令u = x^(1/4),x = u⁴,dx = 4u³ du,√x = √u⁴ = u²
∫ dx/[√x + x^(1/4)]
= ∫ (4u³)/(u² + u) du
= 4∫ u²/(u + 1) du
= 4∫ [(u² - 1) + 1]/(u + 1) du
= 4∫ (u - 1) du + 4∫ du/(u + 1)
= 2u² - 4u + 4ln|u + 1| + C
= 2√x - 4x^(1/4) + 4ln|1 + x^(1/4)| + C