求下列不定积分，谢谢
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(1) 原式 = ∫ [(√x)^2-√x+1]dx = ∫ (x-√x+1)dx = x^2/2 - (2/3)x^(3/2) + x + C.
(2) 令 u = x^(1/4), 则 x = u^4， dx = 4u^3du,
原式 = ∫4u^3du/(u^2+u) = 4∫u^2du/(u+1) = 4∫(u^2+u-u-1+1)du/(u+1)
= 4∫[u-1+1/(u+1)]du = 4[u^2/2 - u + ln|1+u|] + C
= 2√x - 4x^(1/4) + 4ln[1+x^(1/4)] + C
(2) 令 u = x^(1/4), 则 x = u^4， dx = 4u^3du,
原式 = ∫4u^3du/(u^2+u) = 4∫u^2du/(u+1) = 4∫(u^2+u-u-1+1)du/(u+1)
= 4∫[u-1+1/(u+1)]du = 4[u^2/2 - u + ln|1+u|] + C
= 2√x - 4x^(1/4) + 4ln[1+x^(1/4)] + C
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