Evaluate.
-$\int \frac{3 \sqrt{\mathrm{x}}-5}{\mathrm{x}^{2}} \mathrm{dx}$
A) $-\frac{6}{\sqrt{x}}+\frac{5}{x}+C$
B) $\frac{6}{\sqrt{x}}-\frac{5}{x}+C$
C) $\frac{6}{\sqrt{x}}+\frac{5}{x}+C$
D) $-\frac{6}{\sqrt{x}}-\frac{5}{x}+C$

Question

Quizplus · Accepted Answer

The integral can be split into two parts: $\int \frac{3 \sqrt{x}}{x^2} \, dx - \int \frac{5}{x^2} \, dx$. Simplifying gives $\int \frac{3}{x^{3/2}} \, dx - \int 5x^{-2} \, dx$. Integrating each term results in $-\frac{6}{\sqrt{x}} + \frac{5}{x} + C$.