Ta có
$\sqrt{x \sqrt{x\sqrt{x}}} = \sqrt{x \sqrt{x x^{\frac{1}{2}}}} = \sqrt{x \sqrt{x^{\frac{3}{2}}}} = \sqrt{x x^{\frac{3}{4}}} = \sqrt{x^{\frac{7}{4}}} = x^{\frac{7}{8}}$
Vậy
$\displaystyle \int \sqrt{x \sqrt{x\sqrt{x}}} dx = \displaystyle \int x^{\frac{7}{8}} dx = \dfrac{8}{15} x^{\frac{15}{8}} + c$