Integrate $\int \frac{\mathrm{dx}}{\left[\sqrt{\mathrm{x}^{2}+9}\right]^{3}}$
A) $\frac{x}{9 \sqrt{x^{2}+9}}+C$
B) $\frac{2}{\sqrt{\mathrm{x}^{2}+9}}+\mathrm{C}$
C) $\frac{\mathrm{x}}{\sqrt{\mathrm{x}^{2}+9}}+C$
D) $\frac{2}{3 \sqrt{\mathrm{x}^{2}+9}}+C$

Question

Quizplus · Accepted Answer

Let $u = x^2 + 9$, then $du = 2x dx$. Substituting, we get:$\int \frac{dx}{\left[\sqrt{x^2+9}\right]^3} = \int \frac{1}{2\sqrt{u}} \frac{du}{u^{3/2}} = \int \frac{1}{2u^{5/2}} du = -\frac{1}{3u^{3/2}} + C = -\frac{1}{3\sqrt{x^2+9}} + C$Therefore, the correct choice is A.