Question

Value of the integral $\int \frac{x^2+5x-1}{\sqrt{x}}dx$ is

• A. $\frac{2}{5}{x}^{5/2}+\frac{2}{3}5x^{3/2}-2x^{1/2}+C$
• B. $\frac{2}{5}{x}^{5/2}+\frac{2}{3}5x^{1/2}-2x^{1/2}+C$
• C. $\frac{3}{5}{x}^{5/2}+\frac{2}{3}5x^{1/2}-2x^{1/2}+C$
• D. $\frac{2}{5}{x}^{5/2}+\frac{2}{3}5x^{1/2}-2x^{1/2}$

Answer 1

The correct option is A $\frac{2}{5}{x}^{5/2}+\frac{2}{3}5x^{3/2}-2x^{1/2}+C$

Let $I=\int \frac{x^2+5x-1}{\sqrt{x}}dx=\int x^{3/2}+5x^{1/2}-x^{-1/2}$

$\int x^{n}dx=\frac{x^{n+1}}{n+1}$

Thus, $I=\frac{2}{5}{x}^{5/2}+\frac{10}{3}{x}^{3/2}-2x^{1/2}+C$