Science:Math Exam Resources/Courses/MATH101/April 2008/Question 01 (a)/Solution 1

As suggested by the hint, we have

${\begin{aligned}\int {\frac {x^{3}-2x}{\sqrt {x}}}\,dx&=\int {\frac {x^{3}}{\sqrt {x}}}\,dx-\int {\frac {2x}{\sqrt {x}}}\,dx\\&=\int x^{5/2}\,dx-2\int x^{1/2}\,dx\\&={\frac {2x^{7/2}}{7}}-{\frac {4x^{3/2}}{3}}+C.\end{aligned}}$