∫dx/（√x+4√x）
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令x = z⁴，dx = 4z³ dz，x^(1/4) = z，√x = z²
∫ dx/[√x + x^(1/4)]
= ∫ 1/(z² + z) * (4z³ dz)
= 4∫ z²/(1 + z) dz
= 4∫ z[(1 + z) - 1]/(1 + z) dz
= 4∫ z dz - 4∫ z/(1 + z) dz
= 4 * z²/2 - 4∫ [(1 + z) - 1]/(1 + z) dz
= 2z² - 4∫ dz + 4∫ dz/(1 + z)
= 2z² - 4z + 4ln|1 + z| + C
= 2√x - 4x^(1/4) + 4ln|1 + x^(1/4)| + C
∫ dx/[√x + x^(1/4)]
= ∫ 1/(z² + z) * (4z³ dz)
= 4∫ z²/(1 + z) dz
= 4∫ z[(1 + z) - 1]/(1 + z) dz
= 4∫ z dz - 4∫ z/(1 + z) dz
= 4 * z²/2 - 4∫ [(1 + z) - 1]/(1 + z) dz
= 2z² - 4∫ dz + 4∫ dz/(1 + z)
= 2z² - 4z + 4ln|1 + z| + C
= 2√x - 4x^(1/4) + 4ln|1 + x^(1/4)| + C
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