Question

Need help question #3. Show steps please

Answer 1

Answer:

B.

Step-by-step explanation:

We are given:

$\displaystyle \int \sqrt{x}\Big(9x^3-2\sqrt{x}+\frac{8}{x}\Big)\, dx$

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.