Answer
$2x^{3/2}-\frac{3}{2}x^{4/3}+C$
Work Step by Step
Start with function: $\int (3\sqrt x-2\sqrt[3] x)dx$
Rewrite square root and third root in fractional power form:
$\int (3x^{1/2}-2x^{1/3})dx$.
Use power rule for antiderivatives to integrate both terms:
$\frac{3x^{3/2}}{\frac{3}{2}}-\frac{2x^{4/3}}{\frac{4}{3}}+C$.
Simplify fractions to arrive at answer: $2x^{3/2}-\frac{3}{2}x^{4/3}+C$.
