Answer:
B.
Step-by-step explanation:
We are given:
[tex]\displaystyle \int \sqrt{x}\Big(9x^3-2\sqrt{x}+\frac{8}{x}\Big)\, dx[/tex]
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:
[tex]\displaystyle =\int x^{1/2}\Big(9x^3-2x^{1/2}+8x^{-1}\Big)\, dx[/tex]
Distribute. Recall exponent properties;
[tex]\displaystyle =\int(9x^{3+1/2}-2x^{1/2+1/2}+8x^{-1+1/2})\, dx[/tex]
Simplify:
[tex]\displaystyle=\int9x^{7/2}-2x+8x^{1/2}\, dx[/tex]
This can then be separated (since its addition/subtraction) and integrated individually.
Hence, our answer is B.
