On Monday, January 30, 2017 at 11:37:17 AM UTC+8, Nasser M. Abbasi wrote:   
      
   > Hi,   
   >   
   > When you say it is continuous, is there an implied interval   
   > associated with this?   
   >   
   > I am asking, since there are singularities at x=+- 1 in   
   > the above expression.   
   >   
   > r:=(log((2*x*((-1)*x^4+1)^(1/2)+((-1)*x^4+2*x^2+1))/(x^4+1))+2   
   arctan((x^2*((-1)*   
   >    x^4+1)^(1/2)+(x^3+x))/(((-1)*x^4+1)^(1/2)+((-1)*x^3+x))))/4;   
   >   
   > singular(r,x);   
   >   
   > {x = -1}, {x = 1},   
   > {x = -(1/2)*sqrt(2)-(1/2*I)*sqrt(2)},   
   > {x = -(1/2)*sqrt(2)+(1/2*I)*sqrt(2)},   
   > {x = (1/2)*sqrt(2)-(1/2*I)*sqrt(2)},   
   > {x = (1/2)*sqrt(2)+(1/2*I)*sqrt(2)}   
   >   
   > subs(x=1,r);   
   > Error, numeric exception: division by zero   
   > subs(x=-1,r);   
   > Error, numeric exception: division by zero   
   >   
   >   
   > So I assume, the range where it is continuous is meant   
   > to be from [-1,1] only?  Sorry if this meant to be, I did   
   > not follow all of the thread before.   
   >   
   > Thanks,   
   > --Nasser   
      
   The integrand is defined on [-1,1] (we are talking about   
   real valued function), my result integral is continuous   
   on (-1,1). At +-1, it's singular but trival, take a limit and   
   it'll be defined on[-1,1], making definite integration valid   
   and correct on [-1,1].   
      
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