1,1,97,84,0.002000," ","int((b*x^2+a)*(d*x^2+c)^4,x)","\frac{b \,d^{4} x^{11}}{11}+\frac{\left(a \,d^{4}+4 b c \,d^{3}\right) x^{9}}{9}+\frac{\left(4 a c \,d^{3}+6 b \,c^{2} d^{2}\right) x^{7}}{7}+a \,c^{4} x +\frac{\left(6 a \,c^{2} d^{2}+4 b \,c^{3} d \right) x^{5}}{5}+\frac{\left(4 a \,c^{3} d +b \,c^{4}\right) x^{3}}{3}"," ",0,"1/11*b*d^4*x^11+1/9*(a*d^4+4*b*c*d^3)*x^9+1/7*(4*a*c*d^3+6*b*c^2*d^2)*x^7+1/5*(6*a*c^2*d^2+4*b*c^3*d)*x^5+1/3*(4*a*c^3*d+b*c^4)*x^3+a*c^4*x","A"
2,1,73,62,0.002000," ","int((b*x^2+a)*(d*x^2+c)^3,x)","\frac{b \,d^{3} x^{9}}{9}+\frac{\left(a \,d^{3}+3 b c \,d^{2}\right) x^{7}}{7}+a \,c^{3} x +\frac{\left(3 a c \,d^{2}+3 b \,c^{2} d \right) x^{5}}{5}+\frac{\left(3 a \,c^{2} d +b \,c^{3}\right) x^{3}}{3}"," ",0,"1/9*b*d^3*x^9+1/7*(a*d^3+3*b*c*d^2)*x^7+1/5*(3*a*c*d^2+3*b*c^2*d)*x^5+1/3*(3*a*c^2*d+b*c^3)*x^3+a*c^3*x","A"
3,1,49,44,0.001000," ","int((b*x^2+a)*(d*x^2+c)^2,x)","\frac{b \,d^{2} x^{7}}{7}+\frac{\left(a \,d^{2}+2 b c d \right) x^{5}}{5}+a \,c^{2} x +\frac{\left(2 a c d +b \,c^{2}\right) x^{3}}{3}"," ",0,"1/7*b*d^2*x^7+1/5*(a*d^2+2*b*c*d)*x^5+1/3*(2*a*c*d+b*c^2)*x^3+a*c^2*x","A"
4,1,25,24,0.001000," ","int((b*x^2+a)*(d*x^2+c),x)","\frac{b d \,x^{5}}{5}+a c x +\frac{\left(a d +b c \right) x^{3}}{3}"," ",0,"a*c*x+1/3*(a*d+b*c)*x^3+1/5*b*d*x^5","A"
5,1,45,32,0.007000," ","int((b*x^2+a)/(d*x^2+c),x)","\frac{a \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}}-\frac{b c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d}+\frac{b x}{d}"," ",0,"b*x/d+1/(c*d)^(1/2)*arctan(x*d/(c*d)^(1/2))*a-1/d/(c*d)^(1/2)*arctan(x*d/(c*d)^(1/2))*b*c","A"
6,1,68,51,0.008000," ","int((b*x^2+a)/(d*x^2+c)^2,x)","\frac{a \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, c}+\frac{b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, d}+\frac{\left(a d -b c \right) x}{2 \left(d \,x^{2}+c \right) c d}"," ",0,"1/2*(a*d-b*c)/c/d*x/(d*x^2+c)+1/2/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a+1/2/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b","A"
7,1,90,78,0.010000," ","int((b*x^2+a)/(d*x^2+c)^3,x)","\frac{3 a \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, c^{2}}+\frac{b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, c d}+\frac{\frac{\left(3 a d +b c \right) x^{3}}{8 c^{2}}+\frac{\left(5 a d -b c \right) x}{8 c d}}{\left(d \,x^{2}+c \right)^{2}}"," ",0,"(1/8*(3*a*d+b*c)/c^2*x^3+1/8*(5*a*d-b*c)/c/d*x)/(d*x^2+c)^2+3/8/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a+1/8/c/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b","A"
8,1,125,112,0.002000," ","int((b*x^2+a)^2*(d*x^2+c)^3,x)","\frac{b^{2} d^{3} x^{11}}{11}+\frac{\left(2 a b \,d^{3}+3 b^{2} c \,d^{2}\right) x^{9}}{9}+\frac{\left(a^{2} d^{3}+6 a b c \,d^{2}+3 b^{2} c^{2} d \right) x^{7}}{7}+a^{2} c^{3} x +\frac{\left(3 a^{2} c \,d^{2}+6 a b \,c^{2} d +b^{2} c^{3}\right) x^{5}}{5}+\frac{\left(3 a^{2} c^{2} d +2 a b \,c^{3}\right) x^{3}}{3}"," ",0,"1/11*b^2*d^3*x^11+1/9*(2*a*b*d^3+3*b^2*c*d^2)*x^9+1/7*(a^2*d^3+6*a*b*c*d^2+3*b^2*c^2*d)*x^7+1/5*(3*a^2*c*d^2+6*a*b*c^2*d+b^2*c^3)*x^5+1/3*(3*a^2*c^2*d+2*a*b*c^3)*x^3+a^2*c^3*x","A"
9,1,87,74,0.000000," ","int((b*x^2+a)^2*(d*x^2+c)^2,x)","\frac{b^{2} d^{2} x^{9}}{9}+\frac{\left(2 a b \,d^{2}+2 b^{2} c d \right) x^{7}}{7}+a^{2} c^{2} x +\frac{\left(a^{2} d^{2}+4 a b c d +b^{2} c^{2}\right) x^{5}}{5}+\frac{\left(2 a^{2} c d +2 a b \,c^{2}\right) x^{3}}{3}"," ",0,"1/9*b^2*d^2*x^9+1/7*(2*a*b*d^2+2*b^2*c*d)*x^7+1/5*(a^2*d^2+4*a*b*c*d+b^2*c^2)*x^5+1/3*(2*a^2*c*d+2*a*b*c^2)*x^3+a^2*c^2*x","A"
10,1,49,44,0.000000," ","int((b*x^2+a)^2*(d*x^2+c),x)","\frac{b^{2} d \,x^{7}}{7}+\frac{\left(2 a b d +b^{2} c \right) x^{5}}{5}+a^{2} c x +\frac{\left(a^{2} d +2 a b c \right) x^{3}}{3}"," ",0,"1/7*b^2*d*x^7+1/5*(2*a*b*d+b^2*c)*x^5+1/3*(a^2*d+2*a*b*c)*x^3+a^2*c*x","A"
11,1,95,53,0.003000," ","int((b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{2} x^{3}}{3 d}+\frac{a^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}}-\frac{2 a b c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d}+\frac{b^{2} c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d^{2}}+\frac{2 a b x}{d}-\frac{b^{2} c x}{d^{2}}"," ",0,"1/3*b^2*x^3/d+2*b/d*a*x-b^2/d^2*x*c+1/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-2/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b*c+1/d^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2*c^2","A"
12,1,129,70,0.009000," ","int((b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{a^{2} x}{2 \left(d \,x^{2}+c \right) c}+\frac{a^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, c}-\frac{a b x}{\left(d \,x^{2}+c \right) d}+\frac{a b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d}+\frac{b^{2} c x}{2 \left(d \,x^{2}+c \right) d^{2}}-\frac{3 b^{2} c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, d^{2}}+\frac{b^{2} x}{d^{2}}"," ",0,"b^2*x/d^2+1/2/c*x/(d*x^2+c)*a^2-1/d*x/(d*x^2+c)*a*b+1/2/d^2*c*x/(d*x^2+c)*b^2+1/2/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+1/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b-3/2/d^2*c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2","A"
13,1,147,102,0.009000," ","int((b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{3 a^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, c^{2}}+\frac{a b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \sqrt{c d}\, c d}+\frac{3 b^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, d^{2}}+\frac{\frac{\left(3 a^{2} d^{2}+2 a b c d -5 b^{2} c^{2}\right) x^{3}}{8 c^{2} d}+\frac{\left(5 a^{2} d^{2}-2 a b c d -3 b^{2} c^{2}\right) x}{8 c \,d^{2}}}{\left(d \,x^{2}+c \right)^{2}}"," ",0,"(1/8*(3*a^2*d^2+2*a*b*c*d-5*b^2*c^2)/c^2/d*x^3+1/8*(5*a^2*d^2-2*a*b*c*d-3*b^2*c^2)/d^2/c*x)/(d*x^2+c)^2+3/8/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2+1/4/c/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b+3/8/d^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2","A"
14,1,177,144,0.003000," ","int((b*x^2+a)^3*(d*x^2+c)^3,x)","\frac{b^{3} d^{3} x^{13}}{13}+\frac{\left(3 a \,b^{2} d^{3}+3 b^{3} c \,d^{2}\right) x^{11}}{11}+\frac{\left(3 a^{2} b \,d^{3}+9 a \,b^{2} c \,d^{2}+3 b^{3} c^{2} d \right) x^{9}}{9}+a^{3} c^{3} x +\frac{\left(a^{3} d^{3}+9 a^{2} b c \,d^{2}+9 a \,b^{2} c^{2} d +b^{3} c^{3}\right) x^{7}}{7}+\frac{\left(3 a^{3} c \,d^{2}+9 a^{2} b \,c^{2} d +3 a \,b^{2} c^{3}\right) x^{5}}{5}+\frac{\left(3 a^{3} c^{2} d +3 a^{2} b \,c^{3}\right) x^{3}}{3}"," ",0,"1/13*b^3*d^3*x^13+1/11*(3*a*b^2*d^3+3*b^3*c*d^2)*x^11+1/9*(3*a^2*b*d^3+9*a*b^2*c*d^2+3*b^3*c^2*d)*x^9+1/7*(a^3*d^3+9*a^2*b*c*d^2+9*a*b^2*c^2*d+b^3*c^3)*x^7+1/5*(3*a^3*c*d^2+9*a^2*b*c^2*d+3*a*b^2*c^3)*x^5+1/3*(3*a^3*c^2*d+3*a^2*b*c^3)*x^3+a^3*c^3*x","A"
15,1,125,112,0.002000," ","int((b*x^2+a)^3*(d*x^2+c)^2,x)","\frac{b^{3} d^{2} x^{11}}{11}+\frac{\left(3 a \,b^{2} d^{2}+2 b^{3} c d \right) x^{9}}{9}+\frac{\left(3 a^{2} b \,d^{2}+6 a \,b^{2} c d +b^{3} c^{2}\right) x^{7}}{7}+a^{3} c^{2} x +\frac{\left(a^{3} d^{2}+6 a^{2} b c d +3 a \,b^{2} c^{2}\right) x^{5}}{5}+\frac{\left(2 a^{3} c d +3 a^{2} b \,c^{2}\right) x^{3}}{3}"," ",0,"1/11*b^3*d^2*x^11+1/9*(3*a*b^2*d^2+2*b^3*c*d)*x^9+1/7*(3*a^2*b*d^2+6*a*b^2*c*d+b^3*c^2)*x^7+1/5*(a^3*d^2+6*a^2*b*c*d+3*a*b^2*c^2)*x^5+1/3*(2*a^3*c*d+3*a^2*b*c^2)*x^3+a^3*c^2*x","A"
16,1,73,62,0.001000," ","int((b*x^2+a)^3*(d*x^2+c),x)","\frac{b^{3} d \,x^{9}}{9}+\frac{\left(3 a \,b^{2} d +b^{3} c \right) x^{7}}{7}+a^{3} c x +\frac{\left(3 a^{2} b d +3 a \,b^{2} c \right) x^{5}}{5}+\frac{\left(a^{3} d +3 a^{2} b c \right) x^{3}}{3}"," ",0,"1/9*b^3*d*x^9+1/7*(3*a*b^2*d+b^3*c)*x^7+1/5*(3*a^2*b*d+3*a*b^2*c)*x^5+1/3*(a^3*d+3*a^2*b*c)*x^3+c*a^3*x","A"
17,1,161,86,0.004000," ","int((b*x^2+a)^3/(d*x^2+c),x)","\frac{b^{3} x^{5}}{5 d}+\frac{a \,b^{2} x^{3}}{d}-\frac{b^{3} c \,x^{3}}{3 d^{2}}+\frac{a^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}}-\frac{3 a^{2} b c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d}+\frac{3 a \,b^{2} c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d^{2}}-\frac{b^{3} c^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\sqrt{c d}\, d^{3}}+\frac{3 a^{2} b x}{d}-\frac{3 a \,b^{2} c x}{d^{2}}+\frac{b^{3} c^{2} x}{d^{3}}"," ",0,"1/5*b^3*x^5/d+b^2/d*x^3*a-1/3*b^3/d^2*x^3*c+3*b/d*a^2*x-3*b^2/d^2*a*c*x+b^3/d^3*c^2*x+1/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^3-3/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2*b*c+3/d^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b^2*c^2-1/d^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^3*c^3","A"
18,1,205,93,0.010000," ","int((b*x^2+a)^3/(d*x^2+c)^2,x)","\frac{b^{3} x^{3}}{3 d^{2}}+\frac{a^{3} x}{2 \left(d \,x^{2}+c \right) c}+\frac{a^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, c}-\frac{3 a^{2} b x}{2 \left(d \,x^{2}+c \right) d}+\frac{3 a^{2} b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, d}+\frac{3 a \,b^{2} c x}{2 \left(d \,x^{2}+c \right) d^{2}}-\frac{9 a \,b^{2} c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, d^{2}}-\frac{b^{3} c^{2} x}{2 \left(d \,x^{2}+c \right) d^{3}}+\frac{5 b^{3} c^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \sqrt{c d}\, d^{3}}+\frac{3 a \,b^{2} x}{d^{2}}-\frac{2 b^{3} c x}{d^{3}}"," ",0,"1/3*b^3*x^3/d^2+3*b^2/d^2*a*x-2*b^3/d^3*x*c+1/2/c*x/(d*x^2+c)*a^3-3/2/d*x/(d*x^2+c)*a^2*b+3/2/d^2*c*x/(d*x^2+c)*a*b^2-1/2/d^3*c^2*x/(d*x^2+c)*b^3+1/2/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^3+3/2/d/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2*b-9/2/d^2*c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b^2+5/2/d^3*c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^3","B"
19,1,266,116,0.011000," ","int((b*x^2+a)^3/(d*x^2+c)^3,x)","\frac{3 a^{3} d \,x^{3}}{8 \left(d \,x^{2}+c \right)^{2} c^{2}}+\frac{3 a^{2} b \,x^{3}}{8 \left(d \,x^{2}+c \right)^{2} c}-\frac{15 a \,b^{2} x^{3}}{8 \left(d \,x^{2}+c \right)^{2} d}+\frac{9 b^{3} c \,x^{3}}{8 \left(d \,x^{2}+c \right)^{2} d^{2}}+\frac{5 a^{3} x}{8 \left(d \,x^{2}+c \right)^{2} c}-\frac{3 a^{2} b x}{8 \left(d \,x^{2}+c \right)^{2} d}-\frac{9 a \,b^{2} c x}{8 \left(d \,x^{2}+c \right)^{2} d^{2}}+\frac{7 b^{3} c^{2} x}{8 \left(d \,x^{2}+c \right)^{2} d^{3}}+\frac{3 a^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, c^{2}}+\frac{3 a^{2} b \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, c d}+\frac{9 a \,b^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, d^{2}}-\frac{15 b^{3} c \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \sqrt{c d}\, d^{3}}+\frac{b^{3} x}{d^{3}}"," ",0,"b^3*x/d^3+3/8*d/(d*x^2+c)^2/c^2*x^3*a^3+3/8/(d*x^2+c)^2/c*x^3*a^2*b-15/8/d/(d*x^2+c)^2*x^3*a*b^2+9/8/d^2/(d*x^2+c)^2*c*x^3*b^3+5/8/(d*x^2+c)^2/c*x*a^3-3/8/d/(d*x^2+c)^2*x*a^2*b-9/8/d^2/(d*x^2+c)^2*c*x*a*b^2+7/8/d^3/(d*x^2+c)^2*c^2*x*b^3+3/8/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^3+3/8/d/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2*b+9/8/d^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b^2-15/8/d^3*c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^3","B"
20,1,246,128,0.006000," ","int((d*x^2+c)^4/(b*x^2+a),x)","\frac{d^{4} x^{7}}{7 b}-\frac{a \,d^{4} x^{5}}{5 b^{2}}+\frac{4 c \,d^{3} x^{5}}{5 b}+\frac{a^{2} d^{4} x^{3}}{3 b^{3}}-\frac{4 a c \,d^{3} x^{3}}{3 b^{2}}+\frac{2 c^{2} d^{2} x^{3}}{b}+\frac{a^{4} d^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{4}}-\frac{4 a^{3} c \,d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{6 a^{2} c^{2} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{4 a \,c^{3} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{c^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}-\frac{a^{3} d^{4} x}{b^{4}}+\frac{4 a^{2} c \,d^{3} x}{b^{3}}-\frac{6 a \,c^{2} d^{2} x}{b^{2}}+\frac{4 c^{3} d x}{b}"," ",0,"1/7*d^4*x^7/b-1/5*d^4/b^2*x^5*a+4/5*d^3/b*x^5*c+1/3*d^4/b^3*x^3*a^2-4/3*d^3/b^2*x^3*a*c+2*d^2/b*x^3*c^2-d^4/b^4*a^3*x+4*d^3/b^3*a^2*c*x-6*d^2/b^2*a*c^2*x+4*d/b*c^3*x+1/b^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^4*d^4-4/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^3*c*d^3+6/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^2*c^2*d^2-4/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*c^3*d+1/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^4","A"
21,1,161,86,0.004000," ","int((d*x^2+c)^3/(b*x^2+a),x)","\frac{d^{3} x^{5}}{5 b}-\frac{a \,d^{3} x^{3}}{3 b^{2}}+\frac{c \,d^{2} x^{3}}{b}-\frac{a^{3} d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{3 a^{2} c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{3 a \,c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}+\frac{a^{2} d^{3} x}{b^{3}}-\frac{3 a c \,d^{2} x}{b^{2}}+\frac{3 c^{2} d x}{b}"," ",0,"1/5/b*d^3*x^5-1/3*d^3/b^2*x^3*a+d^2/b*x^3*c+d^3/b^3*a^2*x-3*d^2/b^2*a*c*x+3*d/b*c^2*x-1/b^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^3*d^3+3/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^2*c*d^2-3/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*c^2*d+1/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3","A"
22,1,95,53,0.004000," ","int((d*x^2+c)^2/(b*x^2+a),x)","\frac{d^{2} x^{3}}{3 b}+\frac{a^{2} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}-\frac{2 a c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}-\frac{a \,d^{2} x}{b^{2}}+\frac{2 c d x}{b}"," ",0,"1/3/b*d^2*x^3-d^2/b^2*a*x+2*d/b*x*c+1/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a^2*d^2-2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*c*d+1/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","A"
23,1,45,31,0.005000," ","int((d*x^2+c)/(b*x^2+a),x)","-\frac{a d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}}+\frac{d x}{b}"," ",0,"1/b*d*x-1/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*a*d+1/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c","A"
24,1,55,54,0.008000," ","int(1/(b*x^2+a)/(d*x^2+c),x)","-\frac{b \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right) \sqrt{a b}}+\frac{d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right) \sqrt{c d}}"," ",0,"d/(a*d-b*c)/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)-b/(a*d-b*c)/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
25,1,144,89,0.011000," ","int(1/(b*x^2+a)/(d*x^2+c)^2,x)","\frac{a \,d^{2} x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right) c}+\frac{a \,d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}\, c}+\frac{b^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{2} \sqrt{a b}}-\frac{b d x}{2 \left(a d -b c \right)^{2} \left(d \,x^{2}+c \right)}-\frac{3 b d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{c d}}"," ",0,"1/2*d^2/(a*d-b*c)^2/c*x/(d*x^2+c)*a-1/2*d/(a*d-b*c)^2*x/(d*x^2+c)*b+1/2*d^2/(a*d-b*c)^2/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a-3/2*d/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b+b^2/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","A"
26,1,310,138,0.013000," ","int(1/(b*x^2+a)/(d*x^2+c)^3,x)","\frac{3 a^{2} d^{4} x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{5 a b \,d^{3} x^{3}}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}+\frac{7 b^{2} d^{2} x^{3}}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{5 a^{2} d^{3} x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2} c}-\frac{7 a b \,d^{2} x}{4 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{9 b^{2} c d x}{8 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)^{2}}+\frac{3 a^{2} d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}\, c^{2}}-\frac{5 a b \,d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{c d}\, c}-\frac{b^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\left(a d -b c \right)^{3} \sqrt{a b}}+\frac{15 b^{2} d \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{c d}}"," ",0,"3/8*d^4/(a*d-b*c)^3/(d*x^2+c)^2/c^2*x^3*a^2-5/4*d^3/(a*d-b*c)^3/(d*x^2+c)^2/c*x^3*a*b+7/8*d^2/(a*d-b*c)^3/(d*x^2+c)^2*x^3*b^2+5/8*d^3/(a*d-b*c)^3/(d*x^2+c)^2/c*x*a^2-7/4*d^2/(a*d-b*c)^3/(d*x^2+c)^2*x*a*b+9/8*d/(a*d-b*c)^3/(d*x^2+c)^2*c*x*b^2+3/8*d^3/(a*d-b*c)^3/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-5/4*d^2/(a*d-b*c)^3/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b+15/8*d/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-b^3/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)","B"
27,1,402,174,0.012000," ","int((d*x^2+c)^5/(b*x^2+a)^2,x)","\frac{d^{5} x^{7}}{7 b^{2}}-\frac{2 a \,d^{5} x^{5}}{5 b^{3}}+\frac{c \,d^{4} x^{5}}{b^{2}}+\frac{a^{2} d^{5} x^{3}}{b^{4}}-\frac{10 a c \,d^{4} x^{3}}{3 b^{3}}+\frac{10 c^{2} d^{3} x^{3}}{3 b^{2}}-\frac{a^{4} d^{5} x}{2 \left(b \,x^{2}+a \right) b^{5}}+\frac{9 a^{4} d^{5} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{5}}+\frac{5 a^{3} c \,d^{4} x}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{35 a^{3} c \,d^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{4}}-\frac{5 a^{2} c^{2} d^{3} x}{\left(b \,x^{2}+a \right) b^{3}}+\frac{25 a^{2} c^{2} d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{5 a \,c^{3} d^{2} x}{\left(b \,x^{2}+a \right) b^{2}}-\frac{15 a \,c^{3} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}+\frac{c^{5} x}{2 \left(b \,x^{2}+a \right) a}+\frac{c^{5} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}-\frac{5 c^{4} d x}{2 \left(b \,x^{2}+a \right) b}+\frac{5 c^{4} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}-\frac{4 a^{3} d^{5} x}{b^{5}}+\frac{15 a^{2} c \,d^{4} x}{b^{4}}-\frac{20 a \,c^{2} d^{3} x}{b^{3}}+\frac{10 c^{3} d^{2} x}{b^{2}}"," ",0,"1/7*d^5*x^7/b^2-2/5*d^5/b^3*x^5*a+d^4/b^2*x^5*c+d^5/b^4*x^3*a^2-10/3*d^4/b^3*x^3*a*c+10/3*d^3/b^2*x^3*c^2-4*d^5/b^5*a^3*x+15*d^4/b^4*a^2*c*x-20*d^3/b^3*a*c^2*x+10*d^2/b^2*c^3*x-1/2/b^5*a^4*x/(b*x^2+a)*d^5+5/2/b^4*a^3*x/(b*x^2+a)*c*d^4-5/b^3*a^2*x/(b*x^2+a)*c^2*d^3+5/b^2*a*x/(b*x^2+a)*c^3*d^2-5/2/b*x/(b*x^2+a)*c^4*d+1/2/a*x/(b*x^2+a)*c^5+9/2/b^5*a^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^5-35/2/b^4*a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^4+25/b^3*a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d^3-15/b^2*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3*d^2+5/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^4*d+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^5","B"
28,1,296,126,0.012000," ","int((d*x^2+c)^4/(b*x^2+a)^2,x)","\frac{d^{4} x^{5}}{5 b^{2}}-\frac{2 a \,d^{4} x^{3}}{3 b^{3}}+\frac{4 c \,d^{3} x^{3}}{3 b^{2}}+\frac{a^{3} d^{4} x}{2 \left(b \,x^{2}+a \right) b^{4}}-\frac{7 a^{3} d^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{4}}-\frac{2 a^{2} c \,d^{3} x}{\left(b \,x^{2}+a \right) b^{3}}+\frac{10 a^{2} c \,d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{3}}+\frac{3 a \,c^{2} d^{2} x}{\left(b \,x^{2}+a \right) b^{2}}-\frac{9 a \,c^{2} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b^{2}}+\frac{c^{4} x}{2 \left(b \,x^{2}+a \right) a}+\frac{c^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}-\frac{2 c^{3} d x}{\left(b \,x^{2}+a \right) b}+\frac{2 c^{3} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{3 a^{2} d^{4} x}{b^{4}}-\frac{8 a c \,d^{3} x}{b^{3}}+\frac{6 c^{2} d^{2} x}{b^{2}}"," ",0,"1/5*d^4*x^5/b^2-2/3*d^4/b^3*x^3*a+4/3*d^3/b^2*x^3*c+3*d^4/b^4*a^2*x-8*d^3/b^3*a*c*x+6*d^2/b^2*c^2*x+1/2/b^4*a^3*x/(b*x^2+a)*d^4-2/b^3*a^2*x/(b*x^2+a)*c*d^3+3/b^2*a*x/(b*x^2+a)*c^2*d^2-2/b*x/(b*x^2+a)*c^3*d+1/2/a*x/(b*x^2+a)*c^4-7/2/b^4*a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^4+10/b^3*a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^3-9/b^2*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d^2+2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3*d+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^4","B"
29,1,205,92,0.010000," ","int((d*x^2+c)^3/(b*x^2+a)^2,x)","\frac{d^{3} x^{3}}{3 b^{2}}-\frac{a^{2} d^{3} x}{2 \left(b \,x^{2}+a \right) b^{3}}+\frac{5 a^{2} d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{3}}+\frac{3 a c \,d^{2} x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{9 a c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}+\frac{c^{3} x}{2 \left(b \,x^{2}+a \right) a}+\frac{c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}-\frac{3 c^{2} d x}{2 \left(b \,x^{2}+a \right) b}+\frac{3 c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}-\frac{2 a \,d^{3} x}{b^{3}}+\frac{3 c \,d^{2} x}{b^{2}}"," ",0,"1/3/b^2*d^3*x^3-2*d^3/b^3*a*x+3/b^2*c*d^2*x-1/2/b^3*a^2*x/(b*x^2+a)*d^3+3/2/b^2*a*x/(b*x^2+a)*c*d^2-3/2/b*x/(b*x^2+a)*c^2*d+1/2/a*x/(b*x^2+a)*c^3+5/2/b^3*a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^3-9/2/b^2*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^2+3/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3","B"
30,1,129,70,0.009000," ","int((d*x^2+c)^2/(b*x^2+a)^2,x)","\frac{a \,d^{2} x}{2 \left(b \,x^{2}+a \right) b^{2}}-\frac{3 a \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{2}}+\frac{c^{2} x}{2 \left(b \,x^{2}+a \right) a}+\frac{c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}-\frac{c d x}{\left(b \,x^{2}+a \right) b}+\frac{c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{\sqrt{a b}\, b}+\frac{d^{2} x}{b^{2}}"," ",0,"1/b^2*d^2*x+1/2/b^2*a*x/(b*x^2+a)*d^2-1/b*x/(b*x^2+a)*c*d+1/2/a*x/(b*x^2+a)*c^2-3/2/b^2*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2+1/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","A"
31,1,68,51,0.009000," ","int((d*x^2+c)/(b*x^2+a)^2,x)","\frac{c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a}+\frac{d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b}-\frac{\left(a d -b c \right) x}{2 \left(b \,x^{2}+a \right) a b}"," ",0,"-1/2*(a*d-b*c)/a/b*x/(b*x^2+a)+1/2/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+1/2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c","A"
32,1,144,88,0.010000," ","int(1/(b*x^2+a)^2/(d*x^2+c),x)","\frac{b^{2} c x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right) a}+\frac{b^{2} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}\, a}-\frac{b d x}{2 \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right)}-\frac{3 b d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{2} \sqrt{a b}}+\frac{d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right)^{2} \sqrt{c d}}"," ",0,"d^2/(a*d-b*c)^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)-1/2*b/(a*d-b*c)^2*x/(b*x^2+a)*d+1/2*b^2/(a*d-b*c)^2/a*x/(b*x^2+a)*c-3/2*b/(a*d-b*c)^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+1/2*b^2/(a*d-b*c)^2/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c","A"
33,1,238,143,0.015000," ","int(1/(b*x^2+a)^2/(d*x^2+c)^2,x)","\frac{a \,d^{3} x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right) c}+\frac{a \,d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}\, c}-\frac{b^{3} c x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right) a}-\frac{b^{3} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}\, a}+\frac{b^{2} d x}{2 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)}+\frac{5 b^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{a b}}-\frac{b \,d^{2} x}{2 \left(a d -b c \right)^{3} \left(d \,x^{2}+c \right)}-\frac{5 b \,d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{3} \sqrt{c d}}"," ",0,"1/2*d^3/(a*d-b*c)^3/c*x/(d*x^2+c)*a-1/2*d^2/(a*d-b*c)^3*x/(d*x^2+c)*b+1/2*d^3/(a*d-b*c)^3/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a-5/2*d^2/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b+1/2*b^2/(a*d-b*c)^3*x/(b*x^2+a)*d-1/2*b^3/(a*d-b*c)^3/a*x/(b*x^2+a)*c+5/2*b^2/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d-1/2*b^3/(a*d-b*c)^3/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c","A"
34,1,403,204,0.017000," ","int(1/(b*x^2+a)^2/(d*x^2+c)^3,x)","\frac{3 a^{2} d^{5} x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{7 a b \,d^{4} x^{3}}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}+\frac{11 b^{2} d^{3} x^{3}}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{5 a^{2} d^{4} x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2} c}-\frac{9 a b \,d^{3} x}{4 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{13 b^{2} c \,d^{2} x}{8 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)^{2}}+\frac{3 a^{2} d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}\, c^{2}}-\frac{7 a b \,d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{c d}\, c}+\frac{b^{4} c x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right) a}+\frac{b^{4} c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}\, a}-\frac{b^{3} d x}{2 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)}-\frac{7 b^{3} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{a b}}+\frac{35 b^{2} d^{2} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{c d}}"," ",0,"3/8*d^5/(a*d-b*c)^4/(d*x^2+c)^2/c^2*x^3*a^2-7/4*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x^3*a*b+11/8*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x^3*b^2+5/8*d^4/(a*d-b*c)^4/(d*x^2+c)^2/c*x*a^2-9/4*d^3/(a*d-b*c)^4/(d*x^2+c)^2*x*a*b+13/8*d^2/(a*d-b*c)^4/(d*x^2+c)^2*c*x*b^2+3/8*d^4/(a*d-b*c)^4/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-7/4*d^3/(a*d-b*c)^4/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b+35/8*d^2/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-1/2*b^3/(a*d-b*c)^4*x/(b*x^2+a)*d+1/2*b^4/(a*d-b*c)^4/a*x/(b*x^2+a)*c-7/2*b^3/(a*d-b*c)^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+1/2*b^4/(a*d-b*c)^4/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c","A"
35,1,484,178,0.015000," ","int((d*x^2+c)^5/(b*x^2+a)^3,x)","\frac{17 a^{3} d^{5} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b^{4}}-\frac{65 a^{2} c \,d^{4} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b^{3}}+\frac{45 a \,c^{2} d^{3} x^{3}}{4 \left(b \,x^{2}+a \right)^{2} b^{2}}+\frac{5 c^{4} d \,x^{3}}{8 \left(b \,x^{2}+a \right)^{2} a}+\frac{3 b \,c^{5} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} a^{2}}-\frac{25 c^{3} d^{2} x^{3}}{4 \left(b \,x^{2}+a \right)^{2} b}+\frac{d^{5} x^{5}}{5 b^{3}}+\frac{15 a^{4} d^{5} x}{8 \left(b \,x^{2}+a \right)^{2} b^{5}}-\frac{55 a^{3} c \,d^{4} x}{8 \left(b \,x^{2}+a \right)^{2} b^{4}}+\frac{35 a^{2} c^{2} d^{3} x}{4 \left(b \,x^{2}+a \right)^{2} b^{3}}-\frac{15 a \,c^{3} d^{2} x}{4 \left(b \,x^{2}+a \right)^{2} b^{2}}-\frac{a \,d^{5} x^{3}}{b^{4}}+\frac{5 c^{5} x}{8 \left(b \,x^{2}+a \right)^{2} a}-\frac{5 c^{4} d x}{8 \left(b \,x^{2}+a \right)^{2} b}+\frac{5 c \,d^{4} x^{3}}{3 b^{3}}-\frac{63 a^{3} d^{5} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{5}}+\frac{175 a^{2} c \,d^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{4}}-\frac{75 a \,c^{2} d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{4 \sqrt{a b}\, b^{3}}+\frac{5 c^{4} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a b}+\frac{3 c^{5} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{2}}+\frac{15 c^{3} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{4 \sqrt{a b}\, b^{2}}+\frac{6 a^{2} d^{5} x}{b^{5}}-\frac{15 a c \,d^{4} x}{b^{4}}+\frac{10 c^{2} d^{3} x}{b^{3}}"," ",0,"1/5*d^5*x^5/b^3-d^5/b^4*x^3*a+5/3*d^4/b^3*x^3*c+6*d^5/b^5*a^2*x-15*d^4/b^4*a*c*x+10*d^3/b^3*c^2*x+17/8/b^4/(b*x^2+a)^2*a^3*x^3*d^5-65/8/b^3/(b*x^2+a)^2*a^2*x^3*c*d^4+45/4/b^2/(b*x^2+a)^2*a*x^3*c^2*d^3-25/4/b/(b*x^2+a)^2*x^3*c^3*d^2+5/8/(b*x^2+a)^2/a*x^3*c^4*d+3/8*b/(b*x^2+a)^2/a^2*x^3*c^5+15/8/b^5/(b*x^2+a)^2*x*a^4*d^5-55/8/b^4/(b*x^2+a)^2*x*a^3*c*d^4+35/4/b^3/(b*x^2+a)^2*x*a^2*c^2*d^3-15/4/b^2/(b*x^2+a)^2*x*a*c^3*d^2-5/8/b/(b*x^2+a)^2*x*c^4*d+5/8/(b*x^2+a)^2*x/a*c^5-63/8/b^5*a^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^5+175/8/b^4*a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^4-75/4/b^3*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d^3+15/4/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3*d^2+5/8/b/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^4*d+3/8/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^5","B"
36,1,367,144,0.013000," ","int((d*x^2+c)^4/(b*x^2+a)^3,x)","-\frac{13 a^{2} d^{4} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b^{3}}+\frac{9 a c \,d^{3} x^{3}}{2 \left(b \,x^{2}+a \right)^{2} b^{2}}+\frac{c^{3} d \,x^{3}}{2 \left(b \,x^{2}+a \right)^{2} a}+\frac{3 b \,c^{4} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} a^{2}}-\frac{15 c^{2} d^{2} x^{3}}{4 \left(b \,x^{2}+a \right)^{2} b}-\frac{11 a^{3} d^{4} x}{8 \left(b \,x^{2}+a \right)^{2} b^{4}}+\frac{7 a^{2} c \,d^{3} x}{2 \left(b \,x^{2}+a \right)^{2} b^{3}}-\frac{9 a \,c^{2} d^{2} x}{4 \left(b \,x^{2}+a \right)^{2} b^{2}}+\frac{5 c^{4} x}{8 \left(b \,x^{2}+a \right)^{2} a}-\frac{c^{3} d x}{2 \left(b \,x^{2}+a \right)^{2} b}+\frac{d^{4} x^{3}}{3 b^{3}}+\frac{35 a^{2} d^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{4}}-\frac{15 a c \,d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, b^{3}}+\frac{c^{3} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{2 \sqrt{a b}\, a b}+\frac{3 c^{4} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{2}}+\frac{9 c^{2} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{4 \sqrt{a b}\, b^{2}}-\frac{3 a \,d^{4} x}{b^{4}}+\frac{4 c \,d^{3} x}{b^{3}}"," ",0,"1/3*d^4*x^3/b^3-3*d^4/b^4*a*x+4*d^3/b^3*x*c-13/8/b^3/(b*x^2+a)^2*a^2*x^3*d^4+9/2/b^2/(b*x^2+a)^2*a*x^3*c*d^3-15/4/b/(b*x^2+a)^2*x^3*c^2*d^2+1/2/(b*x^2+a)^2/a*x^3*c^3*d+3/8*b/(b*x^2+a)^2/a^2*x^3*c^4-11/8/b^4/(b*x^2+a)^2*x*a^3*d^4+7/2/b^3/(b*x^2+a)^2*x*a^2*c*d^3-9/4/b^2/(b*x^2+a)^2*x*a*c^2*d^2-1/2/b/(b*x^2+a)^2*x*c^3*d+5/8/(b*x^2+a)^2*x/a*c^4+35/8/b^4*a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^4-15/2/b^3*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^3+9/4/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d^2+1/2/b/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3*d+3/8/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^4","B"
37,1,266,116,0.011000," ","int((d*x^2+c)^3/(b*x^2+a)^3,x)","\frac{9 a \,d^{3} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b^{2}}+\frac{3 c^{2} d \,x^{3}}{8 \left(b \,x^{2}+a \right)^{2} a}+\frac{3 b \,c^{3} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} a^{2}}-\frac{15 c \,d^{2} x^{3}}{8 \left(b \,x^{2}+a \right)^{2} b}+\frac{7 a^{2} d^{3} x}{8 \left(b \,x^{2}+a \right)^{2} b^{3}}-\frac{9 a c \,d^{2} x}{8 \left(b \,x^{2}+a \right)^{2} b^{2}}+\frac{5 c^{3} x}{8 \left(b \,x^{2}+a \right)^{2} a}-\frac{3 c^{2} d x}{8 \left(b \,x^{2}+a \right)^{2} b}-\frac{15 a \,d^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{3}}+\frac{3 c^{2} d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a b}+\frac{3 c^{3} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{2}}+\frac{9 c \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{2}}+\frac{d^{3} x}{b^{3}}"," ",0,"1/b^3*d^3*x+9/8/b^2/(b*x^2+a)^2*a*x^3*d^3-15/8/b/(b*x^2+a)^2*x^3*c*d^2+3/8/(b*x^2+a)^2/a*x^3*c^2*d+3/8*b/(b*x^2+a)^2/a^2*x^3*c^3+7/8/b^3/(b*x^2+a)^2*x*a^2*d^3-9/8/b^2/(b*x^2+a)^2*x*a*c*d^2-3/8/b/(b*x^2+a)^2*x*c^2*d+5/8/(b*x^2+a)^2*x/a*c^3-15/8/b^3*a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^3+9/8/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d^2+3/8/b/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2*d+3/8/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^3","B"
38,1,147,102,0.010000," ","int((d*x^2+c)^2/(b*x^2+a)^3,x)","\frac{c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{4 \sqrt{a b}\, a b}+\frac{3 c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{2}}+\frac{3 d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, b^{2}}+\frac{-\frac{\left(5 a^{2} d^{2}-2 a b c d -3 b^{2} c^{2}\right) x^{3}}{8 a^{2} b}-\frac{\left(3 a^{2} d^{2}+2 a b c d -5 b^{2} c^{2}\right) x}{8 a \,b^{2}}}{\left(b \,x^{2}+a \right)^{2}}"," ",0,"(-1/8*(5*a^2*d^2-2*a*b*c*d-3*b^2*c^2)/a^2/b*x^3-1/8*(3*a^2*d^2+2*a*b*c*d-5*b^2*c^2)/a/b^2*x)/(b*x^2+a)^2+3/8/b^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2+1/4/a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d+3/8/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","A"
39,1,89,78,0.009000," ","int((d*x^2+c)/(b*x^2+a)^3,x)","\frac{d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a b}+\frac{3 c \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \sqrt{a b}\, a^{2}}+\frac{\frac{\left(a d +3 b c \right) x^{3}}{8 a^{2}}-\frac{\left(a d -5 b c \right) x}{8 a b}}{\left(b \,x^{2}+a \right)^{2}}"," ",0,"(1/8*(a*d+3*b*c)/a^2*x^3-1/8*(a*d-5*b*c)/a/b*x)/(b*x^2+a)^2+1/8/a/b/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d+3/8/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c","A"
40,1,309,139,0.012000," ","int(1/(b*x^2+a)^3/(d*x^2+c),x)","\frac{5 b^{3} c d \,x^{3}}{4 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)^{2} a}-\frac{3 b^{4} c^{2} x^{3}}{8 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)^{2} a^{2}}-\frac{7 b^{2} d^{2} x^{3}}{8 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)^{2}}-\frac{9 a b \,d^{2} x}{8 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)^{2}}-\frac{5 b^{3} c^{2} x}{8 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)^{2} a}+\frac{7 b^{2} c d x}{4 \left(a d -b c \right)^{3} \left(b \,x^{2}+a \right)^{2}}+\frac{5 b^{2} c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{a b}\, a}-\frac{3 b^{3} c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{a b}\, a^{2}}-\frac{15 b \,d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \left(a d -b c \right)^{3} \sqrt{a b}}+\frac{d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{\left(a d -b c \right)^{3} \sqrt{c d}}"," ",0,"d^3/(a*d-b*c)^3/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)-7/8*b^2/(a*d-b*c)^3/(b*x^2+a)^2*x^3*d^2+5/4*b^3/(a*d-b*c)^3/(b*x^2+a)^2/a*x^3*c*d-3/8*b^4/(a*d-b*c)^3/(b*x^2+a)^2/a^2*x^3*c^2-9/8*b/(a*d-b*c)^3/(b*x^2+a)^2*x*a*d^2+7/4*b^2/(a*d-b*c)^3/(b*x^2+a)^2*x*c*d-5/8*b^3/(a*d-b*c)^3/(b*x^2+a)^2*x/a*c^2-15/8*b/(a*d-b*c)^3/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2+5/4*b^2/(a*d-b*c)^3/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d-3/8*b^3/(a*d-b*c)^3/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","B"
41,1,403,210,0.014000," ","int(1/(b*x^2+a)^3/(d*x^2+c)^2,x)","-\frac{7 b^{4} c d \,x^{3}}{4 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)^{2} a}+\frac{3 b^{5} c^{2} x^{3}}{8 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)^{2} a^{2}}+\frac{11 b^{3} d^{2} x^{3}}{8 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)^{2}}+\frac{13 a \,b^{2} d^{2} x}{8 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)^{2}}+\frac{5 b^{4} c^{2} x}{8 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)^{2} a}-\frac{9 b^{3} c d x}{4 \left(a d -b c \right)^{4} \left(b \,x^{2}+a \right)^{2}}+\frac{a \,d^{4} x}{2 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right) c}+\frac{a \,d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{c d}\, c}-\frac{7 b^{3} c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{4 \left(a d -b c \right)^{4} \sqrt{a b}\, a}+\frac{3 b^{4} c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{a b}\, a^{2}}+\frac{35 b^{2} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \left(a d -b c \right)^{4} \sqrt{a b}}-\frac{b \,d^{3} x}{2 \left(a d -b c \right)^{4} \left(d \,x^{2}+c \right)}-\frac{7 b \,d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{2 \left(a d -b c \right)^{4} \sqrt{c d}}"," ",0,"1/2*d^4/(a*d-b*c)^4/c*x/(d*x^2+c)*a-1/2*d^3/(a*d-b*c)^4*x/(d*x^2+c)*b+1/2*d^4/(a*d-b*c)^4/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a-7/2*d^3/(a*d-b*c)^4/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b+11/8*b^3/(a*d-b*c)^4/(b*x^2+a)^2*x^3*d^2-7/4*b^4/(a*d-b*c)^4/(b*x^2+a)^2/a*x^3*c*d+3/8*b^5/(a*d-b*c)^4/(b*x^2+a)^2/a^2*x^3*c^2+13/8*b^2/(a*d-b*c)^4/(b*x^2+a)^2*x*a*d^2-9/4*b^3/(a*d-b*c)^4/(b*x^2+a)^2*x*c*d+5/8*b^4/(a*d-b*c)^4/(b*x^2+a)^2*x/a*c^2+35/8*b^2/(a*d-b*c)^4/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2-7/4*b^3/(a*d-b*c)^4/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d+3/8*b^4/(a*d-b*c)^4/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","A"
42,1,568,287,0.018000," ","int(1/(b*x^2+a)^3/(d*x^2+c)^3,x)","\frac{3 a^{2} d^{6} x^{3}}{8 \left(a d -b c \right)^{5} \left(d \,x^{2}+c \right)^{2} c^{2}}-\frac{9 a b \,d^{5} x^{3}}{4 \left(a d -b c \right)^{5} \left(d \,x^{2}+c \right)^{2} c}+\frac{9 b^{5} c d \,x^{3}}{4 \left(a d -b c \right)^{5} \left(b \,x^{2}+a \right)^{2} a}-\frac{3 b^{6} c^{2} x^{3}}{8 \left(a d -b c \right)^{5} \left(b \,x^{2}+a \right)^{2} a^{2}}-\frac{15 b^{4} d^{2} x^{3}}{8 \left(a d -b c \right)^{5} \left(b \,x^{2}+a \right)^{2}}+\frac{15 b^{2} d^{4} x^{3}}{8 \left(a d -b c \right)^{5} \left(d \,x^{2}+c \right)^{2}}+\frac{5 a^{2} d^{5} x}{8 \left(a d -b c \right)^{5} \left(d \,x^{2}+c \right)^{2} c}-\frac{17 a \,b^{3} d^{2} x}{8 \left(a d -b c \right)^{5} \left(b \,x^{2}+a \right)^{2}}-\frac{11 a b \,d^{4} x}{4 \left(a d -b c \right)^{5} \left(d \,x^{2}+c \right)^{2}}-\frac{5 b^{5} c^{2} x}{8 \left(a d -b c \right)^{5} \left(b \,x^{2}+a \right)^{2} a}+\frac{11 b^{4} c d x}{4 \left(a d -b c \right)^{5} \left(b \,x^{2}+a \right)^{2}}+\frac{17 b^{2} c \,d^{3} x}{8 \left(a d -b c \right)^{5} \left(d \,x^{2}+c \right)^{2}}+\frac{3 a^{2} d^{5} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{5} \sqrt{c d}\, c^{2}}-\frac{9 a b \,d^{4} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{4 \left(a d -b c \right)^{5} \sqrt{c d}\, c}+\frac{9 b^{4} c d \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{4 \left(a d -b c \right)^{5} \sqrt{a b}\, a}-\frac{3 b^{5} c^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \left(a d -b c \right)^{5} \sqrt{a b}\, a^{2}}-\frac{63 b^{3} d^{2} \arctan \left(\frac{b x}{\sqrt{a b}}\right)}{8 \left(a d -b c \right)^{5} \sqrt{a b}}+\frac{63 b^{2} d^{3} \arctan \left(\frac{d x}{\sqrt{c d}}\right)}{8 \left(a d -b c \right)^{5} \sqrt{c d}}"," ",0,"3/8*d^6/(a*d-b*c)^5/(d*x^2+c)^2/c^2*x^3*a^2-9/4*d^5/(a*d-b*c)^5/(d*x^2+c)^2/c*x^3*a*b+15/8*d^4/(a*d-b*c)^5/(d*x^2+c)^2*x^3*b^2+5/8*d^5/(a*d-b*c)^5/(d*x^2+c)^2/c*x*a^2-11/4*d^4/(a*d-b*c)^5/(d*x^2+c)^2*x*a*b+17/8*d^3/(a*d-b*c)^5/(d*x^2+c)^2*c*x*b^2+3/8*d^5/(a*d-b*c)^5/c^2/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a^2-9/4*d^4/(a*d-b*c)^5/c/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*a*b+63/8*d^3/(a*d-b*c)^5/(c*d)^(1/2)*arctan(1/(c*d)^(1/2)*d*x)*b^2-15/8*b^4/(a*d-b*c)^5/(b*x^2+a)^2*x^3*d^2+9/4*b^5/(a*d-b*c)^5/(b*x^2+a)^2/a*x^3*c*d-3/8*b^6/(a*d-b*c)^5/(b*x^2+a)^2/a^2*x^3*c^2-17/8*b^3/(a*d-b*c)^5/(b*x^2+a)^2*x*a*d^2+11/4*b^4/(a*d-b*c)^5/(b*x^2+a)^2*x*c*d-5/8*b^5/(a*d-b*c)^5/(b*x^2+a)^2*x/a*c^2-63/8*b^3/(a*d-b*c)^5/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*d^2+9/4*b^4/(a*d-b*c)^5/a/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c*d-3/8*b^5/(a*d-b*c)^5/a^2/(a*b)^(1/2)*arctan(1/(a*b)^(1/2)*b*x)*c^2","A"
43,1,23,30,0.007000," ","int((x^2-1)^3/(x^2+1)^4,x)","\frac{-x^{5}-\frac{2}{3} x^{3}-x}{\left(x^{2}+1\right)^{3}}"," ",0,"(-x^5-2/3*x^3-x)/(x^2+1)^3","A"
44,1,33,41,0.007000," ","int((x^2-1)^4/(x^2+1)^5,x)","\frac{3 \arctan \left(x \right)}{8}+\frac{-\frac{5}{8} x^{7}+\frac{3}{8} x^{5}-\frac{3}{8} x^{3}+\frac{5}{8} x}{\left(x^{2}+1\right)^{4}}"," ",0,"(-5/8*x^7+3/8*x^5-3/8*x^3+5/8*x)/(x^2+1)^4+3/8*arctan(x)","A"
45,1,310,207,0.016000," ","int((b*x^2+a)^(1/2)*(d*x^2+c)^3,x)","\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} d^{3} x^{5}}{8 b}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a \,d^{3} x^{3}}{48 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} c \,d^{2} x^{3}}{2 b}-\frac{5 a^{4} d^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{128 b^{\frac{7}{2}}}+\frac{3 a^{3} c \,d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{5}{2}}}-\frac{3 a^{2} c^{2} d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{3}{2}}}+\frac{a \,c^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 \sqrt{b}}-\frac{5 \sqrt{b \,x^{2}+a}\, a^{3} d^{3} x}{128 b^{3}}+\frac{3 \sqrt{b \,x^{2}+a}\, a^{2} c \,d^{2} x}{16 b^{2}}-\frac{3 \sqrt{b \,x^{2}+a}\, a \,c^{2} d x}{8 b}+\frac{\sqrt{b \,x^{2}+a}\, c^{3} x}{2}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2} d^{3} x}{64 b^{3}}-\frac{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a c \,d^{2} x}{8 b^{2}}+\frac{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} c^{2} d x}{4 b}"," ",0,"1/8*d^3*x^5*(b*x^2+a)^(3/2)/b-5/48*d^3*a/b^2*x^3*(b*x^2+a)^(3/2)+5/64*d^3*a^2/b^3*x*(b*x^2+a)^(3/2)-5/128*d^3*a^3/b^3*x*(b*x^2+a)^(1/2)-5/128*d^3*a^4/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*c*d^2*x^3*(b*x^2+a)^(3/2)/b-3/8*c*d^2*a/b^2*x*(b*x^2+a)^(3/2)+3/16*c*d^2*a^2/b^2*x*(b*x^2+a)^(1/2)+3/16*c*d^2*a^3/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+3/4*c^2*d*x*(b*x^2+a)^(3/2)/b-3/8*c^2*d*a/b*x*(b*x^2+a)^(1/2)-3/8*c^2*d*a^2/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*c^3*x*(b*x^2+a)^(1/2)+1/2*c^3*a/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
46,1,190,129,0.010000," ","int((b*x^2+a)^(1/2)*(d*x^2+c)^2,x)","\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} d^{2} x^{3}}{6 b}+\frac{a^{3} d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{5}{2}}}-\frac{a^{2} c d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{4 b^{\frac{3}{2}}}+\frac{a \,c^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 \sqrt{b}}+\frac{\sqrt{b \,x^{2}+a}\, a^{2} d^{2} x}{16 b^{2}}-\frac{\sqrt{b \,x^{2}+a}\, a c d x}{4 b}+\frac{\sqrt{b \,x^{2}+a}\, c^{2} x}{2}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} a \,d^{2} x}{8 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} c d x}{2 b}"," ",0,"1/6*d^2*x^3*(b*x^2+a)^(3/2)/b-1/8*d^2*a/b^2*x*(b*x^2+a)^(3/2)+1/16*d^2*a^2/b^2*x*(b*x^2+a)^(1/2)+1/16*d^2*a^3/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*c*d*x*(b*x^2+a)^(3/2)/b-1/4*c*d*a/b*x*(b*x^2+a)^(1/2)-1/4*c*d*a^2/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*c^2*x*(b*x^2+a)^(1/2)+1/2*c^2*a/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
47,1,96,71,0.005000," ","int((b*x^2+a)^(1/2)*(d*x^2+c),x)","-\frac{a^{2} d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{3}{2}}}+\frac{a c \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 \sqrt{b}}-\frac{\sqrt{b \,x^{2}+a}\, a d x}{8 b}+\frac{\sqrt{b \,x^{2}+a}\, c x}{2}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} d x}{4 b}"," ",0,"1/4*d*x*(b*x^2+a)^(3/2)/b-1/8*d*a/b*x*(b*x^2+a)^(1/2)-1/8*d*a^2/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*c*x*(b*x^2+a)^(1/2)+1/2*c*a/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
48,1,36,34,0.000000," ","int((b*x^2+a)^(1/2),x)","\frac{a \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 \sqrt{b}}+\frac{\sqrt{b \,x^{2}+a}\, x}{2}"," ",0,"1/2*a/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*(b*x^2+a)^(1/2)*x","A"
49,1,932,66,0.045000," ","int((b*x^2+a)^(1/2)/(d*x^2+c),x)","-\frac{a \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}}+\frac{a \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}}+\frac{b c \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, d}-\frac{b c \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, d}+\frac{\sqrt{b}\, \ln \left(\frac{\left(x +\frac{\sqrt{-c d}}{d}\right) b -\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{2 d}+\frac{\sqrt{b}\, \ln \left(\frac{\left(x -\frac{\sqrt{-c d}}{d}\right) b +\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{2 d}+\frac{\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{2 \sqrt{-c d}}-\frac{\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{2 \sqrt{-c d}}"," ",0,"1/2/(-c*d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*b*(-c*d)^(1/2)/d*(x-(-c*d)^(1/2)/d)+(a*d-b*c)/d)^(1/2)+1/2*b^(1/2)/d*ln((b*(-c*d)^(1/2)/d+(x-(-c*d)^(1/2)/d)*b)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*b*(-c*d)^(1/2)/d*(x-(-c*d)^(1/2)/d)+(a*d-b*c)/d)^(1/2))-1/2/(-c*d)^(1/2)/((a*d-b*c)/d)^(1/2)*ln((2*(a*d-b*c)/d+2*b*(-c*d)^(1/2)/d*(x-(-c*d)^(1/2)/d)+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*b*(-c*d)^(1/2)/d*(x-(-c*d)^(1/2)/d)+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a+1/2/(-c*d)^(1/2)/d/((a*d-b*c)/d)^(1/2)*ln((2*(a*d-b*c)/d+2*b*(-c*d)^(1/2)/d*(x-(-c*d)^(1/2)/d)+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*b*(-c*d)^(1/2)/d*(x-(-c*d)^(1/2)/d)+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*b*c-1/2/(-c*d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*b*(-c*d)^(1/2)/d*(x+(-c*d)^(1/2)/d)+(a*d-b*c)/d)^(1/2)+1/2*b^(1/2)/d*ln((-b*(-c*d)^(1/2)/d+(x+(-c*d)^(1/2)/d)*b)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*b*(-c*d)^(1/2)/d*(x+(-c*d)^(1/2)/d)+(a*d-b*c)/d)^(1/2))+1/2/(-c*d)^(1/2)/((a*d-b*c)/d)^(1/2)*ln((2*(a*d-b*c)/d-2*b*(-c*d)^(1/2)/d*(x+(-c*d)^(1/2)/d)+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*b*(-c*d)^(1/2)/d*(x+(-c*d)^(1/2)/d)+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a-1/2/(-c*d)^(1/2)/d/((a*d-b*c)/d)^(1/2)*ln((2*(a*d-b*c)/d-2*b*(-c*d)^(1/2)/d*(x+(-c*d)^(1/2)/d)+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*b*(-c*d)^(1/2)/d*(x+(-c*d)^(1/2)/d)+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*b*c","B"
50,1,2521,66,0.022000," ","int((b*x^2+a)^(1/2)/(d*x^2+c)^2,x)","-\frac{a \sqrt{b}\, \ln \left(\frac{\left(x +\frac{\sqrt{-c d}}{d}\right) b -\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{4 \left(a d -b c \right) c}-\frac{a \sqrt{b}\, \ln \left(\frac{\left(x -\frac{\sqrt{-c d}}{d}\right) b +\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{4 \left(a d -b c \right) c}+\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(x +\frac{\sqrt{-c d}}{d}\right) b -\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{4 \left(a d -b c \right) d}+\frac{b^{\frac{3}{2}} \ln \left(\frac{\left(x -\frac{\sqrt{-c d}}{d}\right) b +\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{4 \left(a d -b c \right) d}+\frac{\sqrt{-c d}\, a b \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{4 \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, c d}-\frac{\sqrt{-c d}\, a b \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{4 \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, c d}-\frac{a \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{4 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, c}+\frac{a \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{4 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, c}-\frac{\sqrt{-c d}\, b^{2} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{4 \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, d^{2}}+\frac{\sqrt{-c d}\, b^{2} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{4 \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, d^{2}}-\frac{\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, b x}{4 \left(a d -b c \right) c}-\frac{\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, b x}{4 \left(a d -b c \right) c}+\frac{b \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{4 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, d}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{4 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, d}+\frac{\sqrt{b}\, \ln \left(\frac{\left(x +\frac{\sqrt{-c d}}{d}\right) b -\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{4 c d}+\frac{\sqrt{b}\, \ln \left(\frac{\left(x -\frac{\sqrt{-c d}}{d}\right) b +\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{4 c d}-\frac{\sqrt{-c d}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, b}{4 \left(a d -b c \right) c d}+\frac{\sqrt{-c d}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, b}{4 \left(a d -b c \right) c d}+\frac{\left(\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-c d}}{d}\right) c}+\frac{\left(\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-c d}}{d}\right) c}+\frac{\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{4 \sqrt{-c d}\, c}-\frac{\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{4 \sqrt{-c d}\, c}"," ",0,"1/4/c/(a*d-b*c)/(x-(-c*d)^(1/2)/d)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-1/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+1/4/d*b^(3/2)/(a*d-b*c)*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))+1/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a-1/4/d^2*(-c*d)^(1/2)*b^2/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-1/4/c*b/(a*d-b*c)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-1/4/c*b^(1/2)/(a*d-b*c)*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*a+1/4/c/(a*d-b*c)/(x+(-c*d)^(1/2)/d)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+1/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+1/4/d*b^(3/2)/(a*d-b*c)*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))-1/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a+1/4/d^2*(-c*d)^(1/2)*b^2/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))-1/4/c*b/(a*d-b*c)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-1/4/c*b^(1/2)/(a*d-b*c)*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*a+1/4/(-c*d)^(1/2)/c*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+1/4/c*b^(1/2)/d*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))-1/4/(-c*d)^(1/2)/c/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a+1/4/(-c*d)^(1/2)/d/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*b-1/4/(-c*d)^(1/2)/c*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+1/4/c*b^(1/2)/d*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))+1/4/(-c*d)^(1/2)/c/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a-1/4/(-c*d)^(1/2)/d/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*b","B"
51,1,5101,129,0.025000," ","int((b*x^2+a)^(1/2)/(d*x^2+c)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
52,1,7922,184,0.029000," ","int((b*x^2+a)^(1/2)/(d*x^2+c)^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
53,1,393,244,0.016000," ","int((b*x^2+a)^(3/2)*(d*x^2+c)^3,x)","\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} d^{3} x^{5}}{10 b}-\frac{3 a^{5} d^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{256 b^{\frac{7}{2}}}+\frac{9 a^{4} c \,d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{128 b^{\frac{5}{2}}}-\frac{3 a^{3} c^{2} d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{3}{2}}}+\frac{3 a^{2} c^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 \sqrt{b}}-\frac{3 \sqrt{b \,x^{2}+a}\, a^{4} d^{3} x}{256 b^{3}}+\frac{9 \sqrt{b \,x^{2}+a}\, a^{3} c \,d^{2} x}{128 b^{2}}-\frac{3 \sqrt{b \,x^{2}+a}\, a^{2} c^{2} d x}{16 b}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} a \,d^{3} x^{3}}{16 b^{2}}+\frac{3 \sqrt{b \,x^{2}+a}\, a \,c^{3} x}{8}+\frac{3 \left(b \,x^{2}+a \right)^{\frac{5}{2}} c \,d^{2} x^{3}}{8 b}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{3} d^{3} x}{128 b^{3}}+\frac{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c \,d^{2} x}{64 b^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} a \,c^{2} d x}{8 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} c^{3} x}{4}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} a^{2} d^{3} x}{32 b^{3}}-\frac{3 \left(b \,x^{2}+a \right)^{\frac{5}{2}} a c \,d^{2} x}{16 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} c^{2} d x}{2 b}"," ",0,"1/10*d^3*x^5*(b*x^2+a)^(5/2)/b-1/16*d^3*a/b^2*x^3*(b*x^2+a)^(5/2)+1/32*d^3*a^2/b^3*x*(b*x^2+a)^(5/2)-1/128*d^3*a^3/b^3*x*(b*x^2+a)^(3/2)-3/256*d^3*a^4/b^3*x*(b*x^2+a)^(1/2)-3/256*d^3*a^5/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+3/8*c*d^2*x^3*(b*x^2+a)^(5/2)/b-3/16*c*d^2*a/b^2*x*(b*x^2+a)^(5/2)+3/64*c*d^2*a^2/b^2*x*(b*x^2+a)^(3/2)+9/128*c*d^2*a^3/b^2*x*(b*x^2+a)^(1/2)+9/128*c*d^2*a^4/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/2*c^2*d*x*(b*x^2+a)^(5/2)/b-1/8*c^2*d*a/b*x*(b*x^2+a)^(3/2)-3/16*c^2*d*a^2/b*x*(b*x^2+a)^(1/2)-3/16*c^2*d*a^3/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/4*c^3*x*(b*x^2+a)^(3/2)+3/8*c^3*a*x*(b*x^2+a)^(1/2)+3/8*c^3*a^2/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
54,1,249,172,0.007000," ","int((b*x^2+a)^(3/2)*(d*x^2+c)^2,x)","\frac{3 a^{4} d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{128 b^{\frac{5}{2}}}-\frac{a^{3} c d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{3}{2}}}+\frac{3 a^{2} c^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 \sqrt{b}}+\frac{3 \sqrt{b \,x^{2}+a}\, a^{3} d^{2} x}{128 b^{2}}-\frac{\sqrt{b \,x^{2}+a}\, a^{2} c d x}{8 b}+\frac{3 \sqrt{b \,x^{2}+a}\, a \,c^{2} x}{8}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} d^{2} x^{3}}{8 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2} d^{2} x}{64 b^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} a c d x}{12 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} c^{2} x}{4}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} a \,d^{2} x}{16 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} c d x}{3 b}"," ",0,"1/8*d^2*x^3*(b*x^2+a)^(5/2)/b-1/16*d^2*a/b^2*x*(b*x^2+a)^(5/2)+1/64*d^2*a^2/b^2*x*(b*x^2+a)^(3/2)+3/128*d^2*a^3/b^2*x*(b*x^2+a)^(1/2)+3/128*d^2*a^4/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/3*c*d*x*(b*x^2+a)^(5/2)/b-1/12*c*d*a/b*x*(b*x^2+a)^(3/2)-1/8*c*d*a^2/b*x*(b*x^2+a)^(1/2)-1/8*c*d*a^3/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/4*c^2*x*(b*x^2+a)^(3/2)+3/8*c^2*a*x*(b*x^2+a)^(1/2)+3/8*c^2*a^2/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
55,1,131,98,0.004000," ","int((b*x^2+a)^(3/2)*(d*x^2+c),x)","-\frac{a^{3} d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{3}{2}}}+\frac{3 a^{2} c \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 \sqrt{b}}-\frac{\sqrt{b \,x^{2}+a}\, a^{2} d x}{16 b}+\frac{3 \sqrt{b \,x^{2}+a}\, a c x}{8}-\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} a d x}{24 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} c x}{4}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} d x}{6 b}"," ",0,"1/6*d*x*(b*x^2+a)^(5/2)/b-1/24*d*a/b*x*(b*x^2+a)^(3/2)-1/16*d*a^2/b*x*(b*x^2+a)^(1/2)-1/16*d*a^3/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/4*c*x*(b*x^2+a)^(3/2)+3/8*c*a*x*(b*x^2+a)^(1/2)+3/8*c*a^2/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
56,1,51,49,0.001000," ","int((b*x^2+a)^(3/2),x)","\frac{3 a^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 \sqrt{b}}+\frac{3 \sqrt{b \,x^{2}+a}\, a x}{8}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} x}{4}"," ",0,"1/4*(b*x^2+a)^(3/2)*x+3/8*(b*x^2+a)^(1/2)*a*x+3/8*a^2/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
57,1,1845,91,0.016000," ","int((b*x^2+a)^(3/2)/(d*x^2+c),x)","-\frac{a^{2} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}}+\frac{a^{2} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}}+\frac{a b c \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{\sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, d}-\frac{a b c \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{\sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, d}-\frac{b^{2} c^{2} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, d^{2}}+\frac{b^{2} c^{2} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, d^{2}}+\frac{3 a \sqrt{b}\, \ln \left(\frac{\left(x +\frac{\sqrt{-c d}}{d}\right) b -\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{4 d}+\frac{3 a \sqrt{b}\, \ln \left(\frac{\left(x -\frac{\sqrt{-c d}}{d}\right) b +\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{4 d}-\frac{b^{\frac{3}{2}} c \ln \left(\frac{\left(x +\frac{\sqrt{-c d}}{d}\right) b -\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{2 d^{2}}-\frac{b^{\frac{3}{2}} c \ln \left(\frac{\left(x -\frac{\sqrt{-c d}}{d}\right) b +\frac{\sqrt{-c d}\, b}{d}}{\sqrt{b}}+\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\right)}{2 d^{2}}+\frac{\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a}{2 \sqrt{-c d}}-\frac{\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a}{2 \sqrt{-c d}}-\frac{\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, b c}{2 \sqrt{-c d}\, d}+\frac{\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, b c}{2 \sqrt{-c d}\, d}+\frac{\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, b x}{4 d}+\frac{\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, b x}{4 d}+\frac{\left(\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}}}{6 \sqrt{-c d}}-\frac{\left(\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}}}{6 \sqrt{-c d}}"," ",0,"1/6/(-c*d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+1/4*b/d*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+3/4/d*b^(1/2)*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*a+1/2/(-c*d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*a-1/2/(-c*d)^(1/2)/d*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*b*c-1/2/d^2*b^(3/2)*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*c-1/2/(-c*d)^(1/2)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a^2+1/(-c*d)^(1/2)/d/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a*b*c-1/2/(-c*d)^(1/2)/d^2/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*b^2*c^2-1/6/(-c*d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+1/4*b/d*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+3/4/d*b^(1/2)*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*a-1/2/(-c*d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*a+1/2/(-c*d)^(1/2)/d*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*b*c-1/2/d^2*b^(3/2)*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*c+1/2/(-c*d)^(1/2)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a^2-1/(-c*d)^(1/2)/d/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a*b*c+1/2/(-c*d)^(1/2)/d^2/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*b^2*c^2","B"
58,1,4621,109,0.021000," ","int((b*x^2+a)^(3/2)/(d*x^2+c)^2,x)","\text{output too large to display}"," ",0,"-3/8/c*b/(a*d-b*c)*a*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+1/2/(-c*d)^(1/2)/d/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a*b-1/4/(-c*d)^(1/2)*c/d^2/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*b^2-1/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-3/8/c*b/(a*d-b*c)*a*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-1/2/(-c*d)^(1/2)/d/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a*b+1/4/(-c*d)^(1/2)*c/d^2/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*b^2+1/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+1/4/c/(a*d-b*c)/(x+(-c*d)^(1/2)/d)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(5/2)-1/4/(-c*d)^(1/2)/c*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*a+1/4/(-c*d)^(1/2)/d*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*b+1/4/(-c*d)^(1/2)/c*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*a-1/4/(-c*d)^(1/2)/d*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*b+1/4/c/(a*d-b*c)/(x-(-c*d)^(1/2)/d)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(5/2)-3/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a^2+3/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a^2+3/8/d*b^2/(a*d-b*c)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+9/8/d*b^(3/2)/(a*d-b*c)*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*a-1/4/d^2*b^(3/2)*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))+1/12/(-c*d)^(1/2)/c*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-1/4/d^2*b^(3/2)*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))-1/12/(-c*d)^(1/2)/c*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-3/4*c/d^2*b^(5/2)/(a*d-b*c)*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))-1/4/c*b/(a*d-b*c)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x-3/8/c*b^(1/2)/(a*d-b*c)*a^2*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))+3/8/d*b^2/(a*d-b*c)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-1/4/c*b/(a*d-b*c)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x-3/8/c*b^(1/2)/(a*d-b*c)*a^2*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))+1/8/c*b/d*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+3/8/c/d*b^(1/2)*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*a+1/4/(-c*d)^(1/2)/c/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a^2+1/8/c*b/d*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+3/8/c/d*b^(1/2)*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*a-1/4/(-c*d)^(1/2)/c/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a^2+9/8/d*b^(3/2)/(a*d-b*c)*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*a-3/4/d^2*(-c*d)^(1/2)*b^2/(a*d-b*c)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+3/4/d^2*(-c*d)^(1/2)*b^2/(a*d-b*c)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-3/4*c/d^2*b^(5/2)/(a*d-b*c)*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))-3/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*a-3/2/d^2*(-c*d)^(1/2)*b^2/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a+3/4*c/d^3*(-c*d)^(1/2)*b^3/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))+3/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*a+3/2/d^2*(-c*d)^(1/2)*b^2/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a-3/4*c/d^3*(-c*d)^(1/2)*b^3/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))","B"
59,1,9059,93,0.025000," ","int((b*x^2+a)^(3/2)/(d*x^2+c)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
60,1,13766,175,0.032000," ","int((b*x^2+a)^(3/2)/(d*x^2+c)^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
61,1,18791,272,0.046000," ","int((b*x^2+a)^(3/2)/(d*x^2+c)^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
62,1,476,317,0.019000," ","int((b*x^2+a)^(5/2)*(d*x^2+c)^3,x)","\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} d^{3} x^{5}}{12 b}-\frac{5 a^{6} d^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{1024 b^{\frac{7}{2}}}+\frac{9 a^{5} c \,d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{256 b^{\frac{5}{2}}}-\frac{15 a^{4} c^{2} d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{128 b^{\frac{3}{2}}}+\frac{5 a^{3} c^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 \sqrt{b}}-\frac{5 \sqrt{b \,x^{2}+a}\, a^{5} d^{3} x}{1024 b^{3}}+\frac{9 \sqrt{b \,x^{2}+a}\, a^{4} c \,d^{2} x}{256 b^{2}}-\frac{15 \sqrt{b \,x^{2}+a}\, a^{3} c^{2} d x}{128 b}+\frac{5 \sqrt{b \,x^{2}+a}\, a^{2} c^{3} x}{16}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{4} d^{3} x}{1536 b^{3}}+\frac{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{3} c \,d^{2} x}{128 b^{2}}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c^{2} d x}{64 b}-\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} a \,d^{3} x^{3}}{24 b^{2}}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a \,c^{3} x}{24}+\frac{3 \left(b \,x^{2}+a \right)^{\frac{7}{2}} c \,d^{2} x^{3}}{10 b}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} a^{3} d^{3} x}{384 b^{3}}+\frac{3 \left(b \,x^{2}+a \right)^{\frac{5}{2}} a^{2} c \,d^{2} x}{160 b^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} a \,c^{2} d x}{16 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} c^{3} x}{6}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} a^{2} d^{3} x}{64 b^{3}}-\frac{9 \left(b \,x^{2}+a \right)^{\frac{7}{2}} a c \,d^{2} x}{80 b^{2}}+\frac{3 \left(b \,x^{2}+a \right)^{\frac{7}{2}} c^{2} d x}{8 b}"," ",0,"1/12*d^3*x^5*(b*x^2+a)^(7/2)/b-1/24*d^3*a/b^2*x^3*(b*x^2+a)^(7/2)+1/64*d^3*a^2/b^3*x*(b*x^2+a)^(7/2)-1/384*d^3*a^3/b^3*x*(b*x^2+a)^(5/2)-5/1536*d^3*a^4/b^3*x*(b*x^2+a)^(3/2)-5/1024*d^3*a^5/b^3*x*(b*x^2+a)^(1/2)-5/1024*d^3*a^6/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+3/10*c*d^2*x^3*(b*x^2+a)^(7/2)/b-9/80*c*d^2*a/b^2*x*(b*x^2+a)^(7/2)+3/160*c*d^2*a^2/b^2*x*(b*x^2+a)^(5/2)+3/128*c*d^2*a^3/b^2*x*(b*x^2+a)^(3/2)+9/256*c*d^2*a^4/b^2*x*(b*x^2+a)^(1/2)+9/256*c*d^2*a^5/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+3/8*c^2*d*x*(b*x^2+a)^(7/2)/b-1/16*c^2*d*a/b*x*(b*x^2+a)^(5/2)-5/64*c^2*d*a^2/b*x*(b*x^2+a)^(3/2)-15/128*c^2*d*a^3/b*x*(b*x^2+a)^(1/2)-15/128*c^2*d*a^4/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/6*c^3*x*(b*x^2+a)^(5/2)+5/24*c^3*a*x*(b*x^2+a)^(3/2)+5/16*c^3*a^2*x*(b*x^2+a)^(1/2)+5/16*c^3*a^3/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
63,1,308,213,0.010000," ","int((b*x^2+a)^(5/2)*(d*x^2+c)^2,x)","\frac{3 a^{5} d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{256 b^{\frac{5}{2}}}-\frac{5 a^{4} c d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{64 b^{\frac{3}{2}}}+\frac{5 a^{3} c^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 \sqrt{b}}+\frac{3 \sqrt{b \,x^{2}+a}\, a^{4} d^{2} x}{256 b^{2}}-\frac{5 \sqrt{b \,x^{2}+a}\, a^{3} c d x}{64 b}+\frac{5 \sqrt{b \,x^{2}+a}\, a^{2} c^{2} x}{16}+\frac{\left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{3} d^{2} x}{128 b^{2}}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c d x}{96 b}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a \,c^{2} x}{24}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} d^{2} x^{3}}{10 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} a^{2} d^{2} x}{160 b^{2}}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} a c d x}{24 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} c^{2} x}{6}-\frac{3 \left(b \,x^{2}+a \right)^{\frac{7}{2}} a \,d^{2} x}{80 b^{2}}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} c d x}{4 b}"," ",0,"1/10*d^2*x^3*(b*x^2+a)^(7/2)/b-3/80*d^2*a/b^2*x*(b*x^2+a)^(7/2)+1/160*d^2*a^2/b^2*x*(b*x^2+a)^(5/2)+1/128*d^2*a^3/b^2*x*(b*x^2+a)^(3/2)+3/256*d^2*a^4/b^2*x*(b*x^2+a)^(1/2)+3/256*d^2*a^5/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/4*c*d*x*(b*x^2+a)^(7/2)/b-1/24*c*d*a/b*x*(b*x^2+a)^(5/2)-5/96*c*d*a^2/b*x*(b*x^2+a)^(3/2)-5/64*c*d*a^3/b*x*(b*x^2+a)^(1/2)-5/64*c*d*a^4/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/6*c^2*x*(b*x^2+a)^(5/2)+5/24*c^2*a*x*(b*x^2+a)^(3/2)+5/16*c^2*a^2*x*(b*x^2+a)^(1/2)+5/16*c^2*a^3/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
64,1,166,125,0.006000," ","int((b*x^2+a)^(5/2)*(d*x^2+c),x)","-\frac{5 a^{4} d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{128 b^{\frac{3}{2}}}+\frac{5 a^{3} c \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 \sqrt{b}}-\frac{5 \sqrt{b \,x^{2}+a}\, a^{3} d x}{128 b}+\frac{5 \sqrt{b \,x^{2}+a}\, a^{2} c x}{16}-\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2} d x}{192 b}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a c x}{24}-\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} a d x}{48 b}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} c x}{6}+\frac{\left(b \,x^{2}+a \right)^{\frac{7}{2}} d x}{8 b}"," ",0,"1/8*d*x*(b*x^2+a)^(7/2)/b-1/48*d*a/b*x*(b*x^2+a)^(5/2)-5/192*d*a^2/b*x*(b*x^2+a)^(3/2)-5/128*d*a^3/b*x*(b*x^2+a)^(1/2)-5/128*d*a^4/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+1/6*c*x*(b*x^2+a)^(5/2)+5/24*c*a*x*(b*x^2+a)^(3/2)+5/16*c*a^2*x*(b*x^2+a)^(1/2)+5/16*c*a^3/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
65,1,66,64,0.003000," ","int((b*x^2+a)^(5/2),x)","\frac{5 a^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 \sqrt{b}}+\frac{5 \sqrt{b \,x^{2}+a}\, a^{2} x}{16}+\frac{5 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a x}{24}+\frac{\left(b \,x^{2}+a \right)^{\frac{5}{2}} x}{6}"," ",0,"1/6*(b*x^2+a)^(5/2)*x+5/24*(b*x^2+a)^(3/2)*a*x+5/16*(b*x^2+a)^(1/2)*a^2*x+5/16*a^3/b^(1/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))","A"
66,1,3053,131,0.019000," ","int((b*x^2+a)^(5/2)/(d*x^2+c),x)","\text{output too large to display}"," ",0,"-1/(-c*d)^(1/2)/d*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*a*b*c+1/2/(-c*d)^(1/2)/d^3/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*b^3*c^3+1/(-c*d)^(1/2)/d*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*a*b*c-1/2/(-c*d)^(1/2)/d^3/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*b^3*c^3+3/2/(-c*d)^(1/2)/d^2/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a*b^2*c^2+3/2/(-c*d)^(1/2)/d/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a^2*b*c-3/2/(-c*d)^(1/2)/d^2/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a*b^2*c^2-3/2/(-c*d)^(1/2)/d/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a^2*b*c+1/8*b/d*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x+1/8*b/d*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x+15/16/d*b^(1/2)*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*a^2+1/2/d^3*b^(5/2)*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*c^2-1/2/(-c*d)^(1/2)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))*a^3+15/16/d*b^(1/2)*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*a^2+1/2/d^3*b^(5/2)*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*c^2+1/2/(-c*d)^(1/2)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))*a^3-1/10/(-c*d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(5/2)+1/10/(-c*d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(5/2)-1/2/(-c*d)^(1/2)/d^2*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*b^2*c^2-1/6/(-c*d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*a-1/2/(-c*d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*a^2+1/6/(-c*d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*a+1/2/(-c*d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*a^2-1/6/(-c*d)^(1/2)/d*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*b*c+7/16*b/d*a*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-1/4/d^2*b^2*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*c-5/4/d^2*b^(3/2)*ln(((x-(-c*d)^(1/2)/d)*b+(-c*d)^(1/2)*b/d)/b^(1/2)+((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*c*a+1/2/(-c*d)^(1/2)/d^2*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*b^2*c^2+7/16*b/d*a*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+1/6/(-c*d)^(1/2)/d*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*b*c-1/4/d^2*b^2*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*c-5/4/d^2*b^(3/2)*ln(((x+(-c*d)^(1/2)/d)*b-(-c*d)^(1/2)*b/d)/b^(1/2)+((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))*c*a","B"
67,1,7345,147,0.023000," ","int((b*x^2+a)^(5/2)/(d*x^2+c)^2,x)","\text{output too large to display}"," ",0,"result too large to display","B"
68,1,14133,168,0.030000," ","int((b*x^2+a)^(5/2)/(d*x^2+c)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
69,1,21220,120,0.040000," ","int((b*x^2+a)^(5/2)/(d*x^2+c)^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
70,1,28625,221,0.053000," ","int((b*x^2+a)^(5/2)/(d*x^2+c)^5,x)","\text{output too large to display}"," ",0,"result too large to display","B"
71,1,33,24,0.023000," ","int((-x^2+1)^(1/2)/(x^2+1),x)","-\arcsin \left(x \right)-\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{-x^{2}+1}\, x}{x^{2}-1}\right)"," ",0,"-arcsin(x)-2^(1/2)*arctan(2^(1/2)*(-x^2+1)^(1/2)/(x^2-1)*x)","A"
72,1,84,21,0.012000," ","int((x^2+1)^(1/2)/(x^2-1),x)","\arcsinh \left(x \right)+\frac{\sqrt{2}\, \arctanh \left(\frac{\left(-2 x +2\right) \sqrt{2}}{4 \sqrt{-2 x +\left(x +1\right)^{2}}}\right)}{2}-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(2 x +2\right) \sqrt{2}}{4 \sqrt{2 x +\left(x -1\right)^{2}}}\right)}{2}-\frac{\sqrt{-2 x +\left(x +1\right)^{2}}}{2}+\frac{\sqrt{2 x +\left(x -1\right)^{2}}}{2}"," ",0,"-1/2*((x+1)^2-2*x)^(1/2)+arcsinh(x)+1/2*2^(1/2)*arctanh(1/4*(2-2*x)*2^(1/2)/((x+1)^2-2*x)^(1/2))+1/2*((x-1)^2+2*x)^(1/2)-1/2*2^(1/2)*arctanh(1/4*(2*x+2)*2^(1/2)/((x-1)^2+2*x)^(1/2))","B"
73,1,187,19,0.043000," ","int((-x^2+1)^(1/2)/(2*x^2-1),x)","-\frac{\sqrt{2}\, \left(-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(\left(x +\frac{\sqrt{2}}{2}\right) \sqrt{2}+1\right) \sqrt{2}}{\sqrt{-4 \left(x +\frac{\sqrt{2}}{2}\right)^{2}+4 \left(x +\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}\right)}{4}+\frac{\sqrt{2}\, \arcsin \left(x \right)}{4}+\frac{\sqrt{-4 \left(x +\frac{\sqrt{2}}{2}\right)^{2}+4 \left(x +\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}{4}\right)}{2}+\frac{\sqrt{2}\, \left(-\frac{\sqrt{2}\, \arctanh \left(\frac{\left(-\left(x -\frac{\sqrt{2}}{2}\right) \sqrt{2}+1\right) \sqrt{2}}{\sqrt{-4 \left(x -\frac{\sqrt{2}}{2}\right)^{2}-4 \left(x -\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}\right)}{4}-\frac{\sqrt{2}\, \arcsin \left(x \right)}{4}+\frac{\sqrt{-4 \left(x -\frac{\sqrt{2}}{2}\right)^{2}-4 \left(x -\frac{\sqrt{2}}{2}\right) \sqrt{2}+2}}{4}\right)}{2}"," ",0,"-1/2*2^(1/2)*(1/4*(-4*(x+1/2*2^(1/2))^2+4*(x+1/2*2^(1/2))*2^(1/2)+2)^(1/2)+1/4*2^(1/2)*arcsin(x)-1/4*2^(1/2)*arctanh(((x+1/2*2^(1/2))*2^(1/2)+1)*2^(1/2)/(-4*(x+1/2*2^(1/2))^2+4*(x+1/2*2^(1/2))*2^(1/2)+2)^(1/2)))+1/2*2^(1/2)*(1/4*(-4*(x-1/2*2^(1/2))^2-4*(x-1/2*2^(1/2))*2^(1/2)+2)^(1/2)-1/4*2^(1/2)*arcsin(x)-1/4*2^(1/2)*arctanh((-(x-1/2*2^(1/2))*2^(1/2)+1)*2^(1/2)/(-4*(x-1/2*2^(1/2))^2-4*(x-1/2*2^(1/2))*2^(1/2)+2)^(1/2)))","B"
74,1,228,149,0.014000," ","int((d*x^2+c)^3/(b*x^2+a)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, d^{3} x^{5}}{6 b}-\frac{5 \sqrt{b \,x^{2}+a}\, a \,d^{3} x^{3}}{24 b^{2}}+\frac{3 \sqrt{b \,x^{2}+a}\, c \,d^{2} x^{3}}{4 b}-\frac{5 a^{3} d^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{7}{2}}}+\frac{9 a^{2} c \,d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{5}{2}}}-\frac{3 a \,c^{2} d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{3}{2}}}+\frac{c^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{\sqrt{b}}+\frac{5 \sqrt{b \,x^{2}+a}\, a^{2} d^{3} x}{16 b^{3}}-\frac{9 \sqrt{b \,x^{2}+a}\, a c \,d^{2} x}{8 b^{2}}+\frac{3 \sqrt{b \,x^{2}+a}\, c^{2} d x}{2 b}"," ",0,"1/6*d^3*x^5/b*(b*x^2+a)^(1/2)-5/24*d^3*a/b^2*x^3*(b*x^2+a)^(1/2)+5/16*d^3*a^2/b^3*x*(b*x^2+a)^(1/2)-5/16*d^3*a^3/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+3/4*c*d^2*x^3/b*(b*x^2+a)^(1/2)-9/8*c*d^2*a/b^2*x*(b*x^2+a)^(1/2)+9/8*c*d^2*a^2/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+3/2*c^2*d*x/b*(b*x^2+a)^(1/2)-3/2*c^2*d*a/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+c^3*ln(b^(1/2)*x+(b*x^2+a)^(1/2))/b^(1/2)","A"
75,1,131,92,0.008000," ","int((d*x^2+c)^2/(b*x^2+a)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, d^{2} x^{3}}{4 b}+\frac{3 a^{2} d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{5}{2}}}-\frac{a c d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{3}{2}}}+\frac{c^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{\sqrt{b}}-\frac{3 \sqrt{b \,x^{2}+a}\, a \,d^{2} x}{8 b^{2}}+\frac{\sqrt{b \,x^{2}+a}\, c d x}{b}"," ",0,"1/4*d^2*x^3/b*(b*x^2+a)^(1/2)-3/8*d^2*a/b^2*x*(b*x^2+a)^(1/2)+3/8*d^2*a^2/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+c*d*x/b*(b*x^2+a)^(1/2)-c*d*a/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+c^2*ln(b^(1/2)*x+(b*x^2+a)^(1/2))/b^(1/2)","A"
76,1,62,46,0.006000," ","int((d*x^2+c)/(b*x^2+a)^(1/2),x)","-\frac{a d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{3}{2}}}+\frac{c \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{\sqrt{b}}+\frac{\sqrt{b \,x^{2}+a}\, d x}{2 b}"," ",0,"1/2*d*x*(b*x^2+a)^(1/2)/b-1/2*d*a/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+c*ln(b^(1/2)*x+(b*x^2+a)^(1/2))/b^(1/2)","A"
77,1,21,19,0.002000," ","int(1/(b*x^2+a)^(1/2),x)","\frac{\ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{\sqrt{b}}"," ",0,"ln(b^(1/2)*x+(b*x^2+a)^(1/2))/b^(1/2)","A"
78,1,300,39,0.015000," ","int(1/(b*x^2+a)^(1/2)/(d*x^2+c),x)","-\frac{\ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}}"," ",0,"-1/2/(-c*d)^(1/2)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))+1/2/(-c*d)^(1/2)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))","B"
79,1,809,85,0.019000," ","int(1/(b*x^2+a)^(1/2)/(d*x^2+c)^2,x)","-\frac{\sqrt{-c d}\, b \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{4 \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, c d}+\frac{\sqrt{-c d}\, b \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{4 \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, c d}-\frac{\ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{4 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, c}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{4 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, c}+\frac{\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-c d}}{d}\right) c}+\frac{\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-c d}}{d}\right) c}"," ",0,"1/4/c/(a*d-b*c)/(x-(-c*d)^(1/2)/d)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-1/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))+1/4/c/(a*d-b*c)/(x+(-c*d)^(1/2)/d)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+1/4/c/d*(-c*d)^(1/2)*b/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))-1/4/c/(-c*d)^(1/2)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))+1/4/c/(-c*d)^(1/2)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))","B"
80,1,1815,143,0.021000," ","int(1/(b*x^2+a)^(1/2)/(d*x^2+c)^3,x)","-\frac{3 b^{2} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{16 \sqrt{-c d}\, \left(a d -b c \right)^{2} \sqrt{\frac{a d -b c}{d}}}+\frac{3 b^{2} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{16 \sqrt{-c d}\, \left(a d -b c \right)^{2} \sqrt{\frac{a d -b c}{d}}}-\frac{b \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{16 \sqrt{-c d}\, \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, c}+\frac{b \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{16 \sqrt{-c d}\, \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, c}-\frac{3 \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, b}{16 \left(a d -b c \right)^{2} \left(x -\frac{\sqrt{-c d}}{d}\right) c}-\frac{3 \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, b}{16 \left(a d -b c \right)^{2} \left(x +\frac{\sqrt{-c d}}{d}\right) c}-\frac{3 \sqrt{-c d}\, b \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{16 \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, c^{2} d}+\frac{3 \sqrt{-c d}\, b \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{16 \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, c^{2} d}+\frac{\sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{16 \sqrt{-c d}\, \left(a d -b c \right) \left(x -\frac{\sqrt{-c d}}{d}\right)^{2} c}-\frac{\sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{16 \sqrt{-c d}\, \left(a d -b c \right) \left(x +\frac{\sqrt{-c d}}{d}\right)^{2} c}-\frac{3 \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{16 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, c^{2}}+\frac{3 \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{16 \sqrt{-c d}\, \sqrt{\frac{a d -b c}{d}}\, c^{2}}+\frac{3 \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{16 \left(a d -b c \right) \left(x +\frac{\sqrt{-c d}}{d}\right) c^{2}}+\frac{3 \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{16 \left(a d -b c \right) \left(x -\frac{\sqrt{-c d}}{d}\right) c^{2}}"," ",0,"1/16/(-c*d)^(1/2)/c/(a*d-b*c)/(x-(-c*d)^(1/2)/d)^2*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-3/16/c*b/(a*d-b*c)^2/(x-(-c*d)^(1/2)/d)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-3/16/(-c*d)^(1/2)*b^2/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-1/16/(-c*d)^(1/2)/c*b/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-1/16/(-c*d)^(1/2)/c/(a*d-b*c)/(x+(-c*d)^(1/2)/d)^2*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-3/16/c*b/(a*d-b*c)^2/(x+(-c*d)^(1/2)/d)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+3/16/(-c*d)^(1/2)*b^2/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))+1/16/(-c*d)^(1/2)/c*b/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))+3/16/c^2/(a*d-b*c)/(x+(-c*d)^(1/2)/d)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+3/16/c^2/d*(-c*d)^(1/2)*b/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))+3/16/c^2/(a*d-b*c)/(x-(-c*d)^(1/2)/d)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-3/16/c^2/d*(-c*d)^(1/2)*b/(a*d-b*c)/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-3/16/(-c*d)^(1/2)/c^2/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))+3/16/(-c*d)^(1/2)/c^2/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))","B"
81,1,340,235,0.019000," ","int((d*x^2+c)^4/(b*x^2+a)^(3/2),x)","\frac{d^{4} x^{7}}{6 \sqrt{b \,x^{2}+a}\, b}-\frac{7 a \,d^{4} x^{5}}{24 \sqrt{b \,x^{2}+a}\, b^{2}}+\frac{c \,d^{3} x^{5}}{\sqrt{b \,x^{2}+a}\, b}+\frac{35 a^{2} d^{4} x^{3}}{48 \sqrt{b \,x^{2}+a}\, b^{3}}-\frac{5 a c \,d^{3} x^{3}}{2 \sqrt{b \,x^{2}+a}\, b^{2}}+\frac{3 c^{2} d^{2} x^{3}}{\sqrt{b \,x^{2}+a}\, b}+\frac{35 a^{3} d^{4} x}{16 \sqrt{b \,x^{2}+a}\, b^{4}}-\frac{15 a^{2} c \,d^{3} x}{2 \sqrt{b \,x^{2}+a}\, b^{3}}+\frac{9 a \,c^{2} d^{2} x}{\sqrt{b \,x^{2}+a}\, b^{2}}+\frac{c^{4} x}{\sqrt{b \,x^{2}+a}\, a}-\frac{4 c^{3} d x}{\sqrt{b \,x^{2}+a}\, b}-\frac{35 a^{3} d^{4} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{16 b^{\frac{9}{2}}}+\frac{15 a^{2} c \,d^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{7}{2}}}-\frac{9 a \,c^{2} d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{5}{2}}}+\frac{4 c^{3} d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{3}{2}}}"," ",0,"1/6*d^4*x^7/b/(b*x^2+a)^(1/2)-7/24*d^4*a/b^2*x^5/(b*x^2+a)^(1/2)+35/48*d^4*a^2/b^3*x^3/(b*x^2+a)^(1/2)+35/16*d^4*a^3/b^4*x/(b*x^2+a)^(1/2)-35/16*d^4*a^3/b^(9/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+c*d^3*x^5/b/(b*x^2+a)^(1/2)-5/2*c*d^3*a/b^2*x^3/(b*x^2+a)^(1/2)-15/2*c*d^3*a^2/b^3*x/(b*x^2+a)^(1/2)+15/2*c*d^3*a^2/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+3*c^2*d^2*x^3/b/(b*x^2+a)^(1/2)+9*c^2*d^2*a/b^2*x/(b*x^2+a)^(1/2)-9*c^2*d^2*a/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-4*c^3*d*x/b/(b*x^2+a)^(1/2)+4*c^3*d/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+c^4*x/a/(b*x^2+a)^(1/2)","A"
82,1,219,151,0.008000," ","int((d*x^2+c)^3/(b*x^2+a)^(3/2),x)","\frac{d^{3} x^{5}}{4 \sqrt{b \,x^{2}+a}\, b}-\frac{5 a \,d^{3} x^{3}}{8 \sqrt{b \,x^{2}+a}\, b^{2}}+\frac{3 c \,d^{2} x^{3}}{2 \sqrt{b \,x^{2}+a}\, b}-\frac{15 a^{2} d^{3} x}{8 \sqrt{b \,x^{2}+a}\, b^{3}}+\frac{9 a c \,d^{2} x}{2 \sqrt{b \,x^{2}+a}\, b^{2}}+\frac{c^{3} x}{\sqrt{b \,x^{2}+a}\, a}-\frac{3 c^{2} d x}{\sqrt{b \,x^{2}+a}\, b}+\frac{15 a^{2} d^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{7}{2}}}-\frac{9 a c \,d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{5}{2}}}+\frac{3 c^{2} d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{3}{2}}}"," ",0,"1/4*d^3*x^5/b/(b*x^2+a)^(1/2)-5/8*d^3*a/b^2*x^3/(b*x^2+a)^(1/2)-15/8*d^3*a^2/b^3*x/(b*x^2+a)^(1/2)+15/8*d^3*a^2/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+3/2*c*d^2*x^3/b/(b*x^2+a)^(1/2)+9/2*c*d^2*a/b^2*x/(b*x^2+a)^(1/2)-9/2*c*d^2*a/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-3*c^2*d*x/b/(b*x^2+a)^(1/2)+3*c^2*d/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+c^3*x/a/(b*x^2+a)^(1/2)","A"
83,1,123,76,0.008000," ","int((d*x^2+c)^2/(b*x^2+a)^(3/2),x)","\frac{d^{2} x^{3}}{2 \sqrt{b \,x^{2}+a}\, b}+\frac{3 a \,d^{2} x}{2 \sqrt{b \,x^{2}+a}\, b^{2}}+\frac{c^{2} x}{\sqrt{b \,x^{2}+a}\, a}-\frac{2 c d x}{\sqrt{b \,x^{2}+a}\, b}-\frac{3 a \,d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{5}{2}}}+\frac{2 c d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{3}{2}}}"," ",0,"1/2*d^2*x^3/b/(b*x^2+a)^(1/2)+3/2*d^2*a/b^2*x/(b*x^2+a)^(1/2)-3/2*d^2*a/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-2*c*d*x/b/(b*x^2+a)^(1/2)+2*c*d/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+c^2*x/a/(b*x^2+a)^(1/2)","A"
84,1,54,46,0.005000," ","int((d*x^2+c)/(b*x^2+a)^(3/2),x)","\frac{c x}{\sqrt{b \,x^{2}+a}\, a}-\frac{d x}{\sqrt{b \,x^{2}+a}\, b}+\frac{d \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{3}{2}}}"," ",0,"-d*x/b/(b*x^2+a)^(1/2)+d/b^(3/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+c*x/a/(b*x^2+a)^(1/2)","A"
85,1,15,14,0.003000," ","int(1/(b*x^2+a)^(3/2),x)","\frac{x}{\sqrt{b \,x^{2}+a}\, a}"," ",0,"1/(b*x^2+a)^(1/2)/a*x","A"
86,1,618,67,0.017000," ","int(1/(b*x^2+a)^(3/2)/(d*x^2+c),x)","-\frac{d \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}}+\frac{d \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}}-\frac{b x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a}-\frac{b x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a}+\frac{d}{2 \sqrt{-c d}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}-\frac{d}{2 \sqrt{-c d}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}"," ",0,"1/2/(-c*d)^(1/2)/(a*d-b*c)*d/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-1/2/(a*d-b*c)/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b-1/2/(-c*d)^(1/2)/(a*d-b*c)*d/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-1/2/(-c*d)^(1/2)/(a*d-b*c)*d/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-1/2/(a*d-b*c)/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b+1/2/(-c*d)^(1/2)/(a*d-b*c)*d/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))","B"
87,1,1439,123,0.022000," ","int(1/(b*x^2+a)^(3/2)/(d*x^2+c)^2,x)","\frac{3 b^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a}+\frac{3 b^{2} x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a}-\frac{3 \sqrt{-c d}\, b \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{\frac{a d -b c}{d}}\, c}+\frac{3 \sqrt{-c d}\, b \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{4 \left(a d -b c \right)^{2} \sqrt{\frac{a d -b c}{d}}\, c}-\frac{d \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{4 \sqrt{-c d}\, \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, c}+\frac{d \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{4 \sqrt{-c d}\, \left(a d -b c \right) \sqrt{\frac{a d -b c}{d}}\, c}+\frac{b x}{4 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a c}+\frac{b x}{4 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a c}-\frac{3 \sqrt{-c d}\, b}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, c}+\frac{3 \sqrt{-c d}\, b}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, c}+\frac{d}{4 \sqrt{-c d}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, c}-\frac{d}{4 \sqrt{-c d}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, c}+\frac{1}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-c d}}{d}\right) \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, c}+\frac{1}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-c d}}{d}\right) \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, c}"," ",0,"1/4/c/(a*d-b*c)/(x+(-c*d)^(1/2)/d)/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-3/4/c*(-c*d)^(1/2)*b/(a*d-b*c)^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+3/4*b^2/(a*d-b*c)^2/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+3/4/c*(-c*d)^(1/2)*b/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))+1/4/c/(a*d-b*c)/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b+1/4/c/(a*d-b*c)/(x-(-c*d)^(1/2)/d)/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+3/4/c*(-c*d)^(1/2)*b/(a*d-b*c)^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+3/4*b^2/(a*d-b*c)^2/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-3/4/c*(-c*d)^(1/2)*b/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))+1/4/c/(a*d-b*c)/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b+1/4/c/(-c*d)^(1/2)/(a*d-b*c)*d/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-1/4/c/(-c*d)^(1/2)/(a*d-b*c)*d/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-1/4/c/(-c*d)^(1/2)/(a*d-b*c)*d/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+1/4/c/(-c*d)^(1/2)/(a*d-b*c)*d/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))","B"
88,1,2919,201,0.026000," ","int(1/(b*x^2+a)^(3/2)/(d*x^2+c)^3,x)","\text{output too large to display}"," ",0,"3/16/c^2/(a*d-b*c)/(x-(-c*d)^(1/2)/d)/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+3/16/c^2/(a*d-b*c)/(x+(-c*d)^(1/2)/d)/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-1/16/(-c*d)^(1/2)/c/(a*d-b*c)/(x+(-c*d)^(1/2)/d)^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-5/16/c*b/(a*d-b*c)^2/(x+(-c*d)^(1/2)/d)/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-3/16/(-c*d)^(1/2)/c^2/(a*d-b*c)*d/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-9/16/c^2*(-c*d)^(1/2)*b/(a*d-b*c)^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+3/16/(-c*d)^(1/2)/c^2/(a*d-b*c)*d/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+15/16/(-c*d)^(1/2)*d*b^2/(a*d-b*c)^3/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-15/16*b^3/(a*d-b*c)^3/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+9/16/c^2*(-c*d)^(1/2)*b/(a*d-b*c)^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-15/16/(-c*d)^(1/2)*d*b^2/(a*d-b*c)^3/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-15/16*b^3/(a*d-b*c)^3/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-3/16/(-c*d)^(1/2)/c*d*b/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))+3/16/(-c*d)^(1/2)/c*d*b/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))+1/16/(-c*d)^(1/2)/c/(a*d-b*c)/(x-(-c*d)^(1/2)/d)^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-5/16/c*b/(a*d-b*c)^2/(x-(-c*d)^(1/2)/d)/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+15/16/(-c*d)^(1/2)*d*b^2/(a*d-b*c)^3/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))-1/4/c*b^2/(a*d-b*c)^2/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-3/16/(-c*d)^(1/2)/c*d*b/(a*d-b*c)^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+9/16/c^2*(-c*d)^(1/2)*b/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))+3/16/c^2/(a*d-b*c)/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b+3/16/c^2/(a*d-b*c)/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b-3/16/(-c*d)^(1/2)/c^2/(a*d-b*c)*d/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))+3/16/(-c*d)^(1/2)/c^2/(a*d-b*c)*d/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))-9/16/c^2*(-c*d)^(1/2)*b/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-15/16/(-c*d)^(1/2)*d*b^2/(a*d-b*c)^3/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-1/4/c*b^2/(a*d-b*c)^2/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+3/16/(-c*d)^(1/2)/c*d*b/(a*d-b*c)^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)","B"
89,1,351,231,0.017000," ","int((d*x^2+c)^4/(b*x^2+a)^(5/2),x)","\frac{d^{4} x^{7}}{4 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}-\frac{7 a \,d^{4} x^{5}}{8 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{2}}+\frac{2 c \,d^{3} x^{5}}{\left(b \,x^{2}+a \right)^{\frac{3}{2}} b}-\frac{35 a^{2} d^{4} x^{3}}{24 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{3}}+\frac{10 a c \,d^{3} x^{3}}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{2}}-\frac{2 c^{2} d^{2} x^{3}}{\left(b \,x^{2}+a \right)^{\frac{3}{2}} b}+\frac{c^{4} x}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a}-\frac{4 c^{3} d x}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}-\frac{35 a^{2} d^{4} x}{8 \sqrt{b \,x^{2}+a}\, b^{4}}+\frac{10 a c \,d^{3} x}{\sqrt{b \,x^{2}+a}\, b^{3}}+\frac{4 c^{3} d x}{3 \sqrt{b \,x^{2}+a}\, a b}+\frac{2 c^{4} x}{3 \sqrt{b \,x^{2}+a}\, a^{2}}-\frac{6 c^{2} d^{2} x}{\sqrt{b \,x^{2}+a}\, b^{2}}+\frac{35 a^{2} d^{4} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{8 b^{\frac{9}{2}}}-\frac{10 a c \,d^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{7}{2}}}+\frac{6 c^{2} d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{5}{2}}}"," ",0,"1/4*d^4*x^7/b/(b*x^2+a)^(3/2)-7/8*d^4*a/b^2*x^5/(b*x^2+a)^(3/2)-35/24*d^4*a^2/b^3*x^3/(b*x^2+a)^(3/2)-35/8*d^4*a^2/b^4*x/(b*x^2+a)^(1/2)+35/8*d^4*a^2/b^(9/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))+2*c*d^3*x^5/b/(b*x^2+a)^(3/2)+10/3*c*d^3*a/b^2*x^3/(b*x^2+a)^(3/2)+10*c*d^3*a/b^3*x/(b*x^2+a)^(1/2)-10*c*d^3*a/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-2*c^2*d^2*x^3/b/(b*x^2+a)^(3/2)-6*c^2*d^2/b^2*x/(b*x^2+a)^(1/2)+6*c^2*d^2/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-4/3*c^3*d/b*x/(b*x^2+a)^(3/2)+4/3*c^3*d/a/b*x/(b*x^2+a)^(1/2)+1/3*c^4*x/a/(b*x^2+a)^(3/2)+2/3*c^4/a^2*x/(b*x^2+a)^(1/2)","A"
90,1,228,152,0.009000," ","int((d*x^2+c)^3/(b*x^2+a)^(5/2),x)","\frac{d^{3} x^{5}}{2 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}+\frac{5 a \,d^{3} x^{3}}{6 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b^{2}}-\frac{c \,d^{2} x^{3}}{\left(b \,x^{2}+a \right)^{\frac{3}{2}} b}+\frac{c^{3} x}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a}-\frac{c^{2} d x}{\left(b \,x^{2}+a \right)^{\frac{3}{2}} b}+\frac{5 a \,d^{3} x}{2 \sqrt{b \,x^{2}+a}\, b^{3}}+\frac{c^{2} d x}{\sqrt{b \,x^{2}+a}\, a b}+\frac{2 c^{3} x}{3 \sqrt{b \,x^{2}+a}\, a^{2}}-\frac{3 c \,d^{2} x}{\sqrt{b \,x^{2}+a}\, b^{2}}-\frac{5 a \,d^{3} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{2 b^{\frac{7}{2}}}+\frac{3 c \,d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{5}{2}}}"," ",0,"1/2*d^3*x^5/b/(b*x^2+a)^(3/2)+5/6*d^3*a/b^2*x^3/(b*x^2+a)^(3/2)+5/2*d^3*a/b^3*x/(b*x^2+a)^(1/2)-5/2*d^3*a/b^(7/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-c*d^2*x^3/b/(b*x^2+a)^(3/2)-3*c*d^2/b^2*x/(b*x^2+a)^(1/2)+3*c*d^2/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-c^2*d/b*x/(b*x^2+a)^(3/2)+c^2*d/a/b*x/(b*x^2+a)^(1/2)+1/3*c^3*x/a/(b*x^2+a)^(3/2)+2/3*c^3/a^2*x/(b*x^2+a)^(1/2)","A"
91,1,136,91,0.007000," ","int((d*x^2+c)^2/(b*x^2+a)^(5/2),x)","-\frac{d^{2} x^{3}}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}+\frac{c^{2} x}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a}-\frac{2 c d x}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} b}+\frac{2 c d x}{3 \sqrt{b \,x^{2}+a}\, a b}+\frac{2 c^{2} x}{3 \sqrt{b \,x^{2}+a}\, a^{2}}-\frac{d^{2} x}{\sqrt{b \,x^{2}+a}\, b^{2}}+\frac{d^{2} \ln \left(\sqrt{b}\, x +\sqrt{b \,x^{2}+a}\right)}{b^{\frac{5}{2}}}"," ",0,"-1/3*d^2*x^3/b/(b*x^2+a)^(3/2)-d^2/b^2*x/(b*x^2+a)^(1/2)+d^2/b^(5/2)*ln(b^(1/2)*x+(b*x^2+a)^(1/2))-2/3*c*d/b*x/(b*x^2+a)^(3/2)+2/3*c*d/a/b*x/(b*x^2+a)^(1/2)+1/3*c^2*x/a/(b*x^2+a)^(3/2)+2/3*c^2/a^2*x/(b*x^2+a)^(1/2)","A"
92,1,34,39,0.004000," ","int((d*x^2+c)/(b*x^2+a)^(5/2),x)","\frac{\left(a d \,x^{2}+2 b c \,x^{2}+3 a c \right) x}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2}}"," ",0,"1/3*x*(a*d*x^2+2*b*c*x^2+3*a*c)/(b*x^2+a)^(3/2)/a^2","A"
93,1,26,31,0.000000," ","int(1/(b*x^2+a)^(5/2),x)","\frac{\left(2 b \,x^{2}+3 a \right) x}{3 \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2}}"," ",0,"1/3*(2*b*x^2+3*a)/(b*x^2+a)^(3/2)/a^2*x","A"
94,1,1070,104,0.020000," ","int(1/(b*x^2+a)^(5/2)/(d*x^2+c),x)","-\frac{d^{2} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \left(a d -b c \right)^{2} \sqrt{\frac{a d -b c}{d}}}+\frac{d^{2} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{2 \sqrt{-c d}\, \left(a d -b c \right)^{2} \sqrt{\frac{a d -b c}{d}}}-\frac{b d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a}-\frac{b d x}{2 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a}+\frac{d^{2}}{2 \sqrt{-c d}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}-\frac{d^{2}}{2 \sqrt{-c d}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}-\frac{b x}{6 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} a}-\frac{b x}{6 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} a}+\frac{d}{6 \sqrt{-c d}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}}}-\frac{d}{6 \sqrt{-c d}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}}}-\frac{b x}{3 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a^{2}}-\frac{b x}{3 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a^{2}}"," ",0,"1/6/(-c*d)^(1/2)/(a*d-b*c)*d/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-1/6*b/(a*d-b*c)/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x-1/3*b/(a*d-b*c)/a^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+1/2/(-c*d)^(1/2)*d^2/(a*d-b*c)^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-1/2*d/(a*d-b*c)^2/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b-1/2/(-c*d)^(1/2)*d^2/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-1/6/(-c*d)^(1/2)/(a*d-b*c)*d/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-1/6*b/(a*d-b*c)/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x-1/3*b/(a*d-b*c)/a^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-1/2/(-c*d)^(1/2)*d^2/(a*d-b*c)^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-1/2*d/(a*d-b*c)^2/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b+1/2/(-c*d)^(1/2)*d^2/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))","B"
95,1,2371,178,0.027000," ","int(1/(b*x^2+a)^(5/2)/(d*x^2+c)^2,x)","\frac{b x}{4 \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} a c}+\frac{b x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a^{2} c}+\frac{5 \sqrt{-c d}\, b d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, c}+\frac{5 b^{2} d x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a}+\frac{1}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-c d}}{d}\right) \left(\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} c}+\frac{1}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-c d}}{d}\right) \left(\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} c}-\frac{5 \sqrt{-c d}\, b d}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, c}+\frac{5 b^{2} d x}{4 \left(a d -b c \right)^{3} \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a}+\frac{b x}{4 \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} a c}-\frac{5 \sqrt{-c d}\, b d \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{\frac{a d -b c}{d}}\, c}+\frac{5 \sqrt{-c d}\, b d \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{4 \left(a d -b c \right)^{3} \sqrt{\frac{a d -b c}{d}}\, c}-\frac{b d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a c}-\frac{b d x}{4 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a c}-\frac{d^{2} \ln \left(\frac{\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x -\frac{\sqrt{-c d}}{d}}\right)}{4 \sqrt{-c d}\, \left(a d -b c \right)^{2} \sqrt{\frac{a d -b c}{d}}\, c}+\frac{d^{2} \ln \left(\frac{-\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{2 a d -2 b c}{d}+2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}}{x +\frac{\sqrt{-c d}}{d}}\right)}{4 \sqrt{-c d}\, \left(a d -b c \right)^{2} \sqrt{\frac{a d -b c}{d}}\, c}-\frac{5 \sqrt{-c d}\, b}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} c}+\frac{5 b^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} a}+\frac{5 \sqrt{-c d}\, b}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} c}+\frac{d}{12 \sqrt{-c d}\, \left(a d -b c \right) \left(\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} c}+\frac{d^{2}}{4 \sqrt{-c d}\, \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, c}-\frac{d}{12 \sqrt{-c d}\, \left(a d -b c \right) \left(\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} c}-\frac{d^{2}}{4 \sqrt{-c d}\, \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, c}+\frac{5 b^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a^{2}}+\frac{5 b^{2} x}{12 \left(a d -b c \right)^{2} \left(\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}\right)^{\frac{3}{2}} a}+\frac{5 b^{2} x}{6 \left(a d -b c \right)^{2} \sqrt{\left(x -\frac{\sqrt{-c d}}{d}\right)^{2} b +\frac{2 \sqrt{-c d}\, \left(x -\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a^{2}}+\frac{b x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-c d}}{d}\right)^{2} b -\frac{2 \sqrt{-c d}\, \left(x +\frac{\sqrt{-c d}}{d}\right) b}{d}+\frac{a d -b c}{d}}\, a^{2} c}"," ",0,"1/4/(-c*d)^(1/2)/c*d^2/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))+1/4/c*b/(a*d-b*c)/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x+1/2/c*b/(a*d-b*c)/a^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+5/4/c*d*(-c*d)^(1/2)*b/(a*d-b*c)^3/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+5/4*d*b^2/(a*d-b*c)^3/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+1/4/c/(a*d-b*c)/(x+(-c*d)^(1/2)/d)/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+1/4/c/(a*d-b*c)/(x-(-c*d)^(1/2)/d)/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-1/4/(-c*d)^(1/2)/c*d^2/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-5/4/c*d*(-c*d)^(1/2)*b/(a*d-b*c)^3/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+5/4*d*b^2/(a*d-b*c)^3/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+1/4/c*b/(a*d-b*c)/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x-5/4/c*d*(-c*d)^(1/2)*b/(a*d-b*c)^3/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-1/4/c*d/(a*d-b*c)^2/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b-1/4/c*d/(a*d-b*c)^2/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b+5/4/c*d*(-c*d)^(1/2)*b/(a*d-b*c)^3/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))-5/12/c*(-c*d)^(1/2)*b/(a*d-b*c)^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+5/12*b^2/(a*d-b*c)^2/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x+5/12/c*(-c*d)^(1/2)*b/(a*d-b*c)^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+1/12/(-c*d)^(1/2)/c/(a*d-b*c)*d/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+1/4/(-c*d)^(1/2)/c*d^2/(a*d-b*c)^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-1/12/(-c*d)^(1/2)/c/(a*d-b*c)*d/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-1/4/(-c*d)^(1/2)/c*d^2/(a*d-b*c)^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+5/6*b^2/(a*d-b*c)^2/a^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+5/12*b^2/(a*d-b*c)^2/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x+5/6*b^2/(a*d-b*c)^2/a^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+1/2/c*b/(a*d-b*c)/a^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x","B"
96,1,4495,285,0.029000," ","int(1/(b*x^2+a)^(5/2)/(d*x^2+c)^3,x)","\text{output too large to display}"," ",0,"3/16/c^2/(a*d-b*c)/(x-(-c*d)^(1/2)/d)/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+3/16/c^2/(a*d-b*c)/(x+(-c*d)^(1/2)/d)/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+1/16/(-c*d)^(1/2)/c/(a*d-b*c)/(x-(-c*d)^(1/2)/d)^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-7/16/c*b/(a*d-b*c)^2/(x-(-c*d)^(1/2)/d)/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-15/16/c^2*d*(-c*d)^(1/2)*b/(a*d-b*c)^3/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))+5/48/(-c*d)^(1/2)/c*d*b/(a*d-b*c)^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+5/16/(-c*d)^(1/2)/c*d^2*b/(a*d-b*c)^3/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+3/16/c^2*b/(a*d-b*c)/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x+3/8/c^2*b/(a*d-b*c)/a^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-3/16/(-c*d)^(1/2)/c^2*d^2/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-7/16/c*b/(a*d-b*c)^2/(x+(-c*d)^(1/2)/d)/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-35/48/(-c*d)^(1/2)*d*b^2/(a*d-b*c)^3/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-35/48*b^3/(a*d-b*c)^3/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x-35/24*b^3/(a*d-b*c)^3/a^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-35/16/(-c*d)^(1/2)*d^2*b^2/(a*d-b*c)^4/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+5/16/c^2*(-c*d)^(1/2)*b/(a*d-b*c)^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+3/16/(-c*d)^(1/2)/c^2*d^2/(a*d-b*c)^2/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))+15/16/c^2*d*(-c*d)^(1/2)*b/(a*d-b*c)^3/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-15/16/c^2*d*(-c*d)^(1/2)*b/(a*d-b*c)^3/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+3/16/c^2*b/(a*d-b*c)/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x+3/8/c^2*b/(a*d-b*c)/a^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-35/16*d*b^3/(a*d-b*c)^4/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+35/16/(-c*d)^(1/2)*d^2*b^2/(a*d-b*c)^4/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))-3/8/c*b^2/(a*d-b*c)^2/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x-3/4/c*b^2/(a*d-b*c)^2/a^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-5/48/(-c*d)^(1/2)/c*d*b/(a*d-b*c)^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-5/16/(-c*d)^(1/2)/c*d^2*b/(a*d-b*c)^3/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-35/16*d*b^3/(a*d-b*c)^4/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-35/16/(-c*d)^(1/2)*d^2*b^2/(a*d-b*c)^4/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-3/8/c*b^2/(a*d-b*c)^2/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x-3/4/c*b^2/(a*d-b*c)^2/a^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+15/16/c^2*d*(-c*d)^(1/2)*b/(a*d-b*c)^3/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))+5/8/c*d*b^2/(a*d-b*c)^3/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+5/16/(-c*d)^(1/2)/c*d^2*b/(a*d-b*c)^3/((a*d-b*c)/d)^(1/2)*ln((-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x+(-c*d)^(1/2)/d))+5/8/c*d*b^2/(a*d-b*c)^3/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x-5/16/(-c*d)^(1/2)/c*d^2*b/(a*d-b*c)^3/((a*d-b*c)/d)^(1/2)*ln((2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+2*(a*d-b*c)/d+2*((a*d-b*c)/d)^(1/2)*((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2))/(x-(-c*d)^(1/2)/d))-3/16/c^2*d/(a*d-b*c)^2/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b-3/16/c^2*d/(a*d-b*c)^2/a/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x*b+35/48/(-c*d)^(1/2)*d*b^2/(a*d-b*c)^3/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-35/48*b^3/(a*d-b*c)^3/a/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)*x-35/24*b^3/(a*d-b*c)^3/a^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)*x+35/16/(-c*d)^(1/2)*d^2*b^2/(a*d-b*c)^4/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)+1/16/(-c*d)^(1/2)/c^2/(a*d-b*c)*d/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)+3/16/(-c*d)^(1/2)/c^2*d^2/(a*d-b*c)^2/((x-(-c*d)^(1/2)/d)^2*b+2*(-c*d)^(1/2)*(x-(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-1/16/(-c*d)^(1/2)/c^2/(a*d-b*c)*d/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-3/16/(-c*d)^(1/2)/c^2*d^2/(a*d-b*c)^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(1/2)-5/16/c^2*(-c*d)^(1/2)*b/(a*d-b*c)^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)-1/16/(-c*d)^(1/2)/c/(a*d-b*c)/(x+(-c*d)^(1/2)/d)^2/((x+(-c*d)^(1/2)/d)^2*b-2*(-c*d)^(1/2)*(x+(-c*d)^(1/2)/d)*b/d+(a*d-b*c)/d)^(3/2)","B"
97,1,190,204,0.007000," ","int((b*x^2+a)^3/(d*x^2+c)^(11/2),x)","\frac{\left(128 a^{3} d^{4} x^{8}+48 a^{2} b c \,d^{3} x^{8}+24 a \,b^{2} c^{2} d^{2} x^{8}+10 b^{3} c^{3} d \,x^{8}+576 a^{3} c \,d^{3} x^{6}+216 a^{2} b \,c^{2} d^{2} x^{6}+108 a \,b^{2} c^{3} d \,x^{6}+45 b^{3} c^{4} x^{6}+1008 a^{3} c^{2} d^{2} x^{4}+378 a^{2} b \,c^{3} d \,x^{4}+189 a \,b^{2} c^{4} x^{4}+840 a^{3} c^{3} d \,x^{2}+315 a^{2} b \,c^{4} x^{2}+315 a^{3} c^{4}\right) x}{315 \left(d \,x^{2}+c \right)^{\frac{9}{2}} c^{5}}"," ",0,"1/315*x*(128*a^3*d^4*x^8+48*a^2*b*c*d^3*x^8+24*a*b^2*c^2*d^2*x^8+10*b^3*c^3*d*x^8+576*a^3*c*d^3*x^6+216*a^2*b*c^2*d^2*x^6+108*a*b^2*c^3*d*x^6+45*b^3*c^4*x^6+1008*a^3*c^2*d^2*x^4+378*a^2*b*c^3*d*x^4+189*a*b^2*c^4*x^4+840*a^3*c^3*d*x^2+315*a^2*b*c^4*x^2+315*a^3*c^4)/(d*x^2+c)^(9/2)/c^5","A"
98,1,115,158,0.008000," ","int((b*x^2+a)^2/(d*x^2+c)^(9/2),x)","\frac{\left(48 a^{2} d^{3} x^{6}+16 a b c \,d^{2} x^{6}+6 b^{2} c^{2} d \,x^{6}+168 a^{2} c \,d^{2} x^{4}+56 a b \,c^{2} d \,x^{4}+21 b^{2} c^{3} x^{4}+210 a^{2} c^{2} d \,x^{2}+70 a b \,c^{3} x^{2}+105 a^{2} c^{3}\right) x}{105 \left(d \,x^{2}+c \right)^{\frac{7}{2}} c^{4}}"," ",0,"1/105*x*(48*a^2*d^3*x^6+16*a*b*c*d^2*x^6+6*b^2*c^2*d*x^6+168*a^2*c*d^2*x^4+56*a*b*c^2*d*x^4+21*b^2*c^3*x^4+210*a^2*c^2*d*x^2+70*a*b*c^3*x^2+105*a^2*c^3)/(d*x^2+c)^(7/2)/c^4","A"
99,1,57,79,0.004000," ","int((b*x^2+a)/(d*x^2+c)^(7/2),x)","\frac{\left(8 a \,d^{2} x^{4}+2 b c d \,x^{4}+20 a c d \,x^{2}+5 b \,c^{2} x^{2}+15 c^{2} a \right) x}{15 \left(d \,x^{2}+c \right)^{\frac{5}{2}} c^{3}}"," ",0,"1/15*x*(8*a*d^2*x^4+2*b*c*d*x^4+20*a*c*d*x^2+5*b*c^2*x^2+15*a*c^2)/(d*x^2+c)^(5/2)/c^3","A"
100,1,26,31,0.003000," ","int(1/(d*x^2+c)^(5/2),x)","\frac{\left(2 d \,x^{2}+3 c \right) x}{3 \left(d \,x^{2}+c \right)^{\frac{3}{2}} c^{2}}"," ",0,"1/3*x*(2*d*x^2+3*c)/(d*x^2+c)^(3/2)/c^2","A"
101,1,628,67,0.042000," ","int(1/(b*x^2+a)/(d*x^2+c)^(3/2),x)","\frac{b \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}}-\frac{b \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}}+\frac{b}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}-\frac{b}{2 \sqrt{-a b}\, \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}+\frac{d x}{2 \left(a d -b c \right) \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}+\frac{d x}{2 \left(a d -b c \right) \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}\, c}"," ",0,"1/2/(-a*b)^(1/2)/(a*d-b*c)*b/((x+1/b*(-a*b)^(1/2))^2*d-2*d*(-a*b)^(1/2)/b*(x+1/b*(-a*b)^(1/2))-(a*d-b*c)/b)^(1/2)+1/2/(a*d-b*c)/c/((x+1/b*(-a*b)^(1/2))^2*d-2*d*(-a*b)^(1/2)/b*(x+1/b*(-a*b)^(1/2))-(a*d-b*c)/b)^(1/2)*x*d-1/2/(-a*b)^(1/2)/(a*d-b*c)*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(a*d-b*c)/b-2*d*(-a*b)^(1/2)/b*(x+1/b*(-a*b)^(1/2))+2*(-(a*d-b*c)/b)^(1/2)*((x+1/b*(-a*b)^(1/2))^2*d-2*d*(-a*b)^(1/2)/b*(x+1/b*(-a*b)^(1/2))-(a*d-b*c)/b)^(1/2))/(x+1/b*(-a*b)^(1/2)))-1/2/(-a*b)^(1/2)/(a*d-b*c)*b/((x-1/b*(-a*b)^(1/2))^2*d+2*d*(-a*b)^(1/2)/b*(x-1/b*(-a*b)^(1/2))-(a*d-b*c)/b)^(1/2)+1/2/(a*d-b*c)/c/((x-1/b*(-a*b)^(1/2))^2*d+2*d*(-a*b)^(1/2)/b*(x-1/b*(-a*b)^(1/2))-(a*d-b*c)/b)^(1/2)*x*d+1/2/(-a*b)^(1/2)/(a*d-b*c)*b/(-(a*d-b*c)/b)^(1/2)*ln((-2*(a*d-b*c)/b+2*d*(-a*b)^(1/2)/b*(x-1/b*(-a*b)^(1/2))+2*(-(a*d-b*c)/b)^(1/2)*((x-1/b*(-a*b)^(1/2))^2*d+2*d*(-a*b)^(1/2)/b*(x-1/b*(-a*b)^(1/2))-(a*d-b*c)/b)^(1/2))/(x-1/b*(-a*b)^(1/2)))","B"
102,1,823,84,0.025000," ","int(1/(b*x^2+a)^2/(d*x^2+c)^(1/2),x)","\frac{\sqrt{-a b}\, d \ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a b}-\frac{\sqrt{-a b}\, d \ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \left(a d -b c \right) \sqrt{-\frac{a d -b c}{b}}\, a b}-\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{4 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}\, a}-\frac{\sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \left(a d -b c \right) \left(x +\frac{\sqrt{-a b}}{b}\right) a}-\frac{\sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{4 \left(a d -b c \right) \left(x -\frac{\sqrt{-a b}}{b}\right) a}"," ",0,"1/4/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/a/(a*d-b*c)/(x+(-a*b)^(1/2)/b)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)-1/4/b/a*d*(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/4/a/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))-1/4/a/(a*d-b*c)/(x-(-a*b)^(1/2)/b)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2)+1/4/b/a*d*(-a*b)^(1/2)/(a*d-b*c)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
103,1,5177,129,0.033000," ","int((d*x^2+c)^(1/2)/(b*x^2+a)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
104,1,13964,175,0.049000," ","int((d*x^2+c)^(3/2)/(b*x^2+a)^4,x)","\text{output too large to display}"," ",0,"result too large to display","B"
105,1,19,18,0.003000," ","int(1/(b*c/d+b*x^2)/(d*x^2+c)^(1/2),x)","\frac{d x}{\sqrt{d \,x^{2}+c}\, b c}"," ",0,"d*x/b/c/(d*x^2+c)^(1/2)","A"
106,1,28,20,0.006000," ","int(1/(x^2+1)/(-x^2+1)^(1/2),x)","-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, \sqrt{-x^{2}+1}\, x}{x^{2}-1}\right)}{2}"," ",0,"-1/2*2^(1/2)*arctan(2^(1/2)*(-x^2+1)^(1/2)/(x^2-1)*x)","A"
107,1,306,39,0.010000," ","int(1/(b*x^2+a)/(d*x^2+c)^(1/2),x)","-\frac{\ln \left(\frac{\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x -\frac{\sqrt{-a b}}{b}\right)^{2} d +\frac{2 \sqrt{-a b}\, \left(x -\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x -\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}+\frac{\ln \left(\frac{-\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{2 \left(a d -b c \right)}{b}+2 \sqrt{-\frac{a d -b c}{b}}\, \sqrt{\left(x +\frac{\sqrt{-a b}}{b}\right)^{2} d -\frac{2 \sqrt{-a b}\, \left(x +\frac{\sqrt{-a b}}{b}\right) d}{b}-\frac{a d -b c}{b}}}{x +\frac{\sqrt{-a b}}{b}}\right)}{2 \sqrt{-a b}\, \sqrt{-\frac{a d -b c}{b}}}"," ",0,"1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x+(-a*b)^(1/2)/b)^2*d-2*(-a*b)^(1/2)*(x+(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x+(-a*b)^(1/2)/b))-1/2/(-a*b)^(1/2)/(-(a*d-b*c)/b)^(1/2)*ln((2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-2*(a*d-b*c)/b+2*(-(a*d-b*c)/b)^(1/2)*((x-(-a*b)^(1/2)/b)^2*d+2*(-a*b)^(1/2)*(x-(-a*b)^(1/2)/b)/b*d-(a*d-b*c)/b)^(1/2))/(x-(-a*b)^(1/2)/b))","B"
108,1,14,13,0.006000," ","int((x^2-1)/(x^2+1)^(3/2),x)","-\frac{2 x}{\sqrt{x^{2}+1}}+\arcsinh \left(x \right)"," ",0,"arcsinh(x)-2*x/(x^2+1)^(1/2)","A"
109,0,0,516,0.311000," ","int((-b*x^2+a)^(2/3)*(b*x^2+3*a)^3,x)","\int \left(-b \,x^{2}+a \right)^{\frac{2}{3}} \left(b \,x^{2}+3 a \right)^{3}\, dx"," ",0,"int((-b*x^2+a)^(2/3)*(b*x^2+3*a)^3,x)","F"
110,0,0,489,0.303000," ","int((-b*x^2+a)^(2/3)*(b*x^2+3*a)^2,x)","\int \left(-b \,x^{2}+a \right)^{\frac{2}{3}} \left(b \,x^{2}+3 a \right)^{2}\, dx"," ",0,"int((-b*x^2+a)^(2/3)*(b*x^2+3*a)^2,x)","F"
111,0,0,464,0.296000," ","int((-b*x^2+a)^(2/3)*(b*x^2+3*a),x)","\int \left(-b \,x^{2}+a \right)^{\frac{2}{3}} \left(b \,x^{2}+3 a \right)\, dx"," ",0,"int((-b*x^2+a)^(2/3)*(b*x^2+3*a),x)","F"
112,0,0,568,0.314000," ","int((-b*x^2+a)^(2/3)/(b*x^2+3*a),x)","\int \frac{\left(-b \,x^{2}+a \right)^{\frac{2}{3}}}{b \,x^{2}+3 a}\, dx"," ",0,"int((-b*x^2+a)^(2/3)/(b*x^2+3*a),x)","F"
113,0,0,464,0.316000," ","int((-b*x^2+a)^(2/3)/(b*x^2+3*a)^2,x)","\int \frac{\left(-b \,x^{2}+a \right)^{\frac{2}{3}}}{\left(b \,x^{2}+3 a \right)^{2}}\, dx"," ",0,"int((-b*x^2+a)^(2/3)/(b*x^2+3*a)^2,x)","F"
114,0,0,626,0.320000," ","int((-b*x^2+a)^(2/3)/(b*x^2+3*a)^3,x)","\int \frac{\left(-b \,x^{2}+a \right)^{\frac{2}{3}}}{\left(b \,x^{2}+3 a \right)^{3}}\, dx"," ",0,"int((-b*x^2+a)^(2/3)/(b*x^2+3*a)^3,x)","F"
115,0,0,653,0.326000," ","int((-b*x^2+a)^(2/3)/(b*x^2+3*a)^4,x)","\int \frac{\left(-b \,x^{2}+a \right)^{\frac{2}{3}}}{\left(b \,x^{2}+3 a \right)^{4}}\, dx"," ",0,"int((-b*x^2+a)^(2/3)/(b*x^2+3*a)^4,x)","F"
116,0,0,532,0.301000," ","int((-b*x^2+a)^(5/3)*(b*x^2+3*a)^3,x)","\int \left(-b \,x^{2}+a \right)^{\frac{5}{3}} \left(b \,x^{2}+3 a \right)^{3}\, dx"," ",0,"int((-b*x^2+a)^(5/3)*(b*x^2+3*a)^3,x)","F"
117,0,0,505,0.299000," ","int((-b*x^2+a)^(5/3)*(b*x^2+3*a)^2,x)","\int \left(-b \,x^{2}+a \right)^{\frac{5}{3}} \left(b \,x^{2}+3 a \right)^{2}\, dx"," ",0,"int((-b*x^2+a)^(5/3)*(b*x^2+3*a)^2,x)","F"
118,0,0,480,0.300000," ","int((-b*x^2+a)^(5/3)*(b*x^2+3*a),x)","\int \left(-b \,x^{2}+a \right)^{\frac{5}{3}} \left(b \,x^{2}+3 a \right)\, dx"," ",0,"int((-b*x^2+a)^(5/3)*(b*x^2+3*a),x)","F"
119,0,0,583,0.313000," ","int((-b*x^2+a)^(5/3)/(b*x^2+3*a),x)","\int \frac{\left(-b \,x^{2}+a \right)^{\frac{5}{3}}}{b \,x^{2}+3 a}\, dx"," ",0,"int((-b*x^2+a)^(5/3)/(b*x^2+3*a),x)","F"
120,0,0,593,0.333000," ","int((-b*x^2+a)^(5/3)/(b*x^2+3*a)^2,x)","\int \frac{\left(-b \,x^{2}+a \right)^{\frac{5}{3}}}{\left(b \,x^{2}+3 a \right)^{2}}\, dx"," ",0,"int((-b*x^2+a)^(5/3)/(b*x^2+3*a)^2,x)","F"
121,0,0,623,0.363000," ","int((-b*x^2+a)^(5/3)/(b*x^2+3*a)^3,x)","\int \frac{\left(-b \,x^{2}+a \right)^{\frac{5}{3}}}{\left(b \,x^{2}+3 a \right)^{3}}\, dx"," ",0,"int((-b*x^2+a)^(5/3)/(b*x^2+3*a)^3,x)","F"
122,0,0,527,0.409000," ","int((b*x^2+3*a)^4/(-b*x^2+a)^(1/3),x)","\int \frac{\left(b \,x^{2}+3 a \right)^{4}}{\left(-b \,x^{2}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*x^2+3*a)^4/(-b*x^2+a)^(1/3),x)","F"
123,0,0,500,0.298000," ","int((b*x^2+3*a)^3/(-b*x^2+a)^(1/3),x)","\int \frac{\left(b \,x^{2}+3 a \right)^{3}}{\left(-b \,x^{2}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*x^2+3*a)^3/(-b*x^2+a)^(1/3),x)","F"
124,0,0,473,0.300000," ","int((b*x^2+3*a)^2/(-b*x^2+a)^(1/3),x)","\int \frac{\left(b \,x^{2}+3 a \right)^{2}}{\left(-b \,x^{2}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*x^2+3*a)^2/(-b*x^2+a)^(1/3),x)","F"
125,0,0,448,0.300000," ","int((b*x^2+3*a)/(-b*x^2+a)^(1/3),x)","\int \frac{b \,x^{2}+3 a}{\left(-b \,x^{2}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((b*x^2+3*a)/(-b*x^2+a)^(1/3),x)","F"
126,0,0,136,0.310000," ","int(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x)","\int \frac{1}{\left(-b \,x^{2}+a \right)^{\frac{1}{3}} \left(b \,x^{2}+3 a \right)}\, dx"," ",0,"int(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x)","F"
127,0,0,599,0.313000," ","int(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^2,x)","\int \frac{1}{\left(-b \,x^{2}+a \right)^{\frac{1}{3}} \left(b \,x^{2}+3 a \right)^{2}}\, dx"," ",0,"int(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^2,x)","F"
128,0,0,626,0.326000," ","int(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^3,x)","\int \frac{1}{\left(-b \,x^{2}+a \right)^{\frac{1}{3}} \left(b \,x^{2}+3 a \right)^{3}}\, dx"," ",0,"int(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a)^3,x)","F"
129,0,0,497,0.321000," ","int((b*x^2+3*a)^3/(-b*x^2+a)^(4/3),x)","\int \frac{\left(b \,x^{2}+3 a \right)^{3}}{\left(-b \,x^{2}+a \right)^{\frac{4}{3}}}\, dx"," ",0,"int((b*x^2+3*a)^3/(-b*x^2+a)^(4/3),x)","F"
130,0,0,470,0.324000," ","int((b*x^2+3*a)^2/(-b*x^2+a)^(4/3),x)","\int \frac{\left(b \,x^{2}+3 a \right)^{2}}{\left(-b \,x^{2}+a \right)^{\frac{4}{3}}}\, dx"," ",0,"int((b*x^2+3*a)^2/(-b*x^2+a)^(4/3),x)","F"
131,0,0,447,0.312000," ","int((b*x^2+3*a)/(-b*x^2+a)^(4/3),x)","\int \frac{b \,x^{2}+3 a}{\left(-b \,x^{2}+a \right)^{\frac{4}{3}}}\, dx"," ",0,"int((b*x^2+3*a)/(-b*x^2+a)^(4/3),x)","F"
132,0,0,588,0.321000," ","int(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a),x)","\int \frac{1}{\left(-b \,x^{2}+a \right)^{\frac{4}{3}} \left(b \,x^{2}+3 a \right)}\, dx"," ",0,"int(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a),x)","F"
133,0,0,615,0.330000," ","int(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a)^2,x)","\int \frac{1}{\left(-b \,x^{2}+a \right)^{\frac{4}{3}} \left(b \,x^{2}+3 a \right)^{2}}\, dx"," ",0,"int(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a)^2,x)","F"
134,0,0,653,0.328000," ","int(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a)^3,x)","\int \frac{1}{\left(-b \,x^{2}+a \right)^{\frac{4}{3}} \left(b \,x^{2}+3 a \right)^{3}}\, dx"," ",0,"int(1/(-b*x^2+a)^(4/3)/(b*x^2+3*a)^3,x)","F"
135,0,0,521,0.316000," ","int((b*x^2+3*a)^4/(-b*x^2+a)^(7/3),x)","\int \frac{\left(b \,x^{2}+3 a \right)^{4}}{\left(-b \,x^{2}+a \right)^{\frac{7}{3}}}\, dx"," ",0,"int((b*x^2+3*a)^4/(-b*x^2+a)^(7/3),x)","F"
136,0,0,472,0.319000," ","int((b*x^2+3*a)^3/(-b*x^2+a)^(7/3),x)","\int \frac{\left(b \,x^{2}+3 a \right)^{3}}{\left(-b \,x^{2}+a \right)^{\frac{7}{3}}}\, dx"," ",0,"int((b*x^2+3*a)^3/(-b*x^2+a)^(7/3),x)","F"
137,1,24,36,0.005000," ","int((b*x^2+3*a)^2/(-b*x^2+a)^(7/3),x)","\frac{3 \left(-b \,x^{2}+3 a \right) x}{\left(-b \,x^{2}+a \right)^{\frac{4}{3}}}"," ",0,"3/(-b*x^2+a)^(4/3)*x*(-b*x^2+3*a)","A"
138,0,0,466,0.312000," ","int((b*x^2+3*a)/(-b*x^2+a)^(7/3),x)","\int \frac{b \,x^{2}+3 a}{\left(-b \,x^{2}+a \right)^{\frac{7}{3}}}\, dx"," ",0,"int((b*x^2+3*a)/(-b*x^2+a)^(7/3),x)","F"
139,0,0,604,0.329000," ","int(1/(-b*x^2+a)^(7/3)/(b*x^2+3*a),x)","\int \frac{1}{\left(-b \,x^{2}+a \right)^{\frac{7}{3}} \left(b \,x^{2}+3 a \right)}\, dx"," ",0,"int(1/(-b*x^2+a)^(7/3)/(b*x^2+3*a),x)","F"
140,0,0,631,0.334000," ","int(1/(-b*x^2+a)^(7/3)/(b*x^2+3*a)^2,x)","\int \frac{1}{\left(-b \,x^{2}+a \right)^{\frac{7}{3}} \left(b \,x^{2}+3 a \right)^{2}}\, dx"," ",0,"int(1/(-b*x^2+a)^(7/3)/(b*x^2+3*a)^2,x)","F"
141,0,0,172,0.322000," ","int(1/(-b*x^2-3*a)/(b*x^2-a)^(1/3),x)","\int \frac{1}{\left(-b \,x^{2}-3 a \right) \left(b \,x^{2}-a \right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(-b*x^2-3*a)/(b*x^2-a)^(1/3),x)","F"
142,0,0,134,0.319000," ","int(1/(-b*x^2+3*a)/(b*x^2+a)^(1/3),x)","\int \frac{1}{\left(-b \,x^{2}+3 a \right) \left(b \,x^{2}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(-b*x^2+3*a)/(b*x^2+a)^(1/3),x)","F"
143,0,0,136,0.324000," ","int(1/(-d*x^2+c)/(3*d*x^2+c)^(1/3),x)","\int \frac{1}{\left(-d \,x^{2}+c \right) \left(3 d \,x^{2}+c \right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(-d*x^2+c)/(3*d*x^2+c)^(1/3),x)","F"
144,0,0,136,0.000000," ","int(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x)","\int \frac{1}{\left(-b \,x^{2}+a \right)^{\frac{1}{3}} \left(b \,x^{2}+3 a \right)}\, dx"," ",0,"int(1/(-b*x^2+a)^(1/3)/(b*x^2+3*a),x)","F"
145,0,0,136,0.333000," ","int(1/(-3*d*x^2+c)^(1/3)/(d*x^2+c),x)","\int \frac{1}{\left(-3 d \,x^{2}+c \right)^{\frac{1}{3}} \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(1/(-3*d*x^2+c)^(1/3)/(d*x^2+c),x)","F"
146,1,938,81,16.872000," ","int(1/(-x^2+1)^(1/3)/(x^2+3),x)","-\frac{\RootOf \left(\textit{\_Z}^{6}+108\right)^{4} \ln \left(\frac{x^{6} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+72 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+225 x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+36 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-72 x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-189 x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+864 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+648 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{4}-648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+27 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+4536 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{3}-324 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+1944 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{2}-1944 \left(-x^{2}+1\right)^{\frac{2}{3}} x}{\left(x^{2}+3\right)^{3}}\right)}{432}-\frac{\RootOf \left(\textit{\_Z}^{6}+108\right) \ln \left(\frac{x^{6} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+72 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+225 x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+36 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-72 x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-189 x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+864 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+648 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{4}-648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+27 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+4536 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{3}-324 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+1944 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{2}-1944 \left(-x^{2}+1\right)^{\frac{2}{3}} x}{\left(x^{2}+3\right)^{3}}\right)}{72}+\frac{\RootOf \left(\textit{\_Z}^{6}+108\right) \ln \left(-\frac{x^{6} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+6 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{5}-72 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}-108 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{5}+225 x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+144 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{5}-18 x^{6} \RootOf \left(\textit{\_Z}^{6}+108\right)-36 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+72 x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+108 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{5}+1296 x^{5} \RootOf \left(\textit{\_Z}^{6}+108\right)+648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-189 x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}-54 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+108\right)^{5}-4050 x^{4} \RootOf \left(\textit{\_Z}^{6}+108\right)-864 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-1296 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{4}-1296 x^{3} \RootOf \left(\textit{\_Z}^{6}+108\right)-648 \left(-x^{2}+1\right)^{\frac{1}{3}} x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}+27 \RootOf \left(\textit{\_Z}^{6}+108\right)^{4}+9072 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{3}+3402 x^{2} \RootOf \left(\textit{\_Z}^{6}+108\right)+324 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+108\right)^{2}-3888 \left(-x^{2}+1\right)^{\frac{2}{3}} x^{2}-3888 \left(-x^{2}+1\right)^{\frac{2}{3}} x -486 \RootOf \left(\textit{\_Z}^{6}+108\right)}{\left(x^{2}+3\right)^{3}}\right)}{36}"," ",0,"1/36*RootOf(_Z^6+108)*ln(-(-4050*RootOf(_Z^6+108)*x^4+RootOf(_Z^6+108)^4*x^6+225*RootOf(_Z^6+108)^4*x^4-72*x^5*RootOf(_Z^6+108)^4+1296*x^5*RootOf(_Z^6+108)+72*x^3*RootOf(_Z^6+108)^4-189*RootOf(_Z^6+108)^4*x^2+3402*RootOf(_Z^6+108)*x^2-1296*RootOf(_Z^6+108)*x^3+6*RootOf(_Z^6+108)^5*(-x^2+1)^(1/3)*x^5-108*RootOf(_Z^6+108)^5*(-x^2+1)^(1/3)*x^4+144*RootOf(_Z^6+108)^5*(-x^2+1)^(1/3)*x^3+108*RootOf(_Z^6+108)^5*(-x^2+1)^(1/3)*x^2-36*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^5-54*RootOf(_Z^6+108)^5*(-x^2+1)^(1/3)*x+648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^4-864*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^3-648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^2+324*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x-486*RootOf(_Z^6+108)+27*RootOf(_Z^6+108)^4-1296*(-x^2+1)^(2/3)*x^4+9072*(-x^2+1)^(2/3)*x^3-3888*(-x^2+1)^(2/3)*x^2-3888*(-x^2+1)^(2/3)*x-18*RootOf(_Z^6+108)*x^6)/(x^2+3)^3)-1/432*ln((RootOf(_Z^6+108)^4*x^6+72*x^5*RootOf(_Z^6+108)^4+225*RootOf(_Z^6+108)^4*x^4+36*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^5-72*x^3*RootOf(_Z^6+108)^4+648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^4-189*RootOf(_Z^6+108)^4*x^2+864*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^3+648*(-x^2+1)^(2/3)*x^4-648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^2+4536*(-x^2+1)^(2/3)*x^3+27*RootOf(_Z^6+108)^4-324*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x+1944*(-x^2+1)^(2/3)*x^2-1944*(-x^2+1)^(2/3)*x)/(x^2+3)^3)*RootOf(_Z^6+108)^4-1/72*ln((RootOf(_Z^6+108)^4*x^6+72*x^5*RootOf(_Z^6+108)^4+225*RootOf(_Z^6+108)^4*x^4+36*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^5-72*x^3*RootOf(_Z^6+108)^4+648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^4-189*RootOf(_Z^6+108)^4*x^2+864*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^3+648*(-x^2+1)^(2/3)*x^4-648*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x^2+4536*(-x^2+1)^(2/3)*x^3+27*RootOf(_Z^6+108)^4-324*RootOf(_Z^6+108)^2*(-x^2+1)^(1/3)*x+1944*(-x^2+1)^(2/3)*x^2-1944*(-x^2+1)^(2/3)*x)/(x^2+3)^3)*RootOf(_Z^6+108)","C"
147,-1,0,77,180.000000," ","int(1/(-x^2+3)/(x^2+1)^(1/3),x)","\int \frac{1}{\left(-x^{2}+3\right) \left(x^{2}+1\right)^{\frac{1}{3}}}\, dx"," ",0,"int(1/(-x^2+3)/(x^2+1)^(1/3),x)","F"
148,1,1033,70,7.834000," ","int((-x+3)/(-x^2+1)^(1/3)/(x^2+3),x)","\RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \ln \left(-\frac{4 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}+12 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+18 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}+2 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+3 x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-6 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-9 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-18 \left(-x^{2}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-6 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-9 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+9 \RootOf \left(\textit{\_Z}^{3}-2\right)-12 \left(-x^{2}+1\right)^{\frac{2}{3}}}{\left(2 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+x -3\right) \left(2 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+x +3\right)}\right)+\frac{\RootOf \left(\textit{\_Z}^{3}-2\right) \ln \left(\frac{12 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+2 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}+36 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+6 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{3}+6 x^{2} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+x^{2} \RootOf \left(\textit{\_Z}^{3}-2\right)-12 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-9 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-18 \left(-x^{2}+1\right)^{\frac{2}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+36 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)+6 x \RootOf \left(\textit{\_Z}^{3}-2\right)-12 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)-9 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}-18 \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right)-3 \RootOf \left(\textit{\_Z}^{3}-2\right)-6 \left(-x^{2}+1\right)^{\frac{2}{3}}}{\left(2 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+x -3\right) \left(2 x \RootOf \left(4 \textit{\_Z}^{2}+2 \textit{\_Z} \RootOf \left(\textit{\_Z}^{3}-2\right)+\RootOf \left(\textit{\_Z}^{3}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{3}-2\right)^{2}+x +3\right)}\right)}{2}"," ",0,"1/2*RootOf(_Z^3-2)*ln((12*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^2+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^2+36*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x+6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x-18*(-x^2+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2-12*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x-9*(-x^2+1)^(1/3)*RootOf(_Z^3-2)^2*x-12*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2-9*(-x^2+1)^(1/3)*RootOf(_Z^3-2)^2+RootOf(_Z^3-2)*x^2+36*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x+6*RootOf(_Z^3-2)*x-6*(-x^2+1)^(2/3)-18*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)-3*RootOf(_Z^3-2))/(2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+x-3)/(2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+x+3))+RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*ln(-(4*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x^2+6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x^2+12*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)^2*RootOf(_Z^3-2)^2*x+18*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^3*x-18*(-x^2+1)^(2/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2-6*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)*x-9*(-x^2+1)^(1/3)*RootOf(_Z^3-2)^2*x-6*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)+2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*x^2-9*(-x^2+1)^(1/3)*RootOf(_Z^3-2)^2+3*RootOf(_Z^3-2)*x^2-12*(-x^2+1)^(2/3)+6*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)+9*RootOf(_Z^3-2))/(2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+x-3)/(2*RootOf(RootOf(_Z^3-2)^2+2*_Z*RootOf(_Z^3-2)+4*_Z^2)*RootOf(_Z^3-2)^2*x+x+3))","C"
149,1,1553,70,7.621000," ","int((x+3)/(-x^2+1)^(1/3)/(x^2+3),x)","\text{Expression too large to display}"," ",0,"-1/2*ln(-(8*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^2-2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^2-24*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x+6*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x+18*(-x^2+1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2-18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x-6*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2*x+18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^2+6*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2+RootOf(_Z^3+2)*x^2-12*(-x^2+1)^(2/3)-12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)+3*RootOf(_Z^3+2))/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x-3)/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x+3))*RootOf(_Z^3+2)-ln(-(8*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^2-2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^2-24*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x+6*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x+18*(-x^2+1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2-18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x-6*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2*x+18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^2+6*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2+RootOf(_Z^3+2)*x^2-12*(-x^2+1)^(2/3)-12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)+3*RootOf(_Z^3+2))/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x-3)/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x+3))*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)+RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*ln(-(8*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x^2+6*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x^2-24*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)^2*RootOf(_Z^3+2)^2*x-18*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^3*x-18*(-x^2+1)^(2/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2+18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)*x+3*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2*x-18*(-x^2+1)^(1/3)*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)-4*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x^2-3*(-x^2+1)^(1/3)*RootOf(_Z^3+2)^2-3*RootOf(_Z^3+2)*x^2+24*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*x+18*RootOf(_Z^3+2)*x+6*(-x^2+1)^(2/3)+12*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)+9*RootOf(_Z^3+2))/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x-3)/(2*RootOf(RootOf(_Z^3+2)^2+2*_Z*RootOf(_Z^3+2)+4*_Z^2)*RootOf(_Z^3+2)^2*x-x+3))","C"
150,0,0,105,0.322000," ","int(1/(b*x^2+a)^(1/3)/(9*a*d/b+d*x^2),x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{1}{3}} \left(d \,x^{2}+\frac{9 a d}{b}\right)}\, dx"," ",0,"int(1/(b*x^2+a)^(1/3)/(9*a*d/b+d*x^2),x)","F"
151,0,0,107,0.321000," ","int(1/(-b*x^2+a)^(1/3)/(-9*a/b*d+d*x^2),x)","\int \frac{1}{\left(-b \,x^{2}+a \right)^{\frac{1}{3}} \left(d \,x^{2}-\frac{9 a d}{b}\right)}\, dx"," ",0,"int(1/(-b*x^2+a)^(1/3)/(-9*a/b*d+d*x^2),x)","F"
152,0,0,105,0.314000," ","int(1/(b*x^2-a)^(1/3)/(d*x^2-9*a/b*d),x)","\int \frac{1}{\left(b \,x^{2}-a \right)^{\frac{1}{3}} \left(d \,x^{2}-\frac{9 a d}{b}\right)}\, dx"," ",0,"int(1/(b*x^2-a)^(1/3)/(d*x^2-9*a/b*d),x)","F"
153,0,0,107,0.325000," ","int(1/(-b*x^2-a)^(1/3)/(d*x^2+9*a/b*d),x)","\int \frac{1}{\left(-b \,x^{2}-a \right)^{\frac{1}{3}} \left(d \,x^{2}+\frac{9 a d}{b}\right)}\, dx"," ",0,"int(1/(-b*x^2-a)^(1/3)/(d*x^2+9*a/b*d),x)","F"
154,0,0,105,0.317000," ","int(1/(b*x^2+2)^(1/3)/(18/b*d+d*x^2),x)","\int \frac{1}{\left(b \,x^{2}+2\right)^{\frac{1}{3}} \left(d \,x^{2}+\frac{18 d}{b}\right)}\, dx"," ",0,"int(1/(b*x^2+2)^(1/3)/(18/b*d+d*x^2),x)","F"
155,0,0,101,0.322000," ","int(1/(b*x^2-2)^(1/3)/(-18/b*d+d*x^2),x)","\int \frac{1}{\left(b \,x^{2}-2\right)^{\frac{1}{3}} \left(d \,x^{2}-\frac{18 d}{b}\right)}\, dx"," ",0,"int(1/(b*x^2-2)^(1/3)/(-18/b*d+d*x^2),x)","F"
156,1,549,90,58.096000," ","int(1/(3*x^2+2)^(1/3)/(d*x^2+6*d),x)","-\frac{24 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \ln \left(-\frac{192 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{6}-4 x \RootOf \left(\textit{\_Z}^{6}+54\right)^{7}+9 x^{2} \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}-288 \left(3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}+6 \left(3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+54\right)^{5}-18 \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}-108 \left(3 x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+54\right)^{2}+324 \left(3 x^{2}+2\right)^{\frac{2}{3}}}{x^{2}+6}\right)-\RootOf \left(\textit{\_Z}^{6}+54\right) \ln \left(-\frac{768 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}+54\right)^{5}-16 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{6}-36 x^{2} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{3}+1152 \left(3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}+54\right)^{3}-72 \left(3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}+\left(3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+54\right)^{5}+72 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{3}-432 \left(3 x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)+18 \left(3 x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+54\right)^{2}+54 \left(3 x^{2}+2\right)^{\frac{2}{3}}}{x^{2}+6}\right)}{24 d}"," ",0,"-1/24*(24*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*ln(-(192*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^6*x-4*RootOf(_Z^6+54)^7*x-288*(3*x^2+2)^(1/3)*RootOf(_Z^6+54)^4*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*x+6*(3*x^2+2)^(1/3)*RootOf(_Z^6+54)^5*x+9*x^2*RootOf(_Z^6+54)^4-18*RootOf(_Z^6+54)^4-108*RootOf(_Z^6+54)^2*(3*x^2+2)^(1/3)+324*(3*x^2+2)^(2/3))/(x^2+6))-RootOf(_Z^6+54)*ln(-(768*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)^2*RootOf(_Z^6+54)^5*x-16*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^6*x+1152*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)^2*RootOf(_Z^6+54)^3*(3*x^2+2)^(1/3)*x-72*(3*x^2+2)^(1/3)*RootOf(_Z^6+54)^4*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*x+(3*x^2+2)^(1/3)*RootOf(_Z^6+54)^5*x-36*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^3*x^2+72*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^3-432*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)*(3*x^2+2)^(1/3)+18*RootOf(_Z^6+54)^2*(3*x^2+2)^(1/3)+54*(3*x^2+2)^(2/3))/(x^2+6)))/d","C"
157,1,1061,90,59.072000," ","int(1/(-3*x^2+2)^(1/3)/(d*x^2-6*d),x)","\frac{-24 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \ln \left(\frac{-768 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{5}+16 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{6}+36 x^{2} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}+1152 \left(-3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}-72 \left(-3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{4}+\left(-3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}-54\right)^{5}+72 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}+432 \left(-3 x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)-18 \left(-3 x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}-54\right)^{2}+54 \left(-3 x^{2}+2\right)^{\frac{2}{3}}}{x^{2}-6}\right)+24 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \ln \left(\frac{-4608 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{5}+288 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{6}-4 x \RootOf \left(\textit{\_Z}^{6}-54\right)^{7}-216 x^{2} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}+9 x^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{4}+6912 \left(-3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}-144 \left(-3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{4}-432 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}+18 \RootOf \left(\textit{\_Z}^{6}-54\right)^{4}-2592 \left(-3 x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)+324 \left(-3 x^{2}+2\right)^{\frac{2}{3}}}{x^{2}-6}\right)+\RootOf \left(\textit{\_Z}^{6}-54\right) \ln \left(\frac{-768 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{5}+16 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{6}+36 x^{2} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}+1152 \left(-3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}-72 \left(-3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{4}+\left(-3 x^{2}+2\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}-54\right)^{5}+72 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}+432 \left(-3 x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)-18 \left(-3 x^{2}+2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}-54\right)^{2}+54 \left(-3 x^{2}+2\right)^{\frac{2}{3}}}{x^{2}-6}\right)}{24 d}"," ",0,"1/24*(24*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*ln((-4608*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*RootOf(_Z^6-54)^5*x+288*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^6*x-4*RootOf(_Z^6-54)^7*x+6912*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*(-3*x^2+2)^(1/3)*x-144*RootOf(_Z^6-54)^4*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*(-3*x^2+2)^(1/3)*x-216*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*x^2+9*x^2*RootOf(_Z^6-54)^4-432*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^3+18*RootOf(_Z^6-54)^4-2592*RootOf(_Z^6-54)*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*(-3*x^2+2)^(1/3)+324*(-3*x^2+2)^(2/3))/(x^2-6))-24*ln((-768*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*RootOf(_Z^6-54)^5*x+16*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^6*x+1152*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*(-3*x^2+2)^(1/3)*x-72*RootOf(_Z^6-54)^4*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*(-3*x^2+2)^(1/3)*x+(-3*x^2+2)^(1/3)*RootOf(_Z^6-54)^5*x+36*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*x^2+72*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^3+432*RootOf(_Z^6-54)*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*(-3*x^2+2)^(1/3)-18*(-3*x^2+2)^(1/3)*RootOf(_Z^6-54)^2+54*(-3*x^2+2)^(2/3))/(x^2-6))*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)+ln((-768*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*RootOf(_Z^6-54)^5*x+16*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^6*x+1152*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*(-3*x^2+2)^(1/3)*x-72*RootOf(_Z^6-54)^4*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*(-3*x^2+2)^(1/3)*x+(-3*x^2+2)^(1/3)*RootOf(_Z^6-54)^5*x+36*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*x^2+72*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^3+432*RootOf(_Z^6-54)*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*(-3*x^2+2)^(1/3)-18*(-3*x^2+2)^(1/3)*RootOf(_Z^6-54)^2+54*(-3*x^2+2)^(2/3))/(x^2-6))*RootOf(_Z^6-54))/d","C"
158,1,1063,86,58.821000," ","int(1/(3*x^2-2)^(1/3)/(d*x^2-6*d),x)","-\frac{24 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \ln \left(\frac{768 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{5}-16 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{6}+36 x^{2} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}+1152 \left(3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}-72 \left(3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{4}+\left(3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}-54\right)^{5}+72 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}-432 \left(3 x^{2}-2\right)^{\frac{1}{3}} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)+18 \left(3 x^{2}-2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}-54\right)^{2}+54 \left(3 x^{2}-2\right)^{\frac{2}{3}}}{x^{2}-6}\right)+24 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \ln \left(-\frac{4608 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{5}-288 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{6}+4 x \RootOf \left(\textit{\_Z}^{6}-54\right)^{7}+216 x^{2} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}-9 x^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{4}+6912 \left(3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}-144 \left(3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{4}+432 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}-18 \RootOf \left(\textit{\_Z}^{6}-54\right)^{4}-2592 \left(3 x^{2}-2\right)^{\frac{1}{3}} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)-324 \left(3 x^{2}-2\right)^{\frac{2}{3}}}{x^{2}-6}\right)-\RootOf \left(\textit{\_Z}^{6}-54\right) \ln \left(\frac{768 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{5}-16 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{6}+36 x^{2} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}+1152 \left(3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}-72 \left(3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{4}+\left(3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}-54\right)^{5}+72 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)^{3}-432 \left(3 x^{2}-2\right)^{\frac{1}{3}} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}-54\right)+\RootOf \left(\textit{\_Z}^{6}-54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}-54\right)+18 \left(3 x^{2}-2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}-54\right)^{2}+54 \left(3 x^{2}-2\right)^{\frac{2}{3}}}{x^{2}-6}\right)}{24 d}"," ",0,"-1/24*(24*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*ln(-(4608*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*RootOf(_Z^6-54)^5*x-288*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^6*x+4*RootOf(_Z^6-54)^7*x+6912*(3*x^2-2)^(1/3)*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*x-144*(3*x^2-2)^(1/3)*RootOf(_Z^6-54)^4*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*x+216*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*x^2-9*x^2*RootOf(_Z^6-54)^4+432*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^3-18*RootOf(_Z^6-54)^4-2592*(3*x^2-2)^(1/3)*RootOf(_Z^6-54)*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)-324*(3*x^2-2)^(2/3))/(x^2-6))+24*ln((768*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*RootOf(_Z^6-54)^5*x-16*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^6*x+1152*(3*x^2-2)^(1/3)*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*x-72*(3*x^2-2)^(1/3)*RootOf(_Z^6-54)^4*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*x+RootOf(_Z^6-54)^5*(3*x^2-2)^(1/3)*x+36*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*x^2+72*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^3-432*(3*x^2-2)^(1/3)*RootOf(_Z^6-54)*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)+18*RootOf(_Z^6-54)^2*(3*x^2-2)^(1/3)+54*(3*x^2-2)^(2/3))/(x^2-6))*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)-ln((768*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*RootOf(_Z^6-54)^5*x-16*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^6*x+1152*(3*x^2-2)^(1/3)*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)^2*x-72*(3*x^2-2)^(1/3)*RootOf(_Z^6-54)^4*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*x+RootOf(_Z^6-54)^5*(3*x^2-2)^(1/3)*x+36*RootOf(_Z^6-54)^3*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*x^2+72*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)*RootOf(_Z^6-54)^3-432*(3*x^2-2)^(1/3)*RootOf(_Z^6-54)*RootOf(RootOf(_Z^6-54)^2-24*_Z*RootOf(_Z^6-54)+576*_Z^2)+18*RootOf(_Z^6-54)^2*(3*x^2-2)^(1/3)+54*(3*x^2-2)^(2/3))/(x^2-6))*RootOf(_Z^6-54))/d","C"
159,1,725,86,77.110000," ","int(1/(-3*x^2-2)^(1/3)/(d*x^2+6*d),x)","-\frac{-24 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \ln \left(-\frac{192 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{6}-4 x \RootOf \left(\textit{\_Z}^{6}+54\right)^{7}+9 x^{2} \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}+288 \left(-3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}-6 \left(-3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+54\right)^{5}-18 \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}+108 \left(-3 x^{2}-2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+54\right)^{2}+324 \left(-3 x^{2}-2\right)^{\frac{2}{3}}}{x^{2}+6}\right)+\RootOf \left(\textit{\_Z}^{6}+54\right) \ln \left(-\frac{192 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{6}-4 x \RootOf \left(\textit{\_Z}^{6}+54\right)^{7}+9 x^{2} \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}+288 \left(-3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}-6 \left(-3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{6}+54\right)^{5}-18 \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}+108 \left(-3 x^{2}-2\right)^{\frac{1}{3}} \RootOf \left(\textit{\_Z}^{6}+54\right)^{2}+324 \left(-3 x^{2}-2\right)^{\frac{2}{3}}}{x^{2}+6}\right)+\RootOf \left(\textit{\_Z}^{6}+54\right) \ln \left(-\frac{4608 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}+54\right)^{5}-288 x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{6}+4 x \RootOf \left(\textit{\_Z}^{6}+54\right)^{7}+216 x^{2} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{3}-9 x^{2} \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}-6912 \left(-3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right)^{2} \RootOf \left(\textit{\_Z}^{6}+54\right)^{3}+144 \left(-3 x^{2}-2\right)^{\frac{1}{3}} x \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}-432 \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)^{3}+18 \RootOf \left(\textit{\_Z}^{6}+54\right)^{4}-2592 \left(-3 x^{2}-2\right)^{\frac{1}{3}} \RootOf \left(576 \textit{\_Z}^{2}-24 \textit{\_Z} \RootOf \left(\textit{\_Z}^{6}+54\right)+\RootOf \left(\textit{\_Z}^{6}+54\right)^{2}\right) \RootOf \left(\textit{\_Z}^{6}+54\right)+324 \left(-3 x^{2}-2\right)^{\frac{2}{3}}}{x^{2}+6}\right)}{24 d}"," ",0,"-1/24*(RootOf(_Z^6+54)*ln(-(4*RootOf(_Z^6+54)^7*x-288*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^6*x+4608*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)^2*RootOf(_Z^6+54)^5*x+144*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^4*(-3*x^2-2)^(1/3)*x-6912*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)^2*RootOf(_Z^6+54)^3*(-3*x^2-2)^(1/3)*x-9*x^2*RootOf(_Z^6+54)^4+216*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^3*x^2+18*RootOf(_Z^6+54)^4-432*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^3-2592*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)*(-3*x^2-2)^(1/3)+324*(-3*x^2-2)^(2/3))/(x^2+6))+ln(-(-4*RootOf(_Z^6+54)^7*x+192*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^6*x-6*(-3*x^2-2)^(1/3)*RootOf(_Z^6+54)^5*x+288*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^4*(-3*x^2-2)^(1/3)*x+9*x^2*RootOf(_Z^6+54)^4-18*RootOf(_Z^6+54)^4+108*(-3*x^2-2)^(1/3)*RootOf(_Z^6+54)^2+324*(-3*x^2-2)^(2/3))/(x^2+6))*RootOf(_Z^6+54)-24*ln(-(-4*RootOf(_Z^6+54)^7*x+192*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^6*x-6*(-3*x^2-2)^(1/3)*RootOf(_Z^6+54)^5*x+288*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2)*RootOf(_Z^6+54)^4*(-3*x^2-2)^(1/3)*x+9*x^2*RootOf(_Z^6+54)^4-18*RootOf(_Z^6+54)^4+108*(-3*x^2-2)^(1/3)*RootOf(_Z^6+54)^2+324*(-3*x^2-2)^(2/3))/(x^2+6))*RootOf(RootOf(_Z^6+54)^2-24*_Z*RootOf(_Z^6+54)+576*_Z^2))/d","C"
160,1,512,52,10.587000," ","int(1/(x^2+1)^(1/3)/(x^2+9),x)","-\RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right) \ln \left(\frac{-x^{2}+48 \left(x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right)+96 x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right)+2 \left(x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{2}+1\right)+4 x \RootOf \left(\textit{\_Z}^{2}+1\right)-6 \left(x^{2}+1\right)^{\frac{2}{3}}-6 \left(x^{2}+1\right)^{\frac{1}{3}}+3}{x^{2}+9}\right)-\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-x^{2}+48 \left(x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right)+96 x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right)+2 \left(x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(\textit{\_Z}^{2}+1\right)+4 x \RootOf \left(\textit{\_Z}^{2}+1\right)-6 \left(x^{2}+1\right)^{\frac{2}{3}}-6 \left(x^{2}+1\right)^{\frac{1}{3}}+3}{x^{2}+9}\right)}{12}+\frac{\RootOf \left(\textit{\_Z}^{2}+1\right) \ln \left(\frac{-12 x^{2} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right) \RootOf \left(\textit{\_Z}^{2}+1\right)+576 \left(x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+1\right)-1152 x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right)^{2} \RootOf \left(\textit{\_Z}^{2}+1\right)+24 \left(x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right) \RootOf \left(\textit{\_Z}^{2}+1\right)^{2}-48 x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right) \RootOf \left(\textit{\_Z}^{2}+1\right)^{2}+x^{2}+96 x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right)+4 x \RootOf \left(\textit{\_Z}^{2}+1\right)+72 \left(x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right) \RootOf \left(\textit{\_Z}^{2}+1\right)+36 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} \RootOf \left(\textit{\_Z}^{2}+1\right)-1\right) \RootOf \left(\textit{\_Z}^{2}+1\right)-6 \left(x^{2}+1\right)^{\frac{2}{3}}-3}{x^{2}+9}\right)}{12}"," ",0,"1/12*RootOf(_Z^2+1)*ln((24*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)*RootOf(_Z^2+1)^2*(x^2+1)^(1/3)*x+576*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)^2*RootOf(_Z^2+1)*(x^2+1)^(1/3)*x-48*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)*RootOf(_Z^2+1)^2*x-1152*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)^2*RootOf(_Z^2+1)*x-12*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)*RootOf(_Z^2+1)*x^2+72*(x^2+1)^(1/3)*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)*RootOf(_Z^2+1)+36*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)*RootOf(_Z^2+1)+4*RootOf(_Z^2+1)*x+96*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)*x-6*(x^2+1)^(2/3)+x^2-3)/(x^2+9))-ln((2*(x^2+1)^(1/3)*RootOf(_Z^2+1)*x+48*(x^2+1)^(1/3)*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)*x+4*RootOf(_Z^2+1)*x+96*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)*x-6*(x^2+1)^(2/3)-x^2-6*(x^2+1)^(1/3)+3)/(x^2+9))*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)-1/12*ln((2*(x^2+1)^(1/3)*RootOf(_Z^2+1)*x+48*(x^2+1)^(1/3)*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)*x+4*RootOf(_Z^2+1)*x+96*RootOf(12*_Z*RootOf(_Z^2+1)+144*_Z^2-1)*x-6*(x^2+1)^(2/3)-x^2-6*(x^2+1)^(1/3)+3)/(x^2+9))*RootOf(_Z^2+1)","C"
161,0,0,74,0.316000," ","int(1/(b*x^2+1)^(1/3)/(b*x^2+9),x)","\int \frac{1}{\left(b \,x^{2}+1\right)^{\frac{1}{3}} \left(b \,x^{2}+9\right)}\, dx"," ",0,"int(1/(b*x^2+1)^(1/3)/(b*x^2+9),x)","F"
162,1,539,56,2.611000," ","int(1/(-x^2+1)^(1/3)/(-x^2+9),x)","-\RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \ln \left(\frac{-6 x^{2} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+288 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-576 x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+36 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-24 x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+\left(-x^{2}+1\right)^{\frac{1}{3}} x -36 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-18 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+3 \left(-x^{2}+1\right)^{\frac{2}{3}}-3 \left(-x^{2}+1\right)^{\frac{1}{3}}}{\left(x -3\right) \left(x +3\right)}\right)+\RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right) \ln \left(\frac{12 x^{2} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+576 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-1152 x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+x^{2}+24 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-144 x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-4 x +72 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+36 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+6 \left(-x^{2}+1\right)^{\frac{2}{3}}+3}{\left(x -3\right) \left(x +3\right)}\right)-\frac{\ln \left(\frac{-6 x^{2} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+288 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}-576 x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)^{2}+36 \left(-x^{2}+1\right)^{\frac{1}{3}} x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-24 x \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+\left(-x^{2}+1\right)^{\frac{1}{3}} x -36 \left(-x^{2}+1\right)^{\frac{1}{3}} \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)-18 \RootOf \left(144 \textit{\_Z}^{2}+12 \textit{\_Z} +1\right)+3 \left(-x^{2}+1\right)^{\frac{2}{3}}-3 \left(-x^{2}+1\right)^{\frac{1}{3}}}{\left(x -3\right) \left(x +3\right)}\right)}{12}"," ",0,"-1/12*ln((288*RootOf(144*_Z^2+12*_Z+1)^2*(-x^2+1)^(1/3)*x-576*RootOf(144*_Z^2+12*_Z+1)^2*x+36*RootOf(144*_Z^2+12*_Z+1)*(-x^2+1)^(1/3)*x-6*RootOf(144*_Z^2+12*_Z+1)*x^2-36*RootOf(144*_Z^2+12*_Z+1)*(-x^2+1)^(1/3)-24*RootOf(144*_Z^2+12*_Z+1)*x+3*(-x^2+1)^(2/3)+(-x^2+1)^(1/3)*x-18*RootOf(144*_Z^2+12*_Z+1)-3*(-x^2+1)^(1/3))/(x-3)/(x+3))-ln((288*RootOf(144*_Z^2+12*_Z+1)^2*(-x^2+1)^(1/3)*x-576*RootOf(144*_Z^2+12*_Z+1)^2*x+36*RootOf(144*_Z^2+12*_Z+1)*(-x^2+1)^(1/3)*x-6*RootOf(144*_Z^2+12*_Z+1)*x^2-36*RootOf(144*_Z^2+12*_Z+1)*(-x^2+1)^(1/3)-24*RootOf(144*_Z^2+12*_Z+1)*x+3*(-x^2+1)^(2/3)+(-x^2+1)^(1/3)*x-18*RootOf(144*_Z^2+12*_Z+1)-3*(-x^2+1)^(1/3))/(x-3)/(x+3))*RootOf(144*_Z^2+12*_Z+1)+RootOf(144*_Z^2+12*_Z+1)*ln((576*RootOf(144*_Z^2+12*_Z+1)^2*(-x^2+1)^(1/3)*x-1152*RootOf(144*_Z^2+12*_Z+1)^2*x+24*RootOf(144*_Z^2+12*_Z+1)*(-x^2+1)^(1/3)*x+12*RootOf(144*_Z^2+12*_Z+1)*x^2+72*RootOf(144*_Z^2+12*_Z+1)*(-x^2+1)^(1/3)-144*RootOf(144*_Z^2+12*_Z+1)*x+6*(-x^2+1)^(2/3)+x^2+36*RootOf(144*_Z^2+12*_Z+1)-4*x+3)/(x-3)/(x+3))","C"
163,1,94,67,0.026000," ","int((c^2*x^2-1)^(1/2)/(-c^2*d*x^2+d)^(5/2),x)","-\frac{\sqrt{-\left(c^{2} x^{2}-1\right) d}\, \left(-c^{2} x^{2} \ln \left(c x -1\right)+c^{2} x^{2} \ln \left(c x +1\right)-2 c x +\ln \left(c x -1\right)-\ln \left(c x +1\right)\right)}{4 \sqrt{c^{2} x^{2}-1}\, \left(c x +1\right) \left(c x -1\right) c \,d^{3}}"," ",0,"-1/4/(c^2*x^2-1)^(1/2)*(-(c^2*x^2-1)*d)^(1/2)*(ln(c*x+1)*x^2*c^2-ln(c*x-1)*x^2*c^2-2*c*x-ln(c*x+1)+ln(c*x-1))/d^3/c/(c*x+1)/(c*x-1)","A"
164,1,94,62,0.022000," ","int(1/(c^2*x^2-1)^(3/2)/(-c^2*d*x^2+d)^(1/2),x)","-\frac{\sqrt{-\left(c^{2} x^{2}-1\right) d}\, \left(-c^{2} x^{2} \ln \left(c x -1\right)+c^{2} x^{2} \ln \left(c x +1\right)-2 c x +\ln \left(c x -1\right)-\ln \left(c x +1\right)\right)}{4 \sqrt{c^{2} x^{2}-1}\, \left(c x +1\right) \left(c x -1\right) c d}"," ",0,"-1/4/(c^2*x^2-1)^(1/2)*(-(c^2*x^2-1)*d)^(1/2)*(-c^2*x^2*ln(c*x-1)+c^2*x^2*ln(c*x+1)-2*c*x+ln(c*x-1)-ln(c*x+1))/d/c/(c*x+1)/(c*x-1)","A"
165,1,94,64,0.022000," ","int(1/(c^2*x^2-1)^(1/2)/(-c^2*d*x^2+d)^(3/2),x)","\frac{\sqrt{-\left(c^{2} x^{2}-1\right) d}\, \left(-c^{2} x^{2} \ln \left(c x -1\right)+c^{2} x^{2} \ln \left(c x +1\right)-2 c x +\ln \left(c x -1\right)-\ln \left(c x +1\right)\right)}{4 \sqrt{c^{2} x^{2}-1}\, \left(c x +1\right) \left(c x -1\right) c \,d^{2}}"," ",0,"1/4/(c^2*x^2-1)^(1/2)*(-(c^2*x^2-1)*d)^(1/2)*(-c^2*x^2*ln(c*x-1)+c^2*x^2*ln(c*x+1)-2*c*x+ln(c*x-1)-ln(c*x+1))/d^2/c/(c*x+1)/(c*x-1)","A"
166,1,543,356,0.045000," ","int((b*x^2+a)^(3/2)*(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(3 \sqrt{-\frac{b}{a}}\, b^{2} d^{3} x^{7}+9 \sqrt{-\frac{b}{a}}\, a b \,d^{3} x^{5}+4 \sqrt{-\frac{b}{a}}\, b^{2} c \,d^{2} x^{5}+6 \sqrt{-\frac{b}{a}}\, a^{2} d^{3} x^{3}+10 \sqrt{-\frac{b}{a}}\, a b c \,d^{2} x^{3}+\sqrt{-\frac{b}{a}}\, b^{2} c^{2} d \,x^{3}+6 \sqrt{-\frac{b}{a}}\, a^{2} c \,d^{2} x +3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+6 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a b \,c^{2} d x +7 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{15 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, d^{2}}"," ",0,"1/15*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(3*(-1/a*b)^(1/2)*x^7*b^2*d^3+9*(-1/a*b)^(1/2)*x^5*a*b*d^3+4*(-1/a*b)^(1/2)*x^5*b^2*c*d^2+6*(-1/a*b)^(1/2)*x^3*a^2*d^3+10*(-1/a*b)^(1/2)*x^3*a*b*c*d^2+(-1/a*b)^(1/2)*x^3*b^2*c^2*d+6*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*a^2*c*d^2-8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*a*b*c^2*d+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*b^2*c^3+3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*a^2*c*d^2+7*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*a*b*c^2*d-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE(x*(-1/a*b)^(1/2),(a*d/b/c)^(1/2))*b^2*c^3+6*(-1/a*b)^(1/2)*x*a^2*c*d^2+(-1/a*b)^(1/2)*x*a*b*c^2*d)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/d^2/(-1/a*b)^(1/2)","A"
167,1,328,283,0.019000," ","int((b*x^2+a)^(1/2)*(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(\sqrt{-\frac{b}{a}}\, b \,d^{2} x^{5}+\sqrt{-\frac{b}{a}}\, a \,d^{2} x^{3}+\sqrt{-\frac{b}{a}}\, b c d \,x^{3}+\sqrt{-\frac{b}{a}}\, a c d x +\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{3 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, d}"," ",0,"1/3*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*((-1/a*b)^(1/2)*x^5*b*d^2+(-1/a*b)^(1/2)*x^3*a*d^2+(-1/a*b)^(1/2)*x^3*b*c*d+a*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2+(-1/a*b)^(1/2)*x*a*c*d)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)/d","A"
168,1,101,250,0.023000," ","int((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}}"," ",0,"(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)","A"
169,1,181,109,0.045000," ","int((d*x^2+c)^(1/2)/(b*x^2+a)^(3/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}\, \left(\sqrt{-\frac{b}{a}}\, d \,x^{3}+\sqrt{-\frac{b}{a}}\, c x -\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, c \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, a}"," ",0,"(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)*(x^3*d*(-1/a*b)^(1/2)+EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+x*c*(-1/a*b)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/a/(-1/a*b)^(1/2)","A"
170,1,617,277,0.051000," ","int((d*x^2+c)^(1/2)/(b*x^2+a)^(5/2),x)","\frac{\sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{5}-2 \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{5}+2 \sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{3}-2 \sqrt{-\frac{b}{a}}\, a b c d \,x^{3}-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{-\frac{b}{a}}\, b^{2} c^{2} x^{3}+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{-\frac{b}{a}}\, a^{2} c d x -\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-3 \sqrt{-\frac{b}{a}}\, a b \,c^{2} x +2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{3 \sqrt{d \,x^{2}+c}\, \sqrt{-\frac{b}{a}}\, \left(a d -b c \right) \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2}}"," ",0,"1/3*(x^5*a*b*d^2*(-1/a*b)^(1/2)-2*x^5*b^2*c*d*(-1/a*b)^(1/2)+2*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-2*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*b^2*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*b^2*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+2*x^3*a^2*d^2*(-1/a*b)^(1/2)-2*x^3*a*b*c*d*(-1/a*b)^(1/2)-2*x^3*b^2*c^2*(-1/a*b)^(1/2)+2*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-2*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+2*x*a^2*c*d*(-1/a*b)^(1/2)-3*x*a*b*c^2*(-1/a*b)^(1/2))/(d*x^2+c)^(1/2)/(-1/a*b)^(1/2)/(a*d-b*c)/a^2/(b*x^2+a)^(3/2)","B"
171,1,1411,343,0.059000," ","int((d*x^2+c)^(1/2)/(b*x^2+a)^(7/2),x)","-\frac{-3 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} d^{3} x^{7}+13 \sqrt{-\frac{b}{a}}\, a \,b^{3} c \,d^{2} x^{7}-8 \sqrt{-\frac{b}{a}}\, b^{4} c^{2} d \,x^{7}-9 \sqrt{-\frac{b}{a}}\, a^{3} b \,d^{3} x^{5}+30 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c \,d^{2} x^{5}+3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c \,d^{2} x^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-9 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c \,d^{2} x^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-7 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{2} d \,x^{5}-13 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{2} d \,x^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+17 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{2} d \,x^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{-\frac{b}{a}}\, b^{4} c^{3} x^{5}+8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{4} c^{3} x^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{4} c^{3} x^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-9 \sqrt{-\frac{b}{a}}\, a^{4} d^{3} x^{3}+17 \sqrt{-\frac{b}{a}}\, a^{3} b c \,d^{2} x^{3}+6 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b c \,d^{2} x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-18 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b c \,d^{2} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+18 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c^{2} d \,x^{3}-26 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{2} d \,x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+34 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{2} d \,x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-20 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{3} x^{3}+16 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{3} x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-16 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{3} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-9 \sqrt{-\frac{b}{a}}\, a^{4} c \,d^{2} x +3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{4} c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-9 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{4} c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+26 \sqrt{-\frac{b}{a}}\, a^{3} b \,c^{2} d x -13 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b \,c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+17 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b \,c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-15 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c^{3} x +8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{15 \sqrt{d \,x^{2}+c}\, \sqrt{-\frac{b}{a}}\, \left(a d -b c \right)^{2} \left(b \,x^{2}+a \right)^{\frac{5}{2}} a^{3}}"," ",0,"-1/15*(30*x^5*a^2*b^2*c*d^2*(-1/a*b)^(1/2)-7*x^5*a*b^3*c^2*d*(-1/a*b)^(1/2)+17*x^3*a^3*b*c*d^2*(-1/a*b)^(1/2)+18*x^3*a^2*b^2*c^2*d*(-1/a*b)^(1/2)+26*x*a^3*b*c^2*d*(-1/a*b)^(1/2)+8*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*b^4*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-8*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*b^4*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+3*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^4*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+8*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-9*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^4*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-8*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-8*x^5*b^4*c^3*(-1/a*b)^(1/2)-9*x^3*a^4*d^3*(-1/a*b)^(1/2)+13*x^7*a*b^3*c*d^2*(-1/a*b)^(1/2)-3*x^7*a^2*b^2*d^3*(-1/a*b)^(1/2)-13*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a*b^3*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+3*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a^2*b^2*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+34*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^2*b^2*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+6*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^3*b*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+17*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a*b^3*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-9*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a^2*b^2*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-18*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^3*b*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-26*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^2*b^2*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+16*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b^3*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-16*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b^3*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-13*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+17*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-8*x^7*b^4*c^2*d*(-1/a*b)^(1/2)-9*x^5*a^3*b*d^3*(-1/a*b)^(1/2)-20*x^3*a*b^3*c^3*(-1/a*b)^(1/2)-9*x*a^4*c*d^2*(-1/a*b)^(1/2)-15*x*a^2*b^2*c^3*(-1/a*b)^(1/2))/(d*x^2+c)^(1/2)/(-1/a*b)^(1/2)/(a*d-b*c)^2/a^3/(b*x^2+a)^(5/2)","B"
172,1,780,432,0.036000," ","int((b*x^2+a)^(3/2)*(d*x^2+c)^(3/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(5 \sqrt{-\frac{b}{a}}\, b^{3} d^{4} x^{9}+13 \sqrt{-\frac{b}{a}}\, a \,b^{2} d^{4} x^{7}+13 \sqrt{-\frac{b}{a}}\, b^{3} c \,d^{3} x^{7}+9 \sqrt{-\frac{b}{a}}\, a^{2} b \,d^{4} x^{5}+38 \sqrt{-\frac{b}{a}}\, a \,b^{2} c \,d^{3} x^{5}+9 \sqrt{-\frac{b}{a}}\, b^{3} c^{2} d^{2} x^{5}+\sqrt{-\frac{b}{a}}\, a^{3} d^{4} x^{3}+26 \sqrt{-\frac{b}{a}}\, a^{2} b c \,d^{3} x^{3}+26 \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{2} d^{2} x^{3}+\sqrt{-\frac{b}{a}}\, b^{3} c^{3} d \,x^{3}+\sqrt{-\frac{b}{a}}\, a^{3} c \,d^{3} x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} c \,d^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} c \,d^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+17 \sqrt{-\frac{b}{a}}\, a^{2} b \,c^{2} d^{2} x +10 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b \,c^{2} d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b \,c^{2} d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a \,b^{2} c^{3} d x +10 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{3} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-11 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{3} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{35 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, b \,d^{2}}"," ",0,"1/35*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(5*(-1/a*b)^(1/2)*x^9*b^3*d^4+13*(-1/a*b)^(1/2)*x^7*a*b^2*d^4+13*(-1/a*b)^(1/2)*x^7*b^3*c*d^3+9*(-1/a*b)^(1/2)*x^5*a^2*b*d^4+38*(-1/a*b)^(1/2)*x^5*a*b^2*c*d^3+9*(-1/a*b)^(1/2)*x^5*b^3*c^2*d^2+(-1/a*b)^(1/2)*x^3*a^3*d^4+26*(-1/a*b)^(1/2)*x^3*a^2*b*c*d^3+26*(-1/a*b)^(1/2)*x^3*a*b^2*c^2*d^2+(-1/a*b)^(1/2)*x^3*b^3*c^3*d+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*c*d^3+8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c^2*d^2-11*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^3*d+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^3*c^4-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*c*d^3+10*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c^2*d^2+10*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^3*d-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^3*c^4+(-1/a*b)^(1/2)*x*a^3*c*d^3+17*(-1/a*b)^(1/2)*x*a^2*b*c^2*d^2+(-1/a*b)^(1/2)*x*a*b^2*c^3*d)/b/d^2/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)","A"
173,1,545,364,0.026000," ","int((b*x^2+a)^(1/2)*(d*x^2+c)^(3/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(3 \sqrt{-\frac{b}{a}}\, b^{2} d^{3} x^{7}+4 \sqrt{-\frac{b}{a}}\, a b \,d^{3} x^{5}+9 \sqrt{-\frac{b}{a}}\, b^{2} c \,d^{2} x^{5}+\sqrt{-\frac{b}{a}}\, a^{2} d^{3} x^{3}+10 \sqrt{-\frac{b}{a}}\, a b c \,d^{2} x^{3}+6 \sqrt{-\frac{b}{a}}\, b^{2} c^{2} d \,x^{3}+\sqrt{-\frac{b}{a}}\, a^{2} c \,d^{2} x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+6 \sqrt{-\frac{b}{a}}\, a b \,c^{2} d x +7 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{15 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, b d}"," ",0,"1/15*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(3*(-1/a*b)^(1/2)*b^2*d^3*x^7+4*(-1/a*b)^(1/2)*a*b*d^3*x^5+9*(-1/a*b)^(1/2)*b^2*c*d^2*x^5+(-1/a*b)^(1/2)*a^2*d^3*x^3+10*(-1/a*b)^(1/2)*a*b*c*d^2*x^3+6*(-1/a*b)^(1/2)*b^2*c^2*d*x^3+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d-3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d^2+7*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*d+3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^3+(-1/a*b)^(1/2)*a^2*c*d^2*x+6*(-1/a*b)^(1/2)*a*b*c^2*d*x)/d/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/b/(-1/a*b)^(1/2)","A"
174,1,330,307,0.027000," ","int((d*x^2+c)^(3/2)/(b*x^2+a)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}\, \left(\sqrt{-\frac{b}{a}}\, b \,d^{2} x^{5}+\sqrt{-\frac{b}{a}}\, a \,d^{2} x^{3}+\sqrt{-\frac{b}{a}}\, b c d \,x^{3}+\sqrt{-\frac{b}{a}}\, a c d x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+4 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{3 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, b}"," ",0,"1/3*(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)*((-1/a*b)^(1/2)*b*d^2*x^5+(-1/a*b)^(1/2)*a*d^2*x^3+(-1/a*b)^(1/2)*b*c*d*x^3+a*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d+4*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2+(-1/a*b)^(1/2)*a*c*d*x)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/b/(-1/a*b)^(1/2)","A"
175,1,332,309,0.041000," ","int((d*x^2+c)^(3/2)/(b*x^2+a)^(3/2),x)","\frac{\left(-\sqrt{-\frac{b}{a}}\, a \,d^{2} x^{3}+\sqrt{-\frac{b}{a}}\, b c d \,x^{3}-\sqrt{-\frac{b}{a}}\, a c d x +2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, b \,c^{2} x -\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b \,c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right) \sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, a b}"," ",0,"(-(-1/a*b)^(1/2)*a*d^2*x^3+(-1/a*b)^(1/2)*b*c*d*x^3-a*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*c*d-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c^2-(-1/a*b)^(1/2)*a*c*d*x+x*b*c^2*(-1/a*b)^(1/2))*(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)/b/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/a/(-1/a*b)^(1/2)","A"
176,1,607,269,0.046000," ","int((d*x^2+c)^(3/2)/(b*x^2+a)^(5/2),x)","\frac{2 \sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{5}+2 \sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{5}+\sqrt{-\frac{b}{a}}\, a^{2} d^{2} x^{3}+5 \sqrt{-\frac{b}{a}}\, a b c d \,x^{3}-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \,x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{-\frac{b}{a}}\, b^{2} c^{2} x^{3}-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a^{2} c d x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+3 \sqrt{-\frac{b}{a}}\, a b \,c^{2} x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b \,c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{3 \sqrt{d \,x^{2}+c}\, \sqrt{-\frac{b}{a}}\, \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2} b}"," ",0,"1/3*(2*(-1/a*b)^(1/2)*a*b*d^2*x^5+2*(-1/a*b)^(1/2)*b^2*c*d*x^5+EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+2*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*b^2*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*b^2*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+(-1/a*b)^(1/2)*a^2*d^2*x^3+5*(-1/a*b)^(1/2)*a*b*c*d*x^3+2*(-1/a*b)^(1/2)*b^2*c^2*x^3+EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+2*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+(-1/a*b)^(1/2)*a^2*c*d*x+3*(-1/a*b)^(1/2)*a*b*c^2*x)/(d*x^2+c)^(1/2)/a^2/(-1/a*b)^(1/2)/(b*x^2+a)^(3/2)/b","B"
177,1,1410,349,0.051000," ","int((d*x^2+c)^(3/2)/(b*x^2+a)^(7/2),x)","\frac{2 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} d^{3} x^{7}+3 \sqrt{-\frac{b}{a}}\, a \,b^{3} c \,d^{2} x^{7}-8 \sqrt{-\frac{b}{a}}\, b^{4} c^{2} d \,x^{7}+6 \sqrt{-\frac{b}{a}}\, a^{3} b \,d^{3} x^{5}+10 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c \,d^{2} x^{5}-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c \,d^{2} x^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c \,d^{2} x^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-17 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{2} d \,x^{5}-3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{2} d \,x^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+7 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{2} d \,x^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{-\frac{b}{a}}\, b^{4} c^{3} x^{5}+8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{4} c^{3} x^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{4} c^{3} x^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a^{4} d^{3} x^{3}+17 \sqrt{-\frac{b}{a}}\, a^{3} b c \,d^{2} x^{3}-4 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b c \,d^{2} x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b c \,d^{2} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-7 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c^{2} d \,x^{3}-6 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{2} d \,x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+14 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{2} d \,x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-20 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{3} x^{3}+16 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{3} x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-16 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{3} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a^{4} c \,d^{2} x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{4} c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{4} c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+11 \sqrt{-\frac{b}{a}}\, a^{3} b \,c^{2} d x -3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b \,c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+7 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b \,c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-15 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c^{3} x +8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{15 \sqrt{d \,x^{2}+c}\, \left(a d -b c \right) \sqrt{-\frac{b}{a}}\, \left(b \,x^{2}+a \right)^{\frac{5}{2}} a^{3} b}"," ",0,"1/15*(-2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^4*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+8*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^4*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-8*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+10*(-1/a*b)^(1/2)*a^2*b^2*c*d^2*x^5-17*(-1/a*b)^(1/2)*a*b^3*c^2*d*x^5+17*(-1/a*b)^(1/2)*a^3*b*c*d^2*x^3-7*(-1/a*b)^(1/2)*a^2*b^2*c^2*d*x^3+11*(-1/a*b)^(1/2)*a^3*b*c^2*d*x+8*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*b^4*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-8*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*b^4*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-8*(-1/a*b)^(1/2)*b^4*c^3*x^5+(-1/a*b)^(1/2)*a^4*d^3*x^3+3*(-1/a*b)^(1/2)*a*b^3*c*d^2*x^7-3*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a*b^3*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+2*(-1/a*b)^(1/2)*a^2*b^2*d^3*x^7-2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a^2*b^2*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+14*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^2*b^2*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-4*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^3*b*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+7*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a*b^3*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a^2*b^2*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+2*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^3*b*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-6*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^2*b^2*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+x*a^4*c*d^2*(-1/a*b)^(1/2)+16*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b^3*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-16*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b^3*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-3*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+7*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-8*(-1/a*b)^(1/2)*b^4*c^2*d*x^7+6*(-1/a*b)^(1/2)*a^3*b*d^3*x^5-20*(-1/a*b)^(1/2)*a*b^3*c^3*x^3-15*(-1/a*b)^(1/2)*a^2*b^2*c^3*x)/(d*x^2+c)^(1/2)/a^3/(a*d-b*c)/(-1/a*b)^(1/2)/(b*x^2+a)^(5/2)/b","B"
178,1,303,259,0.035000," ","int((b*x^2+2)^(1/2)*(d*x^2+3)^(1/2),x)","\frac{\sqrt{b \,x^{2}+2}\, \sqrt{d \,x^{2}+3}\, \left(\sqrt{-d}\, b^{2} d \,x^{5}+3 \sqrt{-d}\, b^{2} x^{3}+2 \sqrt{-d}\, b d \,x^{3}+6 \sqrt{-d}\, b x +3 \sqrt{2}\, \sqrt{b \,x^{2}+2}\, \sqrt{d \,x^{2}+3}\, b \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{2}\, \sqrt{3}\, \sqrt{\frac{b}{d}}}{2}\right)+3 \sqrt{2}\, \sqrt{b \,x^{2}+2}\, \sqrt{d \,x^{2}+3}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{2}\, \sqrt{3}\, \sqrt{\frac{b}{d}}}{2}\right)+2 \sqrt{2}\, \sqrt{b \,x^{2}+2}\, \sqrt{d \,x^{2}+3}\, d \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{2}\, \sqrt{3}\, \sqrt{\frac{b}{d}}}{2}\right)-2 \sqrt{2}\, \sqrt{b \,x^{2}+2}\, \sqrt{d \,x^{2}+3}\, d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{2}\, \sqrt{3}\, \sqrt{\frac{b}{d}}}{2}\right)\right)}{3 \left(b d \,x^{4}+3 b \,x^{2}+2 d \,x^{2}+6\right) \sqrt{-d}\, b}"," ",0,"1/3*(b*x^2+2)^(1/2)*(d*x^2+3)^(1/2)*(x^5*b^2*d*(-d)^(1/2)+3*x^3*b^2*(-d)^(1/2)+2*x^3*b*d*(-d)^(1/2)+3*2^(1/2)*EllipticF(1/3*x*3^(1/2)*(-d)^(1/2),1/2*2^(1/2)*3^(1/2)*(1/d*b)^(1/2))*b*(b*x^2+2)^(1/2)*(d*x^2+3)^(1/2)-2*2^(1/2)*EllipticF(1/3*x*3^(1/2)*(-d)^(1/2),1/2*2^(1/2)*3^(1/2)*(1/d*b)^(1/2))*d*(b*x^2+2)^(1/2)*(d*x^2+3)^(1/2)+3*2^(1/2)*EllipticE(1/3*x*3^(1/2)*(-d)^(1/2),1/2*2^(1/2)*3^(1/2)*(1/d*b)^(1/2))*b*(b*x^2+2)^(1/2)*(d*x^2+3)^(1/2)+2*2^(1/2)*EllipticE(1/3*x*3^(1/2)*(-d)^(1/2),1/2*2^(1/2)*3^(1/2)*(1/d*b)^(1/2))*d*(b*x^2+2)^(1/2)*(d*x^2+3)^(1/2)+6*x*b*(-d)^(1/2))/(b*d*x^4+3*b*x^2+2*d*x^2+6)/(-d)^(1/2)/b","A"
179,1,75,29,0.036000," ","int((-6*x^2+3)^(1/2)*(4*x^2+2)^(1/2),x)","-\frac{\sqrt{-6 x^{2}+3}\, \sqrt{2}\, \sqrt{2 x^{2}+1}\, \left(-12 x^{5}+3 x +\sqrt{2}\, \sqrt{3}\, \sqrt{-6 x^{2}+3}\, \sqrt{2 x^{2}+1}\, \EllipticF \left(\sqrt{2}\, x , i\right)\right)}{9 \left(4 x^{4}-1\right)}"," ",0,"-1/9*(-6*x^2+3)^(1/2)*2^(1/2)*(2*x^2+1)^(1/2)*(2^(1/2)*3^(1/2)*(-6*x^2+3)^(1/2)*(2*x^2+1)^(1/2)*EllipticF(x*2^(1/2),I)-12*x^5+3*x)/(4*x^4-1)","B"
180,1,38,14,0.003000," ","int((4*x^2+2)^(1/2)*(6*x^2+3)^(1/2),x)","\frac{\left(2 x^{2}+3\right) \sqrt{4 x^{2}+2}\, x}{\sqrt{6 x^{2}+3}}"," ",0,"1/3*x*(2*x^2+3)*(4*x^2+2)^(1/2)*(6*x^2+3)^(1/2)/(2*x^2+1)","C"
181,1,37,216,0.027000," ","int((b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x)","\frac{\sqrt{2}\, \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{2}\, \sqrt{3}\, \sqrt{\frac{b}{d}}}{2}\right)}{\sqrt{-d}}"," ",0,"EllipticE(1/3*3^(1/2)*(-d)^(1/2)*x,1/2*2^(1/2)*3^(1/2)*(b/d)^(1/2))*2^(1/2)/(-d)^(1/2)","A"
182,1,78,85,0.033000," ","int((-x^2+4)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\left(-c \EllipticE \left(\frac{x}{2}, 2 \sqrt{-\frac{d}{c}}\right)+c \EllipticF \left(\frac{x}{2}, 2 \sqrt{-\frac{d}{c}}\right)+4 d \EllipticF \left(\frac{x}{2}, 2 \sqrt{-\frac{d}{c}}\right)\right) \sqrt{\frac{d \,x^{2}+c}{c}}}{\sqrt{d \,x^{2}+c}\, d}"," ",0,"(c*EllipticF(1/2*x,2*(-d/c)^(1/2))+4*EllipticF(1/2*x,2*(-d/c)^(1/2))*d-c*EllipticE(1/2*x,2*(-d/c)^(1/2)))*((d*x^2+c)/c)^(1/2)/(d*x^2+c)^(1/2)/d","A"
183,1,53,148,0.032000," ","int((x^2+4)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \frac{\sqrt{\frac{c}{d}}}{2}\right)}{\sqrt{d \,x^{2}+c}\, \sqrt{-\frac{d}{c}}}"," ",0,"2*EllipticE(x*(-1/c*d)^(1/2),1/2*(c/d)^(1/2))*((d*x^2+c)/c)^(1/2)/(d*x^2+c)^(1/2)/(-1/c*d)^(1/2)","A"
184,1,23,17,0.023000," ","int((-x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \left(2 \EllipticE \left(x , \frac{\sqrt{6}}{2}\right)+\EllipticF \left(x , \frac{\sqrt{6}}{2}\right)\right)}{6}"," ",0,"1/6*2^(1/2)*(EllipticF(x,1/2*6^(1/2))+2*EllipticE(x,1/2*6^(1/2)))","A"
185,1,18,17,0.036000," ","int((-x^2+4)^(1/2)/(-3*x^2+2)^(1/2),x)","\frac{2 \sqrt{3}\, \EllipticE \left(\frac{\sqrt{6}\, x}{2}, \frac{\sqrt{6}}{6}\right)}{3}"," ",0,"2/3*EllipticE(1/2*x*6^(1/2),1/6*6^(1/2))*3^(1/2)","A"
186,1,29,17,0.028000," ","int((-4*x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x)","-\frac{\sqrt{2}\, \left(-8 \EllipticE \left(2 x , \frac{\sqrt{6}}{4}\right)+5 \EllipticF \left(2 x , \frac{\sqrt{6}}{4}\right)\right)}{12}"," ",0,"-1/12*2^(1/2)*(5*EllipticF(2*x,1/4*6^(1/2))-8*EllipticE(2*x,1/4*6^(1/2)))","A"
187,1,5,4,0.020000," ","int((x^2+1)^(1/2)/(-x^2+1)^(1/2),x)","\EllipticE \left(x , i\right)"," ",0,"EllipticE(x,I)","A"
188,1,19,18,0.021000," ","int((x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x)","\frac{\sqrt{3}\, \EllipticE \left(\frac{\sqrt{6}\, x}{2}, \frac{i \sqrt{6}}{3}\right)}{3}"," ",0,"1/3*EllipticE(1/2*6^(1/2)*x,1/3*I*6^(1/2))*3^(1/2)","A"
189,1,19,18,0.021000," ","int((x^2+4)^(1/2)/(-3*x^2+2)^(1/2),x)","\frac{2 \sqrt{3}\, \EllipticE \left(\frac{\sqrt{6}\, x}{2}, \frac{i \sqrt{6}}{6}\right)}{3}"," ",0,"2/3*EllipticE(1/2*6^(1/2)*x,1/6*I*6^(1/2))*3^(1/2)","A"
190,1,19,18,0.032000," ","int((4*x^2+1)^(1/2)/(-3*x^2+2)^(1/2),x)","\frac{\sqrt{3}\, \EllipticE \left(\frac{\sqrt{6}\, x}{2}, \frac{2 i \sqrt{6}}{3}\right)}{3}"," ",0,"1/3*EllipticE(1/2*6^(1/2)*x,2/3*I*6^(1/2))*3^(1/2)","A"
191,1,14,13,0.009000," ","int((-x^2+1)^(1/2)/(x^2+1)^(1/2),x)","-\EllipticE \left(x , i\right)+2 \EllipticF \left(x , i\right)"," ",0,"-EllipticE(x,I)+2*EllipticF(x,I)","A"
192,1,27,27,0.018000," ","int((-x^2+1)^(1/2)/(3*x^2+2)^(1/2),x)","\frac{\left(-2 \EllipticE \left(x , \frac{i \sqrt{6}}{2}\right)+5 \EllipticF \left(x , \frac{i \sqrt{6}}{2}\right)\right) \sqrt{2}}{6}"," ",0,"1/6*(5*EllipticF(x,1/2*I*6^(1/2))-2*EllipticE(x,1/2*I*6^(1/2)))*2^(1/2)","A"
193,1,31,31,0.031000," ","int((-x^2+4)^(1/2)/(3*x^2+2)^(1/2),x)","\frac{\left(-\EllipticE \left(\frac{x}{2}, i \sqrt{6}\right)+7 \EllipticF \left(\frac{x}{2}, i \sqrt{6}\right)\right) \sqrt{2}}{3}"," ",0,"1/3*(7*EllipticF(1/2*x,I*6^(1/2))-EllipticE(1/2*x,I*6^(1/2)))*2^(1/2)","A"
194,1,31,31,0.022000," ","int((-4*x^2+1)^(1/2)/(3*x^2+2)^(1/2),x)","\frac{\left(-8 \EllipticE \left(2 x , \frac{i \sqrt{6}}{4}\right)+11 \EllipticF \left(2 x , \frac{i \sqrt{6}}{4}\right)\right) \sqrt{2}}{12}"," ",0,"1/12*(11*EllipticF(2*x,1/4*I*6^(1/2))-8*EllipticE(2*x,1/4*I*6^(1/2)))*2^(1/2)","A"
195,1,30,132,0.020000," ","int((x^2+1)^(1/2)/(3*x^2+2)^(1/2),x)","-\frac{i \left(2 \EllipticE \left(i x , \frac{\sqrt{6}}{2}\right)+\EllipticF \left(i x , \frac{\sqrt{6}}{2}\right)\right) \sqrt{2}}{6}"," ",0,"-1/6*I*(EllipticF(I*x,1/2*6^(1/2))+2*EllipticE(I*x,1/2*6^(1/2)))*2^(1/2)","A"
196,1,26,132,0.019000," ","int((x^2+4)^(1/2)/(3*x^2+2)^(1/2),x)","-\frac{i \left(\EllipticE \left(\frac{i x}{2}, \sqrt{6}\right)+5 \EllipticF \left(\frac{i x}{2}, \sqrt{6}\right)\right) \sqrt{2}}{3}"," ",0,"-1/3*I*(5*EllipticF(1/2*I*x,6^(1/2))+EllipticE(1/2*I*x,6^(1/2)))*2^(1/2)","A"
197,1,20,146,0.030000," ","int((4*x^2+1)^(1/2)/(3*x^2+2)^(1/2),x)","-\frac{i \sqrt{3}\, \EllipticE \left(\frac{i \sqrt{6}\, x}{2}, \frac{2 \sqrt{6}}{3}\right)}{3}"," ",0,"-1/3*I*EllipticE(1/2*I*x*6^(1/2),2/3*6^(1/2))*3^(1/2)","C"
198,1,32,34,0.015000," ","int((-x^2+1)^(1/2)/(2*x^2-1)^(1/2),x)","\frac{\left(\EllipticE \left(x , \sqrt{2}\right)+\EllipticF \left(x , \sqrt{2}\right)\right) \sqrt{-2 x^{2}+1}}{2 \sqrt{2 x^{2}-1}}"," ",0,"1/2*(EllipticF(x,2^(1/2))+EllipticE(x,2^(1/2)))*(-2*x^2+1)^(1/2)/(2*x^2-1)^(1/2)","A"
199,1,852,445,0.041000," ","int((b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(15 \sqrt{-\frac{b}{a}}\, b^{4} d^{4} x^{9}+81 \sqrt{-\frac{b}{a}}\, a \,b^{3} d^{4} x^{7}-3 \sqrt{-\frac{b}{a}}\, b^{4} c \,d^{3} x^{7}+188 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} d^{4} x^{5}-26 \sqrt{-\frac{b}{a}}\, a \,b^{3} c \,d^{3} x^{5}+6 \sqrt{-\frac{b}{a}}\, b^{4} c^{2} d^{2} x^{5}+122 \sqrt{-\frac{b}{a}}\, a^{3} b \,d^{4} x^{3}+99 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c \,d^{3} x^{3}-83 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{2} d^{2} x^{3}+24 \sqrt{-\frac{b}{a}}\, b^{4} c^{3} d \,x^{3}+105 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{4} d^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+122 \sqrt{-\frac{b}{a}}\, a^{3} b c \,d^{3} x +176 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b c \,d^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-298 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b c \,d^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-89 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c^{2} d^{2} x -264 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{2} d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+353 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{2} d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+24 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{3} d x +184 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{3} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-208 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{3} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-48 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{4} c^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+48 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{4} c^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{105 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, d^{4}}"," ",0,"1/105*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(15*(-1/a*b)^(1/2)*x^9*b^4*d^4+81*(-1/a*b)^(1/2)*x^7*a*b^3*d^4-3*(-1/a*b)^(1/2)*x^7*b^4*c*d^3+188*(-1/a*b)^(1/2)*x^5*a^2*b^2*d^4-26*(-1/a*b)^(1/2)*x^5*a*b^3*c*d^3+6*(-1/a*b)^(1/2)*x^5*b^4*c^2*d^2+122*(-1/a*b)^(1/2)*x^3*a^3*b*d^4+99*(-1/a*b)^(1/2)*x^3*a^2*b^2*c*d^3-83*(-1/a*b)^(1/2)*x^3*a*b^3*c^2*d^2+24*(-1/a*b)^(1/2)*x^3*b^4*c^3*d+105*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^4*d^4-298*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c*d^3+353*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^2*d^2-208*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^3*c^3*d+48*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^4*c^4+176*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c*d^3-264*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^2*d^2+184*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^3*c^3*d-48*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^4*c^4+122*(-1/a*b)^(1/2)*x*a^3*b*c*d^3-89*(-1/a*b)^(1/2)*x*a^2*b^2*c^2*d^2+24*(-1/a*b)^(1/2)*x*a*b^3*c^3*d)/d^4/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)","A"
200,1,615,372,0.031000," ","int((b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(3 \sqrt{-\frac{b}{a}}\, b^{3} d^{3} x^{7}+14 \sqrt{-\frac{b}{a}}\, a \,b^{2} d^{3} x^{5}-\sqrt{-\frac{b}{a}}\, b^{3} c \,d^{2} x^{5}+11 \sqrt{-\frac{b}{a}}\, a^{2} b \,d^{3} x^{3}+10 \sqrt{-\frac{b}{a}}\, a \,b^{2} c \,d^{2} x^{3}-4 \sqrt{-\frac{b}{a}}\, b^{3} c^{2} d \,x^{3}+15 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} d^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+11 \sqrt{-\frac{b}{a}}\, a^{2} b c \,d^{2} x +23 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-34 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-4 \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{2} d x -23 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+27 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{15 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, d^{3}}"," ",0,"1/15*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(3*(-1/a*b)^(1/2)*x^7*b^3*d^3+14*(-1/a*b)^(1/2)*x^5*a*b^2*d^3-(-1/a*b)^(1/2)*x^5*b^3*c*d^2+11*(-1/a*b)^(1/2)*x^3*a^2*b*d^3+10*(-1/a*b)^(1/2)*x^3*a*b^2*c*d^2-4*(-1/a*b)^(1/2)*x^3*b^3*c^2*d+15*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*d^3-34*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c*d^2+27*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^2*d-8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^3*c^3+23*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c*d^2-23*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^2*d+8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^3*c^3+11*(-1/a*b)^(1/2)*x*a^2*b*c*d^2-4*(-1/a*b)^(1/2)*x*a*b^2*c^2*d)/d^3/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)","A"
201,1,399,294,0.027000," ","int((b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(\sqrt{-\frac{b}{a}}\, b^{2} d^{2} x^{5}+\sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{3}+\sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{3}+3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, a b c d x +4 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-5 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{3 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, d^{2}}"," ",0,"1/3*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*((-1/a*b)^(1/2)*x^5*b^2*d^2+(-1/a*b)^(1/2)*x^3*a*b*d^2+(-1/a*b)^(1/2)*x^3*b^2*c*d+3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*d^2-5*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c*d+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^2+4*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c*d-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^2+(-1/a*b)^(1/2)*x*a*b*c*d)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/d^2/(-1/a*b)^(1/2)","A"
202,1,158,240,0.020000," ","int((b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \left(a d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+b c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-b c \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, d}"," ",0,"(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*(a*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d-b*c*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))+b*c*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2)))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)/d","A"
203,1,100,112,0.030000," ","int(1/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{\sqrt{-\frac{b}{a}}\, \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)}"," ",0,"EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","A"
204,1,248,315,0.043000," ","int(1/(b*x^2+a)^(3/2)/(d*x^2+c)^(1/2),x)","\frac{\left(-\sqrt{-\frac{b}{a}}\, b d \,x^{3}+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{-\frac{b}{a}}\, b c x +\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, b c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, b c \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right) \sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}}{\sqrt{-\frac{b}{a}}\, \left(a d -b c \right) \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) a}"," ",0,"(-x^3*b*d*(-1/a*b)^(1/2)+EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*d*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)-EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)+EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)-x*b*c*(-1/a*b)^(1/2))*(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)/(-1/a*b)^(1/2)/a/(a*d-b*c)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","A"
205,1,752,295,0.056000," ","int(1/(b*x^2+a)^(5/2)/(d*x^2+c)^(1/2),x)","\frac{-4 \sqrt{-\frac{b}{a}}\, a \,b^{2} d^{2} x^{5}+2 \sqrt{-\frac{b}{a}}\, b^{3} c d \,x^{5}-5 \sqrt{-\frac{b}{a}}\, a^{2} b \,d^{2} x^{3}+3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b \,d^{2} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{-\frac{b}{a}}\, a \,b^{2} c d \,x^{3}+4 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c d \,x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-5 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c d \,x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{-\frac{b}{a}}\, b^{3} c^{2} x^{3}-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{2} x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{2} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-5 \sqrt{-\frac{b}{a}}\, a^{2} b c d x +4 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-5 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+3 \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{2} x -2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{3 \sqrt{d \,x^{2}+c}\, \left(a d -b c \right)^{2} \sqrt{-\frac{b}{a}}\, \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2}}"," ",0,"1/3*(-4*x^5*a*b^2*d^2*(-1/a*b)^(1/2)+2*x^5*b^3*c*d*(-1/a*b)^(1/2)+3*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^2*b*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-5*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b^2*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+2*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*b^3*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+4*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b^2*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*b^3*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-5*x^3*a^2*b*d^2*(-1/a*b)^(1/2)-x^3*a*b^2*c*d*(-1/a*b)^(1/2)+2*x^3*b^3*c^2*(-1/a*b)^(1/2)+3*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-5*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+2*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+4*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-5*x*a^2*b*c*d*(-1/a*b)^(1/2)+3*x*a*b^2*c^2*(-1/a*b)^(1/2))/(d*x^2+c)^(1/2)/(a*d-b*c)^2/a^2/(-1/a*b)^(1/2)/(b*x^2+a)^(3/2)","B"
206,1,1607,368,0.069000," ","int(1/(b*x^2+a)^(7/2)/(d*x^2+c)^(1/2),x)","\frac{-23 \sqrt{-\frac{b}{a}}\, a^{2} b^{3} d^{3} x^{7}+23 \sqrt{-\frac{b}{a}}\, a \,b^{4} c \,d^{2} x^{7}-8 \sqrt{-\frac{b}{a}}\, b^{5} c^{2} d \,x^{7}-54 \sqrt{-\frac{b}{a}}\, a^{3} b^{2} d^{3} x^{5}+15 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b^{2} d^{3} x^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+35 \sqrt{-\frac{b}{a}}\, a^{2} b^{3} c \,d^{2} x^{5}+23 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{3} c \,d^{2} x^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-34 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{3} c \,d^{2} x^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+3 \sqrt{-\frac{b}{a}}\, a \,b^{4} c^{2} d \,x^{5}-23 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{4} c^{2} d \,x^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+27 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{4} c^{2} d \,x^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{-\frac{b}{a}}\, b^{5} c^{3} x^{5}+8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{5} c^{3} x^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{5} c^{3} x^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-34 \sqrt{-\frac{b}{a}}\, a^{4} b \,d^{3} x^{3}+30 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{4} b \,d^{3} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-13 \sqrt{-\frac{b}{a}}\, a^{3} b^{2} c \,d^{2} x^{3}+46 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b^{2} c \,d^{2} x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-68 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b^{2} c \,d^{2} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+43 \sqrt{-\frac{b}{a}}\, a^{2} b^{3} c^{2} d \,x^{3}-46 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{3} c^{2} d \,x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+54 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{3} c^{2} d \,x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-20 \sqrt{-\frac{b}{a}}\, a \,b^{4} c^{3} x^{3}+16 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{4} c^{3} x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-16 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{4} c^{3} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+15 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{5} d^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-34 \sqrt{-\frac{b}{a}}\, a^{4} b c \,d^{2} x +23 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{4} b c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-34 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{4} b c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+41 \sqrt{-\frac{b}{a}}\, a^{3} b^{2} c^{2} d x -23 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b^{2} c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+27 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b^{2} c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-15 \sqrt{-\frac{b}{a}}\, a^{2} b^{3} c^{3} x +8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{3} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{3} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{15 \sqrt{d \,x^{2}+c}\, \left(a d -b c \right)^{3} \sqrt{-\frac{b}{a}}\, \left(b \,x^{2}+a \right)^{\frac{5}{2}} a^{3}}"," ",0,"1/15*(-23*x^7*a^2*b^3*d^3*(-1/a*b)^(1/2)-13*x^3*a^3*b^2*c*d^2*(-1/a*b)^(1/2)-8*x^5*b^5*c^3*(-1/a*b)^(1/2)+43*x^3*a^2*b^3*c^2*d*(-1/a*b)^(1/2)-34*x*a^4*b*c*d^2*(-1/a*b)^(1/2)+23*x^7*a*b^4*c*d^2*(-1/a*b)^(1/2)+41*x*a^3*b^2*c^2*d*(-1/a*b)^(1/2)+35*x^5*a^2*b^3*c*d^2*(-1/a*b)^(1/2)+3*x^5*a*b^4*c^2*d*(-1/a*b)^(1/2)+8*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*b^5*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-8*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*b^5*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+8*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^3*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+46*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^3*b^2*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-8*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^3*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-8*x^7*b^5*c^2*d*(-1/a*b)^(1/2)-54*x^5*a^3*b^2*d^3*(-1/a*b)^(1/2)-34*x^3*a^4*b*d^3*(-1/a*b)^(1/2)-20*x^3*a*b^4*c^3*(-1/a*b)^(1/2)-15*x*a^2*b^3*c^3*(-1/a*b)^(1/2)+15*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^5*d^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+15*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a^3*b^2*d^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+16*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b^4*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+30*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^4*b*d^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-16*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b^4*c^3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+23*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^4*b*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-23*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b^2*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-34*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^4*b*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+27*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b^2*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-46*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^2*b^3*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-68*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^3*b^2*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+54*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^2*b^3*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+23*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a^2*b^3*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-23*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a*b^4*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)-34*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a^2*b^3*c*d^2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)+27*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^4*a*b^4*c^2*d*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2))/(d*x^2+c)^(1/2)/(a*d-b*c)^3/(-1/a*b)^(1/2)/a^3/(b*x^2+a)^(5/2)","B"
207,1,755,469,0.072000," ","int((b*x^2+a)^(7/2)/(d*x^2+c)^(3/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(3 \sqrt{-\frac{b}{a}}\, b^{4} c \,d^{3} x^{7}+19 \sqrt{-\frac{b}{a}}\, a \,b^{3} c \,d^{3} x^{5}-6 \sqrt{-\frac{b}{a}}\, b^{4} c^{2} d^{2} x^{5}+15 \sqrt{-\frac{b}{a}}\, a^{3} b \,d^{4} x^{3}-29 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c \,d^{3} x^{3}+55 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{2} d^{2} x^{3}-24 \sqrt{-\frac{b}{a}}\, b^{4} c^{3} d \,x^{3}+15 \sqrt{-\frac{b}{a}}\, a^{4} d^{4} x -45 \sqrt{-\frac{b}{a}}\, a^{3} b c \,d^{3} x -15 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b c \,d^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+60 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{3} b c \,d^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+61 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c^{2} d^{2} x +103 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{2} d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-164 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b^{2} c^{2} d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-24 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{3} d x -128 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{3} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+152 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{3} c^{3} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+48 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{4} c^{4} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-48 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{4} c^{4} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{15 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, c \,d^{4}}"," ",0,"1/15*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(3*(-1/a*b)^(1/2)*b^4*c*d^3*x^7+19*(-1/a*b)^(1/2)*a*b^3*c*d^3*x^5-6*(-1/a*b)^(1/2)*b^4*c^2*d^2*x^5+15*(-1/a*b)^(1/2)*a^3*b*d^4*x^3-29*(-1/a*b)^(1/2)*a^2*b^2*c*d^3*x^3+55*(-1/a*b)^(1/2)*a*b^3*c^2*d^2*x^3-24*(-1/a*b)^(1/2)*b^4*c^3*d*x^3+60*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c*d^3-164*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^2*d^2+152*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^3*c^3*d-48*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^4*c^4-15*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c*d^3+103*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^2*d^2-128*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^3*c^3*d+48*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^4*c^4+15*x*a^4*d^4*(-1/a*b)^(1/2)-45*(-1/a*b)^(1/2)*a^3*b*c*d^3*x+61*(-1/a*b)^(1/2)*a^2*b^2*c^2*d^2*x-24*(-1/a*b)^(1/2)*a*b^3*c^3*d*x)/d^4/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)/c","A"
208,1,539,376,0.047000," ","int((b*x^2+a)^(5/2)/(d*x^2+c)^(3/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(\sqrt{-\frac{b}{a}}\, b^{3} c \,d^{2} x^{5}+3 \sqrt{-\frac{b}{a}}\, a^{2} b \,d^{3} x^{3}-5 \sqrt{-\frac{b}{a}}\, a \,b^{2} c \,d^{2} x^{3}+4 \sqrt{-\frac{b}{a}}\, b^{3} c^{2} d \,x^{3}+3 \sqrt{-\frac{b}{a}}\, a^{3} d^{3} x -6 \sqrt{-\frac{b}{a}}\, a^{2} b c \,d^{2} x -3 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+9 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a^{2} b c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+4 \sqrt{-\frac{b}{a}}\, a \,b^{2} c^{2} d x +13 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-17 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a \,b^{2} c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+8 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{3} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{3 \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, c \,d^{3}}"," ",0,"1/3*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*((-1/a*b)^(1/2)*b^3*c*d^2*x^5+3*(-1/a*b)^(1/2)*a^2*b*d^3*x^3-5*(-1/a*b)^(1/2)*a*b^2*c*d^2*x^3+4*(-1/a*b)^(1/2)*b^3*c^2*d*x^3+9*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c*d^2-17*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^2*d+8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^3*c^3-3*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b*c*d^2+13*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^2*c^2*d-8*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^3*c^3+3*x*a^3*d^3*(-1/a*b)^(1/2)-6*(-1/a*b)^(1/2)*a^2*b*c*d^2*x+4*(-1/a*b)^(1/2)*a*b^2*c^2*d*x)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/d^3/c/(-1/a*b)^(1/2)","A"
209,1,345,300,0.040000," ","int((b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(\sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{3}-\sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{3}+\sqrt{-\frac{b}{a}}\, a^{2} d^{2} x -\sqrt{-\frac{b}{a}}\, a b c d x -\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-2 \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, c \,d^{2}}"," ",0,"(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*((-1/a*b)^(1/2)*a*b*d^2*x^3-(-1/a*b)^(1/2)*b^2*c*d*x^3+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c*d-2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^2-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c*d+2*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^2+x*a^2*d^2*(-1/a*b)^(1/2)-(-1/a*b)^(1/2)*a*b*c*d*x)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/d^2/c/(-1/a*b)^(1/2)","A"
210,1,188,109,0.031000," ","int((b*x^2+a)^(1/2)/(d*x^2+c)^(3/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \left(\sqrt{-\frac{b}{a}}\, b d \,x^{3}+\sqrt{-\frac{b}{a}}\, a d x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, b c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, b c \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, c d}"," ",0,"(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*((-1/a*b)^(1/2)*b*d*x^3+EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)-EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)+x*a*d*(-1/a*b)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/c/d/(-1/a*b)^(1/2)","A"
211,1,144,244,0.043000," ","int(1/(b*x^2+a)^(1/2)/(d*x^2+c)^(3/2),x)","\frac{\left(\sqrt{-\frac{b}{a}}\, b d \,x^{3}+\sqrt{-\frac{b}{a}}\, a d x -\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, b c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right) \sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}}{\sqrt{-\frac{b}{a}}\, \left(a d -b c \right) \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) c}"," ",0,"((-1/a*b)^(1/2)*b*d*x^3-EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b*c*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)+(-1/a*b)^(1/2)*a*d*x)*(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)/c/(-1/a*b)^(1/2)/(a*d-b*c)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","A"
212,1,354,288,0.052000," ","int(1/(b*x^2+a)^(3/2)/(d*x^2+c)^(3/2),x)","\frac{\left(\sqrt{-\frac{b}{a}}\, a b \,d^{2} x^{3}+\sqrt{-\frac{b}{a}}\, b^{2} c d \,x^{3}+\sqrt{-\frac{b}{a}}\, a^{2} d^{2} x -\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, a b c d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{-\frac{b}{a}}\, b^{2} c^{2} x -\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, b^{2} c^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right) \sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}}{\sqrt{-\frac{b}{a}}\, \left(a d -b c \right)^{2} \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) a c}"," ",0,"((-1/a*b)^(1/2)*a*b*d^2*x^3+(-1/a*b)^(1/2)*b^2*c*d*x^3-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c*d+((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^2-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b*c*d-((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*b^2*c^2+(-1/a*b)^(1/2)*a^2*d^2*x+x*b^2*c^2*(-1/a*b)^(1/2))*(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)/a/c/(-1/a*b)^(1/2)/(a*d-b*c)^2/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","A"
213,1,964,357,0.066000," ","int(1/(b*x^2+a)^(5/2)/(d*x^2+c)^(3/2),x)","-\frac{-3 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} d^{3} x^{5}-7 \sqrt{-\frac{b}{a}}\, a \,b^{3} c \,d^{2} x^{5}+2 \sqrt{-\frac{b}{a}}\, b^{4} c^{2} d \,x^{5}-6 \sqrt{-\frac{b}{a}}\, a^{3} b \,d^{3} x^{3}-8 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c \,d^{2} x^{3}+3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a^{2} b^{2} c \,d^{2} x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a^{2} b^{2} c \,d^{2} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-4 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{2} d \,x^{3}+7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a \,b^{3} c^{2} d \,x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a \,b^{3} c^{2} d \,x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{-\frac{b}{a}}\, b^{4} c^{3} x^{3}-2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, b^{4} c^{3} x^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, b^{4} c^{3} x^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-3 \sqrt{-\frac{b}{a}}\, a^{4} d^{3} x +3 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a^{3} b c \,d^{2} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+6 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a^{3} b c \,d^{2} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{-\frac{b}{a}}\, a^{2} b^{2} c^{2} d x +7 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a^{2} b^{2} c^{2} d \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-8 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a^{2} b^{2} c^{2} d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+3 \sqrt{-\frac{b}{a}}\, a \,b^{3} c^{3} x -2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a \,b^{3} c^{3} \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+2 \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a \,b^{3} c^{3} \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{3 \sqrt{d \,x^{2}+c}\, \left(a d -b c \right)^{3} \sqrt{-\frac{b}{a}}\, \left(b \,x^{2}+a \right)^{\frac{3}{2}} a^{2} c}"," ",0,"-1/3*(-3*x^5*a^2*b^2*d^3*(-1/a*b)^(1/2)-7*x^5*a*b^3*c*d^2*(-1/a*b)^(1/2)+2*x^5*b^4*c^2*d*(-1/a*b)^(1/2)+3*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^2*b^2*c*d^2*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)+7*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b^3*c^2*d*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)-2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*b^4*c^3*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)+6*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a^2*b^2*c*d^2*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)-8*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*a*b^3*c^2*d*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)+2*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*x^2*b^4*c^3*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)-6*x^3*a^3*b*d^3*(-1/a*b)^(1/2)-8*x^3*a^2*b^2*c*d^2*(-1/a*b)^(1/2)-4*x^3*a*b^3*c^2*d*(-1/a*b)^(1/2)+2*x^3*b^4*c^3*(-1/a*b)^(1/2)+3*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c*d^2*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)+7*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^2*d*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)-2*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^3*c^3*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)+6*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^3*b*c*d^2*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)-8*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a^2*b^2*c^2*d*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)+2*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*a*b^3*c^3*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)-3*x*a^4*d^3*(-1/a*b)^(1/2)-8*x*a^2*b^2*c^2*d*(-1/a*b)^(1/2)+3*x*a*b^3*c^3*(-1/a*b)^(1/2))/(d*x^2+c)^(1/2)/(a*d-b*c)^3/(-1/a*b)^(1/2)/a^2/c/(b*x^2+a)^(3/2)","B"
214,1,100,112,0.023000," ","int(1/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{\sqrt{-\frac{b}{a}}\, \left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right)}"," ",0,"EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(-1/a*b)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)","A"
215,1,106,72,0.044000," ","int(1/(-b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","-\frac{\sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{-b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \EllipticF \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)}{\sqrt{\frac{b}{a}}\, \left(b d \,x^{4}-a d \,x^{2}+b c \,x^{2}-a c \right)}"," ",0,"-EllipticF(x*(1/a*b)^(1/2),(-a/b/c*d)^(1/2))*((d*x^2+c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)*(-b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)/(1/a*b)^(1/2)/(b*d*x^4-a*d*x^2+b*c*x^2-a*c)","A"
216,1,106,72,0.041000," ","int(1/(b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x)","-\frac{\sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{b \,x^{2}+a}\, \sqrt{-d \,x^{2}+c}\, \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)}{\sqrt{\frac{d}{c}}\, \left(b d \,x^{4}+a d \,x^{2}-b c \,x^{2}-a c \right)}"," ",0,"-EllipticF(x*(1/c*d)^(1/2),(-b*c/a/d)^(1/2))*((b*x^2+a)/a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*(b*x^2+a)^(1/2)*(-d*x^2+c)^(1/2)/(1/c*d)^(1/2)/(b*d*x^4+a*d*x^2-b*c*x^2-a*c)","A"
217,1,108,73,0.041000," ","int(1/(-b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x)","\frac{\sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{-b \,x^{2}+a}\, \sqrt{-d \,x^{2}+c}\, \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)}{\sqrt{\frac{d}{c}}\, \left(b d \,x^{4}-a d \,x^{2}-b c \,x^{2}+a c \right)}"," ",0,"EllipticF((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))*(-(b*x^2-a)/a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*(-b*x^2+a)^(1/2)*(-d*x^2+c)^(1/2)/(1/c*d)^(1/2)/(b*d*x^4-a*d*x^2-b*c*x^2+a*c)","A"
218,1,14,13,0.033000," ","int(1/(-x^2+1)^(1/2)/(5*x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \EllipticF \left(x , \frac{i \sqrt{10}}{2}\right)}{2}"," ",0,"1/2*EllipticF(x,1/2*I*10^(1/2))*2^(1/2)","A"
219,1,14,13,0.033000," ","int(1/(-x^2+1)^(1/2)/(4*x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \EllipticF \left(x , i \sqrt{2}\right)}{2}"," ",0,"1/2*EllipticF(x,I*2^(1/2))*2^(1/2)","A"
220,1,14,13,0.028000," ","int(1/(-x^2+1)^(1/2)/(3*x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \EllipticF \left(x , \frac{i \sqrt{6}}{2}\right)}{2}"," ",0,"1/2*EllipticF(x,1/2*I*6^(1/2))*2^(1/2)","A"
221,1,10,9,0.028000," ","int(1/(-x^2+1)^(1/2)/(2*x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \EllipticF \left(x , i\right)}{2}"," ",0,"1/2*EllipticF(x,I)*2^(1/2)","A"
222,1,14,13,0.032000," ","int(1/(-x^2+1)^(1/2)/(x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \EllipticF \left(x , \frac{i \sqrt{2}}{2}\right)}{2}"," ",0,"1/2*EllipticF(x,1/2*I*2^(1/2))*2^(1/2)","A"
223,1,13,12,0.029000," ","int(1/(-x^2+1)^(1/2)/(-x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \EllipticF \left(x , \frac{\sqrt{2}}{2}\right)}{2}"," ",0,"1/2*EllipticF(x,1/2*2^(1/2))*2^(1/2)","A"
224,1,8,7,0.317000," ","int(1/(-2*x^2+2)^(1/2)/(-x^2+1)^(1/2),x)","\frac{\sqrt{2}\, \arctanh \left(x \right)}{2}"," ",0,"1/2*arctanh(x)*2^(1/2)","A"
225,1,13,12,0.026000," ","int(1/(-3*x^2+2)^(1/2)/(-x^2+1)^(1/2),x)","\frac{\sqrt{2}\, \EllipticF \left(x , \frac{\sqrt{6}}{2}\right)}{2}"," ",0,"1/2*EllipticF(x,1/2*6^(1/2))*2^(1/2)","A"
226,1,11,10,0.028000," ","int(1/(-4*x^2+2)^(1/2)/(-x^2+1)^(1/2),x)","\frac{\sqrt{2}\, \EllipticF \left(x , \sqrt{2}\right)}{2}"," ",0,"1/2*EllipticF(x,2^(1/2))*2^(1/2)","A"
227,1,13,12,0.031000," ","int(1/(-5*x^2+2)^(1/2)/(-x^2+1)^(1/2),x)","\frac{\sqrt{2}\, \EllipticF \left(x , \frac{\sqrt{10}}{2}\right)}{2}"," ",0,"1/2*EllipticF(x,1/2*10^(1/2))*2^(1/2)","A"
228,1,17,56,0.040000," ","int(1/(x^2+1)^(1/2)/(5*x^2+2)^(1/2),x)","-\frac{i \sqrt{2}\, \EllipticF \left(i x , \frac{\sqrt{10}}{2}\right)}{2}"," ",0,"-1/2*I*EllipticF(I*x,1/2*10^(1/2))*2^(1/2)","A"
229,1,15,52,0.028000," ","int(1/(x^2+1)^(1/2)/(4*x^2+2)^(1/2),x)","-\frac{i \sqrt{2}\, \EllipticF \left(i x , \sqrt{2}\right)}{2}"," ",0,"-1/2*I*EllipticF(I*x,2^(1/2))*2^(1/2)","A"
230,1,17,56,0.026000," ","int(1/(x^2+1)^(1/2)/(3*x^2+2)^(1/2),x)","-\frac{i \sqrt{2}\, \EllipticF \left(i x , \frac{\sqrt{6}}{2}\right)}{2}"," ",0,"-1/2*I*EllipticF(I*x,1/2*6^(1/2))*2^(1/2)","A"
231,1,8,7,0.307000," ","int(1/(x^2+1)^(1/2)/(2*x^2+2)^(1/2),x)","\frac{\sqrt{2}\, \arctan \left(x \right)}{2}"," ",0,"1/2*arctan(x)*2^(1/2)","A"
232,1,15,51,0.033000," ","int(1/(x^2+1)^(1/2)/(x^2+2)^(1/2),x)","-i \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, \sqrt{2}\right)"," ",0,"-I*EllipticF(1/2*I*x*2^(1/2),2^(1/2))","C"
233,1,14,13,0.033000," ","int(1/(-x^2+2)^(1/2)/(x^2+1)^(1/2),x)","\EllipticF \left(\frac{\sqrt{2}\, x}{2}, i \sqrt{2}\right)"," ",0,"EllipticF(1/2*2^(1/2)*x,I*2^(1/2))","A"
234,1,10,9,0.020000," ","int(1/(-2*x^2+2)^(1/2)/(x^2+1)^(1/2),x)","\frac{\sqrt{2}\, \EllipticF \left(x , i\right)}{2}"," ",0,"1/2*EllipticF(x,I)*2^(1/2)","A"
235,1,19,18,0.028000," ","int(1/(-3*x^2+2)^(1/2)/(x^2+1)^(1/2),x)","\frac{\sqrt{3}\, \EllipticF \left(\frac{\sqrt{6}\, x}{2}, \frac{i \sqrt{6}}{3}\right)}{3}"," ",0,"1/3*EllipticF(1/2*6^(1/2)*x,1/3*I*6^(1/2))*3^(1/2)","A"
236,1,15,14,0.028000," ","int(1/(-4*x^2+2)^(1/2)/(x^2+1)^(1/2),x)","\frac{\EllipticF \left(\sqrt{2}\, x , \frac{i \sqrt{2}}{2}\right)}{2}"," ",0,"1/2*EllipticF(2^(1/2)*x,1/2*I*2^(1/2))","A"
237,1,19,18,0.048000," ","int(1/(-5*x^2+2)^(1/2)/(x^2+1)^(1/2),x)","\frac{\sqrt{5}\, \EllipticF \left(\frac{\sqrt{10}\, x}{2}, \frac{i \sqrt{10}}{5}\right)}{5}"," ",0,"1/5*EllipticF(1/2*x*10^(1/2),1/5*I*10^(1/2))*5^(1/2)","A"
238,1,37,29,0.043000," ","int(1/(x^2-1)^(1/2)/(5*x^2+2)^(1/2),x)","-\frac{i \sqrt{-x^{2}+1}\, \sqrt{5}\, \EllipticF \left(\frac{i \sqrt{10}\, x}{2}, \frac{i \sqrt{10}}{5}\right)}{5 \sqrt{x^{2}-1}}"," ",0,"-1/5*I*EllipticF(1/2*I*x*10^(1/2),1/5*I*10^(1/2))*(-x^2+1)^(1/2)*5^(1/2)/(x^2-1)^(1/2)","A"
239,1,34,29,0.040000," ","int(1/(x^2-1)^(1/2)/(4*x^2+2)^(1/2),x)","-\frac{i \sqrt{-x^{2}+1}\, \EllipticF \left(i \sqrt{2}\, x , \frac{i \sqrt{2}}{2}\right)}{2 \sqrt{x^{2}-1}}"," ",0,"-1/2*I*EllipticF(I*x*2^(1/2),1/2*I*2^(1/2))*(-x^2+1)^(1/2)/(x^2-1)^(1/2)","A"
240,1,37,29,0.036000," ","int(1/(x^2-1)^(1/2)/(3*x^2+2)^(1/2),x)","-\frac{i \sqrt{-x^{2}+1}\, \sqrt{3}\, \EllipticF \left(\frac{i \sqrt{6}\, x}{2}, \frac{i \sqrt{6}}{3}\right)}{3 \sqrt{x^{2}-1}}"," ",0,"-1/3*I*EllipticF(1/2*I*x*6^(1/2),1/3*I*6^(1/2))*(-x^2+1)^(1/2)*3^(1/2)/(x^2-1)^(1/2)","A"
241,1,30,20,0.029000," ","int(1/(x^2-1)^(1/2)/(2*x^2+2)^(1/2),x)","-\frac{i \sqrt{-x^{2}+1}\, \sqrt{2}\, \EllipticF \left(i x , i\right)}{2 \sqrt{x^{2}-1}}"," ",0,"-1/2*I*EllipticF(I*x,I)*(-x^2+1)^(1/2)*2^(1/2)/(x^2-1)^(1/2)","C"
242,1,34,29,0.033000," ","int(1/(x^2-1)^(1/2)/(x^2+2)^(1/2),x)","-\frac{i \sqrt{-x^{2}+1}\, \EllipticF \left(\frac{i \sqrt{2}\, x}{2}, i \sqrt{2}\right)}{\sqrt{x^{2}-1}}"," ",0,"-I*EllipticF(1/2*I*2^(1/2)*x,I*2^(1/2))*(-x^2+1)^(1/2)/(x^2-1)^(1/2)","A"
243,1,28,25,0.029000," ","int(1/(-x^2+2)^(1/2)/(x^2-1)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \EllipticF \left(\frac{\sqrt{2}\, x}{2}, \sqrt{2}\right)}{\sqrt{x^{2}-1}}"," ",0,"EllipticF(1/2*2^(1/2)*x,2^(1/2))*(-x^2+1)^(1/2)/(x^2-1)^(1/2)","A"
244,1,24,23,0.010000," ","int(1/(-2*x^2+2)^(1/2)/(x^2-1)^(1/2),x)","\frac{\sqrt{2}\, \sqrt{-x^{2}+1}\, \arctanh \left(x \right)}{2 \sqrt{x^{2}-1}}"," ",0,"1/2*2^(1/2)*(-x^2+1)^(1/2)/(x^2-1)^(1/2)*arctanh(x)","A"
245,1,29,28,0.031000," ","int(1/(-3*x^2+2)^(1/2)/(x^2-1)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{2}\, \EllipticF \left(x , \frac{\sqrt{6}}{2}\right)}{2 \sqrt{x^{2}-1}}"," ",0,"1/2*EllipticF(x,1/2*6^(1/2))*(-x^2+1)^(1/2)*2^(1/2)/(x^2-1)^(1/2)","A"
246,1,27,26,0.030000," ","int(1/(-4*x^2+2)^(1/2)/(x^2-1)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{2}\, \EllipticF \left(x , \sqrt{2}\right)}{2 \sqrt{x^{2}-1}}"," ",0,"1/2*EllipticF(x,2^(1/2))*(-x^2+1)^(1/2)*2^(1/2)/(x^2-1)^(1/2)","A"
247,1,29,28,0.034000," ","int(1/(-5*x^2+2)^(1/2)/(x^2-1)^(1/2),x)","\frac{\sqrt{-x^{2}+1}\, \sqrt{2}\, \EllipticF \left(x , \frac{\sqrt{10}}{2}\right)}{2 \sqrt{x^{2}-1}}"," ",0,"1/2*EllipticF(x,1/2*10^(1/2))*(-x^2+1)^(1/2)*2^(1/2)/(x^2-1)^(1/2)","A"
248,1,36,72,0.033000," ","int(1/(-x^2-1)^(1/2)/(5*x^2+2)^(1/2),x)","\frac{i \sqrt{5}\, \sqrt{-x^{2}-1}\, \EllipticF \left(\frac{i \sqrt{10}\, x}{2}, \frac{\sqrt{10}}{5}\right)}{5 \sqrt{x^{2}+1}}"," ",0,"1/5*I*EllipticF(1/2*I*10^(1/2)*x,1/5*10^(1/2))/(x^2+1)^(1/2)*5^(1/2)*(-x^2-1)^(1/2)","A"
249,1,33,68,0.031000," ","int(1/(-x^2-1)^(1/2)/(4*x^2+2)^(1/2),x)","\frac{i \sqrt{-x^{2}-1}\, \EllipticF \left(i \sqrt{2}\, x , \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{2}+1}}"," ",0,"1/2*I*EllipticF(I*2^(1/2)*x,1/2*2^(1/2))/(x^2+1)^(1/2)*(-x^2-1)^(1/2)","A"
250,1,36,72,0.034000," ","int(1/(-x^2-1)^(1/2)/(3*x^2+2)^(1/2),x)","\frac{i \sqrt{3}\, \sqrt{-x^{2}-1}\, \EllipticF \left(\frac{i \sqrt{6}\, x}{2}, \frac{\sqrt{6}}{3}\right)}{3 \sqrt{x^{2}+1}}"," ",0,"1/3*I*EllipticF(1/2*I*x*6^(1/2),1/3*6^(1/2))/(x^2+1)^(1/2)*3^(1/2)*(-x^2-1)^(1/2)","A"
251,1,24,23,0.010000," ","int(1/(-x^2-1)^(1/2)/(2*x^2+2)^(1/2),x)","-\frac{\sqrt{-x^{2}-1}\, \sqrt{2}\, \arctan \left(x \right)}{2 \sqrt{x^{2}+1}}"," ",0,"-1/2*(-x^2-1)^(1/2)*2^(1/2)/(x^2+1)^(1/2)*arctan(x)","A"
252,1,33,67,0.027000," ","int(1/(-x^2-1)^(1/2)/(x^2+2)^(1/2),x)","\frac{i \sqrt{2}\, \sqrt{-x^{2}-1}\, \EllipticF \left(i x , \frac{\sqrt{2}}{2}\right)}{2 \sqrt{x^{2}+1}}"," ",0,"1/2*I*EllipticF(I*x,1/2*2^(1/2))*2^(1/2)/(x^2+1)^(1/2)*(-x^2-1)^(1/2)","C"
253,1,34,30,0.030000," ","int(1/(-x^2-1)^(1/2)/(-x^2+2)^(1/2),x)","\frac{i \sqrt{2}\, \sqrt{-x^{2}-1}\, \EllipticF \left(i x , \frac{i \sqrt{2}}{2}\right)}{2 \sqrt{x^{2}+1}}"," ",0,"1/2*I*EllipticF(I*x,1/2*I*2^(1/2))/(x^2+1)^(1/2)*2^(1/2)*(-x^2-1)^(1/2)","A"
254,1,30,38,0.023000," ","int(1/(-2*x^2+2)^(1/2)/(-x^2-1)^(1/2),x)","\frac{i \sqrt{2}\, \sqrt{-x^{2}-1}\, \EllipticF \left(i x , i\right)}{2 \sqrt{x^{2}+1}}"," ",0,"1/2*I*EllipticF(I*x,I)*2^(1/2)/(x^2+1)^(1/2)*(-x^2-1)^(1/2)","A"
255,1,34,34,0.033000," ","int(1/(-3*x^2+2)^(1/2)/(-x^2-1)^(1/2),x)","\frac{i \sqrt{-x^{2}-1}\, \sqrt{2}\, \EllipticF \left(i x , \frac{i \sqrt{6}}{2}\right)}{2 \sqrt{x^{2}+1}}"," ",0,"1/2*I*EllipticF(I*x,1/2*I*6^(1/2))/(x^2+1)^(1/2)*(-x^2-1)^(1/2)*2^(1/2)","A"
256,1,34,30,0.027000," ","int(1/(-4*x^2+2)^(1/2)/(-x^2-1)^(1/2),x)","\frac{i \sqrt{2}\, \sqrt{-x^{2}-1}\, \EllipticF \left(i x , i \sqrt{2}\right)}{2 \sqrt{x^{2}+1}}"," ",0,"1/2*I*EllipticF(I*x,I*2^(1/2))*2^(1/2)/(x^2+1)^(1/2)*(-x^2-1)^(1/2)","A"
257,1,34,34,0.033000," ","int(1/(-5*x^2+2)^(1/2)/(-x^2-1)^(1/2),x)","\frac{i \sqrt{2}\, \sqrt{-x^{2}-1}\, \EllipticF \left(i x , \frac{i \sqrt{10}}{2}\right)}{2 \sqrt{x^{2}+1}}"," ",0,"1/2*I*EllipticF(I*x,1/2*I*10^(1/2))*2^(1/2)/(x^2+1)^(1/2)*(-x^2-1)^(1/2)","A"
258,1,106,72,0.018000," ","int((b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{-d \,x^{2}+c}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)}{\left(-b d \,x^{4}-a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{\frac{d}{c}}}"," ",0,"(b*x^2+a)^(1/2)*(-d*x^2+c)^(1/2)*a*(-(d*x^2-c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)*EllipticE((1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))/(-b*d*x^4-a*d*x^2+b*c*x^2+a*c)/(1/c*d)^(1/2)","A"
259,1,171,75,0.026000," ","int((-b*x^2-a)^(1/2)/(-d*x^2+c)^(1/2),x)","\frac{\left(-a d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)+b c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)-b c \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)\right) \sqrt{-b \,x^{2}-a}\, \sqrt{-d \,x^{2}+c}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{-\frac{d \,x^{2}-c}{c}}}{\left(b d \,x^{4}+a d \,x^{2}-b c \,x^{2}-a c \right) \sqrt{-\frac{b}{a}}\, d}"," ",0,"(-a*EllipticF((-1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))*d-b*c*EllipticF((-1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))+b*c*EllipticE((-1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2)))*(-b*x^2-a)^(1/2)*(-d*x^2+c)^(1/2)*((b*x^2+a)/a)^(1/2)*(-(d*x^2-c)/c)^(1/2)/(b*d*x^4+a*d*x^2-b*c*x^2-a*c)/(-1/a*b)^(1/2)/d","B"
260,1,168,73,0.017000," ","int((b*x^2+a)^(1/2)/(d*x^2-c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}-c}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \left(a d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)-b c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)+b c \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)\right)}{\left(b d \,x^{4}+a d \,x^{2}-b c \,x^{2}-a c \right) \sqrt{-\frac{b}{a}}\, d}"," ",0,"(b*x^2+a)^(1/2)*(d*x^2-c)^(1/2)*((b*x^2+a)/a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*(a*EllipticF((-1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))*d+b*c*EllipticF((-1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))-b*c*EllipticE((-1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2)))/(b*d*x^4+a*d*x^2-b*c*x^2-a*c)/(-1/a*b)^(1/2)/d","B"
261,1,110,76,0.017000," ","int((-b*x^2-a)^(1/2)/(d*x^2-c)^(1/2),x)","\frac{\sqrt{-b \,x^{2}-a}\, \sqrt{d \,x^{2}-c}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)}{\left(b d \,x^{4}+a d \,x^{2}-b c \,x^{2}-a c \right) \sqrt{\frac{d}{c}}}"," ",0,"(-b*x^2-a)^(1/2)*(d*x^2-c)^(1/2)*a*(-(d*x^2-c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)*EllipticE((1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))/(b*d*x^4+a*d*x^2-b*c*x^2-a*c)/(1/c*d)^(1/2)","A"
262,1,109,73,0.021000," ","int((-b*x^2+a)^(1/2)/(-d*x^2+c)^(1/2),x)","\frac{\sqrt{-b \,x^{2}+a}\, \sqrt{-d \,x^{2}+c}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, a \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)}{\left(b d \,x^{4}-a d \,x^{2}-b c \,x^{2}+a c \right) \sqrt{\frac{d}{c}}}"," ",0,"(-b*x^2+a)^(1/2)*(-d*x^2+c)^(1/2)*a*(-(d*x^2-c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)*EllipticE((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))/(b*d*x^4-a*d*x^2-b*c*x^2+a*c)/(1/c*d)^(1/2)","A"
263,1,165,74,0.028000," ","int((b*x^2-a)^(1/2)/(-d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}-a}\, \sqrt{-d \,x^{2}+c}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \left(a d \EllipticF \left(\sqrt{\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+b c \EllipticE \left(\sqrt{\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-b c \EllipticF \left(\sqrt{\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{\left(b d \,x^{4}-a d \,x^{2}-b c \,x^{2}+a c \right) \sqrt{\frac{b}{a}}\, d}"," ",0,"(b*x^2-a)^(1/2)*(-d*x^2+c)^(1/2)*(-(b*x^2-a)/a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*(a*EllipticF((1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d-b*c*EllipticF((1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))+b*c*EllipticE((1/a*b)^(1/2)*x,(a/b/c*d)^(1/2)))/(b*d*x^4-a*d*x^2-b*c*x^2+a*c)/(1/a*b)^(1/2)/d","B"
264,1,166,74,0.020000," ","int((-b*x^2+a)^(1/2)/(d*x^2-c)^(1/2),x)","\frac{\left(-a d \EllipticF \left(\sqrt{\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-b c \EllipticE \left(\sqrt{\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+b c \EllipticF \left(\sqrt{\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right) \sqrt{-b \,x^{2}+a}\, \sqrt{d \,x^{2}-c}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{-\frac{d \,x^{2}-c}{c}}}{\left(b d \,x^{4}-a d \,x^{2}-b c \,x^{2}+a c \right) \sqrt{\frac{b}{a}}\, d}"," ",0,"(-a*EllipticF((1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d+b*c*EllipticF((1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))-b*c*EllipticE((1/a*b)^(1/2)*x,(a/b/c*d)^(1/2)))*(-b*x^2+a)^(1/2)*(d*x^2-c)^(1/2)*(-(b*x^2-a)/a)^(1/2)*(-(d*x^2-c)/c)^(1/2)/(b*d*x^4-a*d*x^2-b*c*x^2+a*c)/(1/a*b)^(1/2)/d","B"
265,1,111,75,0.019000," ","int((b*x^2-a)^(1/2)/(d*x^2-c)^(1/2),x)","\frac{\sqrt{b \,x^{2}-a}\, \sqrt{d \,x^{2}-c}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, a \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)}{\left(-b d \,x^{4}+a d \,x^{2}+b c \,x^{2}-a c \right) \sqrt{\frac{d}{c}}}"," ",0,"1/(-b*d*x^4+a*d*x^2+b*c*x^2-a*c)/(1/c*d)^(1/2)*(b*x^2-a)^(1/2)*(d*x^2-c)^(1/2)*a*(-(d*x^2-c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)*EllipticE((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))","A"
266,1,158,240,0.013000," ","int((b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \left(a d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+b c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-b c \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right)}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, d}"," ",0,"(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*(a*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d-b*c*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))+b*c*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2)))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)/d","A"
267,1,104,249,0.026000," ","int((-b*x^2-a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{-b \,x^{2}-a}\, \sqrt{d \,x^{2}+c}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{d}{c}}}"," ",0,"(-b*x^2-a)^(1/2)*(d*x^2+c)^(1/2)*a*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)*EllipticE(x*(-1/c*d)^(1/2),(1/a*b*c/d)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/c*d)^(1/2)","A"
268,1,108,249,0.020000," ","int((b*x^2+a)^(1/2)/(-d*x^2-c)^(1/2),x)","\frac{\sqrt{b \,x^{2}+a}\, \sqrt{-d \,x^{2}-c}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, a \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)}{\left(-b d \,x^{4}-a d \,x^{2}-b c \,x^{2}-a c \right) \sqrt{-\frac{d}{c}}}"," ",0,"(b*x^2+a)^(1/2)*(-d*x^2-c)^(1/2)*a*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))/(-b*d*x^4-a*d*x^2-b*c*x^2-a*c)/(-1/c*d)^(1/2)","A"
269,1,165,258,0.020000," ","int((-b*x^2-a)^(1/2)/(-d*x^2-c)^(1/2),x)","\frac{\left(-a d \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)-b c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)+b c \EllipticF \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)\right) \sqrt{-b \,x^{2}-a}\, \sqrt{-d \,x^{2}-c}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}\, d}"," ",0,"(-a*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))*d+b*c*EllipticF((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))-b*c*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2)))*(-b*x^2-a)^(1/2)*(-d*x^2-c)^(1/2)*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)/d","A"
270,1,164,159,0.019000," ","int((-b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{-b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \left(-a d \EllipticF \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)+b c \EllipticE \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)-b c \EllipticF \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)\right)}{\left(b d \,x^{4}-a d \,x^{2}+b c \,x^{2}-a c \right) \sqrt{\frac{b}{a}}\, d}"," ",0,"(-b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)*(-(b*x^2-a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*(b*c*EllipticE((1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))-a*EllipticF((1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))*d-b*c*EllipticF((1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2)))/(b*d*x^4-a*d*x^2+b*c*x^2-a*c)/(1/a*b)^(1/2)/d","A"
271,1,109,161,0.023000," ","int((b*x^2-a)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{b \,x^{2}-a}\, \sqrt{d \,x^{2}+c}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, a \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)}{\left(-b d \,x^{4}+a d \,x^{2}-b c \,x^{2}+a c \right) \sqrt{-\frac{d}{c}}}"," ",0,"1/(-b*d*x^4+a*d*x^2-b*c*x^2+a*c)/(-1/c*d)^(1/2)*(b*x^2-a)^(1/2)*(d*x^2+c)^(1/2)*a*((d*x^2+c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))","A"
272,1,111,164,0.019000," ","int((-b*x^2+a)^(1/2)/(-d*x^2-c)^(1/2),x)","\frac{\sqrt{-b \,x^{2}+a}\, \sqrt{-d \,x^{2}-c}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, a \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)}{\left(b d \,x^{4}-a d \,x^{2}+b c \,x^{2}-a c \right) \sqrt{-\frac{d}{c}}}"," ",0,"(-b*x^2+a)^(1/2)*(-d*x^2-c)^(1/2)*a*((d*x^2+c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)*EllipticE((-1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))/(b*d*x^4-a*d*x^2+b*c*x^2-a*c)/(-1/c*d)^(1/2)","A"
273,1,167,168,0.019000," ","int((b*x^2-a)^(1/2)/(-d*x^2-c)^(1/2),x)","\frac{\sqrt{b \,x^{2}-a}\, \sqrt{-d \,x^{2}-c}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \left(a d \EllipticF \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)-b c \EllipticE \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)+b c \EllipticF \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)\right)}{\left(b d \,x^{4}-a d \,x^{2}+b c \,x^{2}-a c \right) \sqrt{\frac{b}{a}}\, d}"," ",0,"(b*x^2-a)^(1/2)*(-d*x^2-c)^(1/2)*(-(b*x^2-a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*(a*EllipticF((1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))*d+b*c*EllipticF((1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))-b*c*EllipticE((1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2)))/(b*d*x^4-a*d*x^2+b*c*x^2-a*c)/(1/a*b)^(1/2)/d","A"
274,1,106,72,0.017000," ","int((d*x^2+c)^(1/2)/(-b*x^2+a)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{-b \,x^{2}+a}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, c \EllipticE \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)}{\left(-b d \,x^{4}+a d \,x^{2}-b c \,x^{2}+a c \right) \sqrt{\frac{b}{a}}}"," ",0,"(d*x^2+c)^(1/2)*(-b*x^2+a)^(1/2)*c*(-(b*x^2-a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))/(-b*d*x^4+a*d*x^2-b*c*x^2+a*c)/(1/a*b)^(1/2)","A"
275,1,171,75,0.024000," ","int((-d*x^2-c)^(1/2)/(-b*x^2+a)^(1/2),x)","\frac{\left(a d \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)-a d \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)-b c \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)\right) \sqrt{-d \,x^{2}-c}\, \sqrt{-b \,x^{2}+a}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}}{\left(b d \,x^{4}-a d \,x^{2}+b c \,x^{2}-a c \right) \sqrt{-\frac{d}{c}}\, b}"," ",0,"(-a*d*EllipticF((-1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))-c*EllipticF((-1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))*b+a*d*EllipticE((-1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2)))*(-d*x^2-c)^(1/2)*(-b*x^2+a)^(1/2)*((d*x^2+c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)/(b*d*x^4-a*d*x^2+b*c*x^2-a*c)/(-1/c*d)^(1/2)/b","B"
276,1,168,73,0.019000," ","int((d*x^2+c)^(1/2)/(b*x^2-a)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}-a}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, \left(-a d \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)+a d \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)+b c \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)\right)}{\left(b d \,x^{4}-a d \,x^{2}+b c \,x^{2}-a c \right) \sqrt{-\frac{d}{c}}\, b}"," ",0,"(d*x^2+c)^(1/2)*(b*x^2-a)^(1/2)*((d*x^2+c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)*(a*d*EllipticF((-1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))+c*EllipticF((-1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))*b-a*d*EllipticE((-1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2)))/(b*d*x^4-a*d*x^2+b*c*x^2-a*c)/(-1/c*d)^(1/2)/b","B"
277,1,110,76,0.016000," ","int((-d*x^2-c)^(1/2)/(b*x^2-a)^(1/2),x)","\frac{\sqrt{-d \,x^{2}-c}\, \sqrt{b \,x^{2}-a}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, c \EllipticE \left(\sqrt{\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)}{\left(b d \,x^{4}-a d \,x^{2}+b c \,x^{2}-a c \right) \sqrt{\frac{b}{a}}}"," ",0,"(-d*x^2-c)^(1/2)*(b*x^2-a)^(1/2)*c*(-(b*x^2-a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))/(b*d*x^4-a*d*x^2+b*c*x^2-a*c)/(1/a*b)^(1/2)","A"
278,1,164,73,0.022000," ","int((-d*x^2+c)^(1/2)/(-b*x^2+a)^(1/2),x)","\frac{\left(a d \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)-a d \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)+b c \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{-b \,x^{2}+a}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}}{\left(b d \,x^{4}-a d \,x^{2}-b c \,x^{2}+a c \right) \sqrt{\frac{d}{c}}\, b}"," ",0,"(-a*d*EllipticF((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))+c*EllipticF((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))*b+a*d*EllipticE((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2)))*(-d*x^2+c)^(1/2)*(-b*x^2+a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)/(b*d*x^4-a*d*x^2-b*c*x^2+a*c)/(1/c*d)^(1/2)/b","B"
279,1,110,74,0.027000," ","int((d*x^2-c)^(1/2)/(-b*x^2+a)^(1/2),x)","\frac{\sqrt{d \,x^{2}-c}\, \sqrt{-b \,x^{2}+a}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, c \EllipticE \left(\sqrt{\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{\left(b d \,x^{4}-a d \,x^{2}-b c \,x^{2}+a c \right) \sqrt{\frac{b}{a}}}"," ",0,"(d*x^2-c)^(1/2)*(-b*x^2+a)^(1/2)*c*(-(b*x^2-a)/a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*EllipticE((1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))/(b*d*x^4-a*d*x^2-b*c*x^2+a*c)/(1/a*b)^(1/2)","A"
280,1,110,74,0.019000," ","int((-d*x^2+c)^(1/2)/(b*x^2-a)^(1/2),x)","\frac{\sqrt{-d \,x^{2}+c}\, \sqrt{b \,x^{2}-a}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, c \EllipticE \left(\sqrt{\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{\left(-b d \,x^{4}+a d \,x^{2}+b c \,x^{2}-a c \right) \sqrt{\frac{b}{a}}}"," ",0,"(-d*x^2+c)^(1/2)*(b*x^2-a)^(1/2)*c*(-(b*x^2-a)/a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*EllipticE((1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))/(-b*d*x^4+a*d*x^2+b*c*x^2-a*c)/(1/a*b)^(1/2)","A"
281,1,167,75,0.019000," ","int((d*x^2-c)^(1/2)/(b*x^2-a)^(1/2),x)","\frac{\sqrt{d \,x^{2}-c}\, \sqrt{b \,x^{2}-a}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{-\frac{b \,x^{2}-a}{a}}\, \left(-a d \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)+a d \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)-b c \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)\right)}{\left(b d \,x^{4}-a d \,x^{2}-b c \,x^{2}+a c \right) \sqrt{\frac{d}{c}}\, b}"," ",0,"(d*x^2-c)^(1/2)*(b*x^2-a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*(-(b*x^2-a)/a)^(1/2)*(a*d*EllipticF((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))-c*EllipticF((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))*b-a*d*EllipticE((1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2)))/(b*d*x^4-a*d*x^2-b*c*x^2+a*c)/(1/c*d)^(1/2)/b","B"
282,1,101,250,0.017000," ","int((d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}}"," ",0,"(d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)","A"
283,1,161,260,0.025000," ","int((-d*x^2-c)^(1/2)/(b*x^2+a)^(1/2),x)","\frac{\left(a d \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)-a d \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)+b c \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)\right) \sqrt{-d \,x^{2}-c}\, \sqrt{b \,x^{2}+a}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{d}{c}}\, b}"," ",0,"(-a*d*EllipticF((-1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))+c*EllipticF((-1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))*b+a*d*EllipticE((-1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2)))*(-d*x^2-c)^(1/2)*(b*x^2+a)^(1/2)*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/c*d)^(1/2)/b","A"
284,1,162,260,0.020000," ","int((d*x^2+c)^(1/2)/(-b*x^2-a)^(1/2),x)","\frac{\sqrt{d \,x^{2}+c}\, \sqrt{-b \,x^{2}-a}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \left(-a d \EllipticE \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)+a d \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)-b c \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \sqrt{\frac{b c}{a d}}\right)\right)}{\left(b d \,x^{4}+a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{d}{c}}\, b}"," ",0,"(d*x^2+c)^(1/2)*(-b*x^2-a)^(1/2)*((d*x^2+c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)*(a*d*EllipticF((-1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))-c*EllipticF((-1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2))*b-a*d*EllipticE((-1/c*d)^(1/2)*x,(1/a*b*c/d)^(1/2)))/(b*d*x^4+a*d*x^2+b*c*x^2+a*c)/(-1/c*d)^(1/2)/b","A"
285,1,111,268,0.021000," ","int((-d*x^2-c)^(1/2)/(-b*x^2-a)^(1/2),x)","\frac{\sqrt{-d \,x^{2}-c}\, \sqrt{-b \,x^{2}-a}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{\frac{d \,x^{2}+c}{c}}\, c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{\frac{a d}{b c}}\right)}{\left(-b d \,x^{4}-a d \,x^{2}-b c \,x^{2}-a c \right) \sqrt{-\frac{b}{a}}}"," ",0,"1/(-b*d*x^4-a*d*x^2-b*c*x^2-a*c)/(-1/a*b)^(1/2)*(-d*x^2-c)^(1/2)*(-b*x^2-a)^(1/2)*c*((b*x^2+a)/a)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(a/b/c*d)^(1/2))","A"
286,1,164,159,0.019000," ","int((-d*x^2+c)^(1/2)/(b*x^2+a)^(1/2),x)","\frac{\left(a d \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)-a d \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)-b c \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)\right) \sqrt{-d \,x^{2}+c}\, \sqrt{b \,x^{2}+a}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}}{\left(b d \,x^{4}+a d \,x^{2}-b c \,x^{2}-a c \right) \sqrt{\frac{d}{c}}\, b}"," ",0,"(-a*d*EllipticF((1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))-c*EllipticF((1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))*b+a*d*EllipticE((1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2)))*(-d*x^2+c)^(1/2)*(b*x^2+a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)/(b*d*x^4+a*d*x^2-b*c*x^2-a*c)/(1/c*d)^(1/2)/b","A"
287,1,109,161,0.023000," ","int((d*x^2-c)^(1/2)/(b*x^2+a)^(1/2),x)","\frac{\sqrt{d \,x^{2}-c}\, \sqrt{b \,x^{2}+a}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)}{\left(-b d \,x^{4}-a d \,x^{2}+b c \,x^{2}+a c \right) \sqrt{-\frac{b}{a}}}"," ",0,"1/(-b*d*x^4-a*d*x^2+b*c*x^2+a*c)/(-1/a*b)^(1/2)*(d*x^2-c)^(1/2)*(b*x^2+a)^(1/2)*c*((b*x^2+a)/a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))","A"
288,1,111,164,0.019000," ","int((-d*x^2+c)^(1/2)/(-b*x^2-a)^(1/2),x)","\frac{\sqrt{-d \,x^{2}+c}\, \sqrt{-b \,x^{2}-a}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, c \EllipticE \left(\sqrt{-\frac{b}{a}}\, x , \sqrt{-\frac{a d}{b c}}\right)}{\left(b d \,x^{4}+a d \,x^{2}-b c \,x^{2}-a c \right) \sqrt{-\frac{b}{a}}}"," ",0,"(-d*x^2+c)^(1/2)*(-b*x^2-a)^(1/2)*c*((b*x^2+a)/a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*EllipticE((-1/a*b)^(1/2)*x,(-a/b/c*d)^(1/2))/(b*d*x^4+a*d*x^2-b*c*x^2-a*c)/(-1/a*b)^(1/2)","A"
289,1,167,168,0.019000," ","int((d*x^2-c)^(1/2)/(-b*x^2-a)^(1/2),x)","\frac{\sqrt{d \,x^{2}-c}\, \sqrt{-b \,x^{2}-a}\, \sqrt{-\frac{d \,x^{2}-c}{c}}\, \sqrt{\frac{b \,x^{2}+a}{a}}\, \left(-a d \EllipticE \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)+a d \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)+b c \EllipticF \left(\sqrt{\frac{d}{c}}\, x , \sqrt{-\frac{b c}{a d}}\right)\right)}{\left(b d \,x^{4}+a d \,x^{2}-b c \,x^{2}-a c \right) \sqrt{\frac{d}{c}}\, b}"," ",0,"(d*x^2-c)^(1/2)*(-b*x^2-a)^(1/2)*(-(d*x^2-c)/c)^(1/2)*((b*x^2+a)/a)^(1/2)*(a*d*EllipticF((1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))+c*EllipticF((1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2))*b-a*d*EllipticE((1/c*d)^(1/2)*x,(-1/a*b*c/d)^(1/2)))/(b*d*x^4+a*d*x^2-b*c*x^2-a*c)/(1/c*d)^(1/2)/b","A"
290,1,38,98,0.036000," ","int(1/(b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x)","\frac{\sqrt{2}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{2}\, \sqrt{3}\, \sqrt{\frac{b}{d}}}{2}\right)}{2 \sqrt{-d}}"," ",0,"1/2*2^(1/2)*EllipticF(1/3*3^(1/2)*(-d)^(1/2)*x,1/2*2^(1/2)*3^(1/2)*(b/d)^(1/2))/(-d)^(1/2)","A"
291,1,38,36,0.033000," ","int(1/(-x^2+4)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{\frac{d \,x^{2}+c}{c}}\, \EllipticF \left(\frac{x}{2}, 2 \sqrt{-\frac{d}{c}}\right)}{\sqrt{d \,x^{2}+c}}"," ",0,"1/(d*x^2+c)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF(1/2*x,2*(-1/c*d)^(1/2))","A"
292,1,53,62,0.031000," ","int(1/(x^2+4)^(1/2)/(d*x^2+c)^(1/2),x)","\frac{\sqrt{\frac{d \,x^{2}+c}{c}}\, \EllipticF \left(\sqrt{-\frac{d}{c}}\, x , \frac{\sqrt{\frac{c}{d}}}{2}\right)}{2 \sqrt{d \,x^{2}+c}\, \sqrt{-\frac{d}{c}}}"," ",0,"1/2/(d*x^2+c)^(1/2)*((d*x^2+c)/c)^(1/2)*EllipticF((-1/c*d)^(1/2)*x,1/2*(c/d)^(1/2))/(-1/c*d)^(1/2)","A"
293,1,25,23,0.026000," ","int(1/(-x^2+1)^(1/2)/(2*x^2-1)^(1/2),x)","\frac{\sqrt{-2 x^{2}+1}\, \EllipticF \left(x , \sqrt{2}\right)}{\sqrt{2 x^{2}-1}}"," ",0,"EllipticF(x,2^(1/2))*(-2*x^2+1)^(1/2)/(2*x^2-1)^(1/2)","A"
294,1,28,23,0.023000," ","int((-c^2*x^2+1)^(1/2)/(c^2*x^2+1)^(1/2),x)","\frac{\left(-\EllipticE \left(c x \,\mathrm{csgn}\left(c \right), i\right)+2 \EllipticF \left(c x \,\mathrm{csgn}\left(c \right), i\right)\right) \mathrm{csgn}\left(c \right)}{c}"," ",0,"(2*EllipticF(x*csgn(c)*c,I)-EllipticE(x*csgn(c)*c,I))*csgn(c)/c","C"
295,1,37,216,0.019000," ","int((b*x^2+2)^(1/2)/(d*x^2+3)^(1/2),x)","\frac{\sqrt{2}\, \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-d}\, x}{3}, \frac{\sqrt{2}\, \sqrt{3}\, \sqrt{\frac{b}{d}}}{2}\right)}{\sqrt{-d}}"," ",0,"EllipticE(1/3*3^(1/2)*(-d)^(1/2)*x,1/2*2^(1/2)*3^(1/2)*(b/d)^(1/2))*2^(1/2)/(-d)^(1/2)","A"
296,1,37,28,0.025000," ","int((3*x^2-1)^(1/2)/(-3*x^2+2)^(1/2),x)","-\frac{\sqrt{-3 x^{2}+1}\, \sqrt{3}\, \EllipticE \left(\frac{\sqrt{2}\, \sqrt{3}\, x}{2}, \sqrt{2}\right)}{3 \sqrt{3 x^{2}-1}}"," ",0,"-1/3*EllipticE(1/2*2^(1/2)*3^(1/2)*x,2^(1/2))*(-3*x^2+1)^(1/2)*3^(1/2)/(3*x^2-1)^(1/2)","A"
297,0,0,80,0.374000," ","int((1+2*c*x^2/(b-(-4*a*c+b^2)^(1/2)))^(1/2)/(1-2*c*x^2/(b+(-4*a*c+b^2)^(1/2)))^(1/2),x)","\int \frac{\sqrt{\frac{2 c \,x^{2}}{b -\sqrt{-4 a c +b^{2}}}+1}}{\sqrt{-\frac{2 c \,x^{2}}{b +\sqrt{-4 a c +b^{2}}}+1}}\, dx"," ",0,"int((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)","F"
298,0,0,76,0.336000," ","int((1-2/(b-(-4*a*c+b^2)^(1/2))*c*x^2)^(1/2)/(-2/(b+(-4*a*c+b^2)^(1/2))*c*x^2+1)^(1/2),x)","\int \frac{\sqrt{-\frac{2 c \,x^{2}}{b -\sqrt{-4 a c +b^{2}}}+1}}{\sqrt{-\frac{2 c \,x^{2}}{b +\sqrt{-4 a c +b^{2}}}+1}}\, dx"," ",0,"int((1-2/(b-(-4*a*c+b^2)^(1/2))*c*x^2)^(1/2)/(-2/(b+(-4*a*c+b^2)^(1/2))*c*x^2+1)^(1/2),x)","F"
299,0,0,457,0.333000," ","int((2/(b-(-4*a*c+b^2)^(1/2))*c*x^2+1)^(1/2)/(1+2/(b+(-4*a*c+b^2)^(1/2))*c*x^2)^(1/2),x)","\int \frac{\sqrt{\frac{2 c \,x^{2}}{b -\sqrt{-4 a c +b^{2}}}+1}}{\sqrt{\frac{2 c \,x^{2}}{b +\sqrt{-4 a c +b^{2}}}+1}}\, dx"," ",0,"int((2/(b-(-4*a*c+b^2)^(1/2))*c*x^2+1)^(1/2)/(1+2/(b+(-4*a*c+b^2)^(1/2))*c*x^2)^(1/2),x)","F"
300,0,0,173,0.325000," ","int((-2/(b-(-4*a*c+b^2)^(1/2))*c*x^2+1)^(1/2)/(2/(b+(-4*a*c+b^2)^(1/2))*c*x^2+1)^(1/2),x)","\int \frac{\sqrt{-\frac{2 c \,x^{2}}{b -\sqrt{-4 a c +b^{2}}}+1}}{\sqrt{\frac{2 c \,x^{2}}{b +\sqrt{-4 a c +b^{2}}}+1}}\, dx"," ",0,"int((-2/(b-(-4*a*c+b^2)^(1/2))*c*x^2+1)^(1/2)/(2/(b+(-4*a*c+b^2)^(1/2))*c*x^2+1)^(1/2),x)","F"
301,0,0,56,0.314000," ","int((-2*x^2+1)^m/(-x^2+1)^(1/2),x)","\int \frac{\left(-2 x^{2}+1\right)^{m}}{\sqrt{-x^{2}+1}}\, dx"," ",0,"int((-2*x^2+1)^m/(-x^2+1)^(1/2),x)","F"
302,1,117,37,0.145000," ","int(1/(x^2-1)^(1/2)/(7+x^2-4*3^(1/2))^(1/2),x)","-\frac{i \sqrt{-x^{2}+1}\, \sqrt{-\left(-x^{2}+4 \sqrt{3}-7\right) \left(-4 \sqrt{3}+7\right)}\, \left(-2+\sqrt{3}\right) \sqrt{x^{2}-1}\, \sqrt{x^{2}+7-4 \sqrt{3}}\, \EllipticF \left(\frac{i x}{-2+\sqrt{3}}, 2 i-i \sqrt{3}\right)}{\left(4 \sqrt{3}-7\right) \left(-x^{4}+4 \sqrt{3}\, x^{2}-6 x^{2}-4 \sqrt{3}+7\right)}"," ",0,"-I*EllipticF(I*x/(-2+3^(1/2)),2*I-I*3^(1/2))*(-x^2+1)^(1/2)*(-(-x^2+4*3^(1/2)-7)*(-4*3^(1/2)+7))^(1/2)/(4*3^(1/2)-7)*(-2+3^(1/2))*(x^2-1)^(1/2)*(7+x^2-4*3^(1/2))^(1/2)/(-x^4+4*x^2*3^(1/2)-6*x^2-4*3^(1/2)+7)","B"
303,1,207,64,0.225000," ","int(1/(3+x^2*(-3+3^(1/2)))^(1/2)/(3-3*3^(1/2)+2*3^(1/2)*x^2)^(1/2),x)","\frac{\sqrt{\sqrt{3}\, x^{2}-3 x^{2}+3}\, \sqrt{2 \sqrt{3}\, x^{2}+3-3 \sqrt{3}}\, \sqrt{2}\, \sqrt{-\left(4 \sqrt{3}\, x^{2}-6 x^{2}-3 \sqrt{3}+3\right) \left(\sqrt{3}-1\right)}\, \sqrt{-\left(2 \sqrt{3}\, x^{2}+3-3 \sqrt{3}\right) \left(\sqrt{3}-1\right)}\, \left(-3+\sqrt{3}\right) \EllipticF \left(\frac{\sqrt{2}\, \sqrt{3}\, \sqrt{\left(2 \sqrt{3}-3\right) \left(\sqrt{3}-1\right)}\, x}{3 \sqrt{3}-3}, \frac{\sqrt{\left(\sqrt{3}-1\right) \left(1+\sqrt{3}\right)}}{\sqrt{3}-1}\right)}{18 \left(\sqrt{3}-1\right)^{2} \left(2 \sqrt{3}\, x^{4}-2 x^{4}-6 \sqrt{3}\, x^{2}+6 x^{2}+3 \sqrt{3}-3\right) \sqrt{\left(2 \sqrt{3}-3\right) \left(\sqrt{3}-1\right)}}"," ",0,"1/18*(3^(1/2)*x^2-3*x^2+3)^(1/2)*(3-3*3^(1/2)+2*3^(1/2)*x^2)^(1/2)*2^(1/2)/(3^(1/2)-1)^2*(-(4*3^(1/2)*x^2-6*x^2-3*3^(1/2)+3)*(3^(1/2)-1))^(1/2)*(-(3-3*3^(1/2)+2*3^(1/2)*x^2)*(3^(1/2)-1))^(1/2)*EllipticF(1/3*x*2^(1/2)*3^(1/2)/(3^(1/2)-1)*((2*3^(1/2)-3)*(3^(1/2)-1))^(1/2),1/(3^(1/2)-1)*((3^(1/2)-1)*(1+3^(1/2)))^(1/2))*(-3+3^(1/2))/(2*x^4*3^(1/2)-2*x^4-6*3^(1/2)*x^2+6*x^2+3*3^(1/2)-3)/((2*3^(1/2)-3)*(3^(1/2)-1))^(1/2)","B"
304,1,186,93,1.667000," ","int(1/(3*x^2+2)^(1/4)/(3*x^2+4),x)","\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+72\right)^{2}\right) \ln \left(-\frac{3 x \RootOf \left(\textit{\_Z}^{4}+72\right)^{2}+\left(3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+72\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+72\right)^{2}-18 \sqrt{3 x^{2}+2}\, x -6 \left(3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+72\right)^{2}\right)}{3 x^{2}+4}\right)}{24}+\frac{\RootOf \left(\textit{\_Z}^{4}+72\right) \ln \left(\frac{3 x \RootOf \left(\textit{\_Z}^{4}+72\right)^{2}+\left(3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+72\right)^{3}+18 \sqrt{3 x^{2}+2}\, x +6 \left(3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+72\right)}{3 x^{2}+4}\right)}{24}"," ",0,"1/24*RootOf(_Z^2+RootOf(_Z^4+72)^2)*ln(-((3*x^2+2)^(1/4)*RootOf(_Z^4+72)^2*RootOf(_Z^2+RootOf(_Z^4+72)^2)-6*(3*x^2+2)^(3/4)*RootOf(_Z^2+RootOf(_Z^4+72)^2)+3*RootOf(_Z^4+72)^2*x-18*(3*x^2+2)^(1/2)*x)/(3*x^2+4))+1/24*RootOf(_Z^4+72)*ln(((3*x^2+2)^(1/4)*RootOf(_Z^4+72)^3+6*(3*x^2+2)^(3/4)*RootOf(_Z^4+72)+3*RootOf(_Z^4+72)^2*x+18*(3*x^2+2)^(1/2)*x)/(3*x^2+4))","C"
305,1,187,90,1.596000," ","int(1/(-3*x^2+2)^(1/4)/(-3*x^2+4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+72\right)^{2}\right) \ln \left(-\frac{-3 x \RootOf \left(\textit{\_Z}^{4}+72\right)^{2}+\left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+72\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}+72\right)^{2}-18 \sqrt{-3 x^{2}+2}\, x +6 \left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}+72\right)^{2}\right)}{3 x^{2}-4}\right)}{24}+\frac{\RootOf \left(\textit{\_Z}^{4}+72\right) \ln \left(-\frac{3 x \RootOf \left(\textit{\_Z}^{4}+72\right)^{2}+\left(-3 x^{2}+2\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{4}+72\right)^{3}-18 \sqrt{-3 x^{2}+2}\, x -6 \left(-3 x^{2}+2\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{4}+72\right)}{3 x^{2}-4}\right)}{24}"," ",0,"1/24*RootOf(_Z^4+72)*ln(-((-3*x^2+2)^(1/4)*RootOf(_Z^4+72)^3-6*(-3*x^2+2)^(3/4)*RootOf(_Z^4+72)+3*RootOf(_Z^4+72)^2*x-18*(-3*x^2+2)^(1/2)*x)/(3*x^2-4))-1/24*RootOf(_Z^2+RootOf(_Z^4+72)^2)*ln(-((-3*x^2+2)^(1/4)*RootOf(_Z^4+72)^2*RootOf(_Z^2+RootOf(_Z^4+72)^2)+6*(-3*x^2+2)^(3/4)*RootOf(_Z^2+RootOf(_Z^4+72)^2)-3*RootOf(_Z^4+72)^2*x-18*(-3*x^2+2)^(1/2)*x)/(3*x^2-4))","C"
306,0,0,93,0.331000," ","int(1/(b*x^2+2)^(1/4)/(b*x^2+4),x)","\int \frac{1}{\left(b \,x^{2}+2\right)^{\frac{1}{4}} \left(b \,x^{2}+4\right)}\, dx"," ",0,"int(1/(b*x^2+2)^(1/4)/(b*x^2+4),x)","F"
307,0,0,94,0.335000," ","int(1/(-b*x^2+2)^(1/4)/(-b*x^2+4),x)","\int \frac{1}{\left(-b \,x^{2}+2\right)^{\frac{1}{4}} \left(-b \,x^{2}+4\right)}\, dx"," ",0,"int(1/(-b*x^2+2)^(1/4)/(-b*x^2+4),x)","F"
308,0,0,90,0.344000," ","int(1/(3*x^2+a)^(1/4)/(3*x^2+2*a),x)","\int \frac{1}{\left(3 x^{2}+a \right)^{\frac{1}{4}} \left(3 x^{2}+2 a \right)}\, dx"," ",0,"int(1/(3*x^2+a)^(1/4)/(3*x^2+2*a),x)","F"
309,0,0,90,0.340000," ","int(1/(-3*x^2+a)^(1/4)/(-3*x^2+2*a),x)","\int \frac{1}{\left(-3 x^{2}+a \right)^{\frac{1}{4}} \left(-3 x^{2}+2 a \right)}\, dx"," ",0,"int(1/(-3*x^2+a)^(1/4)/(-3*x^2+2*a),x)","F"
310,0,0,88,0.334000," ","int(1/(b*x^2+a)^(1/4)/(b*x^2+2*a),x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{1}{4}} \left(b \,x^{2}+2 a \right)}\, dx"," ",0,"int(1/(b*x^2+a)^(1/4)/(b*x^2+2*a),x)","F"
311,0,0,92,0.336000," ","int(1/(-b*x^2+a)^(1/4)/(-b*x^2+2*a),x)","\int \frac{1}{\left(-b \,x^{2}+a \right)^{\frac{1}{4}} \left(-b \,x^{2}+2 a \right)}\, dx"," ",0,"int(1/(-b*x^2+a)^(1/4)/(-b*x^2+2*a),x)","F"
312,1,138,43,1.139000," ","int(1/(3*x^2-2)/(3*x^2-1)^(1/4),x)","\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(-\frac{-3 \sqrt{3 x^{2}-1}\, x -3 x +\left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)+\left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)}{3 x^{2}-2}\right)}{12}-\frac{\RootOf \left(\textit{\_Z}^{2}+6\right) \ln \left(\frac{3 \sqrt{3 x^{2}-1}\, x -3 x +\left(3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)-\left(3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)}{3 x^{2}-2}\right)}{12}"," ",0,"-1/12*RootOf(_Z^2+6)*ln((RootOf(_Z^2+6)*(3*x^2-1)^(3/4)+3*(3*x^2-1)^(1/2)*x-RootOf(_Z^2+6)*(3*x^2-1)^(1/4)-3*x)/(3*x^2-2))+1/12*RootOf(_Z^2-6)*ln(-(RootOf(_Z^2-6)*(3*x^2-1)^(3/4)-3*(3*x^2-1)^(1/2)*x+RootOf(_Z^2-6)*(3*x^2-1)^(1/4)-3*x)/(3*x^2-2))","C"
313,1,138,43,1.112000," ","int(1/(-3*x^2-2)/(-3*x^2-1)^(1/4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}-6\right) \ln \left(\frac{3 \sqrt{-3 x^{2}-1}\, x -3 x +\left(-3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)-\left(-3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}-6\right)}{3 x^{2}+2}\right)}{12}+\frac{\RootOf \left(\textit{\_Z}^{2}+6\right) \ln \left(-\frac{-3 \sqrt{-3 x^{2}-1}\, x -3 x +\left(-3 x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)+\left(-3 x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+6\right)}{3 x^{2}+2}\right)}{12}"," ",0,"-1/12*RootOf(_Z^2-6)*ln((RootOf(_Z^2-6)*(-3*x^2-1)^(3/4)+3*(-3*x^2-1)^(1/2)*x-RootOf(_Z^2-6)*(-3*x^2-1)^(1/4)-3*x)/(3*x^2+2))+1/12*RootOf(_Z^2+6)*ln(-(RootOf(_Z^2+6)*(-3*x^2-1)^(3/4)-3*(-3*x^2-1)^(1/2)*x+RootOf(_Z^2+6)*(-3*x^2-1)^(1/4)-3*x)/(3*x^2+2))","C"
314,0,0,55,0.335000," ","int(1/(b*x^2-2)/(b*x^2-1)^(1/4),x)","\int \frac{1}{\left(b \,x^{2}-2\right) \left(b \,x^{2}-1\right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(b*x^2-2)/(b*x^2-1)^(1/4),x)","F"
315,0,0,57,0.334000," ","int(1/(-b*x^2-2)/(-b*x^2-1)^(1/4),x)","\int \frac{1}{\left(-b \,x^{2}-2\right) \left(-b \,x^{2}-1\right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(-b*x^2-2)/(-b*x^2-1)^(1/4),x)","F"
316,0,0,59,0.351000," ","int(1/(3*x^2-2*a)/(3*x^2-a)^(1/4),x)","\int \frac{1}{\left(3 x^{2}-2 a \right) \left(3 x^{2}-a \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(3*x^2-2*a)/(3*x^2-a)^(1/4),x)","F"
317,0,0,59,0.363000," ","int(1/(-3*x^2-2*a)/(-3*x^2-a)^(1/4),x)","\int \frac{1}{\left(-3 x^{2}-2 a \right) \left(-3 x^{2}-a \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(-3*x^2-2*a)/(-3*x^2-a)^(1/4),x)","F"
318,0,0,71,0.342000," ","int(1/(b*x^2-2*a)/(b*x^2-a)^(1/4),x)","\int \frac{1}{\left(b \,x^{2}-2 a \right) \left(b \,x^{2}-a \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(b*x^2-2*a)/(b*x^2-a)^(1/4),x)","F"
319,0,0,73,0.337000," ","int(1/(-b*x^2-2*a)/(-b*x^2-a)^(1/4),x)","\int \frac{1}{\left(-b \,x^{2}-2 a \right) \left(-b \,x^{2}-a \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(-b*x^2-2*a)/(-b*x^2-a)^(1/4),x)","F"
320,1,121,39,1.220000," ","int(1/(-x^2+2)/(x^2-1)^(1/4),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}-2\right) \ln \left(-\frac{-\sqrt{x^{2}-1}\, x -x +\left(x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}-2\right)+\left(x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}-2\right)}{x^{2}-2}\right)}{4}-\frac{\RootOf \left(\textit{\_Z}^{2}+2\right) \ln \left(-\frac{-\sqrt{x^{2}-1}\, x +x +\left(x^{2}-1\right)^{\frac{3}{4}} \RootOf \left(\textit{\_Z}^{2}+2\right)-\left(x^{2}-1\right)^{\frac{1}{4}} \RootOf \left(\textit{\_Z}^{2}+2\right)}{x^{2}-2}\right)}{4}"," ",0,"-1/4*RootOf(_Z^2-2)*ln(-(RootOf(_Z^2-2)*(x^2-1)^(3/4)-(x^2-1)^(1/2)*x+RootOf(_Z^2-2)*(x^2-1)^(1/4)-x)/(x^2-2))-1/4*RootOf(_Z^2+2)*ln(-(RootOf(_Z^2+2)*(x^2-1)^(3/4)-(x^2-1)^(1/2)*x-RootOf(_Z^2+2)*(x^2-1)^(1/4)+x)/(x^2-2))","C"
321,0,0,352,0.344000," ","int((b*x^2+a)^(7/4)/(d*x^2+c),x)","\int \frac{\left(b \,x^{2}+a \right)^{\frac{7}{4}}}{d \,x^{2}+c}\, dx"," ",0,"int((b*x^2+a)^(7/4)/(d*x^2+c),x)","F"
322,0,0,306,0.344000," ","int((b*x^2+a)^(5/4)/(d*x^2+c),x)","\int \frac{\left(b \,x^{2}+a \right)^{\frac{5}{4}}}{d \,x^{2}+c}\, dx"," ",0,"int((b*x^2+a)^(5/4)/(d*x^2+c),x)","F"
323,0,0,225,0.336000," ","int((b*x^2+a)^(3/4)/(d*x^2+c),x)","\int \frac{\left(b \,x^{2}+a \right)^{\frac{3}{4}}}{d \,x^{2}+c}\, dx"," ",0,"int((b*x^2+a)^(3/4)/(d*x^2+c),x)","F"
324,0,0,190,0.329000," ","int((b*x^2+a)^(1/4)/(d*x^2+c),x)","\int \frac{\left(b \,x^{2}+a \right)^{\frac{1}{4}}}{d \,x^{2}+c}\, dx"," ",0,"int((b*x^2+a)^(1/4)/(d*x^2+c),x)","F"
325,0,0,131,0.333000," ","int(1/(b*x^2+a)^(1/4)/(d*x^2+c),x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{1}{4}} \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(1/(b*x^2+a)^(1/4)/(d*x^2+c),x)","F"
326,0,0,124,0.335000," ","int(1/(b*x^2+a)^(3/4)/(d*x^2+c),x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{3}{4}} \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(1/(b*x^2+a)^(3/4)/(d*x^2+c),x)","F"
327,0,0,216,0.339000," ","int(1/(b*x^2+a)^(5/4)/(d*x^2+c),x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{5}{4}} \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(1/(b*x^2+a)^(5/4)/(d*x^2+c),x)","F"
328,0,0,239,0.337000," ","int(1/(b*x^2+a)^(7/4)/(d*x^2+c),x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{7}{4}} \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(1/(b*x^2+a)^(7/4)/(d*x^2+c),x)","F"
329,0,0,251,0.349000," ","int(1/(b*x^2+a)^(9/4)/(d*x^2+c),x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{9}{4}} \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(1/(b*x^2+a)^(9/4)/(d*x^2+c),x)","F"
330,0,0,285,0.351000," ","int(1/(b*x^2+a)^(11/4)/(d*x^2+c),x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{11}{4}} \left(d \,x^{2}+c \right)}\, dx"," ",0,"int(1/(b*x^2+a)^(11/4)/(d*x^2+c),x)","F"
331,0,0,309,0.351000," ","int((b*x^2+a)^(7/4)/(d*x^2+c)^2,x)","\int \frac{\left(b \,x^{2}+a \right)^{\frac{7}{4}}}{\left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int((b*x^2+a)^(7/4)/(d*x^2+c)^2,x)","F"
332,0,0,260,0.344000," ","int((b*x^2+a)^(5/4)/(d*x^2+c)^2,x)","\int \frac{\left(b \,x^{2}+a \right)^{\frac{5}{4}}}{\left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int((b*x^2+a)^(5/4)/(d*x^2+c)^2,x)","F"
333,0,0,278,0.347000," ","int((b*x^2+a)^(3/4)/(d*x^2+c)^2,x)","\int \frac{\left(b \,x^{2}+a \right)^{\frac{3}{4}}}{\left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int((b*x^2+a)^(3/4)/(d*x^2+c)^2,x)","F"
334,0,0,259,0.339000," ","int((b*x^2+a)^(1/4)/(d*x^2+c)^2,x)","\int \frac{\left(b \,x^{2}+a \right)^{\frac{1}{4}}}{\left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int((b*x^2+a)^(1/4)/(d*x^2+c)^2,x)","F"
335,0,0,305,0.344000," ","int(1/(b*x^2+a)^(1/4)/(d*x^2+c)^2,x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{1}{4}} \left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^2+a)^(1/4)/(d*x^2+c)^2,x)","F"
336,0,0,273,0.344000," ","int(1/(b*x^2+a)^(3/4)/(d*x^2+c)^2,x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{3}{4}} \left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^2+a)^(3/4)/(d*x^2+c)^2,x)","F"
337,0,0,287,0.356000," ","int(1/(b*x^2+a)^(5/4)/(d*x^2+c)^2,x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{5}{4}} \left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^2+a)^(5/4)/(d*x^2+c)^2,x)","F"
338,0,0,322,0.357000," ","int(1/(b*x^2+a)^(7/4)/(d*x^2+c)^2,x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{7}{4}} \left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^2+a)^(7/4)/(d*x^2+c)^2,x)","F"
339,0,0,340,0.370000," ","int(1/(b*x^2+a)^(9/4)/(d*x^2+c)^2,x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{9}{4}} \left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^2+a)^(9/4)/(d*x^2+c)^2,x)","F"
340,0,0,392,0.370000," ","int(1/(b*x^2+a)^(11/4)/(d*x^2+c)^2,x)","\int \frac{1}{\left(b \,x^{2}+a \right)^{\frac{11}{4}} \left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^2+a)^(11/4)/(d*x^2+c)^2,x)","F"
341,0,0,75,0.507000," ","int((b*x^2+a)^p*(d*x^2+c)^q,x)","\int \left(b \,x^{2}+a \right)^{p} \left(d \,x^{2}+c \right)^{q}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^q,x)","F"
342,0,0,284,0.361000," ","int((b*x^2+a)^p*(d*x^2+c)^3,x)","\int \left(d \,x^{2}+c \right)^{3} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^3,x)","F"
343,0,0,170,0.308000," ","int((b*x^2+a)^p*(d*x^2+c)^2,x)","\int \left(d \,x^{2}+c \right)^{2} \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c)^2,x)","F"
344,0,0,91,0.304000," ","int((b*x^2+a)^p*(d*x^2+c),x)","\int \left(d \,x^{2}+c \right) \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int((b*x^2+a)^p*(d*x^2+c),x)","F"
345,0,0,42,0.000000," ","int((b*x^2+a)^p,x)","\int \left(b \,x^{2}+a \right)^{p}\, dx"," ",0,"int((b*x^2+a)^p,x)","F"
346,0,0,53,0.320000," ","int((b*x^2+a)^p/(d*x^2+c),x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{d \,x^{2}+c}\, dx"," ",0,"int((b*x^2+a)^p/(d*x^2+c),x)","F"
347,0,0,53,0.311000," ","int((b*x^2+a)^p/(d*x^2+c)^2,x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{\left(d \,x^{2}+c \right)^{2}}\, dx"," ",0,"int((b*x^2+a)^p/(d*x^2+c)^2,x)","F"
348,0,0,53,0.313000," ","int((b*x^2+a)^p/(d*x^2+c)^3,x)","\int \frac{\left(b \,x^{2}+a \right)^{p}}{\left(d \,x^{2}+c \right)^{3}}\, dx"," ",0,"int((b*x^2+a)^p/(d*x^2+c)^3,x)","F"
349,1,71,54,0.005000," ","int((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)","\frac{x \left(b \,x^{2}+a \right)^{1-\frac{2 a d -3 b c}{2 \left(a d -b c \right)}} \left(d \,x^{2}+c \right)^{1-\frac{3 a d -2 b c}{2 \left(a d -b c \right)}}}{a c}"," ",0,"(b*x^2+a)^(1-1/2*(2*a*d-3*b*c)/(a*d-b*c))*(d*x^2+c)^(1-1/2*(3*a*d-2*b*c)/(a*d-b*c))/a/c*x","A"