1,1,98,0,0.566824," ","integrate((b*x^2+a)*(d*x^2+c)^4,x, algorithm=""giac"")","\frac{1}{11} \, b d^{4} x^{11} + \frac{4}{9} \, b c d^{3} x^{9} + \frac{1}{9} \, a d^{4} x^{9} + \frac{6}{7} \, b c^{2} d^{2} x^{7} + \frac{4}{7} \, a c d^{3} x^{7} + \frac{4}{5} \, b c^{3} d x^{5} + \frac{6}{5} \, a c^{2} d^{2} x^{5} + \frac{1}{3} \, b c^{4} x^{3} + \frac{4}{3} \, a c^{3} d x^{3} + a c^{4} x"," ",0,"1/11*b*d^4*x^11 + 4/9*b*c*d^3*x^9 + 1/9*a*d^4*x^9 + 6/7*b*c^2*d^2*x^7 + 4/7*a*c*d^3*x^7 + 4/5*b*c^3*d*x^5 + 6/5*a*c^2*d^2*x^5 + 1/3*b*c^4*x^3 + 4/3*a*c^3*d*x^3 + a*c^4*x","A",0
2,1,73,0,0.564962," ","integrate((b*x^2+a)*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{9} \, b d^{3} x^{9} + \frac{3}{7} \, b c d^{2} x^{7} + \frac{1}{7} \, a d^{3} x^{7} + \frac{3}{5} \, b c^{2} d x^{5} + \frac{3}{5} \, a c d^{2} x^{5} + \frac{1}{3} \, b c^{3} x^{3} + a c^{2} d x^{3} + a c^{3} x"," ",0,"1/9*b*d^3*x^9 + 3/7*b*c*d^2*x^7 + 1/7*a*d^3*x^7 + 3/5*b*c^2*d*x^5 + 3/5*a*c*d^2*x^5 + 1/3*b*c^3*x^3 + a*c^2*d*x^3 + a*c^3*x","A",0
3,1,50,0,0.570417," ","integrate((b*x^2+a)*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{7} \, b d^{2} x^{7} + \frac{2}{5} \, b c d x^{5} + \frac{1}{5} \, a d^{2} x^{5} + \frac{1}{3} \, b c^{2} x^{3} + \frac{2}{3} \, a c d x^{3} + a c^{2} x"," ",0,"1/7*b*d^2*x^7 + 2/5*b*c*d*x^5 + 1/5*a*d^2*x^5 + 1/3*b*c^2*x^3 + 2/3*a*c*d*x^3 + a*c^2*x","A",0
4,1,26,0,0.560879," ","integrate((b*x^2+a)*(d*x^2+c),x, algorithm=""giac"")","\frac{1}{5} \, b d x^{5} + \frac{1}{3} \, b c x^{3} + \frac{1}{3} \, a d x^{3} + a c x"," ",0,"1/5*b*d*x^5 + 1/3*b*c*x^3 + 1/3*a*d*x^3 + a*c*x","A",0
5,1,34,0,0.570706," ","integrate((b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{b x}{d} - \frac{{\left(b c - a d\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} d}"," ",0,"b*x/d - (b*c - a*d)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d)","A",0
6,1,57,0,0.582519," ","integrate((b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(b c + a d\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{c d} c d} - \frac{b c x - a d x}{2 \, {\left(d x^{2} + c\right)} c d}"," ",0,"1/2*(b*c + a*d)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c*d) - 1/2*(b*c*x - a*d*x)/((d*x^2 + c)*c*d)","A",0
7,1,78,0,0.587046," ","integrate((b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{{\left(b c + 3 \, a d\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{c d} c^{2} d} + \frac{b c d x^{3} + 3 \, a d^{2} x^{3} - b c^{2} x + 5 \, a c d x}{8 \, {\left(d x^{2} + c\right)}^{2} c^{2} d}"," ",0,"1/8*(b*c + 3*a*d)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^2*d) + 1/8*(b*c*d*x^3 + 3*a*d^2*x^3 - b*c^2*x + 5*a*c*d*x)/((d*x^2 + c)^2*c^2*d)","A",0
8,1,131,0,0.564343," ","integrate((b*x^2+a)^2*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{11} \, b^{2} d^{3} x^{11} + \frac{1}{3} \, b^{2} c d^{2} x^{9} + \frac{2}{9} \, a b d^{3} x^{9} + \frac{3}{7} \, b^{2} c^{2} d x^{7} + \frac{6}{7} \, a b c d^{2} x^{7} + \frac{1}{7} \, a^{2} d^{3} x^{7} + \frac{1}{5} \, b^{2} c^{3} x^{5} + \frac{6}{5} \, a b c^{2} d x^{5} + \frac{3}{5} \, a^{2} c d^{2} x^{5} + \frac{2}{3} \, a b c^{3} x^{3} + a^{2} c^{2} d x^{3} + a^{2} c^{3} x"," ",0,"1/11*b^2*d^3*x^11 + 1/3*b^2*c*d^2*x^9 + 2/9*a*b*d^3*x^9 + 3/7*b^2*c^2*d*x^7 + 6/7*a*b*c*d^2*x^7 + 1/7*a^2*d^3*x^7 + 1/5*b^2*c^3*x^5 + 6/5*a*b*c^2*d*x^5 + 3/5*a^2*c*d^2*x^5 + 2/3*a*b*c^3*x^3 + a^2*c^2*d*x^3 + a^2*c^3*x","A",0
9,1,91,0,0.572266," ","integrate((b*x^2+a)^2*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{9} \, b^{2} d^{2} x^{9} + \frac{2}{7} \, b^{2} c d x^{7} + \frac{2}{7} \, a b d^{2} x^{7} + \frac{1}{5} \, b^{2} c^{2} x^{5} + \frac{4}{5} \, a b c d x^{5} + \frac{1}{5} \, a^{2} d^{2} x^{5} + \frac{2}{3} \, a b c^{2} x^{3} + \frac{2}{3} \, a^{2} c d x^{3} + a^{2} c^{2} x"," ",0,"1/9*b^2*d^2*x^9 + 2/7*b^2*c*d*x^7 + 2/7*a*b*d^2*x^7 + 1/5*b^2*c^2*x^5 + 4/5*a*b*c*d*x^5 + 1/5*a^2*d^2*x^5 + 2/3*a*b*c^2*x^3 + 2/3*a^2*c*d*x^3 + a^2*c^2*x","A",0
10,1,50,0,0.569108," ","integrate((b*x^2+a)^2*(d*x^2+c),x, algorithm=""giac"")","\frac{1}{7} \, b^{2} d x^{7} + \frac{1}{5} \, b^{2} c x^{5} + \frac{2}{5} \, a b d x^{5} + \frac{2}{3} \, a b c x^{3} + \frac{1}{3} \, a^{2} d x^{3} + a^{2} c x"," ",0,"1/7*b^2*d*x^7 + 1/5*b^2*c*x^5 + 2/5*a*b*d*x^5 + 2/3*a*b*c*x^3 + 1/3*a^2*d*x^3 + a^2*c*x","A",0
11,1,72,0,0.585267," ","integrate((b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} d^{2}} + \frac{b^{2} d^{2} x^{3} - 3 \, b^{2} c d x + 6 \, a b d^{2} x}{3 \, d^{3}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d^2) + 1/3*(b^2*d^2*x^3 - 3*b^2*c*d*x + 6*a*b*d^2*x)/d^3","A",0
12,1,95,0,0.570313," ","integrate((b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{b^{2} x}{d^{2}} - \frac{{\left(3 \, b^{2} c^{2} - 2 \, a b c d - a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{c d} c d^{2}} + \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{2 \, {\left(d x^{2} + c\right)} c d^{2}}"," ",0,"b^2*x/d^2 - 1/2*(3*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c*d^2) + 1/2*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((d*x^2 + c)*c*d^2)","A",0
13,1,126,0,0.585177," ","integrate((b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{c d} c^{2} d^{2}} - \frac{5 \, b^{2} c^{2} d x^{3} - 2 \, a b c d^{2} x^{3} - 3 \, a^{2} d^{3} x^{3} + 3 \, b^{2} c^{3} x + 2 \, a b c^{2} d x - 5 \, a^{2} c d^{2} x}{8 \, {\left(d x^{2} + c\right)}^{2} c^{2} d^{2}}"," ",0,"1/8*(3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^2*d^2) - 1/8*(5*b^2*c^2*d*x^3 - 2*a*b*c*d^2*x^3 - 3*a^2*d^3*x^3 + 3*b^2*c^3*x + 2*a*b*c^2*d*x - 5*a^2*c*d^2*x)/((d*x^2 + c)^2*c^2*d^2)","A",0
14,1,187,0,0.567466," ","integrate((b*x^2+a)^3*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{13} \, b^{3} d^{3} x^{13} + \frac{3}{11} \, b^{3} c d^{2} x^{11} + \frac{3}{11} \, a b^{2} d^{3} x^{11} + \frac{1}{3} \, b^{3} c^{2} d x^{9} + a b^{2} c d^{2} x^{9} + \frac{1}{3} \, a^{2} b d^{3} x^{9} + \frac{1}{7} \, b^{3} c^{3} x^{7} + \frac{9}{7} \, a b^{2} c^{2} d x^{7} + \frac{9}{7} \, a^{2} b c d^{2} x^{7} + \frac{1}{7} \, a^{3} d^{3} x^{7} + \frac{3}{5} \, a b^{2} c^{3} x^{5} + \frac{9}{5} \, a^{2} b c^{2} d x^{5} + \frac{3}{5} \, a^{3} c d^{2} x^{5} + a^{2} b c^{3} x^{3} + a^{3} c^{2} d x^{3} + a^{3} c^{3} x"," ",0,"1/13*b^3*d^3*x^13 + 3/11*b^3*c*d^2*x^11 + 3/11*a*b^2*d^3*x^11 + 1/3*b^3*c^2*d*x^9 + a*b^2*c*d^2*x^9 + 1/3*a^2*b*d^3*x^9 + 1/7*b^3*c^3*x^7 + 9/7*a*b^2*c^2*d*x^7 + 9/7*a^2*b*c*d^2*x^7 + 1/7*a^3*d^3*x^7 + 3/5*a*b^2*c^3*x^5 + 9/5*a^2*b*c^2*d*x^5 + 3/5*a^3*c*d^2*x^5 + a^2*b*c^3*x^3 + a^3*c^2*d*x^3 + a^3*c^3*x","A",0
15,1,131,0,0.590556," ","integrate((b*x^2+a)^3*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{11} \, b^{3} d^{2} x^{11} + \frac{2}{9} \, b^{3} c d x^{9} + \frac{1}{3} \, a b^{2} d^{2} x^{9} + \frac{1}{7} \, b^{3} c^{2} x^{7} + \frac{6}{7} \, a b^{2} c d x^{7} + \frac{3}{7} \, a^{2} b d^{2} x^{7} + \frac{3}{5} \, a b^{2} c^{2} x^{5} + \frac{6}{5} \, a^{2} b c d x^{5} + \frac{1}{5} \, a^{3} d^{2} x^{5} + a^{2} b c^{2} x^{3} + \frac{2}{3} \, a^{3} c d x^{3} + a^{3} c^{2} x"," ",0,"1/11*b^3*d^2*x^11 + 2/9*b^3*c*d*x^9 + 1/3*a*b^2*d^2*x^9 + 1/7*b^3*c^2*x^7 + 6/7*a*b^2*c*d*x^7 + 3/7*a^2*b*d^2*x^7 + 3/5*a*b^2*c^2*x^5 + 6/5*a^2*b*c*d*x^5 + 1/5*a^3*d^2*x^5 + a^2*b*c^2*x^3 + 2/3*a^3*c*d*x^3 + a^3*c^2*x","A",0
16,1,73,0,0.564757," ","integrate((b*x^2+a)^3*(d*x^2+c),x, algorithm=""giac"")","\frac{1}{9} \, b^{3} d x^{9} + \frac{1}{7} \, b^{3} c x^{7} + \frac{3}{7} \, a b^{2} d x^{7} + \frac{3}{5} \, a b^{2} c x^{5} + \frac{3}{5} \, a^{2} b d x^{5} + a^{2} b c x^{3} + \frac{1}{3} \, a^{3} d x^{3} + a^{3} c x"," ",0,"1/9*b^3*d*x^9 + 1/7*b^3*c*x^7 + 3/7*a*b^2*d*x^7 + 3/5*a*b^2*c*x^5 + 3/5*a^2*b*d*x^5 + a^2*b*c*x^3 + 1/3*a^3*d*x^3 + a^3*c*x","A",0
17,1,130,0,0.576787," ","integrate((b*x^2+a)^3/(d*x^2+c),x, algorithm=""giac"")","-\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d} d^{3}} + \frac{3 \, b^{3} d^{4} x^{5} - 5 \, b^{3} c d^{3} x^{3} + 15 \, a b^{2} d^{4} x^{3} + 15 \, b^{3} c^{2} d^{2} x - 45 \, a b^{2} c d^{3} x + 45 \, a^{2} b d^{4} x}{15 \, d^{5}}"," ",0,"-(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*d^3) + 1/15*(3*b^3*d^4*x^5 - 5*b^3*c*d^3*x^3 + 15*a*b^2*d^4*x^3 + 15*b^3*c^2*d^2*x - 45*a*b^2*c*d^3*x + 45*a^2*b*d^4*x)/d^5","A",0
18,1,152,0,0.580682," ","integrate((b*x^2+a)^3/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(5 \, b^{3} c^{3} - 9 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} + a^{3} d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, \sqrt{c d} c d^{3}} - \frac{b^{3} c^{3} x - 3 \, a b^{2} c^{2} d x + 3 \, a^{2} b c d^{2} x - a^{3} d^{3} x}{2 \, {\left(d x^{2} + c\right)} c d^{3}} + \frac{b^{3} d^{4} x^{3} - 6 \, b^{3} c d^{3} x + 9 \, a b^{2} d^{4} x}{3 \, d^{6}}"," ",0,"1/2*(5*b^3*c^3 - 9*a*b^2*c^2*d + 3*a^2*b*c*d^2 + a^3*d^3)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c*d^3) - 1/2*(b^3*c^3*x - 3*a*b^2*c^2*d*x + 3*a^2*b*c*d^2*x - a^3*d^3*x)/((d*x^2 + c)*c*d^3) + 1/3*(b^3*d^4*x^3 - 6*b^3*c*d^3*x + 9*a*b^2*d^4*x)/d^6","A",0
19,1,180,0,0.586861," ","integrate((b*x^2+a)^3/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{3} x}{d^{3}} - \frac{3 \, {\left(5 \, b^{3} c^{3} - 3 \, a b^{2} c^{2} d - a^{2} b c d^{2} - a^{3} d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, \sqrt{c d} c^{2} d^{3}} + \frac{9 \, b^{3} c^{3} d x^{3} - 15 \, a b^{2} c^{2} d^{2} x^{3} + 3 \, a^{2} b c d^{3} x^{3} + 3 \, a^{3} d^{4} x^{3} + 7 \, b^{3} c^{4} x - 9 \, a b^{2} c^{3} d x - 3 \, a^{2} b c^{2} d^{2} x + 5 \, a^{3} c d^{3} x}{8 \, {\left(d x^{2} + c\right)}^{2} c^{2} d^{3}}"," ",0,"b^3*x/d^3 - 3/8*(5*b^3*c^3 - 3*a*b^2*c^2*d - a^2*b*c*d^2 - a^3*d^3)*arctan(d*x/sqrt(c*d))/(sqrt(c*d)*c^2*d^3) + 1/8*(9*b^3*c^3*d*x^3 - 15*a*b^2*c^2*d^2*x^3 + 3*a^2*b*c*d^3*x^3 + 3*a^3*d^4*x^3 + 7*b^3*c^4*x - 9*a*b^2*c^3*d*x - 3*a^2*b*c^2*d^2*x + 5*a^3*c*d^3*x)/((d*x^2 + c)^2*c^2*d^3)","A",0
20,1,198,0,0.578608," ","integrate((d*x^2+c)^4/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{4} c^{4} - 4 \, a b^{3} c^{3} d + 6 \, a^{2} b^{2} c^{2} d^{2} - 4 \, a^{3} b c d^{3} + a^{4} d^{4}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{4}} + \frac{15 \, b^{6} d^{4} x^{7} + 84 \, b^{6} c d^{3} x^{5} - 21 \, a b^{5} d^{4} x^{5} + 210 \, b^{6} c^{2} d^{2} x^{3} - 140 \, a b^{5} c d^{3} x^{3} + 35 \, a^{2} b^{4} d^{4} x^{3} + 420 \, b^{6} c^{3} d x - 630 \, a b^{5} c^{2} d^{2} x + 420 \, a^{2} b^{4} c d^{3} x - 105 \, a^{3} b^{3} d^{4} x}{105 \, b^{7}}"," ",0,"(b^4*c^4 - 4*a*b^3*c^3*d + 6*a^2*b^2*c^2*d^2 - 4*a^3*b*c*d^3 + a^4*d^4)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^4) + 1/105*(15*b^6*d^4*x^7 + 84*b^6*c*d^3*x^5 - 21*a*b^5*d^4*x^5 + 210*b^6*c^2*d^2*x^3 - 140*a*b^5*c*d^3*x^3 + 35*a^2*b^4*d^4*x^3 + 420*b^6*c^3*d*x - 630*a*b^5*c^2*d^2*x + 420*a^2*b^4*c*d^3*x - 105*a^3*b^3*d^4*x)/b^7","A",0
21,1,129,0,0.576174," ","integrate((d*x^2+c)^3/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{3}} + \frac{3 \, b^{4} d^{3} x^{5} + 15 \, b^{4} c d^{2} x^{3} - 5 \, a b^{3} d^{3} x^{3} + 45 \, b^{4} c^{2} d x - 45 \, a b^{3} c d^{2} x + 15 \, a^{2} b^{2} d^{3} x}{15 \, b^{5}}"," ",0,"(b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^3) + 1/15*(3*b^4*d^3*x^5 + 15*b^4*c*d^2*x^3 - 5*a*b^3*d^3*x^3 + 45*b^4*c^2*d*x - 45*a*b^3*c*d^2*x + 15*a^2*b^2*d^3*x)/b^5","A",0
22,1,72,0,0.567502," ","integrate((d*x^2+c)^2/(b*x^2+a),x, algorithm=""giac"")","\frac{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b^{2}} + \frac{b^{2} d^{2} x^{3} + 6 \, b^{2} c d x - 3 \, a b d^{2} x}{3 \, b^{3}}"," ",0,"(b^2*c^2 - 2*a*b*c*d + a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b^2) + 1/3*(b^2*d^2*x^3 + 6*b^2*c*d*x - 3*a*b*d^2*x)/b^3","A",0
23,1,33,0,0.570895," ","integrate((d*x^2+c)/(b*x^2+a),x, algorithm=""giac"")","\frac{d x}{b} + \frac{{\left(b c - a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} b}"," ",0,"d*x/b + (b*c - a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*b)","A",0
24,1,54,0,0.585297," ","integrate(1/(b*x^2+a)/(d*x^2+c),x, algorithm=""giac"")","\frac{b \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b} {\left(b c - a d\right)}} - \frac{d \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b c - a d\right)} \sqrt{c d}}"," ",0,"b*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*(b*c - a*d)) - d*arctan(d*x/sqrt(c*d))/((b*c - a*d)*sqrt(c*d))","A",0
25,1,122,0,0.569308," ","integrate(1/(b*x^2+a)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{b^{2} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{a b}} - \frac{{\left(3 \, b c d - a d^{2}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{c d}} - \frac{d x}{2 \, {\left(b c^{2} - a c d\right)} {\left(d x^{2} + c\right)}}"," ",0,"b^2*arctan(b*x/sqrt(a*b))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(a*b)) - 1/2*(3*b*c*d - a*d^2)*arctan(d*x/sqrt(c*d))/((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(c*d)) - 1/2*d*x/((b*c^2 - a*c*d)*(d*x^2 + c))","A",0
26,1,217,0,0.577513," ","integrate(1/(b*x^2+a)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{3} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{a b}} - \frac{{\left(15 \, b^{2} c^{2} d - 10 \, a b c d^{2} + 3 \, a^{2} d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} \sqrt{c d}} - \frac{7 \, b c d^{2} x^{3} - 3 \, a d^{3} x^{3} + 9 \, b c^{2} d x - 5 \, a c d^{2} x}{8 \, {\left(b^{2} c^{4} - 2 \, a b c^{3} d + a^{2} c^{2} d^{2}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"b^3*arctan(b*x/sqrt(a*b))/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(a*b)) - 1/8*(15*b^2*c^2*d - 10*a*b*c*d^2 + 3*a^2*d^3)*arctan(d*x/sqrt(c*d))/((b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*sqrt(c*d)) - 1/8*(7*b*c*d^2*x^3 - 3*a*d^3*x^3 + 9*b*c^2*d*x - 5*a*c*d^2*x)/((b^2*c^4 - 2*a*b*c^3*d + a^2*c^2*d^2)*(d*x^2 + c)^2)","A",0
27,1,306,0,0.579223," ","integrate((d*x^2+c)^5/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b^{5} c^{5} + 5 \, a b^{4} c^{4} d - 30 \, a^{2} b^{3} c^{3} d^{2} + 50 \, a^{3} b^{2} c^{2} d^{3} - 35 \, a^{4} b c d^{4} + 9 \, a^{5} d^{5}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{5}} + \frac{b^{5} c^{5} x - 5 \, a b^{4} c^{4} d x + 10 \, a^{2} b^{3} c^{3} d^{2} x - 10 \, a^{3} b^{2} c^{2} d^{3} x + 5 \, a^{4} b c d^{4} x - a^{5} d^{5} x}{2 \, {\left(b x^{2} + a\right)} a b^{5}} + \frac{15 \, b^{12} d^{5} x^{7} + 105 \, b^{12} c d^{4} x^{5} - 42 \, a b^{11} d^{5} x^{5} + 350 \, b^{12} c^{2} d^{3} x^{3} - 350 \, a b^{11} c d^{4} x^{3} + 105 \, a^{2} b^{10} d^{5} x^{3} + 1050 \, b^{12} c^{3} d^{2} x - 2100 \, a b^{11} c^{2} d^{3} x + 1575 \, a^{2} b^{10} c d^{4} x - 420 \, a^{3} b^{9} d^{5} x}{105 \, b^{14}}"," ",0,"1/2*(b^5*c^5 + 5*a*b^4*c^4*d - 30*a^2*b^3*c^3*d^2 + 50*a^3*b^2*c^2*d^3 - 35*a^4*b*c*d^4 + 9*a^5*d^5)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^5) + 1/2*(b^5*c^5*x - 5*a*b^4*c^4*d*x + 10*a^2*b^3*c^3*d^2*x - 10*a^3*b^2*c^2*d^3*x + 5*a^4*b*c*d^4*x - a^5*d^5*x)/((b*x^2 + a)*a*b^5) + 1/105*(15*b^12*d^5*x^7 + 105*b^12*c*d^4*x^5 - 42*a*b^11*d^5*x^5 + 350*b^12*c^2*d^3*x^3 - 350*a*b^11*c*d^4*x^3 + 105*a^2*b^10*d^5*x^3 + 1050*b^12*c^3*d^2*x - 2100*a*b^11*c^2*d^3*x + 1575*a^2*b^10*c*d^4*x - 420*a^3*b^9*d^5*x)/b^14","A",0
28,1,220,0,0.575795," ","integrate((d*x^2+c)^4/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b^{4} c^{4} + 4 \, a b^{3} c^{3} d - 18 \, a^{2} b^{2} c^{2} d^{2} + 20 \, a^{3} b c d^{3} - 7 \, a^{4} d^{4}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{4}} + \frac{b^{4} c^{4} x - 4 \, a b^{3} c^{3} d x + 6 \, a^{2} b^{2} c^{2} d^{2} x - 4 \, a^{3} b c d^{3} x + a^{4} d^{4} x}{2 \, {\left(b x^{2} + a\right)} a b^{4}} + \frac{3 \, b^{8} d^{4} x^{5} + 20 \, b^{8} c d^{3} x^{3} - 10 \, a b^{7} d^{4} x^{3} + 90 \, b^{8} c^{2} d^{2} x - 120 \, a b^{7} c d^{3} x + 45 \, a^{2} b^{6} d^{4} x}{15 \, b^{10}}"," ",0,"1/2*(b^4*c^4 + 4*a*b^3*c^3*d - 18*a^2*b^2*c^2*d^2 + 20*a^3*b*c*d^3 - 7*a^4*d^4)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^4) + 1/2*(b^4*c^4*x - 4*a*b^3*c^3*d*x + 6*a^2*b^2*c^2*d^2*x - 4*a^3*b*c*d^3*x + a^4*d^4*x)/((b*x^2 + a)*a*b^4) + 1/15*(3*b^8*d^4*x^5 + 20*b^8*c*d^3*x^3 - 10*a*b^7*d^4*x^3 + 90*b^8*c^2*d^2*x - 120*a*b^7*c*d^3*x + 45*a^2*b^6*d^4*x)/b^10","A",0
29,1,152,0,0.567921," ","integrate((d*x^2+c)^3/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b^{3} c^{3} + 3 \, a b^{2} c^{2} d - 9 \, a^{2} b c d^{2} + 5 \, a^{3} d^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{3}} + \frac{b^{3} c^{3} x - 3 \, a b^{2} c^{2} d x + 3 \, a^{2} b c d^{2} x - a^{3} d^{3} x}{2 \, {\left(b x^{2} + a\right)} a b^{3}} + \frac{b^{4} d^{3} x^{3} + 9 \, b^{4} c d^{2} x - 6 \, a b^{3} d^{3} x}{3 \, b^{6}}"," ",0,"1/2*(b^3*c^3 + 3*a*b^2*c^2*d - 9*a^2*b*c*d^2 + 5*a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^3) + 1/2*(b^3*c^3*x - 3*a*b^2*c^2*d*x + 3*a^2*b*c*d^2*x - a^3*d^3*x)/((b*x^2 + a)*a*b^3) + 1/3*(b^4*d^3*x^3 + 9*b^4*c*d^2*x - 6*a*b^3*d^3*x)/b^6","A",0
30,1,94,0,0.584171," ","integrate((d*x^2+c)^2/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{d^{2} x}{b^{2}} + \frac{{\left(b^{2} c^{2} + 2 \, a b c d - 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b^{2}} + \frac{b^{2} c^{2} x - 2 \, a b c d x + a^{2} d^{2} x}{2 \, {\left(b x^{2} + a\right)} a b^{2}}"," ",0,"d^2*x/b^2 + 1/2*(b^2*c^2 + 2*a*b*c*d - 3*a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b^2) + 1/2*(b^2*c^2*x - 2*a*b*c*d*x + a^2*d^2*x)/((b*x^2 + a)*a*b^2)","A",0
31,1,57,0,0.572414," ","integrate((d*x^2+c)/(b*x^2+a)^2,x, algorithm=""giac"")","\frac{{\left(b c + a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, \sqrt{a b} a b} + \frac{b c x - a d x}{2 \, {\left(b x^{2} + a\right)} a b}"," ",0,"1/2*(b*c + a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a*b) + 1/2*(b*c*x - a*d*x)/((b*x^2 + a)*a*b)","A",0
32,1,121,0,0.575866," ","integrate(1/(b*x^2+a)^2/(d*x^2+c),x, algorithm=""giac"")","\frac{d^{2} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{c d}} + \frac{{\left(b^{2} c - 3 \, a b d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{a b}} + \frac{b x}{2 \, {\left(a b c - a^{2} d\right)} {\left(b x^{2} + a\right)}}"," ",0,"d^2*arctan(d*x/sqrt(c*d))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(c*d)) + 1/2*(b^2*c - 3*a*b*d)*arctan(b*x/sqrt(a*b))/((a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*sqrt(a*b)) + 1/2*b*x/((a*b*c - a^2*d)*(b*x^2 + a))","A",0
33,1,232,0,0.583268," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(b^{3} c - 5 \, a b^{2} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \sqrt{a b}} + \frac{{\left(5 \, b c d^{2} - a d^{3}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} \sqrt{c d}} + \frac{b^{2} c d x^{3} + a b d^{2} x^{3} + b^{2} c^{2} x + a^{2} d^{2} x}{2 \, {\left(a b^{2} c^{3} - 2 \, a^{2} b c^{2} d + a^{3} c d^{2}\right)} {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)}}"," ",0,"1/2*(b^3*c - 5*a*b^2*d)*arctan(b*x/sqrt(a*b))/((a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*sqrt(a*b)) + 1/2*(5*b*c*d^2 - a*d^3)*arctan(d*x/sqrt(c*d))/((b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*sqrt(c*d)) + 1/2*(b^2*c*d*x^3 + a*b*d^2*x^3 + b^2*c^2*x + a^2*d^2*x)/((a*b^2*c^3 - 2*a^2*b*c^2*d + a^3*c*d^2)*(b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c))","A",0
34,1,332,0,0.581802," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{3} x}{2 \, {\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} {\left(b x^{2} + a\right)}} + \frac{{\left(b^{4} c - 7 \, a b^{3} d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{2 \, {\left(a b^{4} c^{4} - 4 \, a^{2} b^{3} c^{3} d + 6 \, a^{3} b^{2} c^{2} d^{2} - 4 \, a^{4} b c d^{3} + a^{5} d^{4}\right)} \sqrt{a b}} + \frac{{\left(35 \, b^{2} c^{2} d^{2} - 14 \, a b c d^{3} + 3 \, a^{2} d^{4}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\left(b^{4} c^{6} - 4 \, a b^{3} c^{5} d + 6 \, a^{2} b^{2} c^{4} d^{2} - 4 \, a^{3} b c^{3} d^{3} + a^{4} c^{2} d^{4}\right)} \sqrt{c d}} + \frac{11 \, b c d^{3} x^{3} - 3 \, a d^{4} x^{3} + 13 \, b c^{2} d^{2} x - 5 \, a c d^{3} x}{8 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} {\left(d x^{2} + c\right)}^{2}}"," ",0,"1/2*b^3*x/((a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*(b*x^2 + a)) + 1/2*(b^4*c - 7*a*b^3*d)*arctan(b*x/sqrt(a*b))/((a*b^4*c^4 - 4*a^2*b^3*c^3*d + 6*a^3*b^2*c^2*d^2 - 4*a^4*b*c*d^3 + a^5*d^4)*sqrt(a*b)) + 1/8*(35*b^2*c^2*d^2 - 14*a*b*c*d^3 + 3*a^2*d^4)*arctan(d*x/sqrt(c*d))/((b^4*c^6 - 4*a*b^3*c^5*d + 6*a^2*b^2*c^4*d^2 - 4*a^3*b*c^3*d^3 + a^4*c^2*d^4)*sqrt(c*d)) + 1/8*(11*b*c*d^3*x^3 - 3*a*d^4*x^3 + 13*b*c^2*d^2*x - 5*a*c*d^3*x)/((b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*(d*x^2 + c)^2)","A",0
35,1,340,0,0.580145," ","integrate((d*x^2+c)^5/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, b^{5} c^{5} + 5 \, a b^{4} c^{4} d + 30 \, a^{2} b^{3} c^{3} d^{2} - 150 \, a^{3} b^{2} c^{2} d^{3} + 175 \, a^{4} b c d^{4} - 63 \, a^{5} d^{5}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b^{5}} + \frac{3 \, b^{6} c^{5} x^{3} + 5 \, a b^{5} c^{4} d x^{3} - 50 \, a^{2} b^{4} c^{3} d^{2} x^{3} + 90 \, a^{3} b^{3} c^{2} d^{3} x^{3} - 65 \, a^{4} b^{2} c d^{4} x^{3} + 17 \, a^{5} b d^{5} x^{3} + 5 \, a b^{5} c^{5} x - 5 \, a^{2} b^{4} c^{4} d x - 30 \, a^{3} b^{3} c^{3} d^{2} x + 70 \, a^{4} b^{2} c^{2} d^{3} x - 55 \, a^{5} b c d^{4} x + 15 \, a^{6} d^{5} x}{8 \, {\left(b x^{2} + a\right)}^{2} a^{2} b^{5}} + \frac{3 \, b^{12} d^{5} x^{5} + 25 \, b^{12} c d^{4} x^{3} - 15 \, a b^{11} d^{5} x^{3} + 150 \, b^{12} c^{2} d^{3} x - 225 \, a b^{11} c d^{4} x + 90 \, a^{2} b^{10} d^{5} x}{15 \, b^{15}}"," ",0,"1/8*(3*b^5*c^5 + 5*a*b^4*c^4*d + 30*a^2*b^3*c^3*d^2 - 150*a^3*b^2*c^2*d^3 + 175*a^4*b*c*d^4 - 63*a^5*d^5)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^5) + 1/8*(3*b^6*c^5*x^3 + 5*a*b^5*c^4*d*x^3 - 50*a^2*b^4*c^3*d^2*x^3 + 90*a^3*b^3*c^2*d^3*x^3 - 65*a^4*b^2*c*d^4*x^3 + 17*a^5*b*d^5*x^3 + 5*a*b^5*c^5*x - 5*a^2*b^4*c^4*d*x - 30*a^3*b^3*c^3*d^2*x + 70*a^4*b^2*c^2*d^3*x - 55*a^5*b*c*d^4*x + 15*a^6*d^5*x)/((b*x^2 + a)^2*a^2*b^5) + 1/15*(3*b^12*d^5*x^5 + 25*b^12*c*d^4*x^3 - 15*a*b^11*d^5*x^3 + 150*b^12*c^2*d^3*x - 225*a*b^11*c*d^4*x + 90*a^2*b^10*d^5*x)/b^15","A",0
36,1,254,0,0.583213," ","integrate((d*x^2+c)^4/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, b^{4} c^{4} + 4 \, a b^{3} c^{3} d + 18 \, a^{2} b^{2} c^{2} d^{2} - 60 \, a^{3} b c d^{3} + 35 \, a^{4} d^{4}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b^{4}} + \frac{3 \, b^{5} c^{4} x^{3} + 4 \, a b^{4} c^{3} d x^{3} - 30 \, a^{2} b^{3} c^{2} d^{2} x^{3} + 36 \, a^{3} b^{2} c d^{3} x^{3} - 13 \, a^{4} b d^{4} x^{3} + 5 \, a b^{4} c^{4} x - 4 \, a^{2} b^{3} c^{3} d x - 18 \, a^{3} b^{2} c^{2} d^{2} x + 28 \, a^{4} b c d^{3} x - 11 \, a^{5} d^{4} x}{8 \, {\left(b x^{2} + a\right)}^{2} a^{2} b^{4}} + \frac{b^{6} d^{4} x^{3} + 12 \, b^{6} c d^{3} x - 9 \, a b^{5} d^{4} x}{3 \, b^{9}}"," ",0,"1/8*(3*b^4*c^4 + 4*a*b^3*c^3*d + 18*a^2*b^2*c^2*d^2 - 60*a^3*b*c*d^3 + 35*a^4*d^4)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^4) + 1/8*(3*b^5*c^4*x^3 + 4*a*b^4*c^3*d*x^3 - 30*a^2*b^3*c^2*d^2*x^3 + 36*a^3*b^2*c*d^3*x^3 - 13*a^4*b*d^4*x^3 + 5*a*b^4*c^4*x - 4*a^2*b^3*c^3*d*x - 18*a^3*b^2*c^2*d^2*x + 28*a^4*b*c*d^3*x - 11*a^5*d^4*x)/((b*x^2 + a)^2*a^2*b^4) + 1/3*(b^6*d^4*x^3 + 12*b^6*c*d^3*x - 9*a*b^5*d^4*x)/b^9","A",0
37,1,178,0,0.570580," ","integrate((d*x^2+c)^3/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{d^{3} x}{b^{3}} + \frac{3 \, {\left(b^{3} c^{3} + a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b^{3}} + \frac{3 \, b^{4} c^{3} x^{3} + 3 \, a b^{3} c^{2} d x^{3} - 15 \, a^{2} b^{2} c d^{2} x^{3} + 9 \, a^{3} b d^{3} x^{3} + 5 \, a b^{3} c^{3} x - 3 \, a^{2} b^{2} c^{2} d x - 9 \, a^{3} b c d^{2} x + 7 \, a^{4} d^{3} x}{8 \, {\left(b x^{2} + a\right)}^{2} a^{2} b^{3}}"," ",0,"d^3*x/b^3 + 3/8*(b^3*c^3 + a*b^2*c^2*d + 3*a^2*b*c*d^2 - 5*a^3*d^3)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^3) + 1/8*(3*b^4*c^3*x^3 + 3*a*b^3*c^2*d*x^3 - 15*a^2*b^2*c*d^2*x^3 + 9*a^3*b*d^3*x^3 + 5*a*b^3*c^3*x - 3*a^2*b^2*c^2*d*x - 9*a^3*b*c*d^2*x + 7*a^4*d^3*x)/((b*x^2 + a)^2*a^2*b^3)","A",0
38,1,126,0,0.569469," ","integrate((d*x^2+c)^2/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, b^{2} c^{2} + 2 \, a b c d + 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b^{2}} + \frac{3 \, b^{3} c^{2} x^{3} + 2 \, a b^{2} c d x^{3} - 5 \, a^{2} b d^{2} x^{3} + 5 \, a b^{2} c^{2} x - 2 \, a^{2} b c d x - 3 \, a^{3} d^{2} x}{8 \, {\left(b x^{2} + a\right)}^{2} a^{2} b^{2}}"," ",0,"1/8*(3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b^2) + 1/8*(3*b^3*c^2*x^3 + 2*a*b^2*c*d*x^3 - 5*a^2*b*d^2*x^3 + 5*a*b^2*c^2*x - 2*a^2*b*c*d*x - 3*a^3*d^2*x)/((b*x^2 + a)^2*a^2*b^2)","A",0
39,1,78,0,0.575731," ","integrate((d*x^2+c)/(b*x^2+a)^3,x, algorithm=""giac"")","\frac{{\left(3 \, b c + a d\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, \sqrt{a b} a^{2} b} + \frac{3 \, b^{2} c x^{3} + a b d x^{3} + 5 \, a b c x - a^{2} d x}{8 \, {\left(b x^{2} + a\right)}^{2} a^{2} b}"," ",0,"1/8*(3*b*c + a*d)*arctan(b*x/sqrt(a*b))/(sqrt(a*b)*a^2*b) + 1/8*(3*b^2*c*x^3 + a*b*d*x^3 + 5*a*b*c*x - a^2*d*x)/((b*x^2 + a)^2*a^2*b)","A",0
40,1,218,0,0.577599," ","integrate(1/(b*x^2+a)^3/(d*x^2+c),x, algorithm=""giac"")","-\frac{d^{3} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{{\left(b^{3} c^{3} - 3 \, a b^{2} c^{2} d + 3 \, a^{2} b c d^{2} - a^{3} d^{3}\right)} \sqrt{c d}} + \frac{{\left(3 \, b^{3} c^{2} - 10 \, a b^{2} c d + 15 \, a^{2} b d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \sqrt{a b}} + \frac{3 \, b^{3} c x^{3} - 7 \, a b^{2} d x^{3} + 5 \, a b^{2} c x - 9 \, a^{2} b d x}{8 \, {\left(a^{2} b^{2} c^{2} - 2 \, a^{3} b c d + a^{4} d^{2}\right)} {\left(b x^{2} + a\right)}^{2}}"," ",0,"-d^3*arctan(d*x/sqrt(c*d))/((b^3*c^3 - 3*a*b^2*c^2*d + 3*a^2*b*c*d^2 - a^3*d^3)*sqrt(c*d)) + 1/8*(3*b^3*c^2 - 10*a*b^2*c*d + 15*a^2*b*d^2)*arctan(b*x/sqrt(a*b))/((a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*sqrt(a*b)) + 1/8*(3*b^3*c*x^3 - 7*a*b^2*d*x^3 + 5*a*b^2*c*x - 9*a^2*b*d*x)/((a^2*b^2*c^2 - 2*a^3*b*c*d + a^4*d^2)*(b*x^2 + a)^2)","A",0
41,1,333,0,0.611710," ","integrate(1/(b*x^2+a)^3/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{d^{3} x}{2 \, {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} {\left(d x^{2} + c\right)}} + \frac{{\left(3 \, b^{4} c^{2} - 14 \, a b^{3} c d + 35 \, a^{2} b^{2} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, {\left(a^{2} b^{4} c^{4} - 4 \, a^{3} b^{3} c^{3} d + 6 \, a^{4} b^{2} c^{2} d^{2} - 4 \, a^{5} b c d^{3} + a^{6} d^{4}\right)} \sqrt{a b}} - \frac{{\left(7 \, b c d^{3} - a d^{4}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{2 \, {\left(b^{4} c^{5} - 4 \, a b^{3} c^{4} d + 6 \, a^{2} b^{2} c^{3} d^{2} - 4 \, a^{3} b c^{2} d^{3} + a^{4} c d^{4}\right)} \sqrt{c d}} + \frac{3 \, b^{4} c x^{3} - 11 \, a b^{3} d x^{3} + 5 \, a b^{3} c x - 13 \, a^{2} b^{2} d x}{8 \, {\left(a^{2} b^{3} c^{3} - 3 \, a^{3} b^{2} c^{2} d + 3 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} {\left(b x^{2} + a\right)}^{2}}"," ",0,"-1/2*d^3*x/((b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*(d*x^2 + c)) + 1/8*(3*b^4*c^2 - 14*a*b^3*c*d + 35*a^2*b^2*d^2)*arctan(b*x/sqrt(a*b))/((a^2*b^4*c^4 - 4*a^3*b^3*c^3*d + 6*a^4*b^2*c^2*d^2 - 4*a^5*b*c*d^3 + a^6*d^4)*sqrt(a*b)) - 1/2*(7*b*c*d^3 - a*d^4)*arctan(d*x/sqrt(c*d))/((b^4*c^5 - 4*a*b^3*c^4*d + 6*a^2*b^2*c^3*d^2 - 4*a^3*b*c^2*d^3 + a^4*c*d^4)*sqrt(c*d)) + 1/8*(3*b^4*c*x^3 - 11*a*b^3*d*x^3 + 5*a*b^3*c*x - 13*a^2*b^2*d*x)/((a^2*b^3*c^3 - 3*a^3*b^2*c^2*d + 3*a^4*b*c*d^2 - a^5*d^3)*(b*x^2 + a)^2)","A",0
42,1,574,0,0.619534," ","integrate(1/(b*x^2+a)^3/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{3 \, {\left(b^{5} c^{2} - 6 \, a b^{4} c d + 21 \, a^{2} b^{3} d^{2}\right)} \arctan\left(\frac{b x}{\sqrt{a b}}\right)}{8 \, {\left(a^{2} b^{5} c^{5} - 5 \, a^{3} b^{4} c^{4} d + 10 \, a^{4} b^{3} c^{3} d^{2} - 10 \, a^{5} b^{2} c^{2} d^{3} + 5 \, a^{6} b c d^{4} - a^{7} d^{5}\right)} \sqrt{a b}} - \frac{3 \, {\left(21 \, b^{2} c^{2} d^{3} - 6 \, a b c d^{4} + a^{2} d^{5}\right)} \arctan\left(\frac{d x}{\sqrt{c d}}\right)}{8 \, {\left(b^{5} c^{7} - 5 \, a b^{4} c^{6} d + 10 \, a^{2} b^{3} c^{5} d^{2} - 10 \, a^{3} b^{2} c^{4} d^{3} + 5 \, a^{4} b c^{3} d^{4} - a^{5} c^{2} d^{5}\right)} \sqrt{c d}} + \frac{3 \, b^{5} c^{3} d^{2} x^{7} - 15 \, a b^{4} c^{2} d^{3} x^{7} - 15 \, a^{2} b^{3} c d^{4} x^{7} + 3 \, a^{3} b^{2} d^{5} x^{7} + 6 \, b^{5} c^{4} d x^{5} - 25 \, a b^{4} c^{3} d^{2} x^{5} - 34 \, a^{2} b^{3} c^{2} d^{3} x^{5} - 25 \, a^{3} b^{2} c d^{4} x^{5} + 6 \, a^{4} b d^{5} x^{5} + 3 \, b^{5} c^{5} x^{3} - 5 \, a b^{4} c^{4} d x^{3} - 34 \, a^{2} b^{3} c^{3} d^{2} x^{3} - 34 \, a^{3} b^{2} c^{2} d^{3} x^{3} - 5 \, a^{4} b c d^{4} x^{3} + 3 \, a^{5} d^{5} x^{3} + 5 \, a b^{4} c^{5} x - 17 \, a^{2} b^{3} c^{4} d x - 17 \, a^{4} b c^{2} d^{3} x + 5 \, a^{5} c d^{4} x}{8 \, {\left(a^{2} b^{4} c^{6} - 4 \, a^{3} b^{3} c^{5} d + 6 \, a^{4} b^{2} c^{4} d^{2} - 4 \, a^{5} b c^{3} d^{3} + a^{6} c^{2} d^{4}\right)} {\left(b d x^{4} + b c x^{2} + a d x^{2} + a c\right)}^{2}}"," ",0,"3/8*(b^5*c^2 - 6*a*b^4*c*d + 21*a^2*b^3*d^2)*arctan(b*x/sqrt(a*b))/((a^2*b^5*c^5 - 5*a^3*b^4*c^4*d + 10*a^4*b^3*c^3*d^2 - 10*a^5*b^2*c^2*d^3 + 5*a^6*b*c*d^4 - a^7*d^5)*sqrt(a*b)) - 3/8*(21*b^2*c^2*d^3 - 6*a*b*c*d^4 + a^2*d^5)*arctan(d*x/sqrt(c*d))/((b^5*c^7 - 5*a*b^4*c^6*d + 10*a^2*b^3*c^5*d^2 - 10*a^3*b^2*c^4*d^3 + 5*a^4*b*c^3*d^4 - a^5*c^2*d^5)*sqrt(c*d)) + 1/8*(3*b^5*c^3*d^2*x^7 - 15*a*b^4*c^2*d^3*x^7 - 15*a^2*b^3*c*d^4*x^7 + 3*a^3*b^2*d^5*x^7 + 6*b^5*c^4*d*x^5 - 25*a*b^4*c^3*d^2*x^5 - 34*a^2*b^3*c^2*d^3*x^5 - 25*a^3*b^2*c*d^4*x^5 + 6*a^4*b*d^5*x^5 + 3*b^5*c^5*x^3 - 5*a*b^4*c^4*d*x^3 - 34*a^2*b^3*c^3*d^2*x^3 - 34*a^3*b^2*c^2*d^3*x^3 - 5*a^4*b*c*d^4*x^3 + 3*a^5*d^5*x^3 + 5*a*b^4*c^5*x - 17*a^2*b^3*c^4*d*x - 17*a^4*b*c^2*d^3*x + 5*a^5*c*d^4*x)/((a^2*b^4*c^6 - 4*a^3*b^3*c^5*d + 6*a^4*b^2*c^4*d^2 - 4*a^5*b*c^3*d^3 + a^6*c^2*d^4)*(b*d*x^4 + b*c*x^2 + a*d*x^2 + a*c)^2)","A",0
43,1,20,0,0.577512," ","integrate((x^2-1)^3/(x^2+1)^4,x, algorithm=""giac"")","-\frac{3 \, {\left(x + \frac{1}{x}\right)}^{2} - 4}{3 \, {\left(x + \frac{1}{x}\right)}^{3}}"," ",0,"-1/3*(3*(x + 1/x)^2 - 4)/(x + 1/x)^3","A",0
44,1,54,0,0.580339," ","integrate((x^2-1)^4/(x^2+1)^5,x, algorithm=""giac"")","\frac{3}{32} \, \pi \mathrm{sgn}\left(x\right) - \frac{5 \, {\left(x - \frac{1}{x}\right)}^{3} + 12 \, x - \frac{12}{x}}{8 \, {\left({\left(x - \frac{1}{x}\right)}^{2} + 4\right)}^{2}} + \frac{3}{16} \, \arctan\left(\frac{x^{2} - 1}{2 \, x}\right)"," ",0,"3/32*pi*sgn(x) - 1/8*(5*(x - 1/x)^3 + 12*x - 12/x)/((x - 1/x)^2 + 4)^2 + 3/16*arctan(1/2*(x^2 - 1)/x)","A",0
45,1,201,0,0.642059," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(6 \, d^{3} x^{2} + \frac{24 \, b^{6} c d^{2} + a b^{5} d^{3}}{b^{6}}\right)} x^{2} + \frac{144 \, b^{6} c^{2} d + 24 \, a b^{5} c d^{2} - 5 \, a^{2} b^{4} d^{3}}{b^{6}}\right)} x^{2} + \frac{3 \, {\left(64 \, b^{6} c^{3} + 48 \, a b^{5} c^{2} d - 24 \, a^{2} b^{4} c d^{2} + 5 \, a^{3} b^{3} d^{3}\right)}}{b^{6}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(64 \, a b^{3} c^{3} - 48 \, a^{2} b^{2} c^{2} d + 24 \, a^{3} b c d^{2} - 5 \, a^{4} d^{3}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{128 \, b^{\frac{7}{2}}}"," ",0,"1/384*(2*(4*(6*d^3*x^2 + (24*b^6*c*d^2 + a*b^5*d^3)/b^6)*x^2 + (144*b^6*c^2*d + 24*a*b^5*c*d^2 - 5*a^2*b^4*d^3)/b^6)*x^2 + 3*(64*b^6*c^3 + 48*a*b^5*c^2*d - 24*a^2*b^4*c*d^2 + 5*a^3*b^3*d^3)/b^6)*sqrt(b*x^2 + a)*x - 1/128*(64*a*b^3*c^3 - 48*a^2*b^2*c^2*d + 24*a^3*b*c*d^2 - 5*a^4*d^3)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
46,1,129,0,0.606582," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(4 \, d^{2} x^{2} + \frac{12 \, b^{4} c d + a b^{3} d^{2}}{b^{4}}\right)} x^{2} + \frac{3 \, {\left(8 \, b^{4} c^{2} + 4 \, a b^{3} c d - a^{2} b^{2} d^{2}\right)}}{b^{4}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(8 \, a b^{2} c^{2} - 4 \, a^{2} b c d + a^{3} d^{2}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{5}{2}}}"," ",0,"1/48*(2*(4*d^2*x^2 + (12*b^4*c*d + a*b^3*d^2)/b^4)*x^2 + 3*(8*b^4*c^2 + 4*a*b^3*c*d - a^2*b^2*d^2)/b^4)*sqrt(b*x^2 + a)*x - 1/16*(8*a*b^2*c^2 - 4*a^2*b*c*d + a^3*d^2)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
47,1,70,0,0.599719," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{b x^{2} + a} {\left(2 \, d x^{2} + \frac{4 \, b^{2} c + a b d}{b^{2}}\right)} x - \frac{{\left(4 \, a b c - a^{2} d\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{3}{2}}}"," ",0,"1/8*sqrt(b*x^2 + a)*(2*d*x^2 + (4*b^2*c + a*b*d)/b^2)*x - 1/8*(4*a*b*c - a^2*d)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
48,1,37,0,0.575818," ","integrate((b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{2} \, \sqrt{b x^{2} + a} x - \frac{a \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, \sqrt{b}}"," ",0,"1/2*sqrt(b*x^2 + a)*x - 1/2*a*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b)","A",0
49,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c),x, algorithm=""giac"")","\mathit{sage}_{0} x"," ",0,"sage0*x","F",0
50,1,217,0,1.641085," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{a \sqrt{b} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{2 \, \sqrt{-b^{2} c^{2} + a b c d} c} + \frac{2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b^{\frac{3}{2}} c - {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a \sqrt{b} d + a^{2} \sqrt{b} d}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)} c d}"," ",0,"-1/2*a*sqrt(b)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/(sqrt(-b^2*c^2 + a*b*c*d)*c) + (2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b^(3/2)*c - (sqrt(b)*x - sqrt(b*x^2 + a))^2*a*sqrt(b)*d + a^2*sqrt(b)*d)/(((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)*c*d)","B",0
51,1,487,0,3.745531," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{{\left(4 \, a b^{\frac{3}{2}} c - 3 \, a^{2} \sqrt{b} d\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{8 \, \sqrt{-b^{2} c^{2} + a b c d} {\left(b c^{3} - a c^{2} d\right)}} - \frac{4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a b^{\frac{3}{2}} c d^{2} - 3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} \sqrt{b} d^{3} - 16 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} b^{\frac{7}{2}} c^{3} + 40 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a b^{\frac{5}{2}} c^{2} d - 30 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} b^{\frac{3}{2}} c d^{2} + 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{3} \sqrt{b} d^{3} - 16 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{2} b^{\frac{5}{2}} c^{2} d + 28 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{3} b^{\frac{3}{2}} c d^{2} - 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{4} \sqrt{b} d^{3} - 2 \, a^{4} b^{\frac{3}{2}} c d^{2} + 3 \, a^{5} \sqrt{b} d^{3}}{4 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}^{2} {\left(b c^{3} d - a c^{2} d^{2}\right)}}"," ",0,"-1/8*(4*a*b^(3/2)*c - 3*a^2*sqrt(b)*d)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/(sqrt(-b^2*c^2 + a*b*c*d)*(b*c^3 - a*c^2*d)) - 1/4*(4*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a*b^(3/2)*c*d^2 - 3*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*sqrt(b)*d^3 - 16*(sqrt(b)*x - sqrt(b*x^2 + a))^4*b^(7/2)*c^3 + 40*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a*b^(5/2)*c^2*d - 30*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*b^(3/2)*c*d^2 + 9*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^3*sqrt(b)*d^3 - 16*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^2*b^(5/2)*c^2*d + 28*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^3*b^(3/2)*c*d^2 - 9*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^4*sqrt(b)*d^3 - 2*a^4*b^(3/2)*c*d^2 + 3*a^5*sqrt(b)*d^3)/(((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)^2*(b*c^3*d - a*c^2*d^2))","B",0
52,1,958,0,2.869810," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^4,x, algorithm=""giac"")","-\frac{{\left(8 \, a b^{\frac{5}{2}} c^{2} - 12 \, a^{2} b^{\frac{3}{2}} c d + 5 \, a^{3} \sqrt{b} d^{2}\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{16 \, {\left(b^{2} c^{5} - 2 \, a b c^{4} d + a^{2} c^{3} d^{2}\right)} \sqrt{-b^{2} c^{2} + a b c d}} - \frac{24 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a b^{\frac{5}{2}} c^{2} d^{3} - 36 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{2} b^{\frac{3}{2}} c d^{4} + 15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{3} \sqrt{b} d^{5} + 240 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a b^{\frac{7}{2}} c^{3} d^{2} - 480 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{2} b^{\frac{5}{2}} c^{2} d^{3} + 330 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{3} b^{\frac{3}{2}} c d^{4} - 75 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{4} \sqrt{b} d^{5} - 256 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} b^{\frac{11}{2}} c^{5} + 1216 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a b^{\frac{9}{2}} c^{4} d - 2016 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} b^{\frac{7}{2}} c^{3} d^{2} + 1736 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{3} b^{\frac{5}{2}} c^{2} d^{3} - 800 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{4} b^{\frac{3}{2}} c d^{4} + 150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{5} \sqrt{b} d^{5} - 384 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} b^{\frac{9}{2}} c^{4} d + 1392 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{3} b^{\frac{7}{2}} c^{3} d^{2} - 1608 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{4} b^{\frac{5}{2}} c^{2} d^{3} + 780 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{5} b^{\frac{3}{2}} c d^{4} - 150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{6} \sqrt{b} d^{5} - 96 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{4} b^{\frac{7}{2}} c^{3} d^{2} + 336 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{5} b^{\frac{5}{2}} c^{2} d^{3} - 300 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{6} b^{\frac{3}{2}} c d^{4} + 75 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{7} \sqrt{b} d^{5} - 8 \, a^{6} b^{\frac{5}{2}} c^{2} d^{3} + 26 \, a^{7} b^{\frac{3}{2}} c d^{4} - 15 \, a^{8} \sqrt{b} d^{5}}{24 \, {\left(b^{2} c^{5} d - 2 \, a b c^{4} d^{2} + a^{2} c^{3} d^{3}\right)} {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}^{3}}"," ",0,"-1/16*(8*a*b^(5/2)*c^2 - 12*a^2*b^(3/2)*c*d + 5*a^3*sqrt(b)*d^2)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/((b^2*c^5 - 2*a*b*c^4*d + a^2*c^3*d^2)*sqrt(-b^2*c^2 + a*b*c*d)) - 1/24*(24*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a*b^(5/2)*c^2*d^3 - 36*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^2*b^(3/2)*c*d^4 + 15*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^3*sqrt(b)*d^5 + 240*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a*b^(7/2)*c^3*d^2 - 480*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^2*b^(5/2)*c^2*d^3 + 330*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^3*b^(3/2)*c*d^4 - 75*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^4*sqrt(b)*d^5 - 256*(sqrt(b)*x - sqrt(b*x^2 + a))^6*b^(11/2)*c^5 + 1216*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a*b^(9/2)*c^4*d - 2016*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*b^(7/2)*c^3*d^2 + 1736*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^3*b^(5/2)*c^2*d^3 - 800*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^4*b^(3/2)*c*d^4 + 150*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^5*sqrt(b)*d^5 - 384*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*b^(9/2)*c^4*d + 1392*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^3*b^(7/2)*c^3*d^2 - 1608*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^4*b^(5/2)*c^2*d^3 + 780*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^5*b^(3/2)*c*d^4 - 150*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^6*sqrt(b)*d^5 - 96*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^4*b^(7/2)*c^3*d^2 + 336*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^5*b^(5/2)*c^2*d^3 - 300*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^6*b^(3/2)*c*d^4 + 75*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^7*sqrt(b)*d^5 - 8*a^6*b^(5/2)*c^2*d^3 + 26*a^7*b^(3/2)*c*d^4 - 15*a^8*sqrt(b)*d^5)/((b^2*c^5*d - 2*a*b*c^4*d^2 + a^2*c^3*d^3)*((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)^3)","B",0
53,1,260,0,0.662396," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{1280} \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, b d^{3} x^{2} + \frac{30 \, b^{9} c d^{2} + 11 \, a b^{8} d^{3}}{b^{8}}\right)} x^{2} + \frac{80 \, b^{9} c^{2} d + 90 \, a b^{8} c d^{2} + a^{2} b^{7} d^{3}}{b^{8}}\right)} x^{2} + \frac{5 \, {\left(32 \, b^{9} c^{3} + 112 \, a b^{8} c^{2} d + 6 \, a^{2} b^{7} c d^{2} - a^{3} b^{6} d^{3}\right)}}{b^{8}}\right)} x^{2} + \frac{5 \, {\left(160 \, a b^{8} c^{3} + 48 \, a^{2} b^{7} c^{2} d - 18 \, a^{3} b^{6} c d^{2} + 3 \, a^{4} b^{5} d^{3}\right)}}{b^{8}}\right)} \sqrt{b x^{2} + a} x - \frac{3 \, {\left(32 \, a^{2} b^{3} c^{3} - 16 \, a^{3} b^{2} c^{2} d + 6 \, a^{4} b c d^{2} - a^{5} d^{3}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{256 \, b^{\frac{7}{2}}}"," ",0,"1/1280*(2*(4*(2*(8*b*d^3*x^2 + (30*b^9*c*d^2 + 11*a*b^8*d^3)/b^8)*x^2 + (80*b^9*c^2*d + 90*a*b^8*c*d^2 + a^2*b^7*d^3)/b^8)*x^2 + 5*(32*b^9*c^3 + 112*a*b^8*c^2*d + 6*a^2*b^7*c*d^2 - a^3*b^6*d^3)/b^8)*x^2 + 5*(160*a*b^8*c^3 + 48*a^2*b^7*c^2*d - 18*a^3*b^6*c*d^2 + 3*a^4*b^5*d^3)/b^8)*sqrt(b*x^2 + a)*x - 3/256*(32*a^2*b^3*c^3 - 16*a^3*b^2*c^2*d + 6*a^4*b*c*d^2 - a^5*d^3)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
54,1,175,0,0.659951," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(6 \, b d^{2} x^{2} + \frac{16 \, b^{7} c d + 9 \, a b^{6} d^{2}}{b^{6}}\right)} x^{2} + \frac{48 \, b^{7} c^{2} + 112 \, a b^{6} c d + 3 \, a^{2} b^{5} d^{2}}{b^{6}}\right)} x^{2} + \frac{3 \, {\left(80 \, a b^{6} c^{2} + 16 \, a^{2} b^{5} c d - 3 \, a^{3} b^{4} d^{2}\right)}}{b^{6}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(48 \, a^{2} b^{2} c^{2} - 16 \, a^{3} b c d + 3 \, a^{4} d^{2}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{128 \, b^{\frac{5}{2}}}"," ",0,"1/384*(2*(4*(6*b*d^2*x^2 + (16*b^7*c*d + 9*a*b^6*d^2)/b^6)*x^2 + (48*b^7*c^2 + 112*a*b^6*c*d + 3*a^2*b^5*d^2)/b^6)*x^2 + 3*(80*a*b^6*c^2 + 16*a^2*b^5*c*d - 3*a^3*b^4*d^2)/b^6)*sqrt(b*x^2 + a)*x - 1/128*(48*a^2*b^2*c^2 - 16*a^3*b*c*d + 3*a^4*d^2)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
55,1,103,0,0.613202," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(4 \, b d x^{2} + \frac{6 \, b^{5} c + 7 \, a b^{4} d}{b^{4}}\right)} x^{2} + \frac{3 \, {\left(10 \, a b^{4} c + a^{2} b^{3} d\right)}}{b^{4}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(6 \, a^{2} b c - a^{3} d\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{3}{2}}}"," ",0,"1/48*(2*(4*b*d*x^2 + (6*b^5*c + 7*a*b^4*d)/b^4)*x^2 + 3*(10*a*b^4*c + a^2*b^3*d)/b^4)*sqrt(b*x^2 + a)*x - 1/16*(6*a^2*b*c - a^3*d)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
56,1,49,0,0.612400," ","integrate((b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{1}{8} \, {\left(2 \, b x^{2} + 5 \, a\right)} \sqrt{b x^{2} + a} x - \frac{3 \, a^{2} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, \sqrt{b}}"," ",0,"1/8*(2*b*x^2 + 5*a)*sqrt(b*x^2 + a)*x - 3/8*a^2*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b)","A",0
57,-2,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
58,1,317,0,0.682091," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^2,x, algorithm=""giac"")","-\frac{b^{\frac{3}{2}} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right)}{2 \, d^{2}} + \frac{{\left(2 \, b^{\frac{5}{2}} c^{2} - a b^{\frac{3}{2}} c d - a^{2} \sqrt{b} d^{2}\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{2 \, \sqrt{-b^{2} c^{2} + a b c d} c d^{2}} - \frac{2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b^{\frac{5}{2}} c^{2} - 3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a b^{\frac{3}{2}} c d + {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{2} \sqrt{b} d^{2} + a^{2} b^{\frac{3}{2}} c d - a^{3} \sqrt{b} d^{2}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)} c d^{2}}"," ",0,"-1/2*b^(3/2)*log((sqrt(b)*x - sqrt(b*x^2 + a))^2)/d^2 + 1/2*(2*b^(5/2)*c^2 - a*b^(3/2)*c*d - a^2*sqrt(b)*d^2)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/(sqrt(-b^2*c^2 + a*b*c*d)*c*d^2) - (2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b^(5/2)*c^2 - 3*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*b^(3/2)*c*d + (sqrt(b)*x - sqrt(b*x^2 + a))^2*a^2*sqrt(b)*d^2 + a^2*b^(3/2)*c*d - a^3*sqrt(b)*d^2)/(((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)*c*d^2)","B",0
59,1,451,0,3.722528," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{3 \, a^{2} \sqrt{b} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{8 \, \sqrt{-b^{2} c^{2} + a b c d} c^{2}} + \frac{8 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} b^{\frac{5}{2}} c^{2} d - 3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} \sqrt{b} d^{3} + 16 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} b^{\frac{7}{2}} c^{3} + 8 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a b^{\frac{5}{2}} c^{2} d - 18 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} b^{\frac{3}{2}} c d^{2} + 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{3} \sqrt{b} d^{3} + 8 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{2} b^{\frac{5}{2}} c^{2} d + 16 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{3} b^{\frac{3}{2}} c d^{2} - 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{4} \sqrt{b} d^{3} + 2 \, a^{4} b^{\frac{3}{2}} c d^{2} + 3 \, a^{5} \sqrt{b} d^{3}}{4 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}^{2} c^{2} d^{2}}"," ",0,"-3/8*a^2*sqrt(b)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/(sqrt(-b^2*c^2 + a*b*c*d)*c^2) + 1/4*(8*(sqrt(b)*x - sqrt(b*x^2 + a))^6*b^(5/2)*c^2*d - 3*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*sqrt(b)*d^3 + 16*(sqrt(b)*x - sqrt(b*x^2 + a))^4*b^(7/2)*c^3 + 8*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a*b^(5/2)*c^2*d - 18*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*b^(3/2)*c*d^2 + 9*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^3*sqrt(b)*d^3 + 8*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^2*b^(5/2)*c^2*d + 16*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^3*b^(3/2)*c*d^2 - 9*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^4*sqrt(b)*d^3 + 2*a^4*b^(3/2)*c*d^2 + 3*a^5*sqrt(b)*d^3)/(((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)^2*c^2*d^2)","B",0
60,1,919,0,2.892632," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^4,x, algorithm=""giac"")","-\frac{{\left(6 \, a^{2} b^{\frac{3}{2}} c - 5 \, a^{3} \sqrt{b} d\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{16 \, {\left(b c^{4} - a c^{3} d\right)} \sqrt{-b^{2} c^{2} + a b c d}} - \frac{18 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{2} b^{\frac{3}{2}} c d^{4} - 15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{3} \sqrt{b} d^{5} - 96 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} b^{\frac{9}{2}} c^{4} d + 96 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a b^{\frac{7}{2}} c^{3} d^{2} + 180 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{2} b^{\frac{5}{2}} c^{2} d^{3} - 240 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{3} b^{\frac{3}{2}} c d^{4} + 75 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{4} \sqrt{b} d^{5} - 128 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} b^{\frac{11}{2}} c^{5} - 64 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a b^{\frac{9}{2}} c^{4} d + 720 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} b^{\frac{7}{2}} c^{3} d^{2} - 968 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{3} b^{\frac{5}{2}} c^{2} d^{3} + 620 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{4} b^{\frac{3}{2}} c d^{4} - 150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{5} \sqrt{b} d^{5} - 96 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} b^{\frac{9}{2}} c^{4} d - 288 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{3} b^{\frac{7}{2}} c^{3} d^{2} + 864 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{4} b^{\frac{5}{2}} c^{2} d^{3} - 600 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{5} b^{\frac{3}{2}} c d^{4} + 150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{6} \sqrt{b} d^{5} - 48 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{4} b^{\frac{7}{2}} c^{3} d^{2} - 72 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{5} b^{\frac{5}{2}} c^{2} d^{3} + 210 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{6} b^{\frac{3}{2}} c d^{4} - 75 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{7} \sqrt{b} d^{5} - 4 \, a^{6} b^{\frac{5}{2}} c^{2} d^{3} - 8 \, a^{7} b^{\frac{3}{2}} c d^{4} + 15 \, a^{8} \sqrt{b} d^{5}}{24 \, {\left(b c^{4} d^{2} - a c^{3} d^{3}\right)} {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}^{3}}"," ",0,"-1/16*(6*a^2*b^(3/2)*c - 5*a^3*sqrt(b)*d)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/((b*c^4 - a*c^3*d)*sqrt(-b^2*c^2 + a*b*c*d)) - 1/24*(18*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^2*b^(3/2)*c*d^4 - 15*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^3*sqrt(b)*d^5 - 96*(sqrt(b)*x - sqrt(b*x^2 + a))^8*b^(9/2)*c^4*d + 96*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a*b^(7/2)*c^3*d^2 + 180*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^2*b^(5/2)*c^2*d^3 - 240*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^3*b^(3/2)*c*d^4 + 75*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^4*sqrt(b)*d^5 - 128*(sqrt(b)*x - sqrt(b*x^2 + a))^6*b^(11/2)*c^5 - 64*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a*b^(9/2)*c^4*d + 720*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*b^(7/2)*c^3*d^2 - 968*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^3*b^(5/2)*c^2*d^3 + 620*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^4*b^(3/2)*c*d^4 - 150*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^5*sqrt(b)*d^5 - 96*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*b^(9/2)*c^4*d - 288*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^3*b^(7/2)*c^3*d^2 + 864*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^4*b^(5/2)*c^2*d^3 - 600*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^5*b^(3/2)*c*d^4 + 150*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^6*sqrt(b)*d^5 - 48*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^4*b^(7/2)*c^3*d^2 - 72*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^5*b^(5/2)*c^2*d^3 + 210*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^6*b^(3/2)*c*d^4 - 75*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^7*sqrt(b)*d^5 - 4*a^6*b^(5/2)*c^2*d^3 - 8*a^7*b^(3/2)*c*d^4 + 15*a^8*sqrt(b)*d^5)/((b*c^4*d^2 - a*c^3*d^3)*((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)^3)","B",0
61,1,1557,0,9.597295," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^5,x, algorithm=""giac"")","-\frac{{\left(48 \, a^{2} b^{\frac{5}{2}} c^{2} - 80 \, a^{3} b^{\frac{3}{2}} c d + 35 \, a^{4} \sqrt{b} d^{2}\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{128 \, {\left(b^{2} c^{6} - 2 \, a b c^{5} d + a^{2} c^{4} d^{2}\right)} \sqrt{-b^{2} c^{2} + a b c d}} - \frac{144 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} a^{2} b^{\frac{5}{2}} c^{2} d^{5} - 240 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} a^{3} b^{\frac{3}{2}} c d^{6} + 105 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} a^{4} \sqrt{b} d^{7} + 2016 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} a^{2} b^{\frac{7}{2}} c^{3} d^{4} - 4368 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} a^{3} b^{\frac{5}{2}} c^{2} d^{5} + 3150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} a^{4} b^{\frac{3}{2}} c d^{6} - 735 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} a^{5} \sqrt{b} d^{7} - 2048 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} b^{\frac{13}{2}} c^{6} d + 4096 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a b^{\frac{11}{2}} c^{5} d^{2} + 7936 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{2} b^{\frac{9}{2}} c^{4} d^{3} - 26624 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{3} b^{\frac{7}{2}} c^{3} d^{4} + 26944 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{4} b^{\frac{5}{2}} c^{2} d^{5} - 12320 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{5} b^{\frac{3}{2}} c d^{6} + 2205 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{6} \sqrt{b} d^{7} - 2048 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} b^{\frac{15}{2}} c^{7} - 1024 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a b^{\frac{13}{2}} c^{6} d + 27392 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{2} b^{\frac{11}{2}} c^{5} d^{2} - 65920 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{3} b^{\frac{9}{2}} c^{4} d^{3} + 81680 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{4} b^{\frac{7}{2}} c^{3} d^{4} - 58840 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{5} b^{\frac{5}{2}} c^{2} d^{5} + 22750 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{6} b^{\frac{3}{2}} c d^{6} - 3675 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{7} \sqrt{b} d^{7} - 2048 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} b^{\frac{13}{2}} c^{6} d - 8192 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{3} b^{\frac{11}{2}} c^{5} d^{2} + 47104 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{4} b^{\frac{9}{2}} c^{4} d^{3} - 74240 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{5} b^{\frac{7}{2}} c^{3} d^{4} + 56416 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{6} b^{\frac{5}{2}} c^{2} d^{5} - 22400 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{7} b^{\frac{3}{2}} c d^{6} + 3675 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{8} \sqrt{b} d^{7} - 1536 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{4} b^{\frac{11}{2}} c^{5} d^{2} - 2304 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{5} b^{\frac{9}{2}} c^{4} d^{3} + 17696 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{6} b^{\frac{7}{2}} c^{3} d^{4} - 23152 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{7} b^{\frac{5}{2}} c^{2} d^{5} + 11690 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{8} b^{\frac{3}{2}} c d^{6} - 2205 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{9} \sqrt{b} d^{7} - 256 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{6} b^{\frac{9}{2}} c^{4} d^{3} - 512 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{7} b^{\frac{7}{2}} c^{3} d^{4} + 2896 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{8} b^{\frac{5}{2}} c^{2} d^{5} - 2800 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{9} b^{\frac{3}{2}} c d^{6} + 735 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{10} \sqrt{b} d^{7} - 16 \, a^{8} b^{\frac{7}{2}} c^{3} d^{4} - 40 \, a^{9} b^{\frac{5}{2}} c^{2} d^{5} + 170 \, a^{10} b^{\frac{3}{2}} c d^{6} - 105 \, a^{11} \sqrt{b} d^{7}}{192 \, {\left(b^{2} c^{6} d^{2} - 2 \, a b c^{5} d^{3} + a^{2} c^{4} d^{4}\right)} {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}^{4}}"," ",0,"-1/128*(48*a^2*b^(5/2)*c^2 - 80*a^3*b^(3/2)*c*d + 35*a^4*sqrt(b)*d^2)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/((b^2*c^6 - 2*a*b*c^5*d + a^2*c^4*d^2)*sqrt(-b^2*c^2 + a*b*c*d)) - 1/192*(144*(sqrt(b)*x - sqrt(b*x^2 + a))^14*a^2*b^(5/2)*c^2*d^5 - 240*(sqrt(b)*x - sqrt(b*x^2 + a))^14*a^3*b^(3/2)*c*d^6 + 105*(sqrt(b)*x - sqrt(b*x^2 + a))^14*a^4*sqrt(b)*d^7 + 2016*(sqrt(b)*x - sqrt(b*x^2 + a))^12*a^2*b^(7/2)*c^3*d^4 - 4368*(sqrt(b)*x - sqrt(b*x^2 + a))^12*a^3*b^(5/2)*c^2*d^5 + 3150*(sqrt(b)*x - sqrt(b*x^2 + a))^12*a^4*b^(3/2)*c*d^6 - 735*(sqrt(b)*x - sqrt(b*x^2 + a))^12*a^5*sqrt(b)*d^7 - 2048*(sqrt(b)*x - sqrt(b*x^2 + a))^10*b^(13/2)*c^6*d + 4096*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a*b^(11/2)*c^5*d^2 + 7936*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^2*b^(9/2)*c^4*d^3 - 26624*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^3*b^(7/2)*c^3*d^4 + 26944*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^4*b^(5/2)*c^2*d^5 - 12320*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^5*b^(3/2)*c*d^6 + 2205*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^6*sqrt(b)*d^7 - 2048*(sqrt(b)*x - sqrt(b*x^2 + a))^8*b^(15/2)*c^7 - 1024*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a*b^(13/2)*c^6*d + 27392*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^2*b^(11/2)*c^5*d^2 - 65920*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^3*b^(9/2)*c^4*d^3 + 81680*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^4*b^(7/2)*c^3*d^4 - 58840*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^5*b^(5/2)*c^2*d^5 + 22750*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^6*b^(3/2)*c*d^6 - 3675*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^7*sqrt(b)*d^7 - 2048*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*b^(13/2)*c^6*d - 8192*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^3*b^(11/2)*c^5*d^2 + 47104*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^4*b^(9/2)*c^4*d^3 - 74240*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^5*b^(7/2)*c^3*d^4 + 56416*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^6*b^(5/2)*c^2*d^5 - 22400*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^7*b^(3/2)*c*d^6 + 3675*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^8*sqrt(b)*d^7 - 1536*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^4*b^(11/2)*c^5*d^2 - 2304*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^5*b^(9/2)*c^4*d^3 + 17696*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^6*b^(7/2)*c^3*d^4 - 23152*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^7*b^(5/2)*c^2*d^5 + 11690*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^8*b^(3/2)*c*d^6 - 2205*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^9*sqrt(b)*d^7 - 256*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^6*b^(9/2)*c^4*d^3 - 512*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^7*b^(7/2)*c^3*d^4 + 2896*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^8*b^(5/2)*c^2*d^5 - 2800*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^9*b^(3/2)*c*d^6 + 735*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^10*sqrt(b)*d^7 - 16*a^8*b^(7/2)*c^3*d^4 - 40*a^9*b^(5/2)*c^2*d^5 + 170*a^10*b^(3/2)*c*d^6 - 105*a^11*sqrt(b)*d^7)/((b^2*c^6*d^2 - 2*a*b*c^5*d^3 + a^2*c^4*d^4)*((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)^4)","B",0
62,1,321,0,0.680362," ","integrate((b*x^2+a)^(5/2)*(d*x^2+c)^3,x, algorithm=""giac"")","\frac{1}{15360} \, {\left(2 \, {\left(4 \, {\left(2 \, {\left(8 \, {\left(10 \, b^{2} d^{3} x^{2} + \frac{36 \, b^{12} c d^{2} + 25 \, a b^{11} d^{3}}{b^{10}}\right)} x^{2} + \frac{9 \, {\left(40 \, b^{12} c^{2} d + 84 \, a b^{11} c d^{2} + 15 \, a^{2} b^{10} d^{3}\right)}}{b^{10}}\right)} x^{2} + \frac{320 \, b^{12} c^{3} + 2040 \, a b^{11} c^{2} d + 1116 \, a^{2} b^{10} c d^{2} + 5 \, a^{3} b^{9} d^{3}}{b^{10}}\right)} x^{2} + \frac{5 \, {\left(832 \, a b^{11} c^{3} + 1416 \, a^{2} b^{10} c^{2} d + 36 \, a^{3} b^{9} c d^{2} - 5 \, a^{4} b^{8} d^{3}\right)}}{b^{10}}\right)} x^{2} + \frac{15 \, {\left(704 \, a^{2} b^{10} c^{3} + 120 \, a^{3} b^{9} c^{2} d - 36 \, a^{4} b^{8} c d^{2} + 5 \, a^{5} b^{7} d^{3}\right)}}{b^{10}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(320 \, a^{3} b^{3} c^{3} - 120 \, a^{4} b^{2} c^{2} d + 36 \, a^{5} b c d^{2} - 5 \, a^{6} d^{3}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{1024 \, b^{\frac{7}{2}}}"," ",0,"1/15360*(2*(4*(2*(8*(10*b^2*d^3*x^2 + (36*b^12*c*d^2 + 25*a*b^11*d^3)/b^10)*x^2 + 9*(40*b^12*c^2*d + 84*a*b^11*c*d^2 + 15*a^2*b^10*d^3)/b^10)*x^2 + (320*b^12*c^3 + 2040*a*b^11*c^2*d + 1116*a^2*b^10*c*d^2 + 5*a^3*b^9*d^3)/b^10)*x^2 + 5*(832*a*b^11*c^3 + 1416*a^2*b^10*c^2*d + 36*a^3*b^9*c*d^2 - 5*a^4*b^8*d^3)/b^10)*x^2 + 15*(704*a^2*b^10*c^3 + 120*a^3*b^9*c^2*d - 36*a^4*b^8*c*d^2 + 5*a^5*b^7*d^3)/b^10)*sqrt(b*x^2 + a)*x - 1/1024*(320*a^3*b^3*c^3 - 120*a^4*b^2*c^2*d + 36*a^5*b*c*d^2 - 5*a^6*d^3)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
63,1,221,0,0.656017," ","integrate((b*x^2+a)^(5/2)*(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{3840} \, {\left(2 \, {\left(4 \, {\left(6 \, {\left(8 \, b^{2} d^{2} x^{2} + \frac{20 \, b^{10} c d + 21 \, a b^{9} d^{2}}{b^{8}}\right)} x^{2} + \frac{80 \, b^{10} c^{2} + 340 \, a b^{9} c d + 93 \, a^{2} b^{8} d^{2}}{b^{8}}\right)} x^{2} + \frac{5 \, {\left(208 \, a b^{9} c^{2} + 236 \, a^{2} b^{8} c d + 3 \, a^{3} b^{7} d^{2}\right)}}{b^{8}}\right)} x^{2} + \frac{15 \, {\left(176 \, a^{2} b^{8} c^{2} + 20 \, a^{3} b^{7} c d - 3 \, a^{4} b^{6} d^{2}\right)}}{b^{8}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(80 \, a^{3} b^{2} c^{2} - 20 \, a^{4} b c d + 3 \, a^{5} d^{2}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{256 \, b^{\frac{5}{2}}}"," ",0,"1/3840*(2*(4*(6*(8*b^2*d^2*x^2 + (20*b^10*c*d + 21*a*b^9*d^2)/b^8)*x^2 + (80*b^10*c^2 + 340*a*b^9*c*d + 93*a^2*b^8*d^2)/b^8)*x^2 + 5*(208*a*b^9*c^2 + 236*a^2*b^8*c*d + 3*a^3*b^7*d^2)/b^8)*x^2 + 15*(176*a^2*b^8*c^2 + 20*a^3*b^7*c*d - 3*a^4*b^6*d^2)/b^8)*sqrt(b*x^2 + a)*x - 1/256*(80*a^3*b^2*c^2 - 20*a^4*b*c*d + 3*a^5*d^2)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
64,1,135,0,0.632263," ","integrate((b*x^2+a)^(5/2)*(d*x^2+c),x, algorithm=""giac"")","\frac{1}{384} \, {\left(2 \, {\left(4 \, {\left(6 \, b^{2} d x^{2} + \frac{8 \, b^{8} c + 17 \, a b^{7} d}{b^{6}}\right)} x^{2} + \frac{104 \, a b^{7} c + 59 \, a^{2} b^{6} d}{b^{6}}\right)} x^{2} + \frac{3 \, {\left(88 \, a^{2} b^{6} c + 5 \, a^{3} b^{5} d\right)}}{b^{6}}\right)} \sqrt{b x^{2} + a} x - \frac{5 \, {\left(8 \, a^{3} b c - a^{4} d\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{128 \, b^{\frac{3}{2}}}"," ",0,"1/384*(2*(4*(6*b^2*d*x^2 + (8*b^8*c + 17*a*b^7*d)/b^6)*x^2 + (104*a*b^7*c + 59*a^2*b^6*d)/b^6)*x^2 + 3*(88*a^2*b^6*c + 5*a^3*b^5*d)/b^6)*sqrt(b*x^2 + a)*x - 5/128*(8*a^3*b*c - a^4*d)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
65,1,63,0,0.607778," ","integrate((b*x^2+a)^(5/2),x, algorithm=""giac"")","-\frac{5 \, a^{3} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, \sqrt{b}} + \frac{1}{48} \, {\left(2 \, {\left(4 \, b^{2} x^{2} + 13 \, a b\right)} x^{2} + 33 \, a^{2}\right)} \sqrt{b x^{2} + a} x"," ",0,"-5/16*a^3*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b) + 1/48*(2*(4*b^2*x^2 + 13*a*b)*x^2 + 33*a^2)*sqrt(b*x^2 + a)*x","A",0
66,-2,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c),x, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:"index.cc index_m i_lex_is_greater Error: Bad Argument Value"","F(-2)",0
67,1,405,0,0.689412," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{\sqrt{b x^{2} + a} b^{2} x}{2 \, d^{2}} + \frac{{\left(4 \, b^{\frac{5}{2}} c - 5 \, a b^{\frac{3}{2}} d\right)} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right)}{4 \, d^{3}} - \frac{{\left(4 \, b^{\frac{7}{2}} c^{3} - 7 \, a b^{\frac{5}{2}} c^{2} d + 2 \, a^{2} b^{\frac{3}{2}} c d^{2} + a^{3} \sqrt{b} d^{3}\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{2 \, \sqrt{-b^{2} c^{2} + a b c d} c d^{3}} + \frac{2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b^{\frac{7}{2}} c^{3} - 5 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a b^{\frac{5}{2}} c^{2} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{2} b^{\frac{3}{2}} c d^{2} - {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{3} \sqrt{b} d^{3} + a^{2} b^{\frac{5}{2}} c^{2} d - 2 \, a^{3} b^{\frac{3}{2}} c d^{2} + a^{4} \sqrt{b} d^{3}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)} c d^{3}}"," ",0,"1/2*sqrt(b*x^2 + a)*b^2*x/d^2 + 1/4*(4*b^(5/2)*c - 5*a*b^(3/2)*d)*log((sqrt(b)*x - sqrt(b*x^2 + a))^2)/d^3 - 1/2*(4*b^(7/2)*c^3 - 7*a*b^(5/2)*c^2*d + 2*a^2*b^(3/2)*c*d^2 + a^3*sqrt(b)*d^3)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/(sqrt(-b^2*c^2 + a*b*c*d)*c*d^3) + (2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b^(7/2)*c^3 - 5*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*b^(5/2)*c^2*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^2*b^(3/2)*c*d^2 - (sqrt(b)*x - sqrt(b*x^2 + a))^2*a^3*sqrt(b)*d^3 + a^2*b^(5/2)*c^2*d - 2*a^3*b^(3/2)*c*d^2 + a^4*sqrt(b)*d^3)/(((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)*c*d^3)","B",0
68,1,659,0,0.733226," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{b^{\frac{5}{2}} \log\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2}\right)}{2 \, d^{3}} + \frac{{\left(8 \, b^{\frac{7}{2}} c^{3} - 4 \, a b^{\frac{5}{2}} c^{2} d - a^{2} b^{\frac{3}{2}} c d^{2} - 3 \, a^{3} \sqrt{b} d^{3}\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{8 \, \sqrt{-b^{2} c^{2} + a b c d} c^{2} d^{3}} - \frac{16 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} b^{\frac{7}{2}} c^{3} d - 20 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a b^{\frac{5}{2}} c^{2} d^{2} + {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} b^{\frac{3}{2}} c d^{3} + 3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{3} \sqrt{b} d^{4} + 48 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} b^{\frac{9}{2}} c^{4} - 72 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a b^{\frac{7}{2}} c^{3} d + 18 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} b^{\frac{5}{2}} c^{2} d^{2} + 15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{3} b^{\frac{3}{2}} c d^{3} - 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{4} \sqrt{b} d^{4} + 32 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{2} b^{\frac{7}{2}} c^{3} d - 28 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{3} b^{\frac{5}{2}} c^{2} d^{2} - 13 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{4} b^{\frac{3}{2}} c d^{3} + 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{5} \sqrt{b} d^{4} + 6 \, a^{4} b^{\frac{5}{2}} c^{2} d^{2} - 3 \, a^{5} b^{\frac{3}{2}} c d^{3} - 3 \, a^{6} \sqrt{b} d^{4}}{4 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}^{2} c^{2} d^{3}}"," ",0,"-1/2*b^(5/2)*log((sqrt(b)*x - sqrt(b*x^2 + a))^2)/d^3 + 1/8*(8*b^(7/2)*c^3 - 4*a*b^(5/2)*c^2*d - a^2*b^(3/2)*c*d^2 - 3*a^3*sqrt(b)*d^3)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/(sqrt(-b^2*c^2 + a*b*c*d)*c^2*d^3) - 1/4*(16*(sqrt(b)*x - sqrt(b*x^2 + a))^6*b^(7/2)*c^3*d - 20*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a*b^(5/2)*c^2*d^2 + (sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*b^(3/2)*c*d^3 + 3*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^3*sqrt(b)*d^4 + 48*(sqrt(b)*x - sqrt(b*x^2 + a))^4*b^(9/2)*c^4 - 72*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a*b^(7/2)*c^3*d + 18*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*b^(5/2)*c^2*d^2 + 15*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^3*b^(3/2)*c*d^3 - 9*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^4*sqrt(b)*d^4 + 32*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^2*b^(7/2)*c^3*d - 28*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^3*b^(5/2)*c^2*d^2 - 13*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^4*b^(3/2)*c*d^3 + 9*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^5*sqrt(b)*d^4 + 6*a^4*b^(5/2)*c^2*d^2 - 3*a^5*b^(3/2)*c*d^3 - 3*a^6*sqrt(b)*d^4)/(((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)^2*c^2*d^3)","B",0
69,1,846,0,2.858195," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^4,x, algorithm=""giac"")","-\frac{5 \, a^{3} \sqrt{b} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{16 \, \sqrt{-b^{2} c^{2} + a b c d} c^{3}} + \frac{48 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} b^{\frac{7}{2}} c^{3} d^{2} - 15 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{3} \sqrt{b} d^{5} + 192 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} b^{\frac{9}{2}} c^{4} d + 48 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a b^{\frac{7}{2}} c^{3} d^{2} - 150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{3} b^{\frac{3}{2}} c d^{4} + 75 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{4} \sqrt{b} d^{5} + 256 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} b^{\frac{11}{2}} c^{5} - 64 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a b^{\frac{9}{2}} c^{4} d + 288 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} b^{\frac{7}{2}} c^{3} d^{2} - 440 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{3} b^{\frac{5}{2}} c^{2} d^{3} + 440 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{4} b^{\frac{3}{2}} c d^{4} - 150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{5} \sqrt{b} d^{5} + 192 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} b^{\frac{9}{2}} c^{4} d + 48 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{3} b^{\frac{7}{2}} c^{3} d^{2} + 360 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{4} b^{\frac{5}{2}} c^{2} d^{3} - 420 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{5} b^{\frac{3}{2}} c d^{4} + 150 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{6} \sqrt{b} d^{5} + 48 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{4} b^{\frac{7}{2}} c^{3} d^{2} + 72 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{5} b^{\frac{5}{2}} c^{2} d^{3} + 120 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{6} b^{\frac{3}{2}} c d^{4} - 75 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{7} \sqrt{b} d^{5} + 8 \, a^{6} b^{\frac{5}{2}} c^{2} d^{3} + 10 \, a^{7} b^{\frac{3}{2}} c d^{4} + 15 \, a^{8} \sqrt{b} d^{5}}{24 \, {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}^{3} c^{3} d^{3}}"," ",0,"-5/16*a^3*sqrt(b)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/(sqrt(-b^2*c^2 + a*b*c*d)*c^3) + 1/24*(48*(sqrt(b)*x - sqrt(b*x^2 + a))^10*b^(7/2)*c^3*d^2 - 15*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^3*sqrt(b)*d^5 + 192*(sqrt(b)*x - sqrt(b*x^2 + a))^8*b^(9/2)*c^4*d + 48*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a*b^(7/2)*c^3*d^2 - 150*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^3*b^(3/2)*c*d^4 + 75*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^4*sqrt(b)*d^5 + 256*(sqrt(b)*x - sqrt(b*x^2 + a))^6*b^(11/2)*c^5 - 64*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a*b^(9/2)*c^4*d + 288*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*b^(7/2)*c^3*d^2 - 440*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^3*b^(5/2)*c^2*d^3 + 440*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^4*b^(3/2)*c*d^4 - 150*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^5*sqrt(b)*d^5 + 192*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*b^(9/2)*c^4*d + 48*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^3*b^(7/2)*c^3*d^2 + 360*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^4*b^(5/2)*c^2*d^3 - 420*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^5*b^(3/2)*c*d^4 + 150*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^6*sqrt(b)*d^5 + 48*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^4*b^(7/2)*c^3*d^2 + 72*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^5*b^(5/2)*c^2*d^3 + 120*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^6*b^(3/2)*c*d^4 - 75*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^7*sqrt(b)*d^5 + 8*a^6*b^(5/2)*c^2*d^3 + 10*a^7*b^(3/2)*c*d^4 + 15*a^8*sqrt(b)*d^5)/(((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)^3*c^3*d^3)","B",0
70,1,1448,0,9.314716," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^5,x, algorithm=""giac"")","-\frac{5 \, {\left(8 \, a^{3} b^{\frac{3}{2}} c - 7 \, a^{4} \sqrt{b} d\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{128 \, {\left(b c^{5} - a c^{4} d\right)} \sqrt{-b^{2} c^{2} + a b c d}} - \frac{120 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} a^{3} b^{\frac{3}{2}} c d^{6} - 105 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{14} a^{4} \sqrt{b} d^{7} - 768 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} b^{\frac{11}{2}} c^{5} d^{2} + 768 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} a b^{\frac{9}{2}} c^{4} d^{3} + 1680 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} a^{3} b^{\frac{5}{2}} c^{2} d^{5} - 2310 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} a^{4} b^{\frac{3}{2}} c d^{6} + 735 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{12} a^{5} \sqrt{b} d^{7} - 2048 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} b^{\frac{13}{2}} c^{6} d + 2048 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{2} b^{\frac{9}{2}} c^{4} d^{3} + 8320 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{3} b^{\frac{7}{2}} c^{3} d^{4} - 15600 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{4} b^{\frac{5}{2}} c^{2} d^{5} + 9800 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{5} b^{\frac{3}{2}} c d^{6} - 2205 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{10} a^{6} \sqrt{b} d^{7} - 2048 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} b^{\frac{15}{2}} c^{7} + 1024 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a b^{\frac{13}{2}} c^{6} d - 4864 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{2} b^{\frac{11}{2}} c^{5} d^{2} + 21888 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{3} b^{\frac{9}{2}} c^{4} d^{3} - 38000 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{4} b^{\frac{7}{2}} c^{3} d^{4} + 37400 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{5} b^{\frac{5}{2}} c^{2} d^{5} - 18550 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{6} b^{\frac{3}{2}} c d^{6} + 3675 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{8} a^{7} \sqrt{b} d^{7} - 2048 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} b^{\frac{13}{2}} c^{6} d - 9472 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{4} b^{\frac{9}{2}} c^{4} d^{3} + 32896 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{5} b^{\frac{7}{2}} c^{3} d^{4} - 35376 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{6} b^{\frac{5}{2}} c^{2} d^{5} + 18200 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{7} b^{\frac{3}{2}} c d^{6} - 3675 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{8} \sqrt{b} d^{7} - 768 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{4} b^{\frac{11}{2}} c^{5} d^{2} - 1536 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{5} b^{\frac{9}{2}} c^{4} d^{3} - 2944 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{6} b^{\frac{7}{2}} c^{3} d^{4} + 12528 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{7} b^{\frac{5}{2}} c^{2} d^{5} - 9170 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{8} b^{\frac{3}{2}} c d^{6} + 2205 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{9} \sqrt{b} d^{7} - 256 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{6} b^{\frac{9}{2}} c^{4} d^{3} - 256 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{7} b^{\frac{7}{2}} c^{3} d^{4} - 608 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{8} b^{\frac{5}{2}} c^{2} d^{5} + 1960 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{9} b^{\frac{3}{2}} c d^{6} - 735 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{10} \sqrt{b} d^{7} - 16 \, a^{8} b^{\frac{7}{2}} c^{3} d^{4} - 24 \, a^{9} b^{\frac{5}{2}} c^{2} d^{5} - 50 \, a^{10} b^{\frac{3}{2}} c d^{6} + 105 \, a^{11} \sqrt{b} d^{7}}{192 \, {\left(b c^{5} d^{3} - a c^{4} d^{4}\right)} {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}^{4}}"," ",0,"-5/128*(8*a^3*b^(3/2)*c - 7*a^4*sqrt(b)*d)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/((b*c^5 - a*c^4*d)*sqrt(-b^2*c^2 + a*b*c*d)) - 1/192*(120*(sqrt(b)*x - sqrt(b*x^2 + a))^14*a^3*b^(3/2)*c*d^6 - 105*(sqrt(b)*x - sqrt(b*x^2 + a))^14*a^4*sqrt(b)*d^7 - 768*(sqrt(b)*x - sqrt(b*x^2 + a))^12*b^(11/2)*c^5*d^2 + 768*(sqrt(b)*x - sqrt(b*x^2 + a))^12*a*b^(9/2)*c^4*d^3 + 1680*(sqrt(b)*x - sqrt(b*x^2 + a))^12*a^3*b^(5/2)*c^2*d^5 - 2310*(sqrt(b)*x - sqrt(b*x^2 + a))^12*a^4*b^(3/2)*c*d^6 + 735*(sqrt(b)*x - sqrt(b*x^2 + a))^12*a^5*sqrt(b)*d^7 - 2048*(sqrt(b)*x - sqrt(b*x^2 + a))^10*b^(13/2)*c^6*d + 2048*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^2*b^(9/2)*c^4*d^3 + 8320*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^3*b^(7/2)*c^3*d^4 - 15600*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^4*b^(5/2)*c^2*d^5 + 9800*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^5*b^(3/2)*c*d^6 - 2205*(sqrt(b)*x - sqrt(b*x^2 + a))^10*a^6*sqrt(b)*d^7 - 2048*(sqrt(b)*x - sqrt(b*x^2 + a))^8*b^(15/2)*c^7 + 1024*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a*b^(13/2)*c^6*d - 4864*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^2*b^(11/2)*c^5*d^2 + 21888*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^3*b^(9/2)*c^4*d^3 - 38000*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^4*b^(7/2)*c^3*d^4 + 37400*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^5*b^(5/2)*c^2*d^5 - 18550*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^6*b^(3/2)*c*d^6 + 3675*(sqrt(b)*x - sqrt(b*x^2 + a))^8*a^7*sqrt(b)*d^7 - 2048*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*b^(13/2)*c^6*d - 9472*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^4*b^(9/2)*c^4*d^3 + 32896*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^5*b^(7/2)*c^3*d^4 - 35376*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^6*b^(5/2)*c^2*d^5 + 18200*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^7*b^(3/2)*c*d^6 - 3675*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^8*sqrt(b)*d^7 - 768*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^4*b^(11/2)*c^5*d^2 - 1536*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^5*b^(9/2)*c^4*d^3 - 2944*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^6*b^(7/2)*c^3*d^4 + 12528*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^7*b^(5/2)*c^2*d^5 - 9170*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^8*b^(3/2)*c*d^6 + 2205*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^9*sqrt(b)*d^7 - 256*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^6*b^(9/2)*c^4*d^3 - 256*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^7*b^(7/2)*c^3*d^4 - 608*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^8*b^(5/2)*c^2*d^5 + 1960*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^9*b^(3/2)*c*d^6 - 735*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^10*sqrt(b)*d^7 - 16*a^8*b^(7/2)*c^3*d^4 - 24*a^9*b^(5/2)*c^2*d^5 - 50*a^10*b^(3/2)*c*d^6 + 105*a^11*sqrt(b)*d^7)/((b*c^5*d^3 - a*c^4*d^4)*((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)^4)","B",0
71,1,95,0,0.607896," ","integrate((-x^2+1)^(1/2)/(x^2+1),x, algorithm=""giac"")","-\frac{1}{2} \, \pi \mathrm{sgn}\left(x\right) + \frac{1}{2} \, \sqrt{2} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(-\frac{\sqrt{2} x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{4 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)\right)} - \arctan\left(-\frac{x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)"," ",0,"-1/2*pi*sgn(x) + 1/2*sqrt(2)*(pi*sgn(x) + 2*arctan(-1/4*sqrt(2)*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1))) - arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1))","B",0
72,1,70,0,0.619702," ","integrate((x^2+1)^(1/2)/(x^2-1),x, algorithm=""giac"")","-\frac{1}{2} \, \sqrt{2} \log\left(\frac{{\left| 2 \, {\left(x - \sqrt{x^{2} + 1}\right)}^{2} - 4 \, \sqrt{2} - 6 \right|}}{{\left| 2 \, {\left(x - \sqrt{x^{2} + 1}\right)}^{2} + 4 \, \sqrt{2} - 6 \right|}}\right) - \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"-1/2*sqrt(2)*log(abs(2*(x - sqrt(x^2 + 1))^2 - 4*sqrt(2) - 6)/abs(2*(x - sqrt(x^2 + 1))^2 + 4*sqrt(2) - 6)) - log(-x + sqrt(x^2 + 1))","B",0
73,1,118,0,0.610888," ","integrate((-x^2+1)^(1/2)/(2*x^2-1),x, algorithm=""giac"")","-\frac{1}{4} \, \pi \mathrm{sgn}\left(x\right) - \frac{1}{2} \, \arctan\left(-\frac{x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{2 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right) - \frac{1}{4} \, \log\left({\left| -\frac{x}{\sqrt{-x^{2} + 1} - 1} + \frac{\sqrt{-x^{2} + 1} - 1}{x} + 2 \right|}\right) + \frac{1}{4} \, \log\left({\left| -\frac{x}{\sqrt{-x^{2} + 1} - 1} + \frac{\sqrt{-x^{2} + 1} - 1}{x} - 2 \right|}\right)"," ",0,"-1/4*pi*sgn(x) - 1/2*arctan(-1/2*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1)) - 1/4*log(abs(-x/(sqrt(-x^2 + 1) - 1) + (sqrt(-x^2 + 1) - 1)/x + 2)) + 1/4*log(abs(-x/(sqrt(-x^2 + 1) - 1) + (sqrt(-x^2 + 1) - 1)/x - 2))","B",0
74,1,150,0,0.638541," ","integrate((d*x^2+c)^3/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{48} \, {\left(2 \, {\left(\frac{4 \, d^{3} x^{2}}{b} + \frac{18 \, b^{4} c d^{2} - 5 \, a b^{3} d^{3}}{b^{5}}\right)} x^{2} + \frac{3 \, {\left(24 \, b^{4} c^{2} d - 18 \, a b^{3} c d^{2} + 5 \, a^{2} b^{2} d^{3}\right)}}{b^{5}}\right)} \sqrt{b x^{2} + a} x - \frac{{\left(16 \, b^{3} c^{3} - 24 \, a b^{2} c^{2} d + 18 \, a^{2} b c d^{2} - 5 \, a^{3} d^{3}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{7}{2}}}"," ",0,"1/48*(2*(4*d^3*x^2/b + (18*b^4*c*d^2 - 5*a*b^3*d^3)/b^5)*x^2 + 3*(24*b^4*c^2*d - 18*a*b^3*c*d^2 + 5*a^2*b^2*d^3)/b^5)*sqrt(b*x^2 + a)*x - 1/16*(16*b^3*c^3 - 24*a*b^2*c^2*d + 18*a^2*b*c*d^2 - 5*a^3*d^3)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
75,1,90,0,0.619220," ","integrate((d*x^2+c)^2/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{1}{8} \, \sqrt{b x^{2} + a} {\left(\frac{2 \, d^{2} x^{2}}{b} + \frac{8 \, b^{2} c d - 3 \, a b d^{2}}{b^{3}}\right)} x - \frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + 3 \, a^{2} d^{2}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{5}{2}}}"," ",0,"1/8*sqrt(b*x^2 + a)*(2*d^2*x^2/b + (8*b^2*c*d - 3*a*b*d^2)/b^3)*x - 1/8*(8*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
76,1,49,0,0.599136," ","integrate((d*x^2+c)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\frac{\sqrt{b x^{2} + a} d x}{2 \, b} - \frac{{\left(2 \, b c - a d\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{3}{2}}}"," ",0,"1/2*sqrt(b*x^2 + a)*d*x/b - 1/2*(2*b*c - a*d)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2)","A",0
77,1,23,0,0.595645," ","integrate(1/(b*x^2+a)^(1/2),x, algorithm=""giac"")","-\frac{\log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{\sqrt{b}}"," ",0,"-log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/sqrt(b)","A",0
78,1,70,0,0.602849," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c),x, algorithm=""giac"")","-\frac{\sqrt{b} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{\sqrt{-b^{2} c^{2} + a b c d}}"," ",0,"-sqrt(b)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/sqrt(-b^2*c^2 + a*b*c*d)","A",0
79,1,242,0,0.627136," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{1}{2} \, b^{\frac{3}{2}} {\left(\frac{{\left(2 \, b c - a d\right)} \arctan\left(-\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{{\left(b^{2} c^{2} - a b c d\right)} \sqrt{-b^{2} c^{2} + a b c d}} - \frac{2 \, {\left(2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}}{{\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)} {\left(b^{2} c^{2} - a b c d\right)}}\right)}"," ",0,"1/2*b^(3/2)*((2*b*c - a*d)*arctan(-1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/((b^2*c^2 - a*b*c*d)*sqrt(-b^2*c^2 + a*b*c*d)) - 2*(2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - (sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)/(((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)*(b^2*c^2 - a*b*c*d)))","B",0
80,1,538,0,3.505445," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c)^3,x, algorithm=""giac"")","-\frac{1}{8} \, b^{\frac{5}{2}} {\left(\frac{{\left(8 \, b^{2} c^{2} - 8 \, a b c d + 3 \, a^{2} d^{2}\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{{\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + a^{2} b^{2} c^{2} d^{2}\right)} \sqrt{-b^{2} c^{2} + a b c d}} + \frac{2 \, {\left(8 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} b^{2} c^{2} d - 8 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a b c d^{2} + 3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} d^{3} + 48 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} b^{3} c^{3} - 72 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a b^{2} c^{2} d + 42 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} b c d^{2} - 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{3} d^{3} + 40 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{2} b^{2} c^{2} d - 40 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{3} b c d^{2} + 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{4} d^{3} + 6 \, a^{4} b c d^{2} - 3 \, a^{5} d^{3}\right)}}{{\left(b^{4} c^{4} - 2 \, a b^{3} c^{3} d + a^{2} b^{2} c^{2} d^{2}\right)} {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}^{2}}\right)}"," ",0,"-1/8*b^(5/2)*((8*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/((b^4*c^4 - 2*a*b^3*c^3*d + a^2*b^2*c^2*d^2)*sqrt(-b^2*c^2 + a*b*c*d)) + 2*(8*(sqrt(b)*x - sqrt(b*x^2 + a))^6*b^2*c^2*d - 8*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a*b*c*d^2 + 3*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*d^3 + 48*(sqrt(b)*x - sqrt(b*x^2 + a))^4*b^3*c^3 - 72*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a*b^2*c^2*d + 42*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*b*c*d^2 - 9*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^3*d^3 + 40*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^2*b^2*c^2*d - 40*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^3*b*c*d^2 + 9*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^4*d^3 + 6*a^4*b*c*d^2 - 3*a^5*d^3)/((b^4*c^4 - 2*a*b^3*c^3*d + a^2*b^2*c^2*d^2)*((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)^2))","B",0
81,1,235,0,0.670331," ","integrate((d*x^2+c)^4/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(2 \, {\left(\frac{4 \, d^{4} x^{2}}{b} + \frac{24 \, a b^{6} c d^{3} - 7 \, a^{2} b^{5} d^{4}}{a b^{7}}\right)} x^{2} + \frac{144 \, a b^{6} c^{2} d^{2} - 120 \, a^{2} b^{5} c d^{3} + 35 \, a^{3} b^{4} d^{4}}{a b^{7}}\right)} x^{2} + \frac{3 \, {\left(16 \, b^{7} c^{4} - 64 \, a b^{6} c^{3} d + 144 \, a^{2} b^{5} c^{2} d^{2} - 120 \, a^{3} b^{4} c d^{3} + 35 \, a^{4} b^{3} d^{4}\right)}}{a b^{7}}\right)} x}{48 \, \sqrt{b x^{2} + a}} - \frac{{\left(64 \, b^{3} c^{3} d - 144 \, a b^{2} c^{2} d^{2} + 120 \, a^{2} b c d^{3} - 35 \, a^{3} d^{4}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{16 \, b^{\frac{9}{2}}}"," ",0,"1/48*((2*(4*d^4*x^2/b + (24*a*b^6*c*d^3 - 7*a^2*b^5*d^4)/(a*b^7))*x^2 + (144*a*b^6*c^2*d^2 - 120*a^2*b^5*c*d^3 + 35*a^3*b^4*d^4)/(a*b^7))*x^2 + 3*(16*b^7*c^4 - 64*a*b^6*c^3*d + 144*a^2*b^5*c^2*d^2 - 120*a^3*b^4*c*d^3 + 35*a^4*b^3*d^4)/(a*b^7))*x/sqrt(b*x^2 + a) - 1/16*(64*b^3*c^3*d - 144*a*b^2*c^2*d^2 + 120*a^2*b*c*d^3 - 35*a^3*d^4)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(9/2)","A",0
82,1,157,0,0.644381," ","integrate((d*x^2+c)^3/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{2 \, d^{3} x^{2}}{b} + \frac{12 \, a b^{4} c d^{2} - 5 \, a^{2} b^{3} d^{3}}{a b^{5}}\right)} x^{2} + \frac{8 \, b^{5} c^{3} - 24 \, a b^{4} c^{2} d + 36 \, a^{2} b^{3} c d^{2} - 15 \, a^{3} b^{2} d^{3}}{a b^{5}}\right)} x}{8 \, \sqrt{b x^{2} + a}} - \frac{3 \, {\left(8 \, b^{2} c^{2} d - 12 \, a b c d^{2} + 5 \, a^{2} d^{3}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{7}{2}}}"," ",0,"1/8*((2*d^3*x^2/b + (12*a*b^4*c*d^2 - 5*a^2*b^3*d^3)/(a*b^5))*x^2 + (8*b^5*c^3 - 24*a*b^4*c^2*d + 36*a^2*b^3*c*d^2 - 15*a^3*b^2*d^3)/(a*b^5))*x/sqrt(b*x^2 + a) - 3/8*(8*b^2*c^2*d - 12*a*b*c*d^2 + 5*a^2*d^3)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
83,1,92,0,0.631962," ","integrate((d*x^2+c)^2/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{{\left(\frac{d^{2} x^{2}}{b} + \frac{2 \, b^{3} c^{2} - 4 \, a b^{2} c d + 3 \, a^{2} b d^{2}}{a b^{3}}\right)} x}{2 \, \sqrt{b x^{2} + a}} - \frac{{\left(4 \, b c d - 3 \, a d^{2}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{5}{2}}}"," ",0,"1/2*(d^2*x^2/b + (2*b^3*c^2 - 4*a*b^2*c*d + 3*a^2*b*d^2)/(a*b^3))*x/sqrt(b*x^2 + a) - 1/2*(4*b*c*d - 3*a*d^2)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
84,1,50,0,0.642829," ","integrate((d*x^2+c)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","-\frac{d \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{b^{\frac{3}{2}}} + \frac{{\left(b c - a d\right)} x}{\sqrt{b x^{2} + a} a b}"," ",0,"-d*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(3/2) + (b*c - a*d)*x/(sqrt(b*x^2 + a)*a*b)","A",0
85,1,14,0,0.595728," ","integrate(1/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\frac{x}{\sqrt{b x^{2} + a} a}"," ",0,"x/(sqrt(b*x^2 + a)*a)","A",0
86,1,107,0,0.618811," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c),x, algorithm=""giac"")","-\frac{\sqrt{b} d \arctan\left(-\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{\sqrt{-b^{2} c^{2} + a b c d} {\left(b c - a d\right)}} + \frac{b x}{{\left(a b c - a^{2} d\right)} \sqrt{b x^{2} + a}}"," ",0,"-sqrt(b)*d*arctan(-1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/(sqrt(-b^2*c^2 + a*b*c*d)*(b*c - a*d)) + b*x/((a*b*c - a^2*d)*sqrt(b*x^2 + a))","A",0
87,1,318,0,1.902397," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{b^{2} x}{{\left(a b^{2} c^{2} - 2 \, a^{2} b c d + a^{3} d^{2}\right)} \sqrt{b x^{2} + a}} + \frac{{\left(4 \, b^{\frac{3}{2}} c d - a \sqrt{b} d^{2}\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{2 \, {\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} \sqrt{-b^{2} c^{2} + a b c d}} + \frac{2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b^{\frac{3}{2}} c d - {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a \sqrt{b} d^{2} + a^{2} \sqrt{b} d^{2}}{{\left(b^{2} c^{3} - 2 \, a b c^{2} d + a^{2} c d^{2}\right)} {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}}"," ",0,"b^2*x/((a*b^2*c^2 - 2*a^2*b*c*d + a^3*d^2)*sqrt(b*x^2 + a)) + 1/2*(4*b^(3/2)*c*d - a*sqrt(b)*d^2)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*sqrt(-b^2*c^2 + a*b*c*d)) + (2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b^(3/2)*c*d - (sqrt(b)*x - sqrt(b*x^2 + a))^2*a*sqrt(b)*d^2 + a^2*sqrt(b)*d^2)/((b^2*c^3 - 2*a*b*c^2*d + a^2*c*d^2)*((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d))","B",0
88,1,643,0,2.698813," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{b^{3} x}{{\left(a b^{3} c^{3} - 3 \, a^{2} b^{2} c^{2} d + 3 \, a^{3} b c d^{2} - a^{4} d^{3}\right)} \sqrt{b x^{2} + a}} + \frac{3 \, {\left(8 \, b^{\frac{5}{2}} c^{2} d - 4 \, a b^{\frac{3}{2}} c d^{2} + a^{2} \sqrt{b} d^{3}\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{8 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} \sqrt{-b^{2} c^{2} + a b c d}} + \frac{16 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} b^{\frac{5}{2}} c^{2} d^{2} - 12 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a b^{\frac{3}{2}} c d^{3} + 3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} \sqrt{b} d^{4} + 80 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} b^{\frac{7}{2}} c^{3} d - 104 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a b^{\frac{5}{2}} c^{2} d^{2} + 54 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} b^{\frac{3}{2}} c d^{3} - 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{3} \sqrt{b} d^{4} + 64 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{2} b^{\frac{5}{2}} c^{2} d^{2} - 52 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{3} b^{\frac{3}{2}} c d^{3} + 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{4} \sqrt{b} d^{4} + 10 \, a^{4} b^{\frac{3}{2}} c d^{3} - 3 \, a^{5} \sqrt{b} d^{4}}{4 \, {\left(b^{3} c^{5} - 3 \, a b^{2} c^{4} d + 3 \, a^{2} b c^{3} d^{2} - a^{3} c^{2} d^{3}\right)} {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}^{2}}"," ",0,"b^3*x/((a*b^3*c^3 - 3*a^2*b^2*c^2*d + 3*a^3*b*c*d^2 - a^4*d^3)*sqrt(b*x^2 + a)) + 3/8*(8*b^(5/2)*c^2*d - 4*a*b^(3/2)*c*d^2 + a^2*sqrt(b)*d^3)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/((b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*sqrt(-b^2*c^2 + a*b*c*d)) + 1/4*(16*(sqrt(b)*x - sqrt(b*x^2 + a))^6*b^(5/2)*c^2*d^2 - 12*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a*b^(3/2)*c*d^3 + 3*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*sqrt(b)*d^4 + 80*(sqrt(b)*x - sqrt(b*x^2 + a))^4*b^(7/2)*c^3*d - 104*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a*b^(5/2)*c^2*d^2 + 54*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*b^(3/2)*c*d^3 - 9*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^3*sqrt(b)*d^4 + 64*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^2*b^(5/2)*c^2*d^2 - 52*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^3*b^(3/2)*c*d^3 + 9*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^4*sqrt(b)*d^4 + 10*a^4*b^(3/2)*c*d^3 - 3*a^5*sqrt(b)*d^4)/((b^3*c^5 - 3*a*b^2*c^4*d + 3*a^2*b*c^3*d^2 - a^3*c^2*d^3)*((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)^2)","B",0
89,1,237,0,0.679334," ","integrate((d*x^2+c)^4/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left(3 \, {\left(\frac{2 \, d^{4} x^{2}}{b} + \frac{16 \, a^{2} b^{6} c d^{3} - 7 \, a^{3} b^{5} d^{4}}{a^{2} b^{7}}\right)} x^{2} + \frac{4 \, {\left(4 \, b^{8} c^{4} + 8 \, a b^{7} c^{3} d - 48 \, a^{2} b^{6} c^{2} d^{2} + 80 \, a^{3} b^{5} c d^{3} - 35 \, a^{4} b^{4} d^{4}\right)}}{a^{2} b^{7}}\right)} x^{2} + \frac{3 \, {\left(8 \, a b^{7} c^{4} - 48 \, a^{3} b^{5} c^{2} d^{2} + 80 \, a^{4} b^{4} c d^{3} - 35 \, a^{5} b^{3} d^{4}\right)}}{a^{2} b^{7}}\right)} x}{24 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} - \frac{{\left(48 \, b^{2} c^{2} d^{2} - 80 \, a b c d^{3} + 35 \, a^{2} d^{4}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{8 \, b^{\frac{9}{2}}}"," ",0,"1/24*((3*(2*d^4*x^2/b + (16*a^2*b^6*c*d^3 - 7*a^3*b^5*d^4)/(a^2*b^7))*x^2 + 4*(4*b^8*c^4 + 8*a*b^7*c^3*d - 48*a^2*b^6*c^2*d^2 + 80*a^3*b^5*c*d^3 - 35*a^4*b^4*d^4)/(a^2*b^7))*x^2 + 3*(8*a*b^7*c^4 - 48*a^3*b^5*c^2*d^2 + 80*a^4*b^4*c*d^3 - 35*a^5*b^3*d^4)/(a^2*b^7))*x/(b*x^2 + a)^(3/2) - 1/8*(48*b^2*c^2*d^2 - 80*a*b*c*d^3 + 35*a^2*d^4)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(9/2)","A",0
90,1,158,0,0.681960," ","integrate((d*x^2+c)^3/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{{\left({\left(\frac{3 \, d^{3} x^{2}}{b} + \frac{2 \, {\left(2 \, b^{6} c^{3} + 3 \, a b^{5} c^{2} d - 12 \, a^{2} b^{4} c d^{2} + 10 \, a^{3} b^{3} d^{3}\right)}}{a^{2} b^{5}}\right)} x^{2} + \frac{3 \, {\left(2 \, a b^{5} c^{3} - 6 \, a^{3} b^{3} c d^{2} + 5 \, a^{4} b^{2} d^{3}\right)}}{a^{2} b^{5}}\right)} x}{6 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} - \frac{{\left(6 \, b c d^{2} - 5 \, a d^{3}\right)} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{2 \, b^{\frac{7}{2}}}"," ",0,"1/6*((3*d^3*x^2/b + 2*(2*b^6*c^3 + 3*a*b^5*c^2*d - 12*a^2*b^4*c*d^2 + 10*a^3*b^3*d^3)/(a^2*b^5))*x^2 + 3*(2*a*b^5*c^3 - 6*a^3*b^3*c*d^2 + 5*a^4*b^2*d^3)/(a^2*b^5))*x/(b*x^2 + a)^(3/2) - 1/2*(6*b*c*d^2 - 5*a*d^3)*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(7/2)","A",0
91,1,103,0,0.631772," ","integrate((d*x^2+c)^2/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{x {\left(\frac{2 \, {\left(b^{4} c^{2} + a b^{3} c d - 2 \, a^{2} b^{2} d^{2}\right)} x^{2}}{a^{2} b^{3}} + \frac{3 \, {\left(a b^{3} c^{2} - a^{3} b d^{2}\right)}}{a^{2} b^{3}}\right)}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} - \frac{d^{2} \log\left({\left| -\sqrt{b} x + \sqrt{b x^{2} + a} \right|}\right)}{b^{\frac{5}{2}}}"," ",0,"1/3*x*(2*(b^4*c^2 + a*b^3*c*d - 2*a^2*b^2*d^2)*x^2/(a^2*b^3) + 3*(a*b^3*c^2 - a^3*b*d^2)/(a^2*b^3))/(b*x^2 + a)^(3/2) - d^2*log(abs(-sqrt(b)*x + sqrt(b*x^2 + a)))/b^(5/2)","A",0
92,1,40,0,0.617583," ","integrate((d*x^2+c)/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{x {\left(\frac{3 \, c}{a} + \frac{{\left(2 \, b^{2} c + a b d\right)} x^{2}}{a^{2} b}\right)}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*x*(3*c/a + (2*b^2*c + a*b*d)*x^2/(a^2*b))/(b*x^2 + a)^(3/2)","A",0
93,1,27,0,0.609195," ","integrate(1/(b*x^2+a)^(5/2),x, algorithm=""giac"")","\frac{x {\left(\frac{2 \, b x^{2}}{a^{2}} + \frac{3}{a}\right)}}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"1/3*x*(2*b*x^2/a^2 + 3/a)/(b*x^2 + a)^(3/2)","A",0
94,1,320,0,0.638830," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c),x, algorithm=""giac"")","-\frac{\sqrt{b} d^{2} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{{\left(b^{2} c^{2} - 2 \, a b c d + a^{2} d^{2}\right)} \sqrt{-b^{2} c^{2} + a b c d}} + \frac{{\left(\frac{{\left(2 \, b^{6} c^{3} - 9 \, a b^{5} c^{2} d + 12 \, a^{2} b^{4} c d^{2} - 5 \, a^{3} b^{3} d^{3}\right)} x^{2}}{a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d + 6 \, a^{4} b^{3} c^{2} d^{2} - 4 \, a^{5} b^{2} c d^{3} + a^{6} b d^{4}} + \frac{3 \, {\left(a b^{5} c^{3} - 4 \, a^{2} b^{4} c^{2} d + 5 \, a^{3} b^{3} c d^{2} - 2 \, a^{4} b^{2} d^{3}\right)}}{a^{2} b^{5} c^{4} - 4 \, a^{3} b^{4} c^{3} d + 6 \, a^{4} b^{3} c^{2} d^{2} - 4 \, a^{5} b^{2} c d^{3} + a^{6} b d^{4}}\right)} x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}}"," ",0,"-sqrt(b)*d^2*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/((b^2*c^2 - 2*a*b*c*d + a^2*d^2)*sqrt(-b^2*c^2 + a*b*c*d)) + 1/3*((2*b^6*c^3 - 9*a*b^5*c^2*d + 12*a^2*b^4*c*d^2 - 5*a^3*b^3*d^3)*x^2/(a^2*b^5*c^4 - 4*a^3*b^4*c^3*d + 6*a^4*b^3*c^2*d^2 - 4*a^5*b^2*c*d^3 + a^6*b*d^4) + 3*(a*b^5*c^3 - 4*a^2*b^4*c^2*d + 5*a^3*b^3*c*d^2 - 2*a^4*b^2*d^3)/(a^2*b^5*c^4 - 4*a^3*b^4*c^3*d + 6*a^4*b^3*c^2*d^2 - 4*a^5*b^2*c*d^3 + a^6*b*d^4))*x/(b*x^2 + a)^(3/2)","B",0
95,1,620,0,2.070340," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c)^2,x, algorithm=""giac"")","\frac{{\left(\frac{2 \, {\left(b^{8} c^{4} - 7 \, a b^{7} c^{3} d + 15 \, a^{2} b^{6} c^{2} d^{2} - 13 \, a^{3} b^{5} c d^{3} + 4 \, a^{4} b^{4} d^{4}\right)} x^{2}}{a^{2} b^{7} c^{6} - 6 \, a^{3} b^{6} c^{5} d + 15 \, a^{4} b^{5} c^{4} d^{2} - 20 \, a^{5} b^{4} c^{3} d^{3} + 15 \, a^{6} b^{3} c^{2} d^{4} - 6 \, a^{7} b^{2} c d^{5} + a^{8} b d^{6}} + \frac{3 \, {\left(a b^{7} c^{4} - 6 \, a^{2} b^{6} c^{3} d + 12 \, a^{3} b^{5} c^{2} d^{2} - 10 \, a^{4} b^{4} c d^{3} + 3 \, a^{5} b^{3} d^{4}\right)}}{a^{2} b^{7} c^{6} - 6 \, a^{3} b^{6} c^{5} d + 15 \, a^{4} b^{5} c^{4} d^{2} - 20 \, a^{5} b^{4} c^{3} d^{3} + 15 \, a^{6} b^{3} c^{2} d^{4} - 6 \, a^{7} b^{2} c d^{5} + a^{8} b d^{6}}\right)} x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} + \frac{{\left(6 \, b^{\frac{3}{2}} c d^{2} - a \sqrt{b} d^{3}\right)} \arctan\left(-\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{2 \, {\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} \sqrt{-b^{2} c^{2} + a b c d}} - \frac{2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b^{\frac{3}{2}} c d^{2} - {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a \sqrt{b} d^{3} + a^{2} \sqrt{b} d^{3}}{{\left(b^{3} c^{4} - 3 \, a b^{2} c^{3} d + 3 \, a^{2} b c^{2} d^{2} - a^{3} c d^{3}\right)} {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}}"," ",0,"1/3*(2*(b^8*c^4 - 7*a*b^7*c^3*d + 15*a^2*b^6*c^2*d^2 - 13*a^3*b^5*c*d^3 + 4*a^4*b^4*d^4)*x^2/(a^2*b^7*c^6 - 6*a^3*b^6*c^5*d + 15*a^4*b^5*c^4*d^2 - 20*a^5*b^4*c^3*d^3 + 15*a^6*b^3*c^2*d^4 - 6*a^7*b^2*c*d^5 + a^8*b*d^6) + 3*(a*b^7*c^4 - 6*a^2*b^6*c^3*d + 12*a^3*b^5*c^2*d^2 - 10*a^4*b^4*c*d^3 + 3*a^5*b^3*d^4)/(a^2*b^7*c^6 - 6*a^3*b^6*c^5*d + 15*a^4*b^5*c^4*d^2 - 20*a^5*b^4*c^3*d^3 + 15*a^6*b^3*c^2*d^4 - 6*a^7*b^2*c*d^5 + a^8*b*d^6))*x/(b*x^2 + a)^(3/2) + 1/2*(6*b^(3/2)*c*d^2 - a*sqrt(b)*d^3)*arctan(-1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/((b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*sqrt(-b^2*c^2 + a*b*c*d)) - (2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b^(3/2)*c*d^2 - (sqrt(b)*x - sqrt(b*x^2 + a))^2*a*sqrt(b)*d^3 + a^2*sqrt(b)*d^3)/((b^3*c^4 - 3*a*b^2*c^3*d + 3*a^2*b*c^2*d^2 - a^3*c*d^3)*((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d))","B",0
96,1,1010,0,3.759628," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c)^3,x, algorithm=""giac"")","\frac{{\left(\frac{{\left(2 \, b^{10} c^{5} - 19 \, a b^{9} c^{4} d + 56 \, a^{2} b^{8} c^{3} d^{2} - 74 \, a^{3} b^{7} c^{2} d^{3} + 46 \, a^{4} b^{6} c d^{4} - 11 \, a^{5} b^{5} d^{5}\right)} x^{2}}{a^{2} b^{9} c^{8} - 8 \, a^{3} b^{8} c^{7} d + 28 \, a^{4} b^{7} c^{6} d^{2} - 56 \, a^{5} b^{6} c^{5} d^{3} + 70 \, a^{6} b^{5} c^{4} d^{4} - 56 \, a^{7} b^{4} c^{3} d^{5} + 28 \, a^{8} b^{3} c^{2} d^{6} - 8 \, a^{9} b^{2} c d^{7} + a^{10} b d^{8}} + \frac{3 \, {\left(a b^{9} c^{5} - 8 \, a^{2} b^{8} c^{4} d + 22 \, a^{3} b^{7} c^{3} d^{2} - 28 \, a^{4} b^{6} c^{2} d^{3} + 17 \, a^{5} b^{5} c d^{4} - 4 \, a^{6} b^{4} d^{5}\right)}}{a^{2} b^{9} c^{8} - 8 \, a^{3} b^{8} c^{7} d + 28 \, a^{4} b^{7} c^{6} d^{2} - 56 \, a^{5} b^{6} c^{5} d^{3} + 70 \, a^{6} b^{5} c^{4} d^{4} - 56 \, a^{7} b^{4} c^{3} d^{5} + 28 \, a^{8} b^{3} c^{2} d^{6} - 8 \, a^{9} b^{2} c d^{7} + a^{10} b d^{8}}\right)} x}{3 \, {\left(b x^{2} + a\right)}^{\frac{3}{2}}} - \frac{{\left(48 \, b^{\frac{5}{2}} c^{2} d^{2} - 16 \, a b^{\frac{3}{2}} c d^{3} + 3 \, a^{2} \sqrt{b} d^{4}\right)} \arctan\left(\frac{{\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} d + 2 \, b c - a d}{2 \, \sqrt{-b^{2} c^{2} + a b c d}}\right)}{8 \, {\left(b^{4} c^{6} - 4 \, a b^{3} c^{5} d + 6 \, a^{2} b^{2} c^{4} d^{2} - 4 \, a^{3} b c^{3} d^{3} + a^{4} c^{2} d^{4}\right)} \sqrt{-b^{2} c^{2} + a b c d}} - \frac{24 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} b^{\frac{5}{2}} c^{2} d^{3} - 16 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a b^{\frac{3}{2}} c d^{4} + 3 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{6} a^{2} \sqrt{b} d^{5} + 112 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} b^{\frac{7}{2}} c^{3} d^{2} - 136 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a b^{\frac{5}{2}} c^{2} d^{3} + 66 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{2} b^{\frac{3}{2}} c d^{4} - 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} a^{3} \sqrt{b} d^{5} + 88 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{2} b^{\frac{5}{2}} c^{2} d^{3} - 64 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{3} b^{\frac{3}{2}} c d^{4} + 9 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a^{4} \sqrt{b} d^{5} + 14 \, a^{4} b^{\frac{3}{2}} c d^{4} - 3 \, a^{5} \sqrt{b} d^{5}}{4 \, {\left(b^{4} c^{6} - 4 \, a b^{3} c^{5} d + 6 \, a^{2} b^{2} c^{4} d^{2} - 4 \, a^{3} b c^{3} d^{3} + a^{4} c^{2} d^{4}\right)} {\left({\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{4} d + 4 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} b c - 2 \, {\left(\sqrt{b} x - \sqrt{b x^{2} + a}\right)}^{2} a d + a^{2} d\right)}^{2}}"," ",0,"1/3*((2*b^10*c^5 - 19*a*b^9*c^4*d + 56*a^2*b^8*c^3*d^2 - 74*a^3*b^7*c^2*d^3 + 46*a^4*b^6*c*d^4 - 11*a^5*b^5*d^5)*x^2/(a^2*b^9*c^8 - 8*a^3*b^8*c^7*d + 28*a^4*b^7*c^6*d^2 - 56*a^5*b^6*c^5*d^3 + 70*a^6*b^5*c^4*d^4 - 56*a^7*b^4*c^3*d^5 + 28*a^8*b^3*c^2*d^6 - 8*a^9*b^2*c*d^7 + a^10*b*d^8) + 3*(a*b^9*c^5 - 8*a^2*b^8*c^4*d + 22*a^3*b^7*c^3*d^2 - 28*a^4*b^6*c^2*d^3 + 17*a^5*b^5*c*d^4 - 4*a^6*b^4*d^5)/(a^2*b^9*c^8 - 8*a^3*b^8*c^7*d + 28*a^4*b^7*c^6*d^2 - 56*a^5*b^6*c^5*d^3 + 70*a^6*b^5*c^4*d^4 - 56*a^7*b^4*c^3*d^5 + 28*a^8*b^3*c^2*d^6 - 8*a^9*b^2*c*d^7 + a^10*b*d^8))*x/(b*x^2 + a)^(3/2) - 1/8*(48*b^(5/2)*c^2*d^2 - 16*a*b^(3/2)*c*d^3 + 3*a^2*sqrt(b)*d^4)*arctan(1/2*((sqrt(b)*x - sqrt(b*x^2 + a))^2*d + 2*b*c - a*d)/sqrt(-b^2*c^2 + a*b*c*d))/((b^4*c^6 - 4*a*b^3*c^5*d + 6*a^2*b^2*c^4*d^2 - 4*a^3*b*c^3*d^3 + a^4*c^2*d^4)*sqrt(-b^2*c^2 + a*b*c*d)) - 1/4*(24*(sqrt(b)*x - sqrt(b*x^2 + a))^6*b^(5/2)*c^2*d^3 - 16*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a*b^(3/2)*c*d^4 + 3*(sqrt(b)*x - sqrt(b*x^2 + a))^6*a^2*sqrt(b)*d^5 + 112*(sqrt(b)*x - sqrt(b*x^2 + a))^4*b^(7/2)*c^3*d^2 - 136*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a*b^(5/2)*c^2*d^3 + 66*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^2*b^(3/2)*c*d^4 - 9*(sqrt(b)*x - sqrt(b*x^2 + a))^4*a^3*sqrt(b)*d^5 + 88*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^2*b^(5/2)*c^2*d^3 - 64*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^3*b^(3/2)*c*d^4 + 9*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a^4*sqrt(b)*d^5 + 14*a^4*b^(3/2)*c*d^4 - 3*a^5*sqrt(b)*d^5)/((b^4*c^6 - 4*a*b^3*c^5*d + 6*a^2*b^2*c^4*d^2 - 4*a^3*b*c^3*d^3 + a^4*c^2*d^4)*((sqrt(b)*x - sqrt(b*x^2 + a))^4*d + 4*(sqrt(b)*x - sqrt(b*x^2 + a))^2*b*c - 2*(sqrt(b)*x - sqrt(b*x^2 + a))^2*a*d + a^2*d)^2)","B",0
97,1,218,0,0.676517," ","integrate((b*x^2+a)^3/(d*x^2+c)^(11/2),x, algorithm=""giac"")","\frac{{\left({\left({\left(x^{2} {\left(\frac{2 \, {\left(5 \, b^{3} c^{3} d^{5} + 12 \, a b^{2} c^{2} d^{6} + 24 \, a^{2} b c d^{7} + 64 \, a^{3} d^{8}\right)} x^{2}}{c^{5} d^{4}} + \frac{9 \, {\left(5 \, b^{3} c^{4} d^{4} + 12 \, a b^{2} c^{3} d^{5} + 24 \, a^{2} b c^{2} d^{6} + 64 \, a^{3} c d^{7}\right)}}{c^{5} d^{4}}\right)} + \frac{63 \, {\left(3 \, a b^{2} c^{4} d^{4} + 6 \, a^{2} b c^{3} d^{5} + 16 \, a^{3} c^{2} d^{6}\right)}}{c^{5} d^{4}}\right)} x^{2} + \frac{105 \, {\left(3 \, a^{2} b c^{4} d^{4} + 8 \, a^{3} c^{3} d^{5}\right)}}{c^{5} d^{4}}\right)} x^{2} + \frac{315 \, a^{3}}{c}\right)} x}{315 \, {\left(d x^{2} + c\right)}^{\frac{9}{2}}}"," ",0,"1/315*(((x^2*(2*(5*b^3*c^3*d^5 + 12*a*b^2*c^2*d^6 + 24*a^2*b*c*d^7 + 64*a^3*d^8)*x^2/(c^5*d^4) + 9*(5*b^3*c^4*d^4 + 12*a*b^2*c^3*d^5 + 24*a^2*b*c^2*d^6 + 64*a^3*c*d^7)/(c^5*d^4)) + 63*(3*a*b^2*c^4*d^4 + 6*a^2*b*c^3*d^5 + 16*a^3*c^2*d^6)/(c^5*d^4))*x^2 + 105*(3*a^2*b*c^4*d^4 + 8*a^3*c^3*d^5)/(c^5*d^4))*x^2 + 315*a^3/c)*x/(d*x^2 + c)^(9/2)","A",0
98,1,138,0,0.641088," ","integrate((b*x^2+a)^2/(d*x^2+c)^(9/2),x, algorithm=""giac"")","\frac{{\left({\left(x^{2} {\left(\frac{2 \, {\left(3 \, b^{2} c^{2} d^{4} + 8 \, a b c d^{5} + 24 \, a^{2} d^{6}\right)} x^{2}}{c^{4} d^{3}} + \frac{7 \, {\left(3 \, b^{2} c^{3} d^{3} + 8 \, a b c^{2} d^{4} + 24 \, a^{2} c d^{5}\right)}}{c^{4} d^{3}}\right)} + \frac{70 \, {\left(a b c^{3} d^{3} + 3 \, a^{2} c^{2} d^{4}\right)}}{c^{4} d^{3}}\right)} x^{2} + \frac{105 \, a^{2}}{c}\right)} x}{105 \, {\left(d x^{2} + c\right)}^{\frac{7}{2}}}"," ",0,"1/105*((x^2*(2*(3*b^2*c^2*d^4 + 8*a*b*c*d^5 + 24*a^2*d^6)*x^2/(c^4*d^3) + 7*(3*b^2*c^3*d^3 + 8*a*b*c^2*d^4 + 24*a^2*c*d^5)/(c^4*d^3)) + 70*(a*b*c^3*d^3 + 3*a^2*c^2*d^4)/(c^4*d^3))*x^2 + 105*a^2/c)*x/(d*x^2 + c)^(7/2)","A",0
99,1,72,0,0.618446," ","integrate((b*x^2+a)/(d*x^2+c)^(7/2),x, algorithm=""giac"")","\frac{{\left(x^{2} {\left(\frac{2 \, {\left(b c d^{3} + 4 \, a d^{4}\right)} x^{2}}{c^{3} d^{2}} + \frac{5 \, {\left(b c^{2} d^{2} + 4 \, a c d^{3}\right)}}{c^{3} d^{2}}\right)} + \frac{15 \, a}{c}\right)} x}{15 \, {\left(d x^{2} + c\right)}^{\frac{5}{2}}}"," ",0,"1/15*(x^2*(2*(b*c*d^3 + 4*a*d^4)*x^2/(c^3*d^2) + 5*(b*c^2*d^2 + 4*a*c*d^3)/(c^3*d^2)) + 15*a/c)*x/(d*x^2 + c)^(5/2)","A",0
100,1,27,0,0.602725," ","integrate(1/(d*x^2+c)^(5/2),x, algorithm=""giac"")","\frac{x {\left(\frac{2 \, d x^{2}}{c^{2}} + \frac{3}{c}\right)}}{3 \, {\left(d x^{2} + c\right)}^{\frac{3}{2}}}"," ",0,"1/3*x*(2*d*x^2/c^2 + 3/c)/(d*x^2 + c)^(3/2)","A",0
101,1,107,0,0.616660," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\frac{b \sqrt{d} \arctan\left(-\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{\sqrt{a b c d - a^{2} d^{2}} {\left(b c - a d\right)}} - \frac{d x}{{\left(b c^{2} - a c d\right)} \sqrt{d x^{2} + c}}"," ",0,"b*sqrt(d)*arctan(-1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(sqrt(a*b*c*d - a^2*d^2)*(b*c - a*d)) - d*x/((b*c^2 - a*c*d)*sqrt(d*x^2 + c))","A",0
102,1,225,0,0.623136," ","integrate(1/(b*x^2+a)^2/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{1}{2} \, d^{\frac{3}{2}} {\left(\frac{{\left(b c - 2 \, a d\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{{\left(a b c d - a^{2} d^{2}\right)}^{\frac{3}{2}}} + \frac{2 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d - b c^{2}\right)}}{{\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)} {\left(a b c d - a^{2} d^{2}\right)}}\right)}"," ",0,"-1/2*d^(3/2)*((b*c - 2*a*d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/(a*b*c*d - a^2*d^2)^(3/2) + 2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d - b*c^2)/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)*(a*b*c*d - a^2*d^2)))","B",0
103,1,487,0,3.131898," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^3,x, algorithm=""giac"")","-\frac{{\left(3 \, b c^{2} \sqrt{d} - 4 \, a c d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{8 \, {\left(a^{2} b c - a^{3} d\right)} \sqrt{a b c d - a^{2} d^{2}}} - \frac{3 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b^{3} c^{2} \sqrt{d} - 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a b^{2} c d^{\frac{3}{2}} - 9 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{3} c^{3} \sqrt{d} + 30 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b^{2} c^{2} d^{\frac{3}{2}} - 40 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} b c d^{\frac{5}{2}} + 16 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{3} d^{\frac{7}{2}} + 9 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{3} c^{4} \sqrt{d} - 28 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{2} c^{3} d^{\frac{3}{2}} + 16 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} b c^{2} d^{\frac{5}{2}} - 3 \, b^{3} c^{5} \sqrt{d} + 2 \, a b^{2} c^{4} d^{\frac{3}{2}}}{4 \, {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)}^{2} {\left(a^{2} b^{2} c - a^{3} b d\right)}}"," ",0,"-1/8*(3*b*c^2*sqrt(d) - 4*a*c*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((a^2*b*c - a^3*d)*sqrt(a*b*c*d - a^2*d^2)) - 1/4*(3*(sqrt(d)*x - sqrt(d*x^2 + c))^6*b^3*c^2*sqrt(d) - 4*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a*b^2*c*d^(3/2) - 9*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^3*c^3*sqrt(d) + 30*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b^2*c^2*d^(3/2) - 40*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*b*c*d^(5/2) + 16*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^3*d^(7/2) + 9*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^3*c^4*sqrt(d) - 28*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^2*c^3*d^(3/2) + 16*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*b*c^2*d^(5/2) - 3*b^3*c^5*sqrt(d) + 2*a*b^2*c^4*d^(3/2))/(((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)^2*(a^2*b^2*c - a^3*b*d))","B",0
104,1,919,0,2.812154," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^4,x, algorithm=""giac"")","-\frac{{\left(5 \, b c^{3} \sqrt{d} - 6 \, a c^{2} d^{\frac{3}{2}}\right)} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{16 \, {\left(a^{3} b c - a^{4} d\right)} \sqrt{a b c d - a^{2} d^{2}}} - \frac{15 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{10} b^{5} c^{3} \sqrt{d} - 18 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{10} a b^{4} c^{2} d^{\frac{3}{2}} - 75 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} b^{5} c^{4} \sqrt{d} + 240 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a b^{4} c^{3} d^{\frac{3}{2}} - 180 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a^{2} b^{3} c^{2} d^{\frac{5}{2}} - 96 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a^{3} b^{2} c d^{\frac{7}{2}} + 96 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{8} a^{4} b d^{\frac{9}{2}} + 150 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} b^{5} c^{5} \sqrt{d} - 620 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a b^{4} c^{4} d^{\frac{3}{2}} + 968 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a^{2} b^{3} c^{3} d^{\frac{5}{2}} - 720 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a^{3} b^{2} c^{2} d^{\frac{7}{2}} + 64 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a^{4} b c d^{\frac{9}{2}} + 128 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{6} a^{5} d^{\frac{11}{2}} - 150 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b^{5} c^{6} \sqrt{d} + 600 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a b^{4} c^{5} d^{\frac{3}{2}} - 864 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{2} b^{3} c^{4} d^{\frac{5}{2}} + 288 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{3} b^{2} c^{3} d^{\frac{7}{2}} + 96 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} a^{4} b c^{2} d^{\frac{9}{2}} + 75 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b^{5} c^{7} \sqrt{d} - 210 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a b^{4} c^{6} d^{\frac{3}{2}} + 72 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{2} b^{3} c^{5} d^{\frac{5}{2}} + 48 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a^{3} b^{2} c^{4} d^{\frac{7}{2}} - 15 \, b^{5} c^{8} \sqrt{d} + 8 \, a b^{4} c^{7} d^{\frac{3}{2}} + 4 \, a^{2} b^{3} c^{6} d^{\frac{5}{2}}}{24 \, {\left(a^{3} b^{3} c - a^{4} b^{2} d\right)} {\left({\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{4} b - 2 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b c + 4 \, {\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} a d + b c^{2}\right)}^{3}}"," ",0,"-1/16*(5*b*c^3*sqrt(d) - 6*a*c^2*d^(3/2))*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/((a^3*b*c - a^4*d)*sqrt(a*b*c*d - a^2*d^2)) - 1/24*(15*(sqrt(d)*x - sqrt(d*x^2 + c))^10*b^5*c^3*sqrt(d) - 18*(sqrt(d)*x - sqrt(d*x^2 + c))^10*a*b^4*c^2*d^(3/2) - 75*(sqrt(d)*x - sqrt(d*x^2 + c))^8*b^5*c^4*sqrt(d) + 240*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a*b^4*c^3*d^(3/2) - 180*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a^2*b^3*c^2*d^(5/2) - 96*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a^3*b^2*c*d^(7/2) + 96*(sqrt(d)*x - sqrt(d*x^2 + c))^8*a^4*b*d^(9/2) + 150*(sqrt(d)*x - sqrt(d*x^2 + c))^6*b^5*c^5*sqrt(d) - 620*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a*b^4*c^4*d^(3/2) + 968*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a^2*b^3*c^3*d^(5/2) - 720*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a^3*b^2*c^2*d^(7/2) + 64*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a^4*b*c*d^(9/2) + 128*(sqrt(d)*x - sqrt(d*x^2 + c))^6*a^5*d^(11/2) - 150*(sqrt(d)*x - sqrt(d*x^2 + c))^4*b^5*c^6*sqrt(d) + 600*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a*b^4*c^5*d^(3/2) - 864*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^2*b^3*c^4*d^(5/2) + 288*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^3*b^2*c^3*d^(7/2) + 96*(sqrt(d)*x - sqrt(d*x^2 + c))^4*a^4*b*c^2*d^(9/2) + 75*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b^5*c^7*sqrt(d) - 210*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*b^4*c^6*d^(3/2) + 72*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^2*b^3*c^5*d^(5/2) + 48*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a^3*b^2*c^4*d^(7/2) - 15*b^5*c^8*sqrt(d) + 8*a*b^4*c^7*d^(3/2) + 4*a^2*b^3*c^6*d^(5/2))/((a^3*b^3*c - a^4*b^2*d)*((sqrt(d)*x - sqrt(d*x^2 + c))^4*b - 2*(sqrt(d)*x - sqrt(d*x^2 + c))^2*b*c + 4*(sqrt(d)*x - sqrt(d*x^2 + c))^2*a*d + b*c^2)^3)","B",0
105,1,18,0,0.603694," ","integrate(1/(b*c/d+b*x^2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\frac{d x}{\sqrt{d x^{2} + c} b c}"," ",0,"d*x/(sqrt(d*x^2 + c)*b*c)","A",0
106,1,51,0,0.603582," ","integrate(1/(x^2+1)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} {\left(\pi \mathrm{sgn}\left(x\right) + 2 \, \arctan\left(-\frac{\sqrt{2} x {\left(\frac{{\left(\sqrt{-x^{2} + 1} - 1\right)}^{2}}{x^{2}} - 1\right)}}{4 \, {\left(\sqrt{-x^{2} + 1} - 1\right)}}\right)\right)}"," ",0,"1/4*sqrt(2)*(pi*sgn(x) + 2*arctan(-1/4*sqrt(2)*x*((sqrt(-x^2 + 1) - 1)^2/x^2 - 1)/(sqrt(-x^2 + 1) - 1)))","B",0
107,1,70,0,0.601566," ","integrate(1/(b*x^2+a)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","-\frac{\sqrt{d} \arctan\left(\frac{{\left(\sqrt{d} x - \sqrt{d x^{2} + c}\right)}^{2} b - b c + 2 \, a d}{2 \, \sqrt{a b c d - a^{2} d^{2}}}\right)}{\sqrt{a b c d - a^{2} d^{2}}}"," ",0,"-sqrt(d)*arctan(1/2*((sqrt(d)*x - sqrt(d*x^2 + c))^2*b - b*c + 2*a*d)/sqrt(a*b*c*d - a^2*d^2))/sqrt(a*b*c*d - a^2*d^2)","A",0
108,1,25,0,0.574291," ","integrate((x^2-1)/(x^2+1)^(3/2),x, algorithm=""giac"")","-\frac{2 \, x}{\sqrt{x^{2} + 1}} - \log\left(-x + \sqrt{x^{2} + 1}\right)"," ",0,"-2*x/sqrt(x^2 + 1) - log(-x + sqrt(x^2 + 1))","A",0
109,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)*(b*x^2+3*a)^3,x, algorithm=""giac"")","\int {\left(b x^{2} + 3 \, a\right)}^{3} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^3*(-b*x^2 + a)^(2/3), x)","F",0
110,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)*(b*x^2+3*a)^2,x, algorithm=""giac"")","\int {\left(b x^{2} + 3 \, a\right)}^{2} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^2*(-b*x^2 + a)^(2/3), x)","F",0
111,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)*(b*x^2+3*a),x, algorithm=""giac"")","\int {\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{2}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)*(-b*x^2 + a)^(2/3), x)","F",0
112,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a),x, algorithm=""giac"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{b x^{2} + 3 \, a}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(2/3)/(b*x^2 + 3*a), x)","F",0
113,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a)^2,x, algorithm=""giac"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{{\left(b x^{2} + 3 \, a\right)}^{2}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(2/3)/(b*x^2 + 3*a)^2, x)","F",0
114,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a)^3,x, algorithm=""giac"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{{\left(b x^{2} + 3 \, a\right)}^{3}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(2/3)/(b*x^2 + 3*a)^3, x)","F",0
115,0,0,0,0.000000," ","integrate((-b*x^2+a)^(2/3)/(b*x^2+3*a)^4,x, algorithm=""giac"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{2}{3}}}{{\left(b x^{2} + 3 \, a\right)}^{4}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(2/3)/(b*x^2 + 3*a)^4, x)","F",0
116,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)*(b*x^2+3*a)^3,x, algorithm=""giac"")","\int {\left(b x^{2} + 3 \, a\right)}^{3} {\left(-b x^{2} + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^3*(-b*x^2 + a)^(5/3), x)","F",0
117,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)*(b*x^2+3*a)^2,x, algorithm=""giac"")","\int {\left(b x^{2} + 3 \, a\right)}^{2} {\left(-b x^{2} + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^2*(-b*x^2 + a)^(5/3), x)","F",0
118,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)*(b*x^2+3*a),x, algorithm=""giac"")","\int {\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{5}{3}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)*(-b*x^2 + a)^(5/3), x)","F",0
119,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)/(b*x^2+3*a),x, algorithm=""giac"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{5}{3}}}{b x^{2} + 3 \, a}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(5/3)/(b*x^2 + 3*a), x)","F",0
120,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)/(b*x^2+3*a)^2,x, algorithm=""giac"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{5}{3}}}{{\left(b x^{2} + 3 \, a\right)}^{2}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(5/3)/(b*x^2 + 3*a)^2, x)","F",0
121,0,0,0,0.000000," ","integrate((-b*x^2+a)^(5/3)/(b*x^2+3*a)^3,x, algorithm=""giac"")","\int \frac{{\left(-b x^{2} + a\right)}^{\frac{5}{3}}}{{\left(b x^{2} + 3 \, a\right)}^{3}}\,{d x}"," ",0,"integrate((-b*x^2 + a)^(5/3)/(b*x^2 + 3*a)^3, x)","F",0
122,0,0,0,0.000000," ","integrate((b*x^2+3*a)^4/(-b*x^2+a)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{4}}{{\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^4/(-b*x^2 + a)^(1/3), x)","F",0
123,0,0,0,0.000000," ","integrate((b*x^2+3*a)^3/(-b*x^2+a)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{3}}{{\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^3/(-b*x^2 + a)^(1/3), x)","F",0
124,0,0,0,0.000000," ","integrate((b*x^2+3*a)^2/(-b*x^2+a)^(1/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{2}}{{\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^2/(-b*x^2 + a)^(1/3), x)","F",0
125,0,0,0,0.000000," ","integrate((b*x^2+3*a)/(-b*x^2+a)^(1/3),x, algorithm=""giac"")","\int \frac{b x^{2} + 3 \, a}{{\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)/(-b*x^2 + a)^(1/3), x)","F",0
126,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)*(-b*x^2 + a)^(1/3)), x)","F",0
127,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)}^{2} {\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)^2*(-b*x^2 + a)^(1/3)), x)","F",0
128,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)}^{3} {\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)^3*(-b*x^2 + a)^(1/3)), x)","F",0
129,0,0,0,0.000000," ","integrate((b*x^2+3*a)^3/(-b*x^2+a)^(4/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{3}}{{\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^3/(-b*x^2 + a)^(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, algorithm=""giac"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{2}}{{\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^2/(-b*x^2 + a)^(4/3), x)","F",0
131,0,0,0,0.000000," ","integrate((b*x^2+3*a)/(-b*x^2+a)^(4/3),x, algorithm=""giac"")","\int \frac{b x^{2} + 3 \, a}{{\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)/(-b*x^2 + a)^(4/3), x)","F",0
132,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)*(-b*x^2 + a)^(4/3)), x)","F",0
133,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)}^{2} {\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)^2*(-b*x^2 + a)^(4/3)), x)","F",0
134,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a)^3,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)}^{3} {\left(-b x^{2} + a\right)}^{\frac{4}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)^3*(-b*x^2 + a)^(4/3)), x)","F",0
135,0,0,0,0.000000," ","integrate((b*x^2+3*a)^4/(-b*x^2+a)^(7/3),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{4}}{{\left(-b x^{2} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^4/(-b*x^2 + a)^(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, algorithm=""giac"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{3}}{{\left(-b x^{2} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^3/(-b*x^2 + a)^(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, algorithm=""giac"")","\int \frac{{\left(b x^{2} + 3 \, a\right)}^{2}}{{\left(-b x^{2} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)^2/(-b*x^2 + a)^(7/3), x)","F",0
138,0,0,0,0.000000," ","integrate((b*x^2+3*a)/(-b*x^2+a)^(7/3),x, algorithm=""giac"")","\int \frac{b x^{2} + 3 \, a}{{\left(-b x^{2} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate((b*x^2 + 3*a)/(-b*x^2 + a)^(7/3), x)","F",0
139,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(7/3)/(b*x^2+3*a),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)*(-b*x^2 + a)^(7/3)), x)","F",0
140,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(7/3)/(b*x^2+3*a)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)}^{2} {\left(-b x^{2} + a\right)}^{\frac{7}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)^2*(-b*x^2 + a)^(7/3)), x)","F",0
141,0,0,0,0.000000," ","integrate(1/(-b*x^2-3*a)/(b*x^2-a)^(1/3),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} + 3 \, a\right)} {\left(b x^{2} - a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-1/((b*x^2 + 3*a)*(b*x^2 - a)^(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, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} + a\right)}^{\frac{1}{3}} {\left(b x^{2} - 3 \, a\right)}}\,{d x}"," ",0,"integrate(-1/((b*x^2 + a)^(1/3)*(b*x^2 - 3*a)), x)","F",0
143,0,0,0,0.000000," ","integrate(1/(-d*x^2+c)/(3*d*x^2+c)^(1/3),x, algorithm=""giac"")","\int -\frac{1}{{\left(3 \, d x^{2} + c\right)}^{\frac{1}{3}} {\left(d x^{2} - c\right)}}\,{d x}"," ",0,"integrate(-1/((3*d*x^2 + c)^(1/3)*(d*x^2 - c)), x)","F",0
144,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 3 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 3*a)*(-b*x^2 + a)^(1/3)), x)","F",0
145,0,0,0,0.000000," ","integrate(1/(-3*d*x^2+c)^(1/3)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{1}{{\left(d x^{2} + c\right)} {\left(-3 \, d x^{2} + c\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((d*x^2 + c)*(-3*d*x^2 + c)^(1/3)), x)","F",0
146,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 + 3)*(-x^2 + 1)^(1/3)), x)","F",0
147,0,0,0,0.000000," ","integrate(1/(-x^2+3)/(x^2+1)^(1/3),x, algorithm=""giac"")","\int -\frac{1}{{\left(x^{2} + 1\right)}^{\frac{1}{3}} {\left(x^{2} - 3\right)}}\,{d x}"," ",0,"integrate(-1/((x^2 + 1)^(1/3)*(x^2 - 3)), x)","F",0
148,0,0,0,0.000000," ","integrate((3-x)/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int -\frac{x - 3}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-(x - 3)/((x^2 + 3)*(-x^2 + 1)^(1/3)), x)","F",0
149,0,0,0,0.000000," ","integrate((3+x)/(-x^2+1)^(1/3)/(x^2+3),x, algorithm=""giac"")","\int \frac{x + 3}{{\left(x^{2} + 3\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate((x + 3)/((x^2 + 3)*(-x^2 + 1)^(1/3)), 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, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{1}{3}} {\left(d x^{2} + \frac{9 \, a d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(1/3)*(d*x^2 + 9*a*d/b)), x)","F",0
151,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/3)/(-9*a*d/b+d*x^2),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{2} + a\right)}^{\frac{1}{3}} {\left(d x^{2} - \frac{9 \, a d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((-b*x^2 + a)^(1/3)*(d*x^2 - 9*a*d/b)), x)","F",0
152,0,0,0,0.000000," ","integrate(1/(b*x^2-a)^(1/3)/(-9*a*d/b+d*x^2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{\frac{1}{3}} {\left(d x^{2} - \frac{9 \, a d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^(1/3)*(d*x^2 - 9*a*d/b)), x)","F",0
153,0,0,0,0.000000," ","integrate(1/(-b*x^2-a)^(1/3)/(9*a*d/b+d*x^2),x, algorithm=""giac"")","\int \frac{1}{{\left(-b x^{2} - a\right)}^{\frac{1}{3}} {\left(d x^{2} + \frac{9 \, a d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((-b*x^2 - a)^(1/3)*(d*x^2 + 9*a*d/b)), x)","F",0
154,0,0,0,0.000000," ","integrate(1/(b*x^2+2)^(1/3)/(18*d/b+d*x^2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 2\right)}^{\frac{1}{3}} {\left(d x^{2} + \frac{18 \, d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 2)^(1/3)*(d*x^2 + 18*d/b)), x)","F",0
155,0,0,0,0.000000," ","integrate(1/(b*x^2-2)^(1/3)/(-18*d/b+d*x^2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - 2\right)}^{\frac{1}{3}} {\left(d x^{2} - \frac{18 \, d}{b}\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 - 2)^(1/3)*(d*x^2 - 18*d/b)), x)","F",0
156,0,0,0,0.000000," ","integrate(1/(3*x^2+2)^(1/3)/(d*x^2+6*d),x, algorithm=""giac"")","\int \frac{1}{{\left(d x^{2} + 6 \, d\right)} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((d*x^2 + 6*d)*(3*x^2 + 2)^(1/3)), x)","F",0
157,0,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(1/3)/(d*x^2-6*d),x, algorithm=""giac"")","\int \frac{1}{{\left(d x^{2} - 6 \, d\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((d*x^2 - 6*d)*(-3*x^2 + 2)^(1/3)), x)","F",0
158,0,0,0,0.000000," ","integrate(1/(3*x^2-2)^(1/3)/(d*x^2-6*d),x, algorithm=""giac"")","\int \frac{1}{{\left(d x^{2} - 6 \, d\right)} {\left(3 \, x^{2} - 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((d*x^2 - 6*d)*(3*x^2 - 2)^(1/3)), x)","F",0
159,0,0,0,0.000000," ","integrate(1/(-3*x^2-2)^(1/3)/(d*x^2+6*d),x, algorithm=""giac"")","\int \frac{1}{{\left(d x^{2} + 6 \, d\right)} {\left(-3 \, x^{2} - 2\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((d*x^2 + 6*d)*(-3*x^2 - 2)^(1/3)), x)","F",0
160,0,0,0,0.000000," ","integrate(1/(x^2+1)^(1/3)/(x^2+9),x, algorithm=""giac"")","\int \frac{1}{{\left(x^{2} + 9\right)} {\left(x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((x^2 + 9)*(x^2 + 1)^(1/3)), x)","F",0
161,0,0,0,0.000000," ","integrate(1/(b*x^2+1)^(1/3)/(b*x^2+9),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 9\right)} {\left(b x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 9)*(b*x^2 + 1)^(1/3)), x)","F",0
162,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/3)/(-x^2+9),x, algorithm=""giac"")","\int -\frac{1}{{\left(x^{2} - 9\right)} {\left(-x^{2} + 1\right)}^{\frac{1}{3}}}\,{d x}"," ",0,"integrate(-1/((x^2 - 9)*(-x^2 + 1)^(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, algorithm=""giac"")","\int \frac{\sqrt{c^{2} x^{2} - 1}}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(c^2*x^2 - 1)/(-c^2*d*x^2 + d)^(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, algorithm=""giac"")","\int \frac{1}{\sqrt{-c^{2} d x^{2} + d} {\left(c^{2} x^{2} - 1\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(-c^2*d*x^2 + d)*(c^2*x^2 - 1)^(3/2)), 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, algorithm=""giac"")","\int \frac{1}{{\left(-c^{2} d x^{2} + d\right)}^{\frac{3}{2}} \sqrt{c^{2} x^{2} - 1}}\,{d x}"," ",0,"integrate(1/((-c^2*d*x^2 + d)^(3/2)*sqrt(c^2*x^2 - 1)), x)","F",0
166,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)*(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)*sqrt(d*x^2 + c), x)","F",0
167,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)*(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{2} + a} \sqrt{d x^{2} + c}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)*sqrt(d*x^2 + c), x)","F",0
168,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} + c}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/sqrt(b*x^2 + a), x)","F",0
169,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/(b*x^2 + a)^(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, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/(b*x^2 + a)^(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, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} + c}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/(b*x^2 + a)^(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, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{\frac{3}{2}} {\left(d x^{2} + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)*(d*x^2 + c)^(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, algorithm=""giac"")","\int \sqrt{b x^{2} + a} {\left(d x^{2} + c\right)}^{\frac{3}{2}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)*(d*x^2 + c)^(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, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/sqrt(b*x^2 + a), x)","F",0
175,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/(b*x^2 + a)^(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, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/(b*x^2 + a)^(5/2), x)","F",0
177,0,0,0,0.000000," ","integrate((d*x^2+c)^(3/2)/(b*x^2+a)^(7/2),x, algorithm=""giac"")","\int \frac{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}{{\left(b x^{2} + a\right)}^{\frac{7}{2}}}\,{d x}"," ",0,"integrate((d*x^2 + c)^(3/2)/(b*x^2 + a)^(7/2), x)","F",0
178,0,0,0,0.000000," ","integrate((b*x^2+2)^(1/2)*(d*x^2+3)^(1/2),x, algorithm=""giac"")","\int \sqrt{b x^{2} + 2} \sqrt{d x^{2} + 3}\,{d x}"," ",0,"integrate(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, algorithm=""giac"")","\int \sqrt{4 \, x^{2} + 2} \sqrt{-6 \, x^{2} + 3}\,{d x}"," ",0,"integrate(sqrt(4*x^2 + 2)*sqrt(-6*x^2 + 3), x)","F",0
180,1,17,0,0.573377," ","integrate((4*x^2+2)^(1/2)*(6*x^2+3)^(1/2),x, algorithm=""giac"")","\frac{1}{3} \, \sqrt{3} \sqrt{2} {\left(2 \, x^{3} + 3 \, x\right)}"," ",0,"1/3*sqrt(3)*sqrt(2)*(2*x^3 + 3*x)","A",0
181,0,0,0,0.000000," ","integrate((b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + 2}}{\sqrt{d x^{2} + 3}}\,{d x}"," ",0,"integrate(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, algorithm=""giac"")","\int \frac{\sqrt{-x^{2} + 4}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 4)/sqrt(d*x^2 + c), x)","F",0
183,0,0,0,0.000000," ","integrate((x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 4}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 4)/sqrt(d*x^2 + c), x)","F",0
184,0,0,0,0.000000," ","integrate((-x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-x^{2} + 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 1)/sqrt(-3*x^2 + 2), x)","F",0
185,0,0,0,0.000000," ","integrate((-x^2+4)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-x^{2} + 4}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 4)/sqrt(-3*x^2 + 2), x)","F",0
186,0,0,0,0.000000," ","integrate((-4*x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-4 \, x^{2} + 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(-4*x^2 + 1)/sqrt(-3*x^2 + 2), x)","F",0
187,0,0,0,0.000000," ","integrate((x^2+1)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1}}{\sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 1)/sqrt(-x^2 + 1), x)","F",0
188,0,0,0,0.000000," ","integrate((x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 1)/sqrt(-3*x^2 + 2), x)","F",0
189,0,0,0,0.000000," ","integrate((x^2+4)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 4}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(x^2 + 4)/sqrt(-3*x^2 + 2), x)","F",0
190,0,0,0,0.000000," ","integrate((4*x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{4 \, x^{2} + 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(4*x^2 + 1)/sqrt(-3*x^2 + 2), x)","F",0
191,0,0,0,0.000000," ","integrate((-x^2+1)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-x^{2} + 1}}{\sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 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, algorithm=""giac"")","\int \frac{\sqrt{-x^{2} + 1}}{\sqrt{3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 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, algorithm=""giac"")","\int \frac{\sqrt{-x^{2} + 4}}{\sqrt{3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 4)/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, algorithm=""giac"")","\int \frac{\sqrt{-4 \, x^{2} + 1}}{\sqrt{3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(-4*x^2 + 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, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 1}}{\sqrt{3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(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, algorithm=""giac"")","\int \frac{\sqrt{x^{2} + 4}}{\sqrt{3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(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, algorithm=""giac"")","\int \frac{\sqrt{4 \, x^{2} + 1}}{\sqrt{3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(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, algorithm=""giac"")","\int \frac{\sqrt{-x^{2} + 1}}{\sqrt{2 \, x^{2} - 1}}\,{d x}"," ",0,"integrate(sqrt(-x^2 + 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, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(7/2)/sqrt(d*x^2 + c), x)","F",0
200,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)/sqrt(d*x^2 + c), x)","F",0
201,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)/sqrt(d*x^2 + c), x)","F",0
202,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
203,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)), x)","F",0
204,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(3/2)*sqrt(d*x^2 + c)), x)","F",0
205,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(5/2)*sqrt(d*x^2 + c)), x)","F",0
206,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{7}{2}} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(7/2)*sqrt(d*x^2 + c)), x)","F",0
207,0,0,0,0.000000," ","integrate((b*x^2+a)^(7/2)/(d*x^2+c)^(3/2),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{7}{2}}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(7/2)/(d*x^2 + c)^(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, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{2}}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/2)/(d*x^2 + c)^(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, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{2}}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/2)/(d*x^2 + c)^(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, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a}}{{\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/(d*x^2 + c)^(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, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{2} + a} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + a)*(d*x^2 + c)^(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, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{3}{2}} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(3/2)*(d*x^2 + c)^(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, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{5}{2}} {\left(d x^{2} + c\right)}^{\frac{3}{2}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(5/2)*(d*x^2 + c)^(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, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{2} + a} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + a)*sqrt(d*x^2 + c)), x)","F",0
215,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b x^{2} + a} \sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(1/(sqrt(-b*x^2 + a)*sqrt(d*x^2 + c)), x)","F",0
216,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{2} + a} \sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + a)*sqrt(-d*x^2 + c)), x)","F",0
217,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-b x^{2} + a} \sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(1/(sqrt(-b*x^2 + a)*sqrt(-d*x^2 + c)), x)","F",0
218,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/2)/(5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{5 \, x^{2} + 2} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(5*x^2 + 2)*sqrt(-x^2 + 1)), x)","F",0
219,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/2)/(4*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{4 \, x^{2} + 2} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(4*x^2 + 2)*sqrt(-x^2 + 1)), x)","F",0
220,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{2} + 2} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(3*x^2 + 2)*sqrt(-x^2 + 1)), x)","F",0
221,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/2)/(2*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{2} + 2} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(2*x^2 + 2)*sqrt(-x^2 + 1)), x)","F",0
222,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/2)/(x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} + 2} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 + 2)*sqrt(-x^2 + 1)), x)","F",0
223,0,0,0,0.000000," ","integrate(1/(-x^2+1)^(1/2)/(-x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{2} + 2} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 + 2)*sqrt(-x^2 + 1)), x)","F",0
224,1,19,0,0.575453," ","integrate(1/(-2*x^2+2)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} \log\left(x + 1\right) - \frac{1}{4} \, \sqrt{2} \log\left(x - 1\right)"," ",0,"1/4*sqrt(2)*log(x + 1) - 1/4*sqrt(2)*log(x - 1)","B",0
225,0,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 + 1)*sqrt(-3*x^2 + 2)), x)","F",0
226,0,0,0,0.000000," ","integrate(1/(-4*x^2+2)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{2} + 1} \sqrt{-4 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 + 1)*sqrt(-4*x^2 + 2)), x)","F",0
227,0,0,0,0.000000," ","integrate(1/(-5*x^2+2)^(1/2)/(-x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{2} + 1} \sqrt{-5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 + 1)*sqrt(-5*x^2 + 2)), x)","F",0
228,0,0,0,0.000000," ","integrate(1/(x^2+1)^(1/2)/(5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{5 \, x^{2} + 2} \sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(5*x^2 + 2)*sqrt(x^2 + 1)), x)","F",0
229,0,0,0,0.000000," ","integrate(1/(x^2+1)^(1/2)/(4*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{4 \, x^{2} + 2} \sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(4*x^2 + 2)*sqrt(x^2 + 1)), x)","F",0
230,0,0,0,0.000000," ","integrate(1/(x^2+1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{2} + 2} \sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(3*x^2 + 2)*sqrt(x^2 + 1)), x)","F",0
231,1,26,0,0.572330," ","integrate(1/(x^2+1)^(1/2)/(2*x^2+2)^(1/2),x, algorithm=""giac"")","\frac{1}{4} \, \sqrt{2} i \log\left(i x - 1\right) - \frac{1}{4} \, \sqrt{2} i \log\left(-i x - 1\right)"," ",0,"1/4*sqrt(2)*i*log(i*x - 1) - 1/4*sqrt(2)*i*log(-i*x - 1)","B",0
232,0,0,0,0.000000," ","integrate(1/(x^2+1)^(1/2)/(x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} + 2} \sqrt{x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 + 2)*sqrt(x^2 + 1)), x)","F",0
233,0,0,0,0.000000," ","integrate(1/(-x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} + 1} \sqrt{-x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 + 1)*sqrt(-x^2 + 2)), x)","F",0
234,0,0,0,0.000000," ","integrate(1/(-2*x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} + 1} \sqrt{-2 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 + 1)*sqrt(-2*x^2 + 2)), x)","F",0
235,0,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} + 1} \sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 + 1)*sqrt(-3*x^2 + 2)), x)","F",0
236,0,0,0,0.000000," ","integrate(1/(-4*x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} + 1} \sqrt{-4 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 + 1)*sqrt(-4*x^2 + 2)), x)","F",0
237,0,0,0,0.000000," ","integrate(1/(-5*x^2+2)^(1/2)/(x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} + 1} \sqrt{-5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 + 1)*sqrt(-5*x^2 + 2)), x)","F",0
238,0,0,0,0.000000," ","integrate(1/(x^2-1)^(1/2)/(5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{5 \, x^{2} + 2} \sqrt{x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(5*x^2 + 2)*sqrt(x^2 - 1)), x)","F",0
239,0,0,0,0.000000," ","integrate(1/(x^2-1)^(1/2)/(4*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{4 \, x^{2} + 2} \sqrt{x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(4*x^2 + 2)*sqrt(x^2 - 1)), x)","F",0
240,0,0,0,0.000000," ","integrate(1/(x^2-1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{2} + 2} \sqrt{x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(3*x^2 + 2)*sqrt(x^2 - 1)), x)","F",0
241,0,0,0,0.000000," ","integrate(1/(x^2-1)^(1/2)/(2*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{2} + 2} \sqrt{x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(2*x^2 + 2)*sqrt(x^2 - 1)), x)","F",0
242,0,0,0,0.000000," ","integrate(1/(x^2-1)^(1/2)/(x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} + 2} \sqrt{x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 + 2)*sqrt(x^2 - 1)), x)","F",0
243,0,0,0,0.000000," ","integrate(1/(-x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} - 1} \sqrt{-x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 - 1)*sqrt(-x^2 + 2)), x)","F",0
244,0,0,0,0.000000," ","integrate(1/(-2*x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} - 1} \sqrt{-2 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 - 1)*sqrt(-2*x^2 + 2)), x)","F",0
245,0,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} - 1} \sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 - 1)*sqrt(-3*x^2 + 2)), x)","F",0
246,0,0,0,0.000000," ","integrate(1/(-4*x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} - 1} \sqrt{-4 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 - 1)*sqrt(-4*x^2 + 2)), x)","F",0
247,0,0,0,0.000000," ","integrate(1/(-5*x^2+2)^(1/2)/(x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} - 1} \sqrt{-5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 - 1)*sqrt(-5*x^2 + 2)), x)","F",0
248,0,0,0,0.000000," ","integrate(1/(-x^2-1)^(1/2)/(5*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{5 \, x^{2} + 2} \sqrt{-x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(5*x^2 + 2)*sqrt(-x^2 - 1)), x)","F",0
249,0,0,0,0.000000," ","integrate(1/(-x^2-1)^(1/2)/(4*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{4 \, x^{2} + 2} \sqrt{-x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(4*x^2 + 2)*sqrt(-x^2 - 1)), x)","F",0
250,0,0,0,0.000000," ","integrate(1/(-x^2-1)^(1/2)/(3*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{3 \, x^{2} + 2} \sqrt{-x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(3*x^2 + 2)*sqrt(-x^2 - 1)), x)","F",0
251,0,0,0,0.000000," ","integrate(1/(-x^2-1)^(1/2)/(2*x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{2} + 2} \sqrt{-x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(2*x^2 + 2)*sqrt(-x^2 - 1)), x)","F",0
252,0,0,0,0.000000," ","integrate(1/(-x^2-1)^(1/2)/(x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} + 2} \sqrt{-x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 + 2)*sqrt(-x^2 - 1)), x)","F",0
253,0,0,0,0.000000," ","integrate(1/(-x^2-1)^(1/2)/(-x^2+2)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{2} + 2} \sqrt{-x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 + 2)*sqrt(-x^2 - 1)), x)","F",0
254,0,0,0,0.000000," ","integrate(1/(-2*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{2} - 1} \sqrt{-2 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 - 1)*sqrt(-2*x^2 + 2)), x)","F",0
255,0,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{2} - 1} \sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 - 1)*sqrt(-3*x^2 + 2)), x)","F",0
256,0,0,0,0.000000," ","integrate(1/(-4*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{2} - 1} \sqrt{-4 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 - 1)*sqrt(-4*x^2 + 2)), x)","F",0
257,0,0,0,0.000000," ","integrate(1/(-5*x^2+2)^(1/2)/(-x^2-1)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{-x^{2} - 1} \sqrt{-5 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(1/(sqrt(-x^2 - 1)*sqrt(-5*x^2 + 2)), x)","F",0
258,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/sqrt(-d*x^2 + c), x)","F",0
259,0,0,0,0.000000," ","integrate((-b*x^2-a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{2} - a}}{\sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 - a)/sqrt(-d*x^2 + c), x)","F",0
260,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/sqrt(d*x^2 - c), x)","F",0
261,0,0,0,0.000000," ","integrate((-b*x^2-a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{2} - a}}{\sqrt{d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 - a)/sqrt(d*x^2 - c), x)","F",0
262,0,0,0,0.000000," ","integrate((-b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{2} + a}}{\sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 + a)/sqrt(-d*x^2 + c), x)","F",0
263,0,0,0,0.000000," ","integrate((b*x^2-a)^(1/2)/(-d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} - a}}{\sqrt{-d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 - a)/sqrt(-d*x^2 + c), x)","F",0
264,0,0,0,0.000000," ","integrate((-b*x^2+a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{2} + a}}{\sqrt{d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 + a)/sqrt(d*x^2 - c), x)","F",0
265,0,0,0,0.000000," ","integrate((b*x^2-a)^(1/2)/(d*x^2-c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} - a}}{\sqrt{d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 - a)/sqrt(d*x^2 - c), x)","F",0
266,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
267,0,0,0,0.000000," ","integrate((-b*x^2-a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{2} - a}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 - a)/sqrt(d*x^2 + c), x)","F",0
268,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + a}}{\sqrt{-d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 + a)/sqrt(-d*x^2 - c), x)","F",0
269,0,0,0,0.000000," ","integrate((-b*x^2-a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{2} - a}}{\sqrt{-d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 - a)/sqrt(-d*x^2 - c), x)","F",0
270,0,0,0,0.000000," ","integrate((-b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{2} + a}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 + a)/sqrt(d*x^2 + c), x)","F",0
271,0,0,0,0.000000," ","integrate((b*x^2-a)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} - a}}{\sqrt{d x^{2} + c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 - a)/sqrt(d*x^2 + c), x)","F",0
272,0,0,0,0.000000," ","integrate((-b*x^2+a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-b x^{2} + a}}{\sqrt{-d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(-b*x^2 + a)/sqrt(-d*x^2 - c), x)","F",0
273,0,0,0,0.000000," ","integrate((b*x^2-a)^(1/2)/(-d*x^2-c)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} - a}}{\sqrt{-d x^{2} - c}}\,{d x}"," ",0,"integrate(sqrt(b*x^2 - a)/sqrt(-d*x^2 - c), x)","F",0
274,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} + c}}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/sqrt(-b*x^2 + a), x)","F",0
275,0,0,0,0.000000," ","integrate((-d*x^2-c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} - c}}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 - c)/sqrt(-b*x^2 + a), x)","F",0
276,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} + c}}{\sqrt{b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/sqrt(b*x^2 - a), x)","F",0
277,0,0,0,0.000000," ","integrate((-d*x^2-c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} - c}}{\sqrt{b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 - c)/sqrt(b*x^2 - a), x)","F",0
278,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} + c}}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)/sqrt(-b*x^2 + a), x)","F",0
279,0,0,0,0.000000," ","integrate((d*x^2-c)^(1/2)/(-b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} - c}}{\sqrt{-b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 - c)/sqrt(-b*x^2 + a), x)","F",0
280,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} + c}}{\sqrt{b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)/sqrt(b*x^2 - a), x)","F",0
281,0,0,0,0.000000," ","integrate((d*x^2-c)^(1/2)/(b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} - c}}{\sqrt{b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 - c)/sqrt(b*x^2 - a), x)","F",0
282,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} + c}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/sqrt(b*x^2 + a), x)","F",0
283,0,0,0,0.000000," ","integrate((-d*x^2-c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} - c}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 - c)/sqrt(b*x^2 + a), x)","F",0
284,0,0,0,0.000000," ","integrate((d*x^2+c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} + c}}{\sqrt{-b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 + c)/sqrt(-b*x^2 - a), x)","F",0
285,0,0,0,0.000000," ","integrate((-d*x^2-c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} - c}}{\sqrt{-b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 - c)/sqrt(-b*x^2 - a), x)","F",0
286,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} + c}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)/sqrt(b*x^2 + a), x)","F",0
287,0,0,0,0.000000," ","integrate((d*x^2-c)^(1/2)/(b*x^2+a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} - c}}{\sqrt{b x^{2} + a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 - c)/sqrt(b*x^2 + a), x)","F",0
288,0,0,0,0.000000," ","integrate((-d*x^2+c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{-d x^{2} + c}}{\sqrt{-b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(-d*x^2 + c)/sqrt(-b*x^2 - a), x)","F",0
289,0,0,0,0.000000," ","integrate((d*x^2-c)^(1/2)/(-b*x^2-a)^(1/2),x, algorithm=""giac"")","\int \frac{\sqrt{d x^{2} - c}}{\sqrt{-b x^{2} - a}}\,{d x}"," ",0,"integrate(sqrt(d*x^2 - c)/sqrt(-b*x^2 - a), x)","F",0
290,0,0,0,0.000000," ","integrate(1/(b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{b x^{2} + 2} \sqrt{d x^{2} + 3}}\,{d x}"," ",0,"integrate(1/(sqrt(b*x^2 + 2)*sqrt(d*x^2 + 3)), x)","F",0
291,0,0,0,0.000000," ","integrate(1/(-x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{d x^{2} + c} \sqrt{-x^{2} + 4}}\,{d x}"," ",0,"integrate(1/(sqrt(d*x^2 + c)*sqrt(-x^2 + 4)), x)","F",0
292,0,0,0,0.000000," ","integrate(1/(x^2+4)^(1/2)/(d*x^2+c)^(1/2),x, algorithm=""giac"")","\int \frac{1}{\sqrt{d x^{2} + c} \sqrt{x^{2} + 4}}\,{d x}"," ",0,"integrate(1/(sqrt(d*x^2 + c)*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, algorithm=""giac"")","\int \frac{1}{\sqrt{2 \, x^{2} - 1} \sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate(1/(sqrt(2*x^2 - 1)*sqrt(-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, algorithm=""giac"")","\int \frac{\sqrt{-c^{2} x^{2} + 1}}{\sqrt{c^{2} x^{2} + 1}}\,{d x}"," ",0,"integrate(sqrt(-c^2*x^2 + 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, algorithm=""giac"")","\int \frac{\sqrt{b x^{2} + 2}}{\sqrt{d x^{2} + 3}}\,{d x}"," ",0,"integrate(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, algorithm=""giac"")","\int \frac{\sqrt{3 \, x^{2} - 1}}{\sqrt{-3 \, x^{2} + 2}}\,{d x}"," ",0,"integrate(sqrt(3*x^2 - 1)/sqrt(-3*x^2 + 2), x)","F",0
297,-2,0,0,0.000000," ","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, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [71.707969239,70,22]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [78.6493344628,0,0]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [50.5901726987,49,-6]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [91.0141688026,0,0]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [51.2413111906,0,0]Warning, choosing root of [1,0,%%%{8,[1,1,0]%%%}+%%%{-4,[1,0,0]%%%}+%%%{-2,[0,0,2]%%%},0,%%%{16,[2,2,0]%%%}+%%%{16,[2,1,0]%%%}+%%%{4,[2,0,0]%%%}+%%%{-8,[1,1,2]%%%}+%%%{-4,[1,0,2]%%%}+%%%{1,[0,0,4]%%%}] at parameters values [-64,2,62]Evaluation time: 11.37"Done"","F(-2)",0
298,-2,0,0,0.000000," ","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, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [71.707969239,70,22]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [78.6493344628,0,0]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [50.5901726987,49,-6]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [91.0141688026,0,0]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [51.2413111906,0,0]Warning, choosing root of [1,0,%%%{8,[1,1,0]%%%}+%%%{-4,[1,0,0]%%%}+%%%{-2,[0,0,2]%%%},0,%%%{16,[2,2,0]%%%}+%%%{16,[2,1,0]%%%}+%%%{4,[2,0,0]%%%}+%%%{-8,[1,1,2]%%%}+%%%{-4,[1,0,2]%%%}+%%%{1,[0,0,4]%%%}] at parameters values [-64,2,62]Evaluation time: 19.19"Done"","F(-2)",0
299,-2,0,0,0.000000," ","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, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [71.707969239,70,22]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [78.6493344628,0,0]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [50.5901726987,49,-6]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [91.0141688026,0,0]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [94.3029591851,0,0]Warning, choosing root of [1,0,%%%{8,[1,1,0]%%%}+%%%{-4,[1,0,0]%%%}+%%%{-2,[0,0,2]%%%},0,%%%{16,[2,2,0]%%%}+%%%{16,[2,1,0]%%%}+%%%{4,[2,0,0]%%%}+%%%{-8,[1,1,2]%%%}+%%%{-4,[1,0,2]%%%}+%%%{1,[0,0,4]%%%}] at parameters values [-64,2,62]Evaluation time: 21.17"Done"","F(-2)",0
300,-2,0,0,0.000000," ","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, algorithm=""giac"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >> An error occurred running a Giac command:INPUT:sage2:=int(sage0,x):;OUTPUT:sym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument Valuesym2poly/r2sym(const gen & e,const index_m & i,const vecteur & l) Error: Bad Argument ValueWarning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [71.707969239,70,22]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [78.6493344628,0,0]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [50.5901726987,49,-6]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [91.0141688026,0,0]Warning, choosing root of [1,0,%%%{8,[1,0,1]%%%}+%%%{-2,[1,0,0]%%%}+%%%{-2,[0,2,0]%%%},0,%%%{16,[2,0,2]%%%}+%%%{8,[2,0,1]%%%}+%%%{1,[2,0,0]%%%}+%%%{-8,[1,2,1]%%%}+%%%{-2,[1,2,0]%%%}+%%%{1,[0,4,0]%%%}] at parameters values [94.3029591851,0,0]Warning, choosing root of [1,0,%%%{8,[1,1,0]%%%}+%%%{-4,[1,0,0]%%%}+%%%{-2,[0,0,2]%%%},0,%%%{16,[2,2,0]%%%}+%%%{16,[2,1,0]%%%}+%%%{4,[2,0,0]%%%}+%%%{-8,[1,1,2]%%%}+%%%{-4,[1,0,2]%%%}+%%%{1,[0,0,4]%%%}] at parameters values [-64,2,62]Evaluation time: 28.88"Done"","F(-2)",0
301,0,0,0,0.000000," ","integrate((-2*x^2+1)^m/(-x^2+1)^(1/2),x, algorithm=""giac"")","\int \frac{{\left(-2 \, x^{2} + 1\right)}^{m}}{\sqrt{-x^{2} + 1}}\,{d x}"," ",0,"integrate((-2*x^2 + 1)^m/sqrt(-x^2 + 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, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} - 4 \, \sqrt{3} + 7} \sqrt{x^{2} - 1}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2 - 4*sqrt(3) + 7)*sqrt(x^2 - 1)), 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, algorithm=""giac"")","\int \frac{1}{\sqrt{x^{2} {\left(\sqrt{3} - 3\right)} + 3} \sqrt{2 \, \sqrt{3} x^{2} - 3 \, \sqrt{3} + 3}}\,{d x}"," ",0,"integrate(1/(sqrt(x^2*(sqrt(3) - 3) + 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, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} + 4\right)} {\left(3 \, x^{2} + 2\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((3*x^2 + 4)*(3*x^2 + 2)^(1/4)), x)","F",0
305,0,0,0,0.000000," ","integrate(1/(-3*x^2+2)^(1/4)/(-3*x^2+4),x, algorithm=""giac"")","\int -\frac{1}{{\left(3 \, x^{2} - 4\right)} {\left(-3 \, x^{2} + 2\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-1/((3*x^2 - 4)*(-3*x^2 + 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, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 4\right)} {\left(b x^{2} + 2\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 4)*(b*x^2 + 2)^(1/4)), x)","F",0
307,0,0,0,0.000000," ","integrate(1/(-b*x^2+2)^(1/4)/(-b*x^2+4),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} - 4\right)} {\left(-b x^{2} + 2\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-1/((b*x^2 - 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, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} + 2 \, a\right)} {\left(3 \, x^{2} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((3*x^2 + 2*a)*(3*x^2 + a)^(1/4)), x)","F",0
309,0,0,0,0.000000," ","integrate(1/(-3*x^2+a)^(1/4)/(-3*x^2+2*a),x, algorithm=""giac"")","\int -\frac{1}{{\left(3 \, x^{2} - 2 \, a\right)} {\left(-3 \, x^{2} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-1/((3*x^2 - 2*a)*(-3*x^2 + a)^(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, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + 2 \, a\right)} {\left(b x^{2} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(1/((b*x^2 + 2*a)*(b*x^2 + a)^(1/4)), x)","F",0
311,0,0,0,0.000000," ","integrate(1/(-b*x^2+a)^(1/4)/(-b*x^2+2*a),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} - 2 \, a\right)} {\left(-b x^{2} + a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-1/((b*x^2 - 2*a)*(-b*x^2 + a)^(1/4)), x)","F",0
312,0,0,0,0.000000," ","integrate(1/(3*x^2-2)/(3*x^2-1)^(1/4),x, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} - 1\right)}^{\frac{1}{4}} {\left(3 \, x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(1/((3*x^2 - 1)^(1/4)*(3*x^2 - 2)), x)","F",0
313,0,0,0,0.000000," ","integrate(1/(-3*x^2-2)/(-3*x^2-1)^(1/4),x, algorithm=""giac"")","\int -\frac{1}{{\left(3 \, x^{2} + 2\right)} {\left(-3 \, x^{2} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-1/((3*x^2 + 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, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - 1\right)}^{\frac{1}{4}} {\left(b x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 - 1)^(1/4)*(b*x^2 - 2)), x)","F",0
315,0,0,0,0.000000," ","integrate(1/(-b*x^2-2)/(-b*x^2-1)^(1/4),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} + 2\right)} {\left(-b x^{2} - 1\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-1/((b*x^2 + 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, algorithm=""giac"")","\int \frac{1}{{\left(3 \, x^{2} - a\right)}^{\frac{1}{4}} {\left(3 \, x^{2} - 2 \, a\right)}}\,{d x}"," ",0,"integrate(1/((3*x^2 - a)^(1/4)*(3*x^2 - 2*a)), x)","F",0
317,0,0,0,0.000000," ","integrate(1/(-3*x^2-2*a)/(-3*x^2-a)^(1/4),x, algorithm=""giac"")","\int -\frac{1}{{\left(3 \, x^{2} + 2 \, a\right)} {\left(-3 \, x^{2} - a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-1/((3*x^2 + 2*a)*(-3*x^2 - a)^(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, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} - a\right)}^{\frac{1}{4}} {\left(b x^{2} - 2 \, a\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 - a)^(1/4)*(b*x^2 - 2*a)), x)","F",0
319,0,0,0,0.000000," ","integrate(1/(-b*x^2-2*a)/(-b*x^2-a)^(1/4),x, algorithm=""giac"")","\int -\frac{1}{{\left(b x^{2} + 2 \, a\right)} {\left(-b x^{2} - a\right)}^{\frac{1}{4}}}\,{d x}"," ",0,"integrate(-1/((b*x^2 + 2*a)*(-b*x^2 - a)^(1/4)), x)","F",0
320,0,0,0,0.000000," ","integrate(1/(-x^2+2)/(x^2-1)^(1/4),x, algorithm=""giac"")","\int -\frac{1}{{\left(x^{2} - 1\right)}^{\frac{1}{4}} {\left(x^{2} - 2\right)}}\,{d x}"," ",0,"integrate(-1/((x^2 - 1)^(1/4)*(x^2 - 2)), x)","F",0
321,0,0,0,0.000000," ","integrate((b*x^2+a)^(7/4)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{7}{4}}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(7/4)/(d*x^2 + c), x)","F",0
322,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/4)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{4}}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/4)/(d*x^2 + c), x)","F",0
323,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/4)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/4)/(d*x^2 + c), x)","F",0
324,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/4)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{1}{4}}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^(1/4)/(d*x^2 + c), x)","F",0
325,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/4)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{1}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(1/4)*(d*x^2 + c)), x)","F",0
326,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(3/4)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(3/4)*(d*x^2 + c)), x)","F",0
327,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(5/4)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{5}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(5/4)*(d*x^2 + c)), x)","F",0
328,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(7/4)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{7}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(7/4)*(d*x^2 + c)), x)","F",0
329,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(9/4)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{9}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(9/4)*(d*x^2 + c)), x)","F",0
330,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(11/4)/(d*x^2+c),x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{11}{4}} {\left(d x^{2} + c\right)}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(11/4)*(d*x^2 + c)), x)","F",0
331,0,0,0,0.000000," ","integrate((b*x^2+a)^(7/4)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{7}{4}}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(7/4)/(d*x^2 + c)^2, x)","F",0
332,0,0,0,0.000000," ","integrate((b*x^2+a)^(5/4)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{5}{4}}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(5/4)/(d*x^2 + c)^2, x)","F",0
333,0,0,0,0.000000," ","integrate((b*x^2+a)^(3/4)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{3}{4}}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(3/4)/(d*x^2 + c)^2, x)","F",0
334,0,0,0,0.000000," ","integrate((b*x^2+a)^(1/4)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{\frac{1}{4}}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^(1/4)/(d*x^2 + c)^2, x)","F",0
335,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(1/4)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{1}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(1/4)*(d*x^2 + c)^2), x)","F",0
336,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(3/4)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{3}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(3/4)*(d*x^2 + c)^2), x)","F",0
337,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(5/4)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{5}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(5/4)*(d*x^2 + c)^2), x)","F",0
338,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(7/4)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{7}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(7/4)*(d*x^2 + c)^2), x)","F",0
339,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(9/4)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{9}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(9/4)*(d*x^2 + c)^2), x)","F",0
340,0,0,0,0.000000," ","integrate(1/(b*x^2+a)^(11/4)/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{1}{{\left(b x^{2} + a\right)}^{\frac{11}{4}} {\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate(1/((b*x^2 + a)^(11/4)*(d*x^2 + c)^2), x)","F",0
341,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^q,x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{p} {\left(d x^{2} + c\right)}^{q}\,{d x}"," ",0,"integrate((b*x^2 + a)^p*(d*x^2 + c)^q, x)","F",0
342,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^3,x, algorithm=""giac"")","\int {\left(d x^{2} + c\right)}^{3} {\left(b x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x^2 + c)^3*(b*x^2 + a)^p, x)","F",0
343,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c)^2,x, algorithm=""giac"")","\int {\left(d x^{2} + c\right)}^{2} {\left(b x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x^2 + c)^2*(b*x^2 + a)^p, x)","F",0
344,0,0,0,0.000000," ","integrate((b*x^2+a)^p*(d*x^2+c),x, algorithm=""giac"")","\int {\left(d x^{2} + c\right)} {\left(b x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((d*x^2 + c)*(b*x^2 + a)^p, x)","F",0
345,0,0,0,0.000000," ","integrate((b*x^2+a)^p,x, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{p}\,{d x}"," ",0,"integrate((b*x^2 + a)^p, x)","F",0
346,0,0,0,0.000000," ","integrate((b*x^2+a)^p/(d*x^2+c),x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{p}}{d x^{2} + c}\,{d x}"," ",0,"integrate((b*x^2 + a)^p/(d*x^2 + c), x)","F",0
347,0,0,0,0.000000," ","integrate((b*x^2+a)^p/(d*x^2+c)^2,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{p}}{{\left(d x^{2} + c\right)}^{2}}\,{d x}"," ",0,"integrate((b*x^2 + a)^p/(d*x^2 + c)^2, x)","F",0
348,0,0,0,0.000000," ","integrate((b*x^2+a)^p/(d*x^2+c)^3,x, algorithm=""giac"")","\int \frac{{\left(b x^{2} + a\right)}^{p}}{{\left(d x^{2} + c\right)}^{3}}\,{d x}"," ",0,"integrate((b*x^2 + a)^p/(d*x^2 + c)^3, x)","F",0
349,0,0,0,0.000000," ","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, algorithm=""giac"")","\int {\left(b x^{2} + a\right)}^{-\frac{b c}{2 \, {\left(b c - a d\right)}} - 1} {\left(d x^{2} + c\right)}^{\frac{a d}{2 \, {\left(b c - a d\right)}} - 1}\,{d x}"," ",0,"integrate((b*x^2 + a)^(-1/2*b*c/(b*c - a*d) - 1)*(d*x^2 + c)^(1/2*a*d/(b*c - a*d) - 1), x)","F",0
