Axel Vogt schrieb:   
   >   
   > On 21.02.2014 10:50, Nasser M. Abbasi wrote:   
   > > Trying different CAS on this hard integral   
   > >   
   > > ArcSin[Sqrt[x]]/(x^4 - 2 x^3 + 2 x^2 - x + 1)   
   > >   
   > > which I saw here   
   > >   
   > > http://math.stackexchange.com/questions/683454/how-find-this   
   intergral-int-01-frac-arcsin-sqrtxx4-2x32x2-x1#684596   
   > ...   
   >   
   > I do not understand what "shobhit.iands" meant by   
   > "averaging the integrals" to eliminate arcsin(sqrt)   
   > at stackexchange.   
   >   
   > Having 1/quadric as integrand all CAS can answer.   
      
   Because the denominator doesn't change when x is replaced by 1-x, one   
   may use ASIN(SQRT(x)) + ASIN(SQRT(1-x)) = pi/2:   
      
   INT(ASIN(SQRT(x))/(x^4 - 2*x^3 + 2*x^2 - x + 1), x, 0, 1)   
      
    = 1/2*INT(ASIN(SQRT(x))/(x^4 - 2*x^3 + 2*x^2 - x + 1)   
    + ASIN(SQRT(1-x))/((1-x)^4 - 2*(1-x)^3 + 2*(1-x)^2 - (1-x) + 1),   
    x, 0, 1)   
      
    = pi/4*INT(1/(x^4 - 2*x^3 + 2*x^2 - x + 1), x, 0, 1)   
      
   Martin.   
      
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