Question

Calculate:
$\int (x^{3/2}-x^{1/2}+5x)dx$.

• A. $\frac{2x^{5/2}}{3}-\frac{2x^{3/2}}{5}+\frac{5}{2}{x}^2+c$
• B. $\frac{2x^{5/2}}{5}-\frac{x^{3/2}}{4}+\frac{5}{2}{x}^2+c$
• C. $\frac{x^{5/2}}{5}-\frac{2x^{3/2}}{3}+\frac{5}{2}{x}^2+c$
• D. $\frac{2x^{5/2}}{5}-\frac{2x^{3/2}}{3}+\frac{5}{2}{x}^2+c$

Answer 1

The correct option is D $\frac{2x^{5/2}}{5}-\frac{2x^{3/2}}{3}+\frac{5}{2}{x}^2+c$

$I=\int (x^{3/2}-x^{1/2}+5x)dx$

$=\frac{x^{3/2+1}}{\frac{3}{2}+1}-\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}+\frac{5x^2}{2}+c$

$=\frac{2}{5}{x}^{5/2}-\frac{2}{3}{x}^{3/2}+5\frac{x^2}{2}+c$