1. ∫(secx)^2dx/[4+(tanx)^2] = ∫dtanx/[4+(tanx)^2]
= (1/2)arctan[(tanx)/2] + C
2. 令 u =√(1-x)， 则 x=1-u^2
∫(x+1)dx/√(1-x) =∫-2(2-u^2)du
= -4u+(2/3)u^3 + C = -4√(1-x)+(2/3)(1-u)^(3/2) + C
3. 令 x = sinu， 则
∫(x+1)dx/√(1-x^2) = ∫(1+sinu)du = u - cosu
= arcsinx - √(1-x^2) + C
4.∫[e^(ex)+x]dx = ∫[e^(ex)dx + ∫xdx
= (1/e)e^(ex) + x^2/2 + C
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