3 ∫
         (√ ------  √ -)
  arcsin    x + 1 −   x  dx



optimal
PIC

(√-  √ ---)∘ √-√------
--x+3--x+1-√--x--x+1−-x−  (x + 3)sin−1 (√x-−  √x-+--1)
         4 2                 8



M 9.01

PIC



Rubi 4.1

PIC



Maple 18

PIC



Sage 5.4

PIC



Fricas 1.2

PIC



sympy 0.7.1

PIC



Axiom 5/12

PIC



Maxima 5.28.02

PIC



reduce 2008

PIC



mupad 2013a

evalin(symengine,'int(asin(sqrt(x+1)-sqrt(x)),x)')  
 
-int(asin(x^(1/2) - (x + 1)^(1/2)), x)



xcas

PIC