1,1,107,0,0.085123," ","integrate((b*x**2+a)*(d*x**2+c)**4,x)","a c^{4} x + \frac{b d^{4} x^{11}}{11} + x^{9} \left(\frac{a d^{4}}{9} + \frac{4 b c d^{3}}{9}\right) + x^{7} \left(\frac{4 a c d^{3}}{7} + \frac{6 b c^{2} d^{2}}{7}\right) + x^{5} \left(\frac{6 a c^{2} d^{2}}{5} + \frac{4 b c^{3} d}{5}\right) + x^{3} \left(\frac{4 a c^{3} d}{3} + \frac{b c^{4}}{3}\right)"," ",0,"a*c**4*x + b*d**4*x**11/11 + x**9*(a*d**4/9 + 4*b*c*d**3/9) + x**7*(4*a*c*d**3/7 + 6*b*c**2*d**2/7) + x**5*(6*a*c**2*d**2/5 + 4*b*c**3*d/5) + x**3*(4*a*c**3*d/3 + b*c**4/3)","A",0
2,1,76,0,0.082079," ","integrate((b*x**2+a)*(d*x**2+c)**3,x)","a c^{3} x + \frac{b d^{3} x^{9}}{9} + x^{7} \left(\frac{a d^{3}}{7} + \frac{3 b c d^{2}}{7}\right) + x^{5} \left(\frac{3 a c d^{2}}{5} + \frac{3 b c^{2} d}{5}\right) + x^{3} \left(a c^{2} d + \frac{b c^{3}}{3}\right)"," ",0,"a*c**3*x + b*d**3*x**9/9 + x**7*(a*d**3/7 + 3*b*c*d**2/7) + x**5*(3*a*c*d**2/5 + 3*b*c**2*d/5) + x**3*(a*c**2*d + b*c**3/3)","A",0
3,1,53,0,0.073683," ","integrate((b*x**2+a)*(d*x**2+c)**2,x)","a c^{2} x + \frac{b d^{2} x^{7}}{7} + x^{5} \left(\frac{a d^{2}}{5} + \frac{2 b c d}{5}\right) + x^{3} \left(\frac{2 a c d}{3} + \frac{b c^{2}}{3}\right)"," ",0,"a*c**2*x + b*d**2*x**7/7 + x**5*(a*d**2/5 + 2*b*c*d/5) + x**3*(2*a*c*d/3 + b*c**2/3)","A",0
4,1,26,0,0.064540," ","integrate((b*x**2+a)*(d*x**2+c),x)","a c x + \frac{b d x^{5}}{5} + x^{3} \left(\frac{a d}{3} + \frac{b c}{3}\right)"," ",0,"a*c*x + b*d*x**5/5 + x**3*(a*d/3 + b*c/3)","A",0
5,1,82,0,0.279785," ","integrate((b*x**2+a)/(d*x**2+c),x)","\frac{b x}{d} - \frac{\sqrt{- \frac{1}{c d^{3}}} \left(a d - b c\right) \log{\left(- c d \sqrt{- \frac{1}{c d^{3}}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{c d^{3}}} \left(a d - b c\right) \log{\left(c d \sqrt{- \frac{1}{c d^{3}}} + x \right)}}{2}"," ",0,"b*x/d - sqrt(-1/(c*d**3))*(a*d - b*c)*log(-c*d*sqrt(-1/(c*d**3)) + x)/2 + sqrt(-1/(c*d**3))*(a*d - b*c)*log(c*d*sqrt(-1/(c*d**3)) + x)/2","B",0
6,1,112,0,0.391507," ","integrate((b*x**2+a)/(d*x**2+c)**2,x)","\frac{x \left(a d - b c\right)}{2 c^{2} d + 2 c d^{2} x^{2}} - \frac{\sqrt{- \frac{1}{c^{3} d^{3}}} \left(a d + b c\right) \log{\left(- c^{2} d \sqrt{- \frac{1}{c^{3} d^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{c^{3} d^{3}}} \left(a d + b c\right) \log{\left(c^{2} d \sqrt{- \frac{1}{c^{3} d^{3}}} + x \right)}}{4}"," ",0,"x*(a*d - b*c)/(2*c**2*d + 2*c*d**2*x**2) - sqrt(-1/(c**3*d**3))*(a*d + b*c)*log(-c**2*d*sqrt(-1/(c**3*d**3)) + x)/4 + sqrt(-1/(c**3*d**3))*(a*d + b*c)*log(c**2*d*sqrt(-1/(c**3*d**3)) + x)/4","B",0
7,1,150,0,0.540588," ","integrate((b*x**2+a)/(d*x**2+c)**3,x)","- \frac{\sqrt{- \frac{1}{c^{5} d^{3}}} \left(3 a d + b c\right) \log{\left(- c^{3} d \sqrt{- \frac{1}{c^{5} d^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{c^{5} d^{3}}} \left(3 a d + b c\right) \log{\left(c^{3} d \sqrt{- \frac{1}{c^{5} d^{3}}} + x \right)}}{16} + \frac{x^{3} \left(3 a d^{2} + b c d\right) + x \left(5 a c d - b c^{2}\right)}{8 c^{4} d + 16 c^{3} d^{2} x^{2} + 8 c^{2} d^{3} x^{4}}"," ",0,"-sqrt(-1/(c**5*d**3))*(3*a*d + b*c)*log(-c**3*d*sqrt(-1/(c**5*d**3)) + x)/16 + sqrt(-1/(c**5*d**3))*(3*a*d + b*c)*log(c**3*d*sqrt(-1/(c**5*d**3)) + x)/16 + (x**3*(3*a*d**2 + b*c*d) + x*(5*a*c*d - b*c**2))/(8*c**4*d + 16*c**3*d**2*x**2 + 8*c**2*d**3*x**4)","A",0
8,1,136,0,0.091078," ","integrate((b*x**2+a)**2*(d*x**2+c)**3,x)","a^{2} c^{3} x + \frac{b^{2} d^{3} x^{11}}{11} + x^{9} \left(\frac{2 a b d^{3}}{9} + \frac{b^{2} c d^{2}}{3}\right) + x^{7} \left(\frac{a^{2} d^{3}}{7} + \frac{6 a b c d^{2}}{7} + \frac{3 b^{2} c^{2} d}{7}\right) + x^{5} \left(\frac{3 a^{2} c d^{2}}{5} + \frac{6 a b c^{2} d}{5} + \frac{b^{2} c^{3}}{5}\right) + x^{3} \left(a^{2} c^{2} d + \frac{2 a b c^{3}}{3}\right)"," ",0,"a**2*c**3*x + b**2*d**3*x**11/11 + x**9*(2*a*b*d**3/9 + b**2*c*d**2/3) + x**7*(a**2*d**3/7 + 6*a*b*c*d**2/7 + 3*b**2*c**2*d/7) + x**5*(3*a**2*c*d**2/5 + 6*a*b*c**2*d/5 + b**2*c**3/5) + x**3*(a**2*c**2*d + 2*a*b*c**3/3)","A",0
9,1,97,0,0.081453," ","integrate((b*x**2+a)**2*(d*x**2+c)**2,x)","a^{2} c^{2} x + \frac{b^{2} d^{2} x^{9}}{9} + x^{7} \left(\frac{2 a b d^{2}}{7} + \frac{2 b^{2} c d}{7}\right) + x^{5} \left(\frac{a^{2} d^{2}}{5} + \frac{4 a b c d}{5} + \frac{b^{2} c^{2}}{5}\right) + x^{3} \left(\frac{2 a^{2} c d}{3} + \frac{2 a b c^{2}}{3}\right)"," ",0,"a**2*c**2*x + b**2*d**2*x**9/9 + x**7*(2*a*b*d**2/7 + 2*b**2*c*d/7) + x**5*(a**2*d**2/5 + 4*a*b*c*d/5 + b**2*c**2/5) + x**3*(2*a**2*c*d/3 + 2*a*b*c**2/3)","A",0
10,1,53,0,0.072554," ","integrate((b*x**2+a)**2*(d*x**2+c),x)","a^{2} c x + \frac{b^{2} d x^{7}}{7} + x^{5} \left(\frac{2 a b d}{5} + \frac{b^{2} c}{5}\right) + x^{3} \left(\frac{a^{2} d}{3} + \frac{2 a b c}{3}\right)"," ",0,"a**2*c*x + b**2*d*x**7/7 + x**5*(2*a*b*d/5 + b**2*c/5) + x**3*(a**2*d/3 + 2*a*b*c/3)","A",0
11,1,172,0,0.419941," ","integrate((b*x**2+a)**2/(d*x**2+c),x)","\frac{b^{2} x^{3}}{3 d} + x \left(\frac{2 a b}{d} - \frac{b^{2} c}{d^{2}}\right) - \frac{\sqrt{- \frac{1}{c d^{5}}} \left(a d - b c\right)^{2} \log{\left(- \frac{c d^{2} \sqrt{- \frac{1}{c d^{5}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{c d^{5}}} \left(a d - b c\right)^{2} \log{\left(\frac{c d^{2} \sqrt{- \frac{1}{c d^{5}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2}"," ",0,"b**2*x**3/(3*d) + x*(2*a*b/d - b**2*c/d**2) - sqrt(-1/(c*d**5))*(a*d - b*c)**2*log(-c*d**2*sqrt(-1/(c*d**5))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + sqrt(-1/(c*d**5))*(a*d - b*c)**2*log(c*d**2*sqrt(-1/(c*d**5))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2","B",0
12,1,236,0,0.697636," ","integrate((b*x**2+a)**2/(d*x**2+c)**2,x)","\frac{b^{2} x}{d^{2}} + \frac{x \left(a^{2} d^{2} - 2 a b c d + b^{2} c^{2}\right)}{2 c^{2} d^{2} + 2 c d^{3} x^{2}} - \frac{\sqrt{- \frac{1}{c^{3} d^{5}}} \left(a d - b c\right) \left(a d + 3 b c\right) \log{\left(- \frac{c^{2} d^{2} \sqrt{- \frac{1}{c^{3} d^{5}}} \left(a d - b c\right) \left(a d + 3 b c\right)}{a^{2} d^{2} + 2 a b c d - 3 b^{2} c^{2}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{c^{3} d^{5}}} \left(a d - b c\right) \left(a d + 3 b c\right) \log{\left(\frac{c^{2} d^{2} \sqrt{- \frac{1}{c^{3} d^{5}}} \left(a d - b c\right) \left(a d + 3 b c\right)}{a^{2} d^{2} + 2 a b c d - 3 b^{2} c^{2}} + x \right)}}{4}"," ",0,"b**2*x/d**2 + x*(a**2*d**2 - 2*a*b*c*d + b**2*c**2)/(2*c**2*d**2 + 2*c*d**3*x**2) - sqrt(-1/(c**3*d**5))*(a*d - b*c)*(a*d + 3*b*c)*log(-c**2*d**2*sqrt(-1/(c**3*d**5))*(a*d - b*c)*(a*d + 3*b*c)/(a**2*d**2 + 2*a*b*c*d - 3*b**2*c**2) + x)/4 + sqrt(-1/(c**3*d**5))*(a*d - b*c)*(a*d + 3*b*c)*log(c**2*d**2*sqrt(-1/(c**3*d**5))*(a*d - b*c)*(a*d + 3*b*c)/(a**2*d**2 + 2*a*b*c*d - 3*b**2*c**2) + x)/4","B",0
13,1,223,0,0.983990," ","integrate((b*x**2+a)**2/(d*x**2+c)**3,x)","- \frac{\sqrt{- \frac{1}{c^{5} d^{5}}} \left(3 a^{2} d^{2} + 2 a b c d + 3 b^{2} c^{2}\right) \log{\left(- c^{3} d^{2} \sqrt{- \frac{1}{c^{5} d^{5}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{c^{5} d^{5}}} \left(3 a^{2} d^{2} + 2 a b c d + 3 b^{2} c^{2}\right) \log{\left(c^{3} d^{2} \sqrt{- \frac{1}{c^{5} d^{5}}} + x \right)}}{16} + \frac{x^{3} \left(3 a^{2} d^{3} + 2 a b c d^{2} - 5 b^{2} c^{2} d\right) + x \left(5 a^{2} c d^{2} - 2 a b c^{2} d - 3 b^{2} c^{3}\right)}{8 c^{4} d^{2} + 16 c^{3} d^{3} x^{2} + 8 c^{2} d^{4} x^{4}}"," ",0,"-sqrt(-1/(c**5*d**5))*(3*a**2*d**2 + 2*a*b*c*d + 3*b**2*c**2)*log(-c**3*d**2*sqrt(-1/(c**5*d**5)) + x)/16 + sqrt(-1/(c**5*d**5))*(3*a**2*d**2 + 2*a*b*c*d + 3*b**2*c**2)*log(c**3*d**2*sqrt(-1/(c**5*d**5)) + x)/16 + (x**3*(3*a**2*d**3 + 2*a*b*c*d**2 - 5*b**2*c**2*d) + x*(5*a**2*c*d**2 - 2*a*b*c**2*d - 3*b**2*c**3))/(8*c**4*d**2 + 16*c**3*d**3*x**2 + 8*c**2*d**4*x**4)","B",0
14,1,189,0,0.099770," ","integrate((b*x**2+a)**3*(d*x**2+c)**3,x)","a^{3} c^{3} x + \frac{b^{3} d^{3} x^{13}}{13} + x^{11} \left(\frac{3 a b^{2} d^{3}}{11} + \frac{3 b^{3} c d^{2}}{11}\right) + x^{9} \left(\frac{a^{2} b d^{3}}{3} + a b^{2} c d^{2} + \frac{b^{3} c^{2} d}{3}\right) + x^{7} \left(\frac{a^{3} d^{3}}{7} + \frac{9 a^{2} b c d^{2}}{7} + \frac{9 a b^{2} c^{2} d}{7} + \frac{b^{3} c^{3}}{7}\right) + x^{5} \left(\frac{3 a^{3} c d^{2}}{5} + \frac{9 a^{2} b c^{2} d}{5} + \frac{3 a b^{2} c^{3}}{5}\right) + x^{3} \left(a^{3} c^{2} d + a^{2} b c^{3}\right)"," ",0,"a**3*c**3*x + b**3*d**3*x**13/13 + x**11*(3*a*b**2*d**3/11 + 3*b**3*c*d**2/11) + x**9*(a**2*b*d**3/3 + a*b**2*c*d**2 + b**3*c**2*d/3) + x**7*(a**3*d**3/7 + 9*a**2*b*c*d**2/7 + 9*a*b**2*c**2*d/7 + b**3*c**3/7) + x**5*(3*a**3*c*d**2/5 + 9*a**2*b*c**2*d/5 + 3*a*b**2*c**3/5) + x**3*(a**3*c**2*d + a**2*b*c**3)","A",0
15,1,136,0,0.090860," ","integrate((b*x**2+a)**3*(d*x**2+c)**2,x)","a^{3} c^{2} x + \frac{b^{3} d^{2} x^{11}}{11} + x^{9} \left(\frac{a b^{2} d^{2}}{3} + \frac{2 b^{3} c d}{9}\right) + x^{7} \left(\frac{3 a^{2} b d^{2}}{7} + \frac{6 a b^{2} c d}{7} + \frac{b^{3} c^{2}}{7}\right) + x^{5} \left(\frac{a^{3} d^{2}}{5} + \frac{6 a^{2} b c d}{5} + \frac{3 a b^{2} c^{2}}{5}\right) + x^{3} \left(\frac{2 a^{3} c d}{3} + a^{2} b c^{2}\right)"," ",0,"a**3*c**2*x + b**3*d**2*x**11/11 + x**9*(a*b**2*d**2/3 + 2*b**3*c*d/9) + x**7*(3*a**2*b*d**2/7 + 6*a*b**2*c*d/7 + b**3*c**2/7) + x**5*(a**3*d**2/5 + 6*a**2*b*c*d/5 + 3*a*b**2*c**2/5) + x**3*(2*a**3*c*d/3 + a**2*b*c**2)","A",0
16,1,76,0,0.078038," ","integrate((b*x**2+a)**3*(d*x**2+c),x)","a^{3} c x + \frac{b^{3} d x^{9}}{9} + x^{7} \left(\frac{3 a b^{2} d}{7} + \frac{b^{3} c}{7}\right) + x^{5} \left(\frac{3 a^{2} b d}{5} + \frac{3 a b^{2} c}{5}\right) + x^{3} \left(\frac{a^{3} d}{3} + a^{2} b c\right)"," ",0,"a**3*c*x + b**3*d*x**9/9 + x**7*(3*a*b**2*d/7 + b**3*c/7) + x**5*(3*a**2*b*d/5 + 3*a*b**2*c/5) + x**3*(a**3*d/3 + a**2*b*c)","A",0
17,1,238,0,0.572590," ","integrate((b*x**2+a)**3/(d*x**2+c),x)","\frac{b^{3} x^{5}}{5 d} + x^{3} \left(\frac{a b^{2}}{d} - \frac{b^{3} c}{3 d^{2}}\right) + x \left(\frac{3 a^{2} b}{d} - \frac{3 a b^{2} c}{d^{2}} + \frac{b^{3} c^{2}}{d^{3}}\right) - \frac{\sqrt{- \frac{1}{c d^{7}}} \left(a d - b c\right)^{3} \log{\left(- \frac{c d^{3} \sqrt{- \frac{1}{c d^{7}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{c d^{7}}} \left(a d - b c\right)^{3} \log{\left(\frac{c d^{3} \sqrt{- \frac{1}{c d^{7}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2}"," ",0,"b**3*x**5/(5*d) + x**3*(a*b**2/d - b**3*c/(3*d**2)) + x*(3*a**2*b/d - 3*a*b**2*c/d**2 + b**3*c**2/d**3) - sqrt(-1/(c*d**7))*(a*d - b*c)**3*log(-c*d**3*sqrt(-1/(c*d**7))*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2 + sqrt(-1/(c*d**7))*(a*d - b*c)**3*log(c*d**3*sqrt(-1/(c*d**7))*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2","B",0
18,1,314,0,1.054373," ","integrate((b*x**2+a)**3/(d*x**2+c)**2,x)","\frac{b^{3} x^{3}}{3 d^{2}} + x \left(\frac{3 a b^{2}}{d^{2}} - \frac{2 b^{3} c}{d^{3}}\right) + \frac{x \left(a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}\right)}{2 c^{2} d^{3} + 2 c d^{4} x^{2}} - \frac{\sqrt{- \frac{1}{c^{3} d^{7}}} \left(a d - b c\right)^{2} \left(a d + 5 b c\right) \log{\left(- \frac{c^{2} d^{3} \sqrt{- \frac{1}{c^{3} d^{7}}} \left(a d - b c\right)^{2} \left(a d + 5 b c\right)}{a^{3} d^{3} + 3 a^{2} b c d^{2} - 9 a b^{2} c^{2} d + 5 b^{3} c^{3}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{c^{3} d^{7}}} \left(a d - b c\right)^{2} \left(a d + 5 b c\right) \log{\left(\frac{c^{2} d^{3} \sqrt{- \frac{1}{c^{3} d^{7}}} \left(a d - b c\right)^{2} \left(a d + 5 b c\right)}{a^{3} d^{3} + 3 a^{2} b c d^{2} - 9 a b^{2} c^{2} d + 5 b^{3} c^{3}} + x \right)}}{4}"," ",0,"b**3*x**3/(3*d**2) + x*(3*a*b**2/d**2 - 2*b**3*c/d**3) + x*(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3)/(2*c**2*d**3 + 2*c*d**4*x**2) - sqrt(-1/(c**3*d**7))*(a*d - b*c)**2*(a*d + 5*b*c)*log(-c**2*d**3*sqrt(-1/(c**3*d**7))*(a*d - b*c)**2*(a*d + 5*b*c)/(a**3*d**3 + 3*a**2*b*c*d**2 - 9*a*b**2*c**2*d + 5*b**3*c**3) + x)/4 + sqrt(-1/(c**3*d**7))*(a*d - b*c)**2*(a*d + 5*b*c)*log(c**2*d**3*sqrt(-1/(c**3*d**7))*(a*d - b*c)**2*(a*d + 5*b*c)/(a**3*d**3 + 3*a**2*b*c*d**2 - 9*a*b**2*c**2*d + 5*b**3*c**3) + x)/4","B",0
19,1,422,0,1.813338," ","integrate((b*x**2+a)**3/(d*x**2+c)**3,x)","\frac{b^{3} x}{d^{3}} - \frac{3 \sqrt{- \frac{1}{c^{5} d^{7}}} \left(a d - b c\right) \left(a^{2} d^{2} + 2 a b c d + 5 b^{2} c^{2}\right) \log{\left(- \frac{3 c^{3} d^{3} \sqrt{- \frac{1}{c^{5} d^{7}}} \left(a d - b c\right) \left(a^{2} d^{2} + 2 a b c d + 5 b^{2} c^{2}\right)}{3 a^{3} d^{3} + 3 a^{2} b c d^{2} + 9 a b^{2} c^{2} d - 15 b^{3} c^{3}} + x \right)}}{16} + \frac{3 \sqrt{- \frac{1}{c^{5} d^{7}}} \left(a d - b c\right) \left(a^{2} d^{2} + 2 a b c d + 5 b^{2} c^{2}\right) \log{\left(\frac{3 c^{3} d^{3} \sqrt{- \frac{1}{c^{5} d^{7}}} \left(a d - b c\right) \left(a^{2} d^{2} + 2 a b c d + 5 b^{2} c^{2}\right)}{3 a^{3} d^{3} + 3 a^{2} b c d^{2} + 9 a b^{2} c^{2} d - 15 b^{3} c^{3}} + x \right)}}{16} + \frac{x^{3} \left(3 a^{3} d^{4} + 3 a^{2} b c d^{3} - 15 a b^{2} c^{2} d^{2} + 9 b^{3} c^{3} d\right) + x \left(5 a^{3} c d^{3} - 3 a^{2} b c^{2} d^{2} - 9 a b^{2} c^{3} d + 7 b^{3} c^{4}\right)}{8 c^{4} d^{3} + 16 c^{3} d^{4} x^{2} + 8 c^{2} d^{5} x^{4}}"," ",0,"b**3*x/d**3 - 3*sqrt(-1/(c**5*d**7))*(a*d - b*c)*(a**2*d**2 + 2*a*b*c*d + 5*b**2*c**2)*log(-3*c**3*d**3*sqrt(-1/(c**5*d**7))*(a*d - b*c)*(a**2*d**2 + 2*a*b*c*d + 5*b**2*c**2)/(3*a**3*d**3 + 3*a**2*b*c*d**2 + 9*a*b**2*c**2*d - 15*b**3*c**3) + x)/16 + 3*sqrt(-1/(c**5*d**7))*(a*d - b*c)*(a**2*d**2 + 2*a*b*c*d + 5*b**2*c**2)*log(3*c**3*d**3*sqrt(-1/(c**5*d**7))*(a*d - b*c)*(a**2*d**2 + 2*a*b*c*d + 5*b**2*c**2)/(3*a**3*d**3 + 3*a**2*b*c*d**2 + 9*a*b**2*c**2*d - 15*b**3*c**3) + x)/16 + (x**3*(3*a**3*d**4 + 3*a**2*b*c*d**3 - 15*a*b**2*c**2*d**2 + 9*b**3*c**3*d) + x*(5*a**3*c*d**3 - 3*a**2*b*c**2*d**2 - 9*a*b**2*c**3*d + 7*b**3*c**4))/(8*c**4*d**3 + 16*c**3*d**4*x**2 + 8*c**2*d**5*x**4)","B",0
20,1,326,0,0.757271," ","integrate((d*x**2+c)**4/(b*x**2+a),x)","x^{5} \left(- \frac{a d^{4}}{5 b^{2}} + \frac{4 c d^{3}}{5 b}\right) + x^{3} \left(\frac{a^{2} d^{4}}{3 b^{3}} - \frac{4 a c d^{3}}{3 b^{2}} + \frac{2 c^{2} d^{2}}{b}\right) + x \left(- \frac{a^{3} d^{4}}{b^{4}} + \frac{4 a^{2} c d^{3}}{b^{3}} - \frac{6 a c^{2} d^{2}}{b^{2}} + \frac{4 c^{3} d}{b}\right) - \frac{\sqrt{- \frac{1}{a b^{9}}} \left(a d - b c\right)^{4} \log{\left(- \frac{a b^{4} \sqrt{- \frac{1}{a b^{9}}} \left(a d - b c\right)^{4}}{a^{4} d^{4} - 4 a^{3} b c d^{3} + 6 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d + b^{4} c^{4}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a b^{9}}} \left(a d - b c\right)^{4} \log{\left(\frac{a b^{4} \sqrt{- \frac{1}{a b^{9}}} \left(a d - b c\right)^{4}}{a^{4} d^{4} - 4 a^{3} b c d^{3} + 6 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d + b^{4} c^{4}} + x \right)}}{2} + \frac{d^{4} x^{7}}{7 b}"," ",0,"x**5*(-a*d**4/(5*b**2) + 4*c*d**3/(5*b)) + x**3*(a**2*d**4/(3*b**3) - 4*a*c*d**3/(3*b**2) + 2*c**2*d**2/b) + x*(-a**3*d**4/b**4 + 4*a**2*c*d**3/b**3 - 6*a*c**2*d**2/b**2 + 4*c**3*d/b) - sqrt(-1/(a*b**9))*(a*d - b*c)**4*log(-a*b**4*sqrt(-1/(a*b**9))*(a*d - b*c)**4/(a**4*d**4 - 4*a**3*b*c*d**3 + 6*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d + b**4*c**4) + x)/2 + sqrt(-1/(a*b**9))*(a*d - b*c)**4*log(a*b**4*sqrt(-1/(a*b**9))*(a*d - b*c)**4/(a**4*d**4 - 4*a**3*b*c*d**3 + 6*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d + b**4*c**4) + x)/2 + d**4*x**7/(7*b)","B",0
21,1,238,0,0.590895," ","integrate((d*x**2+c)**3/(b*x**2+a),x)","x^{3} \left(- \frac{a d^{3}}{3 b^{2}} + \frac{c d^{2}}{b}\right) + x \left(\frac{a^{2} d^{3}}{b^{3}} - \frac{3 a c d^{2}}{b^{2}} + \frac{3 c^{2} d}{b}\right) + \frac{\sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right)^{3} \log{\left(- \frac{a b^{3} \sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2} - \frac{\sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right)^{3} \log{\left(\frac{a b^{3} \sqrt{- \frac{1}{a b^{7}}} \left(a d - b c\right)^{3}}{a^{3} d^{3} - 3 a^{2} b c d^{2} + 3 a b^{2} c^{2} d - b^{3} c^{3}} + x \right)}}{2} + \frac{d^{3} x^{5}}{5 b}"," ",0,"x**3*(-a*d**3/(3*b**2) + c*d**2/b) + x*(a**2*d**3/b**3 - 3*a*c*d**2/b**2 + 3*c**2*d/b) + sqrt(-1/(a*b**7))*(a*d - b*c)**3*log(-a*b**3*sqrt(-1/(a*b**7))*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2 - sqrt(-1/(a*b**7))*(a*d - b*c)**3*log(a*b**3*sqrt(-1/(a*b**7))*(a*d - b*c)**3/(a**3*d**3 - 3*a**2*b*c*d**2 + 3*a*b**2*c**2*d - b**3*c**3) + x)/2 + d**3*x**5/(5*b)","B",0
22,1,172,0,0.435298," ","integrate((d*x**2+c)**2/(b*x**2+a),x)","x \left(- \frac{a d^{2}}{b^{2}} + \frac{2 c d}{b}\right) - \frac{\sqrt{- \frac{1}{a b^{5}}} \left(a d - b c\right)^{2} \log{\left(- \frac{a b^{2} \sqrt{- \frac{1}{a b^{5}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{\sqrt{- \frac{1}{a b^{5}}} \left(a d - b c\right)^{2} \log{\left(\frac{a b^{2} \sqrt{- \frac{1}{a b^{5}}} \left(a d - b c\right)^{2}}{a^{2} d^{2} - 2 a b c d + b^{2} c^{2}} + x \right)}}{2} + \frac{d^{2} x^{3}}{3 b}"," ",0,"x*(-a*d**2/b**2 + 2*c*d/b) - sqrt(-1/(a*b**5))*(a*d - b*c)**2*log(-a*b**2*sqrt(-1/(a*b**5))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + sqrt(-1/(a*b**5))*(a*d - b*c)**2*log(a*b**2*sqrt(-1/(a*b**5))*(a*d - b*c)**2/(a**2*d**2 - 2*a*b*c*d + b**2*c**2) + x)/2 + d**2*x**3/(3*b)","B",0
23,1,82,0,0.275868," ","integrate((d*x**2+c)/(b*x**2+a),x)","\frac{\sqrt{- \frac{1}{a b^{3}}} \left(a d - b c\right) \log{\left(- a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{2} - \frac{\sqrt{- \frac{1}{a b^{3}}} \left(a d - b c\right) \log{\left(a b \sqrt{- \frac{1}{a b^{3}}} + x \right)}}{2} + \frac{d x}{b}"," ",0,"sqrt(-1/(a*b**3))*(a*d - b*c)*log(-a*b*sqrt(-1/(a*b**3)) + x)/2 - sqrt(-1/(a*b**3))*(a*d - b*c)*log(a*b*sqrt(-1/(a*b**3)) + x)/2 + d*x/b","B",0
24,1,712,0,2.798080," ","integrate(1/(b*x**2+a)/(d*x**2+c),x)","\frac{\sqrt{- \frac{b}{a}} \log{\left(x + \frac{- \frac{a^{4} c d^{3} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{3} b c^{2} d^{2} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{2} b^{2} c^{3} d \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{2} d^{2} \sqrt{- \frac{b}{a}}}{a d - b c} - \frac{a b^{3} c^{4} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{2} c^{2} \sqrt{- \frac{b}{a}}}{a d - b c}}{b d} \right)}}{2 \left(a d - b c\right)} - \frac{\sqrt{- \frac{b}{a}} \log{\left(x + \frac{\frac{a^{4} c d^{3} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{3} b c^{2} d^{2} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{2} b^{2} c^{3} d \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{2} d^{2} \sqrt{- \frac{b}{a}}}{a d - b c} + \frac{a b^{3} c^{4} \left(- \frac{b}{a}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{2} c^{2} \sqrt{- \frac{b}{a}}}{a d - b c}}{b d} \right)}}{2 \left(a d - b c\right)} + \frac{\sqrt{- \frac{d}{c}} \log{\left(x + \frac{- \frac{a^{4} c d^{3} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{3} b c^{2} d^{2} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{2} b^{2} c^{3} d \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{2} d^{2} \sqrt{- \frac{d}{c}}}{a d - b c} - \frac{a b^{3} c^{4} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{b^{2} c^{2} \sqrt{- \frac{d}{c}}}{a d - b c}}{b d} \right)}}{2 \left(a d - b c\right)} - \frac{\sqrt{- \frac{d}{c}} \log{\left(x + \frac{\frac{a^{4} c d^{3} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{3} b c^{2} d^{2} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} - \frac{a^{2} b^{2} c^{3} d \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{a^{2} d^{2} \sqrt{- \frac{d}{c}}}{a d - b c} + \frac{a b^{3} c^{4} \left(- \frac{d}{c}\right)^{\frac{3}{2}}}{\left(a d - b c\right)^{3}} + \frac{b^{2} c^{2} \sqrt{- \frac{d}{c}}}{a d - b c}}{b d} \right)}}{2 \left(a d - b c\right)}"," ",0,"sqrt(-b/a)*log(x + (-a**4*c*d**3*(-b/a)**(3/2)/(a*d - b*c)**3 + a**3*b*c**2*d**2*(-b/a)**(3/2)/(a*d - b*c)**3 + a**2*b**2*c**3*d*(-b/a)**(3/2)/(a*d - b*c)**3 - a**2*d**2*sqrt(-b/a)/(a*d - b*c) - a*b**3*c**4*(-b/a)**(3/2)/(a*d - b*c)**3 - b**2*c**2*sqrt(-b/a)/(a*d - b*c))/(b*d))/(2*(a*d - b*c)) - sqrt(-b/a)*log(x + (a**4*c*d**3*(-b/a)**(3/2)/(a*d - b*c)**3 - a**3*b*c**2*d**2*(-b/a)**(3/2)/(a*d - b*c)**3 - a**2*b**2*c**3*d*(-b/a)**(3/2)/(a*d - b*c)**3 + a**2*d**2*sqrt(-b/a)/(a*d - b*c) + a*b**3*c**4*(-b/a)**(3/2)/(a*d - b*c)**3 + b**2*c**2*sqrt(-b/a)/(a*d - b*c))/(b*d))/(2*(a*d - b*c)) + sqrt(-d/c)*log(x + (-a**4*c*d**3*(-d/c)**(3/2)/(a*d - b*c)**3 + a**3*b*c**2*d**2*(-d/c)**(3/2)/(a*d - b*c)**3 + a**2*b**2*c**3*d*(-d/c)**(3/2)/(a*d - b*c)**3 - a**2*d**2*sqrt(-d/c)/(a*d - b*c) - a*b**3*c**4*(-d/c)**(3/2)/(a*d - b*c)**3 - b**2*c**2*sqrt(-d/c)/(a*d - b*c))/(b*d))/(2*(a*d - b*c)) - sqrt(-d/c)*log(x + (a**4*c*d**3*(-d/c)**(3/2)/(a*d - b*c)**3 - a**3*b*c**2*d**2*(-d/c)**(3/2)/(a*d - b*c)**3 - a**2*b**2*c**3*d*(-d/c)**(3/2)/(a*d - b*c)**3 + a**2*d**2*sqrt(-d/c)/(a*d - b*c) + a*b**3*c**4*(-d/c)**(3/2)/(a*d - b*c)**3 + b**2*c**2*sqrt(-d/c)/(a*d - b*c))/(b*d))/(2*(a*d - b*c))","B",0
25,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
26,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
27,1,502,0,1.910177," ","integrate((d*x**2+c)**5/(b*x**2+a)**2,x)","x^{5} \left(- \frac{2 a d^{5}}{5 b^{3}} + \frac{c d^{4}}{b^{2}}\right) + x^{3} \left(\frac{a^{2} d^{5}}{b^{4}} - \frac{10 a c d^{4}}{3 b^{3}} + \frac{10 c^{2} d^{3}}{3 b^{2}}\right) + x \left(- \frac{4 a^{3} d^{5}}{b^{5}} + \frac{15 a^{2} c d^{4}}{b^{4}} - \frac{20 a c^{2} d^{3}}{b^{3}} + \frac{10 c^{3} d^{2}}{b^{2}}\right) + \frac{x \left(- a^{5} d^{5} + 5 a^{4} b c d^{4} - 10 a^{3} b^{2} c^{2} d^{3} + 10 a^{2} b^{3} c^{3} d^{2} - 5 a b^{4} c^{4} d + b^{5} c^{5}\right)}{2 a^{2} b^{5} + 2 a b^{6} x^{2}} - \frac{\sqrt{- \frac{1}{a^{3} b^{11}}} \left(a d - b c\right)^{4} \left(9 a d + b c\right) \log{\left(- \frac{a^{2} b^{5} \sqrt{- \frac{1}{a^{3} b^{11}}} \left(a d - b c\right)^{4} \left(9 a d + b c\right)}{9 a^{5} d^{5} - 35 a^{4} b c d^{4} + 50 a^{3} b^{2} c^{2} d^{3} - 30 a^{2} b^{3} c^{3} d^{2} + 5 a b^{4} c^{4} d + b^{5} c^{5}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} b^{11}}} \left(a d - b c\right)^{4} \left(9 a d + b c\right) \log{\left(\frac{a^{2} b^{5} \sqrt{- \frac{1}{a^{3} b^{11}}} \left(a d - b c\right)^{4} \left(9 a d + b c\right)}{9 a^{5} d^{5} - 35 a^{4} b c d^{4} + 50 a^{3} b^{2} c^{2} d^{3} - 30 a^{2} b^{3} c^{3} d^{2} + 5 a b^{4} c^{4} d + b^{5} c^{5}} + x \right)}}{4} + \frac{d^{5} x^{7}}{7 b^{2}}"," ",0,"x**5*(-2*a*d**5/(5*b**3) + c*d**4/b**2) + x**3*(a**2*d**5/b**4 - 10*a*c*d**4/(3*b**3) + 10*c**2*d**3/(3*b**2)) + x*(-4*a**3*d**5/b**5 + 15*a**2*c*d**4/b**4 - 20*a*c**2*d**3/b**3 + 10*c**3*d**2/b**2) + x*(-a**5*d**5 + 5*a**4*b*c*d**4 - 10*a**3*b**2*c**2*d**3 + 10*a**2*b**3*c**3*d**2 - 5*a*b**4*c**4*d + b**5*c**5)/(2*a**2*b**5 + 2*a*b**6*x**2) - sqrt(-1/(a**3*b**11))*(a*d - b*c)**4*(9*a*d + b*c)*log(-a**2*b**5*sqrt(-1/(a**3*b**11))*(a*d - b*c)**4*(9*a*d + b*c)/(9*a**5*d**5 - 35*a**4*b*c*d**4 + 50*a**3*b**2*c**2*d**3 - 30*a**2*b**3*c**3*d**2 + 5*a*b**4*c**4*d + b**5*c**5) + x)/4 + sqrt(-1/(a**3*b**11))*(a*d - b*c)**4*(9*a*d + b*c)*log(a**2*b**5*sqrt(-1/(a**3*b**11))*(a*d - b*c)**4*(9*a*d + b*c)/(9*a**5*d**5 - 35*a**4*b*c*d**4 + 50*a**3*b**2*c**2*d**3 - 30*a**2*b**3*c**3*d**2 + 5*a*b**4*c**4*d + b**5*c**5) + x)/4 + d**5*x**7/(7*b**2)","B",0
28,1,403,0,1.474772," ","integrate((d*x**2+c)**4/(b*x**2+a)**2,x)","x^{3} \left(- \frac{2 a d^{4}}{3 b^{3}} + \frac{4 c d^{3}}{3 b^{2}}\right) + x \left(\frac{3 a^{2} d^{4}}{b^{4}} - \frac{8 a c d^{3}}{b^{3}} + \frac{6 c^{2} d^{2}}{b^{2}}\right) + \frac{x \left(a^{4} d^{4} - 4 a^{3} b c d^{3} + 6 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d + b^{4} c^{4}\right)}{2 a^{2} b^{4} + 2 a b^{5} x^{2}} + \frac{\sqrt{- \frac{1}{a^{3} b^{9}}} \left(a d - b c\right)^{3} \left(7 a d + b c\right) \log{\left(- \frac{a^{2} b^{4} \sqrt{- \frac{1}{a^{3} b^{9}}} \left(a d - b c\right)^{3} \left(7 a d + b c\right)}{7 a^{4} d^{4} - 20 a^{3} b c d^{3} + 18 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d - b^{4} c^{4}} + x \right)}}{4} - \frac{\sqrt{- \frac{1}{a^{3} b^{9}}} \left(a d - b c\right)^{3} \left(7 a d + b c\right) \log{\left(\frac{a^{2} b^{4} \sqrt{- \frac{1}{a^{3} b^{9}}} \left(a d - b c\right)^{3} \left(7 a d + b c\right)}{7 a^{4} d^{4} - 20 a^{3} b c d^{3} + 18 a^{2} b^{2} c^{2} d^{2} - 4 a b^{3} c^{3} d - b^{4} c^{4}} + x \right)}}{4} + \frac{d^{4} x^{5}}{5 b^{2}}"," ",0,"x**3*(-2*a*d**4/(3*b**3) + 4*c*d**3/(3*b**2)) + x*(3*a**2*d**4/b**4 - 8*a*c*d**3/b**3 + 6*c**2*d**2/b**2) + x*(a**4*d**4 - 4*a**3*b*c*d**3 + 6*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d + b**4*c**4)/(2*a**2*b**4 + 2*a*b**5*x**2) + sqrt(-1/(a**3*b**9))*(a*d - b*c)**3*(7*a*d + b*c)*log(-a**2*b**4*sqrt(-1/(a**3*b**9))*(a*d - b*c)**3*(7*a*d + b*c)/(7*a**4*d**4 - 20*a**3*b*c*d**3 + 18*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d - b**4*c**4) + x)/4 - sqrt(-1/(a**3*b**9))*(a*d - b*c)**3*(7*a*d + b*c)*log(a**2*b**4*sqrt(-1/(a**3*b**9))*(a*d - b*c)**3*(7*a*d + b*c)/(7*a**4*d**4 - 20*a**3*b*c*d**3 + 18*a**2*b**2*c**2*d**2 - 4*a*b**3*c**3*d - b**4*c**4) + x)/4 + d**4*x**5/(5*b**2)","B",0
29,1,314,0,1.075114," ","integrate((d*x**2+c)**3/(b*x**2+a)**2,x)","x \left(- \frac{2 a d^{3}}{b^{3}} + \frac{3 c d^{2}}{b^{2}}\right) + \frac{x \left(- a^{3} d^{3} + 3 a^{2} b c d^{2} - 3 a b^{2} c^{2} d + b^{3} c^{3}\right)}{2 a^{2} b^{3} + 2 a b^{4} x^{2}} - \frac{\sqrt{- \frac{1}{a^{3} b^{7}}} \left(a d - b c\right)^{2} \left(5 a d + b c\right) \log{\left(- \frac{a^{2} b^{3} \sqrt{- \frac{1}{a^{3} b^{7}}} \left(a d - b c\right)^{2} \left(5 a d + b c\right)}{5 a^{3} d^{3} - 9 a^{2} b c d^{2} + 3 a b^{2} c^{2} d + b^{3} c^{3}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} b^{7}}} \left(a d - b c\right)^{2} \left(5 a d + b c\right) \log{\left(\frac{a^{2} b^{3} \sqrt{- \frac{1}{a^{3} b^{7}}} \left(a d - b c\right)^{2} \left(5 a d + b c\right)}{5 a^{3} d^{3} - 9 a^{2} b c d^{2} + 3 a b^{2} c^{2} d + b^{3} c^{3}} + x \right)}}{4} + \frac{d^{3} x^{3}}{3 b^{2}}"," ",0,"x*(-2*a*d**3/b**3 + 3*c*d**2/b**2) + x*(-a**3*d**3 + 3*a**2*b*c*d**2 - 3*a*b**2*c**2*d + b**3*c**3)/(2*a**2*b**3 + 2*a*b**4*x**2) - sqrt(-1/(a**3*b**7))*(a*d - b*c)**2*(5*a*d + b*c)*log(-a**2*b**3*sqrt(-1/(a**3*b**7))*(a*d - b*c)**2*(5*a*d + b*c)/(5*a**3*d**3 - 9*a**2*b*c*d**2 + 3*a*b**2*c**2*d + b**3*c**3) + x)/4 + sqrt(-1/(a**3*b**7))*(a*d - b*c)**2*(5*a*d + b*c)*log(a**2*b**3*sqrt(-1/(a**3*b**7))*(a*d - b*c)**2*(5*a*d + b*c)/(5*a**3*d**3 - 9*a**2*b*c*d**2 + 3*a*b**2*c**2*d + b**3*c**3) + x)/4 + d**3*x**3/(3*b**2)","B",0
30,1,236,0,0.722705," ","integrate((d*x**2+c)**2/(b*x**2+a)**2,x)","\frac{x \left(a^{2} d^{2} - 2 a b c d + b^{2} c^{2}\right)}{2 a^{2} b^{2} + 2 a b^{3} x^{2}} + \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right) \left(3 a d + b c\right) \log{\left(- \frac{a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right) \left(3 a d + b c\right)}{3 a^{2} d^{2} - 2 a b c d - b^{2} c^{2}} + x \right)}}{4} - \frac{\sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right) \left(3 a d + b c\right) \log{\left(\frac{a^{2} b^{2} \sqrt{- \frac{1}{a^{3} b^{5}}} \left(a d - b c\right) \left(3 a d + b c\right)}{3 a^{2} d^{2} - 2 a b c d - b^{2} c^{2}} + x \right)}}{4} + \frac{d^{2} x}{b^{2}}"," ",0,"x*(a**2*d**2 - 2*a*b*c*d + b**2*c**2)/(2*a**2*b**2 + 2*a*b**3*x**2) + sqrt(-1/(a**3*b**5))*(a*d - b*c)*(3*a*d + b*c)*log(-a**2*b**2*sqrt(-1/(a**3*b**5))*(a*d - b*c)*(3*a*d + b*c)/(3*a**2*d**2 - 2*a*b*c*d - b**2*c**2) + x)/4 - sqrt(-1/(a**3*b**5))*(a*d - b*c)*(3*a*d + b*c)*log(a**2*b**2*sqrt(-1/(a**3*b**5))*(a*d - b*c)*(3*a*d + b*c)/(3*a**2*d**2 - 2*a*b*c*d - b**2*c**2) + x)/4 + d**2*x/b**2","B",0
31,1,112,0,0.398687," ","integrate((d*x**2+c)/(b*x**2+a)**2,x)","\frac{x \left(- a d + b c\right)}{2 a^{2} b + 2 a b^{2} x^{2}} - \frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \left(a d + b c\right) \log{\left(- a^{2} b \sqrt{- \frac{1}{a^{3} b^{3}}} + x \right)}}{4} + \frac{\sqrt{- \frac{1}{a^{3} b^{3}}} \left(a d + b c\right) \log{\left(a^{2} b \sqrt{- \frac{1}{a^{3} b^{3}}} + x \right)}}{4}"," ",0,"x*(-a*d + b*c)/(2*a**2*b + 2*a*b**2*x**2) - sqrt(-1/(a**3*b**3))*(a*d + b*c)*log(-a**2*b*sqrt(-1/(a**3*b**3)) + x)/4 + sqrt(-1/(a**3*b**3))*(a*d + b*c)*log(a**2*b*sqrt(-1/(a**3*b**3)) + x)/4","B",0
32,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
33,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
34,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
35,1,615,0,4.405519," ","integrate((d*x**2+c)**5/(b*x**2+a)**3,x)","x^{3} \left(- \frac{a d^{5}}{b^{4}} + \frac{5 c d^{4}}{3 b^{3}}\right) + x \left(\frac{6 a^{2} d^{5}}{b^{5}} - \frac{15 a c d^{4}}{b^{4}} + \frac{10 c^{2} d^{3}}{b^{3}}\right) + \frac{\sqrt{- \frac{1}{a^{5} b^{11}}} \left(a d - b c\right)^{3} \left(63 a^{2} d^{2} + 14 a b c d + 3 b^{2} c^{2}\right) \log{\left(- \frac{a^{3} b^{5} \sqrt{- \frac{1}{a^{5} b^{11}}} \left(a d - b c\right)^{3} \left(63 a^{2} d^{2} + 14 a b c d + 3 b^{2} c^{2}\right)}{63 a^{5} d^{5} - 175 a^{4} b c d^{4} + 150 a^{3} b^{2} c^{2} d^{3} - 30 a^{2} b^{3} c^{3} d^{2} - 5 a b^{4} c^{4} d - 3 b^{5} c^{5}} + x \right)}}{16} - \frac{\sqrt{- \frac{1}{a^{5} b^{11}}} \left(a d - b c\right)^{3} \left(63 a^{2} d^{2} + 14 a b c d + 3 b^{2} c^{2}\right) \log{\left(\frac{a^{3} b^{5} \sqrt{- \frac{1}{a^{5} b^{11}}} \left(a d - b c\right)^{3} \left(63 a^{2} d^{2} + 14 a b c d + 3 b^{2} c^{2}\right)}{63 a^{5} d^{5} - 175 a^{4} b c d^{4} + 150 a^{3} b^{2} c^{2} d^{3} - 30 a^{2} b^{3} c^{3} d^{2} - 5 a b^{4} c^{4} d - 3 b^{5} c^{5}} + x \right)}}{16} + \frac{x^{3} \left(17 a^{5} b d^{5} - 65 a^{4} b^{2} c d^{4} + 90 a^{3} b^{3} c^{2} d^{3} - 50 a^{2} b^{4} c^{3} d^{2} + 5 a b^{5} c^{4} d + 3 b^{6} c^{5}\right) + x \left(15 a^{6} d^{5} - 55 a^{5} b c d^{4} + 70 a^{4} b^{2} c^{2} d^{3} - 30 a^{3} b^{3} c^{3} d^{2} - 5 a^{2} b^{4} c^{4} d + 5 a b^{5} c^{5}\right)}{8 a^{4} b^{5} + 16 a^{3} b^{6} x^{2} + 8 a^{2} b^{7} x^{4}} + \frac{d^{5} x^{5}}{5 b^{3}}"," ",0,"x**3*(-a*d**5/b**4 + 5*c*d**4/(3*b**3)) + x*(6*a**2*d**5/b**5 - 15*a*c*d**4/b**4 + 10*c**2*d**3/b**3) + sqrt(-1/(a**5*b**11))*(a*d - b*c)**3*(63*a**2*d**2 + 14*a*b*c*d + 3*b**2*c**2)*log(-a**3*b**5*sqrt(-1/(a**5*b**11))*(a*d - b*c)**3*(63*a**2*d**2 + 14*a*b*c*d + 3*b**2*c**2)/(63*a**5*d**5 - 175*a**4*b*c*d**4 + 150*a**3*b**2*c**2*d**3 - 30*a**2*b**3*c**3*d**2 - 5*a*b**4*c**4*d - 3*b**5*c**5) + x)/16 - sqrt(-1/(a**5*b**11))*(a*d - b*c)**3*(63*a**2*d**2 + 14*a*b*c*d + 3*b**2*c**2)*log(a**3*b**5*sqrt(-1/(a**5*b**11))*(a*d - b*c)**3*(63*a**2*d**2 + 14*a*b*c*d + 3*b**2*c**2)/(63*a**5*d**5 - 175*a**4*b*c*d**4 + 150*a**3*b**2*c**2*d**3 - 30*a**2*b**3*c**3*d**2 - 5*a*b**4*c**4*d - 3*b**5*c**5) + x)/16 + (x**3*(17*a**5*b*d**5 - 65*a**4*b**2*c*d**4 + 90*a**3*b**3*c**2*d**3 - 50*a**2*b**4*c**3*d**2 + 5*a*b**5*c**4*d + 3*b**6*c**5) + x*(15*a**6*d**5 - 55*a**5*b*c*d**4 + 70*a**4*b**2*c**2*d**3 - 30*a**3*b**3*c**3*d**2 - 5*a**2*b**4*c**4*d + 5*a*b**5*c**5))/(8*a**4*b**5 + 16*a**3*b**6*x**2 + 8*a**2*b**7*x**4) + d**5*x**5/(5*b**3)","B",0
36,1,515,0,2.810718," ","integrate((d*x**2+c)**4/(b*x**2+a)**3,x)","x \left(- \frac{3 a d^{4}}{b^{4}} + \frac{4 c d^{3}}{b^{3}}\right) - \frac{\sqrt{- \frac{1}{a^{5} b^{9}}} \left(a d - b c\right)^{2} \left(35 a^{2} d^{2} + 10 a b c d + 3 b^{2} c^{2}\right) \log{\left(- \frac{a^{3} b^{4} \sqrt{- \frac{1}{a^{5} b^{9}}} \left(a d - b c\right)^{2} \left(35 a^{2} d^{2} + 10 a b c d + 3 b^{2} c^{2}\right)}{35 a^{4} d^{4} - 60 a^{3} b c d^{3} + 18 a^{2} b^{2} c^{2} d^{2} + 4 a b^{3} c^{3} d + 3 b^{4} c^{4}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{5} b^{9}}} \left(a d - b c\right)^{2} \left(35 a^{2} d^{2} + 10 a b c d + 3 b^{2} c^{2}\right) \log{\left(\frac{a^{3} b^{4} \sqrt{- \frac{1}{a^{5} b^{9}}} \left(a d - b c\right)^{2} \left(35 a^{2} d^{2} + 10 a b c d + 3 b^{2} c^{2}\right)}{35 a^{4} d^{4} - 60 a^{3} b c d^{3} + 18 a^{2} b^{2} c^{2} d^{2} + 4 a b^{3} c^{3} d + 3 b^{4} c^{4}} + x \right)}}{16} + \frac{x^{3} \left(- 13 a^{4} b d^{4} + 36 a^{3} b^{2} c d^{3} - 30 a^{2} b^{3} c^{2} d^{2} + 4 a b^{4} c^{3} d + 3 b^{5} c^{4}\right) + x \left(- 11 a^{5} d^{4} + 28 a^{4} b c d^{3} - 18 a^{3} b^{2} c^{2} d^{2} - 4 a^{2} b^{3} c^{3} d + 5 a b^{4} c^{4}\right)}{8 a^{4} b^{4} + 16 a^{3} b^{5} x^{2} + 8 a^{2} b^{6} x^{4}} + \frac{d^{4} x^{3}}{3 b^{3}}"," ",0,"x*(-3*a*d**4/b**4 + 4*c*d**3/b**3) - sqrt(-1/(a**5*b**9))*(a*d - b*c)**2*(35*a**2*d**2 + 10*a*b*c*d + 3*b**2*c**2)*log(-a**3*b**4*sqrt(-1/(a**5*b**9))*(a*d - b*c)**2*(35*a**2*d**2 + 10*a*b*c*d + 3*b**2*c**2)/(35*a**4*d**4 - 60*a**3*b*c*d**3 + 18*a**2*b**2*c**2*d**2 + 4*a*b**3*c**3*d + 3*b**4*c**4) + x)/16 + sqrt(-1/(a**5*b**9))*(a*d - b*c)**2*(35*a**2*d**2 + 10*a*b*c*d + 3*b**2*c**2)*log(a**3*b**4*sqrt(-1/(a**5*b**9))*(a*d - b*c)**2*(35*a**2*d**2 + 10*a*b*c*d + 3*b**2*c**2)/(35*a**4*d**4 - 60*a**3*b*c*d**3 + 18*a**2*b**2*c**2*d**2 + 4*a*b**3*c**3*d + 3*b**4*c**4) + x)/16 + (x**3*(-13*a**4*b*d**4 + 36*a**3*b**2*c*d**3 - 30*a**2*b**3*c**2*d**2 + 4*a*b**4*c**3*d + 3*b**5*c**4) + x*(-11*a**5*d**4 + 28*a**4*b*c*d**3 - 18*a**3*b**2*c**2*d**2 - 4*a**2*b**3*c**3*d + 5*a*b**4*c**4))/(8*a**4*b**4 + 16*a**3*b**5*x**2 + 8*a**2*b**6*x**4) + d**4*x**3/(3*b**3)","B",0
37,1,422,0,1.890442," ","integrate((d*x**2+c)**3/(b*x**2+a)**3,x)","\frac{3 \sqrt{- \frac{1}{a^{5} b^{7}}} \left(a d - b c\right) \left(5 a^{2} d^{2} + 2 a b c d + b^{2} c^{2}\right) \log{\left(- \frac{3 a^{3} b^{3} \sqrt{- \frac{1}{a^{5} b^{7}}} \left(a d - b c\right) \left(5 a^{2} d^{2} + 2 a b c d + b^{2} c^{2}\right)}{15 a^{3} d^{3} - 9 a^{2} b c d^{2} - 3 a b^{2} c^{2} d - 3 b^{3} c^{3}} + x \right)}}{16} - \frac{3 \sqrt{- \frac{1}{a^{5} b^{7}}} \left(a d - b c\right) \left(5 a^{2} d^{2} + 2 a b c d + b^{2} c^{2}\right) \log{\left(\frac{3 a^{3} b^{3} \sqrt{- \frac{1}{a^{5} b^{7}}} \left(a d - b c\right) \left(5 a^{2} d^{2} + 2 a b c d + b^{2} c^{2}\right)}{15 a^{3} d^{3} - 9 a^{2} b c d^{2} - 3 a b^{2} c^{2} d - 3 b^{3} c^{3}} + x \right)}}{16} + \frac{x^{3} \left(9 a^{3} b d^{3} - 15 a^{2} b^{2} c d^{2} + 3 a b^{3} c^{2} d + 3 b^{4} c^{3}\right) + x \left(7 a^{4} d^{3} - 9 a^{3} b c d^{2} - 3 a^{2} b^{2} c^{2} d + 5 a b^{3} c^{3}\right)}{8 a^{4} b^{3} + 16 a^{3} b^{4} x^{2} + 8 a^{2} b^{5} x^{4}} + \frac{d^{3} x}{b^{3}}"," ",0,"3*sqrt(-1/(a**5*b**7))*(a*d - b*c)*(5*a**2*d**2 + 2*a*b*c*d + b**2*c**2)*log(-3*a**3*b**3*sqrt(-1/(a**5*b**7))*(a*d - b*c)*(5*a**2*d**2 + 2*a*b*c*d + b**2*c**2)/(15*a**3*d**3 - 9*a**2*b*c*d**2 - 3*a*b**2*c**2*d - 3*b**3*c**3) + x)/16 - 3*sqrt(-1/(a**5*b**7))*(a*d - b*c)*(5*a**2*d**2 + 2*a*b*c*d + b**2*c**2)*log(3*a**3*b**3*sqrt(-1/(a**5*b**7))*(a*d - b*c)*(5*a**2*d**2 + 2*a*b*c*d + b**2*c**2)/(15*a**3*d**3 - 9*a**2*b*c*d**2 - 3*a*b**2*c**2*d - 3*b**3*c**3) + x)/16 + (x**3*(9*a**3*b*d**3 - 15*a**2*b**2*c*d**2 + 3*a*b**3*c**2*d + 3*b**4*c**3) + x*(7*a**4*d**3 - 9*a**3*b*c*d**2 - 3*a**2*b**2*c**2*d + 5*a*b**3*c**3))/(8*a**4*b**3 + 16*a**3*b**4*x**2 + 8*a**2*b**5*x**4) + d**3*x/b**3","B",0
38,1,223,0,1.049296," ","integrate((d*x**2+c)**2/(b*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{5} b^{5}}} \left(3 a^{2} d^{2} + 2 a b c d + 3 b^{2} c^{2}\right) \log{\left(- a^{3} b^{2} \sqrt{- \frac{1}{a^{5} b^{5}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{5} b^{5}}} \left(3 a^{2} d^{2} + 2 a b c d + 3 b^{2} c^{2}\right) \log{\left(a^{3} b^{2} \sqrt{- \frac{1}{a^{5} b^{5}}} + x \right)}}{16} + \frac{x^{3} \left(- 5 a^{2} b d^{2} + 2 a b^{2} c d + 3 b^{3} c^{2}\right) + x \left(- 3 a^{3} d^{2} - 2 a^{2} b c d + 5 a b^{2} c^{2}\right)}{8 a^{4} b^{2} + 16 a^{3} b^{3} x^{2} + 8 a^{2} b^{4} x^{4}}"," ",0,"-sqrt(-1/(a**5*b**5))*(3*a**2*d**2 + 2*a*b*c*d + 3*b**2*c**2)*log(-a**3*b**2*sqrt(-1/(a**5*b**5)) + x)/16 + sqrt(-1/(a**5*b**5))*(3*a**2*d**2 + 2*a*b*c*d + 3*b**2*c**2)*log(a**3*b**2*sqrt(-1/(a**5*b**5)) + x)/16 + (x**3*(-5*a**2*b*d**2 + 2*a*b**2*c*d + 3*b**3*c**2) + x*(-3*a**3*d**2 - 2*a**2*b*c*d + 5*a*b**2*c**2))/(8*a**4*b**2 + 16*a**3*b**3*x**2 + 8*a**2*b**4*x**4)","B",0
39,1,150,0,0.584798," ","integrate((d*x**2+c)/(b*x**2+a)**3,x)","- \frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \left(a d + 3 b c\right) \log{\left(- a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} + x \right)}}{16} + \frac{\sqrt{- \frac{1}{a^{5} b^{3}}} \left(a d + 3 b c\right) \log{\left(a^{3} b \sqrt{- \frac{1}{a^{5} b^{3}}} + x \right)}}{16} + \frac{x^{3} \left(a b d + 3 b^{2} c\right) + x \left(- a^{2} d + 5 a b c\right)}{8 a^{4} b + 16 a^{3} b^{2} x^{2} + 8 a^{2} b^{3} x^{4}}"," ",0,"-sqrt(-1/(a**5*b**3))*(a*d + 3*b*c)*log(-a**3*b*sqrt(-1/(a**5*b**3)) + x)/16 + sqrt(-1/(a**5*b**3))*(a*d + 3*b*c)*log(a**3*b*sqrt(-1/(a**5*b**3)) + x)/16 + (x**3*(a*b*d + 3*b**2*c) + x*(-a**2*d + 5*a*b*c))/(8*a**4*b + 16*a**3*b**2*x**2 + 8*a**2*b**3*x**4)","A",0
40,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**3/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
41,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**3/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**3/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,1,31,0,0.131963," ","integrate((x**2-1)**3/(x**2+1)**4,x)","\frac{- 3 x^{5} - 2 x^{3} - 3 x}{3 x^{6} + 9 x^{4} + 9 x^{2} + 3}"," ",0,"(-3*x**5 - 2*x**3 - 3*x)/(3*x**6 + 9*x**4 + 9*x**2 + 3)","A",0
44,1,46,0,0.172250," ","integrate((x**2-1)**4/(x**2+1)**5,x)","\frac{- 5 x^{7} + 3 x^{5} - 3 x^{3} + 5 x}{8 x^{8} + 32 x^{6} + 48 x^{4} + 32 x^{2} + 8} + \frac{3 \operatorname{atan}{\left(x \right)}}{8}"," ",0,"(-5*x**7 + 3*x**5 - 3*x**3 + 5*x)/(8*x**8 + 32*x**6 + 48*x**4 + 32*x**2 + 8) + 3*atan(x)/8","A",0
45,1,484,0,20.381418," ","integrate((b*x**2+a)**(1/2)*(d*x**2+c)**3,x)","\frac{5 a^{\frac{7}{2}} d^{3} x}{128 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{\frac{5}{2}} c d^{2} x}{16 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 a^{\frac{5}{2}} d^{3} x^{3}}{384 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{\frac{3}{2}} c^{2} d x}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{\frac{3}{2}} c d^{2} x^{3}}{16 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{\frac{3}{2}} d^{3} x^{5}}{192 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{\sqrt{a} c^{3} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{9 \sqrt{a} c^{2} d x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 \sqrt{a} c d^{2} x^{5}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{7 \sqrt{a} d^{3} x^{7}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 a^{4} d^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{7}{2}}} + \frac{3 a^{3} c d^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{5}{2}}} - \frac{3 a^{2} c^{2} d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{3}{2}}} + \frac{a c^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 \sqrt{b}} + \frac{3 b c^{2} d x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b c d^{2} x^{7}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b d^{3} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"5*a**(7/2)*d**3*x/(128*b**3*sqrt(1 + b*x**2/a)) - 3*a**(5/2)*c*d**2*x/(16*b**2*sqrt(1 + b*x**2/a)) + 5*a**(5/2)*d**3*x**3/(384*b**2*sqrt(1 + b*x**2/a)) + 3*a**(3/2)*c**2*d*x/(8*b*sqrt(1 + b*x**2/a)) - a**(3/2)*c*d**2*x**3/(16*b*sqrt(1 + b*x**2/a)) - a**(3/2)*d**3*x**5/(192*b*sqrt(1 + b*x**2/a)) + sqrt(a)*c**3*x*sqrt(1 + b*x**2/a)/2 + 9*sqrt(a)*c**2*d*x**3/(8*sqrt(1 + b*x**2/a)) + 5*sqrt(a)*c*d**2*x**5/(8*sqrt(1 + b*x**2/a)) + 7*sqrt(a)*d**3*x**7/(48*sqrt(1 + b*x**2/a)) - 5*a**4*d**3*asinh(sqrt(b)*x/sqrt(a))/(128*b**(7/2)) + 3*a**3*c*d**2*asinh(sqrt(b)*x/sqrt(a))/(16*b**(5/2)) - 3*a**2*c**2*d*asinh(sqrt(b)*x/sqrt(a))/(8*b**(3/2)) + a*c**3*asinh(sqrt(b)*x/sqrt(a))/(2*sqrt(b)) + 3*b*c**2*d*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + b*c*d**2*x**7/(2*sqrt(a)*sqrt(1 + b*x**2/a)) + b*d**3*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
46,1,291,0,11.393015," ","integrate((b*x**2+a)**(1/2)*(d*x**2+c)**2,x)","- \frac{a^{\frac{5}{2}} d^{2} x}{16 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{\frac{3}{2}} c d x}{4 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{\frac{3}{2}} d^{2} x^{3}}{48 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{\sqrt{a} c^{2} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{3 \sqrt{a} c d x^{3}}{4 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 \sqrt{a} d^{2} x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{3} d^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{5}{2}}} - \frac{a^{2} c d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{4 b^{\frac{3}{2}}} + \frac{a c^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 \sqrt{b}} + \frac{b c d x^{5}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b d^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-a**(5/2)*d**2*x/(16*b**2*sqrt(1 + b*x**2/a)) + a**(3/2)*c*d*x/(4*b*sqrt(1 + b*x**2/a)) - a**(3/2)*d**2*x**3/(48*b*sqrt(1 + b*x**2/a)) + sqrt(a)*c**2*x*sqrt(1 + b*x**2/a)/2 + 3*sqrt(a)*c*d*x**3/(4*sqrt(1 + b*x**2/a)) + 5*sqrt(a)*d**2*x**5/(24*sqrt(1 + b*x**2/a)) + a**3*d**2*asinh(sqrt(b)*x/sqrt(a))/(16*b**(5/2)) - a**2*c*d*asinh(sqrt(b)*x/sqrt(a))/(4*b**(3/2)) + a*c**2*asinh(sqrt(b)*x/sqrt(a))/(2*sqrt(b)) + b*c*d*x**5/(2*sqrt(a)*sqrt(1 + b*x**2/a)) + b*d**2*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
47,1,144,0,5.680645," ","integrate((b*x**2+a)**(1/2)*(d*x**2+c),x)","\frac{a^{\frac{3}{2}} d x}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{\sqrt{a} c x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{3 \sqrt{a} d x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{2} d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{3}{2}}} + \frac{a c \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 \sqrt{b}} + \frac{b d x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"a**(3/2)*d*x/(8*b*sqrt(1 + b*x**2/a)) + sqrt(a)*c*x*sqrt(1 + b*x**2/a)/2 + 3*sqrt(a)*d*x**3/(8*sqrt(1 + b*x**2/a)) - a**2*d*asinh(sqrt(b)*x/sqrt(a))/(8*b**(3/2)) + a*c*asinh(sqrt(b)*x/sqrt(a))/(2*sqrt(b)) + b*d*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
48,1,41,0,1.855427," ","integrate((b*x**2+a)**(1/2),x)","\frac{\sqrt{a} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{a \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 \sqrt{b}}"," ",0,"sqrt(a)*x*sqrt(1 + b*x**2/a)/2 + a*asinh(sqrt(b)*x/sqrt(a))/(2*sqrt(b))","A",0
49,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(d*x**2+c),x)","\int \frac{\sqrt{a + b x^{2}}}{c + d x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/(c + d*x**2), x)","F",0
50,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(d*x**2+c)**2,x)","\int \frac{\sqrt{a + b x^{2}}}{\left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/(c + d*x**2)**2, x)","F",0
51,-1,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
52,-1,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(d*x**2+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
53,1,665,0,52.752559," ","integrate((b*x**2+a)**(3/2)*(d*x**2+c)**3,x)","\frac{3 a^{\frac{9}{2}} d^{3} x}{256 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{9 a^{\frac{7}{2}} c d^{2} x}{128 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{\frac{7}{2}} d^{3} x^{3}}{256 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{\frac{5}{2}} c^{2} d x}{16 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{\frac{5}{2}} c d^{2} x^{3}}{128 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{\frac{5}{2}} d^{3} x^{5}}{640 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{\frac{3}{2}} c^{3} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{a^{\frac{3}{2}} c^{3} x}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} c^{2} d x^{3}}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{39 a^{\frac{3}{2}} c d^{2} x^{5}}{64 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{23 a^{\frac{3}{2}} d^{3} x^{7}}{160 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 \sqrt{a} b c^{3} x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{11 \sqrt{a} b c^{2} d x^{5}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{15 \sqrt{a} b c d^{2} x^{7}}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{19 \sqrt{a} b d^{3} x^{9}}{80 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{5} d^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{256 b^{\frac{7}{2}}} + \frac{9 a^{4} c d^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{5}{2}}} - \frac{3 a^{3} c^{2} d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{3}{2}}} + \frac{3 a^{2} c^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 \sqrt{b}} + \frac{b^{2} c^{3} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b^{2} c^{2} d x^{7}}{2 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 b^{2} c d^{2} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b^{2} d^{3} x^{11}}{10 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"3*a**(9/2)*d**3*x/(256*b**3*sqrt(1 + b*x**2/a)) - 9*a**(7/2)*c*d**2*x/(128*b**2*sqrt(1 + b*x**2/a)) + a**(7/2)*d**3*x**3/(256*b**2*sqrt(1 + b*x**2/a)) + 3*a**(5/2)*c**2*d*x/(16*b*sqrt(1 + b*x**2/a)) - 3*a**(5/2)*c*d**2*x**3/(128*b*sqrt(1 + b*x**2/a)) - a**(5/2)*d**3*x**5/(640*b*sqrt(1 + b*x**2/a)) + a**(3/2)*c**3*x*sqrt(1 + b*x**2/a)/2 + a**(3/2)*c**3*x/(8*sqrt(1 + b*x**2/a)) + 17*a**(3/2)*c**2*d*x**3/(16*sqrt(1 + b*x**2/a)) + 39*a**(3/2)*c*d**2*x**5/(64*sqrt(1 + b*x**2/a)) + 23*a**(3/2)*d**3*x**7/(160*sqrt(1 + b*x**2/a)) + 3*sqrt(a)*b*c**3*x**3/(8*sqrt(1 + b*x**2/a)) + 11*sqrt(a)*b*c**2*d*x**5/(8*sqrt(1 + b*x**2/a)) + 15*sqrt(a)*b*c*d**2*x**7/(16*sqrt(1 + b*x**2/a)) + 19*sqrt(a)*b*d**3*x**9/(80*sqrt(1 + b*x**2/a)) - 3*a**5*d**3*asinh(sqrt(b)*x/sqrt(a))/(256*b**(7/2)) + 9*a**4*c*d**2*asinh(sqrt(b)*x/sqrt(a))/(128*b**(5/2)) - 3*a**3*c**2*d*asinh(sqrt(b)*x/sqrt(a))/(16*b**(3/2)) + 3*a**2*c**3*asinh(sqrt(b)*x/sqrt(a))/(8*sqrt(b)) + b**2*c**3*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + b**2*c**2*d*x**7/(2*sqrt(a)*sqrt(1 + b*x**2/a)) + 3*b**2*c*d**2*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a)) + b**2*d**3*x**11/(10*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
54,1,440,0,29.419179," ","integrate((b*x**2+a)**(3/2)*(d*x**2+c)**2,x)","- \frac{3 a^{\frac{7}{2}} d^{2} x}{128 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{\frac{5}{2}} c d x}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{\frac{5}{2}} d^{2} x^{3}}{128 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{\frac{3}{2}} c^{2} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{a^{\frac{3}{2}} c^{2} x}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} c d x^{3}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{13 a^{\frac{3}{2}} d^{2} x^{5}}{64 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 \sqrt{a} b c^{2} x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{11 \sqrt{a} b c d x^{5}}{12 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 \sqrt{a} b d^{2} x^{7}}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{4} d^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{5}{2}}} - \frac{a^{3} c d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{3}{2}}} + \frac{3 a^{2} c^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 \sqrt{b}} + \frac{b^{2} c^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b^{2} c d x^{7}}{3 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b^{2} d^{2} x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-3*a**(7/2)*d**2*x/(128*b**2*sqrt(1 + b*x**2/a)) + a**(5/2)*c*d*x/(8*b*sqrt(1 + b*x**2/a)) - a**(5/2)*d**2*x**3/(128*b*sqrt(1 + b*x**2/a)) + a**(3/2)*c**2*x*sqrt(1 + b*x**2/a)/2 + a**(3/2)*c**2*x/(8*sqrt(1 + b*x**2/a)) + 17*a**(3/2)*c*d*x**3/(24*sqrt(1 + b*x**2/a)) + 13*a**(3/2)*d**2*x**5/(64*sqrt(1 + b*x**2/a)) + 3*sqrt(a)*b*c**2*x**3/(8*sqrt(1 + b*x**2/a)) + 11*sqrt(a)*b*c*d*x**5/(12*sqrt(1 + b*x**2/a)) + 5*sqrt(a)*b*d**2*x**7/(16*sqrt(1 + b*x**2/a)) + 3*a**4*d**2*asinh(sqrt(b)*x/sqrt(a))/(128*b**(5/2)) - a**3*c*d*asinh(sqrt(b)*x/sqrt(a))/(8*b**(3/2)) + 3*a**2*c**2*asinh(sqrt(b)*x/sqrt(a))/(8*sqrt(b)) + b**2*c**2*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + b**2*c*d*x**7/(3*sqrt(a)*sqrt(1 + b*x**2/a)) + b**2*d**2*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
55,1,253,0,14.711877," ","integrate((b*x**2+a)**(3/2)*(d*x**2+c),x)","\frac{a^{\frac{5}{2}} d x}{16 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{\frac{3}{2}} c x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{a^{\frac{3}{2}} c x}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{17 a^{\frac{3}{2}} d x^{3}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 \sqrt{a} b c x^{3}}{8 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{11 \sqrt{a} b d x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{3} d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{3}{2}}} + \frac{3 a^{2} c \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 \sqrt{b}} + \frac{b^{2} c x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b^{2} d x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"a**(5/2)*d*x/(16*b*sqrt(1 + b*x**2/a)) + a**(3/2)*c*x*sqrt(1 + b*x**2/a)/2 + a**(3/2)*c*x/(8*sqrt(1 + b*x**2/a)) + 17*a**(3/2)*d*x**3/(48*sqrt(1 + b*x**2/a)) + 3*sqrt(a)*b*c*x**3/(8*sqrt(1 + b*x**2/a)) + 11*sqrt(a)*b*d*x**5/(24*sqrt(1 + b*x**2/a)) - a**3*d*asinh(sqrt(b)*x/sqrt(a))/(16*b**(3/2)) + 3*a**2*c*asinh(sqrt(b)*x/sqrt(a))/(8*sqrt(b)) + b**2*c*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + b**2*d*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
56,1,70,0,2.914761," ","integrate((b*x**2+a)**(3/2),x)","\frac{5 a^{\frac{3}{2}} x \sqrt{1 + \frac{b x^{2}}{a}}}{8} + \frac{\sqrt{a} b x^{3} \sqrt{1 + \frac{b x^{2}}{a}}}{4} + \frac{3 a^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 \sqrt{b}}"," ",0,"5*a**(3/2)*x*sqrt(1 + b*x**2/a)/8 + sqrt(a)*b*x**3*sqrt(1 + b*x**2/a)/4 + 3*a**2*asinh(sqrt(b)*x/sqrt(a))/(8*sqrt(b))","A",0
57,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/(d*x**2+c),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{c + d x^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)/(c + d*x**2), x)","F",0
58,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/(d*x**2+c)**2,x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{\left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)/(c + d*x**2)**2, x)","F",0
59,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/(d*x**2+c)**3,x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{\left(c + d x^{2}\right)^{3}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)/(c + d*x**2)**3, x)","F",0
60,-1,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/(d*x**2+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
61,-1,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/(d*x**2+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
62,1,796,0,102.666344," ","integrate((b*x**2+a)**(5/2)*(d*x**2+c)**3,x)","\frac{5 a^{\frac{11}{2}} d^{3} x}{1024 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{9 a^{\frac{9}{2}} c d^{2} x}{256 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 a^{\frac{9}{2}} d^{3} x^{3}}{3072 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{15 a^{\frac{7}{2}} c^{2} d x}{128 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{3 a^{\frac{7}{2}} c d^{2} x^{3}}{256 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{\frac{7}{2}} d^{3} x^{5}}{1536 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{\frac{5}{2}} c^{3} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{3 a^{\frac{5}{2}} c^{3} x}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{133 a^{\frac{5}{2}} c^{2} d x^{3}}{128 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{387 a^{\frac{5}{2}} c d^{2} x^{5}}{640 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{55 a^{\frac{5}{2}} d^{3} x^{7}}{384 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{35 a^{\frac{3}{2}} b c^{3} x^{3}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{127 a^{\frac{3}{2}} b c^{2} d x^{5}}{64 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{219 a^{\frac{3}{2}} b c d^{2} x^{7}}{160 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{67 a^{\frac{3}{2}} b d^{3} x^{9}}{192 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{17 \sqrt{a} b^{2} c^{3} x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{23 \sqrt{a} b^{2} c^{2} d x^{7}}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{87 \sqrt{a} b^{2} c d^{2} x^{9}}{80 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{7 \sqrt{a} b^{2} d^{3} x^{11}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 a^{6} d^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{1024 b^{\frac{7}{2}}} + \frac{9 a^{5} c d^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{256 b^{\frac{5}{2}}} - \frac{15 a^{4} c^{2} d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{3}{2}}} + \frac{5 a^{3} c^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 \sqrt{b}} + \frac{b^{3} c^{3} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 b^{3} c^{2} d x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 b^{3} c d^{2} x^{11}}{10 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b^{3} d^{3} x^{13}}{12 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"5*a**(11/2)*d**3*x/(1024*b**3*sqrt(1 + b*x**2/a)) - 9*a**(9/2)*c*d**2*x/(256*b**2*sqrt(1 + b*x**2/a)) + 5*a**(9/2)*d**3*x**3/(3072*b**2*sqrt(1 + b*x**2/a)) + 15*a**(7/2)*c**2*d*x/(128*b*sqrt(1 + b*x**2/a)) - 3*a**(7/2)*c*d**2*x**3/(256*b*sqrt(1 + b*x**2/a)) - a**(7/2)*d**3*x**5/(1536*b*sqrt(1 + b*x**2/a)) + a**(5/2)*c**3*x*sqrt(1 + b*x**2/a)/2 + 3*a**(5/2)*c**3*x/(16*sqrt(1 + b*x**2/a)) + 133*a**(5/2)*c**2*d*x**3/(128*sqrt(1 + b*x**2/a)) + 387*a**(5/2)*c*d**2*x**5/(640*sqrt(1 + b*x**2/a)) + 55*a**(5/2)*d**3*x**7/(384*sqrt(1 + b*x**2/a)) + 35*a**(3/2)*b*c**3*x**3/(48*sqrt(1 + b*x**2/a)) + 127*a**(3/2)*b*c**2*d*x**5/(64*sqrt(1 + b*x**2/a)) + 219*a**(3/2)*b*c*d**2*x**7/(160*sqrt(1 + b*x**2/a)) + 67*a**(3/2)*b*d**3*x**9/(192*sqrt(1 + b*x**2/a)) + 17*sqrt(a)*b**2*c**3*x**5/(24*sqrt(1 + b*x**2/a)) + 23*sqrt(a)*b**2*c**2*d*x**7/(16*sqrt(1 + b*x**2/a)) + 87*sqrt(a)*b**2*c*d**2*x**9/(80*sqrt(1 + b*x**2/a)) + 7*sqrt(a)*b**2*d**3*x**11/(24*sqrt(1 + b*x**2/a)) - 5*a**6*d**3*asinh(sqrt(b)*x/sqrt(a))/(1024*b**(7/2)) + 9*a**5*c*d**2*asinh(sqrt(b)*x/sqrt(a))/(256*b**(5/2)) - 15*a**4*c**2*d*asinh(sqrt(b)*x/sqrt(a))/(128*b**(3/2)) + 5*a**3*c**3*asinh(sqrt(b)*x/sqrt(a))/(16*sqrt(b)) + b**3*c**3*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a)) + 3*b**3*c**2*d*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a)) + 3*b**3*c*d**2*x**11/(10*sqrt(a)*sqrt(1 + b*x**2/a)) + b**3*d**3*x**13/(12*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
63,1,537,0,58.629679," ","integrate((b*x**2+a)**(5/2)*(d*x**2+c)**2,x)","- \frac{3 a^{\frac{9}{2}} d^{2} x}{256 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 a^{\frac{7}{2}} c d x}{64 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{a^{\frac{7}{2}} d^{2} x^{3}}{256 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{\frac{5}{2}} c^{2} x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{3 a^{\frac{5}{2}} c^{2} x}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{133 a^{\frac{5}{2}} c d x^{3}}{192 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{129 a^{\frac{5}{2}} d^{2} x^{5}}{640 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{35 a^{\frac{3}{2}} b c^{2} x^{3}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{127 a^{\frac{3}{2}} b c d x^{5}}{96 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{73 a^{\frac{3}{2}} b d^{2} x^{7}}{160 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{17 \sqrt{a} b^{2} c^{2} x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{23 \sqrt{a} b^{2} c d x^{7}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{29 \sqrt{a} b^{2} d^{2} x^{9}}{80 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{5} d^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{256 b^{\frac{5}{2}}} - \frac{5 a^{4} c d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{64 b^{\frac{3}{2}}} + \frac{5 a^{3} c^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 \sqrt{b}} + \frac{b^{3} c^{2} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b^{3} c d x^{9}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b^{3} d^{2} x^{11}}{10 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-3*a**(9/2)*d**2*x/(256*b**2*sqrt(1 + b*x**2/a)) + 5*a**(7/2)*c*d*x/(64*b*sqrt(1 + b*x**2/a)) - a**(7/2)*d**2*x**3/(256*b*sqrt(1 + b*x**2/a)) + a**(5/2)*c**2*x*sqrt(1 + b*x**2/a)/2 + 3*a**(5/2)*c**2*x/(16*sqrt(1 + b*x**2/a)) + 133*a**(5/2)*c*d*x**3/(192*sqrt(1 + b*x**2/a)) + 129*a**(5/2)*d**2*x**5/(640*sqrt(1 + b*x**2/a)) + 35*a**(3/2)*b*c**2*x**3/(48*sqrt(1 + b*x**2/a)) + 127*a**(3/2)*b*c*d*x**5/(96*sqrt(1 + b*x**2/a)) + 73*a**(3/2)*b*d**2*x**7/(160*sqrt(1 + b*x**2/a)) + 17*sqrt(a)*b**2*c**2*x**5/(24*sqrt(1 + b*x**2/a)) + 23*sqrt(a)*b**2*c*d*x**7/(24*sqrt(1 + b*x**2/a)) + 29*sqrt(a)*b**2*d**2*x**9/(80*sqrt(1 + b*x**2/a)) + 3*a**5*d**2*asinh(sqrt(b)*x/sqrt(a))/(256*b**(5/2)) - 5*a**4*c*d*asinh(sqrt(b)*x/sqrt(a))/(64*b**(3/2)) + 5*a**3*c**2*asinh(sqrt(b)*x/sqrt(a))/(16*sqrt(b)) + b**3*c**2*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a)) + b**3*c*d*x**9/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + b**3*d**2*x**11/(10*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
64,1,316,0,29.528319," ","integrate((b*x**2+a)**(5/2)*(d*x**2+c),x)","\frac{5 a^{\frac{7}{2}} d x}{128 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{a^{\frac{5}{2}} c x \sqrt{1 + \frac{b x^{2}}{a}}}{2} + \frac{3 a^{\frac{5}{2}} c x}{16 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{133 a^{\frac{5}{2}} d x^{3}}{384 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{35 a^{\frac{3}{2}} b c x^{3}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{127 a^{\frac{3}{2}} b d x^{5}}{192 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{17 \sqrt{a} b^{2} c x^{5}}{24 \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{23 \sqrt{a} b^{2} d x^{7}}{48 \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 a^{4} d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{128 b^{\frac{3}{2}}} + \frac{5 a^{3} c \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 \sqrt{b}} + \frac{b^{3} c x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{b^{3} d x^{9}}{8 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"5*a**(7/2)*d*x/(128*b*sqrt(1 + b*x**2/a)) + a**(5/2)*c*x*sqrt(1 + b*x**2/a)/2 + 3*a**(5/2)*c*x/(16*sqrt(1 + b*x**2/a)) + 133*a**(5/2)*d*x**3/(384*sqrt(1 + b*x**2/a)) + 35*a**(3/2)*b*c*x**3/(48*sqrt(1 + b*x**2/a)) + 127*a**(3/2)*b*d*x**5/(192*sqrt(1 + b*x**2/a)) + 17*sqrt(a)*b**2*c*x**5/(24*sqrt(1 + b*x**2/a)) + 23*sqrt(a)*b**2*d*x**7/(48*sqrt(1 + b*x**2/a)) - 5*a**4*d*asinh(sqrt(b)*x/sqrt(a))/(128*b**(3/2)) + 5*a**3*c*asinh(sqrt(b)*x/sqrt(a))/(16*sqrt(b)) + b**3*c*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a)) + b**3*d*x**9/(8*sqrt(a)*sqrt(1 + b*x**2/a))","B",0
65,1,97,0,4.281717," ","integrate((b*x**2+a)**(5/2),x)","\frac{11 a^{\frac{5}{2}} x \sqrt{1 + \frac{b x^{2}}{a}}}{16} + \frac{13 a^{\frac{3}{2}} b x^{3} \sqrt{1 + \frac{b x^{2}}{a}}}{24} + \frac{\sqrt{a} b^{2} x^{5} \sqrt{1 + \frac{b x^{2}}{a}}}{6} + \frac{5 a^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 \sqrt{b}}"," ",0,"11*a**(5/2)*x*sqrt(1 + b*x**2/a)/16 + 13*a**(3/2)*b*x**3*sqrt(1 + b*x**2/a)/24 + sqrt(a)*b**2*x**5*sqrt(1 + b*x**2/a)/6 + 5*a**3*asinh(sqrt(b)*x/sqrt(a))/(16*sqrt(b))","A",0
66,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/(d*x**2+c),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{2}}}{c + d x^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(5/2)/(c + d*x**2), x)","F",0
67,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/(d*x**2+c)**2,x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{2}}}{\left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(5/2)/(c + d*x**2)**2, x)","F",0
68,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/(d*x**2+c)**3,x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{2}}}{\left(c + d x^{2}\right)^{3}}\, dx"," ",0,"Integral((a + b*x**2)**(5/2)/(c + d*x**2)**3, x)","F",0
69,-1,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/(d*x**2+c)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
70,-1,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/(d*x**2+c)**5,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
71,0,0,0,0.000000," ","integrate((-x**2+1)**(1/2)/(x**2+1),x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}{x^{2} + 1}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1))/(x**2 + 1), x)","F",0
72,0,0,0,0.000000," ","integrate((x**2+1)**(1/2)/(x**2-1),x)","\int \frac{\sqrt{x^{2} + 1}}{\left(x - 1\right) \left(x + 1\right)}\, dx"," ",0,"Integral(sqrt(x**2 + 1)/((x - 1)*(x + 1)), x)","F",0
73,0,0,0,0.000000," ","integrate((-x**2+1)**(1/2)/(2*x**2-1),x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}{2 x^{2} - 1}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1))/(2*x**2 - 1), x)","F",0
74,1,400,0,13.273396," ","integrate((d*x**2+c)**3/(b*x**2+a)**(1/2),x)","\frac{5 a^{\frac{5}{2}} d^{3} x}{16 b^{3} \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{9 a^{\frac{3}{2}} c d^{2} x}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{5 a^{\frac{3}{2}} d^{3} x^{3}}{48 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 \sqrt{a} c^{2} d x \sqrt{1 + \frac{b x^{2}}{a}}}{2 b} - \frac{3 \sqrt{a} c d^{2} x^{3}}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{\sqrt{a} d^{3} x^{5}}{24 b \sqrt{1 + \frac{b x^{2}}{a}}} - \frac{5 a^{3} d^{3} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{16 b^{\frac{7}{2}}} + \frac{9 a^{2} c d^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} - \frac{3 a c^{2} d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} + c^{3} \left(\begin{cases} \frac{\sqrt{- \frac{a}{b}} \operatorname{asin}{\left(x \sqrt{- \frac{b}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge b < 0 \\\frac{\sqrt{\frac{a}{b}} \operatorname{asinh}{\left(x \sqrt{\frac{b}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge b > 0 \\\frac{\sqrt{- \frac{a}{b}} \operatorname{acosh}{\left(x \sqrt{- \frac{b}{a}} \right)}}{\sqrt{- a}} & \text{for}\: b > 0 \wedge a < 0 \end{cases}\right) + \frac{3 c d^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{d^{3} x^{7}}{6 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"5*a**(5/2)*d**3*x/(16*b**3*sqrt(1 + b*x**2/a)) - 9*a**(3/2)*c*d**2*x/(8*b**2*sqrt(1 + b*x**2/a)) + 5*a**(3/2)*d**3*x**3/(48*b**2*sqrt(1 + b*x**2/a)) + 3*sqrt(a)*c**2*d*x*sqrt(1 + b*x**2/a)/(2*b) - 3*sqrt(a)*c*d**2*x**3/(8*b*sqrt(1 + b*x**2/a)) - sqrt(a)*d**3*x**5/(24*b*sqrt(1 + b*x**2/a)) - 5*a**3*d**3*asinh(sqrt(b)*x/sqrt(a))/(16*b**(7/2)) + 9*a**2*c*d**2*asinh(sqrt(b)*x/sqrt(a))/(8*b**(5/2)) - 3*a*c**2*d*asinh(sqrt(b)*x/sqrt(a))/(2*b**(3/2)) + c**3*Piecewise((sqrt(-a/b)*asin(x*sqrt(-b/a))/sqrt(a), (a > 0) & (b < 0)), (sqrt(a/b)*asinh(x*sqrt(b/a))/sqrt(a), (a > 0) & (b > 0)), (sqrt(-a/b)*acosh(x*sqrt(-b/a))/sqrt(-a), (b > 0) & (a < 0))) + 3*c*d**2*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a)) + d**3*x**7/(6*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
75,1,238,0,6.942552," ","integrate((d*x**2+c)**2/(b*x**2+a)**(1/2),x)","- \frac{3 a^{\frac{3}{2}} d^{2} x}{8 b^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{\sqrt{a} c d x \sqrt{1 + \frac{b x^{2}}{a}}}{b} - \frac{\sqrt{a} d^{2} x^{3}}{8 b \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{3 a^{2} d^{2} \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{8 b^{\frac{5}{2}}} - \frac{a c d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{b^{\frac{3}{2}}} + c^{2} \left(\begin{cases} \frac{\sqrt{- \frac{a}{b}} \operatorname{asin}{\left(x \sqrt{- \frac{b}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge b < 0 \\\frac{\sqrt{\frac{a}{b}} \operatorname{asinh}{\left(x \sqrt{\frac{b}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge b > 0 \\\frac{\sqrt{- \frac{a}{b}} \operatorname{acosh}{\left(x \sqrt{- \frac{b}{a}} \right)}}{\sqrt{- a}} & \text{for}\: b > 0 \wedge a < 0 \end{cases}\right) + \frac{d^{2} x^{5}}{4 \sqrt{a} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"-3*a**(3/2)*d**2*x/(8*b**2*sqrt(1 + b*x**2/a)) + sqrt(a)*c*d*x*sqrt(1 + b*x**2/a)/b - sqrt(a)*d**2*x**3/(8*b*sqrt(1 + b*x**2/a)) + 3*a**2*d**2*asinh(sqrt(b)*x/sqrt(a))/(8*b**(5/2)) - a*c*d*asinh(sqrt(b)*x/sqrt(a))/b**(3/2) + c**2*Piecewise((sqrt(-a/b)*asin(x*sqrt(-b/a))/sqrt(a), (a > 0) & (b < 0)), (sqrt(a/b)*asinh(x*sqrt(b/a))/sqrt(a), (a > 0) & (b > 0)), (sqrt(-a/b)*acosh(x*sqrt(-b/a))/sqrt(-a), (b > 0) & (a < 0))) + d**2*x**5/(4*sqrt(a)*sqrt(1 + b*x**2/a))","A",0
76,1,126,0,2.780250," ","integrate((d*x**2+c)/(b*x**2+a)**(1/2),x)","\frac{\sqrt{a} d x \sqrt{1 + \frac{b x^{2}}{a}}}{2 b} - \frac{a d \operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{2 b^{\frac{3}{2}}} + c \left(\begin{cases} \frac{\sqrt{- \frac{a}{b}} \operatorname{asin}{\left(x \sqrt{- \frac{b}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge b < 0 \\\frac{\sqrt{\frac{a}{b}} \operatorname{asinh}{\left(x \sqrt{\frac{b}{a}} \right)}}{\sqrt{a}} & \text{for}\: a > 0 \wedge b > 0 \\\frac{\sqrt{- \frac{a}{b}} \operatorname{acosh}{\left(x \sqrt{- \frac{b}{a}} \right)}}{\sqrt{- a}} & \text{for}\: b > 0 \wedge a < 0 \end{cases}\right)"," ",0,"sqrt(a)*d*x*sqrt(1 + b*x**2/a)/(2*b) - a*d*asinh(sqrt(b)*x/sqrt(a))/(2*b**(3/2)) + c*Piecewise((sqrt(-a/b)*asin(x*sqrt(-b/a))/sqrt(a), (a > 0) & (b < 0)), (sqrt(a/b)*asinh(x*sqrt(b/a))/sqrt(a), (a > 0) & (b > 0)), (sqrt(-a/b)*acosh(x*sqrt(-b/a))/sqrt(-a), (b > 0) & (a < 0)))","A",0
77,1,17,0,0.997159," ","integrate(1/(b*x**2+a)**(1/2),x)","\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{\sqrt{b}}"," ",0,"asinh(sqrt(b)*x/sqrt(a))/sqrt(b)","A",0
78,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/2)/(d*x**2+c),x)","\int \frac{1}{\sqrt{a + b x^{2}} \left(c + d x^{2}\right)}\, dx"," ",0,"Integral(1/(sqrt(a + b*x**2)*(c + d*x**2)), x)","F",0
79,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/2)/(d*x**2+c)**2,x)","\int \frac{1}{\sqrt{a + b x^{2}} \left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x**2)*(c + d*x**2)**2), x)","F",0
80,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/2)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
81,0,0,0,0.000000," ","integrate((d*x**2+c)**4/(b*x**2+a)**(3/2),x)","\int \frac{\left(c + d x^{2}\right)^{4}}{\left(a + b x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x**2)**4/(a + b*x**2)**(3/2), x)","F",0
82,0,0,0,0.000000," ","integrate((d*x**2+c)**3/(b*x**2+a)**(3/2),x)","\int \frac{\left(c + d x^{2}\right)^{3}}{\left(a + b x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x**2)**3/(a + b*x**2)**(3/2), x)","F",0
83,0,0,0,0.000000," ","integrate((d*x**2+c)**2/(b*x**2+a)**(3/2),x)","\int \frac{\left(c + d x^{2}\right)^{2}}{\left(a + b x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x**2)**2/(a + b*x**2)**(3/2), x)","F",0
84,1,60,0,5.167940," ","integrate((d*x**2+c)/(b*x**2+a)**(3/2),x)","d \left(\frac{\operatorname{asinh}{\left(\frac{\sqrt{b} x}{\sqrt{a}} \right)}}{b^{\frac{3}{2}}} - \frac{x}{\sqrt{a} b \sqrt{1 + \frac{b x^{2}}{a}}}\right) + \frac{c x}{a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"d*(asinh(sqrt(b)*x/sqrt(a))/b**(3/2) - x/(sqrt(a)*b*sqrt(1 + b*x**2/a))) + c*x/(a**(3/2)*sqrt(1 + b*x**2/a))","A",0
85,1,17,0,0.613756," ","integrate(1/(b*x**2+a)**(3/2),x)","\frac{x}{a^{\frac{3}{2}} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"x/(a**(3/2)*sqrt(1 + b*x**2/a))","A",0
86,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(3/2)/(d*x**2+c),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{3}{2}} \left(c + d x^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*x**2)**(3/2)*(c + d*x**2)), x)","F",0
87,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(3/2)/(d*x**2+c)**2,x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{3}{2}} \left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(3/2)*(c + d*x**2)**2), x)","F",0
88,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**(3/2)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
89,0,0,0,0.000000," ","integrate((d*x**2+c)**4/(b*x**2+a)**(5/2),x)","\int \frac{\left(c + d x^{2}\right)^{4}}{\left(a + b x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*x**2)**4/(a + b*x**2)**(5/2), x)","F",0
90,0,0,0,0.000000," ","integrate((d*x**2+c)**3/(b*x**2+a)**(5/2),x)","\int \frac{\left(c + d x^{2}\right)^{3}}{\left(a + b x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*x**2)**3/(a + b*x**2)**(5/2), x)","F",0
91,0,0,0,0.000000," ","integrate((d*x**2+c)**2/(b*x**2+a)**(5/2),x)","\int \frac{\left(c + d x^{2}\right)^{2}}{\left(a + b x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*x**2)**2/(a + b*x**2)**(5/2), x)","F",0
92,1,144,0,11.029748," ","integrate((d*x**2+c)/(b*x**2+a)**(5/2),x)","c \left(\frac{3 a x}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{5}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{2 b x^{3}}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{5}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}\right) + \frac{d x^{3}}{3 a^{\frac{5}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{3}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"c*(3*a*x/(3*a**(7/2)*sqrt(1 + b*x**2/a) + 3*a**(5/2)*b*x**2*sqrt(1 + b*x**2/a)) + 2*b*x**3/(3*a**(7/2)*sqrt(1 + b*x**2/a) + 3*a**(5/2)*b*x**2*sqrt(1 + b*x**2/a))) + d*x**3/(3*a**(5/2)*sqrt(1 + b*x**2/a) + 3*a**(3/2)*b*x**2*sqrt(1 + b*x**2/a))","B",0
93,1,95,0,0.821489," ","integrate(1/(b*x**2+a)**(5/2),x)","\frac{3 a x}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{5}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}} + \frac{2 b x^{3}}{3 a^{\frac{7}{2}} \sqrt{1 + \frac{b x^{2}}{a}} + 3 a^{\frac{5}{2}} b x^{2} \sqrt{1 + \frac{b x^{2}}{a}}}"," ",0,"3*a*x/(3*a**(7/2)*sqrt(1 + b*x**2/a) + 3*a**(5/2)*b*x**2*sqrt(1 + b*x**2/a)) + 2*b*x**3/(3*a**(7/2)*sqrt(1 + b*x**2/a) + 3*a**(5/2)*b*x**2*sqrt(1 + b*x**2/a))","B",0
94,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(5/2)/(d*x**2+c),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{5}{2}} \left(c + d x^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*x**2)**(5/2)*(c + d*x**2)), x)","F",0
95,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(5/2)/(d*x**2+c)**2,x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{5}{2}} \left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(5/2)*(c + d*x**2)**2), x)","F",0
96,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**(5/2)/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
97,-1,0,0,0.000000," ","integrate((b*x**2+a)**3/(d*x**2+c)**(11/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
98,0,0,0,0.000000," ","integrate((b*x**2+a)**2/(d*x**2+c)**(9/2),x)","\int \frac{\left(a + b x^{2}\right)^{2}}{\left(c + d x^{2}\right)^{\frac{9}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**2/(c + d*x**2)**(9/2), x)","F",0
99,1,566,0,27.985673," ","integrate((b*x**2+a)/(d*x**2+c)**(7/2),x)","a \left(\frac{15 c^{5} x}{15 c^{\frac{17}{2}} \sqrt{1 + \frac{d x^{2}}{c}} + 45 c^{\frac{15}{2}} d x^{2} \sqrt{1 + \frac{d x^{2}}{c}} + 45 c^{\frac{13}{2}} d^{2} x^{4} \sqrt{1 + \frac{d x^{2}}{c}} + 15 c^{\frac{11}{2}} d^{3} x^{6} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{35 c^{4} d x^{3}}{15 c^{\frac{17}{2}} \sqrt{1 + \frac{d x^{2}}{c}} + 45 c^{\frac{15}{2}} d x^{2} \sqrt{1 + \frac{d x^{2}}{c}} + 45 c^{\frac{13}{2}} d^{2} x^{4} \sqrt{1 + \frac{d x^{2}}{c}} + 15 c^{\frac{11}{2}} d^{3} x^{6} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{28 c^{3} d^{2} x^{5}}{15 c^{\frac{17}{2}} \sqrt{1 + \frac{d x^{2}}{c}} + 45 c^{\frac{15}{2}} d x^{2} \sqrt{1 + \frac{d x^{2}}{c}} + 45 c^{\frac{13}{2}} d^{2} x^{4} \sqrt{1 + \frac{d x^{2}}{c}} + 15 c^{\frac{11}{2}} d^{3} x^{6} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{8 c^{2} d^{3} x^{7}}{15 c^{\frac{17}{2}} \sqrt{1 + \frac{d x^{2}}{c}} + 45 c^{\frac{15}{2}} d x^{2} \sqrt{1 + \frac{d x^{2}}{c}} + 45 c^{\frac{13}{2}} d^{2} x^{4} \sqrt{1 + \frac{d x^{2}}{c}} + 15 c^{\frac{11}{2}} d^{3} x^{6} \sqrt{1 + \frac{d x^{2}}{c}}}\right) + b \left(\frac{5 c x^{3}}{15 c^{\frac{9}{2}} \sqrt{1 + \frac{d x^{2}}{c}} + 30 c^{\frac{7}{2}} d x^{2} \sqrt{1 + \frac{d x^{2}}{c}} + 15 c^{\frac{5}{2}} d^{2} x^{4} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{2 d x^{5}}{15 c^{\frac{9}{2}} \sqrt{1 + \frac{d x^{2}}{c}} + 30 c^{\frac{7}{2}} d x^{2} \sqrt{1 + \frac{d x^{2}}{c}} + 15 c^{\frac{5}{2}} d^{2} x^{4} \sqrt{1 + \frac{d x^{2}}{c}}}\right)"," ",0,"a*(15*c**5*x/(15*c**(17/2)*sqrt(1 + d*x**2/c) + 45*c**(15/2)*d*x**2*sqrt(1 + d*x**2/c) + 45*c**(13/2)*d**2*x**4*sqrt(1 + d*x**2/c) + 15*c**(11/2)*d**3*x**6*sqrt(1 + d*x**2/c)) + 35*c**4*d*x**3/(15*c**(17/2)*sqrt(1 + d*x**2/c) + 45*c**(15/2)*d*x**2*sqrt(1 + d*x**2/c) + 45*c**(13/2)*d**2*x**4*sqrt(1 + d*x**2/c) + 15*c**(11/2)*d**3*x**6*sqrt(1 + d*x**2/c)) + 28*c**3*d**2*x**5/(15*c**(17/2)*sqrt(1 + d*x**2/c) + 45*c**(15/2)*d*x**2*sqrt(1 + d*x**2/c) + 45*c**(13/2)*d**2*x**4*sqrt(1 + d*x**2/c) + 15*c**(11/2)*d**3*x**6*sqrt(1 + d*x**2/c)) + 8*c**2*d**3*x**7/(15*c**(17/2)*sqrt(1 + d*x**2/c) + 45*c**(15/2)*d*x**2*sqrt(1 + d*x**2/c) + 45*c**(13/2)*d**2*x**4*sqrt(1 + d*x**2/c) + 15*c**(11/2)*d**3*x**6*sqrt(1 + d*x**2/c))) + b*(5*c*x**3/(15*c**(9/2)*sqrt(1 + d*x**2/c) + 30*c**(7/2)*d*x**2*sqrt(1 + d*x**2/c) + 15*c**(5/2)*d**2*x**4*sqrt(1 + d*x**2/c)) + 2*d*x**5/(15*c**(9/2)*sqrt(1 + d*x**2/c) + 30*c**(7/2)*d*x**2*sqrt(1 + d*x**2/c) + 15*c**(5/2)*d**2*x**4*sqrt(1 + d*x**2/c)))","B",0
100,1,95,0,0.826283," ","integrate(1/(d*x**2+c)**(5/2),x)","\frac{3 c x}{3 c^{\frac{7}{2}} \sqrt{1 + \frac{d x^{2}}{c}} + 3 c^{\frac{5}{2}} d x^{2} \sqrt{1 + \frac{d x^{2}}{c}}} + \frac{2 d x^{3}}{3 c^{\frac{7}{2}} \sqrt{1 + \frac{d x^{2}}{c}} + 3 c^{\frac{5}{2}} d x^{2} \sqrt{1 + \frac{d x^{2}}{c}}}"," ",0,"3*c*x/(3*c**(7/2)*sqrt(1 + d*x**2/c) + 3*c**(5/2)*d*x**2*sqrt(1 + d*x**2/c)) + 2*d*x**3/(3*c**(7/2)*sqrt(1 + d*x**2/c) + 3*c**(5/2)*d*x**2*sqrt(1 + d*x**2/c))","B",0
101,0,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)**(3/2),x)","\int \frac{1}{\left(a + b x^{2}\right) \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)*(c + d*x**2)**(3/2)), x)","F",0
102,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**2/(d*x**2+c)**(1/2),x)","\int \frac{1}{\left(a + b x^{2}\right)^{2} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)**2*sqrt(c + d*x**2)), x)","F",0
103,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/(b*x**2+a)**3,x)","\int \frac{\sqrt{c + d x^{2}}}{\left(a + b x^{2}\right)^{3}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(a + b*x**2)**3, x)","F",0
104,-1,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/(b*x**2+a)**4,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
105,0,0,0,0.000000," ","integrate(1/(b*c/d+b*x**2)/(d*x**2+c)**(1/2),x)","\frac{d \int \frac{1}{c \sqrt{c + d x^{2}} + d x^{2} \sqrt{c + d x^{2}}}\, dx}{b}"," ",0,"d*Integral(1/(c*sqrt(c + d*x**2) + d*x**2*sqrt(c + d*x**2)), x)/b","F",0
106,0,0,0,0.000000," ","integrate(1/(x**2+1)/(-x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 1\right)}\, dx"," ",0,"Integral(1/(sqrt(-(x - 1)*(x + 1))*(x**2 + 1)), x)","F",0
107,0,0,0,0.000000," ","integrate(1/(b*x**2+a)/(d*x**2+c)**(1/2),x)","\int \frac{1}{\left(a + b x^{2}\right) \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
108,1,31,0,4.680851," ","integrate((x**2-1)/(x**2+1)**(3/2),x)","\frac{x^{2} \operatorname{asinh}{\left(x \right)}}{x^{2} + 1} - \frac{2 x}{\sqrt{x^{2} + 1}} + \frac{\operatorname{asinh}{\left(x \right)}}{x^{2} + 1}"," ",0,"x**2*asinh(x)/(x**2 + 1) - 2*x/sqrt(x**2 + 1) + asinh(x)/(x**2 + 1)","B",0
109,1,136,0,4.373725," ","integrate((-b*x**2+a)**(2/3)*(b*x**2+3*a)**3,x)","27 a^{\frac{11}{3}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + 9 a^{\frac{8}{3}} b x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + \frac{9 a^{\frac{5}{3}} b^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5} + \frac{a^{\frac{2}{3}} b^{3} x^{7} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{7}"," ",0,"27*a**(11/3)*x*hyper((-2/3, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a) + 9*a**(8/3)*b*x**3*hyper((-2/3, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a) + 9*a**(5/3)*b**2*x**5*hyper((-2/3, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/5 + a**(2/3)*b**3*x**7*hyper((-2/3, 7/2), (9/2,), b*x**2*exp_polar(2*I*pi)/a)/7","A",0
110,1,99,0,3.298132," ","integrate((-b*x**2+a)**(2/3)*(b*x**2+3*a)**2,x)","9 a^{\frac{8}{3}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + 2 a^{\frac{5}{3}} b x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + \frac{a^{\frac{2}{3}} b^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5}"," ",0,"9*a**(8/3)*x*hyper((-2/3, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a) + 2*a**(5/3)*b*x**3*hyper((-2/3, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a) + a**(2/3)*b**2*x**5*hyper((-2/3, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/5","A",0
111,1,63,0,2.427655," ","integrate((-b*x**2+a)**(2/3)*(b*x**2+3*a),x)","3 a^{\frac{5}{3}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + \frac{a^{\frac{2}{3}} b x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3}"," ",0,"3*a**(5/3)*x*hyper((-2/3, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a) + a**(2/3)*b*x**3*hyper((-2/3, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a)/3","A",0
112,0,0,0,0.000000," ","integrate((-b*x**2+a)**(2/3)/(b*x**2+3*a),x)","\int \frac{\left(a - b x^{2}\right)^{\frac{2}{3}}}{3 a + b x^{2}}\, dx"," ",0,"Integral((a - b*x**2)**(2/3)/(3*a + b*x**2), x)","F",0
113,0,0,0,0.000000," ","integrate((-b*x**2+a)**(2/3)/(b*x**2+3*a)**2,x)","\int \frac{\left(a - b x^{2}\right)^{\frac{2}{3}}}{\left(3 a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((a - b*x**2)**(2/3)/(3*a + b*x**2)**2, x)","F",0
114,0,0,0,0.000000," ","integrate((-b*x**2+a)**(2/3)/(b*x**2+3*a)**3,x)","\int \frac{\left(a - b x^{2}\right)^{\frac{2}{3}}}{\left(3 a + b x^{2}\right)^{3}}\, dx"," ",0,"Integral((a - b*x**2)**(2/3)/(3*a + b*x**2)**3, x)","F",0
115,0,0,0,0.000000," ","integrate((-b*x**2+a)**(2/3)/(b*x**2+3*a)**4,x)","\int \frac{\left(a - b x^{2}\right)^{\frac{2}{3}}}{\left(3 a + b x^{2}\right)^{4}}\, dx"," ",0,"Integral((a - b*x**2)**(2/3)/(3*a + b*x**2)**4, x)","F",0
116,1,139,0,5.589499," ","integrate((-b*x**2+a)**(5/3)*(b*x**2+3*a)**3,x)","27 a^{\frac{14}{3}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} - \frac{18 a^{\frac{8}{3}} b^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5} - \frac{8 a^{\frac{5}{3}} b^{3} x^{7} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{7} - \frac{a^{\frac{2}{3}} b^{4} x^{9} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{9}{2} \\ \frac{11}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{9}"," ",0,"27*a**(14/3)*x*hyper((-2/3, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a) - 18*a**(8/3)*b**2*x**5*hyper((-2/3, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/5 - 8*a**(5/3)*b**3*x**7*hyper((-2/3, 7/2), (9/2,), b*x**2*exp_polar(2*I*pi)/a)/7 - a**(2/3)*b**4*x**9*hyper((-2/3, 9/2), (11/2,), b*x**2*exp_polar(2*I*pi)/a)/9","A",0
117,1,131,0,4.895092," ","integrate((-b*x**2+a)**(5/3)*(b*x**2+3*a)**2,x)","9 a^{\frac{11}{3}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} - a^{\frac{8}{3}} b x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} - a^{\frac{5}{3}} b^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} - \frac{a^{\frac{2}{3}} b^{3} x^{7} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{7}"," ",0,"9*a**(11/3)*x*hyper((-2/3, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a) - a**(8/3)*b*x**3*hyper((-2/3, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a) - a**(5/3)*b**2*x**5*hyper((-2/3, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a) - a**(2/3)*b**3*x**7*hyper((-2/3, 7/2), (9/2,), b*x**2*exp_polar(2*I*pi)/a)/7","A",0
118,1,100,0,3.687917," ","integrate((-b*x**2+a)**(5/3)*(b*x**2+3*a),x)","3 a^{\frac{8}{3}} x {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} - \frac{2 a^{\frac{5}{3}} b x^{3} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3} - \frac{a^{\frac{2}{3}} b^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} - \frac{2}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5}"," ",0,"3*a**(8/3)*x*hyper((-2/3, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a) - 2*a**(5/3)*b*x**3*hyper((-2/3, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a)/3 - a**(2/3)*b**2*x**5*hyper((-2/3, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/5","A",0
119,0,0,0,0.000000," ","integrate((-b*x**2+a)**(5/3)/(b*x**2+3*a),x)","\int \frac{\left(a - b x^{2}\right)^{\frac{5}{3}}}{3 a + b x^{2}}\, dx"," ",0,"Integral((a - b*x**2)**(5/3)/(3*a + b*x**2), x)","F",0
120,0,0,0,0.000000," ","integrate((-b*x**2+a)**(5/3)/(b*x**2+3*a)**2,x)","\int \frac{\left(a - b x^{2}\right)^{\frac{5}{3}}}{\left(3 a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral((a - b*x**2)**(5/3)/(3*a + b*x**2)**2, x)","F",0
121,0,0,0,0.000000," ","integrate((-b*x**2+a)**(5/3)/(b*x**2+3*a)**3,x)","\int \frac{\left(a - b x^{2}\right)^{\frac{5}{3}}}{\left(3 a + b x^{2}\right)^{3}}\, dx"," ",0,"Integral((a - b*x**2)**(5/3)/(3*a + b*x**2)**3, x)","F",0
122,1,165,0,5.403935," ","integrate((b*x**2+3*a)**4/(-b*x**2+a)**(1/3),x)","81 a^{\frac{11}{3}} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + 36 a^{\frac{8}{3}} b x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + \frac{54 a^{\frac{5}{3}} b^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5} + \frac{12 a^{\frac{2}{3}} b^{3} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{7} + \frac{b^{4} x^{9} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{9}{2} \\ \frac{11}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{9 \sqrt[3]{a}}"," ",0,"81*a**(11/3)*x*hyper((1/3, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a) + 36*a**(8/3)*b*x**3*hyper((1/3, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a) + 54*a**(5/3)*b**2*x**5*hyper((1/3, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/5 + 12*a**(2/3)*b**3*x**7*hyper((1/3, 7/2), (9/2,), b*x**2*exp_polar(2*I*pi)/a)/7 + b**4*x**9*hyper((1/3, 9/2), (11/2,), b*x**2*exp_polar(2*I*pi)/a)/(9*a**(1/3))","A",0
123,1,129,0,4.378762," ","integrate((b*x**2+3*a)**3/(-b*x**2+a)**(1/3),x)","27 a^{\frac{8}{3}} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + 9 a^{\frac{5}{3}} b x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + \frac{9 a^{\frac{2}{3}} b^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5} + \frac{b^{3} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{7}{2} \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{7 \sqrt[3]{a}}"," ",0,"27*a**(8/3)*x*hyper((1/3, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a) + 9*a**(5/3)*b*x**3*hyper((1/3, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a) + 9*a**(2/3)*b**2*x**5*hyper((1/3, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/5 + b**3*x**7*hyper((1/3, 7/2), (9/2,), b*x**2*exp_polar(2*I*pi)/a)/(7*a**(1/3))","A",0
124,1,94,0,3.346555," ","integrate((b*x**2+3*a)**2/(-b*x**2+a)**(1/3),x)","9 a^{\frac{5}{3}} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + 2 a^{\frac{2}{3}} b x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + \frac{b^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{5}{2} \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{5 \sqrt[3]{a}}"," ",0,"9*a**(5/3)*x*hyper((1/3, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a) + 2*a**(2/3)*b*x**3*hyper((1/3, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a) + b**2*x**5*hyper((1/3, 5/2), (7/2,), b*x**2*exp_polar(2*I*pi)/a)/(5*a**(1/3))","A",0
125,1,60,0,2.007791," ","integrate((b*x**2+3*a)/(-b*x**2+a)**(1/3),x)","3 a^{\frac{2}{3}} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{1}{2} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)} + \frac{b x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3 \sqrt[3]{a}}"," ",0,"3*a**(2/3)*x*hyper((1/3, 1/2), (3/2,), b*x**2*exp_polar(2*I*pi)/a) + b*x**3*hyper((1/3, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a)/(3*a**(1/3))","A",0
126,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(1/3)/(b*x**2+3*a),x)","\int \frac{1}{\sqrt[3]{a - b x^{2}} \left(3 a + b x^{2}\right)}\, dx"," ",0,"Integral(1/((a - b*x**2)**(1/3)*(3*a + b*x**2)), x)","F",0
127,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(1/3)/(b*x**2+3*a)**2,x)","\int \frac{1}{\sqrt[3]{a - b x^{2}} \left(3 a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((a - b*x**2)**(1/3)*(3*a + b*x**2)**2), x)","F",0
128,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(1/3)/(b*x**2+3*a)**3,x)","\int \frac{1}{\sqrt[3]{a - b x^{2}} \left(3 a + b x^{2}\right)^{3}}\, dx"," ",0,"Integral(1/((a - b*x**2)**(1/3)*(3*a + b*x**2)**3), x)","F",0
129,0,0,0,0.000000," ","integrate((b*x**2+3*a)**3/(-b*x**2+a)**(4/3),x)","\int \frac{\left(3 a + b x^{2}\right)^{3}}{\left(a - b x^{2}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((3*a + b*x**2)**3/(a - b*x**2)**(4/3), x)","F",0
130,0,0,0,0.000000," ","integrate((b*x**2+3*a)**2/(-b*x**2+a)**(4/3),x)","\int \frac{\left(3 a + b x^{2}\right)^{2}}{\left(a - b x^{2}\right)^{\frac{4}{3}}}\, dx"," ",0,"Integral((3*a + b*x**2)**2/(a - b*x**2)**(4/3), x)","F",0
131,1,60,0,6.868987," ","integrate((b*x**2+3*a)/(-b*x**2+a)**(4/3),x)","\frac{3 x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{4}{3} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{\sqrt[3]{a}} + \frac{b x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{4}{3}, \frac{3}{2} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3 a^{\frac{4}{3}}}"," ",0,"3*x*hyper((1/2, 4/3), (3/2,), b*x**2*exp_polar(2*I*pi)/a)/a**(1/3) + b*x**3*hyper((4/3, 3/2), (5/2,), b*x**2*exp_polar(2*I*pi)/a)/(3*a**(4/3))","A",0
132,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(4/3)/(b*x**2+3*a),x)","\int \frac{1}{\left(a - b x^{2}\right)^{\frac{4}{3}} \left(3 a + b x^{2}\right)}\, dx"," ",0,"Integral(1/((a - b*x**2)**(4/3)*(3*a + b*x**2)), x)","F",0
133,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(4/3)/(b*x**2+3*a)**2,x)","\int \frac{1}{\left(a - b x^{2}\right)^{\frac{4}{3}} \left(3 a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((a - b*x**2)**(4/3)*(3*a + b*x**2)**2), x)","F",0
134,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(4/3)/(b*x**2+3*a)**3,x)","\int \frac{1}{\left(a - b x^{2}\right)^{\frac{4}{3}} \left(3 a + b x^{2}\right)^{3}}\, dx"," ",0,"Integral(1/((a - b*x**2)**(4/3)*(3*a + b*x**2)**3), x)","F",0
135,0,0,0,0.000000," ","integrate((b*x**2+3*a)**4/(-b*x**2+a)**(7/3),x)","\int \frac{\left(3 a + b x^{2}\right)^{4}}{\left(a - b x^{2}\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral((3*a + b*x**2)**4/(a - b*x**2)**(7/3), x)","F",0
136,0,0,0,0.000000," ","integrate((b*x**2+3*a)**3/(-b*x**2+a)**(7/3),x)","\int \frac{\left(3 a + b x^{2}\right)^{3}}{\left(a - b x^{2}\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral((3*a + b*x**2)**3/(a - b*x**2)**(7/3), x)","F",0
137,0,0,0,0.000000," ","integrate((b*x**2+3*a)**2/(-b*x**2+a)**(7/3),x)","\int \frac{\left(3 a + b x^{2}\right)^{2}}{\left(a - b x^{2}\right)^{\frac{7}{3}}}\, dx"," ",0,"Integral((3*a + b*x**2)**2/(a - b*x**2)**(7/3), x)","F",0
138,1,60,0,12.989542," ","integrate((b*x**2+3*a)/(-b*x**2+a)**(7/3),x)","\frac{3 x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, \frac{7}{3} \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{a^{\frac{4}{3}}} + \frac{b x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, \frac{7}{3} \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{2 i \pi}}{a}} \right)}}{3 a^{\frac{7}{3}}}"," ",0,"3*x*hyper((1/2, 7/3), (3/2,), b*x**2*exp_polar(2*I*pi)/a)/a**(4/3) + b*x**3*hyper((3/2, 7/3), (5/2,), b*x**2*exp_polar(2*I*pi)/a)/(3*a**(7/3))","A",0
139,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(7/3)/(b*x**2+3*a),x)","\int \frac{1}{\left(a - b x^{2}\right)^{\frac{7}{3}} \left(3 a + b x^{2}\right)}\, dx"," ",0,"Integral(1/((a - b*x**2)**(7/3)*(3*a + b*x**2)), x)","F",0
140,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(7/3)/(b*x**2+3*a)**2,x)","\int \frac{1}{\left(a - b x^{2}\right)^{\frac{7}{3}} \left(3 a + b x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((a - b*x**2)**(7/3)*(3*a + b*x**2)**2), x)","F",0
141,0,0,0,0.000000," ","integrate(1/(-b*x**2-3*a)/(b*x**2-a)**(1/3),x)","- \int \frac{1}{3 a \sqrt[3]{- a + b x^{2}} + b x^{2} \sqrt[3]{- a + b x^{2}}}\, dx"," ",0,"-Integral(1/(3*a*(-a + b*x**2)**(1/3) + b*x**2*(-a + b*x**2)**(1/3)), x)","F",0
142,0,0,0,0.000000," ","integrate(1/(-b*x**2+3*a)/(b*x**2+a)**(1/3),x)","- \int \frac{1}{- 3 a \sqrt[3]{a + b x^{2}} + b x^{2} \sqrt[3]{a + b x^{2}}}\, dx"," ",0,"-Integral(1/(-3*a*(a + b*x**2)**(1/3) + b*x**2*(a + b*x**2)**(1/3)), x)","F",0
143,0,0,0,0.000000," ","integrate(1/(-d*x**2+c)/(3*d*x**2+c)**(1/3),x)","- \int \frac{1}{- c \sqrt[3]{c + 3 d x^{2}} + d x^{2} \sqrt[3]{c + 3 d x^{2}}}\, dx"," ",0,"-Integral(1/(-c*(c + 3*d*x**2)**(1/3) + d*x**2*(c + 3*d*x**2)**(1/3)), x)","F",0
144,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(1/3)/(b*x**2+3*a),x)","\int \frac{1}{\sqrt[3]{a - b x^{2}} \left(3 a + b x^{2}\right)}\, dx"," ",0,"Integral(1/((a - b*x**2)**(1/3)*(3*a + b*x**2)), x)","F",0
145,0,0,0,0.000000," ","integrate(1/(-3*d*x**2+c)**(1/3)/(d*x**2+c),x)","\int \frac{1}{\sqrt[3]{c - 3 d x^{2}} \left(c + d x^{2}\right)}\, dx"," ",0,"Integral(1/((c - 3*d*x**2)**(1/3)*(c + d*x**2)), x)","F",0
146,0,0,0,0.000000," ","integrate(1/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{1}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral(1/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
147,0,0,0,0.000000," ","integrate(1/(-x**2+3)/(x**2+1)**(1/3),x)","- \int \frac{1}{x^{2} \sqrt[3]{x^{2} + 1} - 3 \sqrt[3]{x^{2} + 1}}\, dx"," ",0,"-Integral(1/(x**2*(x**2 + 1)**(1/3) - 3*(x**2 + 1)**(1/3)), x)","F",0
148,0,0,0,0.000000," ","integrate((3-x)/(-x**2+1)**(1/3)/(x**2+3),x)","- \int \frac{x}{x^{2} \sqrt[3]{1 - x^{2}} + 3 \sqrt[3]{1 - x^{2}}}\, dx - \int \left(- \frac{3}{x^{2} \sqrt[3]{1 - x^{2}} + 3 \sqrt[3]{1 - x^{2}}}\right)\, dx"," ",0,"-Integral(x/(x**2*(1 - x**2)**(1/3) + 3*(1 - x**2)**(1/3)), x) - Integral(-3/(x**2*(1 - x**2)**(1/3) + 3*(1 - x**2)**(1/3)), x)","F",0
149,0,0,0,0.000000," ","integrate((3+x)/(-x**2+1)**(1/3)/(x**2+3),x)","\int \frac{x + 3}{\sqrt[3]{- \left(x - 1\right) \left(x + 1\right)} \left(x^{2} + 3\right)}\, dx"," ",0,"Integral((x + 3)/((-(x - 1)*(x + 1))**(1/3)*(x**2 + 3)), x)","F",0
150,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/3)/(9*a*d/b+d*x**2),x)","\frac{b \int \frac{1}{9 a \sqrt[3]{a + b x^{2}} + b x^{2} \sqrt[3]{a + b x^{2}}}\, dx}{d}"," ",0,"b*Integral(1/(9*a*(a + b*x**2)**(1/3) + b*x**2*(a + b*x**2)**(1/3)), x)/d","F",0
151,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(1/3)/(-9*a*d/b+d*x**2),x)","\frac{b \int \frac{1}{- 9 a \sqrt[3]{a - b x^{2}} + b x^{2} \sqrt[3]{a - b x^{2}}}\, dx}{d}"," ",0,"b*Integral(1/(-9*a*(a - b*x**2)**(1/3) + b*x**2*(a - b*x**2)**(1/3)), x)/d","F",0
152,0,0,0,0.000000," ","integrate(1/(b*x**2-a)**(1/3)/(-9*a*d/b+d*x**2),x)","\frac{b \int \frac{1}{- 9 a \sqrt[3]{- a + b x^{2}} + b x^{2} \sqrt[3]{- a + b x^{2}}}\, dx}{d}"," ",0,"b*Integral(1/(-9*a*(-a + b*x**2)**(1/3) + b*x**2*(-a + b*x**2)**(1/3)), x)/d","F",0
153,0,0,0,0.000000," ","integrate(1/(-b*x**2-a)**(1/3)/(9*a*d/b+d*x**2),x)","\frac{b \int \frac{1}{9 a \sqrt[3]{- a - b x^{2}} + b x^{2} \sqrt[3]{- a - b x^{2}}}\, dx}{d}"," ",0,"b*Integral(1/(9*a*(-a - b*x**2)**(1/3) + b*x**2*(-a - b*x**2)**(1/3)), x)/d","F",0
154,0,0,0,0.000000," ","integrate(1/(b*x**2+2)**(1/3)/(18*d/b+d*x**2),x)","\frac{b \int \frac{1}{b x^{2} \sqrt[3]{b x^{2} + 2} + 18 \sqrt[3]{b x^{2} + 2}}\, dx}{d}"," ",0,"b*Integral(1/(b*x**2*(b*x**2 + 2)**(1/3) + 18*(b*x**2 + 2)**(1/3)), x)/d","F",0
155,0,0,0,0.000000," ","integrate(1/(b*x**2-2)**(1/3)/(-18*d/b+d*x**2),x)","\frac{b \int \frac{1}{b x^{2} \sqrt[3]{b x^{2} - 2} - 18 \sqrt[3]{b x^{2} - 2}}\, dx}{d}"," ",0,"b*Integral(1/(b*x**2*(b*x**2 - 2)**(1/3) - 18*(b*x**2 - 2)**(1/3)), x)/d","F",0
156,0,0,0,0.000000," ","integrate(1/(3*x**2+2)**(1/3)/(d*x**2+6*d),x)","\frac{\int \frac{1}{x^{2} \sqrt[3]{3 x^{2} + 2} + 6 \sqrt[3]{3 x^{2} + 2}}\, dx}{d}"," ",0,"Integral(1/(x**2*(3*x**2 + 2)**(1/3) + 6*(3*x**2 + 2)**(1/3)), x)/d","F",0
157,0,0,0,0.000000," ","integrate(1/(-3*x**2+2)**(1/3)/(d*x**2-6*d),x)","\frac{\int \frac{1}{x^{2} \sqrt[3]{2 - 3 x^{2}} - 6 \sqrt[3]{2 - 3 x^{2}}}\, dx}{d}"," ",0,"Integral(1/(x**2*(2 - 3*x**2)**(1/3) - 6*(2 - 3*x**2)**(1/3)), x)/d","F",0
158,0,0,0,0.000000," ","integrate(1/(3*x**2-2)**(1/3)/(d*x**2-6*d),x)","\frac{\int \frac{1}{x^{2} \sqrt[3]{3 x^{2} - 2} - 6 \sqrt[3]{3 x^{2} - 2}}\, dx}{d}"," ",0,"Integral(1/(x**2*(3*x**2 - 2)**(1/3) - 6*(3*x**2 - 2)**(1/3)), x)/d","F",0
159,0,0,0,0.000000," ","integrate(1/(-3*x**2-2)**(1/3)/(d*x**2+6*d),x)","\frac{\int \frac{1}{x^{2} \sqrt[3]{- 3 x^{2} - 2} + 6 \sqrt[3]{- 3 x^{2} - 2}}\, dx}{d}"," ",0,"Integral(1/(x**2*(-3*x**2 - 2)**(1/3) + 6*(-3*x**2 - 2)**(1/3)), x)/d","F",0
160,0,0,0,0.000000," ","integrate(1/(x**2+1)**(1/3)/(x**2+9),x)","\int \frac{1}{\sqrt[3]{x^{2} + 1} \left(x^{2} + 9\right)}\, dx"," ",0,"Integral(1/((x**2 + 1)**(1/3)*(x**2 + 9)), x)","F",0
161,0,0,0,0.000000," ","integrate(1/(b*x**2+1)**(1/3)/(b*x**2+9),x)","\int \frac{1}{\sqrt[3]{b x^{2} + 1} \left(b x^{2} + 9\right)}\, dx"," ",0,"Integral(1/((b*x**2 + 1)**(1/3)*(b*x**2 + 9)), x)","F",0
162,0,0,0,0.000000," ","integrate(1/(-x**2+1)**(1/3)/(-x**2+9),x)","- \int \frac{1}{x^{2} \sqrt[3]{1 - x^{2}} - 9 \sqrt[3]{1 - x^{2}}}\, dx"," ",0,"-Integral(1/(x**2*(1 - x**2)**(1/3) - 9*(1 - x**2)**(1/3)), x)","F",0
163,0,0,0,0.000000," ","integrate((c**2*x**2-1)**(1/2)/(-c**2*d*x**2+d)**(5/2),x)","\int \frac{\sqrt{\left(c x - 1\right) \left(c x + 1\right)}}{\left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt((c*x - 1)*(c*x + 1))/(-d*(c*x - 1)*(c*x + 1))**(5/2), x)","F",0
164,0,0,0,0.000000," ","integrate(1/(c**2*x**2-1)**(3/2)/(-c**2*d*x**2+d)**(1/2),x)","\int \frac{1}{\left(\left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}} \sqrt{- d \left(c x - 1\right) \left(c x + 1\right)}}\, dx"," ",0,"Integral(1/(((c*x - 1)*(c*x + 1))**(3/2)*sqrt(-d*(c*x - 1)*(c*x + 1))), x)","F",0
165,0,0,0,0.000000," ","integrate(1/(c**2*x**2-1)**(1/2)/(-c**2*d*x**2+d)**(3/2),x)","\int \frac{1}{\sqrt{\left(c x - 1\right) \left(c x + 1\right)} \left(- d \left(c x - 1\right) \left(c x + 1\right)\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt((c*x - 1)*(c*x + 1))*(-d*(c*x - 1)*(c*x + 1))**(3/2)), x)","F",0
166,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)*(d*x**2+c)**(1/2),x)","\int \left(a + b x^{2}\right)^{\frac{3}{2}} \sqrt{c + d x^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)*sqrt(c + d*x**2), x)","F",0
167,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)*(d*x**2+c)**(1/2),x)","\int \sqrt{a + b x^{2}} \sqrt{c + d x^{2}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)*sqrt(c + d*x**2), x)","F",0
168,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/(b*x**2+a)**(1/2),x)","\int \frac{\sqrt{c + d x^{2}}}{\sqrt{a + b x^{2}}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/sqrt(a + b*x**2), x)","F",0
169,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/(b*x**2+a)**(3/2),x)","\int \frac{\sqrt{c + d x^{2}}}{\left(a + b x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(a + b*x**2)**(3/2), x)","F",0
170,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/(b*x**2+a)**(5/2),x)","\int \frac{\sqrt{c + d x^{2}}}{\left(a + b x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(a + b*x**2)**(5/2), x)","F",0
171,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/(b*x**2+a)**(7/2),x)","\int \frac{\sqrt{c + d x^{2}}}{\left(a + b x^{2}\right)^{\frac{7}{2}}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/(a + b*x**2)**(7/2), x)","F",0
172,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)*(d*x**2+c)**(3/2),x)","\int \left(a + b x^{2}\right)^{\frac{3}{2}} \left(c + d x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)*(c + d*x**2)**(3/2), x)","F",0
173,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)*(d*x**2+c)**(3/2),x)","\int \sqrt{a + b x^{2}} \left(c + d x^{2}\right)^{\frac{3}{2}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)*(c + d*x**2)**(3/2), x)","F",0
174,0,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/(b*x**2+a)**(1/2),x)","\int \frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{\sqrt{a + b x^{2}}}\, dx"," ",0,"Integral((c + d*x**2)**(3/2)/sqrt(a + b*x**2), x)","F",0
175,0,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/(b*x**2+a)**(3/2),x)","\int \frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{\left(a + b x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((c + d*x**2)**(3/2)/(a + b*x**2)**(3/2), x)","F",0
176,0,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/(b*x**2+a)**(5/2),x)","\int \frac{\left(c + d x^{2}\right)^{\frac{3}{2}}}{\left(a + b x^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"Integral((c + d*x**2)**(3/2)/(a + b*x**2)**(5/2), x)","F",0
177,-1,0,0,0.000000," ","integrate((d*x**2+c)**(3/2)/(b*x**2+a)**(7/2),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,0,0,0,0.000000," ","integrate((b*x**2+2)**(1/2)*(d*x**2+3)**(1/2),x)","\int \sqrt{b x^{2} + 2} \sqrt{d x^{2} + 3}\, dx"," ",0,"Integral(sqrt(b*x**2 + 2)*sqrt(d*x**2 + 3), x)","F",0
179,0,0,0,0.000000," ","integrate((-6*x**2+3)**(1/2)*(4*x**2+2)**(1/2),x)","\sqrt{6} \int \sqrt{1 - 2 x^{2}} \sqrt{2 x^{2} + 1}\, dx"," ",0,"sqrt(6)*Integral(sqrt(1 - 2*x**2)*sqrt(2*x**2 + 1), x)","F",0
180,1,17,0,3.433383," ","integrate((4*x**2+2)**(1/2)*(6*x**2+3)**(1/2),x)","\frac{2 \sqrt{6} x^{3}}{3} + \sqrt{6} x"," ",0,"2*sqrt(6)*x**3/3 + sqrt(6)*x","A",0
181,0,0,0,0.000000," ","integrate((b*x**2+2)**(1/2)/(d*x**2+3)**(1/2),x)","\int \frac{\sqrt{b x^{2} + 2}}{\sqrt{d x^{2} + 3}}\, dx"," ",0,"Integral(sqrt(b*x**2 + 2)/sqrt(d*x**2 + 3), x)","F",0
182,0,0,0,0.000000," ","integrate((-x**2+4)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{- \left(x - 2\right) \left(x + 2\right)}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(-(x - 2)*(x + 2))/sqrt(c + d*x**2), x)","F",0
183,0,0,0,0.000000," ","integrate((x**2+4)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{x^{2} + 4}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(x**2 + 4)/sqrt(c + d*x**2), x)","F",0
184,1,34,0,3.939472," ","integrate((-x**2+1)**(1/2)/(-3*x**2+2)**(1/2),x)","\begin{cases} \frac{\sqrt{3} E\left(\operatorname{asin}{\left(\frac{\sqrt{6} x}{2} \right)}\middle| \frac{2}{3}\right)}{3} & \text{for}\: x > - \frac{\sqrt{6}}{3} \wedge x < \frac{\sqrt{6}}{3} \end{cases}"," ",0,"Piecewise((sqrt(3)*elliptic_e(asin(sqrt(6)*x/2), 2/3)/3, (x > -sqrt(6)/3) & (x < sqrt(6)/3)))","A",0
185,1,36,0,4.212054," ","integrate((-x**2+4)**(1/2)/(-3*x**2+2)**(1/2),x)","\begin{cases} \frac{2 \sqrt{3} E\left(\operatorname{asin}{\left(\frac{\sqrt{6} x}{2} \right)}\middle| \frac{1}{6}\right)}{3} & \text{for}\: x > - \frac{\sqrt{6}}{3} \wedge x < \frac{\sqrt{6}}{3} \end{cases}"," ",0,"Piecewise((2*sqrt(3)*elliptic_e(asin(sqrt(6)*x/2), 1/6)/3, (x > -sqrt(6)/3) & (x < sqrt(6)/3)))","A",0
186,1,34,0,4.104609," ","integrate((-4*x**2+1)**(1/2)/(-3*x**2+2)**(1/2),x)","\begin{cases} \frac{\sqrt{3} E\left(\operatorname{asin}{\left(\frac{\sqrt{6} x}{2} \right)}\middle| \frac{8}{3}\right)}{3} & \text{for}\: x > - \frac{\sqrt{6}}{3} \wedge x < \frac{\sqrt{6}}{3} \end{cases}"," ",0,"Piecewise((sqrt(3)*elliptic_e(asin(sqrt(6)*x/2), 8/3)/3, (x > -sqrt(6)/3) & (x < sqrt(6)/3)))","A",0
187,1,10,0,2.393406," ","integrate((x**2+1)**(1/2)/(-x**2+1)**(1/2),x)","\begin{cases} E\left(\operatorname{asin}{\left(x \right)}\middle| -1\right) & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"Piecewise((elliptic_e(asin(x), -1), (x > -1) & (x < 1)))","B",0
188,1,36,0,3.958905," ","integrate((x**2+1)**(1/2)/(-3*x**2+2)**(1/2),x)","\begin{cases} \frac{\sqrt{3} E\left(\operatorname{asin}{\left(\frac{\sqrt{6} x}{2} \right)}\middle| - \frac{2}{3}\right)}{3} & \text{for}\: x > - \frac{\sqrt{6}}{3} \wedge x < \frac{\sqrt{6}}{3} \end{cases}"," ",0,"Piecewise((sqrt(3)*elliptic_e(asin(sqrt(6)*x/2), -2/3)/3, (x > -sqrt(6)/3) & (x < sqrt(6)/3)))","A",0
189,1,37,0,4.165691," ","integrate((x**2+4)**(1/2)/(-3*x**2+2)**(1/2),x)","\begin{cases} \frac{2 \sqrt{3} E\left(\operatorname{asin}{\left(\frac{\sqrt{6} x}{2} \right)}\middle| - \frac{1}{6}\right)}{3} & \text{for}\: x > - \frac{\sqrt{6}}{3} \wedge x < \frac{\sqrt{6}}{3} \end{cases}"," ",0,"Piecewise((2*sqrt(3)*elliptic_e(asin(sqrt(6)*x/2), -1/6)/3, (x > -sqrt(6)/3) & (x < sqrt(6)/3)))","A",0
190,1,36,0,4.049713," ","integrate((4*x**2+1)**(1/2)/(-3*x**2+2)**(1/2),x)","\begin{cases} \frac{\sqrt{3} E\left(\operatorname{asin}{\left(\frac{\sqrt{6} x}{2} \right)}\middle| - \frac{8}{3}\right)}{3} & \text{for}\: x > - \frac{\sqrt{6}}{3} \wedge x < \frac{\sqrt{6}}{3} \end{cases}"," ",0,"Piecewise((sqrt(3)*elliptic_e(asin(sqrt(6)*x/2), -8/3)/3, (x > -sqrt(6)/3) & (x < sqrt(6)/3)))","A",0
191,0,0,0,0.000000," ","integrate((-x**2+1)**(1/2)/(x**2+1)**(1/2),x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}{\sqrt{x^{2} + 1}}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1))/sqrt(x**2 + 1), x)","F",0
192,0,0,0,0.000000," ","integrate((-x**2+1)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}{\sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1))/sqrt(3*x**2 + 2), x)","F",0
193,0,0,0,0.000000," ","integrate((-x**2+4)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{\sqrt{- \left(x - 2\right) \left(x + 2\right)}}{\sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(sqrt(-(x - 2)*(x + 2))/sqrt(3*x**2 + 2), x)","F",0
194,0,0,0,0.000000," ","integrate((-4*x**2+1)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{\sqrt{- \left(2 x - 1\right) \left(2 x + 1\right)}}{\sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(sqrt(-(2*x - 1)*(2*x + 1))/sqrt(3*x**2 + 2), x)","F",0
195,0,0,0,0.000000," ","integrate((x**2+1)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{\sqrt{x^{2} + 1}}{\sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(sqrt(x**2 + 1)/sqrt(3*x**2 + 2), x)","F",0
196,0,0,0,0.000000," ","integrate((x**2+4)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{\sqrt{x^{2} + 4}}{\sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(sqrt(x**2 + 4)/sqrt(3*x**2 + 2), x)","F",0
197,0,0,0,0.000000," ","integrate((4*x**2+1)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{\sqrt{4 x^{2} + 1}}{\sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(sqrt(4*x**2 + 1)/sqrt(3*x**2 + 2), x)","F",0
198,0,0,0,0.000000," ","integrate((-x**2+1)**(1/2)/(2*x**2-1)**(1/2),x)","\int \frac{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}{\sqrt{2 x^{2} - 1}}\, dx"," ",0,"Integral(sqrt(-(x - 1)*(x + 1))/sqrt(2*x**2 - 1), x)","F",0
199,0,0,0,0.000000," ","integrate((b*x**2+a)**(7/2)/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{7}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(7/2)/sqrt(c + d*x**2), x)","F",0
200,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(5/2)/sqrt(c + d*x**2), x)","F",0
201,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/(d*x**2+c)**(1/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)/sqrt(c + d*x**2), x)","F",0
202,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/sqrt(c + d*x**2), x)","F",0
203,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
204,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(3/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{3}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(3/2)*sqrt(c + d*x**2)), x)","F",0
205,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(5/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{5}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(5/2)*sqrt(c + d*x**2)), x)","F",0
206,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(7/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{7}{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(7/2)*sqrt(c + d*x**2)), x)","F",0
207,0,0,0,0.000000," ","integrate((b*x**2+a)**(7/2)/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{7}{2}}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(7/2)/(c + d*x**2)**(3/2), x)","F",0
208,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/2)/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{2}}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(5/2)/(c + d*x**2)**(3/2), x)","F",0
209,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/2)/(d*x**2+c)**(3/2),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{2}}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral((a + b*x**2)**(3/2)/(c + d*x**2)**(3/2), x)","F",0
210,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(d*x**2+c)**(3/2),x)","\int \frac{\sqrt{a + b x^{2}}}{\left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/(c + d*x**2)**(3/2), x)","F",0
211,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/2)/(d*x**2+c)**(3/2),x)","\int \frac{1}{\sqrt{a + b x^{2}} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x**2)*(c + d*x**2)**(3/2)), x)","F",0
212,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(3/2)/(d*x**2+c)**(3/2),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{3}{2}} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(3/2)*(c + d*x**2)**(3/2)), x)","F",0
213,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(5/2)/(d*x**2+c)**(3/2),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{5}{2}} \left(c + d x^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(5/2)*(c + d*x**2)**(3/2)), x)","F",0
214,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{a + b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x**2)*sqrt(c + d*x**2)), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{a - b x^{2}} \sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(a - b*x**2)*sqrt(c + d*x**2)), x)","F",0
216,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/2)/(-d*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{a + b x^{2}} \sqrt{c - d x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(a + b*x**2)*sqrt(c - d*x**2)), x)","F",0
217,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(1/2)/(-d*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{a - b x^{2}} \sqrt{c - d x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(a - b*x**2)*sqrt(c - d*x**2)), x)","F",0
218,1,19,0,3.727369," ","integrate(1/(-x**2+1)**(1/2)/(5*x**2+2)**(1/2),x)","\begin{cases} \frac{\sqrt{2} F\left(\operatorname{asin}{\left(x \right)}\middle| - \frac{5}{2}\right)}{2} & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"Piecewise((sqrt(2)*elliptic_f(asin(x), -5/2)/2, (x > -1) & (x < 1)))","A",0
219,0,0,0,0.000000," ","integrate(1/(-x**2+1)**(1/2)/(4*x**2+2)**(1/2),x)","\frac{\sqrt{2} \int \frac{1}{\sqrt{1 - x^{2}} \sqrt{2 x^{2} + 1}}\, dx}{2}"," ",0,"sqrt(2)*Integral(1/(sqrt(1 - x**2)*sqrt(2*x**2 + 1)), x)/2","F",0
220,1,19,0,4.306137," ","integrate(1/(-x**2+1)**(1/2)/(3*x**2+2)**(1/2),x)","\begin{cases} \frac{\sqrt{2} F\left(\operatorname{asin}{\left(x \right)}\middle| - \frac{3}{2}\right)}{2} & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"Piecewise((sqrt(2)*elliptic_f(asin(x), -3/2)/2, (x > -1) & (x < 1)))","A",0
221,1,73,0,5.471762," ","integrate(1/(-x**2+1)**(1/2)/(2*x**2+2)**(1/2),x)","- \frac{\sqrt{2} {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{1}{2}, 1, 1 & \frac{3}{4}, \frac{3}{4}, \frac{5}{4} \\\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4} & 0 \end{matrix} \middle| {\frac{e^{- 2 i \pi}}{x^{4}}} \right)}}{16 \pi^{\frac{3}{2}}} + \frac{\sqrt{2} {G_{6, 6}^{3, 5}\left(\begin{matrix} - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4} & 1 \\0, \frac{1}{2}, 0 & - \frac{1}{4}, \frac{1}{4}, \frac{1}{4} \end{matrix} \middle| {\frac{1}{x^{4}}} \right)}}{16 \pi^{\frac{3}{2}}}"," ",0,"-sqrt(2)*meijerg(((1/2, 1, 1), (3/4, 3/4, 5/4)), ((1/4, 1/2, 3/4, 1, 5/4), (0,)), exp_polar(-2*I*pi)/x**4)/(16*pi**(3/2)) + sqrt(2)*meijerg(((-1/4, 0, 1/4, 1/2, 3/4), (1,)), ((0, 1/2, 0), (-1/4, 1/4, 1/4)), x**(-4))/(16*pi**(3/2))","B",0
222,1,19,0,2.502735," ","integrate(1/(-x**2+1)**(1/2)/(x**2+2)**(1/2),x)","\begin{cases} \frac{\sqrt{2} F\left(\operatorname{asin}{\left(x \right)}\middle| - \frac{1}{2}\right)}{2} & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"Piecewise((sqrt(2)*elliptic_f(asin(x), -1/2)/2, (x > -1) & (x < 1)))","A",0
223,0,0,0,0.000000," ","integrate(1/(-x**2+1)**(1/2)/(-x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \sqrt{2 - x^{2}}}\, dx"," ",0,"Integral(1/(sqrt(-(x - 1)*(x + 1))*sqrt(2 - x**2)), x)","F",0
224,1,22,0,2.320584," ","integrate(1/(-2*x**2+2)**(1/2)/(-x**2+1)**(1/2),x)","- \sqrt{2} \left(\begin{cases} - \frac{\operatorname{acoth}{\left(x \right)}}{2} & \text{for}\: x^{2} > 1 \\- \frac{\operatorname{atanh}{\left(x \right)}}{2} & \text{for}\: x^{2} < 1 \end{cases}\right)"," ",0,"-sqrt(2)*Piecewise((-acoth(x)/2, x**2 > 1), (-atanh(x)/2, x**2 < 1))","A",0
225,1,17,0,3.647038," ","integrate(1/(-3*x**2+2)**(1/2)/(-x**2+1)**(1/2),x)","\begin{cases} \frac{\sqrt{2} F\left(\operatorname{asin}{\left(x \right)}\middle| \frac{3}{2}\right)}{2} & \text{for}\: x > -1 \wedge x < 1 \end{cases}"," ",0,"Piecewise((sqrt(2)*elliptic_f(asin(x), 3/2)/2, (x > -1) & (x < 1)))","A",0
226,1,39,0,5.854216," ","integrate(1/(-4*x**2+2)**(1/2)/(-x**2+1)**(1/2),x)","\frac{\sqrt{2} \left(\begin{cases} \frac{\sqrt{2} F\left(\operatorname{asin}{\left(\sqrt{2} x \right)}\middle| \frac{1}{2}\right)}{2} & \text{for}\: x > - \frac{\sqrt{2}}{2} \wedge x < \frac{\sqrt{2}}{2} \end{cases}\right)}{2}"," ",0,"sqrt(2)*Piecewise((sqrt(2)*elliptic_f(asin(sqrt(2)*x), 1/2)/2, (x > -sqrt(2)/2) & (x < sqrt(2)/2)))/2","A",0
227,1,34,0,3.760550," ","integrate(1/(-5*x**2+2)**(1/2)/(-x**2+1)**(1/2),x)","\begin{cases} \frac{\sqrt{5} F\left(\operatorname{asin}{\left(\frac{\sqrt{10} x}{2} \right)}\middle| \frac{2}{5}\right)}{5} & \text{for}\: x > - \frac{\sqrt{10}}{5} \wedge x < \frac{\sqrt{10}}{5} \end{cases}"," ",0,"Piecewise((sqrt(5)*elliptic_f(asin(sqrt(10)*x/2), 2/5)/5, (x > -sqrt(10)/5) & (x < sqrt(10)/5)))","A",0
228,0,0,0,0.000000," ","integrate(1/(x**2+1)**(1/2)/(5*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{x^{2} + 1} \sqrt{5 x^{2} + 2}}\, dx"," ",0,"Integral(1/(sqrt(x**2 + 1)*sqrt(5*x**2 + 2)), x)","F",0
229,0,0,0,0.000000," ","integrate(1/(x**2+1)**(1/2)/(4*x**2+2)**(1/2),x)","\frac{\sqrt{2} \int \frac{1}{\sqrt{x^{2} + 1} \sqrt{2 x^{2} + 1}}\, dx}{2}"," ",0,"sqrt(2)*Integral(1/(sqrt(x**2 + 1)*sqrt(2*x**2 + 1)), x)/2","F",0
230,0,0,0,0.000000," ","integrate(1/(x**2+1)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{x^{2} + 1} \sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(1/(sqrt(x**2 + 1)*sqrt(3*x**2 + 2)), x)","F",0
231,1,8,0,2.493991," ","integrate(1/(x**2+1)**(1/2)/(2*x**2+2)**(1/2),x)","\frac{\sqrt{2} \operatorname{atan}{\left(x \right)}}{2}"," ",0,"sqrt(2)*atan(x)/2","A",0
232,0,0,0,0.000000," ","integrate(1/(x**2+1)**(1/2)/(x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{x^{2} + 1} \sqrt{x^{2} + 2}}\, dx"," ",0,"Integral(1/(sqrt(x**2 + 1)*sqrt(x**2 + 2)), x)","F",0
233,0,0,0,0.000000," ","integrate(1/(-x**2+2)**(1/2)/(x**2+1)**(1/2),x)","\int \frac{1}{\sqrt{2 - x^{2}} \sqrt{x^{2} + 1}}\, dx"," ",0,"Integral(1/(sqrt(2 - x**2)*sqrt(x**2 + 1)), x)","F",0
234,1,76,0,5.264272," ","integrate(1/(-2*x**2+2)**(1/2)/(x**2+1)**(1/2),x)","\frac{\sqrt{2} i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{1}{2}, 1, 1 & \frac{3}{4}, \frac{3}{4}, \frac{5}{4} \\\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4} & 0 \end{matrix} \middle| {\frac{1}{x^{4}}} \right)}}{16 \pi^{\frac{3}{2}}} - \frac{\sqrt{2} i {G_{6, 6}^{3, 5}\left(\begin{matrix} - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4} & 1 \\0, \frac{1}{2}, 0 & - \frac{1}{4}, \frac{1}{4}, \frac{1}{4} \end{matrix} \middle| {\frac{e^{- 2 i \pi}}{x^{4}}} \right)}}{16 \pi^{\frac{3}{2}}}"," ",0,"sqrt(2)*I*meijerg(((1/2, 1, 1), (3/4, 3/4, 5/4)), ((1/4, 1/2, 3/4, 1, 5/4), (0,)), x**(-4))/(16*pi**(3/2)) - sqrt(2)*I*meijerg(((-1/4, 0, 1/4, 1/2, 3/4), (1,)), ((0, 1/2, 0), (-1/4, 1/4, 1/4)), exp_polar(-2*I*pi)/x**4)/(16*pi**(3/2))","B",0
235,1,36,0,4.086772," ","integrate(1/(-3*x**2+2)**(1/2)/(x**2+1)**(1/2),x)","\begin{cases} \frac{\sqrt{3} F\left(\operatorname{asin}{\left(\frac{\sqrt{6} x}{2} \right)}\middle| - \frac{2}{3}\right)}{3} & \text{for}\: x > - \frac{\sqrt{6}}{3} \wedge x < \frac{\sqrt{6}}{3} \end{cases}"," ",0,"Piecewise((sqrt(3)*elliptic_f(asin(sqrt(6)*x/2), -2/3)/3, (x > -sqrt(6)/3) & (x < sqrt(6)/3)))","A",0
236,1,41,0,6.020337," ","integrate(1/(-4*x**2+2)**(1/2)/(x**2+1)**(1/2),x)","\frac{\sqrt{2} \left(\begin{cases} \frac{\sqrt{2} F\left(\operatorname{asin}{\left(\sqrt{2} x \right)}\middle| - \frac{1}{2}\right)}{2} & \text{for}\: x > - \frac{\sqrt{2}}{2} \wedge x < \frac{\sqrt{2}}{2} \end{cases}\right)}{2}"," ",0,"sqrt(2)*Piecewise((sqrt(2)*elliptic_f(asin(sqrt(2)*x), -1/2)/2, (x > -sqrt(2)/2) & (x < sqrt(2)/2)))/2","A",0
237,1,36,0,4.091047," ","integrate(1/(-5*x**2+2)**(1/2)/(x**2+1)**(1/2),x)","\begin{cases} \frac{\sqrt{5} F\left(\operatorname{asin}{\left(\frac{\sqrt{10} x}{2} \right)}\middle| - \frac{2}{5}\right)}{5} & \text{for}\: x > - \frac{\sqrt{10}}{5} \wedge x < \frac{\sqrt{10}}{5} \end{cases}"," ",0,"Piecewise((sqrt(5)*elliptic_f(asin(sqrt(10)*x/2), -2/5)/5, (x > -sqrt(10)/5) & (x < sqrt(10)/5)))","A",0
238,0,0,0,0.000000," ","integrate(1/(x**2-1)**(1/2)/(5*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{\left(x - 1\right) \left(x + 1\right)} \sqrt{5 x^{2} + 2}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)*(x + 1))*sqrt(5*x**2 + 2)), x)","F",0
239,0,0,0,0.000000," ","integrate(1/(x**2-1)**(1/2)/(4*x**2+2)**(1/2),x)","\frac{\sqrt{2} \int \frac{1}{\sqrt{x^{2} - 1} \sqrt{2 x^{2} + 1}}\, dx}{2}"," ",0,"sqrt(2)*Integral(1/(sqrt(x**2 - 1)*sqrt(2*x**2 + 1)), x)/2","F",0
240,0,0,0,0.000000," ","integrate(1/(x**2-1)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{\left(x - 1\right) \left(x + 1\right)} \sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)*(x + 1))*sqrt(3*x**2 + 2)), x)","F",0
241,1,75,0,5.550363," ","integrate(1/(x**2-1)**(1/2)/(2*x**2+2)**(1/2),x)","\frac{\sqrt{2} i {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{1}{2}, 1, 1 & \frac{3}{4}, \frac{3}{4}, \frac{5}{4} \\\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4} & 0 \end{matrix} \middle| {\frac{e^{2 i \pi}}{x^{4}}} \right)}}{16 \pi^{\frac{3}{2}}} - \frac{\sqrt{2} i {G_{6, 6}^{3, 5}\left(\begin{matrix} - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4} & 1 \\0, \frac{1}{2}, 0 & - \frac{1}{4}, \frac{1}{4}, \frac{1}{4} \end{matrix} \middle| {\frac{1}{x^{4}}} \right)}}{16 \pi^{\frac{3}{2}}}"," ",0,"sqrt(2)*I*meijerg(((1/2, 1, 1), (3/4, 3/4, 5/4)), ((1/4, 1/2, 3/4, 1, 5/4), (0,)), exp_polar(2*I*pi)/x**4)/(16*pi**(3/2)) - sqrt(2)*I*meijerg(((-1/4, 0, 1/4, 1/2, 3/4), (1,)), ((0, 1/2, 0), (-1/4, 1/4, 1/4)), x**(-4))/(16*pi**(3/2))","C",0
242,0,0,0,0.000000," ","integrate(1/(x**2-1)**(1/2)/(x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{\left(x - 1\right) \left(x + 1\right)} \sqrt{x^{2} + 2}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)*(x + 1))*sqrt(x**2 + 2)), x)","F",0
243,0,0,0,0.000000," ","integrate(1/(-x**2+2)**(1/2)/(x**2-1)**(1/2),x)","\int \frac{1}{\sqrt{\left(x - 1\right) \left(x + 1\right)} \sqrt{2 - x^{2}}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)*(x + 1))*sqrt(2 - x**2)), x)","F",0
244,0,0,0,0.000000," ","integrate(1/(-2*x**2+2)**(1/2)/(x**2-1)**(1/2),x)","\frac{\sqrt{2} \int \frac{1}{\sqrt{1 - x^{2}} \sqrt{x^{2} - 1}}\, dx}{2}"," ",0,"sqrt(2)*Integral(1/(sqrt(1 - x**2)*sqrt(x**2 - 1)), x)/2","F",0
245,1,37,0,4.096036," ","integrate(1/(-3*x**2+2)**(1/2)/(x**2-1)**(1/2),x)","\begin{cases} - \frac{\sqrt{3} i F\left(\operatorname{asin}{\left(\frac{\sqrt{6} x}{2} \right)}\middle| \frac{2}{3}\right)}{3} & \text{for}\: x > - \frac{\sqrt{6}}{3} \wedge x < \frac{\sqrt{6}}{3} \end{cases}"," ",0,"Piecewise((-sqrt(3)*I*elliptic_f(asin(sqrt(6)*x/2), 2/3)/3, (x > -sqrt(6)/3) & (x < sqrt(6)/3)))","C",0
246,1,42,0,6.073056," ","integrate(1/(-4*x**2+2)**(1/2)/(x**2-1)**(1/2),x)","\frac{\sqrt{2} \left(\begin{cases} - \frac{\sqrt{2} i F\left(\operatorname{asin}{\left(\sqrt{2} x \right)}\middle| \frac{1}{2}\right)}{2} & \text{for}\: x > - \frac{\sqrt{2}}{2} \wedge x < \frac{\sqrt{2}}{2} \end{cases}\right)}{2}"," ",0,"sqrt(2)*Piecewise((-sqrt(2)*I*elliptic_f(asin(sqrt(2)*x), 1/2)/2, (x > -sqrt(2)/2) & (x < sqrt(2)/2)))/2","A",0
247,1,37,0,4.146941," ","integrate(1/(-5*x**2+2)**(1/2)/(x**2-1)**(1/2),x)","\begin{cases} - \frac{\sqrt{5} i F\left(\operatorname{asin}{\left(\frac{\sqrt{10} x}{2} \right)}\middle| \frac{2}{5}\right)}{5} & \text{for}\: x > - \frac{\sqrt{10}}{5} \wedge x < \frac{\sqrt{10}}{5} \end{cases}"," ",0,"Piecewise((-sqrt(5)*I*elliptic_f(asin(sqrt(10)*x/2), 2/5)/5, (x > -sqrt(10)/5) & (x < sqrt(10)/5)))","C",0
248,0,0,0,0.000000," ","integrate(1/(-x**2-1)**(1/2)/(5*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{- x^{2} - 1} \sqrt{5 x^{2} + 2}}\, dx"," ",0,"Integral(1/(sqrt(-x**2 - 1)*sqrt(5*x**2 + 2)), x)","F",0
249,0,0,0,0.000000," ","integrate(1/(-x**2-1)**(1/2)/(4*x**2+2)**(1/2),x)","\frac{\sqrt{2} \int \frac{1}{\sqrt{- x^{2} - 1} \sqrt{2 x^{2} + 1}}\, dx}{2}"," ",0,"sqrt(2)*Integral(1/(sqrt(-x**2 - 1)*sqrt(2*x**2 + 1)), x)/2","F",0
250,0,0,0,0.000000," ","integrate(1/(-x**2-1)**(1/2)/(3*x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{- x^{2} - 1} \sqrt{3 x^{2} + 2}}\, dx"," ",0,"Integral(1/(sqrt(-x**2 - 1)*sqrt(3*x**2 + 2)), x)","F",0
251,0,0,0,0.000000," ","integrate(1/(-x**2-1)**(1/2)/(2*x**2+2)**(1/2),x)","\frac{\sqrt{2} \int \frac{1}{\sqrt{- x^{2} - 1} \sqrt{x^{2} + 1}}\, dx}{2}"," ",0,"sqrt(2)*Integral(1/(sqrt(-x**2 - 1)*sqrt(x**2 + 1)), x)/2","F",0
252,0,0,0,0.000000," ","integrate(1/(-x**2-1)**(1/2)/(x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{- x^{2} - 1} \sqrt{x^{2} + 2}}\, dx"," ",0,"Integral(1/(sqrt(-x**2 - 1)*sqrt(x**2 + 2)), x)","F",0
253,0,0,0,0.000000," ","integrate(1/(-x**2-1)**(1/2)/(-x**2+2)**(1/2),x)","\int \frac{1}{\sqrt{2 - x^{2}} \sqrt{- x^{2} - 1}}\, dx"," ",0,"Integral(1/(sqrt(2 - x**2)*sqrt(-x**2 - 1)), x)","F",0
254,1,73,0,5.454826," ","integrate(1/(-2*x**2+2)**(1/2)/(-x**2-1)**(1/2),x)","\frac{\sqrt{2} {G_{6, 6}^{5, 3}\left(\begin{matrix} \frac{1}{2}, 1, 1 & \frac{3}{4}, \frac{3}{4}, \frac{5}{4} \\\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \frac{5}{4} & 0 \end{matrix} \middle| {\frac{1}{x^{4}}} \right)}}{16 \pi^{\frac{3}{2}}} - \frac{\sqrt{2} {G_{6, 6}^{3, 5}\left(\begin{matrix} - \frac{1}{4}, 0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4} & 1 \\0, \frac{1}{2}, 0 & - \frac{1}{4}, \frac{1}{4}, \frac{1}{4} \end{matrix} \middle| {\frac{e^{- 2 i \pi}}{x^{4}}} \right)}}{16 \pi^{\frac{3}{2}}}"," ",0,"sqrt(2)*meijerg(((1/2, 1, 1), (3/4, 3/4, 5/4)), ((1/4, 1/2, 3/4, 1, 5/4), (0,)), x**(-4))/(16*pi**(3/2)) - sqrt(2)*meijerg(((-1/4, 0, 1/4, 1/2, 3/4), (1,)), ((0, 1/2, 0), (-1/4, 1/4, 1/4)), exp_polar(-2*I*pi)/x**4)/(16*pi**(3/2))","A",0
255,0,0,0,0.000000," ","integrate(1/(-3*x**2+2)**(1/2)/(-x**2-1)**(1/2),x)","\int \frac{1}{\sqrt{2 - 3 x^{2}} \sqrt{- x^{2} - 1}}\, dx"," ",0,"Integral(1/(sqrt(2 - 3*x**2)*sqrt(-x**2 - 1)), x)","F",0
256,1,44,0,5.780271," ","integrate(1/(-4*x**2+2)**(1/2)/(-x**2-1)**(1/2),x)","\frac{\sqrt{2} \left(\begin{cases} - \frac{\sqrt{2} i F\left(\operatorname{asin}{\left(\sqrt{2} x \right)}\middle| - \frac{1}{2}\right)}{2} & \text{for}\: x > - \frac{\sqrt{2}}{2} \wedge x < \frac{\sqrt{2}}{2} \end{cases}\right)}{2}"," ",0,"sqrt(2)*Piecewise((-sqrt(2)*I*elliptic_f(asin(sqrt(2)*x), -1/2)/2, (x > -sqrt(2)/2) & (x < sqrt(2)/2)))/2","A",0
257,0,0,0,0.000000," ","integrate(1/(-5*x**2+2)**(1/2)/(-x**2-1)**(1/2),x)","\int \frac{1}{\sqrt{2 - 5 x^{2}} \sqrt{- x^{2} - 1}}\, dx"," ",0,"Integral(1/(sqrt(2 - 5*x**2)*sqrt(-x**2 - 1)), x)","F",0
258,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(-d*x**2+c)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{\sqrt{c - d x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/sqrt(c - d*x**2), x)","F",0
259,0,0,0,0.000000," ","integrate((-b*x**2-a)**(1/2)/(-d*x**2+c)**(1/2),x)","\int \frac{\sqrt{- a - b x^{2}}}{\sqrt{c - d x^{2}}}\, dx"," ",0,"Integral(sqrt(-a - b*x**2)/sqrt(c - d*x**2), x)","F",0
260,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(d*x**2-c)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{\sqrt{- c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/sqrt(-c + d*x**2), x)","F",0
261,0,0,0,0.000000," ","integrate((-b*x**2-a)**(1/2)/(d*x**2-c)**(1/2),x)","\int \frac{\sqrt{- a - b x^{2}}}{\sqrt{- c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(-a - b*x**2)/sqrt(-c + d*x**2), x)","F",0
262,0,0,0,0.000000," ","integrate((-b*x**2+a)**(1/2)/(-d*x**2+c)**(1/2),x)","\int \frac{\sqrt{a - b x^{2}}}{\sqrt{c - d x^{2}}}\, dx"," ",0,"Integral(sqrt(a - b*x**2)/sqrt(c - d*x**2), x)","F",0
263,0,0,0,0.000000," ","integrate((b*x**2-a)**(1/2)/(-d*x**2+c)**(1/2),x)","\int \frac{\sqrt{- a + b x^{2}}}{\sqrt{c - d x^{2}}}\, dx"," ",0,"Integral(sqrt(-a + b*x**2)/sqrt(c - d*x**2), x)","F",0
264,0,0,0,0.000000," ","integrate((-b*x**2+a)**(1/2)/(d*x**2-c)**(1/2),x)","\int \frac{\sqrt{a - b x^{2}}}{\sqrt{- c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(a - b*x**2)/sqrt(-c + d*x**2), x)","F",0
265,0,0,0,0.000000," ","integrate((b*x**2-a)**(1/2)/(d*x**2-c)**(1/2),x)","\int \frac{\sqrt{- a + b x^{2}}}{\sqrt{- c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(-a + b*x**2)/sqrt(-c + d*x**2), x)","F",0
266,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/sqrt(c + d*x**2), x)","F",0
267,0,0,0,0.000000," ","integrate((-b*x**2-a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{- a - b x^{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(-a - b*x**2)/sqrt(c + d*x**2), x)","F",0
268,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/2)/(-d*x**2-c)**(1/2),x)","\int \frac{\sqrt{a + b x^{2}}}{\sqrt{- c - d x^{2}}}\, dx"," ",0,"Integral(sqrt(a + b*x**2)/sqrt(-c - d*x**2), x)","F",0
269,0,0,0,0.000000," ","integrate((-b*x**2-a)**(1/2)/(-d*x**2-c)**(1/2),x)","\int \frac{\sqrt{- a - b x^{2}}}{\sqrt{- c - d x^{2}}}\, dx"," ",0,"Integral(sqrt(-a - b*x**2)/sqrt(-c - d*x**2), x)","F",0
270,0,0,0,0.000000," ","integrate((-b*x**2+a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{a - b x^{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(a - b*x**2)/sqrt(c + d*x**2), x)","F",0
271,0,0,0,0.000000," ","integrate((b*x**2-a)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{\sqrt{- a + b x^{2}}}{\sqrt{c + d x^{2}}}\, dx"," ",0,"Integral(sqrt(-a + b*x**2)/sqrt(c + d*x**2), x)","F",0
272,0,0,0,0.000000," ","integrate((-b*x**2+a)**(1/2)/(-d*x**2-c)**(1/2),x)","\int \frac{\sqrt{a - b x^{2}}}{\sqrt{- c - d x^{2}}}\, dx"," ",0,"Integral(sqrt(a - b*x**2)/sqrt(-c - d*x**2), x)","F",0
273,0,0,0,0.000000," ","integrate((b*x**2-a)**(1/2)/(-d*x**2-c)**(1/2),x)","\int \frac{\sqrt{- a + b x^{2}}}{\sqrt{- c - d x^{2}}}\, dx"," ",0,"Integral(sqrt(-a + b*x**2)/sqrt(-c - d*x**2), x)","F",0
274,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/(-b*x**2+a)**(1/2),x)","\int \frac{\sqrt{c + d x^{2}}}{\sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/sqrt(a - b*x**2), x)","F",0
275,0,0,0,0.000000," ","integrate((-d*x**2-c)**(1/2)/(-b*x**2+a)**(1/2),x)","\int \frac{\sqrt{- c - d x^{2}}}{\sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(-c - d*x**2)/sqrt(a - b*x**2), x)","F",0
276,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/(b*x**2-a)**(1/2),x)","\int \frac{\sqrt{c + d x^{2}}}{\sqrt{- a + b x^{2}}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/sqrt(-a + b*x**2), x)","F",0
277,0,0,0,0.000000," ","integrate((-d*x**2-c)**(1/2)/(b*x**2-a)**(1/2),x)","\int \frac{\sqrt{- c - d x^{2}}}{\sqrt{- a + b x^{2}}}\, dx"," ",0,"Integral(sqrt(-c - d*x**2)/sqrt(-a + b*x**2), x)","F",0
278,0,0,0,0.000000," ","integrate((-d*x**2+c)**(1/2)/(-b*x**2+a)**(1/2),x)","\int \frac{\sqrt{c - d x^{2}}}{\sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(c - d*x**2)/sqrt(a - b*x**2), x)","F",0
279,0,0,0,0.000000," ","integrate((d*x**2-c)**(1/2)/(-b*x**2+a)**(1/2),x)","\int \frac{\sqrt{- c + d x^{2}}}{\sqrt{a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(-c + d*x**2)/sqrt(a - b*x**2), x)","F",0
280,0,0,0,0.000000," ","integrate((-d*x**2+c)**(1/2)/(b*x**2-a)**(1/2),x)","\int \frac{\sqrt{c - d x^{2}}}{\sqrt{- a + b x^{2}}}\, dx"," ",0,"Integral(sqrt(c - d*x**2)/sqrt(-a + b*x**2), x)","F",0
281,0,0,0,0.000000," ","integrate((d*x**2-c)**(1/2)/(b*x**2-a)**(1/2),x)","\int \frac{\sqrt{- c + d x^{2}}}{\sqrt{- a + b x^{2}}}\, dx"," ",0,"Integral(sqrt(-c + d*x**2)/sqrt(-a + b*x**2), x)","F",0
282,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/(b*x**2+a)**(1/2),x)","\int \frac{\sqrt{c + d x^{2}}}{\sqrt{a + b x^{2}}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/sqrt(a + b*x**2), x)","F",0
283,0,0,0,0.000000," ","integrate((-d*x**2-c)**(1/2)/(b*x**2+a)**(1/2),x)","\int \frac{\sqrt{- c - d x^{2}}}{\sqrt{a + b x^{2}}}\, dx"," ",0,"Integral(sqrt(-c - d*x**2)/sqrt(a + b*x**2), x)","F",0
284,0,0,0,0.000000," ","integrate((d*x**2+c)**(1/2)/(-b*x**2-a)**(1/2),x)","\int \frac{\sqrt{c + d x^{2}}}{\sqrt{- a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(c + d*x**2)/sqrt(-a - b*x**2), x)","F",0
285,0,0,0,0.000000," ","integrate((-d*x**2-c)**(1/2)/(-b*x**2-a)**(1/2),x)","\int \frac{\sqrt{- c - d x^{2}}}{\sqrt{- a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(-c - d*x**2)/sqrt(-a - b*x**2), x)","F",0
286,0,0,0,0.000000," ","integrate((-d*x**2+c)**(1/2)/(b*x**2+a)**(1/2),x)","\int \frac{\sqrt{c - d x^{2}}}{\sqrt{a + b x^{2}}}\, dx"," ",0,"Integral(sqrt(c - d*x**2)/sqrt(a + b*x**2), x)","F",0
287,0,0,0,0.000000," ","integrate((d*x**2-c)**(1/2)/(b*x**2+a)**(1/2),x)","\int \frac{\sqrt{- c + d x^{2}}}{\sqrt{a + b x^{2}}}\, dx"," ",0,"Integral(sqrt(-c + d*x**2)/sqrt(a + b*x**2), x)","F",0
288,0,0,0,0.000000," ","integrate((-d*x**2+c)**(1/2)/(-b*x**2-a)**(1/2),x)","\int \frac{\sqrt{c - d x^{2}}}{\sqrt{- a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(c - d*x**2)/sqrt(-a - b*x**2), x)","F",0
289,0,0,0,0.000000," ","integrate((d*x**2-c)**(1/2)/(-b*x**2-a)**(1/2),x)","\int \frac{\sqrt{- c + d x^{2}}}{\sqrt{- a - b x^{2}}}\, dx"," ",0,"Integral(sqrt(-c + d*x**2)/sqrt(-a - b*x**2), x)","F",0
290,0,0,0,0.000000," ","integrate(1/(b*x**2+2)**(1/2)/(d*x**2+3)**(1/2),x)","\int \frac{1}{\sqrt{b x^{2} + 2} \sqrt{d x^{2} + 3}}\, dx"," ",0,"Integral(1/(sqrt(b*x**2 + 2)*sqrt(d*x**2 + 3)), x)","F",0
291,1,20,0,2.379226," ","integrate(1/(-x**2+4)**(1/2)/(d*x**2+c)**(1/2),x)","\begin{cases} \frac{F\left(\operatorname{asin}{\left(\frac{x}{2} \right)}\middle| - \frac{4 d}{c}\right)}{\sqrt{c}} & \text{for}\: x > -2 \wedge x < 2 \end{cases}"," ",0,"Piecewise((elliptic_f(asin(x/2), -4*d/c)/sqrt(c), (x > -2) & (x < 2)))","A",0
292,0,0,0,0.000000," ","integrate(1/(x**2+4)**(1/2)/(d*x**2+c)**(1/2),x)","\int \frac{1}{\sqrt{c + d x^{2}} \sqrt{x^{2} + 4}}\, dx"," ",0,"Integral(1/(sqrt(c + d*x**2)*sqrt(x**2 + 4)), x)","F",0
293,0,0,0,0.000000," ","integrate(1/(-x**2+1)**(1/2)/(2*x**2-1)**(1/2),x)","\int \frac{1}{\sqrt{- \left(x - 1\right) \left(x + 1\right)} \sqrt{2 x^{2} - 1}}\, dx"," ",0,"Integral(1/(sqrt(-(x - 1)*(x + 1))*sqrt(2*x**2 - 1)), x)","F",0
294,0,0,0,0.000000," ","integrate((-c**2*x**2+1)**(1/2)/(c**2*x**2+1)**(1/2),x)","\int \frac{\sqrt{- \left(c x - 1\right) \left(c x + 1\right)}}{\sqrt{c^{2} x^{2} + 1}}\, dx"," ",0,"Integral(sqrt(-(c*x - 1)*(c*x + 1))/sqrt(c**2*x**2 + 1), x)","F",0
295,0,0,0,0.000000," ","integrate((b*x**2+2)**(1/2)/(d*x**2+3)**(1/2),x)","\int \frac{\sqrt{b x^{2} + 2}}{\sqrt{d x^{2} + 3}}\, dx"," ",0,"Integral(sqrt(b*x**2 + 2)/sqrt(d*x**2 + 3), x)","F",0
296,0,0,0,0.000000," ","integrate((3*x**2-1)**(1/2)/(-3*x**2+2)**(1/2),x)","\int \frac{\sqrt{3 x^{2} - 1}}{\sqrt{2 - 3 x^{2}}}\, dx"," ",0,"Integral(sqrt(3*x**2 - 1)/sqrt(2 - 3*x**2), x)","F",0
297,0,0,0,0.000000," ","integrate((1+2*c*x**2/(b-(-4*a*c+b**2)**(1/2)))**(1/2)/(1-2*c*x**2/(b+(-4*a*c+b**2)**(1/2)))**(1/2),x)","\int \frac{\sqrt{\frac{b + 2 c x^{2} - \sqrt{- 4 a c + b^{2}}}{b - \sqrt{- 4 a c + b^{2}}}}}{\sqrt{- \frac{- b + 2 c x^{2} - \sqrt{- 4 a c + b^{2}}}{b + \sqrt{- 4 a c + b^{2}}}}}\, dx"," ",0,"Integral(sqrt((b + 2*c*x**2 - sqrt(-4*a*c + b**2))/(b - sqrt(-4*a*c + b**2)))/sqrt(-(-b + 2*c*x**2 - sqrt(-4*a*c + b**2))/(b + sqrt(-4*a*c + b**2))), x)","F",0
298,0,0,0,0.000000," ","integrate((1-2*c*x**2/(b-(-4*a*c+b**2)**(1/2)))**(1/2)/(1-2*c*x**2/(b+(-4*a*c+b**2)**(1/2)))**(1/2),x)","\int \frac{\sqrt{- \frac{- b + 2 c x^{2} + \sqrt{- 4 a c + b^{2}}}{b - \sqrt{- 4 a c + b^{2}}}}}{\sqrt{- \frac{- b + 2 c x^{2} - \sqrt{- 4 a c + b^{2}}}{b + \sqrt{- 4 a c + b^{2}}}}}\, dx"," ",0,"Integral(sqrt(-(-b + 2*c*x**2 + sqrt(-4*a*c + b**2))/(b - sqrt(-4*a*c + b**2)))/sqrt(-(-b + 2*c*x**2 - sqrt(-4*a*c + b**2))/(b + sqrt(-4*a*c + b**2))), x)","F",0
299,0,0,0,0.000000," ","integrate((1+2*c*x**2/(b-(-4*a*c+b**2)**(1/2)))**(1/2)/(1+2*c*x**2/(b+(-4*a*c+b**2)**(1/2)))**(1/2),x)","\int \frac{\sqrt{\frac{b + 2 c x^{2} - \sqrt{- 4 a c + b^{2}}}{b - \sqrt{- 4 a c + b^{2}}}}}{\sqrt{\frac{b + 2 c x^{2} + \sqrt{- 4 a c + b^{2}}}{b + \sqrt{- 4 a c + b^{2}}}}}\, dx"," ",0,"Integral(sqrt((b + 2*c*x**2 - sqrt(-4*a*c + b**2))/(b - sqrt(-4*a*c + b**2)))/sqrt((b + 2*c*x**2 + sqrt(-4*a*c + b**2))/(b + sqrt(-4*a*c + b**2))), x)","F",0
300,0,0,0,0.000000," ","integrate((1-2*c*x**2/(b-(-4*a*c+b**2)**(1/2)))**(1/2)/(1+2*c*x**2/(b+(-4*a*c+b**2)**(1/2)))**(1/2),x)","\int \frac{\sqrt{- \frac{- b + 2 c x^{2} + \sqrt{- 4 a c + b^{2}}}{b - \sqrt{- 4 a c + b^{2}}}}}{\sqrt{\frac{b + 2 c x^{2} + \sqrt{- 4 a c + b^{2}}}{b + \sqrt{- 4 a c + b^{2}}}}}\, dx"," ",0,"Integral(sqrt(-(-b + 2*c*x**2 + sqrt(-4*a*c + b**2))/(b - sqrt(-4*a*c + b**2)))/sqrt((b + 2*c*x**2 + sqrt(-4*a*c + b**2))/(b + sqrt(-4*a*c + b**2))), x)","F",0
301,0,0,0,0.000000," ","integrate((-2*x**2+1)**m/(-x**2+1)**(1/2),x)","\int \frac{\left(1 - 2 x^{2}\right)^{m}}{\sqrt{- \left(x - 1\right) \left(x + 1\right)}}\, dx"," ",0,"Integral((1 - 2*x**2)**m/sqrt(-(x - 1)*(x + 1)), x)","F",0
302,0,0,0,0.000000," ","integrate(1/(x**2-1)**(1/2)/(7+x**2-4*3**(1/2))**(1/2),x)","\int \frac{1}{\sqrt{\left(x - 1\right) \left(x + 1\right)} \sqrt{x^{2} - 4 \sqrt{3} + 7}}\, dx"," ",0,"Integral(1/(sqrt((x - 1)*(x + 1))*sqrt(x**2 - 4*sqrt(3) + 7)), x)","F",0
303,0,0,0,0.000000," ","integrate(1/(3+x**2*(-3+3**(1/2)))**(1/2)/(3-3*3**(1/2)+2*3**(1/2)*x**2)**(1/2),x)","\int \frac{1}{\sqrt{- 3 x^{2} + \sqrt{3} x^{2} + 3} \sqrt{2 \sqrt{3} x^{2} - 3 \sqrt{3} + 3}}\, dx"," ",0,"Integral(1/(sqrt(-3*x**2 + sqrt(3)*x**2 + 3)*sqrt(2*sqrt(3)*x**2 - 3*sqrt(3) + 3)), x)","F",0
304,0,0,0,0.000000," ","integrate(1/(3*x**2+2)**(1/4)/(3*x**2+4),x)","\int \frac{1}{\sqrt[4]{3 x^{2} + 2} \left(3 x^{2} + 4\right)}\, dx"," ",0,"Integral(1/((3*x**2 + 2)**(1/4)*(3*x**2 + 4)), x)","F",0
305,0,0,0,0.000000," ","integrate(1/(-3*x**2+2)**(1/4)/(-3*x**2+4),x)","- \int \frac{1}{3 x^{2} \sqrt[4]{2 - 3 x^{2}} - 4 \sqrt[4]{2 - 3 x^{2}}}\, dx"," ",0,"-Integral(1/(3*x**2*(2 - 3*x**2)**(1/4) - 4*(2 - 3*x**2)**(1/4)), x)","F",0
306,0,0,0,0.000000," ","integrate(1/(b*x**2+2)**(1/4)/(b*x**2+4),x)","\int \frac{1}{\sqrt[4]{b x^{2} + 2} \left(b x^{2} + 4\right)}\, dx"," ",0,"Integral(1/((b*x**2 + 2)**(1/4)*(b*x**2 + 4)), x)","F",0
307,0,0,0,0.000000," ","integrate(1/(-b*x**2+2)**(1/4)/(-b*x**2+4),x)","- \int \frac{1}{b x^{2} \sqrt[4]{- b x^{2} + 2} - 4 \sqrt[4]{- b x^{2} + 2}}\, dx"," ",0,"-Integral(1/(b*x**2*(-b*x**2 + 2)**(1/4) - 4*(-b*x**2 + 2)**(1/4)), x)","F",0
308,0,0,0,0.000000," ","integrate(1/(3*x**2+a)**(1/4)/(3*x**2+2*a),x)","\int \frac{1}{\sqrt[4]{a + 3 x^{2}} \left(2 a + 3 x^{2}\right)}\, dx"," ",0,"Integral(1/((a + 3*x**2)**(1/4)*(2*a + 3*x**2)), x)","F",0
309,0,0,0,0.000000," ","integrate(1/(-3*x**2+a)**(1/4)/(-3*x**2+2*a),x)","- \int \frac{1}{- 2 a \sqrt[4]{a - 3 x^{2}} + 3 x^{2} \sqrt[4]{a - 3 x^{2}}}\, dx"," ",0,"-Integral(1/(-2*a*(a - 3*x**2)**(1/4) + 3*x**2*(a - 3*x**2)**(1/4)), x)","F",0
310,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/4)/(b*x**2+2*a),x)","\int \frac{1}{\sqrt[4]{a + b x^{2}} \left(2 a + b x^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*x**2)**(1/4)*(2*a + b*x**2)), x)","F",0
311,0,0,0,0.000000," ","integrate(1/(-b*x**2+a)**(1/4)/(-b*x**2+2*a),x)","- \int \frac{1}{- 2 a \sqrt[4]{a - b x^{2}} + b x^{2} \sqrt[4]{a - b x^{2}}}\, dx"," ",0,"-Integral(1/(-2*a*(a - b*x**2)**(1/4) + b*x**2*(a - b*x**2)**(1/4)), x)","F",0
312,0,0,0,0.000000," ","integrate(1/(3*x**2-2)/(3*x**2-1)**(1/4),x)","\int \frac{1}{\left(3 x^{2} - 2\right) \sqrt[4]{3 x^{2} - 1}}\, dx"," ",0,"Integral(1/((3*x**2 - 2)*(3*x**2 - 1)**(1/4)), x)","F",0
313,0,0,0,0.000000," ","integrate(1/(-3*x**2-2)/(-3*x**2-1)**(1/4),x)","- \int \frac{1}{3 x^{2} \sqrt[4]{- 3 x^{2} - 1} + 2 \sqrt[4]{- 3 x^{2} - 1}}\, dx"," ",0,"-Integral(1/(3*x**2*(-3*x**2 - 1)**(1/4) + 2*(-3*x**2 - 1)**(1/4)), x)","F",0
314,0,0,0,0.000000," ","integrate(1/(b*x**2-2)/(b*x**2-1)**(1/4),x)","\int \frac{1}{\left(b x^{2} - 2\right) \sqrt[4]{b x^{2} - 1}}\, dx"," ",0,"Integral(1/((b*x**2 - 2)*(b*x**2 - 1)**(1/4)), x)","F",0
315,0,0,0,0.000000," ","integrate(1/(-b*x**2-2)/(-b*x**2-1)**(1/4),x)","- \int \frac{1}{b x^{2} \sqrt[4]{- b x^{2} - 1} + 2 \sqrt[4]{- b x^{2} - 1}}\, dx"," ",0,"-Integral(1/(b*x**2*(-b*x**2 - 1)**(1/4) + 2*(-b*x**2 - 1)**(1/4)), x)","F",0
316,0,0,0,0.000000," ","integrate(1/(3*x**2-2*a)/(3*x**2-a)**(1/4),x)","\int \frac{1}{\left(- 2 a + 3 x^{2}\right) \sqrt[4]{- a + 3 x^{2}}}\, dx"," ",0,"Integral(1/((-2*a + 3*x**2)*(-a + 3*x**2)**(1/4)), x)","F",0
317,0,0,0,0.000000," ","integrate(1/(-3*x**2-2*a)/(-3*x**2-a)**(1/4),x)","- \int \frac{1}{2 a \sqrt[4]{- a - 3 x^{2}} + 3 x^{2} \sqrt[4]{- a - 3 x^{2}}}\, dx"," ",0,"-Integral(1/(2*a*(-a - 3*x**2)**(1/4) + 3*x**2*(-a - 3*x**2)**(1/4)), x)","F",0
318,0,0,0,0.000000," ","integrate(1/(b*x**2-2*a)/(b*x**2-a)**(1/4),x)","\int \frac{1}{\left(- 2 a + b x^{2}\right) \sqrt[4]{- a + b x^{2}}}\, dx"," ",0,"Integral(1/((-2*a + b*x**2)*(-a + b*x**2)**(1/4)), x)","F",0
319,0,0,0,0.000000," ","integrate(1/(-b*x**2-2*a)/(-b*x**2-a)**(1/4),x)","- \int \frac{1}{2 a \sqrt[4]{- a - b x^{2}} + b x^{2} \sqrt[4]{- a - b x^{2}}}\, dx"," ",0,"-Integral(1/(2*a*(-a - b*x**2)**(1/4) + b*x**2*(-a - b*x**2)**(1/4)), x)","F",0
320,0,0,0,0.000000," ","integrate(1/(-x**2+2)/(x**2-1)**(1/4),x)","- \int \frac{1}{x^{2} \sqrt[4]{x^{2} - 1} - 2 \sqrt[4]{x^{2} - 1}}\, dx"," ",0,"-Integral(1/(x**2*(x**2 - 1)**(1/4) - 2*(x**2 - 1)**(1/4)), x)","F",0
321,0,0,0,0.000000," ","integrate((b*x**2+a)**(7/4)/(d*x**2+c),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{7}{4}}}{c + d x^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(7/4)/(c + d*x**2), x)","F",0
322,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/4)/(d*x**2+c),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{4}}}{c + d x^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(5/4)/(c + d*x**2), x)","F",0
323,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/4)/(d*x**2+c),x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{4}}}{c + d x^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(3/4)/(c + d*x**2), x)","F",0
324,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/4)/(d*x**2+c),x)","\int \frac{\sqrt[4]{a + b x^{2}}}{c + d x^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(1/4)/(c + d*x**2), x)","F",0
325,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/4)/(d*x**2+c),x)","\int \frac{1}{\sqrt[4]{a + b x^{2}} \left(c + d x^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*x**2)**(1/4)*(c + d*x**2)), x)","F",0
326,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(3/4)/(d*x**2+c),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{3}{4}} \left(c + d x^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*x**2)**(3/4)*(c + d*x**2)), x)","F",0
327,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(5/4)/(d*x**2+c),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{5}{4}} \left(c + d x^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*x**2)**(5/4)*(c + d*x**2)), x)","F",0
328,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(7/4)/(d*x**2+c),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{7}{4}} \left(c + d x^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*x**2)**(7/4)*(c + d*x**2)), x)","F",0
329,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(9/4)/(d*x**2+c),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{9}{4}} \left(c + d x^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*x**2)**(9/4)*(c + d*x**2)), x)","F",0
330,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(11/4)/(d*x**2+c),x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{11}{4}} \left(c + d x^{2}\right)}\, dx"," ",0,"Integral(1/((a + b*x**2)**(11/4)*(c + d*x**2)), x)","F",0
331,0,0,0,0.000000," ","integrate((b*x**2+a)**(7/4)/(d*x**2+c)**2,x)","\int \frac{\left(a + b x^{2}\right)^{\frac{7}{4}}}{\left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(7/4)/(c + d*x**2)**2, x)","F",0
332,0,0,0,0.000000," ","integrate((b*x**2+a)**(5/4)/(d*x**2+c)**2,x)","\int \frac{\left(a + b x^{2}\right)^{\frac{5}{4}}}{\left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(5/4)/(c + d*x**2)**2, x)","F",0
333,0,0,0,0.000000," ","integrate((b*x**2+a)**(3/4)/(d*x**2+c)**2,x)","\int \frac{\left(a + b x^{2}\right)^{\frac{3}{4}}}{\left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(3/4)/(c + d*x**2)**2, x)","F",0
334,0,0,0,0.000000," ","integrate((b*x**2+a)**(1/4)/(d*x**2+c)**2,x)","\int \frac{\sqrt[4]{a + b x^{2}}}{\left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral((a + b*x**2)**(1/4)/(c + d*x**2)**2, x)","F",0
335,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(1/4)/(d*x**2+c)**2,x)","\int \frac{1}{\sqrt[4]{a + b x^{2}} \left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(1/4)*(c + d*x**2)**2), x)","F",0
336,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(3/4)/(d*x**2+c)**2,x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{3}{4}} \left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(3/4)*(c + d*x**2)**2), x)","F",0
337,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(5/4)/(d*x**2+c)**2,x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{5}{4}} \left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(5/4)*(c + d*x**2)**2), x)","F",0
338,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(7/4)/(d*x**2+c)**2,x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{7}{4}} \left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(7/4)*(c + d*x**2)**2), x)","F",0
339,0,0,0,0.000000," ","integrate(1/(b*x**2+a)**(9/4)/(d*x**2+c)**2,x)","\int \frac{1}{\left(a + b x^{2}\right)^{\frac{9}{4}} \left(c + d x^{2}\right)^{2}}\, dx"," ",0,"Integral(1/((a + b*x**2)**(9/4)*(c + d*x**2)**2), x)","F",0
340,-1,0,0,0.000000," ","integrate(1/(b*x**2+a)**(11/4)/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
341,-1,0,0,0.000000," ","integrate((b*x**2+a)**p*(d*x**2+c)**q,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
342,1,121,0,39.510939," ","integrate((b*x**2+a)**p*(d*x**2+c)**3,x)","a^{p} c^{3} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} + a^{p} c^{2} d x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} + \frac{3 a^{p} c d^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5} + \frac{a^{p} d^{3} x^{7} {{}_{2}F_{1}\left(\begin{matrix} \frac{7}{2}, - p \\ \frac{9}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{7}"," ",0,"a**p*c**3*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) + a**p*c**2*d*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a) + 3*a**p*c*d**2*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5 + a**p*d**3*x**7*hyper((7/2, -p), (9/2,), b*x**2*exp_polar(I*pi)/a)/7","C",0
343,1,88,0,20.396608," ","integrate((b*x**2+a)**p*(d*x**2+c)**2,x)","a^{p} c^{2} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} + \frac{2 a^{p} c d x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3} + \frac{a^{p} d^{2} x^{5} {{}_{2}F_{1}\left(\begin{matrix} \frac{5}{2}, - p \\ \frac{7}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{5}"," ",0,"a**p*c**2*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) + 2*a**p*c*d*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a)/3 + a**p*d**2*x**5*hyper((5/2, -p), (7/2,), b*x**2*exp_polar(I*pi)/a)/5","C",0
344,1,53,0,9.831706," ","integrate((b*x**2+a)**p*(d*x**2+c),x)","a^{p} c x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)} + \frac{a^{p} d x^{3} {{}_{2}F_{1}\left(\begin{matrix} \frac{3}{2}, - p \\ \frac{5}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}}{3}"," ",0,"a**p*c*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a) + a**p*d*x**3*hyper((3/2, -p), (5/2,), b*x**2*exp_polar(I*pi)/a)/3","C",0
345,1,22,0,2.326351," ","integrate((b*x**2+a)**p,x)","a^{p} x {{}_{2}F_{1}\left(\begin{matrix} \frac{1}{2}, - p \\ \frac{3}{2} \end{matrix}\middle| {\frac{b x^{2} e^{i \pi}}{a}} \right)}"," ",0,"a**p*x*hyper((1/2, -p), (3/2,), b*x**2*exp_polar(I*pi)/a)","C",0
346,-1,0,0,0.000000," ","integrate((b*x**2+a)**p/(d*x**2+c),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
347,-1,0,0,0.000000," ","integrate((b*x**2+a)**p/(d*x**2+c)**2,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,-1,0,0,0.000000," ","integrate((b*x**2+a)**p/(d*x**2+c)**3,x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,-1,0,0,0.000000," ","integrate((b*x**2+a)**(-1-b*c/(-2*a*d+2*b*c))*(d*x**2+c)**(-1+a*d/(-2*a*d+2*b*c)),x)","\text{Timed out}"," ",0,"Timed out","F(-1)",0
