Lời giải

\(I = \int_1^{64} \left( x^{-\frac{1}{3}} + x^{\frac{1}{6}} \right) \, dx\)
   \(= \left( \frac{3}{2} x^{\frac{2}{3}} + \frac{6}{7} x^{\frac{7}{6}} \right) \Big|_1^{64}\)
   \(= \left( 24 + \frac{768}{7} \right) - \left( \frac{3}{2} + \frac{6}{7} \right)   =\frac{1839}{14}\)

\(\Rightarrow\) Vậy chọn đáp án \(\boxed{\text{C}} \)

Cách 2:

Bấm:  \( \int_0^{64} \frac{1 + \sqrt{x}}{\sqrt[3]{x}} \, dx = (\text{đợi 40''}) = 131,357142 (=\frac{1839}{14}) \)