Tìm nguyên hàm 3√x + 1/3√x) dx

Ta có:

\(\int {\left( {3\sqrt x  + \frac{1}{{\sqrt[3]{x}}}} \right)} {\rm{d}}x = \int 3 \sqrt x \;{\rm{d}}x + \int {\frac{1}{{\sqrt[3]{x}}}} \;{\rm{d}}x = 3\int {{x^{\frac{1}{2}}}} \;{\rm{d}}x + \int {{x^{ - \frac{1}{3}}}} \;{\rm{d}}x = 3 \cdot \frac{2}{3}{x^{\frac{3}{2}}} + \frac{3}{2}{x^{\frac{2}{3}}} + C\)

Đáp số: \(\int {\left( {3\sqrt x  + \frac{1}{{\sqrt[3]{x}}}} \right)} {\rm{d}}x = 2x\sqrt x  + \frac{3}{2}\sqrt[3]{{{x^2}}} + C\).