Question

Need help question #3. Show steps please

Answer 1

B.

Explanation:

We are given:

`\displaystyle \int √(x)\Big(9x^3-2√(x)+(8)/(x)\Big)\, dx`

And we want to select its equivalent form.

Note that A is not valid. No integration property allows us to separate factors unless that factor is a constant.

We can simply rewrite and then distribute. First, by rewriting:

`\displaystyle =\int x^(1/2)\Big(9x^3-2x^(1/2)+8x^(-1)\Big)\, dx`

Distribute. Recall exponent properties;

`\displaystyle =\int(9x^(3+1/2)-2x^(1/2+1/2)+8x^(-1+1/2))\, dx`

Simplify:

`\displaystyle=\int9x^(7/2)-2x+8x^(1/2)\, dx`

This can then be separated (since its addition/subtraction) and integrated individually.

Hence, our answer is B.