Some integrals with problematic evaluation

[quinyu]

A curious one that sort of locks up the calculator:

Code:

Int(1/(((x+1)^2)^(1/3)-sqrt(x+1)),x)

Still interruptable by clicking On, doesn't show no hourglass; Enter is pressed in console, where a warning about Check [abs(x)] is given. With assume(x>-1), it works and gives the good result. However, without any assumption,

Code:

Int(1/(1+sqrt(x+1)),x)

calculates just fine. What's the issue here?