## Calculus: Early Transcendentals 8th Edition

$2x^{3/2}-\frac{3}{2}x^{4/3}+C$
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: $2x^{3/2}-\frac{3}{2}x^{4/3}+C$.