d x x (- 7 x^{2}) + d x x (- 3)

Apply minus-plus rules

+ (- a) = - a

= 5 x^{4} x d x - 7 x^{2} x d x - 3 x d x

sin (\frac{x}{2}) (2 sin (\frac{x}{2}) - 1)

(y + 1) e^{x}

(2 x + \frac{1}{3 x})^{18}

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

\frac{4}{x ( x + 2 )}

What is expand dx[sqrt(x)(5x^4-7x^2-3)] ?
The solution to expand dx[sqrt(x)(5x^4-7x^2-3)] is 5x^4sqrt(x)dx-7x^2sqrt(x)dx-3sqrt(x)dx