1,1,97,84,0.038000," ","int((b*x^3+a)*(d*x^3+c)^4,x)","\frac{b \,d^{4} x^{16}}{16}+\frac{\left(a \,d^{4}+4 b c \,d^{3}\right) x^{13}}{13}+\frac{\left(4 a c \,d^{3}+6 c^{2} d^{2} b \right) x^{10}}{10}+\frac{\left(6 a \,c^{2} d^{2}+4 c^{3} d b \right) x^{7}}{7}+a \,c^{4} x +\frac{\left(4 a \,c^{3} d +b \,c^{4}\right) x^{4}}{4}"," ",0,"1/16*b*d^4*x^16+1/13*(a*d^4+4*b*c*d^3)*x^13+1/10*(4*a*c*d^3+6*b*c^2*d^2)*x^10+1/7*(6*a*c^2*d^2+4*b*c^3*d)*x^7+1/4*(4*a*c^3*d+b*c^4)*x^4+a*c^4*x","A"
2,1,73,62,0.044000," ","int((b*x^3+a)*(d*x^3+c)^3,x)","\frac{b \,d^{3} x^{13}}{13}+\frac{\left(a \,d^{3}+3 b c \,d^{2}\right) x^{10}}{10}+\frac{\left(3 a c \,d^{2}+3 b \,c^{2} d \right) x^{7}}{7}+a \,c^{3} x +\frac{\left(3 a \,c^{2} d +b \,c^{3}\right) x^{4}}{4}"," ",0,"1/13*b*d^3*x^13+1/10*(a*d^3+3*b*c*d^2)*x^10+1/7*(3*a*c*d^2+3*b*c^2*d)*x^7+1/4*(3*a*c^2*d+b*c^3)*x^4+a*c^3*x","A"
3,1,49,44,0.044000," ","int((b*x^3+a)*(d*x^3+c)^2,x)","\frac{b \,d^{2} x^{10}}{10}+\frac{\left(a \,d^{2}+2 b c d \right) x^{7}}{7}+a \,c^{2} x +\frac{\left(2 a c d +b \,c^{2}\right) x^{4}}{4}"," ",0,"1/10*b*d^2*x^10+1/7*(a*d^2+2*b*c*d)*x^7+1/4*(2*a*c*d+b*c^2)*x^4+a*c^2*x","A"
4,1,25,24,0.040000," ","int((b*x^3+a)*(d*x^3+c),x)","\frac{b d \,x^{7}}{7}+\frac{\left(a d +b c \right) x^{4}}{4}+a c x"," ",0,"a*c*x+1/4*(a*d+b*c)*x^4+1/7*b*d*x^7","A"
5,1,195,108,0.048000," ","int((b*x^3+a)/(d*x^3+c),x)","\frac{\sqrt{3}\, a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}+\frac{a \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}-\frac{a \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}-\frac{\sqrt{3}\, b c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}-\frac{b c \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{b c \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{b x}{d}"," ",0,"b*x/d+1/3/d/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a-1/3/d^2/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*b*c-1/6/d/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a+1/6/d^2/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*b*c+1/3/d/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a-1/3/d^2/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*b*c","A"
6,1,221,128,0.052000," ","int((b*x^3+a)/(d*x^3+c)^2,x)","\frac{2 \sqrt{3}\, a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} c d}+\frac{2 a \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} c d}-\frac{a \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} c d}+\frac{\sqrt{3}\, b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{b \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}-\frac{b \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{\left(a d -b c \right) x}{3 \left(d \,x^{3}+c \right) c d}"," ",0,"1/3*(a*d-b*c)/d/c*x/(d*x^3+c)+2/9/c/d/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a+1/9/d^2/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*b-1/9/c/d/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a-1/18/d^2/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*b+2/9/c/d/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a+1/9/d^2/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*b","A"
7,1,249,154,0.059000," ","int((b*x^3+a)/(d*x^3+c)^3,x)","\frac{5 \sqrt{3}\, a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{c}{d}\right)^{\frac{2}{3}} c^{2} d}+\frac{5 a \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{c}{d}\right)^{\frac{2}{3}} c^{2} d}-\frac{5 a \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{c}{d}\right)^{\frac{2}{3}} c^{2} d}+\frac{\sqrt{3}\, b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{c}{d}\right)^{\frac{2}{3}} c \,d^{2}}+\frac{b \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{c}{d}\right)^{\frac{2}{3}} c \,d^{2}}-\frac{b \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{c}{d}\right)^{\frac{2}{3}} c \,d^{2}}+\frac{\frac{\left(5 a d +b c \right) x^{4}}{18 c^{2}}+\frac{\left(4 a d -b c \right) x}{9 c d}}{\left(d \,x^{3}+c \right)^{2}}"," ",0,"(1/18*(5*a*d+b*c)/c^2*x^4+1/9*(4*a*d-b*c)/c/d*x)/(d*x^3+c)^2+5/27/c^2/d/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a+1/27/c/d^2/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*b-5/54/c^2/d/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a-1/54/c/d^2/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*b+5/27/c^2/d/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a+1/27/c/d^2/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*b","A"
8,1,125,112,0.050000," ","int((b*x^3+a)^2*(d*x^3+c)^3,x)","\frac{b^{2} d^{3} x^{16}}{16}+\frac{\left(2 a b \,d^{3}+3 b^{2} c \,d^{2}\right) x^{13}}{13}+\frac{\left(a^{2} d^{3}+6 a b c \,d^{2}+3 b^{2} c^{2} d \right) x^{10}}{10}+\frac{\left(3 a^{2} c \,d^{2}+6 a b \,c^{2} d +b^{2} c^{3}\right) x^{7}}{7}+a^{2} c^{3} x +\frac{\left(3 a^{2} c^{2} d +2 a b \,c^{3}\right) x^{4}}{4}"," ",0,"1/16*b^2*d^3*x^16+1/13*(2*a*b*d^3+3*b^2*c*d^2)*x^13+1/10*(a^2*d^3+6*a*b*c*d^2+3*b^2*c^2*d)*x^10+1/7*(3*a^2*c*d^2+6*a*b*c^2*d+b^2*c^3)*x^7+1/4*(3*a^2*c^2*d+2*a*b*c^3)*x^4+a^2*c^3*x","A"
9,1,87,74,0.037000," ","int((b*x^3+a)^2*(d*x^3+c)^2,x)","\frac{b^{2} d^{2} x^{13}}{13}+\frac{\left(2 a b \,d^{2}+2 b^{2} c d \right) x^{10}}{10}+\frac{\left(a^{2} d^{2}+4 a b c d +b^{2} c^{2}\right) x^{7}}{7}+a^{2} c^{2} x +\frac{\left(2 a^{2} c d +2 a b \,c^{2}\right) x^{4}}{4}"," ",0,"1/13*b^2*d^2*x^13+1/10*(2*a*b*d^2+2*b^2*c*d)*x^10+1/7*(a^2*d^2+4*a*b*c*d+b^2*c^2)*x^7+1/4*(2*a^2*c*d+2*a*b*c^2)*x^4+a^2*c^2*x","A"
10,1,49,44,0.039000," ","int((b*x^3+a)^2*(d*x^3+c),x)","\frac{b^{2} d \,x^{10}}{10}+\frac{\left(2 a b d +b^{2} c \right) x^{7}}{7}+a^{2} c x +\frac{\left(a^{2} d +2 a b c \right) x^{4}}{4}"," ",0,"1/10*b^2*d*x^10+1/7*(2*a*b*d+b^2*c)*x^7+1/4*(a^2*d+2*a*b*c)*x^4+a^2*c*x","A"
11,1,334,134,0.046000," ","int((b*x^3+a)^2/(d*x^3+c),x)","\frac{b^{2} x^{4}}{4 d}+\frac{\sqrt{3}\, a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}+\frac{a^{2} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}-\frac{a^{2} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}-\frac{2 \sqrt{3}\, a b c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}-\frac{2 a b c \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{a b c \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{2 a b x}{d}+\frac{\sqrt{3}\, b^{2} c^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{3}}+\frac{b^{2} c^{2} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{3}}-\frac{b^{2} c^{2} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{3}}-\frac{b^{2} c x}{d^{2}}"," ",0,"1/4*b^2*x^4/d+2*b/d*a*x-b^2/d^2*c*x+1/3/d/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a^2-2/3/d^2/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a*b*c+1/3/d^3/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*b^2*c^2-1/6/d/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a^2+1/3/d^2/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a*b*c-1/6/d^3/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*b^2*c^2+1/3/d/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a^2-2/3/d^2/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a*b*c+1/3/d^3/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*b^2*c^2","B"
12,1,367,162,0.062000," ","int((b*x^3+a)^2/(d*x^3+c)^2,x)","\frac{a^{2} x}{3 \left(d \,x^{3}+c \right) c}-\frac{2 a b x}{3 \left(d \,x^{3}+c \right) d}+\frac{b^{2} c x}{3 \left(d \,x^{3}+c \right) d^{2}}+\frac{2 \sqrt{3}\, a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} c d}+\frac{2 a^{2} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} c d}-\frac{a^{2} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} c d}+\frac{2 \sqrt{3}\, a b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{2 a b \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}-\frac{a b \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}-\frac{4 \sqrt{3}\, b^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{3}}-\frac{4 b^{2} c \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{3}}+\frac{2 b^{2} c \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{3}}+\frac{b^{2} x}{d^{2}}"," ",0,"b^2*x/d^2+1/3/c*x/(d*x^3+c)*a^2-2/3/d*x/(d*x^3+c)*a*b+1/3/d^2*c*x/(d*x^3+c)*b^2+2/9/d/c/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a^2+2/9/d^2/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a*b-4/9/d^3*c/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*b^2-1/9/d/c/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a^2-1/9/d^2/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a*b+2/9/d^3*c/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*b^2+2/9/d/c/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a^2+2/9/d^2/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a*b-4/9/d^3*c/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*b^2","B"
13,-1,0,215,180.000000," ","int((b*x^3+a)^2/(d*x^3+c)^3,x)","\text{hanged}"," ",0,"int((b*x^3+a)^2/(d*x^3+c)^3,x)","F"
14,1,661,209,0.047000," ","int((d*x^3+c)^4/(b*x^3+a),x)","\frac{d^{4} x^{10}}{10 b}-\frac{a \,d^{4} x^{7}}{7 b^{2}}+\frac{4 c \,d^{3} x^{7}}{7 b}+\frac{a^{2} d^{4} x^{4}}{4 b^{3}}-\frac{a c \,d^{3} x^{4}}{b^{2}}+\frac{3 c^{2} d^{2} x^{4}}{2 b}+\frac{\sqrt{3}\, a^{4} d^{4} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{a^{4} d^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{a^{4} d^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{4 \sqrt{3}\, a^{3} c \,d^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{4 a^{3} c \,d^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{2 a^{3} c \,d^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{a^{3} d^{4} x}{b^{4}}+\frac{2 \sqrt{3}\, a^{2} c^{2} d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 a^{2} c^{2} d^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{\left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{a^{2} c^{2} d^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{\left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{4 a^{2} c \,d^{3} x}{b^{3}}-\frac{4 \sqrt{3}\, a \,c^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{4 a \,c^{3} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{2 a \,c^{3} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{6 a \,c^{2} d^{2} x}{b^{2}}+\frac{\sqrt{3}\, c^{4} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{c^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{c^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{4 c^{3} d x}{b}"," ",0,"-4/3/b^4/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^3*c*d^3+2/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^2*c^2*d^2-4/3/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a*c^3*d-1/7*d^4/b^2*x^7*a+4/7*d^3/b*x^7*c-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^4+1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^4+4*d/b*c^3*x+1/4*d^4/b^3*x^4*a^2+3/2*d^2/b*x^4*c^2-d^4/b^4*a^3*x-4/3/b^4/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a^3*c*d^3+2/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a^2*c^2*d^2-4/3/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a*c^3*d+2/3/b^4/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^3*c*d^3-1/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^2*c^2*d^2+2/3/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a*c^3*d+1/3/b^5/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^4*d^4-6*d^2/b^2*a*c^2*x-d^3/b^2*x^4*a*c+4*d^3/b^3*a^2*c*x+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^4+1/3/b^5/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a^4*d^4-1/6/b^5/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^4*d^4+1/10*d^4*x^10/b","B"
15,1,486,167,0.046000," ","int((d*x^3+c)^3/(b*x^3+a),x)","\frac{d^{3} x^{7}}{7 b}-\frac{a \,d^{3} x^{4}}{4 b^{2}}+\frac{3 c \,d^{2} x^{4}}{4 b}-\frac{\sqrt{3}\, a^{3} d^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{a^{3} d^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{a^{3} d^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{\sqrt{3}\, a^{2} c \,d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} c \,d^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{\left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{a^{2} c \,d^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} d^{3} x}{b^{3}}-\frac{\sqrt{3}\, a \,c^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a \,c^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{\left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a \,c^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{3 a c \,d^{2} x}{b^{2}}+\frac{\sqrt{3}\, c^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{c^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{c^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{3 c^{2} d x}{b}"," ",0,"1/7*d^3*x^7/b-1/4*d^3/b^2*x^4*a+3/4*d^2/b*x^4*c+d^3/b^3*a^2*x-3*d^2/b^2*a*c*x+3*d/b*c^2*x-1/3/b^4/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a^3*d^3+1/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a^2*c*d^2-1/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a*c^2*d+1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^3+1/6/b^4/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^3*d^3-1/2/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^2*c*d^2+1/2/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a*c^2*d-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^3-1/3/b^4/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^3*d^3+1/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^2*c*d^2-1/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a*c^2*d+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^3","B"
16,1,334,134,0.043000," ","int((d*x^3+c)^2/(b*x^3+a),x)","\frac{d^{2} x^{4}}{4 b}+\frac{\sqrt{3}\, a^{2} d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} d^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{a^{2} d^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{2 \sqrt{3}\, a c d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{2 a c d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a c d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a \,d^{2} x}{b^{2}}+\frac{\sqrt{3}\, c^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{c^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{c^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{2 c d x}{b}"," ",0,"1/4*d^2*x^4/b-d^2/b^2*a*x+2*d/b*c*x+1/3/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a^2*d^2-2/3/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a*c*d+1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^2-1/6/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^2*d^2+1/3/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a*c*d-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^2+1/3/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^2*d^2-2/3/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a*c*d+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^2","B"
17,1,195,108,0.046000," ","int((d*x^3+c)/(b*x^3+a),x)","-\frac{\sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{d x}{b}"," ",0,"d*x/b-1/3/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a*d+1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c+1/6/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a*d-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/3/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a*d+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","A"
18,1,222,215,0.050000," ","int(1/(b*x^3+a)/(d*x^3+c),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{\sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}}}-\frac{\ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{\ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}}}+\frac{\ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{\ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right) \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"-1/3/(a*d-b*c)/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+1/6/(a*d-b*c)/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/(a*d-b*c)/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/(a*d-b*c)/(c/d)^(2/3)*ln(x+(c/d)^(1/3))-1/6/(a*d-b*c)/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))+1/3/(a*d-b*c)/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))","A"
19,1,406,268,0.054000," ","int(1/(b*x^3+a)/(d*x^3+c)^2,x)","\frac{a \,d^{2} x}{3 \left(a d -b c \right)^{2} \left(d \,x^{3}+c \right) c}-\frac{b d x}{3 \left(a d -b c \right)^{2} \left(d \,x^{3}+c \right)}+\frac{2 \sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} c}+\frac{2 a d \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} c}-\frac{a d \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{9 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}} c}+\frac{\sqrt{3}\, b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{5 \sqrt{3}\, b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}}+\frac{b \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{5 b \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}}-\frac{b \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{5 b \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{18 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"1/3*b/(a*d-b*c)^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/6*b/(a*d-b*c)^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*b/(a*d-b*c)^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*d^2/(a*d-b*c)^2/c*x/(d*x^3+c)*a-1/3*d/(a*d-b*c)^2*x/(d*x^3+c)*b+2/9*d/(a*d-b*c)^2/c/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a-5/9/(a*d-b*c)^2/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*b-1/9*d/(a*d-b*c)^2/c/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a+5/18/(a*d-b*c)^2/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*b+2/9*d/(a*d-b*c)^2/c/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a-5/9/(a*d-b*c)^2/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*b","A"
20,1,905,273,0.060000," ","int((d*x^3+c)^5/(b*x^3+a)^2,x)","\frac{d^{5} x^{10}}{10 b^{2}}-\frac{2 a \,d^{5} x^{7}}{7 b^{3}}+\frac{5 c \,d^{4} x^{7}}{7 b^{2}}+\frac{3 a^{2} d^{5} x^{4}}{4 b^{4}}-\frac{5 a c \,d^{4} x^{4}}{2 b^{3}}+\frac{5 c^{2} d^{3} x^{4}}{2 b^{2}}-\frac{a^{4} d^{5} x}{3 \left(b \,x^{3}+a \right) b^{5}}+\frac{5 a^{3} c \,d^{4} x}{3 \left(b \,x^{3}+a \right) b^{4}}-\frac{10 a^{2} c^{2} d^{3} x}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{10 a \,c^{3} d^{2} x}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{c^{5} x}{3 \left(b \,x^{3}+a \right) a}-\frac{5 c^{4} d x}{3 \left(b \,x^{3}+a \right) b}+\frac{13 \sqrt{3}\, a^{4} d^{5} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}+\frac{13 a^{4} d^{5} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{13 a^{4} d^{5} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{50 \sqrt{3}\, a^{3} c \,d^{4} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{50 a^{3} c \,d^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{25 a^{3} c \,d^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{4 a^{3} d^{5} x}{b^{5}}+\frac{70 \sqrt{3}\, a^{2} c^{2} d^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{70 a^{2} c^{2} d^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{35 a^{2} c^{2} d^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{15 a^{2} c \,d^{4} x}{b^{4}}-\frac{40 \sqrt{3}\, a \,c^{3} d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{40 a \,c^{3} d^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{20 a \,c^{3} d^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{20 a \,c^{2} d^{3} x}{b^{3}}+\frac{2 \sqrt{3}\, c^{5} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 c^{5} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{c^{5} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{5 \sqrt{3}\, c^{4} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{5 c^{4} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{5 c^{4} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{10 c^{3} d^{2} x}{b^{2}}"," ",0,"-50/9/b^5*a^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c*d^4+70/9/b^4*a^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^2*d^3-40/9/b^3*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^3*d^2-2/7*d^5/b^3*x^7*a+5/7*d^4/b^2*x^7*c+3/4*d^5/b^4*x^4*a^2+5/2*d^3/b^2*x^4*c^2-4*d^5/b^5*a^3*x+10*d^2/b^2*c^3*x+1/3/a*x/(b*x^3+a)*c^5-35/9/b^4*a^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^2*d^3+20/9/b^3*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^3*d^2-50/9/b^5*a^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c*d^4+70/9/b^4*a^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^2*d^3-40/9/b^3*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^3*d^2+25/9/b^5*a^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c*d^4-10/3/b^3*a^2*x/(b*x^3+a)*c^2*d^3+10/3/b^2*a*x/(b*x^3+a)*c^3*d^2+13/9/b^6*a^4/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d^5+5/9/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^4*d+2/9/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^5+5/3/b^4*a^3*x/(b*x^3+a)*c*d^4-13/18/b^6*a^4/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d^5-5/18/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^4*d-1/9/b/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^5+13/9/b^6*a^4/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d^5+5/9/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^4*d+2/9/b/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^5-5/2*d^4/b^3*x^4*a*c+15*d^4/b^4*a^2*c*x-1/3/b^5*a^4*x/(b*x^3+a)*d^5-5/3/b*x/(b*x^3+a)*c^4*d-20*d^3/b^3*a*c^2*x+1/10*d^5*x^10/b^2","B"
21,1,708,222,0.057000," ","int((d*x^3+c)^4/(b*x^3+a)^2,x)","\frac{d^{4} x^{7}}{7 b^{2}}-\frac{a \,d^{4} x^{4}}{2 b^{3}}+\frac{c \,d^{3} x^{4}}{b^{2}}+\frac{a^{3} d^{4} x}{3 \left(b \,x^{3}+a \right) b^{4}}-\frac{4 a^{2} c \,d^{3} x}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{2 a \,c^{2} d^{2} x}{\left(b \,x^{3}+a \right) b^{2}}+\frac{c^{4} x}{3 \left(b \,x^{3}+a \right) a}-\frac{4 c^{3} d x}{3 \left(b \,x^{3}+a \right) b}-\frac{10 \sqrt{3}\, a^{3} d^{4} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{10 a^{3} d^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{5 a^{3} d^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{28 \sqrt{3}\, a^{2} c \,d^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{28 a^{2} c \,d^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{14 a^{2} c \,d^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{3 a^{2} d^{4} x}{b^{4}}-\frac{8 \sqrt{3}\, a \,c^{2} d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{8 a \,c^{2} d^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{4 a \,c^{2} d^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{8 a c \,d^{3} x}{b^{3}}+\frac{2 \sqrt{3}\, c^{4} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 c^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{c^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{4 \sqrt{3}\, c^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{4 c^{3} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{2 c^{3} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{6 c^{2} d^{2} x}{b^{2}}"," ",0,"-8/3/b^3*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^2*d^2+28/9/b^4*a^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c*d^3+6*d^2/b^2*c^2*x-1/2*d^4/b^3*x^4*a+d^3/b^2*x^4*c+1/3/a*x/(b*x^3+a)*c^4+3*d^4/b^4*a^2*x-10/9/b^5*a^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d^4+4/9/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^3*d+2/9/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^4-4/3/b^3*a^2*x/(b*x^3+a)*c*d^3+2/b^2*a*x/(b*x^3+a)*c^2*d^2+28/9/b^4*a^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c*d^3-8/3/b^3*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^2*d^2-14/9/b^4*a^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c*d^3+4/3/b^3*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^2*d^2+5/9/b^5*a^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d^4-10/9/b^5*a^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d^4-2/9/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^3*d-1/9/b/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^4+1/3/b^4*a^3*x/(b*x^3+a)*d^4-4/3/b*x/(b*x^3+a)*c^3*d-8*d^3/b^3*a*c*x+4/9/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^3*d+2/9/b/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^4+1/7*d^4*x^7/b^2","B"
22,1,529,191,0.053000," ","int((d*x^3+c)^3/(b*x^3+a)^2,x)","\frac{d^{3} x^{4}}{4 b^{2}}-\frac{a^{2} d^{3} x}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a c \,d^{2} x}{\left(b \,x^{3}+a \right) b^{2}}+\frac{c^{3} x}{3 \left(b \,x^{3}+a \right) a}-\frac{c^{2} d x}{\left(b \,x^{3}+a \right) b}+\frac{7 \sqrt{3}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 a^{2} d^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{7 a^{2} d^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{4 \sqrt{3}\, a c \,d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 a c \,d^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 a c \,d^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{2 a \,d^{3} x}{b^{3}}+\frac{2 \sqrt{3}\, c^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 c^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{c^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, c^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{c^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{c^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{3 c \,d^{2} x}{b^{2}}"," ",0,"1/4*d^3*x^4/b^2-2*d^3/b^3*a*x+3*d^2/b^2*c*x-1/3/b^3*a^2*x/(b*x^3+a)*d^3+1/b^2*a*x/(b*x^3+a)*c*d^2-1/b*x/(b*x^3+a)*c^2*d+1/3/a*x/(b*x^3+a)*c^3+7/9/b^4*a^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d^3-4/3/b^3*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c*d^2+1/3/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^2*d+2/9/b/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^3-7/18/b^4*a^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d^3+2/3/b^3*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c*d^2-1/6/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^2*d-1/9/b/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^3+7/9/b^4*a^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d^3-4/3/b^3*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c*d^2+1/3/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^2*d+2/9/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^3","B"
23,1,367,162,0.053000," ","int((d*x^3+c)^2/(b*x^3+a)^2,x)","\frac{a \,d^{2} x}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{c^{2} x}{3 \left(b \,x^{3}+a \right) a}-\frac{2 c d x}{3 \left(b \,x^{3}+a \right) b}-\frac{4 \sqrt{3}\, a \,d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 a \,d^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 a \,d^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 \sqrt{3}\, c^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 c^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{c^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 \sqrt{3}\, c d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{2 c d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{c d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{d^{2} x}{b^{2}}"," ",0,"d^2*x/b^2+1/3/b^2*a*x/(b*x^3+a)*d^2-2/3/b*x/(b*x^3+a)*c*d+1/3/a*x/(b*x^3+a)*c^2-4/9/b^3*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d^2+2/9/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c*d+2/9/b/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c^2+2/9/b^3*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d^2-1/9/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c*d-1/9/b/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c^2-4/9/b^3*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d^2+2/9/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c*d+2/9/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c^2","B"
24,1,221,128,0.054000," ","int((d*x^3+c)/(b*x^3+a)^2,x)","\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{\left(a d -b c \right) x}{3 \left(b \,x^{3}+a \right) a b}"," ",0,"-1/3*(a*d-b*c)/a/b*x/(b*x^3+a)+1/9/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d+2/9/b/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/18/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-1/9/b/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/9/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+2/9/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","A"
25,1,406,268,0.056000," ","int(1/(b*x^3+a)^2/(d*x^3+c),x)","\frac{b^{2} c x}{3 \left(a d -b c \right)^{2} \left(b \,x^{3}+a \right) a}-\frac{b d x}{3 \left(a d -b c \right)^{2} \left(b \,x^{3}+a \right)}+\frac{2 \sqrt{3}\, b c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{2 b c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{b c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{5 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}}-\frac{5 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{d \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}}+\frac{5 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(a d -b c \right)^{2} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{d \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(a d -b c \right)^{2} \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"-1/3*b/(a*d-b*c)^2*x/(b*x^3+a)*d+1/3*b^2/(a*d-b*c)^2/a*x/(b*x^3+a)*c-5/9/(a*d-b*c)^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d+2/9*b/(a*d-b*c)^2/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c+5/18/(a*d-b*c)^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-1/9*b/(a*d-b*c)^2/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-5/9/(a*d-b*c)^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+2/9*b/(a*d-b*c)^2/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c+1/3*d/(a*d-b*c)^2/(c/d)^(2/3)*ln(x+(c/d)^(1/3))-1/6*d/(a*d-b*c)^2/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))+1/3*d/(a*d-b*c)^2/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))","A"
26,1,606,337,0.062000," ","int(1/(b*x^3+a)^2/(d*x^3+c)^2,x)","\frac{a \,d^{3} x}{3 \left(a d -b c \right)^{3} \left(d \,x^{3}+c \right) c}-\frac{b^{3} c x}{3 \left(a d -b c \right)^{3} \left(b \,x^{3}+a \right) a}+\frac{b^{2} d x}{3 \left(a d -b c \right)^{3} \left(b \,x^{3}+a \right)}-\frac{b \,d^{2} x}{3 \left(a d -b c \right)^{3} \left(d \,x^{3}+c \right)}+\frac{2 \sqrt{3}\, a \,d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}} c}+\frac{2 a \,d^{2} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}} c}-\frac{a \,d^{2} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}} c}-\frac{2 \sqrt{3}\, b^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{2 b^{2} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{b^{2} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{8 \sqrt{3}\, b d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{8 \sqrt{3}\, b d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}}+\frac{8 b d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}-\frac{8 b d \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}}-\frac{4 b d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{a}{b}\right)^{\frac{2}{3}}}+\frac{4 b d \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{9 \left(a d -b c \right)^{3} \left(\frac{c}{d}\right)^{\frac{2}{3}}}"," ",0,"1/3*b^2/(a*d-b*c)^3*x/(b*x^3+a)*d-1/3*b^3/(a*d-b*c)^3/a*x/(b*x^3+a)*c+8/9*b/(a*d-b*c)^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d-2/9*b^2/(a*d-b*c)^3/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-4/9*b/(a*d-b*c)^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/9*b^2/(a*d-b*c)^3/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+8/9*b/(a*d-b*c)^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-2/9*b^2/(a*d-b*c)^3/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c+1/3*d^3/(a*d-b*c)^3/c*x/(d*x^3+c)*a-1/3*d^2/(a*d-b*c)^3*x/(d*x^3+c)*b+2/9*d^2/(a*d-b*c)^3/c/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a-8/9*d/(a*d-b*c)^3/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*b-1/9*d^2/(a*d-b*c)^3/c/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a+4/9*d/(a*d-b*c)^3/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*b+2/9*d^2/(a*d-b*c)^3/c/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a-8/9*d/(a*d-b*c)^3/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*b","A"
27,0,0,85,0.429000," ","int((-b*x^3+a)*(b*x^3+a)^(2/3),x)","\int \left(-b \,x^{3}+a \right) \left(b \,x^{3}+a \right)^{\frac{2}{3}}\, dx"," ",0,"int((-b*x^3+a)*(b*x^3+a)^(2/3),x)","F"
28,0,0,68,0.366000," ","int((-b*x^3+a)/(b*x^3+a)^(1/3),x)","\int \frac{-b \,x^{3}+a}{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((-b*x^3+a)/(b*x^3+a)^(1/3),x)","F"
29,0,0,66,0.387000," ","int((-b*x^3+a)/(b*x^3+a)^(4/3),x)","\int \frac{-b \,x^{3}+a}{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}\, dx"," ",0,"int((-b*x^3+a)/(b*x^3+a)^(4/3),x)","F"
30,1,25,39,0.046000," ","int((-b*x^3+a)/(b*x^3+a)^(7/3),x)","\frac{\left(b \,x^{3}+2 a \right) x}{2 \left(b \,x^{3}+a \right)^{\frac{4}{3}} a}"," ",0,"1/2*x*(b*x^3+2*a)/(b*x^3+a)^(4/3)/a","A"
31,1,37,43,0.043000," ","int((-b*x^3+a)/(b*x^3+a)^(10/3),x)","\frac{\left(15 b^{2} x^{6}+35 a b \,x^{3}+28 a^{2}\right) x}{28 \left(b \,x^{3}+a \right)^{\frac{7}{3}} a^{2}}"," ",0,"1/28*x*(15*b^2*x^6+35*a*b*x^3+28*a^2)/(b*x^3+a)^(7/3)/a^2","A"
32,1,48,58,0.048000," ","int((-b*x^3+a)/(b*x^3+a)^(13/3),x)","\frac{\left(18 b^{3} x^{9}+60 a \,b^{2} x^{6}+70 a^{2} b \,x^{3}+35 a^{3}\right) x}{35 \left(b \,x^{3}+a \right)^{\frac{10}{3}} a^{3}}"," ",0,"1/35*x*(18*b^3*x^9+60*a*b^2*x^6+70*a^2*b*x^3+35*a^3)/(b*x^3+a)^(10/3)/a^3","A"
33,1,59,73,0.046000," ","int((-b*x^3+a)/(b*x^3+a)^(16/3),x)","\frac{\left(891 b^{4} x^{12}+3861 b^{3} x^{9} a +6435 b^{2} x^{6} a^{2}+5005 b \,x^{3} a^{3}+1820 a^{4}\right) x}{1820 \left(b \,x^{3}+a \right)^{\frac{13}{3}} a^{4}}"," ",0,"1/1820*x*(891*b^4*x^12+3861*a*b^3*x^9+6435*a^2*b^2*x^6+5005*a^3*b*x^3+1820*a^4)/(b*x^3+a)^(13/3)/a^4","A"
34,0,0,353,0.607000," ","int((b*x^3+a)^(7/3)/(-b*x^3+a),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{7}{3}}}{-b \,x^{3}+a}\, dx"," ",0,"int((b*x^3+a)^(7/3)/(-b*x^3+a),x)","F"
35,0,0,338,0.609000," ","int((b*x^3+a)^(4/3)/(-b*x^3+a),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{-b \,x^{3}+a}\, dx"," ",0,"int((b*x^3+a)^(4/3)/(-b*x^3+a),x)","F"
36,0,0,286,0.698000," ","int((b*x^3+a)^(1/3)/(-b*x^3+a),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{-b \,x^{3}+a}\, dx"," ",0,"int((b*x^3+a)^(1/3)/(-b*x^3+a),x)","F"
37,0,0,328,0.584000," ","int(1/(-b*x^3+a)/(b*x^3+a)^(2/3),x)","\int \frac{1}{\left(-b \,x^{3}+a \right) \left(b \,x^{3}+a \right)^{\frac{2}{3}}}\, dx"," ",0,"int(1/(-b*x^3+a)/(b*x^3+a)^(2/3),x)","F"
38,0,0,343,0.681000," ","int(1/(-b*x^3+a)/(b*x^3+a)^(5/3),x)","\int \frac{1}{\left(-b \,x^{3}+a \right) \left(b \,x^{3}+a \right)^{\frac{5}{3}}}\, dx"," ",0,"int(1/(-b*x^3+a)/(b*x^3+a)^(5/3),x)","F"
39,0,0,358,0.600000," ","int(1/(-b*x^3+a)/(b*x^3+a)^(8/3),x)","\int \frac{1}{\left(-b \,x^{3}+a \right) \left(b \,x^{3}+a \right)^{\frac{8}{3}}}\, dx"," ",0,"int(1/(-b*x^3+a)/(b*x^3+a)^(8/3),x)","F"
40,0,0,108,0.375000," ","int((-b*x^3+a)^2*(b*x^3+a)^(2/3),x)","\int \left(-b \,x^{3}+a \right)^{2} \left(b \,x^{3}+a \right)^{\frac{2}{3}}\, dx"," ",0,"int((-b*x^3+a)^2*(b*x^3+a)^(2/3),x)","F"
41,0,0,93,0.384000," ","int((-b*x^3+a)^2/(b*x^3+a)^(1/3),x)","\int \frac{\left(-b \,x^{3}+a \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((-b*x^3+a)^2/(b*x^3+a)^(1/3),x)","F"
42,0,0,88,0.532000," ","int((-b*x^3+a)^2/(b*x^3+a)^(4/3),x)","\int \frac{\left(-b \,x^{3}+a \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}\, dx"," ",0,"int((-b*x^3+a)^2/(b*x^3+a)^(4/3),x)","F"
43,0,0,86,0.533000," ","int((-b*x^3+a)^2/(b*x^3+a)^(7/3),x)","\int \frac{\left(-b \,x^{3}+a \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{7}{3}}}\, dx"," ",0,"int((-b*x^3+a)^2/(b*x^3+a)^(7/3),x)","F"
44,1,37,64,0.042000," ","int((-b*x^3+a)^2/(b*x^3+a)^(10/3),x)","\frac{\left(4 b^{2} x^{6}+7 a b \,x^{3}+7 a^{2}\right) x}{7 \left(b \,x^{3}+a \right)^{\frac{7}{3}} a}"," ",0,"1/7*x*(4*b^2*x^6+7*a*b*x^3+7*a^2)/(b*x^3+a)^(7/3)/a","A"
45,1,48,89,0.050000," ","int((-b*x^3+a)^2/(b*x^3+a)^(13/3),x)","\frac{\left(69 b^{3} x^{9}+230 a \,b^{2} x^{6}+245 a^{2} b \,x^{3}+140 a^{3}\right) x}{140 \left(b \,x^{3}+a \right)^{\frac{10}{3}} a^{2}}"," ",0,"1/140*x*(69*b^3*x^9+230*a*b^2*x^6+245*a^2*b*x^3+140*a^3)/(b*x^3+a)^(10/3)/a^2","A"
46,1,59,78,0.046000," ","int((-b*x^3+a)^2/(b*x^3+a)^(16/3),x)","\frac{\left(423 b^{4} x^{12}+1833 b^{3} x^{9} a +3055 b^{2} x^{6} a^{2}+2275 b \,x^{3} a^{3}+910 a^{4}\right) x}{910 \left(b \,x^{3}+a \right)^{\frac{13}{3}} a^{3}}"," ",0,"1/910*x*(423*b^4*x^12+1833*a*b^3*x^9+3055*a^2*b^2*x^6+2275*a^3*b*x^3+910*a^4)/(b*x^3+a)^(13/3)/a^3","A"
47,1,70,93,0.049000," ","int((-b*x^3+a)^2/(b*x^3+a)^(19/3),x)","\frac{\left(162 b^{5} x^{15}+864 a \,b^{4} x^{12}+1872 a^{2} b^{3} x^{9}+2080 a^{3} b^{2} x^{6}+1183 a^{4} b \,x^{3}+364 a^{5}\right) x}{364 \left(b \,x^{3}+a \right)^{\frac{16}{3}} a^{4}}"," ",0,"1/364*x*(162*b^5*x^15+864*a*b^4*x^12+1872*a^2*b^3*x^9+2080*a^3*b^2*x^6+1183*a^4*b*x^3+364*a^5)/(b*x^3+a)^(16/3)/a^4","A"
48,0,0,76,0.407000," ","int((-b*x^3+a)^2*(b*x^3+a)^(4/3),x)","\int \left(-b \,x^{3}+a \right)^{2} \left(b \,x^{3}+a \right)^{\frac{4}{3}}\, dx"," ",0,"int((-b*x^3+a)^2*(b*x^3+a)^(4/3),x)","F"
49,0,0,76,0.382000," ","int((-b*x^3+a)^2*(b*x^3+a)^(1/3),x)","\int \left(-b \,x^{3}+a \right)^{2} \left(b \,x^{3}+a \right)^{\frac{1}{3}}\, dx"," ",0,"int((-b*x^3+a)^2*(b*x^3+a)^(1/3),x)","F"
50,0,0,76,0.368000," ","int((-b*x^3+a)^2/(b*x^3+a)^(2/3),x)","\int \frac{\left(-b \,x^{3}+a \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}\, dx"," ",0,"int((-b*x^3+a)^2/(b*x^3+a)^(2/3),x)","F"
51,0,0,62,0.556000," ","int((-b*x^3+a)^2/(b*x^3+a)^(5/3),x)","\int \frac{\left(-b \,x^{3}+a \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{5}{3}}}\, dx"," ",0,"int((-b*x^3+a)^2/(b*x^3+a)^(5/3),x)","F"
52,0,0,60,0.510000," ","int((-b*x^3+a)^2/(b*x^3+a)^(8/3),x)","\int \frac{\left(-b \,x^{3}+a \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{8}{3}}}\, dx"," ",0,"int((-b*x^3+a)^2/(b*x^3+a)^(8/3),x)","F"
53,0,0,63,0.535000," ","int((-b*x^3+a)^2/(b*x^3+a)^(11/3),x)","\int \frac{\left(-b \,x^{3}+a \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{11}{3}}}\, dx"," ",0,"int((-b*x^3+a)^2/(b*x^3+a)^(11/3),x)","F"
54,0,0,75,0.566000," ","int((-b*x^3+a)^2/(b*x^3+a)^(14/3),x)","\int \frac{\left(-b \,x^{3}+a \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{14}{3}}}\, dx"," ",0,"int((-b*x^3+a)^2/(b*x^3+a)^(14/3),x)","F"
55,0,0,75,0.553000," ","int((-b*x^3+a)^2/(b*x^3+a)^(17/3),x)","\int \frac{\left(-b \,x^{3}+a \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{17}{3}}}\, dx"," ",0,"int((-b*x^3+a)^2/(b*x^3+a)^(17/3),x)","F"
56,0,0,143,0.374000," ","int((b*x^3+a)^(5/3)*(d*x^3+c),x)","\int \left(b \,x^{3}+a \right)^{\frac{5}{3}} \left(d \,x^{3}+c \right)\, dx"," ",0,"int((b*x^3+a)^(5/3)*(d*x^3+c),x)","F"
57,0,0,114,0.375000," ","int((b*x^3+a)^(2/3)*(d*x^3+c),x)","\int \left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)\, dx"," ",0,"int((b*x^3+a)^(2/3)*(d*x^3+c),x)","F"
58,0,0,88,0.395000," ","int((d*x^3+c)/(b*x^3+a)^(1/3),x)","\int \frac{d \,x^{3}+c}{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((d*x^3+c)/(b*x^3+a)^(1/3),x)","F"
59,0,0,81,0.380000," ","int((d*x^3+c)/(b*x^3+a)^(4/3),x)","\int \frac{d \,x^{3}+c}{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}\, dx"," ",0,"int((d*x^3+c)/(b*x^3+a)^(4/3),x)","F"
60,1,34,39,0.049000," ","int((d*x^3+c)/(b*x^3+a)^(7/3),x)","\frac{\left(a d \,x^{3}+3 b c \,x^{3}+4 a c \right) x}{4 \left(b \,x^{3}+a \right)^{\frac{4}{3}} a^{2}}"," ",0,"1/4*x*(a*d*x^3+3*b*c*x^3+4*a*c)/(b*x^3+a)^(4/3)/a^2","A"
61,1,57,79,0.045000," ","int((d*x^3+c)/(b*x^3+a)^(10/3),x)","\frac{\left(3 a b d \,x^{6}+18 b^{2} c \,x^{6}+7 a^{2} d \,x^{3}+42 a b c \,x^{3}+28 a^{2} c \right) x}{28 \left(b \,x^{3}+a \right)^{\frac{7}{3}} a^{3}}"," ",0,"1/28*x*(3*a*b*d*x^6+18*b^2*c*x^6+7*a^2*d*x^3+42*a*b*c*x^3+28*a^2*c)/(b*x^3+a)^(7/3)/a^3","A"
62,1,81,105,0.042000," ","int((d*x^3+c)/(b*x^3+a)^(13/3),x)","\frac{\left(9 a \,b^{2} d \,x^{9}+81 b^{3} c \,x^{9}+30 a^{2} b d \,x^{6}+270 a \,b^{2} c \,x^{6}+35 a^{3} d \,x^{3}+315 a^{2} b c \,x^{3}+140 c \,a^{3}\right) x}{140 \left(b \,x^{3}+a \right)^{\frac{10}{3}} a^{4}}"," ",0,"1/140*x*(9*a*b^2*d*x^9+81*b^3*c*x^9+30*a^2*b*d*x^6+270*a*b^2*c*x^6+35*a^3*d*x^3+315*a^2*b*c*x^3+140*a^3*c)/(b*x^3+a)^(10/3)/a^4","A"
63,1,105,131,0.046000," ","int((d*x^3+c)/(b*x^3+a)^(16/3),x)","\frac{\left(81 a \,b^{3} d \,x^{12}+972 b^{4} c \,x^{12}+351 a^{2} b^{2} d \,x^{9}+4212 a \,b^{3} c \,x^{9}+585 a^{3} b d \,x^{6}+7020 a^{2} b^{2} c \,x^{6}+455 a^{4} d \,x^{3}+5460 a^{3} b c \,x^{3}+1820 c \,a^{4}\right) x}{1820 \left(b \,x^{3}+a \right)^{\frac{13}{3}} a^{5}}"," ",0,"1/1820*x*(81*a*b^3*d*x^12+972*b^4*c*x^12+351*a^2*b^2*d*x^9+4212*a*b^3*c*x^9+585*a^3*b*d*x^6+7020*a^2*b^2*c*x^6+455*a^4*d*x^3+5460*a^3*b*c*x^3+1820*a^4*c)/(b*x^3+a)^(13/3)/a^5","A"
64,0,0,71,0.420000," ","int((b*x^3+a)^(7/3)*(d*x^3+c),x)","\int \left(b \,x^{3}+a \right)^{\frac{7}{3}} \left(d \,x^{3}+c \right)\, dx"," ",0,"int((b*x^3+a)^(7/3)*(d*x^3+c),x)","F"
65,0,0,69,0.385000," ","int((b*x^3+a)^(4/3)*(d*x^3+c),x)","\int \left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)\, dx"," ",0,"int((b*x^3+a)^(4/3)*(d*x^3+c),x)","F"
66,0,0,68,0.403000," ","int((b*x^3+a)^(1/3)*(d*x^3+c),x)","\int \left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)\, dx"," ",0,"int((b*x^3+a)^(1/3)*(d*x^3+c),x)","F"
67,0,0,68,0.374000," ","int((d*x^3+c)/(b*x^3+a)^(2/3),x)","\int \frac{d \,x^{3}+c}{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}\, dx"," ",0,"int((d*x^3+c)/(b*x^3+a)^(2/3),x)","F"
68,0,0,79,0.390000," ","int((d*x^3+c)/(b*x^3+a)^(5/3),x)","\int \frac{d \,x^{3}+c}{\left(b \,x^{3}+a \right)^{\frac{5}{3}}}\, dx"," ",0,"int((d*x^3+c)/(b*x^3+a)^(5/3),x)","F"
69,0,0,80,0.400000," ","int((d*x^3+c)/(b*x^3+a)^(8/3),x)","\int \frac{d \,x^{3}+c}{\left(b \,x^{3}+a \right)^{\frac{8}{3}}}\, dx"," ",0,"int((d*x^3+c)/(b*x^3+a)^(8/3),x)","F"
70,0,0,227,0.385000," ","int((b*x^3+a)^(5/3)*(d*x^3+c)^2,x)","\int \left(b \,x^{3}+a \right)^{\frac{5}{3}} \left(d \,x^{3}+c \right)^{2}\, dx"," ",0,"int((b*x^3+a)^(5/3)*(d*x^3+c)^2,x)","F"
71,0,0,188,0.385000," ","int((b*x^3+a)^(2/3)*(d*x^3+c)^2,x)","\int \left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)^{2}\, dx"," ",0,"int((b*x^3+a)^(2/3)*(d*x^3+c)^2,x)","F"
72,0,0,148,0.381000," ","int((d*x^3+c)^2/(b*x^3+a)^(1/3),x)","\int \frac{\left(d \,x^{3}+c \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}\, dx"," ",0,"int((d*x^3+c)^2/(b*x^3+a)^(1/3),x)","F"
73,0,0,134,0.559000," ","int((d*x^3+c)^2/(b*x^3+a)^(4/3),x)","\int \frac{\left(d \,x^{3}+c \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}\, dx"," ",0,"int((d*x^3+c)^2/(b*x^3+a)^(4/3),x)","F"
74,0,0,128,0.550000," ","int((d*x^3+c)^2/(b*x^3+a)^(7/3),x)","\int \frac{\left(d \,x^{3}+c \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{7}{3}}}\, dx"," ",0,"int((d*x^3+c)^2/(b*x^3+a)^(7/3),x)","F"
75,1,76,66,0.049000," ","int((d*x^3+c)^2/(b*x^3+a)^(10/3),x)","\frac{\left(2 a^{2} d^{2} x^{6}+3 a b c d \,x^{6}+9 b^{2} c^{2} x^{6}+7 a^{2} c d \,x^{3}+21 a b \,c^{2} x^{3}+14 a^{2} c^{2}\right) x}{14 \left(b \,x^{3}+a \right)^{\frac{7}{3}} a^{3}}"," ",0,"1/14*x*(2*a^2*d^2*x^6+3*a*b*c*d*x^6+9*b^2*c^2*x^6+7*a^2*c*d*x^3+21*a*b*c^2*x^3+14*a^2*c^2)/(b*x^3+a)^(7/3)/a^3","A"
76,1,115,158,0.046000," ","int((d*x^3+c)^2/(b*x^3+a)^(13/3),x)","\frac{\left(6 a^{2} b \,d^{2} x^{9}+18 a \,b^{2} c d \,x^{9}+81 b^{3} c^{2} x^{9}+20 a^{3} d^{2} x^{6}+60 a^{2} b c d \,x^{6}+270 a \,b^{2} c^{2} x^{6}+70 a^{3} c d \,x^{3}+315 a^{2} b \,c^{2} x^{3}+140 c^{2} a^{3}\right) x}{140 \left(b \,x^{3}+a \right)^{\frac{10}{3}} a^{4}}"," ",0,"1/140*x*(6*a^2*b*d^2*x^9+18*a*b^2*c*d*x^9+81*b^3*c^2*x^9+20*a^3*d^2*x^6+60*a^2*b*c*d*x^6+270*a*b^2*c^2*x^6+70*a^3*c*d*x^3+315*a^2*b*c^2*x^3+140*a^3*c^2)/(b*x^3+a)^(10/3)/a^4","A"
77,1,156,191,0.047000," ","int((d*x^3+c)^2/(b*x^3+a)^(16/3),x)","\frac{\left(18 a^{2} b^{2} d^{2} x^{12}+81 a \,b^{3} c d \,x^{12}+486 b^{4} c^{2} x^{12}+78 a^{3} b \,d^{2} x^{9}+351 a^{2} b^{2} c d \,x^{9}+2106 a \,b^{3} c^{2} x^{9}+130 a^{4} d^{2} x^{6}+585 a^{3} b c d \,x^{6}+3510 a^{2} b^{2} c^{2} x^{6}+455 a^{4} c d \,x^{3}+2730 a^{3} b \,c^{2} x^{3}+910 c^{2} a^{4}\right) x}{910 \left(b \,x^{3}+a \right)^{\frac{13}{3}} a^{5}}"," ",0,"1/910*x*(18*a^2*b^2*d^2*x^12+81*a*b^3*c*d*x^12+486*b^4*c^2*x^12+78*a^3*b*d^2*x^9+351*a^2*b^2*c*d*x^9+2106*a*b^3*c^2*x^9+130*a^4*d^2*x^6+585*a^3*b*c*d*x^6+3510*a^2*b^2*c^2*x^6+455*a^4*c*d*x^3+2730*a^3*b*c^2*x^3+910*a^4*c^2)/(b*x^3+a)^(13/3)/a^5","A"
78,1,197,229,0.049000," ","int((d*x^3+c)^2/(b*x^3+a)^(19/3),x)","\frac{\left(81 a^{2} b^{3} d^{2} x^{15}+486 a \,b^{4} c d \,x^{15}+3645 b^{5} c^{2} x^{15}+432 a^{3} b^{2} d^{2} x^{12}+2592 a^{2} b^{3} c d \,x^{12}+19440 a \,b^{4} c^{2} x^{12}+936 a^{4} b \,d^{2} x^{9}+5616 a^{3} b^{2} c d \,x^{9}+42120 a^{2} b^{3} c^{2} x^{9}+1040 a^{5} d^{2} x^{6}+6240 a^{4} b c d \,x^{6}+46800 a^{3} b^{2} c^{2} x^{6}+3640 a^{5} c d \,x^{3}+27300 a^{4} b \,c^{2} x^{3}+7280 c^{2} a^{5}\right) x}{7280 \left(b \,x^{3}+a \right)^{\frac{16}{3}} a^{6}}"," ",0,"1/7280*x*(81*a^2*b^3*d^2*x^15+486*a*b^4*c*d*x^15+3645*b^5*c^2*x^15+432*a^3*b^2*d^2*x^12+2592*a^2*b^3*c*d*x^12+19440*a*b^4*c^2*x^12+936*a^4*b*d^2*x^9+5616*a^3*b^2*c*d*x^9+42120*a^2*b^3*c^2*x^9+1040*a^5*d^2*x^6+6240*a^4*b*c*d*x^6+46800*a^3*b^2*c^2*x^6+3640*a^5*c*d*x^3+27300*a^4*b*c^2*x^3+7280*a^5*c^2)/(b*x^3+a)^(16/3)/a^6","A"
79,0,0,117,0.416000," ","int((b*x^3+a)^(7/3)*(d*x^3+c)^2,x)","\int \left(b \,x^{3}+a \right)^{\frac{7}{3}} \left(d \,x^{3}+c \right)^{2}\, dx"," ",0,"int((b*x^3+a)^(7/3)*(d*x^3+c)^2,x)","F"
80,0,0,115,0.373000," ","int((b*x^3+a)^(4/3)*(d*x^3+c)^2,x)","\int \left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)^{2}\, dx"," ",0,"int((b*x^3+a)^(4/3)*(d*x^3+c)^2,x)","F"
81,0,0,113,0.388000," ","int((b*x^3+a)^(1/3)*(d*x^3+c)^2,x)","\int \left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)^{2}\, dx"," ",0,"int((b*x^3+a)^(1/3)*(d*x^3+c)^2,x)","F"
82,0,0,114,0.388000," ","int((d*x^3+c)^2/(b*x^3+a)^(2/3),x)","\int \frac{\left(d \,x^{3}+c \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}\, dx"," ",0,"int((d*x^3+c)^2/(b*x^3+a)^(2/3),x)","F"
83,0,0,128,0.605000," ","int((d*x^3+c)^2/(b*x^3+a)^(5/3),x)","\int \frac{\left(d \,x^{3}+c \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{5}{3}}}\, dx"," ",0,"int((d*x^3+c)^2/(b*x^3+a)^(5/3),x)","F"
84,0,0,129,0.604000," ","int((d*x^3+c)^2/(b*x^3+a)^(8/3),x)","\int \frac{\left(d \,x^{3}+c \right)^{2}}{\left(b \,x^{3}+a \right)^{\frac{8}{3}}}\, dx"," ",0,"int((d*x^3+c)^2/(b*x^3+a)^(8/3),x)","F"
85,1,134,93,0.053000," ","int((b*x^3+a)^3/(d*x^3+c)^(13/3),x)","\frac{\left(81 a^{3} d^{3} x^{9}+27 a^{2} b c \,d^{2} x^{9}+18 a \,b^{2} c^{2} d \,x^{9}+14 b^{3} c^{3} x^{9}+270 a^{3} c \,d^{2} x^{6}+90 a^{2} b \,c^{2} d \,x^{6}+60 a \,b^{2} c^{3} x^{6}+315 a^{3} c^{2} d \,x^{3}+105 a^{2} b \,c^{3} x^{3}+140 a^{3} c^{3}\right) x}{140 \left(d \,x^{3}+c \right)^{\frac{10}{3}} c^{4}}"," ",0,"1/140*x*(81*a^3*d^3*x^9+27*a^2*b*c*d^2*x^9+18*a*b^2*c^2*d*x^9+14*b^3*c^3*x^9+270*a^3*c*d^2*x^6+90*a^2*b*c^2*d*x^6+60*a*b^2*c^3*x^6+315*a^3*c^2*d*x^3+105*a^2*b*c^3*x^3+140*a^3*c^3)/(d*x^3+c)^(10/3)/c^4","A"
86,0,0,273,0.701000," ","int((b*x^3+a)^(8/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{8}{3}}}{d \,x^{3}+c}\, dx"," ",0,"int((b*x^3+a)^(8/3)/(d*x^3+c),x)","F"
87,0,0,220,0.559000," ","int((b*x^3+a)^(5/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{5}{3}}}{d \,x^{3}+c}\, dx"," ",0,"int((b*x^3+a)^(5/3)/(d*x^3+c),x)","F"
88,0,0,186,0.570000," ","int((b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{d \,x^{3}+c}\, dx"," ",0,"int((b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
89,0,0,118,0.526000," ","int(1/(b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(1/(b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
90,0,0,146,0.574000," ","int(1/(b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(1/(b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
91,0,0,188,0.558000," ","int(1/(b*x^3+a)^(7/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{7}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(1/(b*x^3+a)^(7/3)/(d*x^3+c),x)","F"
92,0,0,237,0.605000," ","int(1/(b*x^3+a)^(10/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{10}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(1/(b*x^3+a)^(10/3)/(d*x^3+c),x)","F"
93,0,0,50,0.612000," ","int((b*x^3+a)^(4/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{d \,x^{3}+c}\, dx"," ",0,"int((b*x^3+a)^(4/3)/(d*x^3+c),x)","F"
94,0,0,49,0.587000," ","int((b*x^3+a)^(1/3)/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{d \,x^{3}+c}\, dx"," ",0,"int((b*x^3+a)^(1/3)/(d*x^3+c),x)","F"
95,0,0,49,0.613000," ","int(1/(b*x^3+a)^(2/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(1/(b*x^3+a)^(2/3)/(d*x^3+c),x)","F"
96,0,0,52,0.643000," ","int(1/(b*x^3+a)^(5/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{5}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(1/(b*x^3+a)^(5/3)/(d*x^3+c),x)","F"
97,0,0,52,0.629000," ","int(1/(b*x^3+a)^(8/3)/(d*x^3+c),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{8}{3}} \left(d \,x^{3}+c \right)}\, dx"," ",0,"int(1/(b*x^3+a)^(8/3)/(d*x^3+c),x)","F"
98,0,0,291,0.398000," ","int((b*x^3+a)^(8/3)/(d*x^3+c)^2,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{8}{3}}}{\left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int((b*x^3+a)^(8/3)/(d*x^3+c)^2,x)","F"
99,0,0,248,0.582000," ","int((b*x^3+a)^(5/3)/(d*x^3+c)^2,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{5}{3}}}{\left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int((b*x^3+a)^(5/3)/(d*x^3+c)^2,x)","F"
100,0,0,145,0.538000," ","int((b*x^3+a)^(2/3)/(d*x^3+c)^2,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/(d*x^3+c)^2,x)","F"
101,0,0,180,0.555000," ","int(1/(b*x^3+a)^(1/3)/(d*x^3+c)^2,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^3+a)^(1/3)/(d*x^3+c)^2,x)","F"
102,0,0,220,0.600000," ","int(1/(b*x^3+a)^(4/3)/(d*x^3+c)^2,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^3+a)^(4/3)/(d*x^3+c)^2,x)","F"
103,0,0,279,0.594000," ","int(1/(b*x^3+a)^(7/3)/(d*x^3+c)^2,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{7}{3}} \left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^3+a)^(7/3)/(d*x^3+c)^2,x)","F"
104,0,0,50,0.513000," ","int((b*x^3+a)^(4/3)/(d*x^3+c)^2,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int((b*x^3+a)^(4/3)/(d*x^3+c)^2,x)","F"
105,0,0,49,0.572000," ","int((b*x^3+a)^(1/3)/(d*x^3+c)^2,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/(d*x^3+c)^2,x)","F"
106,0,0,49,0.573000," ","int(1/(b*x^3+a)^(2/3)/(d*x^3+c)^2,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^3+a)^(2/3)/(d*x^3+c)^2,x)","F"
107,0,0,52,0.583000," ","int(1/(b*x^3+a)^(5/3)/(d*x^3+c)^2,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{5}{3}} \left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^3+a)^(5/3)/(d*x^3+c)^2,x)","F"
108,0,0,52,0.599000," ","int(1/(b*x^3+a)^(8/3)/(d*x^3+c)^2,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{8}{3}} \left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^3+a)^(8/3)/(d*x^3+c)^2,x)","F"
109,0,0,473,0.395000," ","int((b*x^3+a)^(14/3)/(d*x^3+c)^3,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{14}{3}}}{\left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int((b*x^3+a)^(14/3)/(d*x^3+c)^3,x)","F"
110,0,0,394,0.412000," ","int((b*x^3+a)^(11/3)/(d*x^3+c)^3,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{11}{3}}}{\left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int((b*x^3+a)^(11/3)/(d*x^3+c)^3,x)","F"
111,0,0,334,0.607000," ","int((b*x^3+a)^(8/3)/(d*x^3+c)^3,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{8}{3}}}{\left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int((b*x^3+a)^(8/3)/(d*x^3+c)^3,x)","F"
112,0,0,176,0.572000," ","int((b*x^3+a)^(5/3)/(d*x^3+c)^3,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{5}{3}}}{\left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int((b*x^3+a)^(5/3)/(d*x^3+c)^3,x)","F"
113,0,0,226,0.546000," ","int((b*x^3+a)^(2/3)/(d*x^3+c)^3,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{2}{3}}}{\left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int((b*x^3+a)^(2/3)/(d*x^3+c)^3,x)","F"
114,0,0,266,0.579000," ","int(1/(b*x^3+a)^(1/3)/(d*x^3+c)^3,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{3}} \left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int(1/(b*x^3+a)^(1/3)/(d*x^3+c)^3,x)","F"
115,0,0,332,0.592000," ","int(1/(b*x^3+a)^(4/3)/(d*x^3+c)^3,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{4}{3}} \left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int(1/(b*x^3+a)^(4/3)/(d*x^3+c)^3,x)","F"
116,0,0,414,0.559000," ","int(1/(b*x^3+a)^(7/3)/(d*x^3+c)^3,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{7}{3}} \left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int(1/(b*x^3+a)^(7/3)/(d*x^3+c)^3,x)","F"
117,0,0,50,0.568000," ","int((b*x^3+a)^(4/3)/(d*x^3+c)^3,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{4}{3}}}{\left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int((b*x^3+a)^(4/3)/(d*x^3+c)^3,x)","F"
118,0,0,49,0.560000," ","int((b*x^3+a)^(1/3)/(d*x^3+c)^3,x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{3}}}{\left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int((b*x^3+a)^(1/3)/(d*x^3+c)^3,x)","F"
119,0,0,49,0.590000," ","int(1/(b*x^3+a)^(2/3)/(d*x^3+c)^3,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{2}{3}} \left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int(1/(b*x^3+a)^(2/3)/(d*x^3+c)^3,x)","F"
120,0,0,52,0.585000," ","int(1/(b*x^3+a)^(5/3)/(d*x^3+c)^3,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{5}{3}} \left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int(1/(b*x^3+a)^(5/3)/(d*x^3+c)^3,x)","F"
121,0,0,52,0.585000," ","int(1/(b*x^3+a)^(8/3)/(d*x^3+c)^3,x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{8}{3}} \left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int(1/(b*x^3+a)^(8/3)/(d*x^3+c)^3,x)","F"
122,0,0,131,0.505000," ","int((b*x^3+a)^(7/4)/(d*x^3+c)^(37/12),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{7}{4}}}{\left(d \,x^{3}+c \right)^{\frac{37}{12}}}\, dx"," ",0,"int((b*x^3+a)^(7/4)/(d*x^3+c)^(37/12),x)","F"
123,0,0,131,0.537000," ","int((b*x^3+a)^(5/4)/(d*x^3+c)^(31/12),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{5}{4}}}{\left(d \,x^{3}+c \right)^{\frac{31}{12}}}\, dx"," ",0,"int((b*x^3+a)^(5/4)/(d*x^3+c)^(31/12),x)","F"
124,0,0,104,0.552000," ","int((b*x^3+a)^(3/4)/(d*x^3+c)^(25/12),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{3}{4}}}{\left(d \,x^{3}+c \right)^{\frac{25}{12}}}\, dx"," ",0,"int((b*x^3+a)^(3/4)/(d*x^3+c)^(25/12),x)","F"
125,0,0,104,0.535000," ","int((b*x^3+a)^(1/4)/(d*x^3+c)^(19/12),x)","\int \frac{\left(b \,x^{3}+a \right)^{\frac{1}{4}}}{\left(d \,x^{3}+c \right)^{\frac{19}{12}}}\, dx"," ",0,"int((b*x^3+a)^(1/4)/(d*x^3+c)^(19/12),x)","F"
126,0,0,77,0.538000," ","int(1/(b*x^3+a)^(1/4)/(d*x^3+c)^(13/12),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{1}{4}} \left(d \,x^{3}+c \right)^{\frac{13}{12}}}\, dx"," ",0,"int(1/(b*x^3+a)^(1/4)/(d*x^3+c)^(13/12),x)","F"
127,0,0,77,0.526000," ","int(1/(b*x^3+a)^(3/4)/(d*x^3+c)^(7/12),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{3}{4}} \left(d \,x^{3}+c \right)^{\frac{7}{12}}}\, dx"," ",0,"int(1/(b*x^3+a)^(3/4)/(d*x^3+c)^(7/12),x)","F"
128,0,0,77,0.561000," ","int(1/(b*x^3+a)^(5/4)/(d*x^3+c)^(1/12),x)","\int \frac{1}{\left(b \,x^{3}+a \right)^{\frac{5}{4}} \left(d \,x^{3}+c \right)^{\frac{1}{12}}}\, dx"," ",0,"int(1/(b*x^3+a)^(5/4)/(d*x^3+c)^(1/12),x)","F"
129,0,0,103,0.552000," ","int((d*x^3+c)^(5/12)/(b*x^3+a)^(7/4),x)","\int \frac{\left(d \,x^{3}+c \right)^{\frac{5}{12}}}{\left(b \,x^{3}+a \right)^{\frac{7}{4}}}\, dx"," ",0,"int((d*x^3+c)^(5/12)/(b*x^3+a)^(7/4),x)","F"
130,0,0,103,0.559000," ","int((d*x^3+c)^(11/12)/(b*x^3+a)^(9/4),x)","\int \frac{\left(d \,x^{3}+c \right)^{\frac{11}{12}}}{\left(b \,x^{3}+a \right)^{\frac{9}{4}}}\, dx"," ",0,"int((d*x^3+c)^(11/12)/(b*x^3+a)^(9/4),x)","F"
131,0,0,129,0.496000," ","int((d*x^3+c)^(17/12)/(b*x^3+a)^(11/4),x)","\int \frac{\left(d \,x^{3}+c \right)^{\frac{17}{12}}}{\left(b \,x^{3}+a \right)^{\frac{11}{4}}}\, dx"," ",0,"int((d*x^3+c)^(17/12)/(b*x^3+a)^(11/4),x)","F"
132,0,0,129,0.549000," ","int((d*x^3+c)^(23/12)/(b*x^3+a)^(13/4),x)","\int \frac{\left(d \,x^{3}+c \right)^{\frac{23}{12}}}{\left(b \,x^{3}+a \right)^{\frac{13}{4}}}\, dx"," ",0,"int((d*x^3+c)^(23/12)/(b*x^3+a)^(13/4),x)","F"
133,0,0,75,0.556000," ","int((b*x^3+a)^m*(d*x^3+c)^p,x)","\int \left(b \,x^{3}+a \right)^{m} \left(d \,x^{3}+c \right)^{p}\, dx"," ",0,"int((b*x^3+a)^m*(d*x^3+c)^p,x)","F"
134,0,0,161,0.529000," ","int((b*x^3+a)^2*(d*x^3+c)^q,x)","\int \left(b \,x^{3}+a \right)^{2} \left(d \,x^{3}+c \right)^{q}\, dx"," ",0,"int((b*x^3+a)^2*(d*x^3+c)^q,x)","F"
135,0,0,82,0.396000," ","int((b*x^3+a)*(d*x^3+c)^q,x)","\int \left(b \,x^{3}+a \right) \left(d \,x^{3}+c \right)^{q}\, dx"," ",0,"int((b*x^3+a)*(d*x^3+c)^q,x)","F"
136,0,0,53,0.563000," ","int((d*x^3+c)^q/(b*x^3+a),x)","\int \frac{\left(d \,x^{3}+c \right)^{q}}{b \,x^{3}+a}\, dx"," ",0,"int((d*x^3+c)^q/(b*x^3+a),x)","F"
137,0,0,53,0.580000," ","int((d*x^3+c)^q/(b*x^3+a)^2,x)","\int \frac{\left(d \,x^{3}+c \right)^{q}}{\left(b \,x^{3}+a \right)^{2}}\, dx"," ",0,"int((d*x^3+c)^q/(b*x^3+a)^2,x)","F"
138,0,0,290,0.577000," ","int((b*x^3+a)^m*(d*x^3+c)^3,x)","\int \left(d \,x^{3}+c \right)^{3} \left(b \,x^{3}+a \right)^{m}\, dx"," ",0,"int((b*x^3+a)^m*(d*x^3+c)^3,x)","F"
139,0,0,170,0.540000," ","int((b*x^3+a)^m*(d*x^3+c)^2,x)","\int \left(d \,x^{3}+c \right)^{2} \left(b \,x^{3}+a \right)^{m}\, dx"," ",0,"int((b*x^3+a)^m*(d*x^3+c)^2,x)","F"
140,0,0,91,0.390000," ","int((b*x^3+a)^m*(d*x^3+c),x)","\int \left(d \,x^{3}+c \right) \left(b \,x^{3}+a \right)^{m}\, dx"," ",0,"int((b*x^3+a)^m*(d*x^3+c),x)","F"
141,0,0,42,0.361000," ","int((b*x^3+a)^m,x)","\int \left(b \,x^{3}+a \right)^{m}\, dx"," ",0,"int((b*x^3+a)^m,x)","F"
142,0,0,53,0.566000," ","int((b*x^3+a)^m/(d*x^3+c),x)","\int \frac{\left(b \,x^{3}+a \right)^{m}}{d \,x^{3}+c}\, dx"," ",0,"int((b*x^3+a)^m/(d*x^3+c),x)","F"
143,0,0,53,0.525000," ","int((b*x^3+a)^m/(d*x^3+c)^2,x)","\int \frac{\left(b \,x^{3}+a \right)^{m}}{\left(d \,x^{3}+c \right)^{2}}\, dx"," ",0,"int((b*x^3+a)^m/(d*x^3+c)^2,x)","F"
144,0,0,53,0.557000," ","int((b*x^3+a)^m/(d*x^3+c)^3,x)","\int \frac{\left(b \,x^{3}+a \right)^{m}}{\left(d \,x^{3}+c \right)^{3}}\, dx"," ",0,"int((b*x^3+a)^m/(d*x^3+c)^3,x)","F"
145,1,71,54,0.041000," ","int((b*x^3+a)^(-1-b*c/(-3*a*d+3*b*c))*(d*x^3+c)^(-1+a*d/(-3*a*d+3*b*c)),x)","\frac{x \left(b \,x^{3}+a \right)^{1-\frac{3 a d -4 b c}{3 \left(a d -b c \right)}} \left(d \,x^{3}+c \right)^{1-\frac{4 a d -3 b c}{3 \left(a d -b c \right)}}}{a c}"," ",0,"(b*x^3+a)^(1-1/3*(3*a*d-4*b*c)/(a*d-b*c))*(d*x^3+c)^(1-1/3*(4*a*d-3*b*c)/(a*d-b*c))/a/c*x","A"
146,1,97,84,0.040000," ","int((b*x^4+a)*(d*x^4+c)^4,x)","\frac{b \,d^{4} x^{21}}{21}+\frac{\left(a \,d^{4}+4 b c \,d^{3}\right) x^{17}}{17}+\frac{\left(4 a c \,d^{3}+6 c^{2} d^{2} b \right) x^{13}}{13}+\frac{\left(6 a \,c^{2} d^{2}+4 c^{3} d b \right) x^{9}}{9}+a \,c^{4} x +\frac{\left(4 a \,c^{3} d +b \,c^{4}\right) x^{5}}{5}"," ",0,"1/21*b*d^4*x^21+1/17*(a*d^4+4*b*c*d^3)*x^17+1/13*(4*a*c*d^3+6*b*c^2*d^2)*x^13+1/9*(6*a*c^2*d^2+4*b*c^3*d)*x^9+1/5*(4*a*c^3*d+b*c^4)*x^5+a*c^4*x","A"
147,1,73,62,0.039000," ","int((b*x^4+a)*(d*x^4+c)^3,x)","\frac{b \,d^{3} x^{17}}{17}+\frac{\left(a \,d^{3}+3 b c \,d^{2}\right) x^{13}}{13}+\frac{\left(3 a c \,d^{2}+3 b \,c^{2} d \right) x^{9}}{9}+a \,c^{3} x +\frac{\left(3 a \,c^{2} d +b \,c^{3}\right) x^{5}}{5}"," ",0,"1/17*b*d^3*x^17+1/13*(a*d^3+3*b*c*d^2)*x^13+1/9*(3*a*c*d^2+3*b*c^2*d)*x^9+1/5*(3*a*c^2*d+b*c^3)*x^5+a*c^3*x","A"
148,1,49,44,0.036000," ","int((b*x^4+a)*(d*x^4+c)^2,x)","\frac{b \,d^{2} x^{13}}{13}+\frac{\left(a \,d^{2}+2 b c d \right) x^{9}}{9}+\frac{\left(2 a c d +b \,c^{2}\right) x^{5}}{5}+a \,c^{2} x"," ",0,"1/13*b*d^2*x^13+1/9*(a*d^2+2*b*c*d)*x^9+1/5*(2*a*c*d+b*c^2)*x^5+a*c^2*x","A"
149,1,25,24,0.045000," ","int((b*x^4+a)*(d*x^4+c),x)","\frac{b d \,x^{9}}{9}+\frac{\left(a d +b c \right) x^{5}}{5}+a c x"," ",0,"a*c*x+1/5*(a*d+b*c)*x^5+1/9*b*d*x^9","A"
150,1,266,158,0.048000," ","int((b*x^4+a)/(d*x^4+c),x)","\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 c}+\frac{b x}{d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 d}"," ",0,"b/d*x+1/4*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*a-1/4/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*b+1/8*(c/d)^(1/4)/c*2^(1/2)*ln((x^2+(c/d)^(1/4)*x*2^(1/2)+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*x*2^(1/2)+(c/d)^(1/2)))*a-1/8/d*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*x*2^(1/2)+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*x*2^(1/2)+(c/d)^(1/2)))*b+1/4*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*a-1/4/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*b","A"
151,1,295,178,0.053000," ","int((b*x^4+a)/(d*x^4+c)^2,x)","\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{16 c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{16 c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{32 c^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{16 c d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{16 c d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{32 c d}+\frac{\left(a d -b c \right) x}{4 \left(d \,x^{4}+c \right) c d}"," ",0,"1/4*(a*d-b*c)/d/c*x/(d*x^4+c)+3/16/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*a+1/16/c/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*b+3/16/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*a+1/16/c/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*b+3/32/c^2*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*a+1/32/c/d*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*b","A"
152,1,314,204,0.054000," ","int((b*x^4+a)/(d*x^4+c)^3,x)","\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{128 c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{128 c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{256 c^{3}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{128 c^{2} d}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{128 c^{2} d}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{256 c^{2} d}+\frac{\frac{\left(7 a d +b c \right) x^{5}}{32 c^{2}}+\frac{\left(11 a d -3 b c \right) x}{32 c d}}{\left(d \,x^{4}+c \right)^{2}}"," ",0,"(1/32*(7*a*d+b*c)/c^2*x^5+1/32*(11*a*d-3*b*c)/c/d*x)/(d*x^4+c)^2+21/128/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*a+3/128/c^2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*b+21/256/c^3*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*a+3/256/c^2/d*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*b+21/128/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*a+3/128/c^2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*b","A"
153,1,163,142,0.041000," ","int((b*x^4+a)^2*(d*x^4+c)^4,x)","\frac{b^{2} d^{4} x^{25}}{25}+\frac{\left(2 a b \,d^{4}+4 b^{2} c \,d^{3}\right) x^{21}}{21}+\frac{\left(a^{2} d^{4}+8 a b c \,d^{3}+6 b^{2} c^{2} d^{2}\right) x^{17}}{17}+\frac{\left(4 a^{2} c \,d^{3}+12 a b \,c^{2} d^{2}+4 b^{2} c^{3} d \right) x^{13}}{13}+\frac{\left(6 a^{2} c^{2} d^{2}+8 a b \,c^{3} d +b^{2} c^{4}\right) x^{9}}{9}+a^{2} c^{4} x +\frac{\left(4 a^{2} c^{3} d +2 a b \,c^{4}\right) x^{5}}{5}"," ",0,"1/25*b^2*d^4*x^25+1/21*(2*a*b*d^4+4*b^2*c*d^3)*x^21+1/17*(a^2*d^4+8*a*b*c*d^3+6*b^2*c^2*d^2)*x^17+1/13*(4*a^2*c*d^3+12*a*b*c^2*d^2+4*b^2*c^3*d)*x^13+1/9*(6*a^2*c^2*d^2+8*a*b*c^3*d+b^2*c^4)*x^9+1/5*(4*a^2*c^3*d+2*a*b*c^4)*x^5+a^2*c^4*x","A"
154,1,125,112,0.035000," ","int((b*x^4+a)^2*(d*x^4+c)^3,x)","\frac{b^{2} d^{3} x^{21}}{21}+\frac{\left(2 a b \,d^{3}+3 b^{2} c \,d^{2}\right) x^{17}}{17}+\frac{\left(a^{2} d^{3}+6 a b c \,d^{2}+3 b^{2} c^{2} d \right) x^{13}}{13}+\frac{\left(3 a^{2} c \,d^{2}+6 a b \,c^{2} d +b^{2} c^{3}\right) x^{9}}{9}+a^{2} c^{3} x +\frac{\left(3 a^{2} c^{2} d +2 a b \,c^{3}\right) x^{5}}{5}"," ",0,"1/21*b^2*d^3*x^21+1/17*(2*a*b*d^3+3*b^2*c*d^2)*x^17+1/13*(a^2*d^3+6*a*b*c*d^2+3*b^2*c^2*d)*x^13+1/9*(3*a^2*c*d^2+6*a*b*c^2*d+b^2*c^3)*x^9+1/5*(3*a^2*c^2*d+2*a*b*c^3)*x^5+a^2*c^3*x","A"
155,1,87,74,0.041000," ","int((b*x^4+a)^2*(d*x^4+c)^2,x)","\frac{b^{2} d^{2} x^{17}}{17}+\frac{\left(2 a b \,d^{2}+2 b^{2} c d \right) x^{13}}{13}+\frac{\left(a^{2} d^{2}+4 a b c d +b^{2} c^{2}\right) x^{9}}{9}+a^{2} c^{2} x +\frac{\left(2 a^{2} c d +2 a b \,c^{2}\right) x^{5}}{5}"," ",0,"1/17*b^2*d^2*x^17+1/13*(2*a*b*d^2+2*b^2*c*d)*x^13+1/9*(a^2*d^2+4*a*b*c*d+b^2*c^2)*x^9+1/5*(2*a^2*c*d+2*a*b*c^2)*x^5+a^2*c^2*x","A"
156,1,49,44,0.038000," ","int((b*x^4+a)^2*(d*x^4+c),x)","\frac{b^{2} d \,x^{13}}{13}+\frac{\left(2 a b d +b^{2} c \right) x^{9}}{9}+\frac{\left(a^{2} d +2 a b c \right) x^{5}}{5}+a^{2} c x"," ",0,"1/13*b^2*d*x^13+1/9*(2*a*b*d+b^2*c)*x^9+1/5*(a^2*d+2*a*b*c)*x^5+a^2*c*x","A"
157,1,436,186,0.048000," ","int((b*x^4+a)^2/(d*x^4+c),x)","\frac{b^{2} x^{5}}{5 d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 c}+\frac{2 a b x}{d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{2 d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{2 d}-\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{4 d}-\frac{b^{2} c x}{d^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 d^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 d^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 d^{2}}"," ",0,"1/5*b^2*x^5/d+2*b/d*a*x-b^2/d^2*c*x+1/8*(c/d)^(1/4)/c*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*a^2-1/4/d*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*a*b+1/8/d^2*(c/d)^(1/4)*c*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*b^2+1/4*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*a^2-1/2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*a*b+1/4/d^2*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*b^2+1/4*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*a^2-1/2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*a*b+1/4/d^2*(c/d)^(1/4)*c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*b^2","B"
158,1,475,224,0.056000," ","int((b*x^4+a)^2/(d*x^4+c)^2,x)","\frac{a^{2} x}{4 \left(d \,x^{4}+c \right) c}-\frac{a b x}{2 \left(d \,x^{4}+c \right) d}+\frac{b^{2} c x}{4 \left(d \,x^{4}+c \right) d^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{16 c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{16 c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{32 c^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{8 c d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{8 c d}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{16 c d}+\frac{b^{2} x}{d^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{16 d^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{16 d^{2}}-\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{32 d^{2}}"," ",0,"b^2/d^2*x+1/4/c*x/(d*x^4+c)*a^2-1/2/d*x/(d*x^4+c)*a*b+1/4/d^2*c*x/(d*x^4+c)*b^2+3/16/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*a^2+1/8/d/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*a*b-5/16/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*b^2+3/32/c^2*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*a^2+1/16/d/c*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*a*b-5/32/d^2*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*b^2+3/16/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*a^2+1/8/d/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*a*b-5/16/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*b^2","B"
159,1,499,280,0.058000," ","int((b*x^4+a)^2/(d*x^4+c)^3,x)","\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{128 c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{128 c^{3}}+\frac{21 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{256 c^{3}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{64 c^{2} d}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{64 c^{2} d}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a b \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{128 c^{2} d}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{128 c \,d^{2}}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{128 c \,d^{2}}+\frac{5 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{256 c \,d^{2}}+\frac{\frac{\left(7 a^{2} d^{2}+2 a b c d -9 b^{2} c^{2}\right) x^{5}}{32 c^{2} d}+\frac{\left(11 a^{2} d^{2}-6 a b c d -5 b^{2} c^{2}\right) x}{32 c \,d^{2}}}{\left(d \,x^{4}+c \right)^{2}}"," ",0,"(1/32*(7*a^2*d^2+2*a*b*c*d-9*b^2*c^2)/c^2/d*x^5+1/32*(11*a^2*d^2-6*a*b*c*d-5*b^2*c^2)/d^2/c*x)/(d*x^4+c)^2+21/128/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*a^2+3/64/c^2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*a*b+5/128/c/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*b^2+21/256/c^3*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*a^2+3/128/c^2/d*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*a*b+5/256/c/d^2*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*b^2+21/128/c^3*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*a^2+3/64/c^2/d*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*a*b+5/128/c/d^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*b^2","A"
160,1,837,261,0.047000," ","int((d*x^4+c)^4/(b*x^4+a),x)","\frac{d^{4} x^{13}}{13 b}-\frac{a \,d^{4} x^{9}}{9 b^{2}}+\frac{4 c \,d^{3} x^{9}}{9 b}+\frac{a^{2} d^{4} x^{5}}{5 b^{3}}-\frac{4 a c \,d^{3} x^{5}}{5 b^{2}}+\frac{6 c^{2} d^{2} x^{5}}{5 b}-\frac{a^{3} d^{4} x}{b^{4}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b^{4}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b^{4}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{4} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b^{4}}+\frac{4 a^{2} c \,d^{3} x}{b^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{b^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{b^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{2 b^{3}}-\frac{6 a \,c^{2} d^{2} x}{b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{4 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{4} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{4 c^{3} d x}{b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{2 b}"," ",0,"-4/5*d^3/b^2*x^5*a*c+4*d^3/b^3*a^2*c*x-6*d^2/b^2*a*c^2*x+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^4+1/8*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2)))*c^4+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^4+1/13*d^4*x^13/b+3/4/b^2*(a/b)^(1/4)*a*2^(1/2)*ln((x^2+(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2)))*c^2*d^2-1/b^3*(a/b)^(1/4)*a^2*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c*d^3+3/2/b^2*(a/b)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^2*d^2-1/b^3*(a/b)^(1/4)*a^2*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c*d^3+3/2/b^2*(a/b)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^2*d^2-1/2/b^3*(a/b)^(1/4)*a^2*2^(1/2)*ln((x^2+(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2)))*c*d^3+6/5*d^2/b*x^5*c^2-d^4/b^4*a^3*x+4*d/b*c^3*x-1/9*d^4/b^2*x^9*a+4/9*d^3/b*x^9*c+1/5*d^4/b^3*x^5*a^2+1/4/b^4*(a/b)^(1/4)*a^3*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*d^4-1/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^3*d+1/8/b^4*(a/b)^(1/4)*a^3*2^(1/2)*ln((x^2+(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2)))*d^4-1/2/b*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*x*2^(1/2)+(a/b)^(1/2)))*c^3*d+1/4/b^4*(a/b)^(1/4)*a^3*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*d^4-1/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^3*d","B"
161,1,627,219,0.046000," ","int((d*x^4+c)^3/(b*x^4+a),x)","\frac{d^{3} x^{9}}{9 b}-\frac{a \,d^{3} x^{5}}{5 b^{2}}+\frac{3 c \,d^{2} x^{5}}{5 b}+\frac{a^{2} d^{3} x}{b^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b^{3}}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b^{3}}-\frac{3 a c \,d^{2} x}{b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{3 c^{2} d x}{b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b}"," ",0,"1/9*d^3*x^9/b-1/5*d^3/b^2*x^5*a+3/5*d^2/b*x^5*c+d^3/b^3*a^2*x-3*d^2/b^2*a*c*x+3*d/b*c^2*x-1/8/b^3*(a/b)^(1/4)*a^2*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*d^3+3/8/b^2*(a/b)^(1/4)*a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c*d^2-3/8/b*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^2*d+1/8*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^3-1/4/b^3*(a/b)^(1/4)*a^2*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*d^3+3/4/b^2*(a/b)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c*d^2-3/4/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^2*d+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^3-1/4/b^3*(a/b)^(1/4)*a^2*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*d^3+3/4/b^2*(a/b)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c*d^2-3/4/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^2*d+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^3","B"
162,1,436,186,0.046000," ","int((d*x^4+c)^2/(b*x^4+a),x)","\frac{d^{2} x^{5}}{5 b}-\frac{a \,d^{2} x}{b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{2 c d x}{b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{2 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{2 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{4 b}"," ",0,"1/5*d^2*x^5/b-d^2/b^2*a*x+2*d/b*c*x+1/8/b^2*(a/b)^(1/4)*a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*d^2-1/4/b*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c*d+1/8*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^2+1/4/b^2*(a/b)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*d^2-1/2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c*d+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^2+1/4/b^2*(a/b)^(1/4)*a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*d^2-1/2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c*d+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^2","B"
163,1,266,158,0.048000," ","int((d*x^4+c)/(b*x^4+a),x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{d x}{b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b}"," ",0,"1/b*d*x-1/4/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*d+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c-1/8/b*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*d+1/8*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c-1/4/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*d+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c","A"
164,1,320,319,0.056000," ","int(1/(b*x^4+a)/(d*x^4+c),x)","-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) a}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(a d -b c \right) a}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right) c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right) c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 \left(a d -b c \right) c}"," ",0,"1/8*d/(a*d-b*c)*(c/d)^(1/4)/c*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))+1/4*d/(a*d-b*c)*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)+1/4*d/(a*d-b*c)*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)-1/8*b/(a*d-b*c)*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4*b/(a*d-b*c)*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/4*b/(a*d-b*c)*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
165,1,550,381,0.056000," ","int(1/(b*x^4+a)/(d*x^4+c)^2,x)","\frac{a \,d^{2} x}{4 \left(a d -b c \right)^{2} \left(d \,x^{4}+c \right) c}-\frac{b d x}{4 \left(a d -b c \right)^{2} \left(d \,x^{4}+c \right)}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a d -b c \right)^{2} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a d -b c \right)^{2} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{2} \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{32 \left(a d -b c \right)^{2} c^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right)^{2} a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right)^{2} a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(a d -b c \right)^{2} a}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a d -b c \right)^{2} c}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a d -b c \right)^{2} c}-\frac{7 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b d \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{32 \left(a d -b c \right)^{2} c}"," ",0,"1/4*d^2/(a*d-b*c)^2/c*x/(d*x^4+c)*a-1/4*d/(a*d-b*c)^2*x/(d*x^4+c)*b+3/16*d^2/(a*d-b*c)^2/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*a-7/16*d/(a*d-b*c)^2/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*b+3/32*d^2/(a*d-b*c)^2/c^2*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*a-7/32*d/(a*d-b*c)^2/c*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*b+3/16*d^2/(a*d-b*c)^2/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*a-7/16*d/(a*d-b*c)^2/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*b+1/8*b^2/(a*d-b*c)^2*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4*b^2/(a*d-b*c)^2*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*b^2/(a*d-b*c)^2*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
166,1,1118,334,0.060000," ","int((d*x^4+c)^5/(b*x^4+a)^2,x)","\frac{d^{5} x^{13}}{13 b^{2}}-\frac{2 a \,d^{5} x^{9}}{9 b^{3}}+\frac{5 c \,d^{4} x^{9}}{9 b^{2}}+\frac{3 a^{2} d^{5} x^{5}}{5 b^{4}}-\frac{2 a c \,d^{4} x^{5}}{b^{3}}+\frac{2 c^{2} d^{3} x^{5}}{b^{2}}-\frac{a^{4} d^{5} x}{4 \left(b \,x^{4}+a \right) b^{5}}+\frac{5 a^{3} c \,d^{4} x}{4 \left(b \,x^{4}+a \right) b^{4}}-\frac{5 a^{2} c^{2} d^{3} x}{2 \left(b \,x^{4}+a \right) b^{3}}+\frac{5 a \,c^{3} d^{2} x}{2 \left(b \,x^{4}+a \right) b^{2}}+\frac{c^{5} x}{4 \left(b \,x^{4}+a \right) a}-\frac{5 c^{4} d x}{4 \left(b \,x^{4}+a \right) b}-\frac{4 a^{3} d^{5} x}{b^{5}}+\frac{17 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{5} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 b^{5}}+\frac{17 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{5} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 b^{5}}+\frac{17 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{3} d^{5} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 b^{5}}+\frac{15 a^{2} c \,d^{4} x}{b^{4}}-\frac{65 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 b^{4}}-\frac{65 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 b^{4}}-\frac{65 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} c \,d^{4} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 b^{4}}-\frac{20 a \,c^{2} d^{3} x}{b^{3}}+\frac{45 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{3}}+\frac{45 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{3}}+\frac{45 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,c^{2} d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{16 b^{3}}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{4} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a b}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{4} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a b}+\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{4} d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{5} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{5} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{5} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}+\frac{10 c^{3} d^{2} x}{b^{2}}-\frac{25 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{2}}-\frac{25 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{2}}-\frac{25 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{16 b^{2}}"," ",0,"5/32/b/a*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^4*d-65/16/b^4*a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c*d^4+45/8/b^3*a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^2*d^3+5/16/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^4*d-65/16/b^4*a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c*d^4+45/8/b^3*a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^2*d^3+5/16/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^4*d-65/32/b^4*a^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c*d^4+45/16/b^3*a*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^2*d^3+1/13*d^5*x^13/b^2+2*d^3/b^2*x^5*c^2-4*d^5/b^5*a^3*x+10*d^2/b^2*c^3*x+1/4/a*x/(b*x^4+a)*c^5-2/9*d^5/b^3*x^9*a+5/9*d^4/b^2*x^9*c+3/5*d^5/b^4*x^5*a^2-5/2/b^3*a^2*x/(b*x^4+a)*c^2*d^3+5/2/b^2*a*x/(b*x^4+a)*c^3*d^2+17/16/b^5*a^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*d^5-25/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^3*d^2+17/32/b^5*a^3*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*d^5-25/16/b^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^3*d^2+17/16/b^5*a^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*d^5-25/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^3*d^2+5/4/b^4*a^3*x/(b*x^4+a)*c*d^4-1/4/b^5*a^4*x/(b*x^4+a)*d^5-5/4/b*x/(b*x^4+a)*c^4*d+3/16/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^5+3/32/a^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^5+3/16/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^5-2*d^4/b^3*x^5*a*c+15*d^4/b^4*a^2*c*x-20*a/b^3*c^2*d^3*x","B"
167,1,885,286,0.062000," ","int((d*x^4+c)^4/(b*x^4+a)^2,x)","\frac{d^{4} x^{9}}{9 b^{2}}-\frac{2 a \,d^{4} x^{5}}{5 b^{3}}+\frac{4 c \,d^{3} x^{5}}{5 b^{2}}+\frac{a^{3} d^{4} x}{4 \left(b \,x^{4}+a \right) b^{4}}-\frac{a^{2} c \,d^{3} x}{\left(b \,x^{4}+a \right) b^{3}}+\frac{3 a \,c^{2} d^{2} x}{2 \left(b \,x^{4}+a \right) b^{2}}+\frac{c^{4} x}{4 \left(b \,x^{4}+a \right) a}-\frac{c^{3} d x}{\left(b \,x^{4}+a \right) b}+\frac{3 a^{2} d^{4} x}{b^{4}}-\frac{13 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 b^{4}}-\frac{13 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 b^{4}}-\frac{13 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a^{2} d^{4} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 b^{4}}-\frac{8 a c \,d^{3} x}{b^{3}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b^{3}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b^{3}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a c \,d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b^{3}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{4} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{4} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}+\frac{6 c^{2} d^{2} x}{b^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 b^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 b^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{16 b^{2}}"," ",0,"1/4/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^3*d+9/8/b^3*a*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c*d^3+1/8/b/a*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^3*d+9/4/b^3*a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c*d^3+1/4/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^3*d+9/4/b^3*a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c*d^3+1/9*d^4*x^9/b^2+1/4/a*x/(b*x^4+a)*c^4-2/5*d^4/b^3*x^5*a+4/5*d^3/b^2*x^5*c+6/b^2*c^2*d^2*x+3*a^2/b^4*d^4*x-13/16/b^4*a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*d^4-15/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^2*d^2-1/b^3*a^2*x/(b*x^4+a)*c*d^3+3/2/b^2*a*x/(b*x^4+a)*c^2*d^2-13/16/b^4*a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*d^4-15/8/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^2*d^2-13/32/b^4*a^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*d^4-15/16/b^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^2*d^2+1/4/b^4*a^3*x/(b*x^4+a)*d^4-1/b*x/(b*x^4+a)*c^3*d+3/16/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^4+3/32/a^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^4-8*d^3/b^3*a*c*x+3/16/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^4","B"
168,1,669,248,0.055000," ","int((d*x^4+c)^3/(b*x^4+a)^2,x)","\frac{d^{3} x^{5}}{5 b^{2}}-\frac{a^{2} d^{3} x}{4 \left(b \,x^{4}+a \right) b^{3}}+\frac{3 a c \,d^{2} x}{4 \left(b \,x^{4}+a \right) b^{2}}+\frac{c^{3} x}{4 \left(b \,x^{4}+a \right) a}-\frac{3 c^{2} d x}{4 \left(b \,x^{4}+a \right) b}-\frac{2 a \,d^{3} x}{b^{3}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 b^{3}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 b^{3}}+\frac{9 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 b^{3}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{3} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}+\frac{3 c \,d^{2} x}{b^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 b^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 b^{2}}-\frac{15 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \,d^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 b^{2}}"," ",0,"1/5*d^3*x^5/b^2-2*a/b^3*d^3*x+3/b^2*c*d^2*x-1/4/b^3*a^2*x/(b*x^4+a)*d^3+3/4/b^2*a*x/(b*x^4+a)*c*d^2-3/4/b*x/(b*x^4+a)*c^2*d+1/4/a*x/(b*x^4+a)*c^3+9/16/b^3*a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*d^3-15/16/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c*d^2+3/16/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^2*d+3/16/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^3+9/32/b^3*a*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*d^3-15/32/b^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c*d^2+3/32/b/a*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^2*d+3/32/a^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^3+9/16/b^3*a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*d^3-15/16/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c*d^2+3/16/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^2*d+3/16/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^3","B"
169,1,475,224,0.058000," ","int((d*x^4+c)^2/(b*x^4+a)^2,x)","\frac{a \,d^{2} x}{4 \left(b \,x^{4}+a \right) b^{2}}+\frac{c^{2} x}{4 \left(b \,x^{4}+a \right) a}-\frac{c d x}{2 \left(b \,x^{4}+a \right) b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{8 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{8 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{16 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}+\frac{d^{2} x}{b^{2}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 b^{2}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 b^{2}}-\frac{5 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 b^{2}}"," ",0,"1/b^2*d^2*x+1/4/b^2*a*x/(b*x^4+a)*d^2-1/2/b*x/(b*x^4+a)*c*d+1/4/a*x/(b*x^4+a)*c^2-5/16/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*d^2+1/8/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c*d+3/16/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c^2-5/32/b^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*d^2+1/16/b/a*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c*d+3/32/a^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c^2-5/16/b^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*d^2+1/8/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c*d+3/16/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c^2","B"
170,1,295,178,0.053000," ","int((d*x^4+c)/(b*x^4+a)^2,x)","\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}-\frac{\left(a d -b c \right) x}{4 \left(b \,x^{4}+a \right) a b}"," ",0,"-1/4*(a*d-b*c)/a/b*x/(b*x^4+a)+1/16/a/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*d+3/16/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c+1/32/a/b*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*d+3/32/a^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c+1/16/a/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*d+3/16/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c","A"
171,1,550,381,0.058000," ","int(1/(b*x^4+a)^2/(d*x^4+c),x)","\frac{b^{2} c x}{4 \left(a d -b c \right)^{2} \left(b \,x^{4}+a \right) a}-\frac{b d x}{4 \left(a d -b c \right)^{2} \left(b \,x^{4}+a \right)}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a d -b c \right)^{2} a}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a d -b c \right)^{2} a}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(a d -b c \right)^{2} a}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a d -b c \right)^{2} a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a d -b c \right)^{2} a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(a d -b c \right)^{2} a^{2}}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{4 \left(a d -b c \right)^{2} c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{4 \left(a d -b c \right)^{2} c}+\frac{\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, d^{2} \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{8 \left(a d -b c \right)^{2} c}"," ",0,"1/8*d^2/(a*d-b*c)^2*(c/d)^(1/4)/c*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))+1/4*d^2/(a*d-b*c)^2*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)+1/4*d^2/(a*d-b*c)^2*(c/d)^(1/4)/c*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)-1/4*b/(a*d-b*c)^2*x/(b*x^4+a)*d+1/4*b^2/(a*d-b*c)^2/a*x/(b*x^4+a)*c-7/16*b/(a*d-b*c)^2/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*d+3/16*b^2/(a*d-b*c)^2/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c-7/16*b/(a*d-b*c)^2/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*d+3/16*b^2/(a*d-b*c)^2/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c-7/32*b/(a*d-b*c)^2/a*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*d+3/32*b^2/(a*d-b*c)^2/a^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c","A"
172,1,784,462,0.066000," ","int(1/(b*x^4+a)^2/(d*x^4+c)^2,x)","\frac{a \,d^{3} x}{4 \left(a d -b c \right)^{3} \left(d \,x^{4}+c \right) c}-\frac{b^{3} c x}{4 \left(a d -b c \right)^{3} \left(b \,x^{4}+a \right) a}+\frac{b^{2} d x}{4 \left(a d -b c \right)^{3} \left(b \,x^{4}+a \right)}-\frac{b \,d^{2} x}{4 \left(a d -b c \right)^{3} \left(d \,x^{4}+c \right)}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a d -b c \right)^{3} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a d -b c \right)^{3} c^{2}}+\frac{3 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, a \,d^{3} \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{32 \left(a d -b c \right)^{3} c^{2}}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a d -b c \right)^{3} a}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a d -b c \right)^{3} a}+\frac{11 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{2} d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(a d -b c \right)^{3} a}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a d -b c \right)^{3} a^{2}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a d -b c \right)^{3} a^{2}}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, b^{3} c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(a d -b c \right)^{3} a^{2}}-\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}-1\right)}{16 \left(a d -b c \right)^{3} c}-\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{2} \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{c}{d}\right)^{\frac{1}{4}}}+1\right)}{16 \left(a d -b c \right)^{3} c}-\frac{11 \left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, b \,d^{2} \ln \left(\frac{x^{2}+\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}{x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{c}{d}}}\right)}{32 \left(a d -b c \right)^{3} c}"," ",0,"1/4*d^3/(a*d-b*c)^3/c*x/(d*x^4+c)*a-1/4*d^2/(a*d-b*c)^3*x/(d*x^4+c)*b+3/16*d^3/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*a-11/16*d^2/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x-1)*b+3/32*d^3/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*a-11/32*d^2/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*ln((x^2+(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2))/(x^2-(c/d)^(1/4)*2^(1/2)*x+(c/d)^(1/2)))*b+3/16*d^3/(a*d-b*c)^3/c^2*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*a-11/16*d^2/(a*d-b*c)^3/c*(c/d)^(1/4)*2^(1/2)*arctan(2^(1/2)/(c/d)^(1/4)*x+1)*b+1/4*b^2/(a*d-b*c)^3*x/(b*x^4+a)*d-1/4*b^3/(a*d-b*c)^3/a*x/(b*x^4+a)*c+11/32*b^2/(a*d-b*c)^3/a*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*d-3/32*b^3/(a*d-b*c)^3/a^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*c+11/16*b^2/(a*d-b*c)^3/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*d-3/16*b^3/(a*d-b*c)^3/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c+11/16*b^2/(a*d-b*c)^3/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*d-3/16*b^3/(a*d-b*c)^3/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c","A"
173,1,408,255,0.310000," ","int((-b*x^4+a)^(5/2)/(-d*x^4+c),x)","-\frac{\sqrt{-b \,x^{4}+a}\, b^{2} x^{5}}{7 d}-\frac{\left(\frac{\left(-\frac{5 a \,b^{2}}{7 d}+\frac{\left(3 a d -b c \right) b^{2}}{d^{2}}\right) a}{3 b}-\frac{\left(3 a^{2} d^{2}-3 a b c d +b^{2} c^{2}\right) b}{d^{3}}\right) \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}}+\frac{\left(-\frac{5 a \,b^{2}}{7 d}+\frac{\left(3 a d -b c \right) b^{2}}{d^{2}}\right) \sqrt{-b \,x^{4}+a}\, x}{3 b}+\frac{\left(-a^{3} d^{3}+3 a^{2} b c \,d^{2}-3 a \,b^{2} c^{2} d +b^{3} c^{3}\right) \left(-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{8 d^{4} \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}"," ",0,"-1/7*b^2/d*x^5*(-b*x^4+a)^(1/2)+1/3*(b^2/d^2*(3*a*d-b*c)-5/7*b^2/d*a)/b*x*(-b*x^4+a)^(1/2)-(-b*(3*a^2*d^2-3*a*b*c*d+b^2*c^2)/d^3+1/3*(b^2/d^2*(3*a*d-b*c)-5/7*b^2/d*a)/b*a)/(1/a^(1/2)*b^(1/2))^(1/2)*(1-1/a^(1/2)*b^(1/2)*x^2)^(1/2)*(1+1/a^(1/2)*b^(1/2)*x^2)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/8/d^4*sum((-a^3*d^3+3*a^2*b*c*d^2-3*a*b^2*c^2*d+b^3*c^3)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(1-1/a^(1/2)*b^(1/2)*x^2)^(1/2)*(1+1/a^(1/2)*b^(1/2)*x^2)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,a^(1/2)/b^(1/2)*_alpha^2/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
174,1,311,215,0.293000," ","int((-b*x^4+a)^(3/2)/(-d*x^4+c),x)","\frac{\sqrt{-b \,x^{4}+a}\, b x}{3 d}-\frac{\left(\frac{a b}{3 d}-\frac{\left(2 a d -b c \right) b}{d^{2}}\right) \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}}+\frac{\left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{8 d^{3} \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}"," ",0,"1/3*b*x*(-b*x^4+a)^(1/2)/d-(-b*(2*a*d-b*c)/d^2+1/3*b/d*a)/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/8/d^3*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
175,1,259,184,0.314000," ","int((-b*x^4+a)^(1/2)/(-d*x^4+c),x)","\frac{\sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, d}+\frac{\left(-a d +b c \right) \left(-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{8 d^{2} \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}"," ",0,"b/d/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/8/d^2*sum((-a*d+b*c)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
176,1,183,118,0.309000," ","int(1/(-b*x^4+a)^(1/2)/(-d*x^4+c),x)","-\frac{-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}}{8 d \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}"," ",0,"-1/8/d*sum(1/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
177,1,301,219,0.362000," ","int(1/(-b*x^4+a)^(3/2)/(-d*x^4+c),x)","-\frac{b x}{2 \left(a d -b c \right) \sqrt{-\left(x^{4}-\frac{a}{b}\right) b}\, a}-\frac{\sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \left(a d -b c \right) \sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, a}-\frac{-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}}{8 \left(a d -b c \right) \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}"," ",0,"-1/2*b/a*x/(a*d-b*c)/(-(x^4-a/b)*b)^(1/2)-1/2/a*b/(a*d-b*c)/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/8*sum(1/(a*d-b*c)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
178,1,361,268,0.320000," ","int(1/(-b*x^4+a)^(5/2)/(-d*x^4+c),x)","-\frac{d \left(-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{8 \left(a d -b c \right)^{2} \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}-\frac{\left(11 a d -5 b c \right) b x}{12 \left(a d -b c \right)^{2} \sqrt{-\left(x^{4}-\frac{a}{b}\right) b}\, a^{2}}-\frac{\left(11 a d -5 b c \right) \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{12 \left(a d -b c \right)^{2} \sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, a^{2}}-\frac{\sqrt{-b \,x^{4}+a}\, x}{6 \left(a d -b c \right) \left(x^{4}-\frac{a}{b}\right)^{2} a b}"," ",0,"-1/6/a*x/b/(a*d-b*c)*(-b*x^4+a)^(1/2)/(x^4-a/b)^2-1/12*b/a^2*x*(11*a*d-5*b*c)/(a*d-b*c)^2/(-(x^4-a/b)*b)^(1/2)-1/12/a^2*b*(11*a*d-5*b*c)/(a*d-b*c)^2/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/8*d*sum(1/(a*d-b*c)^2/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
179,1,322,873,0.477000," ","int((b*x^4+a)^(3/2)/(d*x^4+c),x)","\frac{\sqrt{b \,x^{4}+a}\, b x}{3 d}+\frac{\left(-\frac{a b}{3 d}+\frac{\left(2 a d -b c \right) b}{d^{2}}\right) \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{\left(-a^{2} d^{2}+2 a b c d -b^{2} c^{2}\right) \left(\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{3} d \EllipticPi \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , \frac{i \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{2 \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{8 d^{3} \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{3}}"," ",0,"1/3*b*x*(b*x^4+a)^(1/2)/d+((2*a*d-b*c)*b/d^2-1/3*a*b/d)/(I/a^(1/2)*b^(1/2))^(1/2)*(1-I/a^(1/2)*b^(1/2)*x^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*x^2)^(1/2)/(b*x^4+a)^(1/2)*EllipticF(x*(I/a^(1/2)*b^(1/2))^(1/2),I)-1/8/d^3*sum((-a^2*d^2+2*a*b*c*d-b^2*c^2)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(b*x^4+a)^(1/2))+2/(I/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(1-I/a^(1/2)*b^(1/2)*x^2)^(1/2)*(1+I/a^(1/2)*b^(1/2)*x^2)^(1/2)/(b*x^4+a)^(1/2)*EllipticPi(x*(I/a^(1/2)*b^(1/2))^(1/2),I*a^(1/2)/b^(1/2)*_alpha^2/c*d,(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d+c))","C"
180,1,273,834,0.327000," ","int((b*x^4+a)^(1/2)/(d*x^4+c),x)","\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, d}-\frac{\left(-a d +b c \right) \left(\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{3} d \EllipticPi \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , \frac{i \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{2 \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{8 d^{2} \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{3}}"," ",0,"b/d/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/8/d^2*sum((-a*d+b*c)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(b*x^4+a)^(1/2))+2/(I/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*b^(1/2))^(1/2)*x,I*_alpha^2*a^(1/2)/b^(1/2)/c*d,(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d+c))","C"
181,1,191,686,0.332000," ","int(1/(b*x^4+a)^(1/2)/(d*x^4+c),x)","\frac{\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{3} d \EllipticPi \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , \frac{i \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{2 \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}}{8 d \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{3}}"," ",0,"1/8/d*sum(1/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(b*x^4+a)^(1/2))+2/(I/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*b^(1/2))^(1/2)*x,I*_alpha^2*a^(1/2)/b^(1/2)/c*d,(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d+c))","C"
182,1,313,862,0.286000," ","int(1/(b*x^4+a)^(3/2)/(d*x^4+c),x)","-\frac{b x}{2 \left(a d -b c \right) \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a}-\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \left(a d -b c \right) \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}+\frac{\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{3} d \EllipticPi \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , \frac{i \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{2 \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}}{8 \left(a d -b c \right) \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{3}}"," ",0,"-1/2*b/a*x/(a*d-b*c)/((x^4+a/b)*b)^(1/2)-1/2/a*b/(a*d-b*c)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/8*sum(1/(a*d-b*c)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(b*x^4+a)^(1/2))+2/(I/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*b^(1/2))^(1/2)*x,I*_alpha^2*a^(1/2)/b^(1/2)/c*d,(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d+c))","C"
183,1,371,923,0.337000," ","int(1/(b*x^4+a)^(5/2)/(d*x^4+c),x)","\frac{d \left(\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{3} d \EllipticPi \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , \frac{i \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{2 \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{8 \left(a d -b c \right)^{2} \RootOf \left(d \,\textit{\_Z}^{4}+c \right)^{3}}-\frac{\left(11 a d -5 b c \right) b x}{12 \left(a d -b c \right)^{2} \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a^{2}}-\frac{\left(11 a d -5 b c \right) \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{12 \left(a d -b c \right)^{2} \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{2}}-\frac{\sqrt{b \,x^{4}+a}\, x}{6 \left(a d -b c \right) \left(x^{4}+\frac{a}{b}\right)^{2} a b}"," ",0,"-1/6/a*x/b/(a*d-b*c)*(b*x^4+a)^(1/2)/(x^4+a/b)^2-1/12*b/a^2*x*(11*a*d-5*b*c)/(a*d-b*c)^2/((x^4+a/b)*b)^(1/2)-1/12/a^2*b*(11*a*d-5*b*c)/(a*d-b*c)^2/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/8*d*sum(1/(a*d-b*c)^2/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(b*x^4+a)^(1/2))+2/(I/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticPi((I/a^(1/2)*b^(1/2))^(1/2)*x,I*_alpha^2*a^(1/2)/b^(1/2)/c*d,(-I/a^(1/2)*b^(1/2))^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d+c))","C"
184,1,540,356,0.292000," ","int((-b*x^4+a)^(7/2)/(-d*x^4+c)^2,x)","-\frac{\sqrt{-b \,x^{4}+a}\, b^{3} x^{5}}{7 d^{2}}+\frac{\left(\frac{\left(\frac{5 a \,b^{3}}{7 d^{2}}-\frac{2 \left(2 a d -b c \right) b^{3}}{d^{3}}\right) a}{3 b}+\frac{\left(6 a^{2} d^{2}-8 a b c d +3 b^{2} c^{2}\right) b^{2}}{d^{4}}+\frac{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) b}{4 c \,d^{4}}\right) \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}}-\frac{\left(\frac{5 a \,b^{3}}{7 d^{2}}-\frac{2 \left(2 a d -b c \right) b^{3}}{d^{3}}\right) \sqrt{-b \,x^{4}+a}\, x}{3 b}-\frac{\left(a^{3} d^{3}-3 a^{2} b c \,d^{2}+3 a \,b^{2} c^{2} d -b^{3} c^{3}\right) \sqrt{-b \,x^{4}+a}\, x}{4 \left(d \,x^{4}-c \right) c \,d^{3}}-\frac{\left(3 a^{4} d^{4}+2 a^{3} b \,d^{3} c -24 a^{2} b^{2} c^{2} d^{2}+30 c^{3} a \,b^{3} d -11 b^{4} c^{4}\right) \left(-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{32 c \,d^{5} \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}"," ",0,"-1/4*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/c/d^3*x*(-b*x^4+a)^(1/2)/(d*x^4-c)-1/7*b^3/d^2*x^5*(-b*x^4+a)^(1/2)-1/3*(-2*b^3/d^3*(2*a*d-b*c)+5/7*b^3/d^2*a)/b*x*(-b*x^4+a)^(1/2)+(b^2*(6*a^2*d^2-8*a*b*c*d+3*b^2*c^2)/d^4+1/4*b/d^4*(a^3*d^3-3*a^2*b*c*d^2+3*a*b^2*c^2*d-b^3*c^3)/c+1/3*(-2*b^3/d^3*(2*a*d-b*c)+5/7*b^3/d^2*a)/b*a)/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/32/d^5/c*sum((3*a^4*d^4+2*a^3*b*c*d^3-24*a^2*b^2*c^2*d^2+30*a*b^3*c^3*d-11*b^4*c^4)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
185,1,412,299,0.340000," ","int((-b*x^4+a)^(5/2)/(-d*x^4+c)^2,x)","\frac{\sqrt{-b \,x^{4}+a}\, b^{2} x}{3 d^{2}}+\frac{\left(-\frac{a \,b^{2}}{3 d^{2}}+\frac{\left(3 a d -2 b c \right) b^{2}}{d^{3}}+\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) b}{4 c \,d^{3}}\right) \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}}-\frac{\left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \sqrt{-b \,x^{4}+a}\, x}{4 \left(d \,x^{4}-c \right) c \,d^{2}}-\frac{\left(3 a^{3} d^{3}+a^{2} b c \,d^{2}-11 a \,b^{2} c^{2} d +7 b^{3} c^{3}\right) \left(-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{32 c \,d^{4} \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}"," ",0,"-1/4*(a^2*d^2-2*a*b*c*d+b^2*c^2)/c/d^2*x*(-b*x^4+a)^(1/2)/(d*x^4-c)+1/3*b^2/d^2*x*(-b*x^4+a)^(1/2)+(b^2*(3*a*d-2*b*c)/d^3+1/4*b/d^3*(a^2*d^2-2*a*b*c*d+b^2*c^2)/c-1/3*b^2/d^2*a)/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/32/c/d^4*sum((3*a^3*d^3+a^2*b*c*d^2-11*a*b^2*c^2*d+7*b^3*c^3)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
186,1,329,247,0.339000," ","int((-b*x^4+a)^(3/2)/(-d*x^4+c)^2,x)","\frac{\left(\frac{b^{2}}{d^{2}}+\frac{\left(a d -b c \right) b}{4 c \,d^{2}}\right) \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}}-\frac{\left(a d -b c \right) \sqrt{-b \,x^{4}+a}\, x}{4 \left(d \,x^{4}-c \right) c d}-\frac{3 \left(a^{2} d^{2}-b^{2} c^{2}\right) \left(-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{32 c \,d^{3} \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}"," ",0,"-1/4*(a*d-b*c)/d/c*x*(-b*x^4+a)^(1/2)/(d*x^4-c)+(b^2/d^2+1/4*b/d^2*(a*d-b*c)/c)/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)-3/32/c/d^3*sum((a^2*d^2-b^2*c^2)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
187,1,294,214,0.306000," ","int((-b*x^4+a)^(1/2)/(-d*x^4+c)^2,x)","\frac{\sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{4 \sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c d}-\frac{\sqrt{-b \,x^{4}+a}\, x}{4 \left(d \,x^{4}-c \right) c}-\frac{\left(3 a d -b c \right) \left(-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{32 c \,d^{2} \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}"," ",0,"-1/4/c*x*(-b*x^4+a)^(1/2)/(d*x^4-c)+1/4*b/c/d/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/32/c/d^2*sum((3*a*d-b*c)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
188,1,322,248,0.336000," ","int(1/(-b*x^4+a)^(1/2)/(-d*x^4+c)^2,x)","\frac{\sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{4 \left(a d -b c \right) \sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\sqrt{-b \,x^{4}+a}\, d x}{4 \left(a d -b c \right) \left(d \,x^{4}-c \right) c}-\frac{\left(3 a d -5 b c \right) \left(-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{32 c d \left(a d -b c \right) \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}"," ",0,"-1/4*d/(a*d-b*c)/c*x*(-b*x^4+a)^(1/2)/(d*x^4-c)+1/4*b/(a*d-b*c)/c/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/32/c/d*sum((3*a*d-5*b*c)/(a*d-b*c)/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
189,1,375,296,0.351000," ","int(1/(-b*x^4+a)^(3/2)/(-d*x^4+c)^2,x)","\frac{b^{2} x}{2 \left(a d -b c \right)^{2} \sqrt{-\left(x^{4}-\frac{a}{b}\right) b}\, a}-\frac{\sqrt{-b \,x^{4}+a}\, d^{2} x}{4 \left(a d -b c \right)^{2} \left(d \,x^{4}-c \right) c}+\frac{\left(\frac{b^{2}}{2 \left(a d -b c \right)^{2} a}+\frac{b d}{4 \left(a d -b c \right)^{2} c}\right) \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}}-\frac{3 \left(a d -3 b c \right) \left(-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{32 c \left(a d -b c \right)^{2} \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}"," ",0,"1/2*b^2/a*x/(a*d-b*c)^2/(-(x^4-a/b)*b)^(1/2)-1/4*d^2/(a*d-b*c)^2/c*x*(-b*x^4+a)^(1/2)/(d*x^4-c)+(1/2/a*b^2/(a*d-b*c)^2+1/4*d*b/(a*d-b*c)^2/c)/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)-3/32/c*sum((a*d-3*b*c)/(a*d-b*c)^2/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
190,1,484,369,0.349000," ","int(1/(-b*x^4+a)^(5/2)/(-d*x^4+c)^2,x)","-\frac{\sqrt{-b \,x^{4}+a}\, b \,d^{3} x}{4 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(a d -b c \right) \left(b d \,x^{4}-b c \right) c}+\frac{\left(17 a d -5 b c \right) b^{2} x}{12 \left(a d -b c \right)^{3} \sqrt{-\left(x^{4}-\frac{a}{b}\right) b}\, a^{2}}-\frac{d \left(3 a d -13 b c \right) \left(-\frac{2 \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3} d \EllipticPi \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , \frac{\RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} \sqrt{a}\, d}{\sqrt{b}\, c}, \frac{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}}\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}\, c}-\frac{\arctanh \left(\frac{-2 \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{2} b \,x^{2}+2 a}{2 \sqrt{\frac{a d -b c}{d}}\, \sqrt{-b \,x^{4}+a}}\right)}{\sqrt{\frac{a d -b c}{d}}}\right)}{32 c \left(a d -b c \right)^{3} \RootOf \left(d \,\textit{\_Z}^{4}-c \right)^{3}}+\frac{\left(\frac{b \,d^{2}}{4 \left(a^{2} d^{2}-2 a b c d +b^{2} c^{2}\right) \left(a d -b c \right) c}+\frac{\left(17 a d -5 b c \right) b^{2}}{12 \left(a d -b c \right)^{3} a^{2}}\right) \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}}+\frac{\sqrt{-b \,x^{4}+a}\, x}{6 \left(a d -b c \right)^{2} \left(x^{4}-\frac{a}{b}\right)^{2} a}"," ",0,"-1/4*b*d^3/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)/c*x*(-b*x^4+a)^(1/2)/(b*d*x^4-b*c)+1/6/(a*d-b*c)^2/a*x*(-b*x^4+a)^(1/2)/(x^4-a/b)^2+1/12*b^2/a^2*x*(17*a*d-5*b*c)/(a*d-b*c)^3/(-(x^4-a/b)*b)^(1/2)+(1/4*b*d^2/(a^2*d^2-2*a*b*c*d+b^2*c^2)/(a*d-b*c)/c+1/12/a^2*b^2*(17*a*d-5*b*c)/(a*d-b*c)^3)/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/32/c*d*sum((3*a*d-13*b*c)/(a*d-b*c)^3/_alpha^3*(-1/((a*d-b*c)/d)^(1/2)*arctanh(1/2*(-2*_alpha^2*b*x^2+2*a)/((a*d-b*c)/d)^(1/2)/(-b*x^4+a)^(1/2))-2/(1/a^(1/2)*b^(1/2))^(1/2)*_alpha^3*d/c*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticPi((1/a^(1/2)*b^(1/2))^(1/2)*x,_alpha^2*a^(1/2)/b^(1/2)/c*d,(-1/a^(1/2)*b^(1/2))^(1/2)/(1/a^(1/2)*b^(1/2))^(1/2))),_alpha=RootOf(_Z^4*d-c))","C"
191,1,103,71,0.208000," ","int((b*x^4+a)^(1/2)/(-b*c*x^4+a*c),x)","-\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{b \,x^{4}+a}\, \sqrt{2}}{2 \left(a b \right)^{\frac{1}{4}} x}\right)}{4 \left(a b \right)^{\frac{1}{4}} c}+\frac{\sqrt{2}\, \ln \left(\frac{\frac{\sqrt{b \,x^{4}+a}\, \sqrt{2}}{2 x}+\left(a b \right)^{\frac{1}{4}}}{\frac{\sqrt{b \,x^{4}+a}\, \sqrt{2}}{2 x}-\left(a b \right)^{\frac{1}{4}}}\right)}{8 \left(a b \right)^{\frac{1}{4}} c}"," ",0,"-1/4/c*2^(1/2)/(a*b)^(1/4)*arctan(1/2*(b*x^4+a)^(1/2)*2^(1/2)/x/(a*b)^(1/4))+1/8/c*2^(1/2)/(a*b)^(1/4)*ln((1/2*(b*x^4+a)^(1/2)*2^(1/2)/x+(a*b)^(1/4))/(1/2*(b*x^4+a)^(1/2)*2^(1/2)/x-(a*b)^(1/4)))","A"
192,1,158,84,0.221000," ","int((-b*x^4+a)^(1/2)/(b*c*x^4+a*c),x)","\frac{\arctan \left(-\frac{\sqrt{-b \,x^{4}+a}}{\left(a b \right)^{\frac{1}{4}} x}+1\right)}{4 \left(a b \right)^{\frac{1}{4}} c}-\frac{\arctan \left(\frac{\sqrt{-b \,x^{4}+a}}{\left(a b \right)^{\frac{1}{4}} x}+1\right)}{4 \left(a b \right)^{\frac{1}{4}} c}-\frac{\ln \left(\frac{-\frac{\left(a b \right)^{\frac{1}{4}} \sqrt{-b \,x^{4}+a}}{x}+\frac{-b \,x^{4}+a}{2 x^{2}}+\sqrt{a b}}{\frac{\left(a b \right)^{\frac{1}{4}} \sqrt{-b \,x^{4}+a}}{x}+\frac{-b \,x^{4}+a}{2 x^{2}}+\sqrt{a b}}\right)}{8 \left(a b \right)^{\frac{1}{4}} c}"," ",0,"-1/8/c/(a*b)^(1/4)*ln((1/2*(-b*x^4+a)/x^2-(a*b)^(1/4)*(-b*x^4+a)^(1/2)/x+(a*b)^(1/2))/(1/2*(-b*x^4+a)/x^2+(a*b)^(1/4)*(-b*x^4+a)^(1/2)/x+(a*b)^(1/2)))-1/4/c/(a*b)^(1/4)*arctan(1/(a*b)^(1/4)*(-b*x^4+a)^(1/2)/x+1)+1/4/c/(a*b)^(1/4)*arctan(-1/(a*b)^(1/4)*(-b*x^4+a)^(1/2)/x+1)","A"
193,0,0,167,0.587000," ","int((b*x^4+a)^(7/4)/(d*x^4+c),x)","\int \frac{\left(b \,x^{4}+a \right)^{\frac{7}{4}}}{d \,x^{4}+c}\, dx"," ",0,"int((b*x^4+a)^(7/4)/(d*x^4+c),x)","F"
194,0,0,133,0.575000," ","int((b*x^4+a)^(3/4)/(d*x^4+c),x)","\int \frac{\left(b \,x^{4}+a \right)^{\frac{3}{4}}}{d \,x^{4}+c}\, dx"," ",0,"int((b*x^4+a)^(3/4)/(d*x^4+c),x)","F"
195,0,0,81,0.566000," ","int(1/(b*x^4+a)^(1/4)/(d*x^4+c),x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{1}{4}} \left(d \,x^{4}+c \right)}\, dx"," ",0,"int(1/(b*x^4+a)^(1/4)/(d*x^4+c),x)","F"
196,0,0,108,0.598000," ","int(1/(b*x^4+a)^(5/4)/(d*x^4+c),x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{5}{4}} \left(d \,x^{4}+c \right)}\, dx"," ",0,"int(1/(b*x^4+a)^(5/4)/(d*x^4+c),x)","F"
197,0,0,148,0.603000," ","int(1/(b*x^4+a)^(9/4)/(d*x^4+c),x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{9}{4}} \left(d \,x^{4}+c \right)}\, dx"," ",0,"int(1/(b*x^4+a)^(9/4)/(d*x^4+c),x)","F"
198,0,0,197,0.615000," ","int(1/(b*x^4+a)^(13/4)/(d*x^4+c),x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{13}{4}} \left(d \,x^{4}+c \right)}\, dx"," ",0,"int(1/(b*x^4+a)^(13/4)/(d*x^4+c),x)","F"
199,0,0,293,0.557000," ","int((b*x^4+a)^(9/4)/(d*x^4+c),x)","\int \frac{\left(b \,x^{4}+a \right)^{\frac{9}{4}}}{d \,x^{4}+c}\, dx"," ",0,"int((b*x^4+a)^(9/4)/(d*x^4+c),x)","F"
200,0,0,255,0.572000," ","int((b*x^4+a)^(5/4)/(d*x^4+c),x)","\int \frac{\left(b \,x^{4}+a \right)^{\frac{5}{4}}}{d \,x^{4}+c}\, dx"," ",0,"int((b*x^4+a)^(5/4)/(d*x^4+c),x)","F"
201,0,0,130,0.569000," ","int((b*x^4+a)^(1/4)/(d*x^4+c),x)","\int \frac{\left(b \,x^{4}+a \right)^{\frac{1}{4}}}{d \,x^{4}+c}\, dx"," ",0,"int((b*x^4+a)^(1/4)/(d*x^4+c),x)","F"
202,0,0,246,0.550000," ","int(1/(b*x^4+a)^(3/4)/(d*x^4+c),x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{3}{4}} \left(d \,x^{4}+c \right)}\, dx"," ",0,"int(1/(b*x^4+a)^(3/4)/(d*x^4+c),x)","F"
203,0,0,285,0.592000," ","int(1/(b*x^4+a)^(7/4)/(d*x^4+c),x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{7}{4}} \left(d \,x^{4}+c \right)}\, dx"," ",0,"int(1/(b*x^4+a)^(7/4)/(d*x^4+c),x)","F"
204,0,0,334,0.624000," ","int(1/(b*x^4+a)^(11/4)/(d*x^4+c),x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{11}{4}} \left(d \,x^{4}+c \right)}\, dx"," ",0,"int(1/(b*x^4+a)^(11/4)/(d*x^4+c),x)","F"
205,0,0,232,0.430000," ","int((b*x^4+a)^(11/4)/(d*x^4+c)^2,x)","\int \frac{\left(b \,x^{4}+a \right)^{\frac{11}{4}}}{\left(d \,x^{4}+c \right)^{2}}\, dx"," ",0,"int((b*x^4+a)^(11/4)/(d*x^4+c)^2,x)","F"
206,0,0,186,0.646000," ","int((b*x^4+a)^(7/4)/(d*x^4+c)^2,x)","\int \frac{\left(b \,x^{4}+a \right)^{\frac{7}{4}}}{\left(d \,x^{4}+c \right)^{2}}\, dx"," ",0,"int((b*x^4+a)^(7/4)/(d*x^4+c)^2,x)","F"
207,0,0,107,0.608000," ","int((b*x^4+a)^(3/4)/(d*x^4+c)^2,x)","\int \frac{\left(b \,x^{4}+a \right)^{\frac{3}{4}}}{\left(d \,x^{4}+c \right)^{2}}\, dx"," ",0,"int((b*x^4+a)^(3/4)/(d*x^4+c)^2,x)","F"
208,0,0,134,0.595000," ","int(1/(b*x^4+a)^(1/4)/(d*x^4+c)^2,x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{1}{4}} \left(d \,x^{4}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^4+a)^(1/4)/(d*x^4+c)^2,x)","F"
209,0,0,173,0.596000," ","int(1/(b*x^4+a)^(5/4)/(d*x^4+c)^2,x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{5}{4}} \left(d \,x^{4}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^4+a)^(5/4)/(d*x^4+c)^2,x)","F"
210,0,0,230,0.609000," ","int(1/(b*x^4+a)^(9/4)/(d*x^4+c)^2,x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{9}{4}} \left(d \,x^{4}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^4+a)^(9/4)/(d*x^4+c)^2,x)","F"
211,0,0,330,0.410000," ","int((b*x^4+a)^(9/4)/(d*x^4+c)^2,x)","\int \frac{\left(b \,x^{4}+a \right)^{\frac{9}{4}}}{\left(d \,x^{4}+c \right)^{2}}\, dx"," ",0,"int((b*x^4+a)^(9/4)/(d*x^4+c)^2,x)","F"
212,0,0,279,0.589000," ","int((b*x^4+a)^(5/4)/(d*x^4+c)^2,x)","\int \frac{\left(b \,x^{4}+a \right)^{\frac{5}{4}}}{\left(d \,x^{4}+c \right)^{2}}\, dx"," ",0,"int((b*x^4+a)^(5/4)/(d*x^4+c)^2,x)","F"
213,0,0,289,0.657000," ","int((b*x^4+a)^(1/4)/(d*x^4+c)^2,x)","\int \frac{\left(b \,x^{4}+a \right)^{\frac{1}{4}}}{\left(d \,x^{4}+c \right)^{2}}\, dx"," ",0,"int((b*x^4+a)^(1/4)/(d*x^4+c)^2,x)","F"
214,0,0,311,0.675000," ","int(1/(b*x^4+a)^(3/4)/(d*x^4+c)^2,x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{3}{4}} \left(d \,x^{4}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^4+a)^(3/4)/(d*x^4+c)^2,x)","F"
215,0,0,367,0.661000," ","int(1/(b*x^4+a)^(7/4)/(d*x^4+c)^2,x)","\int \frac{1}{\left(b \,x^{4}+a \right)^{\frac{7}{4}} \left(d \,x^{4}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^4+a)^(7/4)/(d*x^4+c)^2,x)","F"
216,1,211,39,3.245000," ","int(1/(x^4+1)^(1/4)/(x^4+2),x)","-\frac{\RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \ln \left(-\frac{-3 x^{4} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)-2 \left(x^{4}+1\right)^{\frac{1}{4}} x^{3} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+2 \sqrt{x^{4}+1}\, x^{2} \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right) \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+4 \left(x^{4}+1\right)^{\frac{3}{4}} x -2 \RootOf \left(\textit{\_Z}^{2}+\RootOf \left(\textit{\_Z}^{4}-2\right)^{2}\right)}{x^{4}+2}\right)}{8}+\frac{\RootOf \left(\textit{\_Z}^{4}-2\right) \ln \left(\frac{3 x^{4} \RootOf \left(\textit{\_Z}^{4}-2\right)+2 \left(x^{4}+1\right)^{\frac{1}{4}} x^{3} \RootOf \left(\textit{\_Z}^{4}-2\right)^{2}+2 \sqrt{x^{4}+1}\, x^{2} \RootOf \left(\textit{\_Z}^{4}-2\right)^{3}+4 \left(x^{4}+1\right)^{\frac{3}{4}} x +2 \RootOf \left(\textit{\_Z}^{4}-2\right)}{x^{4}+2}\right)}{8}"," ",0,"-1/8*RootOf(_Z^2+RootOf(_Z^4-2)^2)*ln(-(2*(x^4+1)^(1/2)*RootOf(_Z^4-2)^2*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^2-2*(x^4+1)^(1/4)*RootOf(_Z^4-2)^2*x^3-3*RootOf(_Z^2+RootOf(_Z^4-2)^2)*x^4+4*(x^4+1)^(3/4)*x-2*RootOf(_Z^2+RootOf(_Z^4-2)^2))/(x^4+2))+1/8*RootOf(_Z^4-2)*ln((2*(x^4+1)^(1/2)*RootOf(_Z^4-2)^3*x^2+2*(x^4+1)^(1/4)*RootOf(_Z^4-2)^2*x^3+3*RootOf(_Z^4-2)*x^4+4*(x^4+1)^(3/4)*x+2*RootOf(_Z^4-2))/(x^4+2))","C"
217,0,0,41,0.619000," ","int(1/(a-(a-b)*x^4)/(b*x^4+a)^(1/4),x)","\int \frac{1}{\left(-\left(a -b \right) x^{4}+a \right) \left(b \,x^{4}+a \right)^{\frac{1}{4}}}\, dx"," ",0,"int(1/(a-(a-b)*x^4)/(b*x^4+a)^(1/4),x)","F"
218,0,0,75,0.553000," ","int((b*x^4+a)^p*(d*x^4+c)^q,x)","\int \left(b \,x^{4}+a \right)^{p} \left(d \,x^{4}+c \right)^{q}\, dx"," ",0,"int((b*x^4+a)^p*(d*x^4+c)^q,x)","F"
219,0,0,170,0.532000," ","int((b*x^4+a)^2*(d*x^4+c)^q,x)","\int \left(b \,x^{4}+a \right)^{2} \left(d \,x^{4}+c \right)^{q}\, dx"," ",0,"int((b*x^4+a)^2*(d*x^4+c)^q,x)","F"
220,0,0,91,0.376000," ","int((b*x^4+a)*(d*x^4+c)^q,x)","\int \left(b \,x^{4}+a \right) \left(d \,x^{4}+c \right)^{q}\, dx"," ",0,"int((b*x^4+a)*(d*x^4+c)^q,x)","F"
221,0,0,53,0.560000," ","int((d*x^4+c)^q/(b*x^4+a),x)","\int \frac{\left(d \,x^{4}+c \right)^{q}}{b \,x^{4}+a}\, dx"," ",0,"int((d*x^4+c)^q/(b*x^4+a),x)","F"
222,0,0,53,0.565000," ","int((d*x^4+c)^q/(b*x^4+a)^2,x)","\int \frac{\left(d \,x^{4}+c \right)^{q}}{\left(b \,x^{4}+a \right)^{2}}\, dx"," ",0,"int((d*x^4+c)^q/(b*x^4+a)^2,x)","F"
223,0,0,413,0.566000," ","int(1/(b*x^5+a)^(1/5)/(d*x^5+c),x)","\int \frac{1}{\left(b \,x^{5}+a \right)^{\frac{1}{5}} \left(d \,x^{5}+c \right)}\, dx"," ",0,"int(1/(b*x^5+a)^(1/5)/(d*x^5+c),x)","F"
224,1,248,124,0.063000," ","int((c+d/x)^3*(a+b/x)^(1/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(90 a \,b^{2} c^{2} d \,x^{4} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+15 b^{3} c^{3} x^{4} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+180 \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} b \,c^{2} d \,x^{4}+30 \sqrt{a \,x^{2}+b x}\, \sqrt{a}\, b^{2} c^{3} x^{4}-180 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b \,c^{2} d \,x^{2}+8 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} d^{3} x -60 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b c \,d^{2} x -12 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b \,d^{3}\right)}{30 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{2} x^{3}}"," ",0,"1/30*((a*x+b)/x)^(1/2)*(180*(a*x^2+b*x)^(1/2)*a^(3/2)*x^4*b*c^2*d+30*(a*x^2+b*x)^(1/2)*a^(1/2)*x^4*b^2*c^3+90*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^4*a*b^2*c^2*d+15*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^4*b^3*c^3+8*(a*x^2+b*x)^(3/2)*a^(3/2)*x*d^3-180*(a*x^2+b*x)^(3/2)*a^(1/2)*x^2*b*c^2*d-60*d^2*c*(a*x^2+b*x)^(3/2)*x*b*a^(1/2)-12*(a*x^2+b*x)^(3/2)*a^(1/2)*b*d^3)/x^3/((a*x+b)*x)^(1/2)/b^2/a^(1/2)","A"
225,1,191,85,0.059000," ","int((c+d/x)^2*(a+b/x)^(1/2),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(-12 a b c d \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 b^{2} c^{2} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-24 \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} c d \,x^{3}-6 \sqrt{a \,x^{2}+b x}\, \sqrt{a}\, b \,c^{2} x^{3}+24 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, c d x +4 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, d^{2}\right)}{6 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b \,x^{2}}"," ",0,"-1/6*((a*x+b)/x)^(1/2)/x^2*(-24*(a*x^2+b*x)^(1/2)*a^(3/2)*x^3*c*d-6*(a*x^2+b*x)^(1/2)*a^(1/2)*x^3*b*c^2-12*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a*b*c*d-3*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*b^2*c^2+24*(a*x^2+b*x)^(3/2)*a^(1/2)*x*c*d+4*d^2*(a*x^2+b*x)^(3/2)*a^(1/2))/((a*x+b)*x)^(1/2)/b/a^(1/2)","B"
226,1,163,64,0.057000," ","int((c+d/x)*(a+b/x)^(1/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(2 a b d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+b^{2} c \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} d \,x^{2}+2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}\, b c \,x^{2}-4 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, d \right)}{2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b x}"," ",0,"1/2*((a*x+b)/x)^(1/2)*(4*a^(3/2)*(a*x^2+b*x)^(1/2)*x^2*d+2*a^(1/2)*(a*x^2+b*x)^(1/2)*x^2*b*c+2*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a*b*d+ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*b^2*c-4*a^(1/2)*(a*x^2+b*x)^(3/2)*d)/x/((a*x+b)*x)^(1/2)/b/a^(1/2)","B"
227,1,74,31,0.049000," ","int((a+b/x)^(1/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(b \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}\right) x}{2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}"," ",0,"1/2*((a*x+b)/x)^(1/2)*x*(2*(a*x^2+b*x)^(1/2)*a^(1/2)+b*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2)))/((a*x+b)*x)^(1/2)/a^(1/2)","B"
228,1,287,86,0.108000," ","int((a+b/x)^(1/2)/(c+d/x),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(2 a^{\frac{3}{2}} d^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-2 \sqrt{a}\, b c d \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a c d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, b \,c^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a}\, c^{2}\right) x}{2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a}\, c^{3}}"," ",0,"-1/2*((a*x+b)/x)^(1/2)*x*(2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*(d*(a*d-b*c)/c^2)^(1/2)*a*c*d-ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*(d*(a*d-b*c)/c^2)^(1/2)*b*c^2+2*ln((2*(d*(a*d-b*c)/c^2)^(1/2)*((a*x+b)*x)^(1/2)*c-2*a*d*x+b*c*x-b*d)/(c*x+d))*a^(3/2)*d^2-2*ln((2*(d*(a*d-b*c)/c^2)^(1/2)*((a*x+b)*x)^(1/2)*c-2*a*d*x+b*c*x-b*d)/(c*x+d))*a^(1/2)*b*c*d-2*((a*x+b)*x)^(1/2)*c^2*a^(1/2)*(d*(a*d-b*c)/c^2)^(1/2))/((a*x+b)*x)^(1/2)/c^3/a^(1/2)/(d*(a*d-b*c)/c^2)^(1/2)","B"
229,1,943,127,0.066000," ","int((a+b/x)^(1/2)/(c+d/x)^2,x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(4 a^{\frac{7}{2}} c \,d^{3} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-7 a^{\frac{5}{2}} b \,c^{2} d^{2} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+3 a^{\frac{3}{2}} b^{2} c^{3} d x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} c^{2} d^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-5 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b \,c^{3} d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{2} c^{4} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 a^{\frac{7}{2}} d^{4} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-7 a^{\frac{5}{2}} b c \,d^{3} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{4} x^{2}+3 a^{\frac{3}{2}} b^{2} c^{2} d^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} c \,d^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-5 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b \,c^{2} d^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{2} c^{3} d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{3} d x +4 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b \,c^{4} x -4 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{2} d^{2}+4 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b \,c^{3} d -2 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} c^{4}\right) x}{2 \sqrt{\left(a x +b \right) x}\, \left(a d -b c \right) \left(c x +d \right) \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} c^{4}}"," ",0,"-1/2*((a*x+b)/x)^(1/2)*x*(4*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*c*d^3+2*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*c^4+4*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*d^4-2*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*c^3*d-7*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b*c^2*d^2-4*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*c^2*d^2-7*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b*c*d^3-2*c^4*((a*x+b)*x)^(3/2)*a^(3/2)*((a*d-b*c)/c^2*d)^(1/2)+4*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^4+3*a^(3/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^2*c^3*d+4*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b*c^3*d+3*a^(3/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^2*c^2*d^2+4*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*c^2*d^2-5*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^3*d+a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^4+4*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*c*d^3-5*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b*c^2*d^2+a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^2*c^3*d)/c^4/((a*x+b)*x)^(1/2)/(a*d-b*c)/(c*x+d)/a^(3/2)/((a*d-b*c)/c^2*d)^(1/2)","B"
230,1,1972,185,0.068000," ","int((a+b/x)^(1/2)/(c+d/x)^3,x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(24 a^{\frac{9}{2}} c^{2} d^{4} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-64 a^{\frac{7}{2}} b \,c^{3} d^{3} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+55 a^{\frac{5}{2}} b^{2} c^{4} d^{2} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-15 a^{\frac{3}{2}} b^{3} c^{5} d \,x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c^{3} d^{3} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-52 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{4} d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+32 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{2} c^{5} d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{3} c^{6} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+48 a^{\frac{9}{2}} c \,d^{5} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-128 a^{\frac{7}{2}} b \,c^{2} d^{4} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+12 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{5} d \,x^{3}+110 a^{\frac{5}{2}} b^{2} c^{3} d^{3} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-14 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{6} x^{3}-30 a^{\frac{3}{2}} b^{3} c^{4} d^{2} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+48 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c^{2} d^{4} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-104 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{3} d^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+64 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{2} c^{4} d^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-8 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{3} c^{5} d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+24 a^{\frac{9}{2}} d^{6} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-64 a^{\frac{7}{2}} b c \,d^{5} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+55 a^{\frac{5}{2}} b^{2} c^{2} d^{4} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+18 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{5} d \,x^{2}-15 a^{\frac{3}{2}} b^{3} c^{3} d^{3} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-22 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{2} c^{6} x^{2}+24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c \,d^{5} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-52 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{2} d^{4} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+32 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{2} c^{3} d^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{3} c^{4} d^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-36 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{3} d^{3} x +78 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{4} d^{2} x -44 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{2} c^{5} d x -24 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{2} d^{4}+46 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{3} d^{3}-12 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{5} d x -22 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{2} c^{4} d^{2}+14 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b \,c^{6} x -8 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{4} d^{2}+10 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b \,c^{5} d \right) x}{8 \sqrt{\left(a x +b \right) x}\, \left(a d -b c \right)^{2} \left(c x +d \right)^{2} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} c^{5}}"," ",0,"-1/8*((a*x+b)/x)^(1/2)*x*(55*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b^2*c^4*d^2+24*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*c^3*d^3-36*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*c^3*d^3-128*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b*c^2*d^4+110*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^2*c^3*d^3+48*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*c^2*d^4+46*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b*c^3*d^3-52*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b*c^2*d^4+32*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^2*c^3*d^3-22*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^2*c^4*d^2-4*a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^3*c^4*d^2+14*a^(3/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^6-22*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^2*c^6-15*a^(3/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b^3*c^5*d-4*a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^3*c^6+10*a^(3/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*b*c^5*d+12*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*c^5*d-14*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b*c^6-12*a^(5/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*c^5*d-64*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b*c^3*d^3-30*a^(3/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^3*c^4*d^2+24*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*d^6+64*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^4*d^2+78*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^4*d^2-104*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^3*d^3+18*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b*c^5*d-52*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b*c^4*d^2+32*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^2*c^5*d-44*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^5*d-8*a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^3*c^5*d+48*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*c*d^5-24*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*c^2*d^4-64*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b*c*d^5+55*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^2*c^2*d^4+24*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*c*d^5+24*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*c^2*d^4-8*a^(5/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*c^4*d^2-15*a^(3/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^3*c^3*d^3)/c^5/((a*x+b)*x)^(1/2)/(a*d-b*c)^2/(c*x+d)^2/a^(3/2)/((a*d-b*c)/c^2*d)^(1/2)","B"
231,1,353,146,0.060000," ","int((a+b/x)^(3/2)*(c+d/x)^3,x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(210 a^{2} b^{2} c^{2} d \,x^{5} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+105 a \,b^{3} c^{3} x^{5} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+420 \sqrt{a \,x^{2}+b x}\, a^{\frac{5}{2}} b \,c^{2} d \,x^{5}+210 \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} b^{2} c^{3} x^{5}-420 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b \,c^{2} d \,x^{3}-140 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{2} c^{3} x^{3}+8 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{5}{2}} d^{3} x^{2}-84 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b c \,d^{2} x^{2}-140 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{2} c^{2} d \,x^{2}-12 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b \,d^{3} x -84 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{2} c \,d^{2} x -20 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{2} d^{3}\right)}{70 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{2} x^{4}}"," ",0,"1/70*((a*x+b)/x)^(1/2)*(420*(a*x^2+b*x)^(1/2)*a^(5/2)*x^5*b*c^2*d+210*(a*x^2+b*x)^(1/2)*a^(3/2)*x^5*b^2*c^3+8*(a*x^2+b*x)^(3/2)*a^(5/2)*x^2*d^3-420*(a*x^2+b*x)^(3/2)*a^(3/2)*x^3*b*c^2*d+210*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^5*a^2*b^2*c^2*d+105*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^5*a*b^3*c^3-84*(a*x^2+b*x)^(3/2)*a^(3/2)*x^2*b*c*d^2-140*(a*x^2+b*x)^(3/2)*a^(1/2)*x^3*b^2*c^3-12*(a*x^2+b*x)^(3/2)*a^(3/2)*x*b*d^3-140*(a*x^2+b*x)^(3/2)*a^(1/2)*x^2*b^2*c^2*d-84*(a*x^2+b*x)^(3/2)*a^(1/2)*x*b^2*c*d^2-20*(a*x^2+b*x)^(3/2)*a^(1/2)*b^2*d^3)/x^4/b^2/((a*x+b)*x)^(1/2)/a^(1/2)","B"
232,1,260,108,0.060000," ","int((a+b/x)^(3/2)*(c+d/x)^2,x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(-60 a^{2} b c d \,x^{4} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-45 a \,b^{2} c^{2} x^{4} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-120 \sqrt{a \,x^{2}+b x}\, a^{\frac{5}{2}} c d \,x^{4}-90 \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} b \,c^{2} x^{4}+120 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} c d \,x^{2}+60 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b \,c^{2} x^{2}+12 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} d^{2} x +40 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b c d x +12 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b \,d^{2}\right)}{30 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b \,x^{3}}"," ",0,"-1/30*((a*x+b)/x)^(1/2)/x^3/b*(-120*(a*x^2+b*x)^(1/2)*a^(5/2)*x^4*c*d-90*(a*x^2+b*x)^(1/2)*a^(3/2)*x^4*b*c^2-60*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^4*a^2*b*c*d-45*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^4*a*b^2*c^2+120*(a*x^2+b*x)^(3/2)*a^(3/2)*x^2*c*d+60*(a*x^2+b*x)^(3/2)*a^(1/2)*x^2*b*c^2+12*(a*x^2+b*x)^(3/2)*a^(3/2)*x*d^2+40*(a*x^2+b*x)^(3/2)*a^(1/2)*x*b*c*d+12*(a*x^2+b*x)^(3/2)*a^(1/2)*b*d^2)/((a*x+b)*x)^(1/2)/a^(1/2)","B"
233,1,205,86,0.057000," ","int((a+b/x)^(3/2)*(c+d/x),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(6 a^{2} b d \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+9 a \,b^{2} c \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+12 \sqrt{a \,x^{2}+b x}\, a^{\frac{5}{2}} d \,x^{3}+18 \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} b c \,x^{3}-12 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} d x -12 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b c x -4 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b d \right)}{6 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b \,x^{2}}"," ",0,"1/6*((a*x+b)/x)^(1/2)*(12*a^(5/2)*(a*x^2+b*x)^(1/2)*x^3*d+18*a^(3/2)*(a*x^2+b*x)^(1/2)*x^3*b*c-12*a^(3/2)*(a*x^2+b*x)^(3/2)*x*d+6*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^2*b*d+9*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a*b^2*c-12*a^(1/2)*(a*x^2+b*x)^(3/2)*x*b*c-4*d*(a*x^2+b*x)^(3/2)*b*a^(1/2))/x^2/((a*x+b)*x)^(1/2)/b/a^(1/2)","B"
234,1,100,44,0.052000," ","int((a+b/x)^(3/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(3 a b \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+6 \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} x^{2}-4 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\right)}{2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, x}"," ",0,"1/2*((a*x+b)/x)^(1/2)*(6*a^(3/2)*(a*x^2+b*x)^(1/2)*x^2+3*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a*b-4*(a*x^2+b*x)^(3/2)*a^(1/2))/x/((a*x+b)*x)^(1/2)/a^(1/2)","B"
235,1,528,88,0.061000," ","int((a+b/x)^(3/2)/(c+d/x),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(2 a^{\frac{5}{2}} d^{3} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-4 a^{\frac{3}{2}} b c \,d^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{a}\, b^{2} c^{2} d \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} c \,d^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a b \,c^{2} d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, b^{2} c^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, b^{2} c^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} c^{2} d +2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a}\, b \,c^{3}-2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a \,x^{2}+b x}\, \sqrt{a}\, b \,c^{3}\right) x}{2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a}\, c^{3} d}"," ",0,"-1/2*((a*x+b)/x)^(1/2)*x*(2*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*d^3-2*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*c^2*d-4*a^(3/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b*c*d^2+2*a^(1/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b*c^3-2*a^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*(a*x^2+b*x)^(1/2)*b*c^3+2*a^(1/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^2*c^2*d+2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*a^2*c*d^2-3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*a*b*c^2*d+ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^2*c^3-((a*d-b*c)/c^2*d)^(1/2)*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*b^2*c^3)/((a*x+b)*x)^(1/2)/d/c^3/a^(1/2)/((a*d-b*c)/c^2*d)^(1/2)","B"
236,1,834,136,0.062000," ","int((a+b/x)^(3/2)/(c+d/x)^2,x)","-\frac{\left(4 a^{\frac{7}{2}} c \,d^{3} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-5 a^{\frac{5}{2}} b \,c^{2} d^{2} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+a^{\frac{3}{2}} b^{2} c^{3} d x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} c^{2} d^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b \,c^{3} d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 a^{\frac{7}{2}} d^{4} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-5 a^{\frac{5}{2}} b c \,d^{3} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{4} x^{2}+a^{\frac{3}{2}} b^{2} c^{2} d^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} c \,d^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b \,c^{2} d^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{3} d x +2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b \,c^{4} x -4 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{2} d^{2}+2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b \,c^{3} d -2 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} c^{4}\right) \sqrt{\frac{a x +b}{x}}\, x}{2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \left(c x +d \right) \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} c^{4} d}"," ",0,"-1/2*(4*a^(7/2)*c*d^3*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+2*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*c^4*x^2+4*a^(7/2)*d^4*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-2*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*c^3*d*x-5*a^(5/2)*b*c^2*d^2*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-4*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*c^2*d^2-5*a^(5/2)*b*c*d^3*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-2*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*c^4+2*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b*c^4*x+a^(3/2)*b^2*c^3*d*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+2*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b*c^3*d+a^(3/2)*b^2*c^2*d^2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+4*((a*d-b*c)/c^2*d)^(1/2)*a^3*c^2*d^2*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))-3*((a*d-b*c)/c^2*d)^(1/2)*a^2*b*c^3*d*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+4*((a*d-b*c)/c^2*d)^(1/2)*a^3*c*d^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))-3*((a*d-b*c)/c^2*d)^(1/2)*a^2*b*c^2*d^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2)))*x*((a*x+b)/x)^(1/2)/c^4/((a*d-b*c)/c^2*d)^(1/2)/a^(3/2)/(c*x+d)/d/((a*x+b)*x)^(1/2)","B"
237,1,1817,181,0.067000," ","int((a+b/x)^(3/2)/(c+d/x)^3,x)","-\frac{\left(24 a^{\frac{9}{2}} c^{2} d^{4} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-48 a^{\frac{7}{2}} b \,c^{3} d^{3} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+27 a^{\frac{5}{2}} b^{2} c^{4} d^{2} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-3 a^{\frac{3}{2}} b^{3} c^{5} d \,x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c^{3} d^{3} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-36 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{4} d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+12 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{2} c^{5} d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+48 a^{\frac{9}{2}} c \,d^{5} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-96 a^{\frac{7}{2}} b \,c^{2} d^{4} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+12 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{5} d \,x^{3}+54 a^{\frac{5}{2}} b^{2} c^{3} d^{3} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-6 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{6} x^{3}-6 a^{\frac{3}{2}} b^{3} c^{4} d^{2} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+48 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c^{2} d^{4} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-72 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{3} d^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{2} c^{4} d^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+24 a^{\frac{9}{2}} d^{6} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-48 a^{\frac{7}{2}} b c \,d^{5} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+27 a^{\frac{5}{2}} b^{2} c^{2} d^{4} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+18 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{5} d \,x^{2}-3 a^{\frac{3}{2}} b^{3} c^{3} d^{3} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-6 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{2} c^{6} x^{2}+24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c \,d^{5} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-36 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{2} d^{4} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+12 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{2} c^{3} d^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-36 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{3} d^{3} x +54 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{4} d^{2} x -12 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{2} c^{5} d x -24 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{2} d^{4}+30 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{3} d^{3}-12 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{5} d x -6 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{2} c^{4} d^{2}+6 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b \,c^{6} x -8 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{4} d^{2}+2 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b \,c^{5} d \right) \sqrt{\frac{a x +b}{x}}\, x}{8 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \left(c x +d \right)^{2} \left(a d -b c \right) \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} c^{5} d}"," ",0,"-1/8*(27*a^(5/2)*b^2*c^4*d^2*x^2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+24*((a*d-b*c)/c^2*d)^(1/2)*a^4*c^3*d^3*x^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))-36*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(7/2)*c^3*d^3*x-96*a^(7/2)*b*c^2*d^4*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+54*a^(5/2)*b^2*c^3*d^3*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+48*((a*d-b*c)/c^2*d)^(1/2)*a^4*c^2*d^4*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+30*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*b*c^3*d^3-36*((a*d-b*c)/c^2*d)^(1/2)*a^3*b*c^2*d^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+12*((a*d-b*c)/c^2*d)^(1/2)*a^2*b^2*c^3*d^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))-6*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b^2*c^4*d^2+6*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b*c^6*x-6*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b^2*c^6*x^2-3*a^(3/2)*b^3*c^5*d*x^2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+2*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b*c^5*d+12*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(7/2)*c^5*d*x^3-6*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*b*c^6*x^3-12*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*c^5*d*x-48*a^(7/2)*b*c^3*d^3*x^2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-6*a^(3/2)*b^3*c^4*d^2*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+24*a^(9/2)*d^6*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+24*((a*d-b*c)/c^2*d)^(1/2)*a^2*b^2*c^4*d^2*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+54*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*b*c^4*d^2*x-72*((a*d-b*c)/c^2*d)^(1/2)*a^3*b*c^3*d^3*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+18*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*b*c^5*d*x^2-36*((a*d-b*c)/c^2*d)^(1/2)*a^3*b*c^4*d^2*x^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+12*((a*d-b*c)/c^2*d)^(1/2)*a^2*b^2*c^5*d*x^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))-12*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b^2*c^5*d*x+48*a^(9/2)*c*d^5*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-24*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(7/2)*c^2*d^4-48*a^(7/2)*b*c*d^5*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+27*a^(5/2)*b^2*c^2*d^4*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+24*((a*d-b*c)/c^2*d)^(1/2)*a^4*c*d^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+24*a^(9/2)*c^2*d^4*x^2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-8*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*c^4*d^2-3*a^(3/2)*b^3*c^3*d^3*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d)))*x*((a*x+b)/x)^(1/2)/c^5/d/((a*d-b*c)/c^2*d)^(1/2)/a^(3/2)/(c*x+d)^2/(a*d-b*c)/((a*x+b)*x)^(1/2)","B"
238,1,457,173,0.067000," ","int((a+b/x)^(5/2)*(c+d/x)^3,x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(1890 a^{3} b^{2} c^{2} d \,x^{6} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+1575 a^{2} b^{3} c^{3} x^{6} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+3780 \sqrt{a \,x^{2}+b x}\, a^{\frac{7}{2}} b \,c^{2} d \,x^{6}+3150 \sqrt{a \,x^{2}+b x}\, a^{\frac{5}{2}} b^{2} c^{3} x^{6}-3780 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b \,c^{2} d \,x^{4}-2520 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{2} c^{3} x^{4}+40 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{7}{2}} d^{3} x^{3}-540 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b c \,d^{2} x^{3}-2016 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{2} c^{2} d \,x^{3}-420 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{3} c^{3} x^{3}-60 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b \,d^{3} x^{2}-1080 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{2} c \,d^{2} x^{2}-756 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{3} c^{2} d \,x^{2}-240 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{2} d^{3} x -540 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{3} c \,d^{2} x -140 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{3} d^{3}\right)}{630 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{2} x^{5}}"," ",0,"1/630*((a*x+b)/x)^(1/2)*(3780*(a*x^2+b*x)^(1/2)*a^(7/2)*x^6*b*c^2*d+3150*(a*x^2+b*x)^(1/2)*a^(5/2)*x^6*b^2*c^3+40*(a*x^2+b*x)^(3/2)*a^(7/2)*x^3*d^3-3780*(a*x^2+b*x)^(3/2)*a^(5/2)*x^4*b*c^2*d-540*(a*x^2+b*x)^(3/2)*a^(5/2)*x^3*b*c*d^2-2520*(a*x^2+b*x)^(3/2)*a^(3/2)*x^4*b^2*c^3+1890*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^6*a^3*b^2*c^2*d+1575*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^6*a^2*b^3*c^3-60*(a*x^2+b*x)^(3/2)*a^(5/2)*x^2*b*d^3-2016*(a*x^2+b*x)^(3/2)*a^(3/2)*x^3*b^2*c^2*d-1080*(a*x^2+b*x)^(3/2)*a^(3/2)*x^2*b^2*c*d^2-420*(a*x^2+b*x)^(3/2)*a^(1/2)*x^3*b^3*c^3-240*(a*x^2+b*x)^(3/2)*a^(3/2)*x*b^2*d^3-756*(a*x^2+b*x)^(3/2)*a^(1/2)*x^2*b^3*c^2*d-540*(a*x^2+b*x)^(3/2)*a^(1/2)*x*b^3*c*d^2-140*(a*x^2+b*x)^(3/2)*a^(1/2)*b^3*d^3)/x^5/b^2/((a*x+b)*x)^(1/2)/a^(1/2)","B"
239,1,336,130,0.060000," ","int((a+b/x)^(5/2)*(c+d/x)^2,x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(-420 a^{3} b c d \,x^{5} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-525 a^{2} b^{2} c^{2} x^{5} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-840 \sqrt{a \,x^{2}+b x}\, a^{\frac{7}{2}} c d \,x^{5}-1050 \sqrt{a \,x^{2}+b x}\, a^{\frac{5}{2}} b \,c^{2} x^{5}+840 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{5}{2}} c d \,x^{3}+840 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b \,c^{2} x^{3}+60 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{5}{2}} d^{2} x^{2}+448 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b c d \,x^{2}+140 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{2} c^{2} x^{2}+120 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b \,d^{2} x +168 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{2} c d x +60 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{2} d^{2}\right)}{210 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b \,x^{4}}"," ",0,"-1/210*((a*x+b)/x)^(1/2)/x^4/b*(-840*(a*x^2+b*x)^(1/2)*a^(7/2)*x^5*c*d-1050*(a*x^2+b*x)^(1/2)*a^(5/2)*x^5*b*c^2-420*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^5*a^3*b*c*d-525*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^5*a^2*b^2*c^2+840*(a*x^2+b*x)^(3/2)*a^(5/2)*x^3*c*d+840*(a*x^2+b*x)^(3/2)*a^(3/2)*x^3*b*c^2+60*(a*x^2+b*x)^(3/2)*a^(5/2)*x^2*d^2+448*(a*x^2+b*x)^(3/2)*a^(3/2)*x^2*b*c*d+140*(a*x^2+b*x)^(3/2)*a^(1/2)*x^2*b^2*c^2+120*(a*x^2+b*x)^(3/2)*a^(3/2)*x*b*d^2+168*(a*x^2+b*x)^(3/2)*a^(1/2)*x*b^2*c*d+60*(a*x^2+b*x)^(3/2)*a^(1/2)*b^2*d^2)/((a*x+b)*x)^(1/2)/a^(1/2)","B"
240,1,253,107,0.060000," ","int((a+b/x)^(5/2)*(c+d/x),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(-30 a^{3} b d \,x^{4} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-75 a^{2} b^{2} c \,x^{4} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-60 \sqrt{a \,x^{2}+b x}\, a^{\frac{7}{2}} d \,x^{4}-150 \sqrt{a \,x^{2}+b x}\, a^{\frac{5}{2}} b c \,x^{4}+60 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{5}{2}} d \,x^{2}+120 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b c \,x^{2}+32 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b d x +20 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{2} c x +12 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b^{2} d \right)}{30 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b \,x^{3}}"," ",0,"-1/30*((a*x+b)/x)^(1/2)/x^3/b*(-60*(a*x^2+b*x)^(1/2)*a^(7/2)*x^4*d-150*(a*x^2+b*x)^(1/2)*a^(5/2)*x^4*b*c-30*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^4*a^3*b*d-75*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^4*a^2*b^2*c+60*(a*x^2+b*x)^(3/2)*a^(5/2)*x^2*d+120*(a*x^2+b*x)^(3/2)*a^(3/2)*x^2*b*c+32*(a*x^2+b*x)^(3/2)*a^(3/2)*x*b*d+20*(a*x^2+b*x)^(3/2)*a^(1/2)*x*b^2*c+12*(a*x^2+b*x)^(3/2)*a^(1/2)*b^2*d)/((a*x+b)*x)^(1/2)/a^(1/2)","B"
241,1,120,57,0.058000," ","int((a+b/x)^(5/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(15 a^{2} b \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+30 \sqrt{a \,x^{2}+b x}\, a^{\frac{5}{2}} x^{3}-24 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} x -4 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b \right)}{6 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, x^{2}}"," ",0,"1/6*((a*x+b)/x)^(1/2)*(30*a^(5/2)*(a*x^2+b*x)^(1/2)*x^3-24*a^(3/2)*(a*x^2+b*x)^(3/2)*x+15*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^2*b-4*b*(a*x^2+b*x)^(3/2)*a^(1/2))/x^2/((a*x+b)*x)^(1/2)/a^(1/2)","B"
242,1,859,114,0.056000," ","int((a+b/x)^(5/2)/(c+d/x),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(2 a^{\frac{7}{2}} d^{4} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-6 a^{\frac{5}{2}} b c \,d^{3} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+6 a^{\frac{3}{2}} b^{2} c^{2} d^{2} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-2 \sqrt{a}\, b^{3} c^{3} d \,x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} c \,d^{3} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-5 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b \,c^{2} d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{2} c^{3} d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{2} c^{3} d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, b^{3} c^{4} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, b^{3} c^{4} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} c^{2} d^{2} x^{2}-8 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} b \,c^{3} d \,x^{2}+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b \,c^{3} d \,x^{2}+2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a \,x^{2}+b x}\, \sqrt{a}\, b^{2} c^{4} x^{2}-2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{2} c^{4} x^{2}+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \left(a \,x^{2}+b x \right)^{\frac{3}{2}} \sqrt{a}\, b \,c^{3} d \right)}{2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a}\, c^{3} d^{2} x}"," ",0,"-1/2*((a*x+b)/x)^(1/2)/x*(2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*a^3*c*d^3-5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*a^2*b*c^2*d^2+4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*a*b^2*c^3*d-ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^3*c^4-8*((a*d-b*c)/c^2*d)^(1/2)*(a*x^2+b*x)^(1/2)*a^(3/2)*x^2*b*c^3*d+2*((a*d-b*c)/c^2*d)^(1/2)*(a*x^2+b*x)^(1/2)*a^(1/2)*x^2*b^2*c^4-4*((a*d-b*c)/c^2*d)^(1/2)*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a*b^2*c^3*d+((a*d-b*c)/c^2*d)^(1/2)*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*b^3*c^4-2*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*((a*x+b)*x)^(1/2)*x^2*c^2*d^2+4*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*((a*x+b)*x)^(1/2)*x^2*b*c^3*d-2*((a*d-b*c)/c^2*d)^(1/2)*a^(1/2)*((a*x+b)*x)^(1/2)*x^2*b^2*c^4+2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*a^(7/2)*x^2*d^4-6*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*a^(5/2)*x^2*b*c*d^3+6*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*a^(3/2)*x^2*b^2*c^2*d^2-2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*a^(1/2)*x^2*b^3*c^3*d+4*((a*d-b*c)/c^2*d)^(1/2)*(a*x^2+b*x)^(3/2)*a^(1/2)*b*c^3*d)/((a*x+b)*x)^(1/2)/d^2/c^3/a^(1/2)/((a*d-b*c)/c^2*d)^(1/2)","B"
243,1,1323,146,0.063000," ","int((a+b/x)^(5/2)/(c+d/x)^2,x)","-\frac{\left(4 a^{\frac{9}{2}} c \,d^{4} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-7 a^{\frac{7}{2}} b \,c^{2} d^{3} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 a^{\frac{5}{2}} b^{2} c^{3} d^{2} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+a^{\frac{3}{2}} b^{3} c^{4} d x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c^{2} d^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-5 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{3} d^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{3} c^{5} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{3} c^{5} x \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 a^{\frac{9}{2}} d^{5} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-7 a^{\frac{7}{2}} b c \,d^{4} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{4} d \,x^{2}+2 a^{\frac{5}{2}} b^{2} c^{2} d^{3} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{5} x^{2}+a^{\frac{3}{2}} b^{3} c^{3} d^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c \,d^{4} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-5 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{2} d^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{3} c^{4} d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{3} c^{4} d \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{3} d^{2} x +2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{4} d x -2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} b^{2} c^{5} x -4 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{2} d^{3}+4 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{3} d^{2}-2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} b^{2} c^{4} d -2 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{4} d +2 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b \,c^{5}\right) \sqrt{\frac{a x +b}{x}}\, x}{2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \left(c x +d \right) \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} c^{4} d^{2}}"," ",0,"-1/2*(2*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^4*d-5*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^3*d^2-5*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b*c^2*d^3+a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^3*c^4*d-a*((a*d-b*c)/c^2*d)^(1/2)*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*b^3*c^4*d-2*a^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*(a*x^2+b*x)^(1/2)*x*b^2*c^5+a^(3/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^3*c^4*d+a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^3*c^5-a*((a*d-b*c)/c^2*d)^(1/2)*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x*b^3*c^5-2*a^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*(a*x^2+b*x)^(1/2)*b^2*c^4*d-2*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b*c^5-2*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*c^3*d^2-7*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b*c^2*d^3+2*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^2*c^3*d^2+4*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*c^2*d^3+4*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b*c^3*d^2+2*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*c^4*d+4*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*d^5-2*a^(5/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*c^4*d+4*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*c*d^4-4*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*c^2*d^3-7*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b*c*d^4+2*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^2*c^2*d^3+4*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*c*d^4+2*a^(3/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*b*c^5+a^(3/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^3*c^3*d^2)*x*((a*x+b)/x)^(1/2)/c^4/((a*d-b*c)/c^2*d)^(1/2)/a^(3/2)/(c*x+d)/d^2/((a*x+b)*x)^(1/2)","B"
244,1,1638,209,0.071000," ","int((a+b/x)^(5/2)/(c+d/x)^3,x)","-\frac{\left(24 a^{\frac{9}{2}} c^{2} d^{4} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-32 a^{\frac{7}{2}} b \,c^{3} d^{3} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+7 a^{\frac{5}{2}} b^{2} c^{4} d^{2} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+a^{\frac{3}{2}} b^{3} c^{5} d \,x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c^{3} d^{3} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-20 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{4} d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+48 a^{\frac{9}{2}} c \,d^{5} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-64 a^{\frac{7}{2}} b \,c^{2} d^{4} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+12 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{5} d \,x^{3}+14 a^{\frac{5}{2}} b^{2} c^{3} d^{3} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{6} x^{3}+2 a^{\frac{3}{2}} b^{3} c^{4} d^{2} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+48 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c^{2} d^{4} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-40 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{3} d^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+24 a^{\frac{9}{2}} d^{6} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-32 a^{\frac{7}{2}} b c \,d^{5} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+7 a^{\frac{5}{2}} b^{2} c^{2} d^{4} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+18 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{5} d \,x^{2}+a^{\frac{3}{2}} b^{3} c^{3} d^{3} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{2} c^{6} x^{2}+24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c \,d^{5} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-20 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{2} d^{4} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-36 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{3} d^{3} x +30 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{4} d^{2} x +4 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{2} c^{5} d x -24 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{2} d^{4}+14 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{3} d^{3}-12 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{5} d x +2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{2} c^{4} d^{2}-2 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b \,c^{6} x -8 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{4} d^{2}-6 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b \,c^{5} d \right) \sqrt{\frac{a x +b}{x}}\, x}{8 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \left(c x +d \right)^{2} \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} c^{5} d^{2}}"," ",0,"-1/8*(7*a^(5/2)*b^2*c^4*d^2*x^2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+24*((a*d-b*c)/c^2*d)^(1/2)*a^4*c^3*d^3*x^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))-36*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(7/2)*c^3*d^3*x-64*a^(7/2)*b*c^2*d^4*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+14*a^(5/2)*b^2*c^3*d^3*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+48*((a*d-b*c)/c^2*d)^(1/2)*a^4*c^2*d^4*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+14*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*b*c^3*d^3-20*((a*d-b*c)/c^2*d)^(1/2)*a^3*b*c^2*d^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+2*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b^2*c^4*d^2-2*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b*c^6*x+2*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b^2*c^6*x^2+a^(3/2)*b^3*c^5*d*x^2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-6*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b*c^5*d+12*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(7/2)*c^5*d*x^3+2*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*b*c^6*x^3-12*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*c^5*d*x-32*a^(7/2)*b*c^3*d^3*x^2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+2*a^(3/2)*b^3*c^4*d^2*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+24*a^(9/2)*d^6*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+30*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*b*c^4*d^2*x-40*((a*d-b*c)/c^2*d)^(1/2)*a^3*b*c^3*d^3*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+18*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*b*c^5*d*x^2-20*((a*d-b*c)/c^2*d)^(1/2)*a^3*b*c^4*d^2*x^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+4*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(3/2)*b^2*c^5*d*x+48*a^(9/2)*c*d^5*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-24*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(7/2)*c^2*d^4-32*a^(7/2)*b*c*d^5*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+7*a^(5/2)*b^2*c^2*d^4*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+24*((a*d-b*c)/c^2*d)^(1/2)*a^4*c*d^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+24*a^(9/2)*c^2*d^4*x^2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-8*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*c^4*d^2+a^(3/2)*b^3*c^3*d^3*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d)))*x*((a*x+b)/x)^(1/2)/c^5/((a*d-b*c)/c^2*d)^(1/2)/a^(3/2)/(c*x+d)^2/d^2/((a*x+b)*x)^(1/2)","B"
245,1,535,111,0.063000," ","int((c+d/x)^3/(a+b/x)^(1/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(3 a^{3} b \,d^{3} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 a^{3} b \,d^{3} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-9 a^{2} b^{2} c \,d^{2} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+9 a^{2} b^{2} c \,d^{2} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+9 a \,b^{3} c^{2} d \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+9 a \,b^{3} c^{2} d \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 b^{4} c^{3} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 \sqrt{a \,x^{2}+b x}\, a^{\frac{7}{2}} d^{3} x^{3}-6 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} d^{3} x^{3}+18 \sqrt{a \,x^{2}+b x}\, a^{\frac{5}{2}} b c \,d^{2} x^{3}+18 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b c \,d^{2} x^{3}+18 \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} b^{2} c^{2} d \,x^{3}-18 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{2} c^{2} d \,x^{3}+6 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{3} c^{3} x^{3}+12 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{5}{2}} d^{3} x -36 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b c \,d^{2} x -4 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b \,d^{3}\right)}{6 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{3} x^{2}}"," ",0,"1/6*((a*x+b)/x)^(1/2)/x^2*(3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^3*b*d^3-9*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^2*b^2*c*d^2+9*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a*b^3*c^2*d-3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*b^4*c^3-6*(a*x^2+b*x)^(1/2)*a^(7/2)*x^3*d^3+18*(a*x^2+b*x)^(1/2)*a^(5/2)*x^3*b*c*d^2+18*(a*x^2+b*x)^(1/2)*a^(3/2)*x^3*b^2*c^2*d-3*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^3*b*d^3+9*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^2*b^2*c*d^2+9*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a*b^3*c^2*d-6*a^(7/2)*((a*x+b)*x)^(1/2)*x^3*d^3+18*a^(5/2)*((a*x+b)*x)^(1/2)*x^3*b*c*d^2-18*a^(3/2)*((a*x+b)*x)^(1/2)*x^3*b^2*c^2*d+6*a^(1/2)*((a*x+b)*x)^(1/2)*x^3*b^3*c^3+12*(a*x^2+b*x)^(3/2)*a^(5/2)*x*d^3-36*(a*x^2+b*x)^(3/2)*a^(3/2)*x*b*c*d^2-4*d^3*(a*x^2+b*x)^(3/2)*b*a^(3/2))/((a*x+b)*x)^(1/2)/b^3/a^(3/2)","B"
246,1,348,63,0.063000," ","int((c+d/x)^2/(a+b/x)^(1/2),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(a^{2} b \,d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-a^{2} b \,d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 a \,b^{2} c d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 a \,b^{2} c d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+b^{3} c^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 \sqrt{a \,x^{2}+b x}\, a^{\frac{5}{2}} d^{2} x^{2}-2 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} d^{2} x^{2}-4 \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} b c d \,x^{2}+4 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b c d \,x^{2}-2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{2} c^{2} x^{2}+4 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{3}{2}} d^{2}\right)}{2 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{2} x}"," ",0,"-1/2*((a*x+b)/x)^(1/2)/x*(ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^2*b*d^2-2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a*b^2*c*d+ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*b^3*c^2-2*(a*x^2+b*x)^(1/2)*a^(5/2)*x^2*d^2-4*(a*x^2+b*x)^(1/2)*a^(3/2)*x^2*b*c*d-ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^2*b*d^2-2*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a*b^2*c*d-2*a^(5/2)*((a*x+b)*x)^(1/2)*x^2*d^2+4*a^(3/2)*((a*x+b)*x)^(1/2)*x^2*b*c*d-2*a^(1/2)*((a*x+b)*x)^(1/2)*x^2*b^2*c^2+4*(a*x^2+b*x)^(3/2)*a^(3/2)*d^2)/((a*x+b)*x)^(1/2)/b^2/a^(3/2)","B"
247,1,173,43,0.059000," ","int((c+d/x)/(a+b/x)^(1/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(a b d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+a b d \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-b^{2} c \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{a \,x^{2}+b x}\, a^{\frac{3}{2}} d -2 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} d +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b c \right) x}{2 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b}"," ",0,"1/2*((a*x+b)/x)^(1/2)*x*(2*a^(3/2)*(a*x^2+b*x)^(1/2)*d-2*a^(3/2)*((a*x+b)*x)^(1/2)*d+2*a^(1/2)*((a*x+b)*x)^(1/2)*b*c+ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*a*b*d-ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*b^2*c+ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*a*b*d)/((a*x+b)*x)^(1/2)/b/a^(3/2)","B"
248,1,71,35,0.046000," ","int(1/(a+b/x)^(1/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(-b \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\right) x}{2 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}}}"," ",0,"1/2*((a*x+b)/x)^(1/2)*x*(2*((a*x+b)*x)^(1/2)*a^(1/2)-b*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2)))/((a*x+b)*x)^(1/2)/a^(3/2)","A"
249,1,228,90,0.064000," ","int(1/(c+d/x)/(a+b/x)^(1/2),x)","-\frac{\left(2 a^{\frac{3}{2}} d^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a c d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, b \,c^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a}\, c^{2}\right) \sqrt{\frac{a x +b}{x}}\, x}{2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} c^{3}}"," ",0,"-1/2*(2*a^(3/2)*d^2*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-2*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(1/2)*c^2+2*((a*d-b*c)/c^2*d)^(1/2)*a*c*d*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+((a*d-b*c)/c^2*d)^(1/2)*b*c^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2)))*x*((a*x+b)/x)^(1/2)/((a*d-b*c)/c^2*d)^(1/2)/c^3/a^(3/2)/((a*x+b)*x)^(1/2)","B"
250,1,1135,152,0.069000," ","int(1/(c+d/x)^2/(a+b/x)^(1/2),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(4 a^{\frac{9}{2}} c \,d^{4} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-9 a^{\frac{7}{2}} b \,c^{2} d^{3} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+5 a^{\frac{5}{2}} b^{2} c^{3} d^{2} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c^{2} d^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-7 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{3} d^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{2} c^{4} d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{3} c^{5} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 a^{\frac{9}{2}} d^{5} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-9 a^{\frac{7}{2}} b c \,d^{4} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{4} d \,x^{2}+5 a^{\frac{5}{2}} b^{2} c^{2} d^{3} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c \,d^{4} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-7 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{2} d^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{2} c^{3} d^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{3} c^{4} d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{3} d^{2} x +6 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{4} d x -2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{2} c^{5} x -4 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{2} d^{3}+6 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{3} d^{2}-2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{2} c^{4} d -2 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{4} d \right) x}{2 \sqrt{\left(a x +b \right) x}\, \left(a d -b c \right)^{2} \left(c x +d \right) \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{4}}"," ",0,"-1/2*((a*x+b)/x)^(1/2)*x*(4*a^(9/2)*c*d^4*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+2*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(7/2)*c^4*d*x^2+4*a^(9/2)*d^5*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-2*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(7/2)*c^3*d^2*x-9*a^(7/2)*b*c^2*d^3*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-4*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(7/2)*c^2*d^3-9*a^(7/2)*b*c*d^4*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-2*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*c^4*d+6*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*b*c^4*d*x+5*a^(5/2)*b^2*c^3*d^2*x*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))+6*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*a^(5/2)*b*c^3*d^2+5*a^(5/2)*b^2*c^2*d^3*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))-2*a^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*x*b^2*c^5-2*a^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*b^2*c^4*d+4*((a*d-b*c)/c^2*d)^(1/2)*a^4*c^2*d^3*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))-7*((a*d-b*c)/c^2*d)^(1/2)*a^3*b*c^3*d^2*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+2*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^4*d+((a*d-b*c)/c^2*d)^(1/2)*a*b^3*c^5*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+4*((a*d-b*c)/c^2*d)^(1/2)*a^4*c*d^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))-7*((a*d-b*c)/c^2*d)^(1/2)*a^3*b*c^2*d^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+2*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^2*c^3*d^2+((a*d-b*c)/c^2*d)^(1/2)*a*b^3*c^4*d*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2)))/c^4/((a*x+b)*x)^(1/2)/(a*d-b*c)^2/(c*x+d)/a^(5/2)/((a*d-b*c)/c^2*d)^(1/2)","B"
251,1,2269,222,0.069000," ","int(1/(c+d/x)^3/(a+b/x)^(1/2),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(24 a^{\frac{11}{2}} c^{2} d^{5} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-80 a^{\frac{9}{2}} b \,c^{3} d^{4} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+91 a^{\frac{7}{2}} b^{2} c^{4} d^{3} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-35 a^{\frac{5}{2}} b^{3} c^{5} d^{2} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{5} c^{3} d^{4} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-68 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} b \,c^{4} d^{3} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+60 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b^{2} c^{5} d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-12 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{3} c^{6} d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{4} c^{7} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+48 a^{\frac{11}{2}} c \,d^{6} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-160 a^{\frac{9}{2}} b \,c^{2} d^{5} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+12 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{9}{2}} c^{5} d^{2} x^{3}+182 a^{\frac{7}{2}} b^{2} c^{3} d^{4} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-22 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} b \,c^{6} d \,x^{3}-70 a^{\frac{5}{2}} b^{3} c^{4} d^{3} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+48 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{5} c^{2} d^{5} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-136 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} b \,c^{3} d^{4} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+120 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b^{2} c^{4} d^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{3} c^{5} d^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-8 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{4} c^{6} d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+24 a^{\frac{11}{2}} d^{7} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-80 a^{\frac{9}{2}} b c \,d^{6} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+91 a^{\frac{7}{2}} b^{2} c^{2} d^{5} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+18 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} b \,c^{5} d^{2} x^{2}-35 a^{\frac{5}{2}} b^{3} c^{3} d^{4} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)-46 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b^{2} c^{6} d \,x^{2}+8 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{3} c^{7} x^{2}+24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{5} c \,d^{6} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-68 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} b \,c^{2} d^{5} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+60 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b^{2} c^{3} d^{4} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-12 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{3} c^{4} d^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{4} c^{5} d^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-36 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{9}{2}} c^{3} d^{4} x +102 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} b \,c^{4} d^{3} x -92 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b^{2} c^{5} d^{2} x +16 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{3} c^{6} d x -24 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{9}{2}} c^{2} d^{5}+62 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} b \,c^{3} d^{4}-12 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{5} d^{2} x -46 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b^{2} c^{4} d^{3}+22 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{6} d x +8 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{3} c^{5} d^{2}-8 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} c^{4} d^{3}+18 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b \,c^{5} d^{2}\right) x}{8 \sqrt{\left(a x +b \right) x}\, \left(a d -b c \right)^{3} \left(c x +d \right)^{2} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} c^{5}}"," ",0,"-1/8*((a*x+b)/x)^(1/2)*x*(60*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^2*c^3*d^4-12*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^3*c^4*d^3+12*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*c^5*d^2-12*a^(7/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*c^5*d^2-80*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b*c^3*d^4+91*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b^2*c^4*d^3-35*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b^3*c^5*d^2+24*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*c^3*d^4+18*a^(5/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*b*c^5*d^2-36*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*c^3*d^4-160*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b*c^2*d^5-4*a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^4*c^7+8*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^3*c^5*d^2-4*a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^4*c^5*d^2+182*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^2*c^3*d^4-70*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^3*c^4*d^3+48*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*c^2*d^5+62*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b*c^3*d^4-46*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^2*c^4*d^3-68*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b*c^2*d^5+8*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^3*c^7+24*a^(11/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*d^7-92*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^5*d^2-136*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^3*d^4+120*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^4*d^3-24*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^3*c^5*d^2+60*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^2*c^5*d^2-12*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^3*c^6*d+102*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^4*d^3+22*a^(5/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^6*d+18*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b*c^5*d^2-46*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^2*c^6*d-68*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b*c^4*d^3-22*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b*c^6*d-8*a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^4*c^6*d+16*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^3*c^6*d-24*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*c^2*d^5-80*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b*c*d^6+91*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^2*c^2*d^5-35*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^3*c^3*d^4+24*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*c*d^6+24*a^(11/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*c^2*d^5-8*a^(7/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*c^4*d^3+48*a^(11/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*c*d^6)/c^5/((a*x+b)*x)^(1/2)/(a*d-b*c)^3/(c*x+d)^2/a^(5/2)/((a*d-b*c)/c^2*d)^(1/2)","B"
252,1,969,122,0.067000," ","int((c+d/x)^3/(a+b/x)^(3/2),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(3 a^{4} b^{2} c \,d^{2} x^{4} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 a^{4} b^{2} c \,d^{2} x^{4} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 a^{3} b^{3} c^{2} d \,x^{4} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+3 a^{2} b^{4} c^{3} x^{4} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+6 a^{3} b^{3} c \,d^{2} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 a^{3} b^{3} c \,d^{2} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-12 a^{2} b^{4} c^{2} d \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+6 a \,b^{5} c^{3} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 \sqrt{a \,x^{2}+b x}\, a^{\frac{9}{2}} b c \,d^{2} x^{4}-6 \sqrt{\left(a x +b \right) x}\, a^{\frac{9}{2}} b c \,d^{2} x^{4}+12 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} b^{2} c^{2} d \,x^{4}-6 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{3} c^{3} x^{4}+3 a^{2} b^{4} c \,d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 a^{2} b^{4} c \,d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 a \,b^{5} c^{2} d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+3 b^{6} c^{3} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-12 \sqrt{a \,x^{2}+b x}\, a^{\frac{7}{2}} b^{2} c \,d^{2} x^{3}-12 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} b^{2} c \,d^{2} x^{3}+24 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{3} c^{2} d \,x^{3}-12 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{4} c^{3} x^{3}-6 \sqrt{a \,x^{2}+b x}\, a^{\frac{5}{2}} b^{3} c \,d^{2} x^{2}-6 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{3} c \,d^{2} x^{2}+12 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{4} c^{2} d \,x^{2}-6 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{5} c^{3} x^{2}+4 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{9}{2}} d^{3} x^{2}-4 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{9}{2}} d^{3} x^{2}+12 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{7}{2}} b c \,d^{2} x^{2}-12 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{2} c^{2} d \,x^{2}+4 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{3} c^{3} x^{2}+8 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{7}{2}} b \,d^{3} x +4 \left(a \,x^{2}+b x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{2} d^{3}\right)}{2 \sqrt{\left(a x +b \right) x}\, \left(a x +b \right)^{2} a^{\frac{5}{2}} b^{3} x}"," ",0,"-1/2*((a*x+b)/x)^(1/2)/x/a^(5/2)*(3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*b^6*c^3+4*(a*x^2+b*x)^(3/2)*a^(9/2)*x^2*d^3-4*a^(9/2)*((a*x+b)*x)^(3/2)*x^2*d^3+4*(a*x^2+b*x)^(3/2)*a^(5/2)*b^2*d^3+6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^3*b^3*c*d^2-12*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^2*b^4*c^2*d-6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^4*a^3*b^3*c^2*d-3*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^4*a^4*b^2*c*d^2+3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^4*a^4*b^2*c*d^2-6*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^3*b^3*c*d^2+12*a^(3/2)*((a*x+b)*x)^(1/2)*x^2*b^4*c^2*d-6*(a*x^2+b*x)^(1/2)*a^(9/2)*x^4*b*c*d^2-6*a^(9/2)*((a*x+b)*x)^(1/2)*x^4*b*c*d^2+12*a^(7/2)*((a*x+b)*x)^(1/2)*x^4*b^2*c^2*d-12*(a*x^2+b*x)^(1/2)*a^(7/2)*x^3*b^2*c*d^2+12*a^(7/2)*((a*x+b)*x)^(3/2)*x^2*b*c*d^2-12*a^(5/2)*((a*x+b)*x)^(3/2)*x^2*b^2*c^2*d-12*a^(7/2)*((a*x+b)*x)^(1/2)*x^3*b^2*c*d^2+24*a^(5/2)*((a*x+b)*x)^(1/2)*x^3*b^3*c^2*d-6*(a*x^2+b*x)^(1/2)*a^(5/2)*x^2*b^3*c*d^2-6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a*b^5*c^2*d-3*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^2*b^4*c*d^2+3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^2*b^4*c*d^2-6*a^(5/2)*((a*x+b)*x)^(1/2)*x^2*b^3*c*d^2+8*(a*x^2+b*x)^(3/2)*a^(7/2)*x*b*d^3-12*a^(3/2)*((a*x+b)*x)^(1/2)*x^3*b^4*c^3+4*a^(3/2)*((a*x+b)*x)^(3/2)*x^2*b^3*c^3-6*a^(5/2)*((a*x+b)*x)^(1/2)*x^4*b^3*c^3+3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^4*a^2*b^4*c^3+6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a*b^5*c^3-6*a^(1/2)*((a*x+b)*x)^(1/2)*x^2*b^5*c^3)/((a*x+b)*x)^(1/2)/b^3/(a*x+b)^2","B"
253,1,789,84,0.064000," ","int((c+d/x)^2/(a+b/x)^(3/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(-a^{4} b \,d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+a^{4} b \,d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 a^{3} b^{2} c d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 a^{2} b^{3} c^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 a^{3} b^{2} d^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 a^{3} b^{2} d^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+8 a^{2} b^{3} c d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 a \,b^{4} c^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{\left(a x +b \right) x}\, a^{\frac{9}{2}} d^{2} x^{2}+2 \sqrt{a \,x^{2}+b x}\, a^{\frac{9}{2}} d^{2} x^{2}-8 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} b c d \,x^{2}+6 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{2} c^{2} x^{2}-a^{2} b^{3} d^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+a^{2} b^{3} d^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 a \,b^{4} c d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 b^{5} c^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} b \,d^{2} x +4 \sqrt{a \,x^{2}+b x}\, a^{\frac{7}{2}} b \,d^{2} x -16 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{2} c d x +12 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{3} c^{2} x +2 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{2} d^{2}+2 \sqrt{a \,x^{2}+b x}\, a^{\frac{5}{2}} b^{2} d^{2}-8 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{3} c d +6 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{4} c^{2}-4 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{7}{2}} d^{2}+8 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b c d -4 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{2} c^{2}\right) x}{2 \sqrt{\left(a x +b \right) x}\, \left(a x +b \right)^{2} a^{\frac{5}{2}} b^{2}}"," ",0,"1/2*((a*x+b)/x)^(1/2)*x*(ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*a^2*b^3*d^2+2*a^(9/2)*((a*x+b)*x)^(1/2)*x^2*d^2+2*a^(9/2)*(a*x^2+b*x)^(1/2)*x^2*d^2-4*a^(3/2)*((a*x+b)*x)^(3/2)*b^2*c^2+2*a^(5/2)*((a*x+b)*x)^(1/2)*b^2*d^2+2*a^(5/2)*(a*x^2+b*x)^(1/2)*b^2*d^2-ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*a^2*b^3*d^2+6*a^(1/2)*((a*x+b)*x)^(1/2)*b^4*c^2-16*a^(5/2)*((a*x+b)*x)^(1/2)*x*b^2*c*d+8*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a^2*b^3*c*d+4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^3*b^2*c*d-8*a^(7/2)*((a*x+b)*x)^(1/2)*x^2*b*c*d-3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*b^5*c^2-4*a^(7/2)*((a*x+b)*x)^(3/2)*d^2-2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a^3*b^2*d^2-6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a*b^4*c^2+2*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x*a^3*b^2*d^2+4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*a*b^4*c*d+4*a^(7/2)*((a*x+b)*x)^(1/2)*x*b*d^2+12*a^(3/2)*((a*x+b)*x)^(1/2)*x*b^3*c^2+4*a^(7/2)*(a*x^2+b*x)^(1/2)*x*b*d^2-8*a^(3/2)*((a*x+b)*x)^(1/2)*b^3*c*d+6*a^(5/2)*((a*x+b)*x)^(1/2)*x^2*b^2*c^2+8*a^(5/2)*((a*x+b)*x)^(3/2)*b*c*d-ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^4*b*d^2-3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^2*b^3*c^2+ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^4*b*d^2)/a^(5/2)/((a*x+b)*x)^(1/2)/b^2/(a*x+b)^2","B"
254,1,387,66,0.056000," ","int((c+d/x)/(a+b/x)^(3/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(2 a^{3} b d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 a^{2} b^{2} c \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 a^{2} b^{2} d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 a \,b^{3} c x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-4 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} d \,x^{2}+6 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b c \,x^{2}+2 a \,b^{3} d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 b^{4} c \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-8 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b d x +12 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{2} c x -4 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{2} d +6 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{3} c +4 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{5}{2}} d -4 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b c \right) x}{2 \sqrt{\left(a x +b \right) x}\, \left(a x +b \right)^{2} a^{\frac{5}{2}} b}"," ",0,"1/2*((a*x+b)/x)^(1/2)*x/a^(5/2)*(2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^3*b*d-3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^2*b^2*c-4*a^(7/2)*((a*x+b)*x)^(1/2)*x^2*d+6*a^(5/2)*((a*x+b)*x)^(1/2)*x^2*b*c+4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a^2*b^2*d-6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a*b^3*c+4*a^(5/2)*((a*x+b)*x)^(3/2)*d-4*a^(3/2)*((a*x+b)*x)^(3/2)*b*c-8*a^(5/2)*((a*x+b)*x)^(1/2)*x*b*d+12*a^(3/2)*((a*x+b)*x)^(1/2)*x*b^2*c+2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*a*b^3*d-3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*b^4*c-4*a^(3/2)*((a*x+b)*x)^(1/2)*b^2*d+6*a^(1/2)*((a*x+b)*x)^(1/2)*b^3*c)/((a*x+b)*x)^(1/2)/b/(a*x+b)^2","B"
255,1,198,50,0.058000," ","int(1/(a+b/x)^(3/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(-3 a^{2} b \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 a \,b^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+6 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} x^{2}-3 b^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+12 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b x +6 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{2}-4 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{3}{2}}\right) x}{2 \sqrt{\left(a x +b \right) x}\, \left(a x +b \right)^{2} a^{\frac{5}{2}}}"," ",0,"1/2*((a*x+b)/x)^(1/2)*x*(6*a^(5/2)*((a*x+b)*x)^(1/2)*x^2-4*a^(3/2)*((a*x+b)*x)^(3/2)+12*a^(3/2)*((a*x+b)*x)^(1/2)*x*b-3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^2*b-6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a*b^2+6*a^(1/2)*((a*x+b)*x)^(1/2)*b^2-3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*b^3)/a^(5/2)/((a*x+b)*x)^(1/2)/(a*x+b)^2","B"
256,1,962,127,0.074000," ","int(1/(a+b/x)^(3/2)/(c+d/x),x)","-\frac{\left(2 a^{\frac{9}{2}} d^{3} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} c \,d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b \,c^{2} d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{2} c^{3} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+4 a^{\frac{7}{2}} b \,d^{3} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b c \,d^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{2} c^{2} d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{3} c^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} c^{2} d \,x^{2}+2 a^{\frac{5}{2}} b^{2} d^{3} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+6 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b \,c^{3} x^{2}+2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{2} c \,d^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+\sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{3} c^{2} d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, b^{4} c^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b \,c^{2} d x +12 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{2} c^{3} x -2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{2} c^{2} d +6 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{3} c^{3}-4 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b \,c^{3}\right) \sqrt{\frac{a x +b}{x}}\, x}{2 \left(a x +b \right)^{2} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \left(a d -b c \right) \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} c^{3}}"," ",0,"-1/2*(2*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*d^3-2*a^(7/2)*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*x^2*c^2*d+4*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b*d^3+6*a^(5/2)*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*x^2*b*c^3-4*a^(5/2)*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*x*b*c^2*d+2*a^(5/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^2*d^3-4*a^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(3/2)*b*c^3+12*a^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*x*b^2*c^3+2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*a^4*c*d^2+ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*a^3*b*c^2*d-3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*a^2*b^2*c^3-2*a^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*b^2*c^2*d+4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*a^3*b*c*d^2+2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*a^2*b^2*c^2*d-6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*a*b^3*c^3+6*a^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*b^3*c^3+2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*a^2*b^2*c*d^2+ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*a*b^3*c^2*d-3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^4*c^3)*x*((a*x+b)/x)^(1/2)/a^(5/2)/(a*x+b)^2/((a*d-b*c)/c^2*d)^(1/2)/c^3/(a*d-b*c)/((a*x+b)*x)^(1/2)","B"
257,1,3119,202,0.073000," ","int(1/(a+b/x)^(3/2)/(c+d/x)^2,x)","\text{output too large to display}"," ",0,"-1/2*((a*x+b)/x)^(1/2)*x*(4*a^(15/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*d^6+4*a^(11/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^2*d^6-6*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^5*c^6+2*a^(7/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*b^2*c^4*d^2-4*a^(5/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*b^3*c^5*d-3*a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^6*c^6+6*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^5*c^5*d-3*a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^6*c^5*d+2*a^(13/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^4*c^4*d^2-2*a^(11/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*c^4*d^2-2*a^(13/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*c^3*d^3+6*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^3*c^6-11*a^(13/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^3*b*c^2*d^4+7*a^(11/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^3*b^2*c^3*d^3+4*a^7*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*c^2*d^4-3*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^4*c^6-4*a^(5/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^3*c^6-4*a^(13/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*c^2*d^4+12*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^4*c^6-3*a^(13/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b*c*d^5-18*a^(11/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^2*c*d^5+3*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^3*c^2*d^4+7*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^4*c^3*d^3-4*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^2*c^2*d^4+8*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^3*c^3*d^3-10*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^4*c^4*d^2+4*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^2*c*d^5-9*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^3*c^2*d^4+3*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^4*c^3*d^3+5*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^5*c^4*d^2-15*a^(11/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b^2*c^2*d^4+14*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b^3*c^3*d^3+4*a^7*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*c*d^5+6*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^5*c^6+13*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^4*c^4*d^2-8*a^(11/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^2*d^4+14*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^3*d^3-12*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^3*c^4*d^2+2*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^4*c^5*d+8*a^6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b*c*d^5-14*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^2*d^4+11*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^3*c^4*d^2+7*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^4*c^5*d-a^6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b*c^2*d^4-15*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^2*c^3*d^3+8*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^2*c^4*d^2-14*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^3*c^5*d-10*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^2*c^5*d-9*a^6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*b*c^3*d^3+3*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^2*c^4*d^2+5*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^3*c^5*d-4*a^(9/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^4*d^2+4*a^(7/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^5*d+4*a^(11/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b*c^3*d^3+12*a^(11/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b*c^4*d^2-a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^5*c^5*d-3*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^3*c^3*d^3+4*a^(15/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^3*c*d^5+8*a^(13/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b*d^6-11*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^3*c*d^5+7*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^4*c^2*d^4)/a^(7/2)/c^4/((a*x+b)*x)^(1/2)/(a*d-b*c)^3/(c*x+d)/((a*d-b*c)/c^2*d)^(1/2)/(a*x+b)^2","B"
258,1,5158,288,0.079000," ","int(1/(a+b/x)^(3/2)/(c+d/x)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
259,1,1150,131,0.061000," ","int((c+d/x)^3/(a+b/x)^(5/2),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(3 a^{6} b \,d^{3} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 a^{6} b \,d^{3} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-18 a^{4} b^{3} c^{2} d \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+15 a^{3} b^{4} c^{3} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+9 a^{5} b^{2} d^{3} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-9 a^{5} b^{2} d^{3} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-54 a^{3} b^{4} c^{2} d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+45 a^{2} b^{5} c^{3} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 \sqrt{a \,x^{2}+b x}\, a^{\frac{13}{2}} d^{3} x^{3}-6 \sqrt{\left(a x +b \right) x}\, a^{\frac{13}{2}} d^{3} x^{3}+36 \sqrt{\left(a x +b \right) x}\, a^{\frac{9}{2}} b^{2} c^{2} d \,x^{3}-30 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} b^{3} c^{3} x^{3}+9 a^{4} b^{3} d^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-9 a^{4} b^{3} d^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-54 a^{2} b^{5} c^{2} d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+45 a \,b^{6} c^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-18 \sqrt{\left(a x +b \right) x}\, a^{\frac{11}{2}} b \,d^{3} x^{2}-18 \sqrt{a \,x^{2}+b x}\, a^{\frac{11}{2}} b \,d^{3} x^{2}+108 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} b^{3} c^{2} d \,x^{2}-90 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{4} c^{3} x^{2}+3 a^{3} b^{4} d^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-3 a^{3} b^{4} d^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x}\, \sqrt{a}}{2 \sqrt{a}}\right)-18 a \,b^{6} c^{2} d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+15 b^{7} c^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-18 \sqrt{a \,x^{2}+b x}\, a^{\frac{9}{2}} b^{2} d^{3} x -18 \sqrt{\left(a x +b \right) x}\, a^{\frac{9}{2}} b^{2} d^{3} x +108 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{4} c^{2} d x -90 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{5} c^{3} x +12 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{11}{2}} d^{3} x -6 \sqrt{a \,x^{2}+b x}\, a^{\frac{7}{2}} b^{3} d^{3}-6 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} b^{3} d^{3}-36 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{7}{2}} b^{2} c^{2} d x +24 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{3} c^{3} x +36 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{5} c^{2} d -30 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{6} c^{3}+16 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{9}{2}} b \,d^{3}-12 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{7}{2}} b^{2} c \,d^{2}-24 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{3} c^{2} d +20 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{4} c^{3}\right) x}{6 \sqrt{\left(a x +b \right) x}\, \left(a x +b \right)^{3} a^{\frac{7}{2}} b^{3}}"," ",0,"-1/6*((a*x+b)/x)^(1/2)*x/a^(7/2)*(3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*a^3*b^4*d^3-3*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*a^3*b^4*d^3-30*a^(1/2)*((a*x+b)*x)^(1/2)*b^6*c^3-6*(a*x^2+b*x)^(1/2)*a^(13/2)*x^3*d^3-6*a^(13/2)*((a*x+b)*x)^(1/2)*x^3*d^3+12*a^(11/2)*((a*x+b)*x)^(3/2)*x*d^3+16*a^(9/2)*((a*x+b)*x)^(3/2)*b*d^3+20*a^(3/2)*((a*x+b)*x)^(3/2)*b^4*c^3-6*(a*x^2+b*x)^(1/2)*a^(7/2)*b^3*d^3-6*a^(7/2)*((a*x+b)*x)^(1/2)*b^3*d^3+36*a^(9/2)*((a*x+b)*x)^(1/2)*x^3*b^2*c^2*d-36*a^(7/2)*((a*x+b)*x)^(3/2)*x*b^2*c^2*d+108*a^(7/2)*((a*x+b)*x)^(1/2)*x^2*b^3*c^2*d-54*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a^2*b^5*c^2*d-54*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^3*b^4*c^2*d-18*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^4*b^3*c^2*d+108*a^(5/2)*((a*x+b)*x)^(1/2)*x*b^4*c^2*d+15*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*b^7*c^3+9*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a^4*b^3*d^3+45*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a*b^6*c^3-9*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x*a^4*b^3*d^3-18*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*a*b^6*c^2*d-18*(a*x^2+b*x)^(1/2)*a^(9/2)*x*b^2*d^3-12*a^(7/2)*((a*x+b)*x)^(3/2)*b^2*c*d^2-24*a^(5/2)*((a*x+b)*x)^(3/2)*b^3*c^2*d-18*a^(9/2)*((a*x+b)*x)^(1/2)*x*b^2*d^3-90*a^(3/2)*((a*x+b)*x)^(1/2)*x*b^5*c^3+36*a^(3/2)*((a*x+b)*x)^(1/2)*b^5*c^2*d-90*a^(5/2)*((a*x+b)*x)^(1/2)*x^2*b^4*c^3+24*a^(5/2)*((a*x+b)*x)^(3/2)*x*b^3*c^3-18*a^(11/2)*((a*x+b)*x)^(1/2)*x^2*b*d^3-18*(a*x^2+b*x)^(1/2)*a^(11/2)*x^2*b*d^3-30*a^(7/2)*((a*x+b)*x)^(1/2)*x^3*b^3*c^3+3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^6*b*d^3+15*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^3*b^4*c^3-3*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^6*b*d^3+9*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^5*b^2*d^3+45*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^2*b^5*c^3-9*ln(1/2*(2*a*x+b+2*(a*x^2+b*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^5*b^2*d^3)/((a*x+b)*x)^(1/2)/b^3/(a*x+b)^3","B"
260,1,588,108,0.065000," ","int((c+d/x)^2/(a+b/x)^(5/2),x)","-\frac{\sqrt{\frac{a x +b}{x}}\, \left(-12 a^{4} b c d \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+15 a^{3} b^{2} c^{2} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-36 a^{3} b^{2} c d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+45 a^{2} b^{3} c^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+24 \sqrt{\left(a x +b \right) x}\, a^{\frac{9}{2}} c d \,x^{3}-30 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} b \,c^{2} x^{3}-36 a^{2} b^{3} c d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+45 a \,b^{4} c^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+72 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} b c d \,x^{2}-90 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{2} c^{2} x^{2}-12 a \,b^{4} c d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+15 b^{5} c^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+72 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{2} c d x -90 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{3} c^{2} x -24 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{7}{2}} c d x +24 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b \,c^{2} x +24 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{3} c d -30 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{4} c^{2}-4 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{7}{2}} d^{2}-16 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b c d +20 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{2} c^{2}\right) x}{6 \sqrt{\left(a x +b \right) x}\, \left(a x +b \right)^{3} a^{\frac{7}{2}} b}"," ",0,"-1/6*((a*x+b)/x)^(1/2)*x*(24*a^(9/2)*((a*x+b)*x)^(1/2)*x^3*c*d-30*a^(7/2)*((a*x+b)*x)^(1/2)*x^3*b*c^2-24*a^(7/2)*((a*x+b)*x)^(3/2)*x*c*d+72*((a*x+b)*x)^(1/2)*a^(7/2)*b*c*d*x^2-4*((a*x+b)*x)^(3/2)*a^(7/2)*d^2+24*a^(5/2)*((a*x+b)*x)^(3/2)*x*b*c^2-90*((a*x+b)*x)^(1/2)*a^(5/2)*b^2*c^2*x^2-16*((a*x+b)*x)^(3/2)*a^(5/2)*b*c*d+72*((a*x+b)*x)^(1/2)*a^(5/2)*b^2*c*d*x-12*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^4*b*c*d+15*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^3*b^2*c^2+20*((a*x+b)*x)^(3/2)*a^(3/2)*b^2*c^2-90*((a*x+b)*x)^(1/2)*a^(3/2)*b^3*c^2*x-36*a^3*b^2*c*d*x^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+45*a^2*b^3*c^2*x^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+24*((a*x+b)*x)^(1/2)*a^(3/2)*b^3*c*d-36*a^2*b^3*c*d*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+45*a*b^4*c^2*x*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))-30*((a*x+b)*x)^(1/2)*a^(1/2)*b^4*c^2-12*a*b^4*c*d*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))+15*b^5*c^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2)))/a^(7/2)/((a*x+b)*x)^(1/2)/b/(a*x+b)^3","B"
261,1,541,89,0.064000," ","int((c+d/x)/(a+b/x)^(5/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(6 a^{4} b d \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-15 a^{3} b^{2} c \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+18 a^{3} b^{2} d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-45 a^{2} b^{3} c \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-12 \sqrt{\left(a x +b \right) x}\, a^{\frac{9}{2}} d \,x^{3}+30 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} b c \,x^{3}+18 a^{2} b^{3} d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-45 a \,b^{4} c x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-36 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} b d \,x^{2}+90 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{2} c \,x^{2}+6 a \,b^{4} d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-15 b^{5} c \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-36 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b^{2} d x +90 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{3} c x +12 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{7}{2}} d x -24 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b c x -12 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{3} d +30 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{4} c +8 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{5}{2}} b d -20 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{2} c \right) x}{6 \sqrt{\left(a x +b \right) x}\, \left(a x +b \right)^{3} a^{\frac{7}{2}} b}"," ",0,"1/6*((a*x+b)/x)^(1/2)*x/a^(7/2)*(6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^4*b*d-15*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^3*b^2*c-12*a^(9/2)*((a*x+b)*x)^(1/2)*x^3*d+30*a^(7/2)*((a*x+b)*x)^(1/2)*x^3*b*c+18*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^3*b^2*d-45*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^2*b^3*c+12*a^(7/2)*((a*x+b)*x)^(3/2)*x*d-24*a^(5/2)*((a*x+b)*x)^(3/2)*x*b*c-36*a^(7/2)*((a*x+b)*x)^(1/2)*x^2*b*d+90*a^(5/2)*((a*x+b)*x)^(1/2)*x^2*b^2*c+18*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a^2*b^3*d-45*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a*b^4*c+8*a^(5/2)*((a*x+b)*x)^(3/2)*b*d-20*a^(3/2)*((a*x+b)*x)^(3/2)*b^2*c-36*a^(5/2)*((a*x+b)*x)^(1/2)*x*b^2*d+90*a^(3/2)*((a*x+b)*x)^(1/2)*x*b^3*c+6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*a*b^4*d-15*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*b^5*c-12*a^(3/2)*((a*x+b)*x)^(1/2)*b^3*d+30*a^(1/2)*((a*x+b)*x)^(1/2)*b^4*c)/((a*x+b)*x)^(1/2)/b/(a*x+b)^3","B"
262,1,271,65,0.068000," ","int(1/(a+b/x)^(5/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \left(-15 a^{3} b \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-45 a^{2} b^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+30 \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} x^{3}-45 a \,b^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+90 \sqrt{\left(a x +b \right) x}\, a^{\frac{5}{2}} b \,x^{2}-15 b^{4} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+90 \sqrt{\left(a x +b \right) x}\, a^{\frac{3}{2}} b^{2} x -24 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{5}{2}} x +30 \sqrt{\left(a x +b \right) x}\, \sqrt{a}\, b^{3}-20 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} a^{\frac{3}{2}} b \right) x}{6 \sqrt{\left(a x +b \right) x}\, \left(a x +b \right)^{3} a^{\frac{7}{2}}}"," ",0,"1/6*((a*x+b)/x)^(1/2)*x*(30*a^(7/2)*((a*x+b)*x)^(1/2)*x^3-24*a^(5/2)*((a*x+b)*x)^(3/2)*x+90*a^(5/2)*((a*x+b)*x)^(1/2)*x^2*b-15*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^3*a^3*b-20*b*a^(3/2)*((a*x+b)*x)^(3/2)+90*a^(3/2)*((a*x+b)*x)^(1/2)*x*b^2-45*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x^2*a^2*b^2-45*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*x*a*b^3+30*a^(1/2)*((a*x+b)*x)^(1/2)*b^3-15*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*b^4)/a^(7/2)/((a*x+b)*x)^(1/2)/(a*x+b)^3","B"
263,1,1767,177,0.071000," ","int(1/(a+b/x)^(5/2)/(c+d/x),x)","-\frac{\left(6 a^{\frac{13}{2}} d^{4} x^{3} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+6 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{6} c \,d^{3} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+3 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{5} b \,c^{2} d^{2} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} b^{2} c^{3} d \,x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+15 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b^{3} c^{4} x^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+18 a^{\frac{11}{2}} b \,d^{4} x^{2} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+18 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{5} b c \,d^{3} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+9 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} b^{2} c^{2} d^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-72 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b^{3} c^{3} d \,x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+45 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{4} c^{4} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-6 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{11}{2}} c^{2} d^{2} x^{3}+18 a^{\frac{9}{2}} b^{2} d^{4} x \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+48 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{9}{2}} b \,c^{3} d \,x^{3}-30 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} b^{2} c^{4} x^{3}+18 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{4} b^{2} c \,d^{3} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+9 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b^{3} c^{2} d^{2} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-72 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{4} c^{3} d x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+45 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{5} c^{4} x \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-18 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{9}{2}} b \,c^{2} d^{2} x^{2}+6 a^{\frac{7}{2}} b^{3} d^{4} \ln \left(\frac{-2 a d x +b c x -b d +2 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{\left(a x +b \right) x}\, c}{c x +d}\right)+144 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} b^{2} c^{3} d \,x^{2}-90 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b^{3} c^{4} x^{2}+6 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{3} b^{3} c \,d^{3} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+3 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{2} b^{4} c^{2} d^{2} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-24 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a \,b^{5} c^{3} d \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)+15 \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, b^{6} c^{4} \ln \left(\frac{2 a x +b +2 \sqrt{\left(a x +b \right) x}\, \sqrt{a}}{2 \sqrt{a}}\right)-18 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} b^{2} c^{2} d^{2} x +144 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b^{3} c^{3} d x -90 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{4} c^{4} x -36 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{7}{2}} b \,c^{3} d x -6 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b^{3} c^{2} d^{2}+24 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b^{2} c^{4} x +48 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{4} c^{3} d -30 \sqrt{\left(a x +b \right) x}\, \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \sqrt{a}\, b^{5} c^{4}-32 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{5}{2}} b^{2} c^{3} d +20 \left(\left(a x +b \right) x \right)^{\frac{3}{2}} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, a^{\frac{3}{2}} b^{3} c^{4}\right) \sqrt{\frac{a x +b}{x}}\, x}{6 \left(a x +b \right)^{3} \sqrt{\frac{\left(a d -b c \right) d}{c^{2}}}\, \left(a d -b c \right)^{2} \sqrt{\left(a x +b \right) x}\, a^{\frac{7}{2}} c^{3}}"," ",0,"-1/6*(15*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^6*c^4+6*a^(13/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^3*d^4+6*a^(7/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^3*d^4+3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*a^2*b^4*c^2*d^2+45*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*a^2*b^4*c^4+6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*a^6*c*d^3+15*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*a^3*b^3*c^4-30*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^2*c^4+24*a^(5/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^4-90*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^3*c^4-32*a^(5/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*b^2*c^3*d-90*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^4*c^4-6*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^3*c^2*d^2+48*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^4*c^3*d-6*a^(11/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*c^2*d^2+45*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*a*b^5*c^4+6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*a^3*b^3*c*d^3-24*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*a*b^5*c^3*d+144*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^2*c^3*d-18*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^2*d^2+144*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^3*c^3*d-18*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b*c^2*d^2+48*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b*c^3*d-36*a^(7/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b*c^3*d+3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*a^5*b*c^2*d^2-24*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*a^4*b^2*c^3*d+18*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*a^5*b*c*d^3+9*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*a^4*b^2*c^2*d^2-72*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*a^3*b^3*c^3*d+18*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*a^4*b^2*c*d^3+9*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*a^3*b^3*c^2*d^2-72*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*a^2*b^4*c^3*d+18*a^(11/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b*d^4-30*a^(1/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^5*c^4+20*a^(3/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*b^3*c^4+18*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^2*d^4)*x*((a*x+b)/x)^(1/2)/a^(7/2)/(a*x+b)^3/((a*d-b*c)/c^2*d)^(1/2)/c^3/(a*d-b*c)^2/((a*x+b)*x)^(1/2)","B"
264,1,4644,261,0.080000," ","int(1/(a+b/x)^(5/2)/(c+d/x)^2,x)","\text{output too large to display}"," ",0,"-1/6*((a*x+b)/x)^(1/2)*x*(12*a^(19/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^3*d^7+12*a^(13/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^3*d^7+30*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^4*c^3*d^4-84*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^5*c^4*d^3+96*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^6*c^5*d^2+12*a^6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^3*c*d^6-33*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^4*c^2*d^5+12*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^5*c^3*d^4-6*a^(17/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^4*c^3*d^4-30*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^4*b^4*c^7-39*a^(17/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^4*b*c^2*d^5+27*a^(15/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^4*b^2*c^3*d^4+12*a^9*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^4*c^2*d^5+15*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^4*b^5*c^7+24*a^(7/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^4*c^7-12*a^(17/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*c^2*d^5-90*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^5*c^7-3*a^(17/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^3*b*c*d^6-90*a^(15/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^3*b^2*c^2*d^5+81*a^(13/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^3*b^3*c^3*d^4+12*a^9*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*c*d^6+45*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^6*c^7+20*a^(5/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^5*c^7-90*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^6*c^7-81*a^(15/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b^2*c*d^6-36*a^(13/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b^3*c^2*d^5+81*a^(11/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b^4*c^3*d^4+45*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^7*c^7+38*a^(9/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*b^3*c^4*d^3-64*a^(7/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*b^4*c^5*d^2+20*a^(5/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*b^5*c^6*d-105*a^(13/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^3*c*d^6+42*a^(11/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^4*c^2*d^5+27*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^5*c^3*d^4-12*a^(11/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^3*c^2*d^5+15*a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^8*c^7-30*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*b^7*c^6*d+15*a*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^8*c^6*d+42*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^6*c^4*d^3-48*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*b^7*c^5*d^2+6*a^(17/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^5*c^4*d^3-6*a^(15/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*c^4*d^3-30*a^(3/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^7*c^7-102*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^6*c^5*d^2-3*a^2*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^7*c^6*d+36*a^8*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b*c*d^6-63*a^7*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^2*c^2*d^5+12*a^(15/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b*c^3*d^4+24*a^(13/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^2*c^4*d^3-33*a^8*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^4*b*c^3*d^4+12*a^7*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^4*b^2*c^4*d^3+42*a^6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^4*b^3*c^5*d^2-48*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^4*b^4*c^6*d+48*a^(15/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^4*b*c^4*d^3-84*a^(13/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^4*b^2*c^5*d^2+96*a^(11/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^4*b^3*c^6*d-36*a^(13/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^2*d^5-63*a^6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^3*c^3*d^4+162*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^4*c^4*d^3-18*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^5*c^5*d^2-99*a^3*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^6*c^6*d+198*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^5*c^6*d-28*a^(9/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^3*c^5*d^2-40*a^(7/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^4*c^6*d-36*a^(15/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b*c^2*d^5+72*a^(13/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^2*c^3*d^4-156*a^(11/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^3*c^4*d^3+36*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^4*c^5*d^2+78*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^4*c^5*d^2-129*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^5*c^6*d+30*a^(11/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c^4*d^3+3*a^8*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*b*c^2*d^5-87*a^7*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^2*c^3*d^4+78*a^6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^3*c^4*d^3-156*a^(11/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^3*c^5*d^2+258*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x^3*b^4*c^6*d-18*a^(13/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b*c^4*d^3+48*a^(11/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^2*c^5*d^2-72*a^(9/2)*((a*x+b)*x)^(3/2)*((a*d-b*c)/c^2*d)^(1/2)*x^2*b^3*c^6*d+84*a^(11/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^3*c^3*d^4-222*a^(9/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^4*c^4*d^3+204*a^(7/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^5*c^5*d^2+6*a^(5/2)*((a*x+b)*x)^(1/2)*((a*d-b*c)/c^2*d)^(1/2)*x*b^6*c^6*d+36*a^7*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^2*c*d^6-87*a^6*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^3*c^2*d^5+3*a^5*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^4*c^3*d^4+138*a^4*ln(1/2*(2*a*x+b+2*((a*x+b)*x)^(1/2)*a^(1/2))/a^(1/2))*((a*d-b*c)/c^2*d)^(1/2)*x*b^5*c^4*d^3+12*a^(19/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^4*c*d^6+36*a^(17/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x^2*b*d^7+36*a^(15/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*x*b^2*d^7-39*a^(11/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^4*c*d^6+27*a^(9/2)*ln((-2*a*d*x+b*c*x-b*d+2*((a*d-b*c)/c^2*d)^(1/2)*((a*x+b)*x)^(1/2)*c)/(c*x+d))*b^5*c^2*d^5)/a^(9/2)/c^4/((a*x+b)*x)^(1/2)/(a*d-b*c)^4/(c*x+d)/((a*d-b*c)/c^2*d)^(1/2)/(a*x+b)^3","B"
265,1,7300,373,0.079000," ","int(1/(a+b/x)^(5/2)/(c+d/x)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
266,1,253,95,0.096000," ","int((c+d/x)^(1/2)*(a+b/x)^(1/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \sqrt{\frac{c x +d}{x}}\, \left(\sqrt{b d}\, a d \ln \left(\frac{2 a c x +a d +b c +2 \sqrt{a c \,x^{2}+a d x +b c x +b d}\, \sqrt{a c}}{2 \sqrt{a c}}\right)+\sqrt{b d}\, b c \ln \left(\frac{2 a c x +a d +b c +2 \sqrt{a c \,x^{2}+a d x +b c x +b d}\, \sqrt{a c}}{2 \sqrt{a c}}\right)-2 \sqrt{a c}\, b d \ln \left(\frac{a d x +b c x +2 b d +2 \sqrt{b d}\, \sqrt{a c \,x^{2}+a d x +b c x +b d}}{x}\right)+2 \sqrt{a c \,x^{2}+a d x +b c x +b d}\, \sqrt{a c}\, \sqrt{b d}\right) x}{2 \sqrt{a c \,x^{2}+a d x +b c x +b d}\, \sqrt{a c}\, \sqrt{b d}}"," ",0,"1/2*((a*x+b)/x)^(1/2)*x*((c*x+d)/x)^(1/2)*((b*d)^(1/2)*ln(1/2*(2*a*c*x+2*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)+a*d+b*c)/(a*c)^(1/2))*a*d+(b*d)^(1/2)*ln(1/2*(2*a*c*x+2*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)+a*d+b*c)/(a*c)^(1/2))*b*c-2*b*d*ln((a*d*x+b*c*x+2*(b*d)^(1/2)*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)+2*b*d)/x)*(a*c)^(1/2)+2*(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)*(a*c)^(1/2)*(b*d)^(1/2))/(a*c*x^2+a*d*x+b*c*x+b*d)^(1/2)/(a*c)^(1/2)/(b*d)^(1/2)","B"
267,1,155,65,0.096000," ","int((a+b/x)^(1/2)/(c+d/x)^(1/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \sqrt{\frac{c x +d}{x}}\, \left(-a d \ln \left(\frac{2 a c x +a d +b c +2 \sqrt{\left(a x +b \right) \left(c x +d \right)}\, \sqrt{a c}}{2 \sqrt{a c}}\right)+b c \ln \left(\frac{2 a c x +a d +b c +2 \sqrt{\left(a x +b \right) \left(c x +d \right)}\, \sqrt{a c}}{2 \sqrt{a c}}\right)+2 \sqrt{\left(a x +b \right) \left(c x +d \right)}\, \sqrt{a c}\right) x}{2 \sqrt{\left(a x +b \right) \left(c x +d \right)}\, \sqrt{a c}\, c}"," ",0,"1/2*((a*x+b)/x)^(1/2)*x*((c*x+d)/x)^(1/2)*(-ln(1/2*(2*a*c*x+2*((a*x+b)*(c*x+d))^(1/2)*(a*c)^(1/2)+a*d+b*c)/(a*c)^(1/2))*a*d+ln(1/2*(2*a*c*x+2*((a*x+b)*(c*x+d))^(1/2)*(a*c)^(1/2)+a*d+b*c)/(a*c)^(1/2))*b*c+2*((a*x+b)*(c*x+d))^(1/2)*(a*c)^(1/2))/((a*x+b)*(c*x+d))^(1/2)/c/(a*c)^(1/2)","B"
268,1,280,102,0.080000," ","int((a+b/x)^(1/2)/(c+d/x)^(3/2),x)","\frac{\sqrt{\frac{a x +b}{x}}\, \sqrt{\frac{c x +d}{x}}\, \left(-3 a c d x \ln \left(\frac{2 a c x +a d +b c +2 \sqrt{\left(a x +b \right) \left(c x +d \right)}\, \sqrt{a c}}{2 \sqrt{a c}}\right)+b \,c^{2} x \ln \left(\frac{2 a c x +a d +b c +2 \sqrt{\left(a x +b \right) \left(c x +d \right)}\, \sqrt{a c}}{2 \sqrt{a c}}\right)-3 a \,d^{2} \ln \left(\frac{2 a c x +a d +b c +2 \sqrt{\left(a x +b \right) \left(c x +d \right)}\, \sqrt{a c}}{2 \sqrt{a c}}\right)+b c d \ln \left(\frac{2 a c x +a d +b c +2 \sqrt{\left(a x +b \right) \left(c x +d \right)}\, \sqrt{a c}}{2 \sqrt{a c}}\right)+2 \sqrt{\left(a x +b \right) \left(c x +d \right)}\, \sqrt{a c}\, c x +6 \sqrt{\left(a x +b \right) \left(c x +d \right)}\, \sqrt{a c}\, d \right) x}{2 \sqrt{a c}\, \left(c x +d \right) \sqrt{\left(a x +b \right) \left(c x +d \right)}\, c^{2}}"," ",0,"1/2*((a*x+b)/x)^(1/2)*x*((c*x+d)/x)^(1/2)*(-3*ln(1/2*(2*a*c*x+a*d+b*c+2*((a*x+b)*(c*x+d))^(1/2)*(a*c)^(1/2))/(a*c)^(1/2))*x*a*c*d+ln(1/2*(2*a*c*x+a*d+b*c+2*((a*x+b)*(c*x+d))^(1/2)*(a*c)^(1/2))/(a*c)^(1/2))*x*b*c^2+2*x*c*((a*x+b)*(c*x+d))^(1/2)*(a*c)^(1/2)-3*ln(1/2*(2*a*c*x+a*d+b*c+2*((a*x+b)*(c*x+d))^(1/2)*(a*c)^(1/2))/(a*c)^(1/2))*a*d^2+ln(1/2*(2*a*c*x+a*d+b*c+2*((a*x+b)*(c*x+d))^(1/2)*(a*c)^(1/2))/(a*c)^(1/2))*b*c*d+6*d*((a*x+b)*(c*x+d))^(1/2)*(a*c)^(1/2))/(a*c)^(1/2)/(c*x+d)/((a*x+b)*(c*x+d))^(1/2)/c^2","B"
269,0,0,96,0.297000," ","int((a+b/x)^p*(c+d/x)^q,x)","\int \left(a +\frac{b}{x}\right)^{p} \left(c +\frac{d}{x}\right)^{q}\, dx"," ",0,"int((a+b/x)^p*(c+d/x)^q,x)","F"
270,1,45,31,0.046000," ","int((a+b/x^2)/(c+d/x^2),x)","-\frac{a d \arctan \left(\frac{c x}{\sqrt{c d}}\right)}{\sqrt{c d}\, c}+\frac{b \arctan \left(\frac{c x}{\sqrt{c d}}\right)}{\sqrt{c d}}+\frac{a x}{c}"," ",0,"a*x/c-1/c/(c*d)^(1/2)*arctan(c*x/(c*d)^(1/2))*a*d+1/(c*d)^(1/2)*arctan(c*x/(c*d)^(1/2))*b","A"
271,1,277,270,0.142000," ","int((c+d/x^2)^(1/2)*(a+b/x^2)^(1/2),x)","\frac{\sqrt{\frac{a \,x^{2}+b}{x^{2}}}\, \sqrt{\frac{c \,x^{2}+d}{x^{2}}}\, \left(-\sqrt{-\frac{c}{d}}\, a c \,x^{4}-\sqrt{-\frac{c}{d}}\, a d \,x^{2}+\sqrt{\frac{c \,x^{2}+d}{d}}\, \sqrt{\frac{a \,x^{2}+b}{b}}\, a d x \EllipticF \left(\sqrt{-\frac{c}{d}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{-\frac{c}{d}}\, b c \,x^{2}+2 \sqrt{\frac{c \,x^{2}+d}{d}}\, \sqrt{\frac{a \,x^{2}+b}{b}}\, b c x \EllipticE \left(\sqrt{-\frac{c}{d}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{\frac{c \,x^{2}+d}{d}}\, \sqrt{\frac{a \,x^{2}+b}{b}}\, b c x \EllipticF \left(\sqrt{-\frac{c}{d}}\, x , \sqrt{\frac{a d}{b c}}\right)-\sqrt{-\frac{c}{d}}\, b d \right) x}{\left(a c \,x^{4}+a d \,x^{2}+b c \,x^{2}+b d \right) \sqrt{-\frac{c}{d}}}"," ",0,"((a*x^2+b)/x^2)^(1/2)*x*((c*x^2+d)/x^2)^(1/2)*(-(-c/d)^(1/2)*x^4*a*c+((c*x^2+d)/d)^(1/2)*((a*x^2+b)/b)^(1/2)*EllipticF(x*(-c/d)^(1/2),(a/b/c*d)^(1/2))*x*a*d-c*b*((c*x^2+d)/d)^(1/2)*((a*x^2+b)/b)^(1/2)*x*EllipticF(x*(-c/d)^(1/2),(a/b/c*d)^(1/2))+2*c*b*((c*x^2+d)/d)^(1/2)*((a*x^2+b)/b)^(1/2)*x*EllipticE(x*(-c/d)^(1/2),(a/b/c*d)^(1/2))-(-c/d)^(1/2)*x^2*a*d-(-c/d)^(1/2)*x^2*b*c-(-c/d)^(1/2)*b*d)/(a*c*x^4+a*d*x^2+b*c*x^2+b*d)/(-c/d)^(1/2)","A"
272,1,94,272,0.069000," ","int((a+b/x^2)^(1/2)/(c+d/x^2)^(1/2),x)","\frac{\sqrt{\frac{a \,x^{2}+b}{x^{2}}}\, \sqrt{\frac{a \,x^{2}+b}{b}}\, \sqrt{\frac{c \,x^{2}+d}{d}}\, b \EllipticE \left(\sqrt{-\frac{c}{d}}\, x , \sqrt{\frac{a d}{b c}}\right)}{\left(a \,x^{2}+b \right) \sqrt{-\frac{c}{d}}\, \sqrt{\frac{c \,x^{2}+d}{x^{2}}}}"," ",0,"((a*x^2+b)/x^2)^(1/2)/(a*x^2+b)*EllipticE((-c/d)^(1/2)*x,(a/b/c*d)^(1/2))*((a*x^2+b)/b)^(1/2)*((c*x^2+d)/d)^(1/2)*b/(-c/d)^(1/2)/((c*x^2+d)/x^2)^(1/2)","A"
273,1,185,301,0.172000," ","int((a+b/x^2)^(1/2)/(c+d/x^2)^(3/2),x)","-\frac{\sqrt{\frac{a \,x^{2}+b}{x^{2}}}\, \left(\sqrt{-\frac{c}{d}}\, a \,x^{3}+\sqrt{-\frac{c}{d}}\, b x -2 \sqrt{\frac{c \,x^{2}+d}{d}}\, \sqrt{\frac{a \,x^{2}+b}{b}}\, b \EllipticE \left(\sqrt{-\frac{c}{d}}\, x , \sqrt{\frac{a d}{b c}}\right)+\sqrt{\frac{c \,x^{2}+d}{d}}\, \sqrt{\frac{a \,x^{2}+b}{b}}\, b \EllipticF \left(\sqrt{-\frac{c}{d}}\, x , \sqrt{\frac{a d}{b c}}\right)\right) \left(c \,x^{2}+d \right)}{\left(a \,x^{2}+b \right) \sqrt{-\frac{c}{d}}\, \left(\frac{c \,x^{2}+d}{x^{2}}\right)^{\frac{3}{2}} c \,x^{2}}"," ",0,"-((a*x^2+b)/x^2)^(1/2)/x^2/(a*x^2+b)*(x^3*a*(-c/d)^(1/2)+EllipticF((-c/d)^(1/2)*x,(a/b/c*d)^(1/2))*b*((c*x^2+d)/d)^(1/2)*((a*x^2+b)/b)^(1/2)-2*EllipticE((-c/d)^(1/2)*x,(a/b/c*d)^(1/2))*b*((c*x^2+d)/d)^(1/2)*((a*x^2+b)/b)^(1/2)+x*b*(-c/d)^(1/2))*(c*x^2+d)/(-c/d)^(1/2)/c/((c*x^2+d)/x^2)^(3/2)","A"
274,0,0,75,0.225000," ","int((a+b/x^2)^p*(c+d/x^2)^q,x)","\int \left(a +\frac{b}{x^{2}}\right)^{p} \left(c +\frac{d}{x^{2}}\right)^{q}\, dx"," ",0,"int((a+b/x^2)^p*(c+d/x^2)^q,x)","F"
275,1,195,108,0.050000," ","int((a+b/x^3)/(c+d/x^3),x)","\frac{a x}{c}-\frac{\sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{c}\right)^{\frac{2}{3}} c^{2}}-\frac{a d \ln \left(x +\left(\frac{d}{c}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{c}\right)^{\frac{2}{3}} c^{2}}+\frac{a d \ln \left(x^{2}-\left(\frac{d}{c}\right)^{\frac{1}{3}} x +\left(\frac{d}{c}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{c}\right)^{\frac{2}{3}} c^{2}}+\frac{\sqrt{3}\, b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{c}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{c}\right)^{\frac{2}{3}} c}+\frac{b \ln \left(x +\left(\frac{d}{c}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{c}\right)^{\frac{2}{3}} c}-\frac{b \ln \left(x^{2}-\left(\frac{d}{c}\right)^{\frac{1}{3}} x +\left(\frac{d}{c}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{c}\right)^{\frac{2}{3}} c}"," ",0,"a/c*x-1/3/c^2/(1/c*d)^(2/3)*ln(x+(1/c*d)^(1/3))*a*d+1/3/c/(1/c*d)^(2/3)*ln(x+(1/c*d)^(1/3))*b+1/6/c^2/(1/c*d)^(2/3)*ln(x^2-(1/c*d)^(1/3)*x+(1/c*d)^(2/3))*a*d-1/6/c/(1/c*d)^(2/3)*ln(x^2-(1/c*d)^(1/3)*x+(1/c*d)^(2/3))*b-1/3/c^2/(1/c*d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c*d)^(1/3)*x-1))*a*d+1/3/c/(1/c*d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(1/c*d)^(1/3)*x-1))*b","A"
276,1,59,45,0.052000," ","int((b*x^(1/2)+a)/(c+d*x^(1/2)),x)","-\frac{2 a c \ln \left(d \sqrt{x}+c \right)}{d^{2}}+\frac{2 b \,c^{2} \ln \left(d \sqrt{x}+c \right)}{d^{3}}+\frac{b x}{d}+\frac{2 a \sqrt{x}}{d}-\frac{2 b c \sqrt{x}}{d^{2}}"," ",0,"b/d*x+2/d*a*x^(1/2)-2/d^2*b*c*x^(1/2)-2*c/d^2*ln(c+d*x^(1/2))*a+2*c^2/d^3*ln(c+d*x^(1/2))*b","A"
277,1,21,20,0.040000," ","int((x^(1/3)-1)/(x^(1/3)+1),x)","x -6 \ln \left(x^{\frac{1}{3}}+1\right)-3 x^{\frac{2}{3}}+6 x^{\frac{1}{3}}"," ",0,"6*x^(1/3)-3*x^(2/3)+x-6*ln(x^(1/3)+1)","A"
278,1,24,13,0.048000," ","int((x^(2/3)+1)/(x^(2/3)-1),x)","x -3 \ln \left(x^{\frac{1}{3}}+1\right)+3 \ln \left(x^{\frac{1}{3}}-1\right)+6 x^{\frac{1}{3}}"," ",0,"x+6*x^(1/3)+3*ln(x^(1/3)-1)-3*ln(x^(1/3)+1)","A"
279,1,66,71,0.044000," ","int((-16+x^(3/4))/(16+x^(3/4)),x)","x +\frac{128 \,16^{\frac{1}{3}} \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(\frac{16^{\frac{2}{3}} x^{\frac{1}{4}}}{8}-1\right)}{3}\right)}{3}+\frac{128 \,16^{\frac{1}{3}} \ln \left(x^{\frac{1}{4}}+16^{\frac{1}{3}}\right)}{3}-\frac{64 \,16^{\frac{1}{3}} \ln \left(\sqrt{x}-16^{\frac{1}{3}} x^{\frac{1}{4}}+16^{\frac{2}{3}}\right)}{3}-128 x^{\frac{1}{4}}"," ",0,"x-128*x^(1/4)+128/3*16^(1/3)*ln(x^(1/4)+16^(1/3))-64/3*16^(1/3)*ln(x^(1/2)-16^(1/3)*x^(1/4)+16^(2/3))+128/3*16^(1/3)*3^(1/2)*arctan(1/3*3^(1/2)*(1/8*16^(2/3)*x^(1/4)-1))","A"
280,1,23,24,0.042000," ","int((1+1/x^(1/3))/(-1+1/x^(1/3)),x)","-x -6 \ln \left(x^{\frac{1}{3}}-1\right)-3 x^{\frac{2}{3}}-6 x^{\frac{1}{3}}"," ",0,"-x-3*x^(2/3)-6*x^(1/3)-6*ln(x^(1/3)-1)","A"
281,0,0,69,0.767000," ","int((a-b*x^n)^(3/2)*(b*x^n+a)^(3/2),x)","\int \left(-b \,x^{n}+a \right)^{\frac{3}{2}} \left(b \,x^{n}+a \right)^{\frac{3}{2}}\, dx"," ",0,"int((a-b*x^n)^(3/2)*(b*x^n+a)^(3/2),x)","F"
282,0,0,66,0.594000," ","int((-b*x^n+a)^(1/2)*(b*x^n+a)^(1/2),x)","\int \sqrt{-b \,x^{n}+a}\, \sqrt{b \,x^{n}+a}\, dx"," ",0,"int((-b*x^n+a)^(1/2)*(b*x^n+a)^(1/2),x)","F"
283,0,0,70,0.928000," ","int((-b*x^n+a)^p*(b*x^n+a)^p,x)","\int \left(-b \,x^{n}+a \right)^{p} \left(b \,x^{n}+a \right)^{p}\, dx"," ",0,"int((-b*x^n+a)^p*(b*x^n+a)^p,x)","F"
284,1,138,132,0.053000," ","int((b*x^n+a)*(c+d*x^n)^4,x)","\frac{b \,d^{4} x \,{\mathrm e}^{5 n \ln \left(x \right)}}{5 n +1}+a \,c^{4} x +\frac{\left(4 a d +b c \right) c^{3} x \,{\mathrm e}^{n \ln \left(x \right)}}{n +1}+\frac{2 \left(3 a d +2 b c \right) c^{2} d x \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 n +1}+\frac{2 \left(2 a d +3 b c \right) c \,d^{2} x \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 n +1}+\frac{\left(a d +4 b c \right) d^{3} x \,{\mathrm e}^{4 n \ln \left(x \right)}}{4 n +1}"," ",0,"a*c^4*x+b*d^4/(1+5*n)*x*exp(n*ln(x))^5+c^3*(4*a*d+b*c)/(n+1)*x*exp(n*ln(x))+d^3*(a*d+4*b*c)/(4*n+1)*x*exp(n*ln(x))^4+2*c*d^2*(2*a*d+3*b*c)/(3*n+1)*x*exp(n*ln(x))^3+2*c^2*d*(3*a*d+2*b*c)/(2*n+1)*x*exp(n*ln(x))^2","A"
285,1,104,99,0.055000," ","int((b*x^n+a)*(c+d*x^n)^3,x)","\frac{b \,d^{3} x \,{\mathrm e}^{4 n \ln \left(x \right)}}{4 n +1}+a \,c^{3} x +\frac{\left(3 a d +b c \right) c^{2} x \,{\mathrm e}^{n \ln \left(x \right)}}{n +1}+\frac{3 \left(a d +b c \right) c d x \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 n +1}+\frac{\left(a d +3 b c \right) d^{2} x \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 n +1}"," ",0,"a*c^3*x+b*d^3/(4*n+1)*x*exp(n*ln(x))^4+c^2*(3*a*d+b*c)/(n+1)*x*exp(n*ln(x))+d^2*(a*d+3*b*c)/(3*n+1)*x*exp(n*ln(x))^3+3*c*d*(a*d+b*c)/(2*n+1)*x*exp(n*ln(x))^2","A"
286,1,74,70,0.054000," ","int((b*x^n+a)*(c+d*x^n)^2,x)","\frac{b \,d^{2} x \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 n +1}+a \,c^{2} x +\frac{\left(2 a d +b c \right) c x \,{\mathrm e}^{n \ln \left(x \right)}}{n +1}+\frac{\left(a d +2 b c \right) d x \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 n +1}"," ",0,"a*c^2*x+b*d^2/(3*n+1)*x*exp(n*ln(x))^3+c*(2*a*d+b*c)/(n+1)*x*exp(n*ln(x))+d*(a*d+2*b*c)/(2*n+1)*x*exp(n*ln(x))^2","A"
287,1,43,40,0.045000," ","int((b*x^n+a)*(c+d*x^n),x)","\frac{b d x \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 n +1}+a c x +\frac{\left(a d +b c \right) x \,{\mathrm e}^{n \ln \left(x \right)}}{n +1}"," ",0,"a*c*x+(a*d+b*c)/(n+1)*x*exp(n*ln(x))+b*d/(2*n+1)*x*exp(n*ln(x))^2","A"
288,0,0,45,0.632000," ","int((b*x^n+a)/(c+d*x^n),x)","\int \frac{b \,x^{n}+a}{d \,x^{n}+c}\, dx"," ",0,"int((b*x^n+a)/(c+d*x^n),x)","F"
289,0,0,75,0.587000," ","int((b*x^n+a)/(d*x^n+c)^2,x)","\int \frac{b \,x^{n}+a}{\left(d \,x^{n}+c \right)^{2}}\, dx"," ",0,"int((b*x^n+a)/(d*x^n+c)^2,x)","F"
290,0,0,76,0.609000," ","int((b*x^n+a)/(d*x^n+c)^3,x)","\int \frac{b \,x^{n}+a}{\left(d \,x^{n}+c \right)^{3}}\, dx"," ",0,"int((b*x^n+a)/(d*x^n+c)^3,x)","F"
291,0,0,76,0.585000," ","int((b*x^n+a)/(d*x^n+c)^4,x)","\int \frac{b \,x^{n}+a}{\left(d \,x^{n}+c \right)^{4}}\, dx"," ",0,"int((b*x^n+a)/(d*x^n+c)^4,x)","F"
292,1,164,158,0.057000," ","int((b*x^n+a)^2*(d+e*x^n)^3,x)","\frac{b^{2} e^{3} x \,{\mathrm e}^{5 n \ln \left(x \right)}}{5 n +1}+a^{2} d^{3} x +\frac{\left(3 a e +2 b d \right) a \,d^{2} x \,{\mathrm e}^{n \ln \left(x \right)}}{n +1}+\frac{\left(2 a e +3 b d \right) b \,e^{2} x \,{\mathrm e}^{4 n \ln \left(x \right)}}{4 n +1}+\frac{\left(3 a^{2} e^{2}+6 a b d e +b^{2} d^{2}\right) d x \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 n +1}+\frac{\left(a^{2} e^{2}+6 a b d e +3 b^{2} d^{2}\right) e x \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 n +1}"," ",0,"a^2*d^3*x+b^2*e^3/(5*n+1)*x*exp(n*ln(x))^5+d*(3*a^2*e^2+6*a*b*d*e+b^2*d^2)/(2*n+1)*x*exp(n*ln(x))^2+e*(a^2*e^2+6*a*b*d*e+3*b^2*d^2)/(3*n+1)*x*exp(n*ln(x))^3+a*d^2*(3*a*e+2*b*d)/(n+1)*x*exp(n*ln(x))+b*e^2*(2*a*e+3*b*d)/(4*n+1)*x*exp(n*ln(x))^4","A"
293,1,117,112,0.055000," ","int((b*x^n+a)^2*(d+e*x^n)^2,x)","\frac{b^{2} e^{2} x \,{\mathrm e}^{4 n \ln \left(x \right)}}{4 n +1}+a^{2} d^{2} x +\frac{2 \left(a e +b d \right) a d x \,{\mathrm e}^{n \ln \left(x \right)}}{n +1}+\frac{2 \left(a e +b d \right) b e x \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 n +1}+\frac{\left(a^{2} e^{2}+4 a b d e +b^{2} d^{2}\right) x \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 n +1}"," ",0,"a^2*d^2*x+(a^2*e^2+4*a*b*d*e+b^2*d^2)/(2*n+1)*x*exp(n*ln(x))^2+b^2*e^2/(4*n+1)*x*exp(n*ln(x))^4+2*a*d*(a*e+b*d)/(n+1)*x*exp(n*ln(x))+2*b*e*(a*e+b*d)/(3*n+1)*x*exp(n*ln(x))^3","A"
294,1,74,70,0.049000," ","int((b*x^n+a)^2*(d*x^n+c),x)","\frac{b^{2} d x \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 n +1}+a^{2} c x +\frac{\left(a d +2 b c \right) a x \,{\mathrm e}^{n \ln \left(x \right)}}{n +1}+\frac{\left(2 a d +b c \right) b x \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 n +1}"," ",0,"a^2*c*x+a*(a*d+2*b*c)/(n+1)*x*exp(n*ln(x))+b*(2*a*d+b*c)/(2*n+1)*x*exp(n*ln(x))^2+b^2*d/(3*n+1)*x*exp(n*ln(x))^3","A"
295,0,0,86,0.602000," ","int((b*x^n+a)^2/(d*x^n+c),x)","\int \frac{\left(b \,x^{n}+a \right)^{2}}{d \,x^{n}+c}\, dx"," ",0,"int((b*x^n+a)^2/(d*x^n+c),x)","F"
296,0,0,117,0.585000," ","int((b*x^n+a)^2/(d*x^n+c)^2,x)","\int \frac{\left(b \,x^{n}+a \right)^{2}}{\left(d \,x^{n}+c \right)^{2}}\, dx"," ",0,"int((b*x^n+a)^2/(d*x^n+c)^2,x)","F"
297,0,0,156,0.614000," ","int((b*x^n+a)^2/(d*x^n+c)^3,x)","\int \frac{\left(b \,x^{n}+a \right)^{2}}{\left(d \,x^{n}+c \right)^{3}}\, dx"," ",0,"int((b*x^n+a)^2/(d*x^n+c)^3,x)","F"
298,0,0,308,0.654000," ","int((d*x^n+c)^4/(b*x^n+a),x)","\int \frac{\left(d \,x^{n}+c \right)^{4}}{b \,x^{n}+a}\, dx"," ",0,"int((d*x^n+c)^4/(b*x^n+a),x)","F"
299,0,0,175,0.634000," ","int((d*x^n+c)^3/(b*x^n+a),x)","\int \frac{\left(d \,x^{n}+c \right)^{3}}{b \,x^{n}+a}\, dx"," ",0,"int((d*x^n+c)^3/(b*x^n+a),x)","F"
300,0,0,86,0.604000," ","int((d*x^n+c)^2/(b*x^n+a),x)","\int \frac{\left(d \,x^{n}+c \right)^{2}}{b \,x^{n}+a}\, dx"," ",0,"int((d*x^n+c)^2/(b*x^n+a),x)","F"
301,0,0,44,0.614000," ","int((d*x^n+c)/(b*x^n+a),x)","\int \frac{d \,x^{n}+c}{b \,x^{n}+a}\, dx"," ",0,"int((d*x^n+c)/(b*x^n+a),x)","F"
302,0,0,76,0.912000," ","int(1/(b*x^n+a)/(d*x^n+c),x)","\int \frac{1}{\left(b \,x^{n}+a \right) \left(d \,x^{n}+c \right)}\, dx"," ",0,"int(1/(b*x^n+a)/(d*x^n+c),x)","F"
303,0,0,127,0.928000," ","int(1/(b*x^n+a)/(d*x^n+c)^2,x)","\int \frac{1}{\left(b \,x^{n}+a \right) \left(d \,x^{n}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^n+a)/(d*x^n+c)^2,x)","F"
304,0,0,208,0.902000," ","int(1/(b*x^n+a)/(d*x^n+c)^3,x)","\int \frac{1}{\left(b \,x^{n}+a \right) \left(d \,x^{n}+c \right)^{3}}\, dx"," ",0,"int(1/(b*x^n+a)/(d*x^n+c)^3,x)","F"
305,0,0,344,0.617000," ","int((d*x^n+c)^4/(b*x^n+a)^2,x)","\int \frac{\left(d \,x^{n}+c \right)^{4}}{\left(b \,x^{n}+a \right)^{2}}\, dx"," ",0,"int((d*x^n+c)^4/(b*x^n+a)^2,x)","F"
306,0,0,202,0.676000," ","int((d*x^n+c)^3/(b*x^n+a)^2,x)","\int \frac{\left(d \,x^{n}+c \right)^{3}}{\left(b \,x^{n}+a \right)^{2}}\, dx"," ",0,"int((d*x^n+c)^3/(b*x^n+a)^2,x)","F"
307,0,0,117,0.608000," ","int((d*x^n+c)^2/(b*x^n+a)^2,x)","\int \frac{\left(d \,x^{n}+c \right)^{2}}{\left(b \,x^{n}+a \right)^{2}}\, dx"," ",0,"int((d*x^n+c)^2/(b*x^n+a)^2,x)","F"
308,0,0,74,0.590000," ","int((d*x^n+c)/(b*x^n+a)^2,x)","\int \frac{d \,x^{n}+c}{\left(b \,x^{n}+a \right)^{2}}\, dx"," ",0,"int((d*x^n+c)/(b*x^n+a)^2,x)","F"
309,0,0,126,0.910000," ","int(1/(b*x^n+a)^2/(d*x^n+c),x)","\int \frac{1}{\left(b \,x^{n}+a \right)^{2} \left(d \,x^{n}+c \right)}\, dx"," ",0,"int(1/(b*x^n+a)^2/(d*x^n+c),x)","F"
310,0,0,197,0.913000," ","int(1/(b*x^n+a)^2/(d*x^n+c)^2,x)","\int \frac{1}{\left(b \,x^{n}+a \right)^{2} \left(d \,x^{n}+c \right)^{2}}\, dx"," ",0,"int(1/(b*x^n+a)^2/(d*x^n+c)^2,x)","F"
311,0,0,297,0.927000," ","int(1/(b*x^n+a)^2/(d*x^n+c)^3,x)","\int \frac{1}{\left(b \,x^{n}+a \right)^{2} \left(d \,x^{n}+c \right)^{3}}\, dx"," ",0,"int(1/(b*x^n+a)^2/(d*x^n+c)^3,x)","F"
312,0,0,81,0.889000," ","int((b*x^n+a)^p*(d*x^n+c)^q,x)","\int \left(b \,x^{n}+a \right)^{p} \left(d \,x^{n}+c \right)^{q}\, dx"," ",0,"int((b*x^n+a)^p*(d*x^n+c)^q,x)","F"
313,0,0,404,0.742000," ","int((b*x^n+a)^p*(d*x^n+c)^3,x)","\int \left(d \,x^{n}+c \right)^{3} \left(b \,x^{n}+a \right)^{p}\, dx"," ",0,"int((b*x^n+a)^p*(d*x^n+c)^3,x)","F"
314,0,0,204,0.720000," ","int((b*x^n+a)^p*(d*x^n+c)^2,x)","\int \left(d \,x^{n}+c \right)^{2} \left(b \,x^{n}+a \right)^{p}\, dx"," ",0,"int((b*x^n+a)^p*(d*x^n+c)^2,x)","F"
315,0,0,100,0.604000," ","int((b*x^n+a)^p*(d*x^n+c),x)","\int \left(d \,x^{n}+c \right) \left(b \,x^{n}+a \right)^{p}\, dx"," ",0,"int((b*x^n+a)^p*(d*x^n+c),x)","F"
316,0,0,48,0.036000," ","int((b*x^n+a)^p,x)","\int \left(b \,x^{n}+a \right)^{p}\, dx"," ",0,"int((b*x^n+a)^p,x)","F"
317,0,0,59,0.914000," ","int((b*x^n+a)^p/(d*x^n+c),x)","\int \frac{\left(b \,x^{n}+a \right)^{p}}{d \,x^{n}+c}\, dx"," ",0,"int((b*x^n+a)^p/(d*x^n+c),x)","F"
318,0,0,59,0.900000," ","int((b*x^n+a)^p/(d*x^n+c)^2,x)","\int \frac{\left(b \,x^{n}+a \right)^{p}}{\left(d \,x^{n}+c \right)^{2}}\, dx"," ",0,"int((b*x^n+a)^p/(d*x^n+c)^2,x)","F"
319,0,0,59,0.930000," ","int((b*x^n+a)^p/(d*x^n+c)^3,x)","\int \frac{\left(b \,x^{n}+a \right)^{p}}{\left(d \,x^{n}+c \right)^{3}}\, dx"," ",0,"int((b*x^n+a)^p/(d*x^n+c)^3,x)","F"
320,0,0,95,0.910000," ","int((b*x^n+a)^p*(d*x^n+c)^(-1-1/n-p),x)","\int \left(b \,x^{n}+a \right)^{p} \left(d \,x^{n}+c \right)^{-p -\frac{1}{n}-1}\, dx"," ",0,"int((b*x^n+a)^p*(d*x^n+c)^(-1-1/n-p),x)","F"
321,0,0,174,0.828000," ","int((b*x^n+a)^3*(d*x^n+c)^(-1/n-4),x)","\int \left(b \,x^{n}+a \right)^{3} \left(d \,x^{n}+c \right)^{-\frac{1}{n}-4}\, dx"," ",0,"int((b*x^n+a)^3*(d*x^n+c)^(-1/n-4),x)","F"
322,0,0,116,0.797000," ","int((b*x^n+a)^2*(d*x^n+c)^(-1/n-3),x)","\int \left(b \,x^{n}+a \right)^{2} \left(d \,x^{n}+c \right)^{-\frac{1}{n}-3}\, dx"," ",0,"int((b*x^n+a)^2*(d*x^n+c)^(-1/n-3),x)","F"
323,0,0,58,0.598000," ","int((b*x^n+a)*(d*x^n+c)^(-1/n-2),x)","\int \left(b \,x^{n}+a \right) \left(d \,x^{n}+c \right)^{-\frac{1}{n}-2}\, dx"," ",0,"int((b*x^n+a)*(d*x^n+c)^(-1/n-2),x)","F"
324,1,53,18,0.073000," ","int((d*x^n+c)^(-1/n-1),x)","\frac{d x \,{\mathrm e}^{n \ln \left(x \right)} {\mathrm e}^{\left(-\frac{1}{n}-1\right) \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}}{c}+x \,{\mathrm e}^{\left(-\frac{1}{n}-1\right) \ln \left(d \,{\mathrm e}^{n \ln \left(x \right)}+c \right)}"," ",0,"x*exp((-1/n-1)*ln(c+d*exp(n*ln(x))))+1/c*d*x*exp(n*ln(x))*exp((-1/n-1)*ln(c+d*exp(n*ln(x))))","B"
325,0,0,55,0.979000," ","int(1/(b*x^n+a)/((d*x^n+c)^(1/n)),x)","\int \frac{\left(d \,x^{n}+c \right)^{-\frac{1}{n}}}{b \,x^{n}+a}\, dx"," ",0,"int(1/(b*x^n+a)/((d*x^n+c)^(1/n)),x)","F"
326,0,0,56,0.925000," ","int((d*x^n+c)^(-1/n+1)/(b*x^n+a)^2,x)","\int \frac{\left(d \,x^{n}+c \right)^{-\frac{1}{n}+1}}{\left(b \,x^{n}+a \right)^{2}}\, dx"," ",0,"int((d*x^n+c)^(-1/n+1)/(b*x^n+a)^2,x)","F"
327,0,0,58,0.947000," ","int((d*x^n+c)^(-1/n+2)/(b*x^n+a)^3,x)","\int \frac{\left(d \,x^{n}+c \right)^{-\frac{1}{n}+2}}{\left(b \,x^{n}+a \right)^{3}}\, dx"," ",0,"int((d*x^n+c)^(-1/n+2)/(b*x^n+a)^3,x)","F"
328,0,0,195,0.921000," ","int((b*x^n+a)^p*(d*x^n+c)^(-2-1/n-p),x)","\int \left(b \,x^{n}+a \right)^{p} \left(d \,x^{n}+c \right)^{-p -\frac{1}{n}-2}\, dx"," ",0,"int((b*x^n+a)^p*(d*x^n+c)^(-2-1/n-p),x)","F"
329,0,0,58,0.904000," ","int((b*x^n+a)^((a*d*n-b*c*(n+1))/(-a*d+b*c)/n)*(d*x^n+c)^((a*d*n-b*c*n+a*d)/(-a*d*n+b*c*n)),x)","\int \left(b \,x^{n}+a \right)^{\frac{a d n -\left(n +1\right) b c}{\left(-a d +b c \right) n}} \left(d \,x^{n}+c \right)^{\frac{a d n -b c n +a d}{-a d n +b c n}}\, dx"," ",0,"int((b*x^n+a)^((a*d*n-b*c*(n+1))/(-a*d+b*c)/n)*(d*x^n+c)^((a*d*n-b*c*n+a*d)/(-a*d*n+b*c*n)),x)","F"
330,0,0,319,0.766000," ","int((b*x^n+a)^2*(d*x^n+c)^(-1/n-4),x)","\int \left(b \,x^{n}+a \right)^{2} \left(d \,x^{n}+c \right)^{-\frac{1}{n}-4}\, dx"," ",0,"int((b*x^n+a)^2*(d*x^n+c)^(-1/n-4),x)","F"
331,0,0,127,0.632000," ","int((b*x^n+a)*(d*x^n+c)^(-1/n-3),x)","\int \left(b \,x^{n}+a \right) \left(d \,x^{n}+c \right)^{-\frac{1}{n}-3}\, dx"," ",0,"int((b*x^n+a)*(d*x^n+c)^(-1/n-3),x)","F"
332,0,0,50,0.605000," ","int((d*x^n+c)^(-1/n-2),x)","\int \left(d \,x^{n}+c \right)^{-\frac{1}{n}-2}\, dx"," ",0,"int((d*x^n+c)^(-1/n-2),x)","F"
333,0,0,97,0.836000," ","int((d*x^n+c)^(-1/n-1)/(b*x^n+a),x)","\int \frac{\left(d \,x^{n}+c \right)^{-\frac{1}{n}-1}}{b \,x^{n}+a}\, dx"," ",0,"int((d*x^n+c)^(-1/n-1)/(b*x^n+a),x)","F"
334,0,0,130,1.038000," ","int(1/(b*x^n+a)^2/((d*x^n+c)^(1/n)),x)","\int \frac{\left(d \,x^{n}+c \right)^{-\frac{1}{n}}}{\left(b \,x^{n}+a \right)^{2}}\, dx"," ",0,"int(1/(b*x^n+a)^2/((d*x^n+c)^(1/n)),x)","F"
335,0,0,129,1.131000," ","int((d*x^n+c)^(-1/n+1)/(b*x^n+a)^3,x)","\int \frac{\left(d \,x^{n}+c \right)^{-\frac{1}{n}+1}}{\left(b \,x^{n}+a \right)^{3}}\, dx"," ",0,"int((d*x^n+c)^(-1/n+1)/(b*x^n+a)^3,x)","F"
336,0,0,131,0.952000," ","int((d*x^n+c)^(-1/n+2)/(b*x^n+a)^4,x)","\int \frac{\left(d \,x^{n}+c \right)^{-\frac{1}{n}+2}}{\left(b \,x^{n}+a \right)^{4}}\, dx"," ",0,"int((d*x^n+c)^(-1/n+2)/(b*x^n+a)^4,x)","F"
337,1,92,128,0.043000," ","int(x^5*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x)","\frac{\left(d x +c \right)^{\frac{3}{2}} \left(35 b \,x^{6} d^{6}+45 a \,d^{6} x^{4}+30 b \,c^{2} d^{4} x^{4}+36 a \,c^{2} d^{4} x^{2}+24 b \,c^{4} d^{2} x^{2}+24 a \,c^{4} d^{2}+16 b \,c^{6}\right) \left(d x -c \right)^{\frac{3}{2}}}{315 d^{8}}"," ",0,"1/315*(d*x+c)^(3/2)*(35*b*d^6*x^6+45*a*d^6*x^4+30*b*c^2*d^4*x^4+36*a*c^2*d^4*x^2+24*b*c^4*d^2*x^2+24*a*c^4*d^2+16*b*c^6)*(d*x-c)^(3/2)/d^8","A"
338,1,68,91,0.046000," ","int(x^3*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x)","\frac{\left(d x +c \right)^{\frac{3}{2}} \left(15 b \,d^{4} x^{4}+21 a \,d^{4} x^{2}+12 b \,c^{2} d^{2} x^{2}+14 a \,c^{2} d^{2}+8 b \,c^{4}\right) \left(d x -c \right)^{\frac{3}{2}}}{105 d^{6}}"," ",0,"1/105*(d*x+c)^(3/2)*(15*b*d^4*x^4+21*a*d^4*x^2+12*b*c^2*d^2*x^2+14*a*c^2*d^2+8*b*c^4)*(d*x-c)^(3/2)/d^6","A"
339,1,44,55,0.046000," ","int(x*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x)","\frac{\left(d x +c \right)^{\frac{3}{2}} \left(3 b \,d^{2} x^{2}+5 a \,d^{2}+2 b \,c^{2}\right) \left(d x -c \right)^{\frac{3}{2}}}{15 d^{4}}"," ",0,"1/15*(d*x+c)^(3/2)*(3*b*d^2*x^2+5*a*d^2+2*b*c^2)*(d*x-c)^(3/2)/d^4","A"
340,1,174,66,0.101000," ","int((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x,x)","\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(3 a \,c^{2} d^{2} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)+\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, b \,d^{2} x^{2}+3 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2}\right)}{3 \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{-c^{2}}\, d^{2}}"," ",0,"1/3*(d*x-c)^(1/2)*(d*x+c)^(1/2)*(x^2*b*d^2*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)+3*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*a*c^2*d^2+3*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*a*d^2-b*c^2*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/(d^2*x^2-c^2)^(1/2)/d^2/(-c^2)^(1/2)","B"
341,1,182,80,0.067000," ","int((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^3,x)","-\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(a \,d^{2} x^{2} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-2 b \,c^{2} x^{2} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-2 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, b \,x^{2}+\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, a \right)}{2 \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{-c^{2}}\, x^{2}}"," ",0,"-1/2*(d*x-c)^(1/2)*(d*x+c)^(1/2)*(ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^2*a*d^2-2*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^2*b*c^2-2*x^2*b*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)+(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*a)/(d^2*x^2-c^2)^(1/2)/x^2/(-c^2)^(1/2)","B"
342,1,226,103,0.066000," ","int((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^5,x)","-\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(a \,d^{4} x^{4} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)+4 b \,c^{2} d^{2} x^{4} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{2} x^{2}+4 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} x^{2}+2 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, a \,c^{2}\right)}{8 \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{-c^{2}}\, c^{2} x^{4}}"," ",0,"-1/8*(d*x-c)^(1/2)*(d*x+c)^(1/2)/c^2*(ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^4*a*d^4+4*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^4*b*c^2*d^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*x^2*a*d^2+4*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*x^2*b*c^2+2*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*a*c^2)/(d^2*x^2-c^2)^(1/2)/x^4/(-c^2)^(1/2)","B"
343,1,298,178,0.095000," ","int(x^4*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x)","\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(48 \sqrt{d^{2} x^{2}-c^{2}}\, b \,d^{7} x^{7} \mathrm{csgn}\left(d \right)+64 \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{7} x^{5} \mathrm{csgn}\left(d \right)-8 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} d^{5} x^{5} \mathrm{csgn}\left(d \right)-16 \sqrt{d^{2} x^{2}-c^{2}}\, a \,c^{2} d^{5} x^{3} \mathrm{csgn}\left(d \right)-10 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{4} d^{3} x^{3} \mathrm{csgn}\left(d \right)-24 a \,c^{6} d^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-24 \sqrt{d^{2} x^{2}-c^{2}}\, a \,c^{4} d^{3} x \,\mathrm{csgn}\left(d \right)-15 b \,c^{8} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-15 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{6} d x \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{384 \sqrt{d^{2} x^{2}-c^{2}}\, d^{7}}"," ",0,"1/384*(d*x-c)^(1/2)*(d*x+c)^(1/2)*(48*csgn(d)*x^7*b*d^7*(d^2*x^2-c^2)^(1/2)+64*csgn(d)*x^5*a*d^7*(d^2*x^2-c^2)^(1/2)-8*csgn(d)*x^5*b*c^2*d^5*(d^2*x^2-c^2)^(1/2)-16*csgn(d)*x^3*a*c^2*d^5*(d^2*x^2-c^2)^(1/2)-10*csgn(d)*x^3*b*c^4*d^3*(d^2*x^2-c^2)^(1/2)-24*csgn(d)*d^3*(d^2*x^2-c^2)^(1/2)*x*a*c^4-15*csgn(d)*d*(d^2*x^2-c^2)^(1/2)*x*b*c^6-24*ln((csgn(d)*(d^2*x^2-c^2)^(1/2)+d*x)*csgn(d))*a*c^6*d^2-15*ln((csgn(d)*(d^2*x^2-c^2)^(1/2)+d*x)*csgn(d))*b*c^8)*csgn(d)/(d^2*x^2-c^2)^(1/2)/d^7","C"
344,1,240,135,0.067000," ","int(x^2*(b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x)","\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(8 \sqrt{d^{2} x^{2}-c^{2}}\, b \,d^{5} x^{5} \mathrm{csgn}\left(d \right)+12 \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{5} x^{3} \mathrm{csgn}\left(d \right)-2 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} d^{3} x^{3} \mathrm{csgn}\left(d \right)-6 a \,c^{4} d^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-6 \sqrt{d^{2} x^{2}-c^{2}}\, a \,c^{2} d^{3} x \,\mathrm{csgn}\left(d \right)-3 b \,c^{6} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-3 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{4} d x \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{48 \sqrt{d^{2} x^{2}-c^{2}}\, d^{5}}"," ",0,"1/48*(d*x-c)^(1/2)*(d*x+c)^(1/2)*(8*csgn(d)*x^5*b*d^5*(d^2*x^2-c^2)^(1/2)+12*csgn(d)*x^3*a*d^5*(d^2*x^2-c^2)^(1/2)-2*csgn(d)*x^3*b*c^2*d^3*(d^2*x^2-c^2)^(1/2)-6*csgn(d)*d^3*(d^2*x^2-c^2)^(1/2)*x*a*c^2-3*csgn(d)*d*(d^2*x^2-c^2)^(1/2)*x*b*c^4-6*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*a*c^4*d^2-3*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*b*c^6)*csgn(d)/(d^2*x^2-c^2)^(1/2)/d^5","C"
345,1,182,96,0.059000," ","int((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2),x)","\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(2 \sqrt{d^{2} x^{2}-c^{2}}\, b \,d^{3} x^{3} \mathrm{csgn}\left(d \right)-4 a \,c^{2} d^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+4 \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{3} x \,\mathrm{csgn}\left(d \right)-b \,c^{4} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-\sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} d x \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{8 \sqrt{d^{2} x^{2}-c^{2}}\, d^{3}}"," ",0,"1/8*(d*x-c)^(1/2)*(d*x+c)^(1/2)*(2*csgn(d)*x^3*b*d^3*(d^2*x^2-c^2)^(1/2)+4*csgn(d)*d^3*(d^2*x^2-c^2)^(1/2)*x*a-csgn(d)*d*(d^2*x^2-c^2)^(1/2)*x*b*c^2-4*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*a*c^2*d^2-ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*b*c^4)*csgn(d)/(d^2*x^2-c^2)^(1/2)/d^3","C"
346,1,153,90,0.064000," ","int((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^2,x)","\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(2 a \,d^{2} x \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-b \,c^{2} x \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+\sqrt{d^{2} x^{2}-c^{2}}\, b d \,x^{2} \mathrm{csgn}\left(d \right)-2 \sqrt{d^{2} x^{2}-c^{2}}\, a d \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{2 \sqrt{d^{2} x^{2}-c^{2}}\, d x}"," ",0,"1/2*(d*x-c)^(1/2)*(d*x+c)^(1/2)*(csgn(d)*x^2*b*d*(d^2*x^2-c^2)^(1/2)+2*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*x*a*d^2-ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*x*b*c^2-2*csgn(d)*d*(d^2*x^2-c^2)^(1/2)*a)*csgn(d)/(d^2*x^2-c^2)^(1/2)/x/d","C"
347,1,153,70,0.066000," ","int((b*x^2+a)*(d*x-c)^(1/2)*(d*x+c)^(1/2)/x^4,x)","\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(3 b \,c^{2} d \,x^{3} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+\sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{2} x^{2} \mathrm{csgn}\left(d \right)-3 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} x^{2} \mathrm{csgn}\left(d \right)-\sqrt{d^{2} x^{2}-c^{2}}\, a \,c^{2} \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{3 \sqrt{d^{2} x^{2}-c^{2}}\, c^{2} x^{3}}"," ",0,"1/3*(d*x-c)^(1/2)*(d*x+c)^(1/2)*(3*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*x^3*b*c^2*d+csgn(d)*x^2*a*d^2*(d^2*x^2-c^2)^(1/2)-3*csgn(d)*x^2*b*c^2*(d^2*x^2-c^2)^(1/2)-csgn(d)*a*c^2*(d^2*x^2-c^2)^(1/2))*csgn(d)/(d^2*x^2-c^2)^(1/2)/c^2/x^3","C"
348,1,191,105,0.106000," ","int(x^4*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x)","\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(8 \sqrt{c^{2} x^{2}-1}\, b \,c^{5} x^{5} \mathrm{csgn}\left(c \right)+12 \sqrt{c^{2} x^{2}-1}\, a \,c^{5} x^{3} \mathrm{csgn}\left(c \right)+10 \sqrt{c^{2} x^{2}-1}\, b \,c^{3} x^{3} \mathrm{csgn}\left(c \right)+18 \sqrt{c^{2} x^{2}-1}\, a \,c^{3} x \,\mathrm{csgn}\left(c \right)+18 a \,c^{2} \ln \left(\left(c x +\sqrt{c^{2} x^{2}-1}\, \mathrm{csgn}\left(c \right)\right) \mathrm{csgn}\left(c \right)\right)+15 \sqrt{c^{2} x^{2}-1}\, b c x \,\mathrm{csgn}\left(c \right)+15 b \ln \left(\left(c x +\sqrt{c^{2} x^{2}-1}\, \mathrm{csgn}\left(c \right)\right) \mathrm{csgn}\left(c \right)\right)\right) \mathrm{csgn}\left(c \right)}{48 \sqrt{c^{2} x^{2}-1}\, c^{7}}"," ",0,"1/48*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(8*csgn(c)*x^5*b*c^5*(c^2*x^2-1)^(1/2)+12*csgn(c)*x^3*a*c^5*(c^2*x^2-1)^(1/2)+10*(c^2*x^2-1)^(1/2)*csgn(c)*c^3*x^3*b+18*(c^2*x^2-1)^(1/2)*csgn(c)*c^3*x*a+15*(c^2*x^2-1)^(1/2)*csgn(c)*c*x*b+18*ln(((c^2*x^2-1)^(1/2)*csgn(c)+c*x)*csgn(c))*a*c^2+15*ln(((c^2*x^2-1)^(1/2)*csgn(c)+c*x)*csgn(c))*b)*csgn(c)/c^7/(c^2*x^2-1)^(1/2)","C"
349,1,57,85,0.046000," ","int(x^3*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x)","\frac{\sqrt{c x +1}\, \sqrt{c x -1}\, \left(3 b \,x^{4} c^{4}+5 a \,c^{4} x^{2}+4 b \,c^{2} x^{2}+10 a \,c^{2}+8 b \right)}{15 c^{6}}"," ",0,"1/15*(c*x+1)^(1/2)*(c*x-1)^(1/2)*(3*b*c^4*x^4+5*a*c^4*x^2+4*b*c^2*x^2+10*a*c^2+8*b)/c^6","A"
350,1,147,73,0.078000," ","int(x^2*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x)","\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(2 \sqrt{c^{2} x^{2}-1}\, b \,c^{3} x^{3} \mathrm{csgn}\left(c \right)+4 \sqrt{c^{2} x^{2}-1}\, a \,c^{3} x \,\mathrm{csgn}\left(c \right)+4 a \,c^{2} \ln \left(\left(c x +\sqrt{c^{2} x^{2}-1}\, \mathrm{csgn}\left(c \right)\right) \mathrm{csgn}\left(c \right)\right)+3 \sqrt{c^{2} x^{2}-1}\, b c x \,\mathrm{csgn}\left(c \right)+3 b \ln \left(\left(c x +\sqrt{c^{2} x^{2}-1}\, \mathrm{csgn}\left(c \right)\right) \mathrm{csgn}\left(c \right)\right)\right) \mathrm{csgn}\left(c \right)}{8 \sqrt{c^{2} x^{2}-1}\, c^{5}}"," ",0,"1/8*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(2*(c^2*x^2-1)^(1/2)*b*c^3*x^3*csgn(c)+4*(c^2*x^2-1)^(1/2)*a*c^3*x*csgn(c)+3*(c^2*x^2-1)^(1/2)*b*c*x*csgn(c)+4*a*c^2*ln((c*x+(c^2*x^2-1)^(1/2)*csgn(c))*csgn(c))+3*b*ln((c*x+(c^2*x^2-1)^(1/2)*csgn(c))*csgn(c)))*csgn(c)/c^5/(c^2*x^2-1)^(1/2)","C"
351,1,38,53,0.044000," ","int(x*(b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x)","\frac{\sqrt{c x +1}\, \sqrt{c x -1}\, \left(b \,c^{2} x^{2}+3 a \,c^{2}+2 b \right)}{3 c^{4}}"," ",0,"1/3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*(b*c^2*x^2+3*a*c^2+2*b)/c^4","A"
352,1,103,39,0.066000," ","int((b*x^2+a)/(c*x-1)^(1/2)/(c*x+1)^(1/2),x)","\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(2 a \,c^{2} \ln \left(\left(c x +\sqrt{c^{2} x^{2}-1}\, \mathrm{csgn}\left(c \right)\right) \mathrm{csgn}\left(c \right)\right)+\sqrt{c^{2} x^{2}-1}\, b c x \,\mathrm{csgn}\left(c \right)+b \ln \left(\left(c x +\sqrt{c^{2} x^{2}-1}\, \mathrm{csgn}\left(c \right)\right) \mathrm{csgn}\left(c \right)\right)\right) \mathrm{csgn}\left(c \right)}{2 \sqrt{c^{2} x^{2}-1}\, c^{3}}"," ",0,"1/2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*((c^2*x^2-1)^(1/2)*b*c*x*csgn(c)+2*a*c^2*ln((c*x+(c^2*x^2-1)^(1/2)*csgn(c))*csgn(c))+b*ln((c*x+(c^2*x^2-1)^(1/2)*csgn(c))*csgn(c)))*csgn(c)/c^3/(c^2*x^2-1)^(1/2)","C"
353,1,62,38,0.072000," ","int((b*x^2+a)/x/(c*x-1)^(1/2)/(c*x+1)^(1/2),x)","\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(-a \,c^{2} \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)+\sqrt{c^{2} x^{2}-1}\, b \right)}{\sqrt{c^{2} x^{2}-1}\, c^{2}}"," ",0,"(c*x-1)^(1/2)*(c*x+1)^(1/2)*(-arctan(1/(c^2*x^2-1)^(1/2))*a*c^2+(c^2*x^2-1)^(1/2)*b)/(c^2*x^2-1)^(1/2)/c^2","A"
354,1,77,29,0.072000," ","int((b*x^2+a)/x^2/(c*x-1)^(1/2)/(c*x+1)^(1/2),x)","\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(\sqrt{c^{2} x^{2}-1}\, a c \,\mathrm{csgn}\left(c \right)+b x \ln \left(\left(c x +\sqrt{c^{2} x^{2}-1}\, \mathrm{csgn}\left(c \right)\right) \mathrm{csgn}\left(c \right)\right)\right) \mathrm{csgn}\left(c \right)}{\sqrt{c^{2} x^{2}-1}\, c x}"," ",0,"(c*x-1)^(1/2)*(c*x+1)^(1/2)*(csgn(c)*c*(c^2*x^2-1)^(1/2)*a+ln((c*x+(c^2*x^2-1)^(1/2)*csgn(c))*csgn(c))*x*b)*csgn(c)/(c^2*x^2-1)^(1/2)/c/x","C"
355,1,84,48,0.082000," ","int((b*x^2+a)/x^3/(c*x-1)^(1/2)/(c*x+1)^(1/2),x)","-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(a \,c^{2} x^{2} \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)+2 b \,x^{2} \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)-\sqrt{c^{2} x^{2}-1}\, a \right)}{2 \sqrt{c^{2} x^{2}-1}\, x^{2}}"," ",0,"-1/2*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(arctan(1/(c^2*x^2-1)^(1/2))*x^2*a*c^2+2*arctan(1/(c^2*x^2-1)^(1/2))*x^2*b-(c^2*x^2-1)^(1/2)*a)/(c^2*x^2-1)^(1/2)/x^2","A"
356,1,37,50,0.050000," ","int((b*x^2+a)/x^4/(c*x-1)^(1/2)/(c*x+1)^(1/2),x)","\frac{\sqrt{c x +1}\, \sqrt{c x -1}\, \left(2 a \,c^{2} x^{2}+3 b \,x^{2}+a \right)}{3 x^{3}}"," ",0,"1/3*(c*x+1)^(1/2)*(c*x-1)^(1/2)*(2*a*c^2*x^2+3*b*x^2+a)/x^3","A"
357,1,125,81,0.074000," ","int((b*x^2+a)/x^5/(c*x-1)^(1/2)/(c*x+1)^(1/2),x)","-\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(3 a \,c^{4} x^{4} \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)+4 b \,c^{2} x^{4} \arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)-3 \sqrt{c^{2} x^{2}-1}\, a \,c^{2} x^{2}-4 \sqrt{c^{2} x^{2}-1}\, b \,x^{2}-2 \sqrt{c^{2} x^{2}-1}\, a \right)}{8 \sqrt{c^{2} x^{2}-1}\, x^{4}}"," ",0,"-1/8*(c*x-1)^(1/2)*(c*x+1)^(1/2)*(3*arctan(1/(c^2*x^2-1)^(1/2))*x^4*a*c^4+4*arctan(1/(c^2*x^2-1)^(1/2))*x^4*b*c^2-3*(c^2*x^2-1)^(1/2)*x^2*a*c^2-4*(c^2*x^2-1)^(1/2)*x^2*b-2*(c^2*x^2-1)^(1/2)*a)/(c^2*x^2-1)^(1/2)/x^4","A"
358,1,240,140,0.099000," ","int(x^4*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x)","\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(8 \sqrt{d^{2} x^{2}-c^{2}}\, b \,d^{5} x^{5} \mathrm{csgn}\left(d \right)+12 \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{5} x^{3} \mathrm{csgn}\left(d \right)+10 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} d^{3} x^{3} \mathrm{csgn}\left(d \right)+18 a \,c^{4} d^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+18 \sqrt{d^{2} x^{2}-c^{2}}\, a \,c^{2} d^{3} x \,\mathrm{csgn}\left(d \right)+15 b \,c^{6} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+15 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{4} d x \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{48 \sqrt{d^{2} x^{2}-c^{2}}\, d^{7}}"," ",0,"1/48*(d*x-c)^(1/2)*(d*x+c)^(1/2)*(8*(d^2*x^2-c^2)^(1/2)*b*d^5*x^5*csgn(d)+12*(d^2*x^2-c^2)^(1/2)*a*d^5*x^3*csgn(d)+10*(d^2*x^2-c^2)^(1/2)*b*c^2*d^3*x^3*csgn(d)+18*(d^2*x^2-c^2)^(1/2)*a*c^2*d^3*x*csgn(d)+15*(d^2*x^2-c^2)^(1/2)*b*c^4*d*x*csgn(d)+18*a*c^4*d^2*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))+15*b*c^6*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d)))*csgn(d)/d^7/(d^2*x^2-c^2)^(1/2)","C"
359,1,68,100,0.046000," ","int(x^3*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x)","\frac{\sqrt{d x +c}\, \left(3 b \,d^{4} x^{4}+5 a \,d^{4} x^{2}+4 b \,c^{2} d^{2} x^{2}+10 a \,c^{2} d^{2}+8 b \,c^{4}\right) \sqrt{d x -c}}{15 d^{6}}"," ",0,"1/15*(d*x+c)^(1/2)*(3*b*d^4*x^4+5*a*d^4*x^2+4*b*c^2*d^2*x^2+10*a*c^2*d^2+8*b*c^4)/d^6*(d*x-c)^(1/2)","A"
360,1,182,100,0.075000," ","int(x^2*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x)","\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(2 \sqrt{d^{2} x^{2}-c^{2}}\, b \,d^{3} x^{3} \mathrm{csgn}\left(d \right)+4 a \,c^{2} d^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+4 \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{3} x \,\mathrm{csgn}\left(d \right)+3 b \,c^{4} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+3 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} d x \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{8 \sqrt{d^{2} x^{2}-c^{2}}\, d^{5}}"," ",0,"1/8*(d*x-c)^(1/2)*(d*x+c)^(1/2)*(2*(d^2*x^2-c^2)^(1/2)*b*d^3*x^3*csgn(d)+4*(d^2*x^2-c^2)^(1/2)*a*d^3*x*csgn(d)+3*(d^2*x^2-c^2)^(1/2)*b*c^2*d*x*csgn(d)+4*a*c^2*d^2*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))+3*b*c^4*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d)))*csgn(d)/d^5/(d^2*x^2-c^2)^(1/2)","C"
361,1,43,60,0.040000," ","int(x*(b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x)","\frac{\sqrt{d x +c}\, \left(b \,d^{2} x^{2}+3 a \,d^{2}+2 b \,c^{2}\right) \sqrt{d x -c}}{3 d^{4}}"," ",0,"1/3*(d*x+c)^(1/2)*(b*d^2*x^2+3*a*d^2+2*b*c^2)/d^4*(d*x-c)^(1/2)","A"
362,1,124,58,0.071000," ","int((b*x^2+a)/(d*x-c)^(1/2)/(d*x+c)^(1/2),x)","\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(2 a \,d^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+b \,c^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+\sqrt{d^{2} x^{2}-c^{2}}\, b d x \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{2 \sqrt{d^{2} x^{2}-c^{2}}\, d^{3}}"," ",0,"1/2*(d*x-c)^(1/2)*(d*x+c)^(1/2)/d^3*((d^2*x^2-c^2)^(1/2)*csgn(d)*d*x*b+ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*b*c^2+2*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*a*d^2)/(d^2*x^2-c^2)^(1/2)*csgn(d)","C"
363,1,108,48,0.077000," ","int((b*x^2+a)/x/(d*x-c)^(1/2)/(d*x+c)^(1/2),x)","\frac{\left(-a \,d^{2} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)+\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, b \right) \sqrt{d x -c}\, \sqrt{d x +c}}{\sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{-c^{2}}\, d^{2}}"," ",0,"(-ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*a*d^2+b*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))*(d*x-c)^(1/2)*(d*x+c)^(1/2)/(d^2*x^2-c^2)^(1/2)/d^2/(-c^2)^(1/2)","B"
364,1,97,49,0.069000," ","int((b*x^2+a)/x^2/(d*x-c)^(1/2)/(d*x+c)^(1/2),x)","\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(b \,c^{2} x \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+\sqrt{d^{2} x^{2}-c^{2}}\, a d \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{\sqrt{d^{2} x^{2}-c^{2}}\, c^{2} d x}"," ",0,"(d*x-c)^(1/2)*(d*x+c)^(1/2)/c^2*(b*c^2*x*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))+(d^2*x^2-c^2)^(1/2)*a*d*csgn(d))*csgn(d)/(d^2*x^2-c^2)^(1/2)/d/x","C"
365,1,158,64,0.072000," ","int((b*x^2+a)/x^3/(d*x-c)^(1/2)/(d*x+c)^(1/2),x)","-\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(a \,d^{2} x^{2} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)+2 b \,c^{2} x^{2} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, a \right)}{2 \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{-c^{2}}\, c^{2} x^{2}}"," ",0,"-1/2*(d*x-c)^(1/2)*(d*x+c)^(1/2)/c^2*(a*d^2*x^2*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)+2*b*c^2*x^2*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*a)/(d^2*x^2-c^2)^(1/2)/x^2/(-c^2)^(1/2)","B"
366,1,49,63,0.041000," ","int((b*x^2+a)/x^4/(d*x-c)^(1/2)/(d*x+c)^(1/2),x)","\frac{\sqrt{d x +c}\, \left(2 a \,d^{2} x^{2}+3 b \,c^{2} x^{2}+a \,c^{2}\right) \sqrt{d x -c}}{3 c^{4} x^{3}}"," ",0,"1/3*(d*x+c)^(1/2)*(2*a*d^2*x^2+3*b*c^2*x^2+a*c^2)/x^3/c^4*(d*x-c)^(1/2)","A"
367,1,227,105,0.070000," ","int((b*x^2+a)/x^5/(d*x-c)^(1/2)/(d*x+c)^(1/2),x)","-\frac{\sqrt{d x -c}\, \sqrt{d x +c}\, \left(3 a \,d^{4} x^{4} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)+4 b \,c^{2} d^{2} x^{4} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-3 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{2} x^{2}-4 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} x^{2}-2 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, a \,c^{2}\right)}{8 \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{-c^{2}}\, c^{4} x^{4}}"," ",0,"-1/8*(d*x-c)^(1/2)*(d*x+c)^(1/2)/c^4*(3*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^4*a*d^4+4*b*c^2*d^2*x^4*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)-3*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*x^2*a*d^2-4*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*x^2*b*c^2-2*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*a*c^2)/(d^2*x^2-c^2)^(1/2)/x^4/(-c^2)^(1/2)","B"
368,1,316,137,0.087000," ","int(x^4*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x)","\frac{\left(2 \sqrt{d^{2} x^{2}-c^{2}}\, b \,d^{5} x^{5} \mathrm{csgn}\left(d \right)+12 a \,c^{2} d^{4} x^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+4 \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{5} x^{3} \mathrm{csgn}\left(d \right)+15 b \,c^{4} d^{2} x^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+5 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} d^{3} x^{3} \mathrm{csgn}\left(d \right)-12 a \,c^{4} d^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-12 \sqrt{d^{2} x^{2}-c^{2}}\, a \,c^{2} d^{3} x \,\mathrm{csgn}\left(d \right)-15 b \,c^{6} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-15 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{4} d x \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{8 \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{d x +c}\, \sqrt{d x -c}\, d^{7}}"," ",0,"1/8*(2*(d^2*x^2-c^2)^(1/2)*b*d^5*x^5*csgn(d)+4*(d^2*x^2-c^2)^(1/2)*a*d^5*x^3*csgn(d)+5*(d^2*x^2-c^2)^(1/2)*b*c^2*d^3*x^3*csgn(d)+12*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*x^2*a*c^2*d^4+15*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*x^2*b*c^4*d^2-12*(d^2*x^2-c^2)^(1/2)*a*c^2*d^3*x*csgn(d)-15*(d^2*x^2-c^2)^(1/2)*b*c^4*d*x*csgn(d)-12*a*c^4*d^2*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))-15*b*c^6*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d)))*csgn(d)/(d^2*x^2-c^2)^(1/2)/d^7/(d*x+c)^(1/2)/(d*x-c)^(1/2)","C"
369,1,68,97,0.049000," ","int(x^3*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x)","-\frac{-b \,d^{4} x^{4}-3 a \,d^{4} x^{2}-4 b \,c^{2} d^{2} x^{2}+6 a \,c^{2} d^{2}+8 b \,c^{4}}{3 \sqrt{d x +c}\, \sqrt{d x -c}\, d^{6}}"," ",0,"-1/3*(-b*d^4*x^4-3*a*d^4*x^2-4*b*c^2*d^2*x^2+6*a*c^2*d^2+8*b*c^4)/(d*x+c)^(1/2)/d^6/(d*x-c)^(1/2)","A"
370,1,254,130,0.077000," ","int(x^2*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x)","\frac{\left(2 a \,d^{4} x^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+3 b \,c^{2} d^{2} x^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)+\sqrt{d^{2} x^{2}-c^{2}}\, b \,d^{3} x^{3} \mathrm{csgn}\left(d \right)-2 a \,c^{2} d^{2} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-2 \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{3} x \,\mathrm{csgn}\left(d \right)-3 b \,c^{4} \ln \left(\left(d x +\sqrt{d^{2} x^{2}-c^{2}}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-3 \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} d x \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{2 \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{d x +c}\, \sqrt{d x -c}\, d^{5}}"," ",0,"1/2*((d^2*x^2-c^2)^(1/2)*b*d^3*x^3*csgn(d)+2*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*x^2*a*d^4+3*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))*x^2*b*c^2*d^2-2*(d^2*x^2-c^2)^(1/2)*a*d^3*x*csgn(d)-3*(d^2*x^2-c^2)^(1/2)*b*c^2*d*x*csgn(d)-2*a*c^2*d^2*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d))-3*b*c^4*ln((d*x+(d^2*x^2-c^2)^(1/2)*csgn(d))*csgn(d)))*csgn(d)/(d^2*x^2-c^2)^(1/2)/d^5/(d*x+c)^(1/2)/(d*x-c)^(1/2)","C"
371,1,43,68,0.043000," ","int(x*(b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x)","-\frac{-b \,d^{2} x^{2}+a \,d^{2}+2 b \,c^{2}}{\sqrt{d x +c}\, \sqrt{d x -c}\, d^{4}}"," ",0,"-(-b*d^2*x^2+a*d^2+2*b*c^2)/(d*x+c)^(1/2)/d^4/(d*x-c)^(1/2)","A"
372,1,160,55,0.073000," ","int((b*x^2+a)/(d*x-c)^(3/2)/(d*x+c)^(3/2),x)","\frac{\left(b \,c^{2} d^{2} x^{2} \ln \left(\left(d x +\sqrt{\left(d x -c \right) \left(d x +c \right)}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-\sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{3} x \,\mathrm{csgn}\left(d \right)-b \,c^{4} \ln \left(\left(d x +\sqrt{\left(d x -c \right) \left(d x +c \right)}\, \mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)\right)-\sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} d x \,\mathrm{csgn}\left(d \right)\right) \mathrm{csgn}\left(d \right)}{\sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{d x +c}\, \sqrt{d x -c}\, c^{2} d^{3}}"," ",0,"(ln((csgn(d)*((d*x-c)*(d*x+c))^(1/2)+d*x)*csgn(d))*x^2*b*c^2*d^2-(d^2*x^2-c^2)^(1/2)*a*d^3*x*csgn(d)-(d^2*x^2-c^2)^(1/2)*b*c^2*d*x*csgn(d)-ln((csgn(d)*((d*x-c)*(d*x+c))^(1/2)+d*x)*csgn(d))*b*c^4)*csgn(d)/(d^2*x^2-c^2)^(1/2)/c^2/d^3/(d*x+c)^(1/2)/(d*x-c)^(1/2)","C"
373,1,188,58,0.076000," ","int((b*x^2+a)/x/(d*x-c)^(3/2)/(d*x+c)^(3/2),x)","\frac{a \,d^{4} x^{2} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-a \,c^{2} d^{2} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2}}{\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{d x +c}\, \sqrt{d x -c}\, c^{2} d^{2}}"," ",0,"1/c^2*(ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^2*a*d^4-ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*a*c^2*d^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*a*d^2-b*c^2*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/(-c^2)^(1/2)/(d^2*x^2-c^2)^(1/2)/d^2/(d*x+c)^(1/2)/(d*x-c)^(1/2)","B"
374,1,48,59,0.050000," ","int((b*x^2+a)/x^2/(d*x-c)^(3/2)/(d*x+c)^(3/2),x)","\frac{-2 a \,d^{2} x^{2}-b \,c^{2} x^{2}+a \,c^{2}}{\sqrt{d x +c}\, \sqrt{d x -c}\, c^{4} x}"," ",0,"(-2*a*d^2*x^2-b*c^2*x^2+a*c^2)/(d*x+c)^(1/2)/x/c^4/(d*x-c)^(1/2)","A"
375,1,315,99,0.091000," ","int((b*x^2+a)/x^3/(d*x-c)^(3/2)/(d*x+c)^(3/2),x)","\frac{3 a \,d^{4} x^{4} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)+2 b \,c^{2} d^{2} x^{4} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-3 a \,c^{2} d^{2} x^{2} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-2 b \,c^{4} x^{2} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-3 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{2} x^{2}-2 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} x^{2}+\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, a \,c^{2}}{2 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{d x +c}\, \sqrt{d x -c}\, c^{4} x^{2}}"," ",0,"1/2/c^4*(3*a*d^4*x^4*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)+2*b*c^2*d^2*x^4*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)-3*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^2*a*c^2*d^2-2*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^2*b*c^4-3*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*a*d^2*x^2-2*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*b*c^2*x^2+(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*a*c^2)/(-c^2)^(1/2)/x^2/(d^2*x^2-c^2)^(1/2)/(d*x+c)^(1/2)/(d*x-c)^(1/2)","B"
376,1,73,101,0.046000," ","int((b*x^2+a)/x^4/(d*x-c)^(3/2)/(d*x+c)^(3/2),x)","\frac{-8 a \,d^{4} x^{4}-6 b \,c^{2} d^{2} x^{4}+4 a \,c^{2} d^{2} x^{2}+3 b \,c^{4} x^{2}+a \,c^{4}}{3 \sqrt{d x +c}\, \sqrt{d x -c}\, c^{6} x^{3}}"," ",0,"1/3*(-8*a*d^4*x^4-6*b*c^2*d^2*x^4+4*a*c^2*d^2*x^2+3*b*c^4*x^2+a*c^4)/(d*x+c)^(1/2)/x^3/c^6/(d*x-c)^(1/2)","A"
377,1,387,142,0.084000," ","int((b*x^2+a)/x^5/(d*x-c)^(3/2)/(d*x+c)^(3/2),x)","\frac{15 a \,d^{6} x^{6} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)+12 b \,c^{2} d^{4} x^{6} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-15 a \,c^{2} d^{4} x^{4} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-12 b \,c^{4} d^{2} x^{4} \ln \left(-\frac{2 \left(c^{2}-\sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\right)}{x}\right)-15 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, a \,d^{4} x^{4}-12 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, b \,c^{2} d^{2} x^{4}+5 \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{-c^{2}}\, a \,c^{2} d^{2} x^{2}+4 \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{-c^{2}}\, b \,c^{4} x^{2}+2 \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{-c^{2}}\, a \,c^{4}}{8 \sqrt{-c^{2}}\, \sqrt{d^{2} x^{2}-c^{2}}\, \sqrt{d x +c}\, \sqrt{d x -c}\, c^{6} x^{4}}"," ",0,"1/8/c^6*(15*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^6*a*d^6+12*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^6*b*c^2*d^4-15*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^4*a*c^2*d^4-12*ln(-2*(c^2-(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2))/x)*x^4*b*c^4*d^2-15*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*x^4*a*d^4-12*(-c^2)^(1/2)*(d^2*x^2-c^2)^(1/2)*x^4*b*c^2*d^2+5*x^2*a*c^2*d^2*(d^2*x^2-c^2)^(1/2)*(-c^2)^(1/2)+4*x^2*b*c^4*(d^2*x^2-c^2)^(1/2)*(-c^2)^(1/2)+2*a*c^4*(d^2*x^2-c^2)^(1/2)*(-c^2)^(1/2))/(-c^2)^(1/2)/x^4/(d^2*x^2-c^2)^(1/2)/(d*x+c)^(1/2)/(d*x-c)^(1/2)","B"
378,1,53,32,0.069000," ","int((c^2*x^2+1)/x/(c*x-1)^(1/2)/(c*x+1)^(1/2),x)","\frac{\sqrt{c x -1}\, \sqrt{c x +1}\, \left(-\arctan \left(\frac{1}{\sqrt{c^{2} x^{2}-1}}\right)+\sqrt{c^{2} x^{2}-1}\right)}{\sqrt{c^{2} x^{2}-1}}"," ",0,"(c*x-1)^(1/2)*(c*x+1)^(1/2)/(c^2*x^2-1)^(1/2)*((c^2*x^2-1)^(1/2)-arctan(1/(c^2*x^2-1)^(1/2)))","A"
379,1,66,50,0.053000," ","int((d*x^2+c)/(x^((a^2*d+2*b^2*c)/(a^2*d+b^2*c)))/(b*x-a)^(1/2)/(b*x+a)^(1/2),x)","\frac{\left(a^{2} d +b^{2} c \right) \sqrt{b x +a}\, \sqrt{b x -a}\, x \,x^{-\frac{a^{2} d +2 b^{2} c}{a^{2} d +b^{2} c}}}{a^{2} b^{2}}"," ",0,"x*(a^2*d+b^2*c)*(b*x+a)^(1/2)/b^2/a^2/(x^((a^2*d+2*b^2*c)/(a^2*d+b^2*c)))*(b*x-a)^(1/2)","A"
380,0,0,26,0.857000," ","int(1/(x+1)^(1/2)/(-1-x^(1/2))^(1/2)/(-1+x^(1/2))^(1/2),x)","\int \frac{1}{\sqrt{x +1}\, \sqrt{-\sqrt{x}-1}\, \sqrt{\sqrt{x}-1}}\, dx"," ",0,"int(1/(x+1)^(1/2)/(-1-x^(1/2))^(1/2)/(-1+x^(1/2))^(1/2),x)","F"
381,0,0,61,0.877000," ","int(1/(b^2*x+a^2)^(1/2)/(a-b*x^(1/2))^(1/2)/(b*x^(1/2)+a)^(1/2),x)","\int \frac{1}{\sqrt{b^{2} x +a^{2}}\, \sqrt{-b \sqrt{x}+a}\, \sqrt{b \sqrt{x}+a}}\, dx"," ",0,"int(1/(b^2*x+a^2)^(1/2)/(a-b*x^(1/2))^(1/2)/(b*x^(1/2)+a)^(1/2),x)","F"
382,0,0,109,1.602000," ","int((-b*x^n+a)^p*(b*x^n+a)^p*(c+d*x^(2*n))^q,x)","\int \left(-b \,x^{n}+a \right)^{p} \left(b \,x^{n}+a \right)^{p} \left(d \,x^{2 n}+c \right)^{q}\, dx"," ",0,"int((-b*x^n+a)^p*(b*x^n+a)^p*(c+d*x^(2*n))^q,x)","F"
383,0,0,85,1.495000," ","int((-b*x^n+a)^p*(b*x^n+a)^p*(a^2+b^2*x^(2*n))^p,x)","\int \left(-b \,x^{n}+a \right)^{p} \left(b \,x^{n}+a \right)^{p} \left(b^{2} x^{2 n}+a^{2}\right)^{p}\, dx"," ",0,"int((-b*x^n+a)^p*(b*x^n+a)^p*(a^2+b^2*x^(2*n))^p,x)","F"
384,0,0,72,1.225000," ","int((d*x^(2*n)+c)^p/(-b*x^n+a)/(b*x^n+a),x)","\int \frac{\left(d \,x^{2 n}+c \right)^{p}}{\left(-b \,x^{n}+a \right) \left(b \,x^{n}+a \right)}\, dx"," ",0,"int((d*x^(2*n)+c)^p/(-b*x^n+a)/(b*x^n+a),x)","F"
385,0,0,93,2.167000," ","int((a-b*x^(1/2*n))^p*(a+b*x^(1/2*n))^p*(a^2*d*(p+1)/b^2/(1+(-n*p-2*n-1)/n)+d*x^n)^((-n*p-2*n-1)/n),x)","\int \left(-b \,x^{\frac{n}{2}}+a \right)^{p} \left(b \,x^{\frac{n}{2}}+a \right)^{p} \left(d \,x^{n}+\frac{\left(p +1\right) a^{2} d}{\left(\frac{-n p -2 n -1}{n}+1\right) b^{2}}\right)^{\frac{-n p -2 n -1}{n}}\, dx"," ",0,"int((a-b*x^(1/2*n))^p*(a+b*x^(1/2*n))^p*(a^2*d*(p+1)/b^2/(1+(-n*p-2*n-1)/n)+d*x^n)^((-n*p-2*n-1)/n),x)","F"