1,1,145,0,0.1777376,"\int \frac{1}{\left(2^{2/3}+x\right) \sqrt{1+x^3}} \, dx","Int[1/((2^(2/3) + x)*Sqrt[1 + x^3]),x]","\frac{2 \sqrt[3]{2} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right),-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{3 \sqrt{3}}","\frac{2 \sqrt[3]{2} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right),-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{3 \sqrt{3}}",1,"(2*ArcTan[(Sqrt[3]*(1 + 2^(1/3)*x))/Sqrt[1 + x^3]])/(3*Sqrt[3]) + (2*2^(1/3)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,19,0.2105,1,"{2134, 218, 2137, 203}"
2,1,160,0,0.1902676,"\int \frac{1}{\left(2^{2/3}-x\right) \sqrt{1-x^3}} \, dx","Int[1/((2^(2/3) - x)*Sqrt[1 - x^3]),x]","-\frac{2 \sqrt[3]{2} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right),-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{3 \sqrt{3}}","-\frac{2 \sqrt[3]{2} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right),-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{3 \sqrt{3}}",1,"(-2*ArcTan[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[1 - x^3]])/(3*Sqrt[3]) - (2*2^(1/3)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",4,4,23,0.1739,1,"{2134, 218, 2137, 203}"
3,1,163,0,0.1889601,"\int \frac{1}{\left(2^{2/3}-x\right) \sqrt{-1+x^3}} \, dx","Int[1/((2^(2/3) - x)*Sqrt[-1 + x^3]),x]","-\frac{2 \sqrt[3]{2} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right),4 \sqrt{3}-7\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{x^3-1}}\right)}{3 \sqrt{3}}","-\frac{2 \sqrt[3]{2} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right),4 \sqrt{3}-7\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{x^3-1}}\right)}{3 \sqrt{3}}",1,"(-2*ArcTanh[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[-1 + x^3]])/(3*Sqrt[3]) - (2*2^(1/3)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",4,4,21,0.1905,1,"{2134, 219, 2137, 206}"
4,1,156,0,0.178302,"\int \frac{1}{\left(2^{2/3}+x\right) \sqrt{-1-x^3}} \, dx","Int[1/((2^(2/3) + x)*Sqrt[-1 - x^3]),x]","\frac{2 \sqrt[3]{2} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right),4 \sqrt{3}-7\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{-x^3-1}}\right)}{3 \sqrt{3}}","\frac{2 \sqrt[3]{2} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right),4 \sqrt{3}-7\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{-x^3-1}}\right)}{3 \sqrt{3}}",1,"(2*ArcTanh[(Sqrt[3]*(1 + 2^(1/3)*x))/Sqrt[-1 - x^3]])/(3*Sqrt[3]) + (2*2^(1/3)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",4,4,21,0.1905,1,"{2134, 219, 2137, 206}"
5,1,280,0,0.3344375,"\int \frac{1}{\left(2^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a+b x^3}} \, dx","Int[1/((2^(2/3)*a^(1/3) + b^(1/3)*x)*Sqrt[a + b*x^3]),x]","\frac{2 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}\right),-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{3 \sqrt{3} \sqrt{a} \sqrt[3]{b}}","\frac{2 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}\right),-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{3 \sqrt{3} \sqrt{a} \sqrt[3]{b}}",1,"(2*ArcTan[(Sqrt[3]*a^(1/6)*(a^(1/3) + 2^(1/3)*b^(1/3)*x))/Sqrt[a + b*x^3]])/(3*Sqrt[3]*Sqrt[a]*b^(1/3)) + (2*2^(1/3)*Sqrt[2 + Sqrt[3]]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,33,0.1212,1,"{2134, 218, 2137, 203}"
6,1,288,0,0.3324585,"\int \frac{1}{\left(2^{2/3} \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{a-b x^3}} \, dx","Int[1/((2^(2/3)*a^(1/3) - b^(1/3)*x)*Sqrt[a - b*x^3]),x]","-\frac{2 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right),-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{3 \sqrt{3} \sqrt{a} \sqrt[3]{b}}","-\frac{2 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right),-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{3 \sqrt{3} \sqrt{a} \sqrt[3]{b}}",1,"(-2*ArcTan[(Sqrt[3]*a^(1/6)*(a^(1/3) - 2^(1/3)*b^(1/3)*x))/Sqrt[a - b*x^3]])/(3*Sqrt[3]*Sqrt[a]*b^(1/3)) - (2*2^(1/3)*Sqrt[2 + Sqrt[3]]*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",4,4,35,0.1143,1,"{2134, 218, 2137, 203}"
7,1,297,0,0.3436233,"\int \frac{1}{\left(2^{2/3} \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{-a+b x^3}} \, dx","Int[1/((2^(2/3)*a^(1/3) - b^(1/3)*x)*Sqrt[-a + b*x^3]),x]","-\frac{2 \sqrt[3]{2} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right),4 \sqrt{3}-7\right)}{3 \sqrt[4]{3} \sqrt[3]{a} \sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{3 \sqrt{3} \sqrt{a} \sqrt[3]{b}}","-\frac{2 \sqrt[3]{2} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right),4 \sqrt{3}-7\right)}{3 \sqrt[4]{3} \sqrt[3]{a} \sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{3 \sqrt{3} \sqrt{a} \sqrt[3]{b}}",1,"(-2*ArcTanh[(Sqrt[3]*a^(1/6)*(a^(1/3) - 2^(1/3)*b^(1/3)*x))/Sqrt[-a + b*x^3]])/(3*Sqrt[3]*Sqrt[a]*b^(1/3)) - (2*2^(1/3)*Sqrt[2 - Sqrt[3]]*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(1/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",4,4,36,0.1111,1,"{2134, 219, 2137, 206}"
8,1,293,0,0.3290292,"\int \frac{1}{\left(2^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{-a-b x^3}} \, dx","Int[1/((2^(2/3)*a^(1/3) + b^(1/3)*x)*Sqrt[-a - b*x^3]),x]","\frac{2 \sqrt[3]{2} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}\right),4 \sqrt{3}-7\right)}{3 \sqrt[4]{3} \sqrt[3]{a} \sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{3 \sqrt{3} \sqrt{a} \sqrt[3]{b}}","\frac{2 \sqrt[3]{2} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}\right),4 \sqrt{3}-7\right)}{3 \sqrt[4]{3} \sqrt[3]{a} \sqrt[3]{b} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{3 \sqrt{3} \sqrt{a} \sqrt[3]{b}}",1,"(2*ArcTanh[(Sqrt[3]*a^(1/6)*(a^(1/3) + 2^(1/3)*b^(1/3)*x))/Sqrt[-a - b*x^3]])/(3*Sqrt[3]*Sqrt[a]*b^(1/3)) + (2*2^(1/3)*Sqrt[2 - Sqrt[3]]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(1/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",4,4,36,0.1111,1,"{2134, 219, 2137, 206}"
9,1,249,0,0.2865993,"\int \frac{1}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx","Int[1/((c + d*x)*Sqrt[c^3 + 4*d^3*x^3]),x]","\frac{2 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(c+2^{2/3} d x\right) \sqrt{\frac{c^2-2^{2/3} c d x+2 \sqrt[3]{2} d^2 x^2}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) c+2^{2/3} d x}{\left(1+\sqrt{3}\right) c+2^{2/3} d x}\right),-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} c d \sqrt{\frac{c \left(c+2^{2/3} d x\right)}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} \sqrt{c^3+4 d^3 x^3}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{c} (c+2 d x)}{\sqrt{c^3+4 d^3 x^3}}\right)}{3 \sqrt{3} c^{3/2} d}","\frac{2 \sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(c+2^{2/3} d x\right) \sqrt{\frac{c^2-2^{2/3} c d x+2 \sqrt[3]{2} d^2 x^2}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) c+2^{2/3} d x}{\left(1+\sqrt{3}\right) c+2^{2/3} d x}\right),-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} c d \sqrt{\frac{c \left(c+2^{2/3} d x\right)}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} \sqrt{c^3+4 d^3 x^3}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{c} (c+2 d x)}{\sqrt{c^3+4 d^3 x^3}}\right)}{3 \sqrt{3} c^{3/2} d}",1,"(2*ArcTan[(Sqrt[3]*Sqrt[c]*(c + 2*d*x))/Sqrt[c^3 + 4*d^3*x^3]])/(3*Sqrt[3]*c^(3/2)*d) + (2*2^(1/3)*Sqrt[2 + Sqrt[3]]*(c + 2^(2/3)*d*x)*Sqrt[(c^2 - 2^(2/3)*c*d*x + 2*2^(1/3)*d^2*x^2)/((1 + Sqrt[3])*c + 2^(2/3)*d*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c + 2^(2/3)*d*x)/((1 + Sqrt[3])*c + 2^(2/3)*d*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*c*d*Sqrt[(c*(c + 2^(2/3)*d*x))/((1 + Sqrt[3])*c + 2^(2/3)*d*x)^2]*Sqrt[c^3 + 4*d^3*x^3])","A",4,4,24,0.1667,1,"{2134, 218, 2137, 203}"
10,1,146,0,0.2173814,"\int \frac{1}{\left(1+\sqrt{3}+x\right) \sqrt{1+x^3}} \, dx","Int[1/((1 + Sqrt[3] + x)*Sqrt[1 + x^3]),x]","\frac{\sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right),-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}","\frac{\sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right),-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}",1,"ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]]/Sqrt[3*(3 + 2*Sqrt[3])] + (Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,20,0.2000,1,"{2135, 218, 2140, 203}"
11,1,164,0,0.1788962,"\int \frac{1}{\left(1+\sqrt{3}-x\right) \sqrt{1-x^3}} \, dx","Int[1/((1 + Sqrt[3] - x)*Sqrt[1 - x^3]),x]","-\frac{\sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right),-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{1-x^3}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}","-\frac{\sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right),-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{1-x^3}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}",1,"-(ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[1 - x^3]]/Sqrt[3*(3 + 2*Sqrt[3])]) - (Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",4,4,24,0.1667,1,"{2135, 218, 2140, 203}"
12,1,167,0,0.1671711,"\int \frac{1}{\left(1+\sqrt{3}-x\right) \sqrt{-1+x^3}} \, dx","Int[1/((1 + Sqrt[3] - x)*Sqrt[-1 + x^3]),x]","-\frac{\sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right),4 \sqrt{3}-7\right)}{3^{3/4} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}","-\frac{\sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right),4 \sqrt{3}-7\right)}{3^{3/4} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}",1,"-(ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]]/Sqrt[3*(3 + 2*Sqrt[3])]) - (Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(3/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",4,4,22,0.1818,1,"{2135, 219, 2140, 206}"
13,1,157,0,0.1589932,"\int \frac{1}{\left(1+\sqrt{3}+x\right) \sqrt{-1-x^3}} \, dx","Int[1/((1 + Sqrt[3] + x)*Sqrt[-1 - x^3]),x]","\frac{\sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right),4 \sqrt{3}-7\right)}{3^{3/4} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{-x^3-1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}","\frac{\sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right),4 \sqrt{3}-7\right)}{3^{3/4} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{-x^3-1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}",1,"ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[-1 - x^3]]/Sqrt[3*(3 + 2*Sqrt[3])] + (Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(3/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",4,4,22,0.1818,1,"{2135, 219, 2140, 206}"
14,1,331,0,0.6633719,"\int \frac{1}{(3+x) \sqrt{1+x^3}} \, dx","Int[1/((3 + x)*Sqrt[1 + x^3]),x]","\frac{2 \sqrt{26+15 \sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \text{EllipticF}\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right),-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt{\frac{13}{2}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{\sqrt{26} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{4 \sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(97-56 \sqrt{3};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{2-\sqrt{3}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt{\frac{13}{2}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{\sqrt{26} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{2 \sqrt{26+15 \sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}+\frac{4 \sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(97-56 \sqrt{3};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{2-\sqrt{3}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"((1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(Sqrt[13/2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]])/(Sqrt[26]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (2*Sqrt[26 + 15*Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (4*3^(1/4)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[97 - 56*Sqrt[3], -ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[2 - Sqrt[3]]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",8,8,15,0.5333,1,"{2136, 218, 2142, 2113, 537, 571, 93, 204}"
15,1,382,0,0.723202,"\int \frac{1}{(3+x) \sqrt{1-x^3}} \, dx","Int[1/((3 + x)*Sqrt[1 - x^3]),x]","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}}}{2 \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}}}\right)}{2 \sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \left(4+\sqrt{3}\right) \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{1}{169} \left(553+304 \sqrt{3}\right);-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}}}{2 \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}}}\right)}{2 \sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \left(4+\sqrt{3}\right) \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{1}{169} \left(553+304 \sqrt{3}\right);-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"-((1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*ArcTanh[(Sqrt[7]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2])/(2*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2])])/(2*Sqrt[7]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) - (2*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(1/4)*(4 + Sqrt[3])*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) + (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticPi[(553 + 304*Sqrt[3])/169, -ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(13*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",8,8,17,0.4706,1,"{2136, 218, 2142, 2113, 537, 571, 93, 206}"
16,1,376,0,0.5769692,"\int \frac{1}{(3+x) \sqrt{-1+x^3}} \, dx","Int[1/((3 + x)*Sqrt[-1 + x^3]),x]","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}}}{2 \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}}}\right)}{2 \sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 \sqrt{62-35 \sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{13 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{1}{169} \left(553+304 \sqrt{3}\right);-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}}}{2 \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}}}\right)}{2 \sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 \sqrt{62-35 \sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{13 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{1}{169} \left(553+304 \sqrt{3}\right);-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"-((1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*ArcTanh[(Sqrt[7]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2])/(2*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2])])/(2*Sqrt[7]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[-1 + x^3]) - (2*Sqrt[62 - 35*Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(13*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticPi[(553 + 304*Sqrt[3])/169, -ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(13*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[-1 + x^3])","A",8,8,15,0.5333,1,"{2136, 219, 2142, 2113, 537, 571, 93, 206}"
17,1,342,0,0.5751109,"\int \frac{1}{(3+x) \sqrt{-1-x^3}} \, dx","Int[1/((3 + x)*Sqrt[-1 - x^3]),x]","\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt{\frac{13}{2}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{\sqrt{26} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{2 (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{4 \sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(97-56 \sqrt{3};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{2-\sqrt{3}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt{\frac{13}{2}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{\sqrt{26} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{2 (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}+\frac{4 \sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(97-56 \sqrt{3};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{2-\sqrt{3}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"((1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(Sqrt[13/2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]])/(Sqrt[26]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[-1 - x^3]) + (2*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[2 - Sqrt[3]]*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3]) + (4*3^(1/4)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[97 - 56*Sqrt[3], -ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[2 - Sqrt[3]]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[-1 - x^3])","A",8,8,17,0.4706,1,"{2136, 219, 2142, 2113, 537, 571, 93, 204}"
18,1,139,0,0.0704251,"\int \frac{1}{(c+d x) \sqrt[3]{-c^3+d^3 x^3}} \, dx","Int[1/((c + d*x)*(-c^3 + d^3*x^3)^(1/3)),x]","-\frac{3 \log \left(2^{2/3} d \sqrt[3]{d^3 x^3-c^3}+d (c-d x)\right)}{4 \sqrt[3]{2} c d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{\sqrt[3]{2} (c-d x)}{\sqrt[3]{d^3 x^3-c^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} c d}+\frac{\log \left((c-d x) (c+d x)^2\right)}{4 \sqrt[3]{2} c d}","-\frac{3 \log \left(2^{2/3} d \sqrt[3]{d^3 x^3-c^3}+d (c-d x)\right)}{4 \sqrt[3]{2} c d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{\sqrt[3]{2} (c-d x)}{\sqrt[3]{d^3 x^3-c^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} c d}+\frac{\log \left((c-d x) (c+d x)^2\right)}{4 \sqrt[3]{2} c d}",1,"(Sqrt[3]*ArcTan[(1 - (2^(1/3)*(c - d*x))/(-c^3 + d^3*x^3)^(1/3))/Sqrt[3]])/(2*2^(1/3)*c*d) + Log[(c - d*x)*(c + d*x)^2]/(4*2^(1/3)*c*d) - (3*Log[d*(c - d*x) + 2^(2/3)*d*(-c^3 + d^3*x^3)^(1/3)])/(4*2^(1/3)*c*d)","A",1,1,25,0.04000,1,"{2148}"
19,1,186,0,0.2035214,"\int \frac{1}{(c+d x) \sqrt[3]{2 c^3+d^3 x^3}} \, dx","Int[1/((c + d*x)*(2*c^3 + d^3*x^3)^(1/3)),x]","-\frac{\log \left(\sqrt[3]{2 c^3+d^3 x^3}-d x\right)}{4 c d}+\frac{3 \log \left(d (2 c+d x)-d \sqrt[3]{2 c^3+d^3 x^3}\right)}{4 c d}+\frac{\tan ^{-1}\left(\frac{\frac{2 d x}{\sqrt[3]{2 c^3+d^3 x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} c d}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (2 c+d x)}{\sqrt[3]{2 c^3+d^3 x^3}}+1}{\sqrt{3}}\right)}{2 c d}-\frac{\log (c+d x)}{2 c d}","-\frac{\log \left(\sqrt[3]{2 c^3+d^3 x^3}-d x\right)}{4 c d}+\frac{3 \log \left(d (2 c+d x)-d \sqrt[3]{2 c^3+d^3 x^3}\right)}{4 c d}+\frac{\tan ^{-1}\left(\frac{\frac{2 d x}{\sqrt[3]{2 c^3+d^3 x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} c d}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (2 c+d x)}{\sqrt[3]{2 c^3+d^3 x^3}}+1}{\sqrt{3}}\right)}{2 c d}-\frac{\log (c+d x)}{2 c d}",1,"ArcTan[(1 + (2*d*x)/(2*c^3 + d^3*x^3)^(1/3))/Sqrt[3]]/(2*Sqrt[3]*c*d) - (Sqrt[3]*ArcTan[(1 + (2*(2*c + d*x))/(2*c^3 + d^3*x^3)^(1/3))/Sqrt[3]])/(2*c*d) - Log[c + d*x]/(2*c*d) - Log[-(d*x) + (2*c^3 + d^3*x^3)^(1/3)]/(4*c*d) + (3*Log[d*(2*c + d*x) - d*(2*c^3 + d^3*x^3)^(1/3)])/(4*c*d)","A",3,3,25,0.1200,1,"{2149, 239, 2151}"
20,0,0,0,0.1055456,"\int \frac{1}{(c+d x) \left(2 c^3+d^3 x^3\right)^{2/3}} \, dx","Int[1/((c + d*x)*(2*c^3 + d^3*x^3)^(2/3)),x]","\int \frac{1}{(c+d x) \left(2 c^3+d^3 x^3\right)^{2/3}} \, dx","-\frac{\log \left(d x-\sqrt[3]{2 c^3+d^3 x^3}\right)}{4 c^2 d}+\frac{3 \log \left(d (2 c+d x)-d \sqrt[3]{2 c^3+d^3 x^3}\right)}{4 c^2 d}-\frac{\tan ^{-1}\left(\frac{\frac{2 d x}{\sqrt[3]{2 c^3+d^3 x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt{3} c^2 d}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (2 c+d x)}{\sqrt[3]{2 c^3+d^3 x^3}}+1}{\sqrt{3}}\right)}{2 c^2 d}-\frac{\log (c+d x)}{2 c^2 d}",1,"Defer[Int][1/((c + d*x)*(2*c^3 + d^3*x^3)^(2/3)), x]","F",0,0,0,0,-1,"{}"
21,0,0,0,0.0854677,"\int \frac{1}{\left(1+\sqrt[3]{2} x\right) \left(1+x^3\right)^{2/3}} \, dx","Int[1/((1 + 2^(1/3)*x)*(1 + x^3)^(2/3)),x]","\int \frac{1}{\left(1+\sqrt[3]{2} x\right) \left(1+x^3\right)^{2/3}} \, dx","-\frac{\log \left(x-\sqrt[3]{x^3+1}\right)}{2\ 2^{2/3}}+\frac{3 \log \left(-\sqrt[3]{2} \sqrt[3]{x^3+1}+\sqrt[3]{2} x+2\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 x}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 \left(x+2^{2/3}\right)}{\sqrt[3]{x^3+1}}+1}{\sqrt{3}}\right)}{2^{2/3}}-\frac{\log \left(\sqrt[3]{2} x+1\right)}{2^{2/3}}",1,"Defer[Int][1/((1 + 2^(1/3)*x)*(1 + x^3)^(2/3)), x]","F",0,0,0,0,-1,"{}"
22,0,0,0,0.1022828,"\int \frac{1}{\left(1-\sqrt[3]{2} x\right) \left(1-x^3\right)^{2/3}} \, dx","Int[1/((1 - 2^(1/3)*x)*(1 - x^3)^(2/3)),x]","\int \frac{1}{\left(1-\sqrt[3]{2} x\right) \left(1-x^3\right)^{2/3}} \, dx","\frac{\log \left(-\sqrt[3]{1-x^3}-x\right)}{2\ 2^{2/3}}-\frac{3 \log \left(\sqrt[3]{2} \sqrt[3]{1-x^3}+\sqrt[3]{2} x-2\right)}{2\ 2^{2/3}}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2\ 2^{2/3}-2 x}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}+\frac{\log \left(1-\sqrt[3]{2} x\right)}{2^{2/3}}",1,"Defer[Int][1/((1 - 2^(1/3)*x)*(1 - x^3)^(2/3)), x]","F",0,0,0,0,-1,"{}"
23,1,498,0,0.396989,"\int (c+d x)^4 \sqrt[3]{a+b x^3} \, dx","Int[(c + d*x)^4*(a + b*x^3)^(1/3),x]","\frac{a^2 d^4 \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{27 b^{5/3}}-\frac{a^2 d^4 \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{54 b^{5/3}}+\frac{a^2 d^4 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{5/3}}-\frac{4 a c^3 d \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{9 b^{2/3}}+\frac{2 a c^3 d \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{9 b^{2/3}}-\frac{4 a c^3 d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3}}+\frac{3 a c^2 d^2 \sqrt[3]{a+b x^3}}{2 b}+\frac{1}{30} \sqrt[3]{a+b x^3} \left(45 c^2 d^2 x^3+40 c^3 d x^2+15 c^4 x+24 c d^3 x^4+5 d^4 x^5\right)+\frac{a c^4 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 \left(a+b x^3\right)^{2/3}}+\frac{a c d^3 x^4 \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{5 \left(a+b x^3\right)^{2/3}}+\frac{a d^4 x^2 \sqrt[3]{a+b x^3}}{18 b}","\frac{a^2 d^4 \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{18 b^{5/3}}+\frac{a^2 d^4 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{5/3}}-\frac{2 a c^3 d \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{3 b^{2/3}}-\frac{4 a c^3 d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3}}+\frac{3 a c^2 d^2 \sqrt[3]{a+b x^3}}{2 b}+\frac{1}{30} \sqrt[3]{a+b x^3} \left(45 c^2 d^2 x^3+40 c^3 d x^2+15 c^4 x+24 c d^3 x^4+5 d^4 x^5\right)+\frac{a c^4 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 \left(a+b x^3\right)^{2/3}}+\frac{a c d^3 x^4 \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{5 \left(a+b x^3\right)^{2/3}}+\frac{a d^4 x^2 \sqrt[3]{a+b x^3}}{18 b}",1,"(3*a*c^2*d^2*(a + b*x^3)^(1/3))/(2*b) + (a*d^4*x^2*(a + b*x^3)^(1/3))/(18*b) + ((a + b*x^3)^(1/3)*(15*c^4*x + 40*c^3*d*x^2 + 45*c^2*d^2*x^3 + 24*c*d^3*x^4 + 5*d^4*x^5))/30 - (4*a*c^3*d*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(2/3)) + (a^2*d^4*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(9*Sqrt[3]*b^(5/3)) + (a*c^4*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(2*(a + b*x^3)^(2/3)) + (a*c*d^3*x^4*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[2/3, 4/3, 7/3, -((b*x^3)/a)])/(5*(a + b*x^3)^(2/3)) - (4*a*c^3*d*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(2/3)) + (a^2*d^4*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(27*b^(5/3)) + (2*a*c^3*d*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(2/3)) - (a^2*d^4*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(54*b^(5/3))","A",23,15,19,0.7895,1,"{1853, 1893, 246, 245, 331, 292, 31, 634, 617, 204, 628, 261, 365, 364, 321}"
24,1,297,0,0.305283,"\int (c+d x)^3 \sqrt[3]{a+b x^3} \, dx","Int[(c + d*x)^3*(a + b*x^3)^(1/3),x]","-\frac{a c^2 d \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3 b^{2/3}}+\frac{a c^2 d \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{6 b^{2/3}}-\frac{a c^2 d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}+\frac{a x \left(\frac{b x^3}{a}+1\right)^{2/3} \left(5 b c^3-a d^3\right) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{10 b \left(a+b x^3\right)^{2/3}}+\frac{1}{20} \sqrt[3]{a+b x^3} \left(20 c^2 d x^2+10 c^3 x+15 c d^2 x^3+4 d^3 x^4\right)+\frac{3 a c d^2 \sqrt[3]{a+b x^3}}{4 b}+\frac{a d^3 x \sqrt[3]{a+b x^3}}{10 b}","-\frac{a c^2 d \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2 b^{2/3}}-\frac{a c^2 d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}+\frac{a x \left(\frac{b x^3}{a}+1\right)^{2/3} \left(5 b c^3-a d^3\right) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{10 b \left(a+b x^3\right)^{2/3}}+\frac{1}{20} \sqrt[3]{a+b x^3} \left(20 c^2 d x^2+10 c^3 x+15 c d^2 x^3+4 d^3 x^4\right)+\frac{3 a c d^2 \sqrt[3]{a+b x^3}}{4 b}+\frac{a d^3 x \sqrt[3]{a+b x^3}}{10 b}",1,"(3*a*c*d^2*(a + b*x^3)^(1/3))/(4*b) + (a*d^3*x*(a + b*x^3)^(1/3))/(10*b) + ((a + b*x^3)^(1/3)*(10*c^3*x + 20*c^2*d*x^2 + 15*c*d^2*x^3 + 4*d^3*x^4))/20 - (a*c^2*d*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(2/3)) + (a*(5*b*c^3 - a*d^3)*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(10*b*(a + b*x^3)^(2/3)) - (a*c^2*d*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*b^(2/3)) + (a*c^2*d*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*b^(2/3))","A",15,14,19,0.7368,1,"{1853, 1888, 1886, 261, 1893, 246, 245, 331, 292, 31, 634, 617, 204, 628}"
25,1,245,0,0.2040673,"\int (c+d x)^2 \sqrt[3]{a+b x^3} \, dx","Int[(c + d*x)^2*(a + b*x^3)^(1/3),x]","-\frac{2 a c d \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{9 b^{2/3}}+\frac{a c d \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{9 b^{2/3}}-\frac{2 a c d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3}}+\frac{1}{12} \sqrt[3]{a+b x^3} \left(6 c^2 x+8 c d x^2+3 d^2 x^3\right)+\frac{a c^2 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 \left(a+b x^3\right)^{2/3}}+\frac{a d^2 \sqrt[3]{a+b x^3}}{4 b}","-\frac{a c d \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{3 b^{2/3}}-\frac{2 a c d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3}}+\frac{1}{12} \sqrt[3]{a+b x^3} \left(6 c^2 x+8 c d x^2+3 d^2 x^3\right)+\frac{a c^2 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 \left(a+b x^3\right)^{2/3}}+\frac{a d^2 \sqrt[3]{a+b x^3}}{4 b}",1,"(a*d^2*(a + b*x^3)^(1/3))/(4*b) + ((a + b*x^3)^(1/3)*(6*c^2*x + 8*c*d*x^2 + 3*d^2*x^3))/12 - (2*a*c*d*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(2/3)) + (a*c^2*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(2*(a + b*x^3)^(2/3)) - (2*a*c*d*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(2/3)) + (a*c*d*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(2/3))","A",14,13,19,0.6842,1,"{1853, 1886, 261, 1893, 246, 245, 331, 292, 31, 634, 617, 204, 628}"
26,1,207,0,0.1503363,"\int (c+d x) \sqrt[3]{a+b x^3} \, dx","Int[(c + d*x)*(a + b*x^3)^(1/3),x]","-\frac{a d \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{9 b^{2/3}}+\frac{a d \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{18 b^{2/3}}-\frac{a d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3}}+\frac{1}{6} \sqrt[3]{a+b x^3} \left(3 c x+2 d x^2\right)+\frac{a c x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 \left(a+b x^3\right)^{2/3}}","-\frac{a d \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{6 b^{2/3}}-\frac{a d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3}}+\frac{1}{6} \sqrt[3]{a+b x^3} \left(3 c x+2 d x^2\right)+\frac{a c x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 \left(a+b x^3\right)^{2/3}}",1,"((3*c*x + 2*d*x^2)*(a + b*x^3)^(1/3))/6 - (a*d*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(2/3)) + (a*c*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(2*(a + b*x^3)^(2/3)) - (a*d*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(2/3)) + (a*d*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(18*b^(2/3))","A",12,11,17,0.6471,1,"{1853, 1893, 246, 245, 331, 292, 31, 634, 617, 204, 628}"
27,0,0,0,0.0815726,"\int \frac{\sqrt[3]{a+b x^3}}{c+d x} \, dx","Int[(a + b*x^3)^(1/3)/(c + d*x),x]","\int \frac{\sqrt[3]{a+b x^3}}{c+d x} \, dx","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right)}{c \sqrt[3]{\frac{b x^3}{a}+1}}+\frac{\sqrt[3]{b c^3-a d^3} \log \left(c^3+d^3 x^3\right)}{3 d^2}-\frac{\sqrt[3]{b c^3-a d^3} \log \left(\frac{x \sqrt[3]{b c^3-a d^3}}{c}-\sqrt[3]{a+b x^3}\right)}{2 d^2}-\frac{\sqrt[3]{b c^3-a d^3} \log \left(\sqrt[3]{b c^3-a d^3}+d \sqrt[3]{a+b x^3}\right)}{2 d^2}-\frac{\sqrt[3]{b c^3-a d^3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c^3-a d^3}}{c \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^2}+\frac{\sqrt[3]{b c^3-a d^3} \tan ^{-1}\left(\frac{1-\frac{2 d \sqrt[3]{a+b x^3}}{\sqrt[3]{b c^3-a d^3}}}{\sqrt{3}}\right)}{\sqrt{3} d^2}+\frac{\sqrt[3]{b} c \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2 d^2}+\frac{\sqrt[3]{b} c \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^2}+\frac{\sqrt[3]{a+b x^3}}{d}",1,"Defer[Int][(a + b*x^3)^(1/3)/(c + d*x), x]","F",0,0,0,0,-1,"{}"
28,0,0,0,0.0794583,"\int \frac{\sqrt[3]{a+b x^3}}{(c+d x)^2} \, dx","Int[(a + b*x^3)^(1/3)/(c + d*x)^2,x]","\int \frac{\sqrt[3]{a+b x^3}}{(c+d x)^2} \, dx","-\frac{d^3 \sqrt[3]{b x^3+a} F_1\left(\frac{4}{3};-\frac{1}{3},2;\frac{7}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right) x^4}{2 c^5 \sqrt[3]{\frac{b x^3}{a}+1}}-\frac{d \sqrt[3]{b x^3+a} x^2}{c^3+d^3 x^3}+\frac{\sqrt[3]{b x^3+a} F_1\left(\frac{1}{3};-\frac{1}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right) x}{c^2 \sqrt[3]{\frac{b x^3}{a}+1}}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{b x^3+a}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^2}+\frac{2 a d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b c^3-a d^3} x}{c \sqrt[3]{b x^3+a}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c \left(b c^3-a d^3\right)^{2/3}}+\frac{\left(3 b c^3-2 a d^3\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b c^3-a d^3} x}{c \sqrt[3]{b x^3+a}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c d^2 \left(b c^3-a d^3\right)^{2/3}}-\frac{b c^2 \tan ^{-1}\left(\frac{1-\frac{2 d \sqrt[3]{b x^3+a}}{\sqrt[3]{b c^3-a d^3}}}{\sqrt{3}}\right)}{\sqrt{3} d^2 \left(b c^3-a d^3\right)^{2/3}}-\frac{a d \log \left(c^3+d^3 x^3\right)}{9 c \left(b c^3-a d^3\right)^{2/3}}-\frac{\left(3 b c^3-2 a d^3\right) \log \left(c^3+d^3 x^3\right)}{18 c d^2 \left(b c^3-a d^3\right)^{2/3}}-\frac{b c^2 \log \left(c^3+d^3 x^3\right)}{6 d^2 \left(b c^3-a d^3\right)^{2/3}}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{b} x-\sqrt[3]{b x^3+a}\right)}{2 d^2}+\frac{a d \log \left(\frac{\sqrt[3]{b c^3-a d^3} x}{c}-\sqrt[3]{b x^3+a}\right)}{3 c \left(b c^3-a d^3\right)^{2/3}}+\frac{\left(3 b c^3-2 a d^3\right) \log \left(\frac{\sqrt[3]{b c^3-a d^3} x}{c}-\sqrt[3]{b x^3+a}\right)}{6 c d^2 \left(b c^3-a d^3\right)^{2/3}}+\frac{b c^2 \log \left(\sqrt[3]{b x^3+a} d+\sqrt[3]{b c^3-a d^3}\right)}{2 d^2 \left(b c^3-a d^3\right)^{2/3}}-\frac{c^2 \sqrt[3]{b x^3+a}}{d \left(c^3+d^3 x^3\right)}",1,"Defer[Int][(a + b*x^3)^(1/3)/(c + d*x)^2, x]","F",0,0,0,0,-1,"{}"
29,1,310,0,0.1782395,"\int \frac{(c+d x)^4}{\sqrt[3]{a+b x^3}} \, dx","Int[(c + d*x)^4/(a + b*x^3)^(1/3),x]","\frac{2 a c d^3 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{3 b^{4/3}}-\frac{4 a c d^3 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3}}+\frac{3 c^2 d^2 \left(a+b x^3\right)^{2/3}}{b}+\frac{2 c^3 d x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{\sqrt[3]{a+b x^3}}-\frac{c^4 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}+\frac{c^4 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}+\frac{4 c d^3 x \left(a+b x^3\right)^{2/3}}{3 b}+\frac{d^4 x^5 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{5}{3};\frac{8}{3};-\frac{b x^3}{a}\right)}{5 \sqrt[3]{a+b x^3}}","\frac{2 a c d^3 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{3 b^{4/3}}-\frac{4 a c d^3 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3}}+\frac{3 c^2 d^2 \left(a+b x^3\right)^{2/3}}{b}+\frac{2 c^3 d x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{\sqrt[3]{a+b x^3}}-\frac{c^4 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}+\frac{c^4 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}+\frac{4 c d^3 x \left(a+b x^3\right)^{2/3}}{3 b}+\frac{d^4 x^5 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{5}{3};\frac{8}{3};-\frac{b x^3}{a}\right)}{5 \sqrt[3]{a+b x^3}}",1,"(3*c^2*d^2*(a + b*x^3)^(2/3))/b + (4*c*d^3*x*(a + b*x^3)^(2/3))/(3*b) + (c^4*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(1/3)) - (4*a*c*d^3*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(4/3)) + (2*c^3*d*x^2*(1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, -((b*x^3)/a)])/(a + b*x^3)^(1/3) + (d^4*x^5*(1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[1/3, 5/3, 8/3, -((b*x^3)/a)])/(5*(a + b*x^3)^(1/3)) - (c^4*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(2*b^(1/3)) + (2*a*c*d^3*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(3*b^(4/3))","A",10,6,19,0.3158,1,"{1893, 239, 365, 364, 261, 321}"
30,1,255,0,0.1376526,"\int \frac{(c+d x)^3}{\sqrt[3]{a+b x^3}} \, dx","Int[(c + d*x)^3/(a + b*x^3)^(1/3),x]","\frac{a d^3 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 b^{4/3}}-\frac{a d^3 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3}}+\frac{3 c^2 d x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 \sqrt[3]{a+b x^3}}-\frac{c^3 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}+\frac{c^3 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}+\frac{3 c d^2 \left(a+b x^3\right)^{2/3}}{2 b}+\frac{d^3 x \left(a+b x^3\right)^{2/3}}{3 b}","\frac{a d^3 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 b^{4/3}}-\frac{a d^3 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3}}+\frac{3 c^2 d x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 \sqrt[3]{a+b x^3}}-\frac{c^3 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}+\frac{c^3 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}+\frac{3 c d^2 \left(a+b x^3\right)^{2/3}}{2 b}+\frac{d^3 x \left(a+b x^3\right)^{2/3}}{3 b}",1,"(3*c*d^2*(a + b*x^3)^(2/3))/(2*b) + (d^3*x*(a + b*x^3)^(2/3))/(3*b) + (c^3*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(1/3)) - (a*d^3*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(4/3)) + (3*c^2*d*x^2*(1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, -((b*x^3)/a)])/(2*(a + b*x^3)^(1/3)) - (c^3*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(2*b^(1/3)) + (a*d^3*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(6*b^(4/3))","A",8,6,19,0.3158,1,"{1893, 239, 365, 364, 261, 321}"
31,1,147,0,0.1019358,"\int \frac{(c+d x)^2}{\sqrt[3]{a+b x^3}} \, dx","Int[(c + d*x)^2/(a + b*x^3)^(1/3),x]","-\frac{c^2 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}+\frac{c^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}+\frac{c d x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{\sqrt[3]{a+b x^3}}+\frac{d^2 \left(a+b x^3\right)^{2/3}}{2 b}","-\frac{c^2 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}+\frac{c^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}+\frac{c d x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{\sqrt[3]{a+b x^3}}+\frac{d^2 \left(a+b x^3\right)^{2/3}}{2 b}",1,"(d^2*(a + b*x^3)^(2/3))/(2*b) + (c^2*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(1/3)) + (c*d*x^2*(1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, -((b*x^3)/a)])/(a + b*x^3)^(1/3) - (c^2*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(2*b^(1/3))","A",7,6,19,0.3158,1,"{1886, 261, 1893, 239, 365, 364}"
32,1,124,0,0.0663397,"\int \frac{c+d x}{\sqrt[3]{a+b x^3}} \, dx","Int[(c + d*x)/(a + b*x^3)^(1/3),x]","-\frac{c \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}+\frac{c \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}+\frac{d x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 \sqrt[3]{a+b x^3}}","-\frac{c \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b}}+\frac{c \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b}}+\frac{d x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 \sqrt[3]{a+b x^3}}",1,"(c*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(1/3)) + (d*x^2*(1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[1/3, 2/3, 5/3, -((b*x^3)/a)])/(2*(a + b*x^3)^(1/3)) - (c*Log[-(b^(1/3)*x) + (a + b*x^3)^(1/3)])/(2*b^(1/3))","A",5,4,17,0.2353,1,"{1893, 239, 365, 364}"
33,0,0,0,0.0475809,"\int \frac{1}{(c+d x) \sqrt[3]{a+b x^3}} \, dx","Int[1/((c + d*x)*(a + b*x^3)^(1/3)),x]","\int \frac{1}{(c+d x) \sqrt[3]{a+b x^3}} \, dx","-\frac{d x^2 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right)}{2 c^2 \sqrt[3]{a+b x^3}}+\frac{\log \left(c^3+d^3 x^3\right)}{3 \sqrt[3]{b c^3-a d^3}}-\frac{\log \left(\frac{x \sqrt[3]{b c^3-a d^3}}{c}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{b c^3-a d^3}}-\frac{\log \left(\sqrt[3]{b c^3-a d^3}+d \sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{b c^3-a d^3}}+\frac{\tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c^3-a d^3}}{c \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b c^3-a d^3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 d \sqrt[3]{a+b x^3}}{\sqrt[3]{b c^3-a d^3}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b c^3-a d^3}}",1,"Defer[Int][1/((c + d*x)*(a + b*x^3)^(1/3)), x]","F",0,0,0,0,-1,"{}"
34,0,0,0,0.0830621,"\int \frac{1}{(c+d x)^2 \sqrt[3]{a+b x^3}} \, dx","Int[1/((c + d*x)^2*(a + b*x^3)^(1/3)),x]","\int \frac{1}{(c+d x)^2 \sqrt[3]{a+b x^3}} \, dx","\frac{d^4 x^5 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{5}{3};\frac{1}{3},2;\frac{8}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right)}{5 c^6 \sqrt[3]{a+b x^3}}-\frac{d x^2 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{2}{3};\frac{1}{3},2;\frac{5}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right)}{c^3 \sqrt[3]{a+b x^3}}-\frac{c d^3 x \left(a+b x^3\right)^{2/3}}{\left(c^3+d^3 x^3\right) \left(b c^3-a d^3\right)}+\frac{c^2 d^2 \left(a+b x^3\right)^{2/3}}{\left(c^3+d^3 x^3\right) \left(b c^3-a d^3\right)}+\frac{a d^3 \log \left(c^3+d^3 x^3\right)}{9 c \left(b c^3-a d^3\right)^{4/3}}+\frac{b c^2 \log \left(c^3+d^3 x^3\right)}{6 \left(b c^3-a d^3\right)^{4/3}}+\frac{\left(3 b c^3-2 a d^3\right) \log \left(c^3+d^3 x^3\right)}{18 c \left(b c^3-a d^3\right)^{4/3}}-\frac{a d^3 \log \left(\frac{x \sqrt[3]{b c^3-a d^3}}{c}-\sqrt[3]{a+b x^3}\right)}{3 c \left(b c^3-a d^3\right)^{4/3}}-\frac{\left(3 b c^3-2 a d^3\right) \log \left(\frac{x \sqrt[3]{b c^3-a d^3}}{c}-\sqrt[3]{a+b x^3}\right)}{6 c \left(b c^3-a d^3\right)^{4/3}}-\frac{b c^2 \log \left(\sqrt[3]{b c^3-a d^3}+d \sqrt[3]{a+b x^3}\right)}{2 \left(b c^3-a d^3\right)^{4/3}}+\frac{2 a d^3 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c^3-a d^3}}{c \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c \left(b c^3-a d^3\right)^{4/3}}+\frac{\left(3 b c^3-2 a d^3\right) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c^3-a d^3}}{c \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c \left(b c^3-a d^3\right)^{4/3}}-\frac{b c^2 \tan ^{-1}\left(\frac{1-\frac{2 d \sqrt[3]{a+b x^3}}{\sqrt[3]{b c^3-a d^3}}}{\sqrt{3}}\right)}{\sqrt{3} \left(b c^3-a d^3\right)^{4/3}}",1,"Defer[Int][1/((c + d*x)^2*(a + b*x^3)^(1/3)), x]","F",0,0,0,0,-1,"{}"
35,0,0,0,0.0825825,"\int \frac{1}{(c+d x)^3 \sqrt[3]{a+b x^3}} \, dx","Int[1/((c + d*x)^3*(a + b*x^3)^(1/3)),x]","\int \frac{1}{(c+d x)^3 \sqrt[3]{a+b x^3}} \, dx","\frac{2 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b c^3-a d^3} x}{c \sqrt[3]{b x^3+a}}+1}{\sqrt{3}}\right) d^6}{9 \sqrt{3} c^2 \left(b c^3-a d^3\right)^{7/3}}+\frac{a^2 \log \left(c^3+d^3 x^3\right) d^6}{27 c^2 \left(b c^3-a d^3\right)^{7/3}}-\frac{a^2 \log \left(\frac{\sqrt[3]{b c^3-a d^3} x}{c}-\sqrt[3]{b x^3+a}\right) d^6}{9 c^2 \left(b c^3-a d^3\right)^{7/3}}+\frac{6 x^5 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{5}{3};\frac{1}{3},3;\frac{8}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right) d^4}{5 c^7 \sqrt[3]{b x^3+a}}+\frac{7 a \left(3 b c^3-a d^3\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b c^3-a d^3} x}{c \sqrt[3]{b x^3+a}}+1}{\sqrt{3}}\right) d^3}{9 \sqrt{3} c^2 \left(b c^3-a d^3\right)^{7/3}}+\frac{7 a \left(3 b c^3-a d^3\right) \log \left(c^3+d^3 x^3\right) d^3}{54 c^2 \left(b c^3-a d^3\right)^{7/3}}-\frac{7 a \left(3 b c^3-a d^3\right) \log \left(\frac{\sqrt[3]{b c^3-a d^3} x}{c}-\sqrt[3]{b x^3+a}\right) d^3}{18 c^2 \left(b c^3-a d^3\right)^{7/3}}-\frac{7 \left(3 b c^3+a d^3\right) x \left(b x^3+a\right)^{2/3} d^3}{18 \left(b c^3-a d^3\right)^2 \left(c^3+d^3 x^3\right)}+\frac{\left(3 b c^3-7 a d^3\right) x \left(b x^3+a\right)^{2/3} d^3}{18 \left(b c^3-a d^3\right)^2 \left(c^3+d^3 x^3\right)}-\frac{\left(9 b c^3-5 a d^3\right) x \left(b x^3+a\right)^{2/3} d^3}{18 \left(b c^3-a d^3\right)^2 \left(c^3+d^3 x^3\right)}-\frac{3 c^3 x \left(b x^3+a\right)^{2/3} d^3}{2 \left(b c^3-a d^3\right) \left(c^3+d^3 x^3\right)^2}+\frac{4 b c^4 \left(b x^3+a\right)^{2/3} d^2}{3 \left(b c^3-a d^3\right)^2 \left(c^3+d^3 x^3\right)}-\frac{c \left(b c^3-3 a d^3\right) \left(b x^3+a\right)^{2/3} d^2}{3 \left(b c^3-a d^3\right)^2 \left(c^3+d^3 x^3\right)}+\frac{3 c^4 \left(b x^3+a\right)^{2/3} d^2}{2 \left(b c^3-a d^3\right) \left(c^3+d^3 x^3\right)^2}-\frac{3 x^2 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{2}{3};\frac{1}{3},3;\frac{5}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right) d}{2 c^4 \sqrt[3]{b x^3+a}}+\frac{\left(9 b^2 c^6-12 a b d^3 c^3+5 a^2 d^6\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b c^3-a d^3} x}{c \sqrt[3]{b x^3+a}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} c^2 \left(b c^3-a d^3\right)^{7/3}}-\frac{4 b^2 c^4 \tan ^{-1}\left(\frac{1-\frac{2 d \sqrt[3]{b x^3+a}}{\sqrt[3]{b c^3-a d^3}}}{\sqrt{3}}\right)}{3 \sqrt{3} \left(b c^3-a d^3\right)^{7/3}}+\frac{b c \left(b c^3-3 a d^3\right) \tan ^{-1}\left(\frac{1-\frac{2 d \sqrt[3]{b x^3+a}}{\sqrt[3]{b c^3-a d^3}}}{\sqrt{3}}\right)}{3 \sqrt{3} \left(b c^3-a d^3\right)^{7/3}}+\frac{\left(9 b^2 c^6-12 a b d^3 c^3+5 a^2 d^6\right) \log \left(c^3+d^3 x^3\right)}{54 c^2 \left(b c^3-a d^3\right)^{7/3}}+\frac{2 b^2 c^4 \log \left(c^3+d^3 x^3\right)}{9 \left(b c^3-a d^3\right)^{7/3}}-\frac{b c \left(b c^3-3 a d^3\right) \log \left(c^3+d^3 x^3\right)}{18 \left(b c^3-a d^3\right)^{7/3}}-\frac{\left(9 b^2 c^6-12 a b d^3 c^3+5 a^2 d^6\right) \log \left(\frac{\sqrt[3]{b c^3-a d^3} x}{c}-\sqrt[3]{b x^3+a}\right)}{18 c^2 \left(b c^3-a d^3\right)^{7/3}}-\frac{2 b^2 c^4 \log \left(\sqrt[3]{b x^3+a} d+\sqrt[3]{b c^3-a d^3}\right)}{3 \left(b c^3-a d^3\right)^{7/3}}+\frac{b c \left(b c^3-3 a d^3\right) \log \left(\sqrt[3]{b x^3+a} d+\sqrt[3]{b c^3-a d^3}\right)}{6 \left(b c^3-a d^3\right)^{7/3}}",1,"Defer[Int][1/((c + d*x)^3*(a + b*x^3)^(1/3)), x]","F",0,0,0,0,-1,"{}"
36,1,416,0,0.2676706,"\int \frac{(c+d x)^4}{\left(a+b x^3\right)^{2/3}} \, dx","Int[(c + d*x)^4/(a + b*x^3)^(2/3),x]","-\frac{4 c^3 d \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3 b^{2/3}}+\frac{2 c^3 d \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{3 b^{2/3}}-\frac{4 c^3 d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}+\frac{2 a d^4 \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{9 b^{5/3}}-\frac{a d^4 \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{9 b^{5/3}}+\frac{2 a d^4 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{5/3}}+\frac{6 c^2 d^2 \sqrt[3]{a+b x^3}}{b}+\frac{c^4 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\left(a+b x^3\right)^{2/3}}+\frac{c d^3 x^4 \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{\left(a+b x^3\right)^{2/3}}+\frac{d^4 x^2 \sqrt[3]{a+b x^3}}{3 b}","-\frac{2 c^3 d \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{b^{2/3}}-\frac{4 c^3 d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}+\frac{a d^4 \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{3 b^{5/3}}+\frac{2 a d^4 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{5/3}}+\frac{6 c^2 d^2 \sqrt[3]{a+b x^3}}{b}+\frac{c^4 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\left(a+b x^3\right)^{2/3}}+\frac{c d^3 x^4 \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{2}{3},\frac{4}{3};\frac{7}{3};-\frac{b x^3}{a}\right)}{\left(a+b x^3\right)^{2/3}}+\frac{d^4 x^2 \sqrt[3]{a+b x^3}}{3 b}",1,"(6*c^2*d^2*(a + b*x^3)^(1/3))/b + (d^4*x^2*(a + b*x^3)^(1/3))/(3*b) - (4*c^3*d*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(2/3)) + (2*a*d^4*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(5/3)) + (c^4*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(a + b*x^3)^(2/3) + (c*d^3*x^4*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[2/3, 4/3, 7/3, -((b*x^3)/a)])/(a + b*x^3)^(2/3) - (4*c^3*d*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*b^(2/3)) + (2*a*d^4*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(5/3)) + (2*c^3*d*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*b^(2/3)) - (a*d^4*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(5/3))","A",22,14,19,0.7368,1,"{1893, 246, 245, 331, 292, 31, 634, 617, 204, 628, 261, 365, 364, 321}"
37,1,239,0,0.2370102,"\int \frac{(c+d x)^3}{\left(a+b x^3\right)^{2/3}} \, dx","Int[(c + d*x)^3/(a + b*x^3)^(2/3),x]","-\frac{c^2 d \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{b^{2/3}}+\frac{c^2 d \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{2 b^{2/3}}-\frac{\sqrt{3} c^2 d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{b^{2/3}}+\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} \left(2 b c^3-a d^3\right) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 b \left(a+b x^3\right)^{2/3}}+\frac{3 c d^2 \sqrt[3]{a+b x^3}}{b}+\frac{d^3 x \sqrt[3]{a+b x^3}}{2 b}","-\frac{3 c^2 d \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2 b^{2/3}}-\frac{\sqrt{3} c^2 d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{b^{2/3}}+\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} \left(2 b c^3-a d^3\right) \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 b \left(a+b x^3\right)^{2/3}}+\frac{3 c d^2 \sqrt[3]{a+b x^3}}{b}+\frac{d^3 x \sqrt[3]{a+b x^3}}{2 b}",1,"(3*c*d^2*(a + b*x^3)^(1/3))/b + (d^3*x*(a + b*x^3)^(1/3))/(2*b) - (Sqrt[3]*c^2*d*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/b^(2/3) + ((2*b*c^3 - a*d^3)*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(2*b*(a + b*x^3)^(2/3)) - (c^2*d*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/b^(2/3) + (c^2*d*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(2*b^(2/3))","A",14,13,19,0.6842,1,"{1888, 1886, 261, 1893, 246, 245, 331, 292, 31, 634, 617, 204, 628}"
38,1,195,0,0.1477772,"\int \frac{(c+d x)^2}{\left(a+b x^3\right)^{2/3}} \, dx","Int[(c + d*x)^2/(a + b*x^3)^(2/3),x]","-\frac{2 c d \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3 b^{2/3}}+\frac{c d \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{3 b^{2/3}}-\frac{2 c d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}+\frac{c^2 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\left(a+b x^3\right)^{2/3}}+\frac{d^2 \sqrt[3]{a+b x^3}}{b}","-\frac{c d \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{b^{2/3}}-\frac{2 c d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}+\frac{c^2 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\left(a+b x^3\right)^{2/3}}+\frac{d^2 \sqrt[3]{a+b x^3}}{b}",1,"(d^2*(a + b*x^3)^(1/3))/b - (2*c*d*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(2/3)) + (c^2*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(a + b*x^3)^(2/3) - (2*c*d*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*b^(2/3)) + (c*d*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*b^(2/3))","A",13,12,19,0.6316,1,"{1886, 261, 1893, 246, 245, 331, 292, 31, 634, 617, 204, 628}"
39,1,172,0,0.1149444,"\int \frac{c+d x}{\left(a+b x^3\right)^{2/3}} \, dx","Int[(c + d*x)/(a + b*x^3)^(2/3),x]","-\frac{d \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3 b^{2/3}}+\frac{d \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{6 b^{2/3}}-\frac{d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}+\frac{c x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\left(a+b x^3\right)^{2/3}}","-\frac{d \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2 b^{2/3}}-\frac{d \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3}}+\frac{c x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{\left(a+b x^3\right)^{2/3}}",1,"-((d*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(2/3))) + (c*x*(1 + (b*x^3)/a)^(2/3)*Hypergeometric2F1[1/3, 2/3, 4/3, -((b*x^3)/a)])/(a + b*x^3)^(2/3) - (d*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*b^(2/3)) + (d*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*b^(2/3))","A",11,10,17,0.5882,1,"{1893, 246, 245, 331, 292, 31, 634, 617, 204, 628}"
40,0,0,0,0.0913542,"\int \frac{1}{(c+d x) \left(a+b x^3\right)^{2/3}} \, dx","Int[1/((c + d*x)*(a + b*x^3)^(2/3)),x]","\int \frac{1}{(c+d x) \left(a+b x^3\right)^{2/3}} \, dx","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{2}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right)}{c \left(a+b x^3\right)^{2/3}}-\frac{d \log \left(c^3+d^3 x^3\right)}{3 \left(b c^3-a d^3\right)^{2/3}}+\frac{d \log \left(\frac{x \sqrt[3]{b c^3-a d^3}}{c}-\sqrt[3]{a+b x^3}\right)}{2 \left(b c^3-a d^3\right)^{2/3}}+\frac{d \log \left(\sqrt[3]{b c^3-a d^3}+d \sqrt[3]{a+b x^3}\right)}{2 \left(b c^3-a d^3\right)^{2/3}}+\frac{d \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c^3-a d^3}}{c \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \left(b c^3-a d^3\right)^{2/3}}-\frac{d \tan ^{-1}\left(\frac{1-\frac{2 d \sqrt[3]{a+b x^3}}{\sqrt[3]{b c^3-a d^3}}}{\sqrt{3}}\right)}{\sqrt{3} \left(b c^3-a d^3\right)^{2/3}}",1,"Defer[Int][1/((c + d*x)*(a + b*x^3)^(2/3)), x]","F",0,0,0,0,-1,"{}"
41,0,0,0,0.0848816,"\int \frac{1}{(c+d x)^2 \left(a+b x^3\right)^{2/3}} \, dx","Int[1/((c + d*x)^2*(a + b*x^3)^(2/3)),x]","\int \frac{1}{(c+d x)^2 \left(a+b x^3\right)^{2/3}} \, dx","-\frac{d^3 x^4 \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},2;\frac{7}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right)}{2 c^5 \left(a+b x^3\right)^{2/3}}+\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{2}{3},2;\frac{4}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right)}{c^2 \left(a+b x^3\right)^{2/3}}+\frac{d^4 x^2 \sqrt[3]{a+b x^3}}{\left(c^3+d^3 x^3\right) \left(b c^3-a d^3\right)}+\frac{c^2 d^2 \sqrt[3]{a+b x^3}}{\left(c^3+d^3 x^3\right) \left(b c^3-a d^3\right)}-\frac{a d^4 \log \left(c^3+d^3 x^3\right)}{9 c \left(b c^3-a d^3\right)^{5/3}}+\frac{a d^4 \log \left(\frac{x \sqrt[3]{b c^3-a d^3}}{c}-\sqrt[3]{a+b x^3}\right)}{3 c \left(b c^3-a d^3\right)^{5/3}}-\frac{d \left(3 b c^3-a d^3\right) \log \left(c^3+d^3 x^3\right)}{9 c \left(b c^3-a d^3\right)^{5/3}}-\frac{b c^2 d \log \left(c^3+d^3 x^3\right)}{3 \left(b c^3-a d^3\right)^{5/3}}+\frac{d \left(3 b c^3-a d^3\right) \log \left(\frac{x \sqrt[3]{b c^3-a d^3}}{c}-\sqrt[3]{a+b x^3}\right)}{3 c \left(b c^3-a d^3\right)^{5/3}}+\frac{b c^2 d \log \left(\sqrt[3]{b c^3-a d^3}+d \sqrt[3]{a+b x^3}\right)}{\left(b c^3-a d^3\right)^{5/3}}+\frac{2 a d^4 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c^3-a d^3}}{c \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c \left(b c^3-a d^3\right)^{5/3}}+\frac{2 d \left(3 b c^3-a d^3\right) \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c^3-a d^3}}{c \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c \left(b c^3-a d^3\right)^{5/3}}-\frac{2 b c^2 d \tan ^{-1}\left(\frac{1-\frac{2 d \sqrt[3]{a+b x^3}}{\sqrt[3]{b c^3-a d^3}}}{\sqrt{3}}\right)}{\sqrt{3} \left(b c^3-a d^3\right)^{5/3}}",1,"Defer[Int][1/((c + d*x)^2*(a + b*x^3)^(2/3)), x]","F",0,0,0,0,-1,"{}"
42,0,0,0,0.0831781,"\int \frac{1}{(c+d x)^3 \left(a+b x^3\right)^{2/3}} \, dx","Int[1/((c + d*x)^3*(a + b*x^3)^(2/3)),x]","\int \frac{1}{(c+d x)^3 \left(a+b x^3\right)^{2/3}} \, dx","\frac{d^6 \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{7}{3};\frac{2}{3},3;\frac{10}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right) x^7}{7 c^9 \left(b x^3+a\right)^{2/3}}-\frac{7 d^3 \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},3;\frac{7}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right) x^4}{4 c^6 \left(b x^3+a\right)^{2/3}}+\frac{d^4 \left(3 b c^3+2 a d^3\right) \sqrt[3]{b x^3+a} x^2}{3 c \left(b c^3-a d^3\right)^2 \left(c^3+d^3 x^3\right)}+\frac{d^4 \left(9 b c^3-4 a d^3\right) \sqrt[3]{b x^3+a} x^2}{6 c \left(b c^3-a d^3\right)^2 \left(c^3+d^3 x^3\right)}+\frac{3 c^2 d^4 \sqrt[3]{b x^3+a} x^2}{2 \left(b c^3-a d^3\right) \left(c^3+d^3 x^3\right)^2}+\frac{\left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{2}{3},3;\frac{4}{3};-\frac{b x^3}{a},-\frac{d^3 x^3}{c^3}\right) x}{c^3 \left(b x^3+a\right)^{2/3}}+\frac{2 a d^4 \left(6 b c^3-a d^3\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b c^3-a d^3} x}{c \sqrt[3]{b x^3+a}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c^2 \left(b c^3-a d^3\right)^{8/3}}+\frac{d \left(9 b^2 c^6-6 a b d^3 c^3+2 a^2 d^6\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b c^3-a d^3} x}{c \sqrt[3]{b x^3+a}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} c^2 \left(b c^3-a d^3\right)^{8/3}}-\frac{10 b^2 c^4 d \tan ^{-1}\left(\frac{1-\frac{2 d \sqrt[3]{b x^3+a}}{\sqrt[3]{b c^3-a d^3}}}{\sqrt{3}}\right)}{3 \sqrt{3} \left(b c^3-a d^3\right)^{8/3}}+\frac{b c d \left(b c^3-6 a d^3\right) \tan ^{-1}\left(\frac{1-\frac{2 d \sqrt[3]{b x^3+a}}{\sqrt[3]{b c^3-a d^3}}}{\sqrt{3}}\right)}{3 \sqrt{3} \left(b c^3-a d^3\right)^{8/3}}-\frac{a d^4 \left(6 b c^3-a d^3\right) \log \left(c^3+d^3 x^3\right)}{9 c^2 \left(b c^3-a d^3\right)^{8/3}}-\frac{d \left(9 b^2 c^6-6 a b d^3 c^3+2 a^2 d^6\right) \log \left(c^3+d^3 x^3\right)}{18 c^2 \left(b c^3-a d^3\right)^{8/3}}-\frac{5 b^2 c^4 d \log \left(c^3+d^3 x^3\right)}{9 \left(b c^3-a d^3\right)^{8/3}}+\frac{b c d \left(b c^3-6 a d^3\right) \log \left(c^3+d^3 x^3\right)}{18 \left(b c^3-a d^3\right)^{8/3}}+\frac{a d^4 \left(6 b c^3-a d^3\right) \log \left(\frac{\sqrt[3]{b c^3-a d^3} x}{c}-\sqrt[3]{b x^3+a}\right)}{3 c^2 \left(b c^3-a d^3\right)^{8/3}}+\frac{d \left(9 b^2 c^6-6 a b d^3 c^3+2 a^2 d^6\right) \log \left(\frac{\sqrt[3]{b c^3-a d^3} x}{c}-\sqrt[3]{b x^3+a}\right)}{6 c^2 \left(b c^3-a d^3\right)^{8/3}}+\frac{5 b^2 c^4 d \log \left(\sqrt[3]{b x^3+a} d+\sqrt[3]{b c^3-a d^3}\right)}{3 \left(b c^3-a d^3\right)^{8/3}}-\frac{b c d \left(b c^3-6 a d^3\right) \log \left(\sqrt[3]{b x^3+a} d+\sqrt[3]{b c^3-a d^3}\right)}{6 \left(b c^3-a d^3\right)^{8/3}}+\frac{5 b c^4 d^2 \sqrt[3]{b x^3+a}}{3 \left(b c^3-a d^3\right)^2 \left(c^3+d^3 x^3\right)}-\frac{c d^2 \left(b c^3-6 a d^3\right) \sqrt[3]{b x^3+a}}{6 \left(b c^3-a d^3\right)^2 \left(c^3+d^3 x^3\right)}+\frac{3 c^4 d^2 \sqrt[3]{b x^3+a}}{2 \left(b c^3-a d^3\right) \left(c^3+d^3 x^3\right)^2}",1,"Defer[Int][1/((c + d*x)^3*(a + b*x^3)^(2/3)), x]","F",0,0,0,0,-1,"{}"
43,1,37,0,0.1048993,"\int \frac{2^{2/3}-2 x}{\left(2^{2/3}+x\right) \sqrt{1+x^3}} \, dx","Int[(2^(2/3) - 2*x)/((2^(2/3) + x)*Sqrt[1 + x^3]),x]","\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{\sqrt{3}}","\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{\sqrt{3}}",1,"(2*2^(2/3)*ArcTan[(Sqrt[3]*(1 + 2^(1/3)*x))/Sqrt[1 + x^3]])/Sqrt[3]","A",2,2,28,0.07143,1,"{2137, 203}"
44,1,40,0,0.1225248,"\int \frac{2^{2/3}+2 x}{\left(2^{2/3}-x\right) \sqrt{1-x^3}} \, dx","Int[(2^(2/3) + 2*x)/((2^(2/3) - x)*Sqrt[1 - x^3]),x]","-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{\sqrt{3}}","-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{\sqrt{3}}",1,"(-2*2^(2/3)*ArcTan[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[1 - x^3]])/Sqrt[3]","A",2,2,32,0.06250,1,"{2137, 203}"
45,1,38,0,0.1124266,"\int \frac{2^{2/3}+2 x}{\left(2^{2/3}-x\right) \sqrt{-1+x^3}} \, dx","Int[(2^(2/3) + 2*x)/((2^(2/3) - x)*Sqrt[-1 + x^3]),x]","-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{x^3-1}}\right)}{\sqrt{3}}","-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{x^3-1}}\right)}{\sqrt{3}}",1,"(-2*2^(2/3)*ArcTanh[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[-1 + x^3]])/Sqrt[3]","A",2,2,30,0.06667,1,"{2137, 206}"
46,1,39,0,0.1135434,"\int \frac{2^{2/3}-2 x}{\left(2^{2/3}+x\right) \sqrt{-1-x^3}} \, dx","Int[(2^(2/3) - 2*x)/((2^(2/3) + x)*Sqrt[-1 - x^3]),x]","\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{-x^3-1}}\right)}{\sqrt{3}}","\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{-x^3-1}}\right)}{\sqrt{3}}",1,"(2*2^(2/3)*ArcTanh[(Sqrt[3]*(1 + 2^(1/3)*x))/Sqrt[-1 - x^3]])/Sqrt[3]","A",2,2,30,0.06667,1,"{2137, 206}"
47,1,63,0,0.1787089,"\int \frac{2^{2/3} \sqrt[3]{a}-2 \sqrt[3]{b} x}{\left(2^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a+b x^3}} \, dx","Int[(2^(2/3)*a^(1/3) - 2*b^(1/3)*x)/((2^(2/3)*a^(1/3) + b^(1/3)*x)*Sqrt[a + b*x^3]),x]","\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{b}}","\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{b}}",1,"(2*2^(2/3)*ArcTan[(Sqrt[3]*a^(1/6)*(a^(1/3) + 2^(1/3)*b^(1/3)*x))/Sqrt[a + b*x^3]])/(Sqrt[3]*a^(1/6)*b^(1/3))","A",2,2,53,0.03774,1,"{2137, 203}"
48,1,65,0,0.1991905,"\int \frac{2^{2/3} \sqrt[3]{a}+2 \sqrt[3]{b} x}{\left(2^{2/3} \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{a-b x^3}} \, dx","Int[(2^(2/3)*a^(1/3) + 2*b^(1/3)*x)/((2^(2/3)*a^(1/3) - b^(1/3)*x)*Sqrt[a - b*x^3]),x]","-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{b}}","-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{b}}",1,"(-2*2^(2/3)*ArcTan[(Sqrt[3]*a^(1/6)*(a^(1/3) - 2^(1/3)*b^(1/3)*x))/Sqrt[a - b*x^3]])/(Sqrt[3]*a^(1/6)*b^(1/3))","A",2,2,55,0.03636,1,"{2137, 203}"
49,1,66,0,0.2007211,"\int \frac{2^{2/3} \sqrt[3]{a}+2 \sqrt[3]{b} x}{\left(2^{2/3} \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{-a+b x^3}} \, dx","Int[(2^(2/3)*a^(1/3) + 2*b^(1/3)*x)/((2^(2/3)*a^(1/3) - b^(1/3)*x)*Sqrt[-a + b*x^3]),x]","-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{b}}","-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{b}}",1,"(-2*2^(2/3)*ArcTanh[(Sqrt[3]*a^(1/6)*(a^(1/3) - 2^(1/3)*b^(1/3)*x))/Sqrt[-a + b*x^3]])/(Sqrt[3]*a^(1/6)*b^(1/3))","A",2,2,56,0.03571,1,"{2137, 206}"
50,1,66,0,0.1930787,"\int \frac{2^{2/3} \sqrt[3]{a}-2 \sqrt[3]{b} x}{\left(2^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{-a-b x^3}} \, dx","Int[(2^(2/3)*a^(1/3) - 2*b^(1/3)*x)/((2^(2/3)*a^(1/3) + b^(1/3)*x)*Sqrt[-a - b*x^3]),x]","\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{b}}","\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{3} \sqrt[6]{a} \sqrt[3]{b}}",1,"(2*2^(2/3)*ArcTanh[(Sqrt[3]*a^(1/6)*(a^(1/3) + 2^(1/3)*b^(1/3)*x))/Sqrt[-a - b*x^3]])/(Sqrt[3]*a^(1/6)*b^(1/3))","A",2,2,56,0.03571,1,"{2137, 206}"
51,1,49,0,0.123039,"\int \frac{c-2 d x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx","Int[(c - 2*d*x)/((c + d*x)*Sqrt[c^3 + 4*d^3*x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{c} (c+2 d x)}{\sqrt{c^3+4 d^3 x^3}}\right)}{\sqrt{3} \sqrt{c} d}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{c} (c+2 d x)}{\sqrt{c^3+4 d^3 x^3}}\right)}{\sqrt{3} \sqrt{c} d}",1,"(2*ArcTan[(Sqrt[3]*Sqrt[c]*(c + 2*d*x))/Sqrt[c^3 + 4*d^3*x^3]])/(Sqrt[3]*Sqrt[c]*d)","A",2,2,30,0.06667,1,"{2137, 203}"
52,1,158,0,0.2131548,"\int \frac{2+3 x}{\left(2^{2/3}+x\right) \sqrt{1+x^3}} \, dx","Int[(2 + 3*x)/((2^(2/3) + x)*Sqrt[1 + x^3]),x]","\frac{2 \left(2-3\ 2^{2/3}\right) \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{3 \sqrt{3}}+\frac{2 \left(3+2 \sqrt[3]{2}\right) \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2 \left(2-3\ 2^{2/3}\right) \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{3 \sqrt{3}}+\frac{2 \left(3+2 \sqrt[3]{2}\right) \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(2*(2 - 3*2^(2/3))*ArcTan[(Sqrt[3]*(1 + 2^(1/3)*x))/Sqrt[1 + x^3]])/(3*Sqrt[3]) + (2*(3 + 2*2^(1/3))*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,24,0.1667,1,"{2139, 218, 2137, 203}"
53,1,173,0,0.2422654,"\int \frac{2+3 x}{\left(2^{2/3}-x\right) \sqrt{1-x^3}} \, dx","Int[(2 + 3*x)/((2^(2/3) - x)*Sqrt[1 - x^3]),x]","\frac{2 \left(3-2 \sqrt[3]{2}\right) \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2 \left(2+3\ 2^{2/3}\right) \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{3 \sqrt{3}}","\frac{2 \left(3-2 \sqrt[3]{2}\right) \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2 \left(2+3\ 2^{2/3}\right) \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{3 \sqrt{3}}",1,"(-2*(2 + 3*2^(2/3))*ArcTan[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[1 - x^3]])/(3*Sqrt[3]) + (2*(3 - 2*2^(1/3))*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",4,4,28,0.1429,1,"{2139, 218, 2137, 203}"
54,1,176,0,0.2249158,"\int \frac{2+3 x}{\left(2^{2/3}-x\right) \sqrt{-1+x^3}} \, dx","Int[(2 + 3*x)/((2^(2/3) - x)*Sqrt[-1 + x^3]),x]","\frac{2 \left(3-2 \sqrt[3]{2}\right) \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 \left(2+3\ 2^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{x^3-1}}\right)}{3 \sqrt{3}}","\frac{2 \left(3-2 \sqrt[3]{2}\right) \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 \left(2+3\ 2^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{x^3-1}}\right)}{3 \sqrt{3}}",1,"(-2*(2 + 3*2^(2/3))*ArcTanh[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[-1 + x^3]])/(3*Sqrt[3]) + (2*(3 - 2*2^(1/3))*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",4,4,26,0.1538,1,"{2139, 219, 2137, 206}"
55,1,169,0,0.2292964,"\int \frac{2+3 x}{\left(2^{2/3}+x\right) \sqrt{-1-x^3}} \, dx","Int[(2 + 3*x)/((2^(2/3) + x)*Sqrt[-1 - x^3]),x]","\frac{2 \left(2-3\ 2^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{-x^3-1}}\right)}{3 \sqrt{3}}+\frac{2 \left(3+2 \sqrt[3]{2}\right) \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{2 \left(2-3\ 2^{2/3}\right) \tanh ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{-x^3-1}}\right)}{3 \sqrt{3}}+\frac{2 \left(3+2 \sqrt[3]{2}\right) \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(2*(2 - 3*2^(2/3))*ArcTanh[(Sqrt[3]*(1 + 2^(1/3)*x))/Sqrt[-1 - x^3]])/(3*Sqrt[3]) + (2*(3 + 2*2^(1/3))*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",4,4,26,0.1538,1,"{2139, 219, 2137, 206}"
56,1,159,0,0.2321604,"\int \frac{e+f x}{\left(2^{2/3}+x\right) \sqrt{1+x^3}} \, dx","Int[(e + f*x)/((2^(2/3) + x)*Sqrt[1 + x^3]),x]","\frac{2 \left(e-2^{2/3} f\right) \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{3 \sqrt{3}}+\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(\sqrt[3]{2} e+f\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2 \left(e-2^{2/3} f\right) \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{3 \sqrt{3}}+\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(\sqrt[3]{2} e+f\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(2*(e - 2^(2/3)*f)*ArcTan[(Sqrt[3]*(1 + 2^(1/3)*x))/Sqrt[1 + x^3]])/(3*Sqrt[3]) + (2*Sqrt[2 + Sqrt[3]]*(2^(1/3)*e + f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,24,0.1667,1,"{2139, 218, 2137, 203}"
57,1,175,0,0.2596304,"\int \frac{e+f x}{\left(2^{2/3}-x\right) \sqrt{1-x^3}} \, dx","Int[(e + f*x)/((2^(2/3) - x)*Sqrt[1 - x^3]),x]","-\frac{2 \left(e+2^{2/3} f\right) \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{3 \sqrt{3}}-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(\sqrt[3]{2} e-f\right) F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{2 \left(e+2^{2/3} f\right) \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{3 \sqrt{3}}-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(\sqrt[3]{2} e-f\right) F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(-2*(e + 2^(2/3)*f)*ArcTan[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[1 - x^3]])/(3*Sqrt[3]) - (2*Sqrt[2 + Sqrt[3]]*(2^(1/3)*e - f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",4,4,28,0.1429,1,"{2139, 218, 2137, 203}"
58,1,178,0,0.2244026,"\int \frac{e+f x}{\left(2^{2/3}-x\right) \sqrt{-1+x^3}} \, dx","Int[(e + f*x)/((2^(2/3) - x)*Sqrt[-1 + x^3]),x]","-\frac{2 \left(e+2^{2/3} f\right) \tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{x^3-1}}\right)}{3 \sqrt{3}}-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(\sqrt[3]{2} e-f\right) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","-\frac{2 \left(e+2^{2/3} f\right) \tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{x^3-1}}\right)}{3 \sqrt{3}}-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(\sqrt[3]{2} e-f\right) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(-2*(e + 2^(2/3)*f)*ArcTanh[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[-1 + x^3]])/(3*Sqrt[3]) - (2*Sqrt[2 - Sqrt[3]]*(2^(1/3)*e - f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",4,4,26,0.1538,1,"{2139, 219, 2137, 206}"
59,1,170,0,0.2217449,"\int \frac{e+f x}{\left(2^{2/3}+x\right) \sqrt{-1-x^3}} \, dx","Int[(e + f*x)/((2^(2/3) + x)*Sqrt[-1 - x^3]),x]","\frac{2 \left(e-2^{2/3} f\right) \tanh ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{-x^3-1}}\right)}{3 \sqrt{3}}+\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(\sqrt[3]{2} e+f\right) F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{2 \left(e-2^{2/3} f\right) \tanh ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{-x^3-1}}\right)}{3 \sqrt{3}}+\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(\sqrt[3]{2} e+f\right) F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(2*(e - 2^(2/3)*f)*ArcTanh[(Sqrt[3]*(1 + 2^(1/3)*x))/Sqrt[-1 - x^3]])/(3*Sqrt[3]) + (2*Sqrt[2 - Sqrt[3]]*(2^(1/3)*e + f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",4,4,26,0.1538,1,"{2139, 219, 2137, 206}"
60,1,316,0,0.4086529,"\int \frac{e+f x}{\left(2^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a+b x^3}} \, dx","Int[(e + f*x)/((2^(2/3)*a^(1/3) + b^(1/3)*x)*Sqrt[a + b*x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{a} f+\sqrt[3]{2} \sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \left(\sqrt[3]{b} e-2^{2/3} \sqrt[3]{a} f\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{3 \sqrt{3} \sqrt{a} b^{2/3}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{a} f+\sqrt[3]{2} \sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \left(\sqrt[3]{b} e-2^{2/3} \sqrt[3]{a} f\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{3 \sqrt{3} \sqrt{a} b^{2/3}}",1,"(2*(b^(1/3)*e - 2^(2/3)*a^(1/3)*f)*ArcTan[(Sqrt[3]*a^(1/6)*(a^(1/3) + 2^(1/3)*b^(1/3)*x))/Sqrt[a + b*x^3]])/(3*Sqrt[3]*Sqrt[a]*b^(2/3)) + (2*Sqrt[2 + Sqrt[3]]*(2^(1/3)*b^(1/3)*e + a^(1/3)*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,38,0.1053,1,"{2139, 218, 2137, 203}"
61,1,324,0,0.429667,"\int \frac{e+f x}{\left(2^{2/3} \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{a-b x^3}} \, dx","Int[(e + f*x)/((2^(2/3)*a^(1/3) - b^(1/3)*x)*Sqrt[a - b*x^3]),x]","-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{2} \sqrt[3]{b} e-\sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \left(2^{2/3} \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{3 \sqrt{3} \sqrt{a} b^{2/3}}","-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{2} \sqrt[3]{b} e-\sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \left(2^{2/3} \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{3 \sqrt{3} \sqrt{a} b^{2/3}}",1,"(-2*(b^(1/3)*e + 2^(2/3)*a^(1/3)*f)*ArcTan[(Sqrt[3]*a^(1/6)*(a^(1/3) - 2^(1/3)*b^(1/3)*x))/Sqrt[a - b*x^3]])/(3*Sqrt[3]*Sqrt[a]*b^(2/3)) - (2*Sqrt[2 + Sqrt[3]]*(2^(1/3)*b^(1/3)*e - a^(1/3)*f)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",4,4,40,0.1000,1,"{2139, 218, 2137, 203}"
62,1,333,0,0.4128703,"\int \frac{e+f x}{\left(2^{2/3} \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{-a+b x^3}} \, dx","Int[(e + f*x)/((2^(2/3)*a^(1/3) - b^(1/3)*x)*Sqrt[-a + b*x^3]),x]","-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{2} \sqrt[3]{b} e-\sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2 \left(2^{2/3} \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{3 \sqrt{3} \sqrt{a} b^{2/3}}","-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{2} \sqrt[3]{b} e-\sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2 \left(2^{2/3} \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{3 \sqrt{3} \sqrt{a} b^{2/3}}",1,"(-2*(b^(1/3)*e + 2^(2/3)*a^(1/3)*f)*ArcTanh[(Sqrt[3]*a^(1/6)*(a^(1/3) - 2^(1/3)*b^(1/3)*x))/Sqrt[-a + b*x^3]])/(3*Sqrt[3]*Sqrt[a]*b^(2/3)) - (2*Sqrt[2 - Sqrt[3]]*(2^(1/3)*b^(1/3)*e - a^(1/3)*f)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",4,4,41,0.09756,1,"{2139, 219, 2137, 206}"
63,1,329,0,0.3975151,"\int \frac{e+f x}{\left(2^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{-a-b x^3}} \, dx","Int[(e + f*x)/((2^(2/3)*a^(1/3) + b^(1/3)*x)*Sqrt[-a - b*x^3]),x]","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{a} f+\sqrt[3]{2} \sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{2 \left(\sqrt[3]{b} e-2^{2/3} \sqrt[3]{a} f\right) \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{3 \sqrt{3} \sqrt{a} b^{2/3}}","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{a} f+\sqrt[3]{2} \sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{2 \left(\sqrt[3]{b} e-2^{2/3} \sqrt[3]{a} f\right) \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{3 \sqrt{3} \sqrt{a} b^{2/3}}",1,"(2*(b^(1/3)*e - 2^(2/3)*a^(1/3)*f)*ArcTanh[(Sqrt[3]*a^(1/6)*(a^(1/3) + 2^(1/3)*b^(1/3)*x))/Sqrt[-a - b*x^3]])/(3*Sqrt[3]*Sqrt[a]*b^(2/3)) + (2*Sqrt[2 - Sqrt[3]]*(2^(1/3)*b^(1/3)*e + a^(1/3)*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",4,4,41,0.09756,1,"{2139, 219, 2137, 206}"
64,1,265,0,0.2964528,"\int \frac{e+f x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx","Int[(e + f*x)/((c + d*x)*Sqrt[c^3 + 4*d^3*x^3]),x]","\frac{2 (d e-c f) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{c} (c+2 d x)}{\sqrt{c^3+4 d^3 x^3}}\right)}{3 \sqrt{3} c^{3/2} d^2}+\frac{\sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(c+2^{2/3} d x\right) \sqrt{\frac{c^2-2^{2/3} c d x+2 \sqrt[3]{2} d^2 x^2}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} (c f+2 d e) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) c+2^{2/3} d x}{\left(1+\sqrt{3}\right) c+2^{2/3} d x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} c d^2 \sqrt{\frac{c \left(c+2^{2/3} d x\right)}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} \sqrt{c^3+4 d^3 x^3}}","\frac{2 (d e-c f) \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{c} (c+2 d x)}{\sqrt{c^3+4 d^3 x^3}}\right)}{3 \sqrt{3} c^{3/2} d^2}+\frac{\sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(c+2^{2/3} d x\right) \sqrt{\frac{c^2-2^{2/3} c d x+2 \sqrt[3]{2} d^2 x^2}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} (c f+2 d e) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) c+2^{2/3} d x}{\left(1+\sqrt{3}\right) c+2^{2/3} d x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} c d^2 \sqrt{\frac{c \left(c+2^{2/3} d x\right)}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} \sqrt{c^3+4 d^3 x^3}}",1,"(2*(d*e - c*f)*ArcTan[(Sqrt[3]*Sqrt[c]*(c + 2*d*x))/Sqrt[c^3 + 4*d^3*x^3]])/(3*Sqrt[3]*c^(3/2)*d^2) + (2^(1/3)*Sqrt[2 + Sqrt[3]]*(2*d*e + c*f)*(c + 2^(2/3)*d*x)*Sqrt[(c^2 - 2^(2/3)*c*d*x + 2*2^(1/3)*d^2*x^2)/((1 + Sqrt[3])*c + 2^(2/3)*d*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c + 2^(2/3)*d*x)/((1 + Sqrt[3])*c + 2^(2/3)*d*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*c*d^2*Sqrt[(c*(c + 2^(2/3)*d*x))/((1 + Sqrt[3])*c + 2^(2/3)*d*x)^2]*Sqrt[c^3 + 4*d^3*x^3])","A",4,4,29,0.1379,1,"{2139, 218, 2137, 203}"
65,1,145,0,0.2090899,"\int \frac{x}{\left(2^{2/3}+x\right) \sqrt{1+x^3}} \, dx","Int[x/((2^(2/3) + x)*Sqrt[1 + x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{3 \sqrt{3}}","\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{x^3+1}}\right)}{3 \sqrt{3}}",1,"(-2*2^(2/3)*ArcTan[(Sqrt[3]*(1 + 2^(1/3)*x))/Sqrt[1 + x^3]])/(3*Sqrt[3]) + (2*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,20,0.2000,1,"{2139, 218, 2137, 203}"
66,1,160,0,0.2412805,"\int \frac{x}{\left(2^{2/3}-x\right) \sqrt{1-x^3}} \, dx","Int[x/((2^(2/3) - x)*Sqrt[1 - x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{3 \sqrt{3}}","\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{3 \sqrt{3}}",1,"(-2*2^(2/3)*ArcTan[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[1 - x^3]])/(3*Sqrt[3]) + (2*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",4,4,24,0.1667,1,"{2139, 218, 2137, 203}"
67,1,163,0,0.2245782,"\int \frac{x}{\left(2^{2/3}-x\right) \sqrt{-1+x^3}} \, dx","Int[x/((2^(2/3) - x)*Sqrt[-1 + x^3]),x]","\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{x^3-1}}\right)}{3 \sqrt{3}}","\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{x^3-1}}\right)}{3 \sqrt{3}}",1,"(-2*2^(2/3)*ArcTanh[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[-1 + x^3]])/(3*Sqrt[3]) + (2*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",4,4,22,0.1818,1,"{2139, 219, 2137, 206}"
68,1,156,0,0.2278261,"\int \frac{x}{\left(2^{2/3}+x\right) \sqrt{-1-x^3}} \, dx","Int[x/((2^(2/3) + x)*Sqrt[-1 - x^3]),x]","\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{-x^3-1}}\right)}{3 \sqrt{3}}","\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \left(\sqrt[3]{2} x+1\right)}{\sqrt{-x^3-1}}\right)}{3 \sqrt{3}}",1,"(-2*2^(2/3)*ArcTanh[(Sqrt[3]*(1 + 2^(1/3)*x))/Sqrt[-1 - x^3]])/(3*Sqrt[3]) + (2*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",4,4,22,0.1818,1,"{2139, 219, 2137, 206}"
69,1,275,0,0.3590809,"\int \frac{x}{\left(2^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a+b x^3}} \, dx","Int[x/((2^(2/3)*a^(1/3) + b^(1/3)*x)*Sqrt[a + b*x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{3 \sqrt{3} \sqrt[6]{a} b^{2/3}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{3 \sqrt{3} \sqrt[6]{a} b^{2/3}}",1,"(-2*2^(2/3)*ArcTan[(Sqrt[3]*a^(1/6)*(a^(1/3) + 2^(1/3)*b^(1/3)*x))/Sqrt[a + b*x^3]])/(3*Sqrt[3]*a^(1/6)*b^(2/3)) + (2*Sqrt[2 + Sqrt[3]]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,34,0.1176,1,"{2139, 218, 2137, 203}"
70,1,283,0,0.3758625,"\int \frac{x}{\left(2^{2/3} \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{a-b x^3}} \, dx","Int[x/((2^(2/3)*a^(1/3) - b^(1/3)*x)*Sqrt[a - b*x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{3 \sqrt{3} \sqrt[6]{a} b^{2/3}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2\ 2^{2/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{3 \sqrt{3} \sqrt[6]{a} b^{2/3}}",1,"(-2*2^(2/3)*ArcTan[(Sqrt[3]*a^(1/6)*(a^(1/3) - 2^(1/3)*b^(1/3)*x))/Sqrt[a - b*x^3]])/(3*Sqrt[3]*a^(1/6)*b^(2/3)) + (2*Sqrt[2 + Sqrt[3]]*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",4,4,36,0.1111,1,"{2139, 218, 2137, 203}"
71,1,292,0,0.387256,"\int \frac{x}{\left(2^{2/3} \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{-a+b x^3}} \, dx","Int[x/((2^(2/3)*a^(1/3) - b^(1/3)*x)*Sqrt[-a + b*x^3]),x]","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{3 \sqrt{3} \sqrt[6]{a} b^{2/3}}","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{3 \sqrt{3} \sqrt[6]{a} b^{2/3}}",1,"(-2*2^(2/3)*ArcTanh[(Sqrt[3]*a^(1/6)*(a^(1/3) - 2^(1/3)*b^(1/3)*x))/Sqrt[-a + b*x^3]])/(3*Sqrt[3]*a^(1/6)*b^(2/3)) + (2*Sqrt[2 - Sqrt[3]]*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",4,4,37,0.1081,1,"{2139, 219, 2137, 206}"
72,1,288,0,0.3703835,"\int \frac{x}{\left(2^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{-a-b x^3}} \, dx","Int[x/((2^(2/3)*a^(1/3) + b^(1/3)*x)*Sqrt[-a - b*x^3]),x]","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{3 \sqrt{3} \sqrt[6]{a} b^{2/3}}","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2\ 2^{2/3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{2} \sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{3 \sqrt{3} \sqrt[6]{a} b^{2/3}}",1,"(-2*2^(2/3)*ArcTanh[(Sqrt[3]*a^(1/6)*(a^(1/3) + 2^(1/3)*b^(1/3)*x))/Sqrt[-a - b*x^3]])/(3*Sqrt[3]*a^(1/6)*b^(2/3)) + (2*Sqrt[2 - Sqrt[3]]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",4,4,37,0.1081,1,"{2139, 219, 2137, 206}"
73,1,246,0,0.2705586,"\int \frac{x}{(c+d x) \sqrt{c^3+4 d^3 x^3}} \, dx","Int[x/((c + d*x)*Sqrt[c^3 + 4*d^3*x^3]),x]","\frac{\sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(c+2^{2/3} d x\right) \sqrt{\frac{c^2-2^{2/3} c d x+2 \sqrt[3]{2} d^2 x^2}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) c+2^{2/3} d x}{\left(1+\sqrt{3}\right) c+2^{2/3} d x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} d^2 \sqrt{\frac{c \left(c+2^{2/3} d x\right)}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} \sqrt{c^3+4 d^3 x^3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{c} (c+2 d x)}{\sqrt{c^3+4 d^3 x^3}}\right)}{3 \sqrt{3} \sqrt{c} d^2}","\frac{\sqrt[3]{2} \sqrt{2+\sqrt{3}} \left(c+2^{2/3} d x\right) \sqrt{\frac{c^2-2^{2/3} c d x+2 \sqrt[3]{2} d^2 x^2}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) c+2^{2/3} d x}{\left(1+\sqrt{3}\right) c+2^{2/3} d x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} d^2 \sqrt{\frac{c \left(c+2^{2/3} d x\right)}{\left(\left(1+\sqrt{3}\right) c+2^{2/3} d x\right)^2}} \sqrt{c^3+4 d^3 x^3}}-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt{c} (c+2 d x)}{\sqrt{c^3+4 d^3 x^3}}\right)}{3 \sqrt{3} \sqrt{c} d^2}",1,"(-2*ArcTan[(Sqrt[3]*Sqrt[c]*(c + 2*d*x))/Sqrt[c^3 + 4*d^3*x^3]])/(3*Sqrt[3]*Sqrt[c]*d^2) + (2^(1/3)*Sqrt[2 + Sqrt[3]]*(c + 2^(2/3)*d*x)*Sqrt[(c^2 - 2^(2/3)*c*d*x + 2*2^(1/3)*d^2*x^2)/((1 + Sqrt[3])*c + 2^(2/3)*d*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c + 2^(2/3)*d*x)/((1 + Sqrt[3])*c + 2^(2/3)*d*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*d^2*Sqrt[(c*(c + 2^(2/3)*d*x))/((1 + Sqrt[3])*c + 2^(2/3)*d*x)^2]*Sqrt[c^3 + 4*d^3*x^3])","A",4,4,25,0.1600,1,"{2139, 218, 2137, 203}"
74,1,23,0,0.0592311,"\int \frac{1+x}{(2-x) \sqrt{1+x^3}} \, dx","Int[(1 + x)/((2 - x)*Sqrt[1 + x^3]),x]","\frac{2}{3} \tanh ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{x^3+1}}\right)","\frac{2}{3} \tanh ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{x^3+1}}\right)",1,"(2*ArcTanh[(1 + x)^2/(3*Sqrt[1 + x^3])])/3","A",2,2,20,0.1000,1,"{2138, 206}"
75,1,27,0,0.0650662,"\int \frac{1-x}{(2+x) \sqrt{1-x^3}} \, dx","Int[(1 - x)/((2 + x)*Sqrt[1 - x^3]),x]","-\frac{2}{3} \tanh ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{1-x^3}}\right)","-\frac{2}{3} \tanh ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{1-x^3}}\right)",1,"(-2*ArcTanh[(1 - x)^2/(3*Sqrt[1 - x^3])])/3","A",2,2,22,0.09091,1,"{2138, 206}"
76,1,25,0,0.0588041,"\int \frac{1-x}{(2+x) \sqrt{-1+x^3}} \, dx","Int[(1 - x)/((2 + x)*Sqrt[-1 + x^3]),x]","-\frac{2}{3} \tan ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{x^3-1}}\right)","-\frac{2}{3} \tan ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{x^3-1}}\right)",1,"(-2*ArcTan[(1 - x)^2/(3*Sqrt[-1 + x^3])])/3","A",2,2,20,0.1000,1,"{2138, 203}"
77,1,25,0,0.0674888,"\int \frac{1+x}{(2-x) \sqrt{-1-x^3}} \, dx","Int[(1 + x)/((2 - x)*Sqrt[-1 - x^3]),x]","\frac{2}{3} \tan ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{-x^3-1}}\right)","\frac{2}{3} \tan ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{-x^3-1}}\right)",1,"(2*ArcTan[(1 + x)^2/(3*Sqrt[-1 - x^3])])/3","A",2,2,22,0.09091,1,"{2138, 203}"
78,1,50,0,0.1323165,"\int \frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\left(2 \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{a+b x^3}} \, dx","Int[(a^(1/3) + b^(1/3)*x)/((2*a^(1/3) - b^(1/3)*x)*Sqrt[a + b*x^3]),x]","\frac{2 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a+b x^3}}\right)}{3 \sqrt[6]{a} \sqrt[3]{b}}","\frac{2 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a+b x^3}}\right)}{3 \sqrt[6]{a} \sqrt[3]{b}}",1,"(2*ArcTanh[(a^(1/3) + b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[a + b*x^3])])/(3*a^(1/6)*b^(1/3))","A",2,2,43,0.04651,1,"{2138, 206}"
79,1,52,0,0.1381344,"\int \frac{\sqrt[3]{a}-\sqrt[3]{b} x}{\left(2 \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a-b x^3}} \, dx","Int[(a^(1/3) - b^(1/3)*x)/((2*a^(1/3) + b^(1/3)*x)*Sqrt[a - b*x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a-b x^3}}\right)}{3 \sqrt[6]{a} \sqrt[3]{b}}","-\frac{2 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a-b x^3}}\right)}{3 \sqrt[6]{a} \sqrt[3]{b}}",1,"(-2*ArcTanh[(a^(1/3) - b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[a - b*x^3])])/(3*a^(1/6)*b^(1/3))","A",2,2,44,0.04545,1,"{2138, 206}"
80,1,53,0,0.1418401,"\int \frac{\sqrt[3]{a}-\sqrt[3]{b} x}{\left(2 \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{-a+b x^3}} \, dx","Int[(a^(1/3) - b^(1/3)*x)/((2*a^(1/3) + b^(1/3)*x)*Sqrt[-a + b*x^3]),x]","-\frac{2 \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{b x^3-a}}\right)}{3 \sqrt[6]{a} \sqrt[3]{b}}","-\frac{2 \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{b x^3-a}}\right)}{3 \sqrt[6]{a} \sqrt[3]{b}}",1,"(-2*ArcTan[(a^(1/3) - b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[-a + b*x^3])])/(3*a^(1/6)*b^(1/3))","A",2,2,45,0.04444,1,"{2138, 203}"
81,1,53,0,0.1413677,"\int \frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\left(2 \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{-a-b x^3}} \, dx","Int[(a^(1/3) + b^(1/3)*x)/((2*a^(1/3) - b^(1/3)*x)*Sqrt[-a - b*x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{-a-b x^3}}\right)}{3 \sqrt[6]{a} \sqrt[3]{b}}","\frac{2 \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{-a-b x^3}}\right)}{3 \sqrt[6]{a} \sqrt[3]{b}}",1,"(2*ArcTan[(a^(1/3) + b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[-a - b*x^3])])/(3*a^(1/6)*b^(1/3))","A",2,2,46,0.04348,1,"{2138, 203}"
82,1,46,0,0.1159306,"\int \frac{c-2 d x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx","Int[(c - 2*d*x)/((c + d*x)*Sqrt[c^3 - 8*d^3*x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{(c-2 d x)^2}{3 \sqrt{c} \sqrt{c^3-8 d^3 x^3}}\right)}{3 \sqrt{c} d}","-\frac{2 \tanh ^{-1}\left(\frac{(c-2 d x)^2}{3 \sqrt{c} \sqrt{c^3-8 d^3 x^3}}\right)}{3 \sqrt{c} d}",1,"(-2*ArcTanh[(c - 2*d*x)^2/(3*Sqrt[c]*Sqrt[c^3 - 8*d^3*x^3])])/(3*Sqrt[c]*d)","A",2,2,30,0.06667,1,"{2138, 206}"
83,1,139,0,0.149903,"\int \frac{e+f x}{(2-x) \sqrt{1+x^3}} \, dx","Int[(e + f*x)/((2 - x)*Sqrt[1 + x^3]),x]","\frac{2}{9} (e+2 f) \tanh ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{x^3+1}}\right)+\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (e-f) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2}{9} (e+2 f) \tanh ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{x^3+1}}\right)+\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (e-f) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(2*(e + 2*f)*ArcTanh[(1 + x)^2/(3*Sqrt[1 + x^3])])/9 + (2*Sqrt[2 + Sqrt[3]]*(e - f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,22,0.1818,1,"{2139, 218, 2138, 206}"
84,1,153,0,0.1605957,"\int \frac{e+f x}{(2+x) \sqrt{1-x^3}} \, dx","Int[(e + f*x)/((2 + x)*Sqrt[1 - x^3]),x]","-\frac{2}{9} (e-2 f) \tanh ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{1-x^3}}\right)-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (e+f) F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{2}{9} (e-2 f) \tanh ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{1-x^3}}\right)-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (e+f) F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(-2*(e - 2*f)*ArcTanh[(1 - x)^2/(3*Sqrt[1 - x^3])])/9 - (2*Sqrt[2 + Sqrt[3]]*(e + f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",4,4,22,0.1818,1,"{2139, 218, 2138, 206}"
85,1,156,0,0.1458914,"\int \frac{e+f x}{(2+x) \sqrt{-1+x^3}} \, dx","Int[(e + f*x)/((2 + x)*Sqrt[-1 + x^3]),x]","-\frac{2}{9} (e-2 f) \tan ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{x^3-1}}\right)-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} (e+f) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","-\frac{2}{9} (e-2 f) \tan ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{x^3-1}}\right)-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} (e+f) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(-2*(e - 2*f)*ArcTan[(1 - x)^2/(3*Sqrt[-1 + x^3])])/9 - (2*Sqrt[2 - Sqrt[3]]*(e + f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",4,4,20,0.2000,1,"{2139, 219, 2138, 203}"
86,1,150,0,0.1629716,"\int \frac{e+f x}{(2-x) \sqrt{-1-x^3}} \, dx","Int[(e + f*x)/((2 - x)*Sqrt[-1 - x^3]),x]","\frac{2}{9} (e+2 f) \tan ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{-x^3-1}}\right)+\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} (e-f) F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{2}{9} (e+2 f) \tan ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{-x^3-1}}\right)+\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} (e-f) F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(2*(e + 2*f)*ArcTan[(1 + x)^2/(3*Sqrt[-1 - x^3])])/9 + (2*Sqrt[2 - Sqrt[3]]*(e - f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",4,4,24,0.1667,1,"{2139, 219, 2138, 203}"
87,1,297,0,0.3149858,"\int \frac{e+f x}{\left(2 \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{a+b x^3}} \, dx","Int[(e + f*x)/((2*a^(1/3) - b^(1/3)*x)*Sqrt[a + b*x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \left(2 \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a+b x^3}}\right)}{9 \sqrt{a} b^{2/3}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \left(2 \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a+b x^3}}\right)}{9 \sqrt{a} b^{2/3}}",1,"(2*(b^(1/3)*e + 2*a^(1/3)*f)*ArcTanh[(a^(1/3) + b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[a + b*x^3])])/(9*Sqrt[a]*b^(2/3)) + (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*e - a^(1/3)*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,35,0.1143,1,"{2139, 218, 2138, 206}"
88,1,304,0,0.3175093,"\int \frac{e+f x}{\left(2 \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a-b x^3}} \, dx","Int[(e + f*x)/((2*a^(1/3) + b^(1/3)*x)*Sqrt[a - b*x^3]),x]","-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{a} f+\sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \left(\sqrt[3]{b} e-2 \sqrt[3]{a} f\right) \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a-b x^3}}\right)}{9 \sqrt{a} b^{2/3}}","-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{a} f+\sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{2 \left(\sqrt[3]{b} e-2 \sqrt[3]{a} f\right) \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a-b x^3}}\right)}{9 \sqrt{a} b^{2/3}}",1,"(-2*(b^(1/3)*e - 2*a^(1/3)*f)*ArcTanh[(a^(1/3) - b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[a - b*x^3])])/(9*Sqrt[a]*b^(2/3)) - (2*Sqrt[2 + Sqrt[3]]*(b^(1/3)*e + a^(1/3)*f)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",4,4,35,0.1143,1,"{2139, 218, 2138, 206}"
89,1,313,0,0.3204727,"\int \frac{e+f x}{\left(2 \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{-a+b x^3}} \, dx","Int[(e + f*x)/((2*a^(1/3) + b^(1/3)*x)*Sqrt[-a + b*x^3]),x]","-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{a} f+\sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2 \left(\sqrt[3]{b} e-2 \sqrt[3]{a} f\right) \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{b x^3-a}}\right)}{9 \sqrt{a} b^{2/3}}","-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{a} f+\sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2 \left(\sqrt[3]{b} e-2 \sqrt[3]{a} f\right) \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{b x^3-a}}\right)}{9 \sqrt{a} b^{2/3}}",1,"(-2*(b^(1/3)*e - 2*a^(1/3)*f)*ArcTan[(a^(1/3) - b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[-a + b*x^3])])/(9*Sqrt[a]*b^(2/3)) - (2*Sqrt[2 - Sqrt[3]]*(b^(1/3)*e + a^(1/3)*f)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",4,4,36,0.1111,1,"{2139, 219, 2138, 203}"
90,1,310,0,0.337208,"\int \frac{e+f x}{\left(2 \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{-a-b x^3}} \, dx","Int[(e + f*x)/((2*a^(1/3) - b^(1/3)*x)*Sqrt[-a - b*x^3]),x]","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{2 \left(2 \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{-a-b x^3}}\right)}{9 \sqrt{a} b^{2/3}}","\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{2 \left(2 \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{-a-b x^3}}\right)}{9 \sqrt{a} b^{2/3}}",1,"(2*(b^(1/3)*e + 2*a^(1/3)*f)*ArcTan[(a^(1/3) + b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[-a - b*x^3])])/(9*Sqrt[a]*b^(2/3)) + (2*Sqrt[2 - Sqrt[3]]*(b^(1/3)*e - a^(1/3)*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*a^(1/3)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",4,4,38,0.1053,1,"{2139, 219, 2138, 203}"
91,1,221,0,0.284123,"\int \frac{e+f x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx","Int[(e + f*x)/((c + d*x)*Sqrt[c^3 - 8*d^3*x^3]),x]","-\frac{2 (d e-c f) \tanh ^{-1}\left(\frac{(c-2 d x)^2}{3 \sqrt{c} \sqrt{c^3-8 d^3 x^3}}\right)}{9 c^{3/2} d^2}-\frac{\sqrt{2+\sqrt{3}} (c-2 d x) \sqrt{\frac{c^2+2 c d x+4 d^2 x^2}{\left(\left(1+\sqrt{3}\right) c-2 d x\right)^2}} (c f+2 d e) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) c-2 d x}{\left(1+\sqrt{3}\right) c-2 d x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} c d^2 \sqrt{\frac{c (c-2 d x)}{\left(\left(1+\sqrt{3}\right) c-2 d x\right)^2}} \sqrt{c^3-8 d^3 x^3}}","-\frac{2 (d e-c f) \tanh ^{-1}\left(\frac{(c-2 d x)^2}{3 \sqrt{c} \sqrt{c^3-8 d^3 x^3}}\right)}{9 c^{3/2} d^2}-\frac{\sqrt{2+\sqrt{3}} (c-2 d x) \sqrt{\frac{c^2+2 c d x+4 d^2 x^2}{\left(\left(1+\sqrt{3}\right) c-2 d x\right)^2}} (c f+2 d e) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) c-2 d x}{\left(1+\sqrt{3}\right) c-2 d x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} c d^2 \sqrt{\frac{c (c-2 d x)}{\left(\left(1+\sqrt{3}\right) c-2 d x\right)^2}} \sqrt{c^3-8 d^3 x^3}}",1,"(-2*(d*e - c*f)*ArcTanh[(c - 2*d*x)^2/(3*Sqrt[c]*Sqrt[c^3 - 8*d^3*x^3])])/(9*c^(3/2)*d^2) - (Sqrt[2 + Sqrt[3]]*(2*d*e + c*f)*(c - 2*d*x)*Sqrt[(c^2 + 2*c*d*x + 4*d^2*x^2)/((1 + Sqrt[3])*c - 2*d*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c - 2*d*x)/((1 + Sqrt[3])*c - 2*d*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*c*d^2*Sqrt[(c*(c - 2*d*x))/((1 + Sqrt[3])*c - 2*d*x)^2]*Sqrt[c^3 - 8*d^3*x^3])","A",4,4,29,0.1379,1,"{2139, 218, 2138, 206}"
92,1,129,0,0.1423365,"\int \frac{x}{(2-x) \sqrt{1+x^3}} \, dx","Int[x/((2 - x)*Sqrt[1 + x^3]),x]","\frac{4}{9} \tanh ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{x^3+1}}\right)-\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{4}{9} \tanh ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{x^3+1}}\right)-\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(4*ArcTanh[(1 + x)^2/(3*Sqrt[1 + x^3])])/9 - (2*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,18,0.2222,1,"{2139, 218, 2138, 206}"
93,1,145,0,0.1491378,"\int \frac{x}{(2+x) \sqrt{1-x^3}} \, dx","Int[x/((2 + x)*Sqrt[1 - x^3]),x]","\frac{4}{9} \tanh ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{1-x^3}}\right)-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","\frac{4}{9} \tanh ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{1-x^3}}\right)-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(4*ArcTanh[(1 - x)^2/(3*Sqrt[1 - x^3])])/9 - (2*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",4,4,18,0.2222,1,"{2139, 218, 2138, 206}"
94,1,148,0,0.1345641,"\int \frac{x}{(2+x) \sqrt{-1+x^3}} \, dx","Int[x/((2 + x)*Sqrt[-1 + x^3]),x]","\frac{4}{9} \tan ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{x^3-1}}\right)-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{4}{9} \tan ^{-1}\left(\frac{(1-x)^2}{3 \sqrt{x^3-1}}\right)-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(4*ArcTan[(1 - x)^2/(3*Sqrt[-1 + x^3])])/9 - (2*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",4,4,16,0.2500,1,"{2139, 219, 2138, 203}"
95,1,140,0,0.1549917,"\int \frac{x}{(2-x) \sqrt{-1-x^3}} \, dx","Int[x/((2 - x)*Sqrt[-1 - x^3]),x]","\frac{4}{9} \tan ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{-x^3-1}}\right)-\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{4}{9} \tan ^{-1}\left(\frac{(x+1)^2}{3 \sqrt{-x^3-1}}\right)-\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(4*ArcTan[(1 + x)^2/(3*Sqrt[-1 - x^3])])/9 - (2*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",4,4,20,0.2000,1,"{2139, 219, 2138, 203}"
96,1,260,0,0.280211,"\int \frac{x}{\left(2 \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{a+b x^3}} \, dx","Int[x/((2*a^(1/3) - b^(1/3)*x)*Sqrt[a + b*x^3]),x]","\frac{4 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a+b x^3}}\right)}{9 \sqrt[6]{a} b^{2/3}}-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}","\frac{4 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a+b x^3}}\right)}{9 \sqrt[6]{a} b^{2/3}}-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}",1,"(4*ArcTanh[(a^(1/3) + b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[a + b*x^3])])/(9*a^(1/6)*b^(2/3)) - (2*Sqrt[2 + Sqrt[3]]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,31,0.1290,1,"{2139, 218, 2138, 206}"
97,1,268,0,0.2874736,"\int \frac{x}{\left(2 \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a-b x^3}} \, dx","Int[x/((2*a^(1/3) + b^(1/3)*x)*Sqrt[a - b*x^3]),x]","\frac{4 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a-b x^3}}\right)}{9 \sqrt[6]{a} b^{2/3}}-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}","\frac{4 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{a-b x^3}}\right)}{9 \sqrt[6]{a} b^{2/3}}-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}",1,"(4*ArcTanh[(a^(1/3) - b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[a - b*x^3])])/(9*a^(1/6)*b^(2/3)) - (2*Sqrt[2 + Sqrt[3]]*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",4,4,31,0.1290,1,"{2139, 218, 2138, 206}"
98,1,277,0,0.3383234,"\int \frac{x}{\left(2 \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{-a+b x^3}} \, dx","Int[x/((2*a^(1/3) + b^(1/3)*x)*Sqrt[-a + b*x^3]),x]","\frac{4 \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{b x^3-a}}\right)}{9 \sqrt[6]{a} b^{2/3}}-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}","\frac{4 \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{b x^3-a}}\right)}{9 \sqrt[6]{a} b^{2/3}}-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}",1,"(4*ArcTan[(a^(1/3) - b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[-a + b*x^3])])/(9*a^(1/6)*b^(2/3)) - (2*Sqrt[2 - Sqrt[3]]*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",4,4,32,0.1250,1,"{2139, 219, 2138, 203}"
99,1,273,0,0.3217561,"\int \frac{x}{\left(2 \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{-a-b x^3}} \, dx","Int[x/((2*a^(1/3) - b^(1/3)*x)*Sqrt[-a - b*x^3]),x]","\frac{4 \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{-a-b x^3}}\right)}{9 \sqrt[6]{a} b^{2/3}}-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}","\frac{4 \tan ^{-1}\left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{3 \sqrt[6]{a} \sqrt{-a-b x^3}}\right)}{9 \sqrt[6]{a} b^{2/3}}-\frac{2 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}",1,"(4*ArcTan[(a^(1/3) + b^(1/3)*x)^2/(3*a^(1/6)*Sqrt[-a - b*x^3])])/(9*a^(1/6)*b^(2/3)) - (2*Sqrt[2 - Sqrt[3]]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3*3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",4,4,34,0.1176,1,"{2139, 219, 2138, 203}"
100,1,202,0,0.2559565,"\int \frac{x}{(c+d x) \sqrt{c^3-8 d^3 x^3}} \, dx","Int[x/((c + d*x)*Sqrt[c^3 - 8*d^3*x^3]),x]","\frac{2 \tanh ^{-1}\left(\frac{(c-2 d x)^2}{3 \sqrt{c} \sqrt{c^3-8 d^3 x^3}}\right)}{9 \sqrt{c} d^2}-\frac{\sqrt{2+\sqrt{3}} (c-2 d x) \sqrt{\frac{c^2+2 c d x+4 d^2 x^2}{\left(\left(1+\sqrt{3}\right) c-2 d x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) c-2 d x}{\left(1+\sqrt{3}\right) c-2 d x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} d^2 \sqrt{\frac{c (c-2 d x)}{\left(\left(1+\sqrt{3}\right) c-2 d x\right)^2}} \sqrt{c^3-8 d^3 x^3}}","\frac{2 \tanh ^{-1}\left(\frac{(c-2 d x)^2}{3 \sqrt{c} \sqrt{c^3-8 d^3 x^3}}\right)}{9 \sqrt{c} d^2}-\frac{\sqrt{2+\sqrt{3}} (c-2 d x) \sqrt{\frac{c^2+2 c d x+4 d^2 x^2}{\left(\left(1+\sqrt{3}\right) c-2 d x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) c-2 d x}{\left(1+\sqrt{3}\right) c-2 d x}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} d^2 \sqrt{\frac{c (c-2 d x)}{\left(\left(1+\sqrt{3}\right) c-2 d x\right)^2}} \sqrt{c^3-8 d^3 x^3}}",1,"(2*ArcTanh[(c - 2*d*x)^2/(3*Sqrt[c]*Sqrt[c^3 - 8*d^3*x^3])])/(9*Sqrt[c]*d^2) - (Sqrt[2 + Sqrt[3]]*(c - 2*d*x)*Sqrt[(c^2 + 2*c*d*x + 4*d^2*x^2)/((1 + Sqrt[3])*c - 2*d*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c - 2*d*x)/((1 + Sqrt[3])*c - 2*d*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*d^2*Sqrt[(c*(c - 2*d*x))/((1 + Sqrt[3])*c - 2*d*x)^2]*Sqrt[c^3 - 8*d^3*x^3])","A",4,4,25,0.1600,1,"{2139, 218, 2138, 206}"
101,1,42,0,0.1135168,"\int \frac{1+\sqrt{3}+x}{\left(1-\sqrt{3}+x\right) \sqrt{1+x^3}} \, dx","Int[(1 + Sqrt[3] + x)/((1 - Sqrt[3] + x)*Sqrt[1 + x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{2 \sqrt{3}-3}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{2 \sqrt{3}-3}}",1,"(-2*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]])/Sqrt[-3 + 2*Sqrt[3]]","A",2,2,30,0.06667,1,"{2140, 206}"
102,1,46,0,0.1143194,"\int \frac{1+\sqrt{3}-x}{\left(1-\sqrt{3}-x\right) \sqrt{1-x^3}} \, dx","Int[(1 + Sqrt[3] - x)/((1 - Sqrt[3] - x)*Sqrt[1 - x^3]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (1-x)}{\sqrt{1-x^3}}\right)}{\sqrt{2 \sqrt{3}-3}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (1-x)}{\sqrt{1-x^3}}\right)}{\sqrt{2 \sqrt{3}-3}}",1,"(2*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*(1 - x))/Sqrt[1 - x^3]])/Sqrt[-3 + 2*Sqrt[3]]","A",2,2,36,0.05556,1,"{2140, 206}"
103,1,44,0,0.104045,"\int \frac{1+\sqrt{3}-x}{\left(1-\sqrt{3}-x\right) \sqrt{-1+x^3}} \, dx","Int[(1 + Sqrt[3] - x)/((1 - Sqrt[3] - x)*Sqrt[-1 + x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (1-x)}{\sqrt{x^3-1}}\right)}{\sqrt{2 \sqrt{3}-3}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (1-x)}{\sqrt{x^3-1}}\right)}{\sqrt{2 \sqrt{3}-3}}",1,"(2*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]])/Sqrt[-3 + 2*Sqrt[3]]","A",2,2,34,0.05882,1,"{2140, 203}"
104,1,44,0,0.0936181,"\int \frac{1+\sqrt{3}+x}{\left(1-\sqrt{3}+x\right) \sqrt{-1-x^3}} \, dx","Int[(1 + Sqrt[3] + x)/((1 - Sqrt[3] + x)*Sqrt[-1 - x^3]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{-x^3-1}}\right)}{\sqrt{2 \sqrt{3}-3}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{-x^3-1}}\right)}{\sqrt{2 \sqrt{3}-3}}",1,"(-2*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*(1 + x))/Sqrt[-1 - x^3]])/Sqrt[-3 + 2*Sqrt[3]]","A",2,2,32,0.06250,1,"{2140, 203}"
105,1,69,0,0.2040679,"\int \frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a+b x^3}} \, dx","Int[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/(((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)*Sqrt[a + b*x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \sqrt[3]{b}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \sqrt[3]{b}}",1,"(-2*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) + b^(1/3)*x))/Sqrt[a + b*x^3]])/(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*b^(1/3))","A",2,2,58,0.03448,1,"{2140, 206}"
106,1,71,0,0.1922219,"\int \frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{a-b x^3}} \, dx","Int[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/(((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)*Sqrt[a - b*x^3]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \sqrt[3]{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \sqrt[3]{b}}",1,"(2*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) - b^(1/3)*x))/Sqrt[a - b*x^3]])/(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*b^(1/3))","A",2,2,61,0.03279,1,"{2140, 206}"
107,1,72,0,0.1853514,"\int \frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{-a+b x^3}} \, dx","Int[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/(((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)*Sqrt[-a + b*x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \sqrt[3]{b}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \sqrt[3]{b}}",1,"(2*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) - b^(1/3)*x))/Sqrt[-a + b*x^3]])/(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*b^(1/3))","A",2,2,62,0.03226,1,"{2140, 203}"
108,1,72,0,0.1687355,"\int \frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{-a-b x^3}} \, dx","Int[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/(((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)*Sqrt[-a - b*x^3]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \sqrt[3]{b}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \sqrt[3]{b}}",1,"(-2*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) + b^(1/3)*x))/Sqrt[-a - b*x^3]])/(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*b^(1/3))","A",2,2,61,0.03279,1,"{2140, 203}"
109,1,73,0,0.1988141,"\int \frac{1+\sqrt{3}+\sqrt[3]{\frac{b}{a}} x}{\left(1-\sqrt{3}+\sqrt[3]{\frac{b}{a}} x\right) \sqrt{a+b x^3}} \, dx","Int[(1 + Sqrt[3] + (b/a)^(1/3)*x)/((1 - Sqrt[3] + (b/a)^(1/3)*x)*Sqrt[a + b*x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{a} \left(x \sqrt[3]{\frac{b}{a}}+1\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt{a} \sqrt[3]{\frac{b}{a}}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{a} \left(x \sqrt[3]{\frac{b}{a}}+1\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt{a} \sqrt[3]{\frac{b}{a}}}",1,"(-2*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*Sqrt[a]*(1 + (b/a)^(1/3)*x))/Sqrt[a + b*x^3]])/(Sqrt[-3 + 2*Sqrt[3]]*Sqrt[a]*(b/a)^(1/3))","A",2,2,52,0.03846,1,"{2140, 206}"
110,1,75,0,0.2012008,"\int \frac{1+\sqrt{3}-\sqrt[3]{\frac{b}{a}} x}{\left(1-\sqrt{3}-\sqrt[3]{\frac{b}{a}} x\right) \sqrt{a-b x^3}} \, dx","Int[(1 + Sqrt[3] - (b/a)^(1/3)*x)/((1 - Sqrt[3] - (b/a)^(1/3)*x)*Sqrt[a - b*x^3]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{a} \left(1-x \sqrt[3]{\frac{b}{a}}\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt{a} \sqrt[3]{\frac{b}{a}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{a} \left(1-x \sqrt[3]{\frac{b}{a}}\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt{a} \sqrt[3]{\frac{b}{a}}}",1,"(2*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*Sqrt[a]*(1 - (b/a)^(1/3)*x))/Sqrt[a - b*x^3]])/(Sqrt[-3 + 2*Sqrt[3]]*Sqrt[a]*(b/a)^(1/3))","A",2,2,55,0.03636,1,"{2140, 206}"
111,1,76,0,0.1922141,"\int \frac{1+\sqrt{3}-\sqrt[3]{\frac{b}{a}} x}{\left(1-\sqrt{3}-\sqrt[3]{\frac{b}{a}} x\right) \sqrt{-a+b x^3}} \, dx","Int[(1 + Sqrt[3] - (b/a)^(1/3)*x)/((1 - Sqrt[3] - (b/a)^(1/3)*x)*Sqrt[-a + b*x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{a} \left(1-x \sqrt[3]{\frac{b}{a}}\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt{a} \sqrt[3]{\frac{b}{a}}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{a} \left(1-x \sqrt[3]{\frac{b}{a}}\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt{a} \sqrt[3]{\frac{b}{a}}}",1,"(2*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*Sqrt[a]*(1 - (b/a)^(1/3)*x))/Sqrt[-a + b*x^3]])/(Sqrt[-3 + 2*Sqrt[3]]*Sqrt[a]*(b/a)^(1/3))","A",2,2,56,0.03571,1,"{2140, 203}"
112,1,76,0,0.1800126,"\int \frac{1+\sqrt{3}+\sqrt[3]{\frac{b}{a}} x}{\left(1-\sqrt{3}+\sqrt[3]{\frac{b}{a}} x\right) \sqrt{-a-b x^3}} \, dx","Int[(1 + Sqrt[3] + (b/a)^(1/3)*x)/((1 - Sqrt[3] + (b/a)^(1/3)*x)*Sqrt[-a - b*x^3]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{a} \left(x \sqrt[3]{\frac{b}{a}}+1\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt{a} \sqrt[3]{\frac{b}{a}}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt{a} \left(x \sqrt[3]{\frac{b}{a}}+1\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{2 \sqrt{3}-3} \sqrt{a} \sqrt[3]{\frac{b}{a}}}",1,"(-2*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*Sqrt[a]*(1 + (b/a)^(1/3)*x))/Sqrt[-a - b*x^3]])/(Sqrt[-3 + 2*Sqrt[3]]*Sqrt[a]*(b/a)^(1/3))","A",2,2,55,0.03636,1,"{2140, 203}"
113,1,42,0,0.0895657,"\int \frac{1-\sqrt{3}+x}{\left(1+\sqrt{3}+x\right) \sqrt{1+x^3}} \, dx","Int[(1 - Sqrt[3] + x)/((1 + Sqrt[3] + x)*Sqrt[1 + x^3]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{3+2 \sqrt{3}}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{3+2 \sqrt{3}}}",1,"(-2*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]])/Sqrt[3 + 2*Sqrt[3]]","A",2,2,30,0.06667,1,"{2140, 203}"
114,1,46,0,0.1019859,"\int \frac{1-\sqrt{3}-x}{\left(1+\sqrt{3}-x\right) \sqrt{1-x^3}} \, dx","Int[(1 - Sqrt[3] - x)/((1 + Sqrt[3] - x)*Sqrt[1 - x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{1-x^3}}\right)}{\sqrt{3+2 \sqrt{3}}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{1-x^3}}\right)}{\sqrt{3+2 \sqrt{3}}}",1,"(2*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[1 - x^3]])/Sqrt[3 + 2*Sqrt[3]]","A",2,2,36,0.05556,1,"{2140, 203}"
115,1,44,0,0.0898745,"\int \frac{1-\sqrt{3}-x}{\left(1+\sqrt{3}-x\right) \sqrt{-1+x^3}} \, dx","Int[(1 - Sqrt[3] - x)/((1 + Sqrt[3] - x)*Sqrt[-1 + x^3]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)}{\sqrt{3+2 \sqrt{3}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)}{\sqrt{3+2 \sqrt{3}}}",1,"(2*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]])/Sqrt[3 + 2*Sqrt[3]]","A",2,2,34,0.05882,1,"{2140, 206}"
116,1,44,0,0.0866499,"\int \frac{1-\sqrt{3}+x}{\left(1+\sqrt{3}+x\right) \sqrt{-1-x^3}} \, dx","Int[(1 - Sqrt[3] + x)/((1 + Sqrt[3] + x)*Sqrt[-1 - x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{-x^3-1}}\right)}{\sqrt{3+2 \sqrt{3}}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{-x^3-1}}\right)}{\sqrt{3+2 \sqrt{3}}}",1,"(-2*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[-1 - x^3]])/Sqrt[3 + 2*Sqrt[3]]","A",2,2,32,0.06250,1,"{2140, 206}"
117,1,69,0,0.1758788,"\int \frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a+b x^3}} \, dx","Int[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/(((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)*Sqrt[a + b*x^3]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \sqrt[3]{b}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \sqrt[3]{b}}",1,"(-2*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) + b^(1/3)*x))/Sqrt[a + b*x^3]])/(Sqrt[3 + 2*Sqrt[3]]*a^(1/6)*b^(1/3))","A",2,2,58,0.03448,1,"{2140, 203}"
118,1,71,0,0.1848453,"\int \frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{a-b x^3}} \, dx","Int[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/(((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)*Sqrt[a - b*x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \sqrt[3]{b}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \sqrt[3]{b}}",1,"(2*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) - b^(1/3)*x))/Sqrt[a - b*x^3]])/(Sqrt[3 + 2*Sqrt[3]]*a^(1/6)*b^(1/3))","A",2,2,61,0.03279,1,"{2140, 203}"
119,1,72,0,0.1884831,"\int \frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{-a+b x^3}} \, dx","Int[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/(((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)*Sqrt[-a + b*x^3]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \sqrt[3]{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \sqrt[3]{b}}",1,"(2*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) - b^(1/3)*x))/Sqrt[-a + b*x^3]])/(Sqrt[3 + 2*Sqrt[3]]*a^(1/6)*b^(1/3))","A",2,2,62,0.03226,1,"{2140, 206}"
120,1,72,0,0.1675135,"\int \frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{-a-b x^3}} \, dx","Int[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/(((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)*Sqrt[-a - b*x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \sqrt[3]{b}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt[6]{a} \sqrt[3]{b}}",1,"(-2*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) + b^(1/3)*x))/Sqrt[-a - b*x^3]])/(Sqrt[3 + 2*Sqrt[3]]*a^(1/6)*b^(1/3))","A",2,2,61,0.03279,1,"{2140, 206}"
121,1,73,0,0.1758011,"\int \frac{1-\sqrt{3}+\sqrt[3]{\frac{b}{a}} x}{\left(1+\sqrt{3}+\sqrt[3]{\frac{b}{a}} x\right) \sqrt{a+b x^3}} \, dx","Int[(1 - Sqrt[3] + (b/a)^(1/3)*x)/((1 + Sqrt[3] + (b/a)^(1/3)*x)*Sqrt[a + b*x^3]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{a} \left(x \sqrt[3]{\frac{b}{a}}+1\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt{a} \sqrt[3]{\frac{b}{a}}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{a} \left(x \sqrt[3]{\frac{b}{a}}+1\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt{a} \sqrt[3]{\frac{b}{a}}}",1,"(-2*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*Sqrt[a]*(1 + (b/a)^(1/3)*x))/Sqrt[a + b*x^3]])/(Sqrt[3 + 2*Sqrt[3]]*Sqrt[a]*(b/a)^(1/3))","A",2,2,52,0.03846,1,"{2140, 203}"
122,1,75,0,0.1854398,"\int \frac{1-\sqrt{3}-\sqrt[3]{\frac{b}{a}} x}{\left(1+\sqrt{3}-\sqrt[3]{\frac{b}{a}} x\right) \sqrt{a-b x^3}} \, dx","Int[(1 - Sqrt[3] - (b/a)^(1/3)*x)/((1 + Sqrt[3] - (b/a)^(1/3)*x)*Sqrt[a - b*x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{a} \left(1-x \sqrt[3]{\frac{b}{a}}\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt{a} \sqrt[3]{\frac{b}{a}}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{a} \left(1-x \sqrt[3]{\frac{b}{a}}\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt{a} \sqrt[3]{\frac{b}{a}}}",1,"(2*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*Sqrt[a]*(1 - (b/a)^(1/3)*x))/Sqrt[a - b*x^3]])/(Sqrt[3 + 2*Sqrt[3]]*Sqrt[a]*(b/a)^(1/3))","A",2,2,55,0.03636,1,"{2140, 203}"
123,1,76,0,0.1852706,"\int \frac{1-\sqrt{3}-\sqrt[3]{\frac{b}{a}} x}{\left(1+\sqrt{3}-\sqrt[3]{\frac{b}{a}} x\right) \sqrt{-a+b x^3}} \, dx","Int[(1 - Sqrt[3] - (b/a)^(1/3)*x)/((1 + Sqrt[3] - (b/a)^(1/3)*x)*Sqrt[-a + b*x^3]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{a} \left(1-x \sqrt[3]{\frac{b}{a}}\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt{a} \sqrt[3]{\frac{b}{a}}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{a} \left(1-x \sqrt[3]{\frac{b}{a}}\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt{a} \sqrt[3]{\frac{b}{a}}}",1,"(2*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*Sqrt[a]*(1 - (b/a)^(1/3)*x))/Sqrt[-a + b*x^3]])/(Sqrt[3 + 2*Sqrt[3]]*Sqrt[a]*(b/a)^(1/3))","A",2,2,56,0.03571,1,"{2140, 206}"
124,1,76,0,0.1741887,"\int \frac{1-\sqrt{3}+\sqrt[3]{\frac{b}{a}} x}{\left(1+\sqrt{3}+\sqrt[3]{\frac{b}{a}} x\right) \sqrt{-a-b x^3}} \, dx","Int[(1 - Sqrt[3] + (b/a)^(1/3)*x)/((1 + Sqrt[3] + (b/a)^(1/3)*x)*Sqrt[-a - b*x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{a} \left(x \sqrt[3]{\frac{b}{a}}+1\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt{a} \sqrt[3]{\frac{b}{a}}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} \sqrt{a} \left(x \sqrt[3]{\frac{b}{a}}+1\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{3+2 \sqrt{3}} \sqrt{a} \sqrt[3]{\frac{b}{a}}}",1,"(-2*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*Sqrt[a]*(1 + (b/a)^(1/3)*x))/Sqrt[-a - b*x^3]])/(Sqrt[3 + 2*Sqrt[3]]*Sqrt[a]*(b/a)^(1/3))","A",2,2,55,0.03636,1,"{2140, 206}"
125,1,145,0,0.2397853,"\int \frac{1+x}{\left(1+\sqrt{3}+x\right) \sqrt{1+x^3}} \, dx","Int[(1 + x)/((1 + Sqrt[3] + x)*Sqrt[1 + x^3]),x]","\frac{\sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{3+2 \sqrt{3}}}","\frac{\sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{3+2 \sqrt{3}}}",1,"-(ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]]/Sqrt[3 + 2*Sqrt[3]]) + (Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,23,0.1739,1,"{2141, 218, 2140, 203}"
126,1,145,0,0.2277217,"\int \frac{1+x}{\left(1-\sqrt{3}+x\right) \sqrt{1+x^3}} \, dx","Int[(1 + x)/((1 - Sqrt[3] + x)*Sqrt[1 + x^3]),x]","\frac{\sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{2 \sqrt{3}-3}}","\frac{\sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{2 \sqrt{3}-3}}",1,"-(ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]]/Sqrt[-3 + 2*Sqrt[3]]) + (Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,25,0.1600,1,"{2141, 218, 2140, 206}"
127,1,173,0,0.2471634,"\int \frac{e+f x}{\left(1+\sqrt{3}+x\right) \sqrt{1+x^3}} \, dx","Int[(e + f*x)/((1 + Sqrt[3] + x)*Sqrt[1 + x^3]),x]","\frac{\left(e-\sqrt{3} f-f\right) \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}+\frac{\sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(e-\left(1-\sqrt{3}\right) f\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{\left(e-\sqrt{3} f-f\right) \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}+\frac{\sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(e-\left(1-\sqrt{3}\right) f\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"((e - f - Sqrt[3]*f)*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]])/Sqrt[3*(3 + 2*Sqrt[3])] + (Sqrt[2 + Sqrt[3]]*(e - (1 - Sqrt[3])*f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,25,0.1600,1,"{2141, 218, 2140, 203}"
128,1,187,0,0.2765212,"\int \frac{e+f x}{\left(1+\sqrt{3}-x\right) \sqrt{1-x^3}} \, dx","Int[(e + f*x)/((1 + Sqrt[3] - x)*Sqrt[1 - x^3]),x]","-\frac{\left(e+\sqrt{3} f+f\right) \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{1-x^3}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}-\frac{\sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(e+\left(1-\sqrt{3}\right) f\right) F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{\left(e+\sqrt{3} f+f\right) \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{1-x^3}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}-\frac{\sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(e+\left(1-\sqrt{3}\right) f\right) F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"-(((e + f + Sqrt[3]*f)*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[1 - x^3]])/Sqrt[3*(3 + 2*Sqrt[3])]) - (Sqrt[2 + Sqrt[3]]*(e + (1 - Sqrt[3])*f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",4,4,29,0.1379,1,"{2141, 218, 2140, 203}"
129,1,190,0,0.2456861,"\int \frac{e+f x}{\left(1+\sqrt{3}-x\right) \sqrt{-1+x^3}} \, dx","Int[(e + f*x)/((1 + Sqrt[3] - x)*Sqrt[-1 + x^3]),x]","-\frac{\left(e+\sqrt{3} f+f\right) \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}-\frac{\sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(e+\left(1-\sqrt{3}\right) f\right) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","-\frac{\left(e+\sqrt{3} f+f\right) \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}-\frac{\sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(e+\left(1-\sqrt{3}\right) f\right) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"-(((e + f + Sqrt[3]*f)*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]])/Sqrt[3*(3 + 2*Sqrt[3])]) - (Sqrt[2 - Sqrt[3]]*(e + (1 - Sqrt[3])*f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(3/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",4,4,27,0.1481,1,"{2141, 219, 2140, 206}"
130,1,183,0,0.2364499,"\int \frac{e+f x}{\left(1+\sqrt{3}+x\right) \sqrt{-1-x^3}} \, dx","Int[(e + f*x)/((1 + Sqrt[3] + x)*Sqrt[-1 - x^3]),x]","\frac{\left(e-\left(1+\sqrt{3}\right) f\right) \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{-x^3-1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}+\frac{\sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(e-\left(1-\sqrt{3}\right) f\right) F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{\left(e-\left(1+\sqrt{3}\right) f\right) \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{-x^3-1}}\right)}{\sqrt{3 \left(3+2 \sqrt{3}\right)}}+\frac{\sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(e-\left(1-\sqrt{3}\right) f\right) F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"((e - (1 + Sqrt[3])*f)*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[-1 - x^3]])/Sqrt[3*(3 + 2*Sqrt[3])] + (Sqrt[2 - Sqrt[3]]*(e - (1 - Sqrt[3])*f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(3/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",4,4,27,0.1481,1,"{2141, 219, 2140, 206}"
131,1,332,0,0.540226,"\int \frac{e+f x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a+b x^3}} \, dx","Int[(e + f*x)/(((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)*Sqrt[a + b*x^3]),x]","-\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} e-\left(1+\sqrt{3}\right) \sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\left(\sqrt[3]{b} e-\left(1-\sqrt{3}\right) \sqrt[3]{a} f\right) \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{a} b^{2/3}}","-\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} e-\left(1+\sqrt{3}\right) \sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\left(\sqrt[3]{b} e-\left(1-\sqrt{3}\right) \sqrt[3]{a} f\right) \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{\sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{a} b^{2/3}}",1,"-(((b^(1/3)*e - (1 - Sqrt[3])*a^(1/3)*f)*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) + b^(1/3)*x))/Sqrt[a + b*x^3]])/(Sqrt[3*(-3 + 2*Sqrt[3])]*Sqrt[a]*b^(2/3))) - (Sqrt[2 + Sqrt[3]]*(b^(1/3)*e - (1 + Sqrt[3])*a^(1/3)*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*a^(1/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,42,0.09524,1,"{2141, 218, 2140, 206}"
132,1,336,0,0.5679149,"\int \frac{e+f x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{a-b x^3}} \, dx","Int[(e + f*x)/(((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)*Sqrt[a - b*x^3]),x]","\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a} f+\sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{a} b^{2/3}}","\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a} f+\sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt[3]{a} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{\sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{a} b^{2/3}}",1,"((b^(1/3)*e + (1 - Sqrt[3])*a^(1/3)*f)*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) - b^(1/3)*x))/Sqrt[a - b*x^3]])/(Sqrt[3*(-3 + 2*Sqrt[3])]*Sqrt[a]*b^(2/3)) + (Sqrt[2 + Sqrt[3]]*(b^(1/3)*e + (1 + Sqrt[3])*a^(1/3)*f)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*a^(1/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",4,4,44,0.09091,1,"{2141, 218, 2140, 206}"
133,1,345,0,0.4911079,"\int \frac{e+f x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{-a+b x^3}} \, dx","Int[(e + f*x)/(((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)*Sqrt[-a + b*x^3]),x]","\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a} f+\sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{a} b^{2/3}}","\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a} f+\sqrt[3]{b} e\right) F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a} f+\sqrt[3]{b} e\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{\sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{a} b^{2/3}}",1,"((b^(1/3)*e + (1 - Sqrt[3])*a^(1/3)*f)*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) - b^(1/3)*x))/Sqrt[-a + b*x^3]])/(Sqrt[3*(-3 + 2*Sqrt[3])]*Sqrt[a]*b^(2/3)) + (Sqrt[2 - Sqrt[3]]*(b^(1/3)*e + (1 + Sqrt[3])*a^(1/3)*f)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(3/4)*a^(1/3)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",4,4,45,0.08889,1,"{2141, 219, 2140, 203}"
134,1,345,0,0.4749914,"\int \frac{e+f x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{-a-b x^3}} \, dx","Int[(e + f*x)/(((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)*Sqrt[-a - b*x^3]),x]","-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} e-\left(1+\sqrt{3}\right) \sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{\left(\sqrt[3]{b} e-\left(1-\sqrt{3}\right) \sqrt[3]{a} f\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{a} b^{2/3}}","-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \left(\sqrt[3]{b} e-\left(1+\sqrt{3}\right) \sqrt[3]{a} f\right) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} \sqrt[3]{a} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{\left(\sqrt[3]{b} e-\left(1-\sqrt{3}\right) \sqrt[3]{a} f\right) \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{\sqrt{3 \left(2 \sqrt{3}-3\right)} \sqrt{a} b^{2/3}}",1,"-(((b^(1/3)*e - (1 - Sqrt[3])*a^(1/3)*f)*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) + b^(1/3)*x))/Sqrt[-a - b*x^3]])/(Sqrt[3*(-3 + 2*Sqrt[3])]*Sqrt[a]*b^(2/3))) - (Sqrt[2 - Sqrt[3]]*(b^(1/3)*e - (1 + Sqrt[3])*a^(1/3)*f)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(3/4)*a^(1/3)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",4,4,45,0.08889,1,"{2141, 219, 2140, 203}"
135,1,136,0,0.2204131,"\int \frac{x}{\left(1+\sqrt{3}+x\right) \sqrt{1+x^3}} \, dx","Int[x/((1 + Sqrt[3] + x)*Sqrt[1 + x^3]),x]","\frac{\sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{3^{3/4}}","\frac{\sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{x^3+1}}\right)}{3^{3/4}}",1,"-((Sqrt[2]*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]])/3^(3/4)) + (Sqrt[2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,21,0.1905,1,"{2141, 218, 2140, 203}"
136,1,152,0,0.2209812,"\int \frac{x}{\left(1+\sqrt{3}-x\right) \sqrt{1-x^3}} \, dx","Int[x/((1 + Sqrt[3] - x)*Sqrt[1 - x^3]),x]","\frac{\sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{1-x^3}}\right)}{3^{3/4}}","\frac{\sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{1-x^3}}\right)}{3^{3/4}}",1,"-((Sqrt[2]*ArcTan[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[1 - x^3]])/3^(3/4)) + (Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",4,4,25,0.1600,1,"{2141, 218, 2140, 203}"
137,1,164,0,0.2184465,"\int \frac{x}{\left(1+\sqrt{3}-x\right) \sqrt{-1+x^3}} \, dx","Int[x/((1 + Sqrt[3] - x)*Sqrt[-1 + x^3]),x]","\frac{2 \sqrt{\frac{7}{6}-\frac{2}{\sqrt{3}}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)}{3^{3/4}}","\frac{2 \sqrt{\frac{7}{6}-\frac{2}{\sqrt{3}}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (1-x)}{\sqrt{x^3-1}}\right)}{3^{3/4}}",1,"-((Sqrt[2]*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 - x))/Sqrt[-1 + x^3]])/3^(3/4)) + (2*Sqrt[7/6 - 2/Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",4,4,23,0.1739,1,"{2141, 219, 2140, 206}"
138,1,156,0,0.2077269,"\int \frac{x}{\left(1+\sqrt{3}+x\right) \sqrt{-1-x^3}} \, dx","Int[x/((1 + Sqrt[3] + x)*Sqrt[-1 - x^3]),x]","\frac{2 \sqrt{\frac{7}{6}-\frac{2}{\sqrt{3}}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{-x^3-1}}\right)}{3^{3/4}}","\frac{2 \sqrt{\frac{7}{6}-\frac{2}{\sqrt{3}}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{3+2 \sqrt{3}} (x+1)}{\sqrt{-x^3-1}}\right)}{3^{3/4}}",1,"-((Sqrt[2]*ArcTanh[(Sqrt[3 + 2*Sqrt[3]]*(1 + x))/Sqrt[-1 - x^3]])/3^(3/4)) + (2*Sqrt[7/6 - 2/Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",4,4,23,0.1739,1,"{2141, 219, 2140, 206}"
139,1,147,0,0.2246729,"\int \frac{x}{\left(1-\sqrt{3}+x\right) \sqrt{1+x^3}} \, dx","Int[x/((1 - Sqrt[3] + x)*Sqrt[1 + x^3]),x]","\frac{2 \sqrt{\frac{7}{6}+\frac{2}{\sqrt{3}}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{x^3+1}}\right)}{3^{3/4}}","\frac{2 \sqrt{\frac{7}{6}+\frac{2}{\sqrt{3}}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} (x+1)}{\sqrt{x^3+1}}\right)}{3^{3/4}}",1,"-((Sqrt[2]*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*(1 + x))/Sqrt[1 + x^3]])/3^(3/4)) + (2*Sqrt[7/6 + 2/Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,23,0.1739,1,"{2141, 218, 2140, 206}"
140,1,278,0,0.4073508,"\int \frac{x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{a+b x^3}} \, dx","Int[x/(((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)*Sqrt[a + b*x^3]),x]","\frac{2 \sqrt{\frac{7}{6}+\frac{2}{\sqrt{3}}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{3^{3/4} \sqrt[6]{a} b^{2/3}}","\frac{2 \sqrt{\frac{7}{6}+\frac{2}{\sqrt{3}}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{a+b x^3}}\right)}{3^{3/4} \sqrt[6]{a} b^{2/3}}",1,"-((Sqrt[2]*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) + b^(1/3)*x))/Sqrt[a + b*x^3]])/(3^(3/4)*a^(1/6)*b^(2/3))) + (2*Sqrt[7/6 + 2/Sqrt[3]]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,38,0.1053,1,"{2141, 218, 2140, 206}"
141,1,286,0,0.4127697,"\int \frac{x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{a-b x^3}} \, dx","Int[x/(((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)*Sqrt[a - b*x^3]),x]","\frac{2 \sqrt{\frac{7}{6}+\frac{2}{\sqrt{3}}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{3^{3/4} \sqrt[6]{a} b^{2/3}}","\frac{2 \sqrt{\frac{7}{6}+\frac{2}{\sqrt{3}}} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{a-b x^3}}\right)}{3^{3/4} \sqrt[6]{a} b^{2/3}}",1,"-((Sqrt[2]*ArcTanh[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) - b^(1/3)*x))/Sqrt[a - b*x^3]])/(3^(3/4)*a^(1/6)*b^(2/3))) + (2*Sqrt[7/6 + 2/Sqrt[3]]*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",4,4,40,0.1000,1,"{2141, 218, 2140, 206}"
142,1,282,0,0.4410035,"\int \frac{x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{-a+b x^3}} \, dx","Int[x/(((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)*Sqrt[-a + b*x^3]),x]","\frac{\sqrt{2} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{3^{3/4} \sqrt[6]{a} b^{2/3}}","\frac{\sqrt{2} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{b x^3-a}}\right)}{3^{3/4} \sqrt[6]{a} b^{2/3}}",1,"-((Sqrt[2]*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) - b^(1/3)*x))/Sqrt[-a + b*x^3]])/(3^(3/4)*a^(1/6)*b^(2/3))) + (Sqrt[2]*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(3/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",4,4,41,0.09756,1,"{2141, 219, 2140, 203}"
143,1,278,0,0.4143202,"\int \frac{x}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{-a-b x^3}} \, dx","Int[x/(((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)*Sqrt[-a - b*x^3]),x]","\frac{\sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{3^{3/4} \sqrt[6]{a} b^{2/3}}","\frac{\sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{3^{3/4} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{\sqrt{2} \tan ^{-1}\left(\frac{\sqrt{2 \sqrt{3}-3} \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{-a-b x^3}}\right)}{3^{3/4} \sqrt[6]{a} b^{2/3}}",1,"-((Sqrt[2]*ArcTan[(Sqrt[-3 + 2*Sqrt[3]]*a^(1/6)*(a^(1/3) + b^(1/3)*x))/Sqrt[-a - b*x^3]])/(3^(3/4)*a^(1/6)*b^(2/3))) + (Sqrt[2]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(3/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",4,4,41,0.09756,1,"{2141, 219, 2140, 203}"
144,1,319,0,1.2398242,"\int \frac{1+\sqrt{3}+x}{(c+d x) \sqrt{1+x^3}} \, dx","Int[(1 + Sqrt[3] + x)/((c + d*x)*Sqrt[1 + x^3]),x]","-\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(c-\left(1+\sqrt{3}\right) d\right) \tan ^{-1}\left(\frac{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\left(1+\sqrt{3}\right) d\right)^2}{\left(c-\left(1-\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \left(c-\left(1-\sqrt{3}\right) d\right)}","-\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(c-\left(1+\sqrt{3}\right) d\right) \tan ^{-1}\left(\frac{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\left(1+\sqrt{3}\right) d\right)^2}{\left(c-\left(1-\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \left(c-\left(1-\sqrt{3}\right) d\right)}",1,"-(((c - (1 + Sqrt[3])*d)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(Sqrt[c^2 + c*d + d^2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/(Sqrt[c - d]*Sqrt[d]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2])])/(Sqrt[c - d]*Sqrt[d]*Sqrt[c^2 + c*d + d^2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])) - (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[(c - (1 + Sqrt[3])*d)^2/(c - (1 - Sqrt[3])*d)^2, -ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/((c - (1 - Sqrt[3])*d)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",6,6,25,0.2400,1,"{2142, 2113, 537, 571, 93, 205}"
145,1,331,0,1.2978164,"\int \frac{1+\sqrt{3}-x}{(c+d x) \sqrt{1-x^3}} \, dx","Int[(1 + Sqrt[3] - x)/((c + d*x)*Sqrt[1 - x^3]),x]","\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c+\sqrt{3} d+d\right)^2}{\left(c-\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \left(c-\sqrt{3} d+d\right)}-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(c+\sqrt{3} d+d\right) \tanh ^{-1}\left(\frac{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \sqrt{c+d} \sqrt{c^2-c d+d^2}}","\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c+\sqrt{3} d+d\right)^2}{\left(c-\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \left(c-\sqrt{3} d+d\right)}-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(c+\sqrt{3} d+d\right) \tanh ^{-1}\left(\frac{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \sqrt{c+d} \sqrt{c^2-c d+d^2}}",1,"-(((c + d + Sqrt[3]*d)*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*ArcTanh[(Sqrt[c^2 - c*d + d^2]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2])/(Sqrt[d]*Sqrt[c + d]*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2])])/(Sqrt[d]*Sqrt[c + d]*Sqrt[c^2 - c*d + d^2]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])) + (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticPi[(c + d + Sqrt[3]*d)^2/(c + d - Sqrt[3]*d)^2, -ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/((c + d - Sqrt[3]*d)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",6,6,29,0.2069,1,"{2142, 2113, 537, 571, 93, 208}"
146,1,327,0,0.7832951,"\int \frac{1+\sqrt{3}-x}{(c+d x) \sqrt{-1+x^3}} \, dx","Int[(1 + Sqrt[3] - x)/((c + d*x)*Sqrt[-1 + x^3]),x]","\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c+\sqrt{3} d+d\right)^2}{\left(c-\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \left(c-\sqrt{3} d+d\right)}-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(c+\sqrt{3} d+d\right) \tanh ^{-1}\left(\frac{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \sqrt{c+d} \sqrt{c^2-c d+d^2}}","\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c+\sqrt{3} d+d\right)^2}{\left(c-\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \left(c-\sqrt{3} d+d\right)}-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(c+\sqrt{3} d+d\right) \tanh ^{-1}\left(\frac{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \sqrt{c+d} \sqrt{c^2-c d+d^2}}",1,"-(((c + d + Sqrt[3]*d)*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*ArcTanh[(Sqrt[c^2 - c*d + d^2]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2])/(Sqrt[d]*Sqrt[c + d]*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2])])/(Sqrt[d]*Sqrt[c + d]*Sqrt[c^2 - c*d + d^2]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[-1 + x^3])) + (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticPi[(c + d + Sqrt[3]*d)^2/(c + d - Sqrt[3]*d)^2, -ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/((c + d - Sqrt[3]*d)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[-1 + x^3])","A",6,6,27,0.2222,1,"{2142, 2113, 537, 571, 93, 208}"
147,1,323,0,0.8542691,"\int \frac{1+\sqrt{3}+x}{(c+d x) \sqrt{-1-x^3}} \, dx","Int[(1 + Sqrt[3] + x)/((c + d*x)*Sqrt[-1 - x^3]),x]","-\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(c-\left(1+\sqrt{3}\right) d\right) \tan ^{-1}\left(\frac{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\left(1+\sqrt{3}\right) d\right)^2}{\left(c-\left(1-\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \left(c-\left(1-\sqrt{3}\right) d\right)}","-\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(c-\left(1+\sqrt{3}\right) d\right) \tan ^{-1}\left(\frac{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\left(1+\sqrt{3}\right) d\right)^2}{\left(c-\left(1-\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \left(c-\left(1-\sqrt{3}\right) d\right)}",1,"-(((c - (1 + Sqrt[3])*d)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(Sqrt[c^2 + c*d + d^2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/(Sqrt[c - d]*Sqrt[d]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2])])/(Sqrt[c - d]*Sqrt[d]*Sqrt[c^2 + c*d + d^2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[-1 - x^3])) - (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[(c - (1 + Sqrt[3])*d)^2/(c - (1 - Sqrt[3])*d)^2, -ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/((c - (1 - Sqrt[3])*d)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[-1 - x^3])","A",6,6,27,0.2222,1,"{2142, 2113, 537, 571, 93, 205}"
148,1,360,0,1.0041255,"\int \frac{1-\sqrt{3}+x}{(c+d x) \sqrt{1+x^3}} \, dx","Int[(1 - Sqrt[3] + x)/((c + d*x)*Sqrt[1 + x^3]),x]","\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\left(1-\sqrt{3}\right) d\right)^2}{\left(c-\left(1+\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \left(c-\sqrt{3} d-d\right)}-\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(c-\left(1-\sqrt{3}\right) d\right) \tanh ^{-1}\left(\frac{2 \sqrt{2+\sqrt{3}} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{\left(x+\sqrt{3}+1\right)^2}{\left(x-\sqrt{3}+1\right)^2}+4 \sqrt{3}+7} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}","\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\left(1-\sqrt{3}\right) d\right)^2}{\left(c-\left(1+\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \left(c-\sqrt{3} d-d\right)}-\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(c-\left(1-\sqrt{3}\right) d\right) \tanh ^{-1}\left(\frac{2 \sqrt{2+\sqrt{3}} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{\left(x+\sqrt{3}+1\right)^2}{\left(x-\sqrt{3}+1\right)^2}+4 \sqrt{3}+7} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}",1,"-(((c - (1 - Sqrt[3])*d)*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*ArcTanh[(2*Sqrt[2 + Sqrt[3]]*Sqrt[c^2 + c*d + d^2]*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)])/(Sqrt[c - d]*Sqrt[d]*Sqrt[7 + 4*Sqrt[3] + (1 + Sqrt[3] + x)^2/(1 - Sqrt[3] + x)^2])])/(Sqrt[c - d]*Sqrt[d]*Sqrt[c^2 + c*d + d^2]*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[1 + x^3])) + (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticPi[(c - (1 - Sqrt[3])*d)^2/(c - (1 + Sqrt[3])*d)^2, -ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/((c - d - Sqrt[3]*d)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[1 + x^3])","A",6,6,27,0.2222,1,"{2143, 2113, 537, 571, 93, 208}"
149,1,348,0,0.9849063,"\int \frac{1-\sqrt{3}-x}{(c+d x) \sqrt{1-x^3}} \, dx","Int[(1 - Sqrt[3] - x)/((c + d*x)*Sqrt[1 - x^3]),x]","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(c-\sqrt{3} d+d\right) \tan ^{-1}\left(\frac{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \sqrt{c+d} \sqrt{c^2-c d+d^2}}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\sqrt{3} d+d\right)^2}{\left(c+\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \left(c+\sqrt{3} d+d\right)}","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(c-\sqrt{3} d+d\right) \tan ^{-1}\left(\frac{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \sqrt{c+d} \sqrt{c^2-c d+d^2}}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\sqrt{3} d+d\right)^2}{\left(c+\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \left(c+\sqrt{3} d+d\right)}",1,"-(((c + d - Sqrt[3]*d)*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*ArcTan[(Sqrt[c^2 - c*d + d^2]*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)])/(Sqrt[d]*Sqrt[c + d]*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2])])/(Sqrt[d]*Sqrt[c + d]*Sqrt[c^2 - c*d + d^2]*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[1 - x^3])) - (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticPi[(c + d - Sqrt[3]*d)^2/(c + d + Sqrt[3]*d)^2, -ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/((c + d + Sqrt[3]*d)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[1 - x^3])","A",6,6,31,0.1935,1,"{2143, 2113, 537, 571, 93, 205}"
150,1,344,0,0.6959473,"\int \frac{1-\sqrt{3}-x}{(c+d x) \sqrt{-1+x^3}} \, dx","Int[(1 - Sqrt[3] - x)/((c + d*x)*Sqrt[-1 + x^3]),x]","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(c-\sqrt{3} d+d\right) \tan ^{-1}\left(\frac{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \sqrt{c+d} \sqrt{c^2-c d+d^2}}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\sqrt{3} d+d\right)^2}{\left(c+\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \left(c+\sqrt{3} d+d\right)}","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(c-\sqrt{3} d+d\right) \tan ^{-1}\left(\frac{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \sqrt{c+d} \sqrt{c^2-c d+d^2}}-\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\sqrt{3} d+d\right)^2}{\left(c+\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \left(c+\sqrt{3} d+d\right)}",1,"-(((c + d - Sqrt[3]*d)*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*ArcTan[(Sqrt[c^2 - c*d + d^2]*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)])/(Sqrt[d]*Sqrt[c + d]*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2])])/(Sqrt[d]*Sqrt[c + d]*Sqrt[c^2 - c*d + d^2]*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])) - (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticPi[(c + d - Sqrt[3]*d)^2/(c + d + Sqrt[3]*d)^2, -ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/((c + d + Sqrt[3]*d)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",6,6,29,0.2069,1,"{2143, 2113, 537, 571, 93, 205}"
151,1,364,0,0.7923846,"\int \frac{1-\sqrt{3}+x}{(c+d x) \sqrt{-1-x^3}} \, dx","Int[(1 - Sqrt[3] + x)/((c + d*x)*Sqrt[-1 - x^3]),x]","\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\left(1-\sqrt{3}\right) d\right)^2}{\left(c-\left(1+\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \left(c-\sqrt{3} d-d\right)}-\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(c-\left(1-\sqrt{3}\right) d\right) \tanh ^{-1}\left(\frac{2 \sqrt{2+\sqrt{3}} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{\left(x+\sqrt{3}+1\right)^2}{\left(x-\sqrt{3}+1\right)^2}+4 \sqrt{3}+7} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}","\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \Pi \left(\frac{\left(c-\left(1-\sqrt{3}\right) d\right)^2}{\left(c-\left(1+\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \left(c-\sqrt{3} d-d\right)}-\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(c-\left(1-\sqrt{3}\right) d\right) \tanh ^{-1}\left(\frac{2 \sqrt{2+\sqrt{3}} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{\left(x+\sqrt{3}+1\right)^2}{\left(x-\sqrt{3}+1\right)^2}+4 \sqrt{3}+7} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}",1,"-(((c - (1 - Sqrt[3])*d)*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*ArcTanh[(2*Sqrt[2 + Sqrt[3]]*Sqrt[c^2 + c*d + d^2]*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)])/(Sqrt[c - d]*Sqrt[d]*Sqrt[7 + 4*Sqrt[3] + (1 + Sqrt[3] + x)^2/(1 - Sqrt[3] + x)^2])])/(Sqrt[c - d]*Sqrt[d]*Sqrt[c^2 + c*d + d^2]*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])) + (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticPi[(c - (1 - Sqrt[3])*d)^2/(c - (1 + Sqrt[3])*d)^2, -ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/((c - d - Sqrt[3]*d)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",6,6,29,0.2069,1,"{2143, 2113, 537, 571, 93, 208}"
152,1,125,0,0.0455044,"\int \frac{1+\sqrt{3}+x}{x \sqrt{1+x^3}} \, dx","Int[(1 + Sqrt[3] + x)/(x*Sqrt[1 + x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2}{3} \left(1+\sqrt{3}\right) \tanh ^{-1}\left(\sqrt{x^3+1}\right)","\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2}{3} \left(1+\sqrt{3}\right) \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(-2*(1 + Sqrt[3])*ArcTanh[Sqrt[1 + x^3]])/3 + (2*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",5,5,21,0.2381,1,"{1832, 266, 63, 207, 218}"
153,1,139,0,0.0534554,"\int \frac{1+\sqrt{3}-x}{x \sqrt{1-x^3}} \, dx","Int[(1 + Sqrt[3] - x)/(x*Sqrt[1 - x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2}{3} \left(1+\sqrt{3}\right) \tanh ^{-1}\left(\sqrt{1-x^3}\right)","\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2}{3} \left(1+\sqrt{3}\right) \tanh ^{-1}\left(\sqrt{1-x^3}\right)",1,"(-2*(1 + Sqrt[3])*ArcTanh[Sqrt[1 - x^3]])/3 + (2*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",5,5,25,0.2000,1,"{1832, 266, 63, 206, 218}"
154,1,142,0,0.0497874,"\int \frac{1+\sqrt{3}-x}{x \sqrt{-1+x^3}} \, dx","Int[(1 + Sqrt[3] - x)/(x*Sqrt[-1 + x^3]),x]","\frac{2}{3} \left(1+\sqrt{3}\right) \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{2}{3} \left(1+\sqrt{3}\right) \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(2*(1 + Sqrt[3])*ArcTan[Sqrt[-1 + x^3]])/3 + (2*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",5,5,23,0.2174,1,"{1832, 266, 63, 203, 219}"
155,1,136,0,0.0499955,"\int \frac{1+\sqrt{3}+x}{x \sqrt{-1-x^3}} \, dx","Int[(1 + Sqrt[3] + x)/(x*Sqrt[-1 - x^3]),x]","\frac{2}{3} \left(1+\sqrt{3}\right) \tan ^{-1}\left(\sqrt{-x^3-1}\right)+\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{2}{3} \left(1+\sqrt{3}\right) \tan ^{-1}\left(\sqrt{-x^3-1}\right)+\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(2*(1 + Sqrt[3])*ArcTan[Sqrt[-1 - x^3]])/3 + (2*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",5,5,23,0.2174,1,"{1832, 266, 63, 204, 219}"
156,1,127,0,0.0456327,"\int \frac{1-\sqrt{3}+x}{x \sqrt{1+x^3}} \, dx","Int[(1 - Sqrt[3] + x)/(x*Sqrt[1 + x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2}{3} \left(1-\sqrt{3}\right) \tanh ^{-1}\left(\sqrt{x^3+1}\right)","\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2}{3} \left(1-\sqrt{3}\right) \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(-2*(1 - Sqrt[3])*ArcTanh[Sqrt[1 + x^3]])/3 + (2*Sqrt[2 + Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",5,5,23,0.2174,1,"{1832, 266, 63, 207, 218}"
157,1,141,0,0.0514084,"\int \frac{1-\sqrt{3}-x}{x \sqrt{1-x^3}} \, dx","Int[(1 - Sqrt[3] - x)/(x*Sqrt[1 - x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2}{3} \left(1-\sqrt{3}\right) \tanh ^{-1}\left(\sqrt{1-x^3}\right)","\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2}{3} \left(1-\sqrt{3}\right) \tanh ^{-1}\left(\sqrt{1-x^3}\right)",1,"(-2*(1 - Sqrt[3])*ArcTanh[Sqrt[1 - x^3]])/3 + (2*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",5,5,27,0.1852,1,"{1832, 266, 63, 206, 218}"
158,1,144,0,0.046942,"\int \frac{1-\sqrt{3}-x}{x \sqrt{-1+x^3}} \, dx","Int[(1 - Sqrt[3] - x)/(x*Sqrt[-1 + x^3]),x]","\frac{2}{3} \left(1-\sqrt{3}\right) \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{2}{3} \left(1-\sqrt{3}\right) \tan ^{-1}\left(\sqrt{x^3-1}\right)+\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(2*(1 - Sqrt[3])*ArcTan[Sqrt[-1 + x^3]])/3 + (2*Sqrt[2 - Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",5,5,25,0.2000,1,"{1832, 266, 63, 203, 219}"
159,1,138,0,0.0481781,"\int \frac{1-\sqrt{3}+x}{x \sqrt{-1-x^3}} \, dx","Int[(1 - Sqrt[3] + x)/(x*Sqrt[-1 - x^3]),x]","\frac{2}{3} \left(1-\sqrt{3}\right) \tan ^{-1}\left(\sqrt{-x^3-1}\right)+\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{2}{3} \left(1-\sqrt{3}\right) \tan ^{-1}\left(\sqrt{-x^3-1}\right)+\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(2*(1 - Sqrt[3])*ArcTan[Sqrt[-1 - x^3]])/3 + (2*Sqrt[2 - Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",5,5,25,0.2000,1,"{1832, 266, 63, 204, 219}"
160,1,334,0,0.6400567,"\int \frac{x}{(3+x) \sqrt{1+x^3}} \, dx","Int[x/((3 + x)*Sqrt[1 + x^3]),x]","-\frac{3 (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt{\frac{13}{2}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{\sqrt{26} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2 \sqrt{2 \left(97+56 \sqrt{3}\right)} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{12 \sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(97-56 \sqrt{3};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{2-\sqrt{3}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","-\frac{3 (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt{\frac{13}{2}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{\sqrt{26} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2 \sqrt{2 \left(97+56 \sqrt{3}\right)} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{12 \sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(97-56 \sqrt{3};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{2-\sqrt{3}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(-3*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(Sqrt[13/2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]])/(Sqrt[26]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (2*Sqrt[2*(97 + 56*Sqrt[3])]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) - (12*3^(1/4)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[97 - 56*Sqrt[3], -ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[2 - Sqrt[3]]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",8,8,16,0.5000,1,"{2144, 218, 2142, 2113, 537, 571, 93, 204}"
161,1,379,0,0.7001034,"\int \frac{x}{(3+x) \sqrt{1-x^3}} \, dx","Int[x/((3 + x)*Sqrt[1 - x^3]),x]","\frac{3 (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}}}{2 \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}}}\right)}{2 \sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2 \sqrt{2 \left(37+20 \sqrt{3}\right)} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{12 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{1}{169} \left(553+304 \sqrt{3}\right);-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","\frac{3 (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}}}{2 \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}}}\right)}{2 \sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{2 \sqrt{2 \left(37+20 \sqrt{3}\right)} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}-\frac{12 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{1}{169} \left(553+304 \sqrt{3}\right);-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(3*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*ArcTanh[(Sqrt[7]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2])/(2*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2])])/(2*Sqrt[7]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) - (2*Sqrt[2*(37 + 20*Sqrt[3])]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(13*3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) - (12*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticPi[(553 + 304*Sqrt[3])/169, -ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(13*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",8,8,18,0.4444,1,"{2144, 218, 2142, 2113, 537, 571, 93, 206}"
162,1,375,0,0.5968483,"\int \frac{x}{(3+x) \sqrt{-1+x^3}} \, dx","Int[x/((3 + x)*Sqrt[-1 + x^3]),x]","\frac{3 (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}}}{2 \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}}}\right)}{2 \sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \left(4+\sqrt{3}\right) \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{12 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{1}{169} \left(553+304 \sqrt{3}\right);-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{3 (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}}}{2 \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}}}\right)}{2 \sqrt{7} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{2 \sqrt{2} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \left(4+\sqrt{3}\right) \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}-\frac{12 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \Pi \left(\frac{1}{169} \left(553+304 \sqrt{3}\right);-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(3*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*ArcTanh[(Sqrt[7]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2])/(2*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2])])/(2*Sqrt[7]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[-1 + x^3]) - (2*Sqrt[2]*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*(4 + Sqrt[3])*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) - (12*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticPi[(553 + 304*Sqrt[3])/169, -ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(13*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[-1 + x^3])","A",8,8,16,0.5000,1,"{2144, 219, 2142, 2113, 537, 571, 93, 206}"
163,1,343,0,0.6037849,"\int \frac{x}{(3+x) \sqrt{-1-x^3}} \, dx","Int[x/((3 + x)*Sqrt[-1 - x^3]),x]","-\frac{3 (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt{\frac{13}{2}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{\sqrt{26} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{2 \sqrt{14+8 \sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{12 \sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(97-56 \sqrt{3};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{2-\sqrt{3}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","-\frac{3 (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \tan ^{-1}\left(\frac{\sqrt{\frac{13}{2}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}}}{\sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}}}\right)}{\sqrt{26} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{2 \sqrt{14+8 \sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}-\frac{12 \sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \Pi \left(97-56 \sqrt{3};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{2-\sqrt{3}} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(-3*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(Sqrt[13/2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]])/(Sqrt[26]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[-1 - x^3]) - (2*Sqrt[14 + 8*Sqrt[3]]*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3]) - (12*3^(1/4)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[97 - 56*Sqrt[3], -ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[2 - Sqrt[3]]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[-1 - x^3])","A",8,8,18,0.4444,1,"{2144, 219, 2142, 2113, 537, 571, 93, 204}"
164,1,452,0,1.0601092,"\int \frac{e+f x}{(c+d x) \sqrt{1+x^3}} \, dx","Int[(e + f*x)/((c + d*x)*Sqrt[1 + x^3]),x]","\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (d e-c f) \tan ^{-1}\left(\frac{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (d e-c f) \Pi \left(\frac{\left(c-\left(1+\sqrt{3}\right) d\right)^2}{\left(c-\left(1-\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \left(c^2-2 c d-2 d^2\right)}+\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(e-\sqrt{3} f-f\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \left(c-\sqrt{3} d-d\right)}","\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (d e-c f) \tan ^{-1}\left(\frac{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (d e-c f) \Pi \left(\frac{\left(c-\left(1+\sqrt{3}\right) d\right)^2}{\left(c-\left(1-\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \left(c^2-2 c d-2 d^2\right)}+\frac{2 \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(e-\sqrt{3} f-f\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1} \left(c-\sqrt{3} d-d\right)}",1,"((d*e - c*f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(Sqrt[c^2 + c*d + d^2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/(Sqrt[c - d]*Sqrt[d]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2])])/(Sqrt[c - d]*Sqrt[d]*Sqrt[c^2 + c*d + d^2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (2*Sqrt[2 + Sqrt[3]]*(e - f - Sqrt[3]*f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*(c - d - Sqrt[3]*d)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(d*e - c*f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[(c - (1 + Sqrt[3])*d)^2/(c - (1 - Sqrt[3])*d)^2, -ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/((c^2 - 2*c*d - 2*d^2)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",8,8,22,0.3636,1,"{2144, 218, 2142, 2113, 537, 571, 93, 205}"
165,1,476,0,1.1055858,"\int \frac{e+f x}{(c+d x) \sqrt{1-x^3}} \, dx","Int[(e + f*x)/((c + d*x)*Sqrt[1 - x^3]),x]","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (d e-c f) \tanh ^{-1}\left(\frac{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \sqrt{c+d} \sqrt{c^2-c d+d^2}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (d e-c f) \Pi \left(\frac{\left(c+\sqrt{3} d+d\right)^2}{\left(c-\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \left(c^2+2 c d-2 d^2\right)}-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(e+\sqrt{3} f+f\right) F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \left(c+\sqrt{3} d+d\right)}","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (d e-c f) \tanh ^{-1}\left(\frac{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \sqrt{c+d} \sqrt{c^2-c d+d^2}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (d e-c f) \Pi \left(\frac{\left(c+\sqrt{3} d+d\right)^2}{\left(c-\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \left(c^2+2 c d-2 d^2\right)}-\frac{2 \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \left(e+\sqrt{3} f+f\right) F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3} \left(c+\sqrt{3} d+d\right)}",1,"-(((d*e - c*f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*ArcTanh[(Sqrt[c^2 - c*d + d^2]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2])/(Sqrt[d]*Sqrt[c + d]*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2])])/(Sqrt[d]*Sqrt[c + d]*Sqrt[c^2 - c*d + d^2]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])) - (2*Sqrt[2 + Sqrt[3]]*(e + f + Sqrt[3]*f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(1/4)*(c + d + Sqrt[3]*d)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3]) + (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(d*e - c*f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticPi[(c + d + Sqrt[3]*d)^2/(c + d - Sqrt[3]*d)^2, -ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/((c^2 + 2*c*d - 2*d^2)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",8,8,24,0.3333,1,"{2144, 218, 2142, 2113, 537, 571, 93, 208}"
166,1,477,0,0.9243448,"\int \frac{e+f x}{(c+d x) \sqrt{-1+x^3}} \, dx","Int[(e + f*x)/((c + d*x)*Sqrt[-1 + x^3]),x]","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (d e-c f) \tanh ^{-1}\left(\frac{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \sqrt{c+d} \sqrt{c^2-c d+d^2}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (d e-c f) \Pi \left(\frac{\left(c+\sqrt{3} d+d\right)^2}{\left(c-\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \left(c^2+2 c d-2 d^2\right)}-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(e+\sqrt{3} f+f\right) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \left(c+\sqrt{3} d+d\right)}","-\frac{(1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (d e-c f) \tanh ^{-1}\left(\frac{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c^2-c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{c+d}}\right)}{\sqrt{d} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \sqrt{c+d} \sqrt{c^2-c d+d^2}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} (d e-c f) \Pi \left(\frac{\left(c+\sqrt{3} d+d\right)^2}{\left(c-\sqrt{3} d+d\right)^2};-\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \left(c^2+2 c d-2 d^2\right)}-\frac{2 \sqrt{2-\sqrt{3}} (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} \left(e+\sqrt{3} f+f\right) F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1} \left(c+\sqrt{3} d+d\right)}",1,"-(((d*e - c*f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*ArcTanh[(Sqrt[c^2 - c*d + d^2]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2])/(Sqrt[d]*Sqrt[c + d]*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2])])/(Sqrt[d]*Sqrt[c + d]*Sqrt[c^2 - c*d + d^2]*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[-1 + x^3])) - (2*Sqrt[2 - Sqrt[3]]*(e + f + Sqrt[3]*f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*(c + d + Sqrt[3]*d)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3]) + (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(d*e - c*f)*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticPi[(c + d + Sqrt[3]*d)^2/(c + d - Sqrt[3]*d)^2, -ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/((c^2 + 2*c*d - 2*d^2)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[-1 + x^3])","A",8,8,22,0.3636,1,"{2144, 219, 2142, 2113, 537, 571, 93, 208}"
167,1,465,0,1.0344608,"\int \frac{e+f x}{(c+d x) \sqrt{-1-x^3}} \, dx","Int[(e + f*x)/((c + d*x)*Sqrt[-1 - x^3]),x]","\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (d e-c f) \tan ^{-1}\left(\frac{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (d e-c f) \Pi \left(\frac{\left(c-\left(1+\sqrt{3}\right) d\right)^2}{\left(c-\left(1-\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \left(c^2-2 c d-2 d^2\right)}+\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(e-\sqrt{3} f-f\right) F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \left(c-\sqrt{3} d-d\right)}","\frac{(x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (d e-c f) \tan ^{-1}\left(\frac{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c^2+c d+d^2}}{\sqrt{d} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{c-d}}\right)}{\sqrt{d} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \sqrt{c-d} \sqrt{c^2+c d+d^2}}+\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (d e-c f) \Pi \left(\frac{\left(c-\left(1+\sqrt{3}\right) d\right)^2}{\left(c-\left(1-\sqrt{3}\right) d\right)^2};-\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \left(c^2-2 c d-2 d^2\right)}+\frac{2 \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} \left(e-\sqrt{3} f-f\right) F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1} \left(c-\sqrt{3} d-d\right)}",1,"((d*e - c*f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*ArcTan[(Sqrt[c^2 + c*d + d^2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2])/(Sqrt[c - d]*Sqrt[d]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2])])/(Sqrt[c - d]*Sqrt[d]*Sqrt[c^2 + c*d + d^2]*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[-1 - x^3]) + (2*Sqrt[2 - Sqrt[3]]*(e - f - Sqrt[3]*f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(1/4)*(c - d - Sqrt[3]*d)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3]) + (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*(d*e - c*f)*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticPi[(c - (1 + Sqrt[3])*d)^2/(c - (1 - Sqrt[3])*d)^2, -ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/((c^2 - 2*c*d - 2*d^2)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[-1 - x^3])","A",8,8,24,0.3333,1,"{2144, 219, 2142, 2113, 537, 571, 93, 205}"
168,1,120,0,0.0492872,"\int \frac{e+f x}{x \sqrt{1+x^3}} \, dx","Int[(e + f*x)/(x*Sqrt[1 + x^3]),x]","\frac{2 \sqrt{2+\sqrt{3}} f (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2}{3} e \tanh ^{-1}\left(\sqrt{x^3+1}\right)","\frac{2 \sqrt{2+\sqrt{3}} f (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{2}{3} e \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(-2*e*ArcTanh[Sqrt[1 + x^3]])/3 + (2*Sqrt[2 + Sqrt[3]]*f*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",6,6,18,0.3333,1,"{1832, 266, 63, 207, 12, 218}"
169,1,134,0,0.0588458,"\int \frac{e+f x}{x \sqrt{1-x^3}} \, dx","Int[(e + f*x)/(x*Sqrt[1 - x^3]),x]","-\frac{2}{3} e \tanh ^{-1}\left(\sqrt{1-x^3}\right)-\frac{2 \sqrt{2+\sqrt{3}} f (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}","-\frac{2}{3} e \tanh ^{-1}\left(\sqrt{1-x^3}\right)-\frac{2 \sqrt{2+\sqrt{3}} f (1-x) \sqrt{\frac{x^2+x+1}{\left(-x+\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x-\sqrt{3}+1}{-x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{1-x}{\left(-x+\sqrt{3}+1\right)^2}} \sqrt{1-x^3}}",1,"(-2*e*ArcTanh[Sqrt[1 - x^3]])/3 - (2*Sqrt[2 + Sqrt[3]]*f*(1 - x)*Sqrt[(1 + x + x^2)/(1 + Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] - x)/(1 + Sqrt[3] - x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 - x)/(1 + Sqrt[3] - x)^2]*Sqrt[1 - x^3])","A",6,6,20,0.3000,1,"{1832, 266, 63, 206, 12, 218}"
170,1,137,0,0.0512827,"\int \frac{e+f x}{x \sqrt{-1+x^3}} \, dx","Int[(e + f*x)/(x*Sqrt[-1 + x^3]),x]","\frac{2}{3} e \tan ^{-1}\left(\sqrt{x^3-1}\right)-\frac{2 \sqrt{2-\sqrt{3}} f (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}","\frac{2}{3} e \tan ^{-1}\left(\sqrt{x^3-1}\right)-\frac{2 \sqrt{2-\sqrt{3}} f (1-x) \sqrt{\frac{x^2+x+1}{\left(-x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-x+\sqrt{3}+1}{-x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{1-x}{\left(-x-\sqrt{3}+1\right)^2}} \sqrt{x^3-1}}",1,"(2*e*ArcTan[Sqrt[-1 + x^3]])/3 - (2*Sqrt[2 - Sqrt[3]]*f*(1 - x)*Sqrt[(1 + x + x^2)/(1 - Sqrt[3] - x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] - x)/(1 - Sqrt[3] - x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 - x)/(1 - Sqrt[3] - x)^2)]*Sqrt[-1 + x^3])","A",6,6,18,0.3333,1,"{1832, 266, 63, 203, 12, 219}"
171,1,131,0,0.0535521,"\int \frac{e+f x}{x \sqrt{-1-x^3}} \, dx","Int[(e + f*x)/(x*Sqrt[-1 - x^3]),x]","\frac{2}{3} e \tan ^{-1}\left(\sqrt{-x^3-1}\right)+\frac{2 \sqrt{2-\sqrt{3}} f (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}","\frac{2}{3} e \tan ^{-1}\left(\sqrt{-x^3-1}\right)+\frac{2 \sqrt{2-\sqrt{3}} f (x+1) \sqrt{\frac{x^2-x+1}{\left(x-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{x+\sqrt{3}+1}{x-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{-\frac{x+1}{\left(x-\sqrt{3}+1\right)^2}} \sqrt{-x^3-1}}",1,"(2*e*ArcTan[Sqrt[-1 - x^3]])/3 + (2*Sqrt[2 - Sqrt[3]]*f*(1 + x)*Sqrt[(1 - x + x^2)/(1 - Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 + Sqrt[3] + x)/(1 - Sqrt[3] + x)], -7 + 4*Sqrt[3]])/(3^(1/4)*Sqrt[-((1 + x)/(1 - Sqrt[3] + x)^2)]*Sqrt[-1 - x^3])","A",6,6,20,0.3000,1,"{1832, 266, 63, 204, 12, 219}"
172,1,95,0,0.1246657,"\int \frac{c-d x}{(c+d x) \sqrt[3]{2 c^3+d^3 x^3}} \, dx","Int[(c - d*x)/((c + d*x)*(2*c^3 + d^3*x^3)^(1/3)),x]","\frac{3 \log \left(d (2 c+d x)-d \sqrt[3]{2 c^3+d^3 x^3}\right)}{2 d}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (2 c+d x)}{\sqrt[3]{2 c^3+d^3 x^3}}+1}{\sqrt{3}}\right)}{d}-\frac{\log (c+d x)}{d}","\frac{3 \log \left(d (2 c+d x)-d \sqrt[3]{2 c^3+d^3 x^3}\right)}{2 d}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\frac{2 (2 c+d x)}{\sqrt[3]{2 c^3+d^3 x^3}}+1}{\sqrt{3}}\right)}{d}-\frac{\log (c+d x)}{d}",1,"-((Sqrt[3]*ArcTan[(1 + (2*(2*c + d*x))/(2*c^3 + d^3*x^3)^(1/3))/Sqrt[3]])/d) - Log[c + d*x]/d + (3*Log[d*(2*c + d*x) - d*(2*c^3 + d^3*x^3)^(1/3)])/(2*d)","A",1,1,31,0.03226,1,"{2151}"
173,1,234,0,0.2200863,"\int \frac{e+f x}{(c+d x) \sqrt[3]{-c^3+d^3 x^3}} \, dx","Int[(e + f*x)/((c + d*x)*(-c^3 + d^3*x^3)^(1/3)),x]","-\frac{3 (d e-c f) \log \left(2^{2/3} d \sqrt[3]{d^3 x^3-c^3}+d (c-d x)\right)}{4 \sqrt[3]{2} c d^2}+\frac{\sqrt{3} (d e-c f) \tan ^{-1}\left(\frac{1-\frac{\sqrt[3]{2} (c-d x)}{\sqrt[3]{d^3 x^3-c^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} c d^2}-\frac{f \log \left(\sqrt[3]{d^3 x^3-c^3}-d x\right)}{2 d^2}+\frac{f \tan ^{-1}\left(\frac{\frac{2 d x}{\sqrt[3]{d^3 x^3-c^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^2}+\frac{(d e-c f) \log \left((c-d x) (c+d x)^2\right)}{4 \sqrt[3]{2} c d^2}","-\frac{3 (d e-c f) \log \left(2^{2/3} d \sqrt[3]{d^3 x^3-c^3}+d (c-d x)\right)}{4 \sqrt[3]{2} c d^2}+\frac{\sqrt{3} (d e-c f) \tan ^{-1}\left(\frac{1-\frac{\sqrt[3]{2} (c-d x)}{\sqrt[3]{d^3 x^3-c^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} c d^2}-\frac{f \log \left(\sqrt[3]{d^3 x^3-c^3}-d x\right)}{2 d^2}+\frac{f \tan ^{-1}\left(\frac{\frac{2 d x}{\sqrt[3]{d^3 x^3-c^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^2}+\frac{(d e-c f) \log \left((c-d x) (c+d x)^2\right)}{4 \sqrt[3]{2} c d^2}",1,"(f*ArcTan[(1 + (2*d*x)/(-c^3 + d^3*x^3)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^2) + (Sqrt[3]*(d*e - c*f)*ArcTan[(1 - (2^(1/3)*(c - d*x))/(-c^3 + d^3*x^3)^(1/3))/Sqrt[3]])/(2*2^(1/3)*c*d^2) + ((d*e - c*f)*Log[(c - d*x)*(c + d*x)^2])/(4*2^(1/3)*c*d^2) - (f*Log[-(d*x) + (-c^3 + d^3*x^3)^(1/3)])/(2*d^2) - (3*(d*e - c*f)*Log[d*(c - d*x) + 2^(2/3)*d*(-c^3 + d^3*x^3)^(1/3)])/(4*2^(1/3)*c*d^2)","A",3,3,30,0.1000,1,"{2152, 239, 2148}"
174,1,160,0,0.1057878,"\int x^2 (a+b x)^n \left(c+d x^3\right) \, dx","Int[x^2*(a + b*x)^n*(c + d*x^3),x]","\frac{a^2 \left(b^3 c-a^3 d\right) (a+b x)^{n+1}}{b^6 (n+1)}-\frac{a \left(2 b^3 c-5 a^3 d\right) (a+b x)^{n+2}}{b^6 (n+2)}+\frac{\left(b^3 c-10 a^3 d\right) (a+b x)^{n+3}}{b^6 (n+3)}+\frac{10 a^2 d (a+b x)^{n+4}}{b^6 (n+4)}-\frac{5 a d (a+b x)^{n+5}}{b^6 (n+5)}+\frac{d (a+b x)^{n+6}}{b^6 (n+6)}","\frac{a^2 \left(b^3 c-a^3 d\right) (a+b x)^{n+1}}{b^6 (n+1)}-\frac{a \left(2 b^3 c-5 a^3 d\right) (a+b x)^{n+2}}{b^6 (n+2)}+\frac{\left(b^3 c-10 a^3 d\right) (a+b x)^{n+3}}{b^6 (n+3)}+\frac{10 a^2 d (a+b x)^{n+4}}{b^6 (n+4)}-\frac{5 a d (a+b x)^{n+5}}{b^6 (n+5)}+\frac{d (a+b x)^{n+6}}{b^6 (n+6)}",1,"(a^2*(b^3*c - a^3*d)*(a + b*x)^(1 + n))/(b^6*(1 + n)) - (a*(2*b^3*c - 5*a^3*d)*(a + b*x)^(2 + n))/(b^6*(2 + n)) + ((b^3*c - 10*a^3*d)*(a + b*x)^(3 + n))/(b^6*(3 + n)) + (10*a^2*d*(a + b*x)^(4 + n))/(b^6*(4 + n)) - (5*a*d*(a + b*x)^(5 + n))/(b^6*(5 + n)) + (d*(a + b*x)^(6 + n))/(b^6*(6 + n))","A",2,1,18,0.05556,1,"{1620}"
175,1,126,0,0.0682909,"\int x (a+b x)^n \left(c+d x^3\right) \, dx","Int[x*(a + b*x)^n*(c + d*x^3),x]","-\frac{a \left(b^3 c-a^3 d\right) (a+b x)^{n+1}}{b^5 (n+1)}+\frac{\left(b^3 c-4 a^3 d\right) (a+b x)^{n+2}}{b^5 (n+2)}+\frac{6 a^2 d (a+b x)^{n+3}}{b^5 (n+3)}-\frac{4 a d (a+b x)^{n+4}}{b^5 (n+4)}+\frac{d (a+b x)^{n+5}}{b^5 (n+5)}","-\frac{a \left(b^3 c-a^3 d\right) (a+b x)^{n+1}}{b^5 (n+1)}+\frac{\left(b^3 c-4 a^3 d\right) (a+b x)^{n+2}}{b^5 (n+2)}+\frac{6 a^2 d (a+b x)^{n+3}}{b^5 (n+3)}-\frac{4 a d (a+b x)^{n+4}}{b^5 (n+4)}+\frac{d (a+b x)^{n+5}}{b^5 (n+5)}",1,"-((a*(b^3*c - a^3*d)*(a + b*x)^(1 + n))/(b^5*(1 + n))) + ((b^3*c - 4*a^3*d)*(a + b*x)^(2 + n))/(b^5*(2 + n)) + (6*a^2*d*(a + b*x)^(3 + n))/(b^5*(3 + n)) - (4*a*d*(a + b*x)^(4 + n))/(b^5*(4 + n)) + (d*(a + b*x)^(5 + n))/(b^5*(5 + n))","A",2,1,16,0.06250,1,"{1620}"
176,1,94,0,0.0460304,"\int (a+b x)^n \left(c+d x^3\right) \, dx","Int[(a + b*x)^n*(c + d*x^3),x]","\frac{\left(b^3 c-a^3 d\right) (a+b x)^{n+1}}{b^4 (n+1)}+\frac{3 a^2 d (a+b x)^{n+2}}{b^4 (n+2)}-\frac{3 a d (a+b x)^{n+3}}{b^4 (n+3)}+\frac{d (a+b x)^{n+4}}{b^4 (n+4)}","\frac{\left(b^3 c-a^3 d\right) (a+b x)^{n+1}}{b^4 (n+1)}+\frac{3 a^2 d (a+b x)^{n+2}}{b^4 (n+2)}-\frac{3 a d (a+b x)^{n+3}}{b^4 (n+3)}+\frac{d (a+b x)^{n+4}}{b^4 (n+4)}",1,"((b^3*c - a^3*d)*(a + b*x)^(1 + n))/(b^4*(1 + n)) + (3*a^2*d*(a + b*x)^(2 + n))/(b^4*(2 + n)) - (3*a*d*(a + b*x)^(3 + n))/(b^4*(3 + n)) + (d*(a + b*x)^(4 + n))/(b^4*(4 + n))","A",2,1,15,0.06667,1,"{1850}"
177,1,99,0,0.0578469,"\int \frac{(a+b x)^n \left(c+d x^3\right)}{x} \, dx","Int[((a + b*x)^n*(c + d*x^3))/x,x]","\frac{a^2 d (a+b x)^{n+1}}{b^3 (n+1)}-\frac{2 a d (a+b x)^{n+2}}{b^3 (n+2)}+\frac{d (a+b x)^{n+3}}{b^3 (n+3)}-\frac{c (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}","\frac{a^2 d (a+b x)^{n+1}}{b^3 (n+1)}-\frac{2 a d (a+b x)^{n+2}}{b^3 (n+2)}+\frac{d (a+b x)^{n+3}}{b^3 (n+3)}-\frac{c (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"(a^2*d*(a + b*x)^(1 + n))/(b^3*(1 + n)) - (2*a*d*(a + b*x)^(2 + n))/(b^3*(2 + n)) + (d*(a + b*x)^(3 + n))/(b^3*(3 + n)) - (c*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n))","A",3,2,18,0.1111,1,"{1620, 65}"
178,1,294,0,0.201699,"\int x^2 (a+b x)^n \left(c+d x^3\right)^2 \, dx","Int[x^2*(a + b*x)^n*(c + d*x^3)^2,x]","\frac{\left(-20 a^3 b^3 c d+28 a^6 d^2+b^6 c^2\right) (a+b x)^{n+3}}{b^9 (n+3)}+\frac{a^2 \left(b^3 c-a^3 d\right)^2 (a+b x)^{n+1}}{b^9 (n+1)}-\frac{2 a \left(b^3 c-4 a^3 d\right) \left(b^3 c-a^3 d\right) (a+b x)^{n+2}}{b^9 (n+2)}+\frac{4 a^2 d \left(5 b^3 c-14 a^3 d\right) (a+b x)^{n+4}}{b^9 (n+4)}-\frac{10 a d \left(b^3 c-7 a^3 d\right) (a+b x)^{n+5}}{b^9 (n+5)}+\frac{2 d \left(b^3 c-28 a^3 d\right) (a+b x)^{n+6}}{b^9 (n+6)}+\frac{28 a^2 d^2 (a+b x)^{n+7}}{b^9 (n+7)}-\frac{8 a d^2 (a+b x)^{n+8}}{b^9 (n+8)}+\frac{d^2 (a+b x)^{n+9}}{b^9 (n+9)}","\frac{\left(-20 a^3 b^3 c d+28 a^6 d^2+b^6 c^2\right) (a+b x)^{n+3}}{b^9 (n+3)}+\frac{a^2 \left(b^3 c-a^3 d\right)^2 (a+b x)^{n+1}}{b^9 (n+1)}-\frac{2 a \left(b^3 c-4 a^3 d\right) \left(b^3 c-a^3 d\right) (a+b x)^{n+2}}{b^9 (n+2)}+\frac{4 a^2 d \left(5 b^3 c-14 a^3 d\right) (a+b x)^{n+4}}{b^9 (n+4)}-\frac{10 a d \left(b^3 c-7 a^3 d\right) (a+b x)^{n+5}}{b^9 (n+5)}+\frac{2 d \left(b^3 c-28 a^3 d\right) (a+b x)^{n+6}}{b^9 (n+6)}+\frac{28 a^2 d^2 (a+b x)^{n+7}}{b^9 (n+7)}-\frac{8 a d^2 (a+b x)^{n+8}}{b^9 (n+8)}+\frac{d^2 (a+b x)^{n+9}}{b^9 (n+9)}",1,"(a^2*(b^3*c - a^3*d)^2*(a + b*x)^(1 + n))/(b^9*(1 + n)) - (2*a*(b^3*c - 4*a^3*d)*(b^3*c - a^3*d)*(a + b*x)^(2 + n))/(b^9*(2 + n)) + ((b^6*c^2 - 20*a^3*b^3*c*d + 28*a^6*d^2)*(a + b*x)^(3 + n))/(b^9*(3 + n)) + (4*a^2*d*(5*b^3*c - 14*a^3*d)*(a + b*x)^(4 + n))/(b^9*(4 + n)) - (10*a*d*(b^3*c - 7*a^3*d)*(a + b*x)^(5 + n))/(b^9*(5 + n)) + (2*d*(b^3*c - 28*a^3*d)*(a + b*x)^(6 + n))/(b^9*(6 + n)) + (28*a^2*d^2*(a + b*x)^(7 + n))/(b^9*(7 + n)) - (8*a*d^2*(a + b*x)^(8 + n))/(b^9*(8 + n)) + (d^2*(a + b*x)^(9 + n))/(b^9*(9 + n))","A",2,1,20,0.05000,1,"{1620}"
179,1,248,0,0.1483797,"\int x (a+b x)^n \left(c+d x^3\right)^2 \, dx","Int[x*(a + b*x)^n*(c + d*x^3)^2,x]","-\frac{a \left(b^3 c-a^3 d\right)^2 (a+b x)^{n+1}}{b^8 (n+1)}+\frac{\left(b^3 c-7 a^3 d\right) \left(b^3 c-a^3 d\right) (a+b x)^{n+2}}{b^8 (n+2)}+\frac{3 a^2 d \left(4 b^3 c-7 a^3 d\right) (a+b x)^{n+3}}{b^8 (n+3)}-\frac{a d \left(8 b^3 c-35 a^3 d\right) (a+b x)^{n+4}}{b^8 (n+4)}+\frac{d \left(2 b^3 c-35 a^3 d\right) (a+b x)^{n+5}}{b^8 (n+5)}+\frac{21 a^2 d^2 (a+b x)^{n+6}}{b^8 (n+6)}-\frac{7 a d^2 (a+b x)^{n+7}}{b^8 (n+7)}+\frac{d^2 (a+b x)^{n+8}}{b^8 (n+8)}","-\frac{a \left(b^3 c-a^3 d\right)^2 (a+b x)^{n+1}}{b^8 (n+1)}+\frac{\left(b^3 c-7 a^3 d\right) \left(b^3 c-a^3 d\right) (a+b x)^{n+2}}{b^8 (n+2)}+\frac{3 a^2 d \left(4 b^3 c-7 a^3 d\right) (a+b x)^{n+3}}{b^8 (n+3)}-\frac{a d \left(8 b^3 c-35 a^3 d\right) (a+b x)^{n+4}}{b^8 (n+4)}+\frac{d \left(2 b^3 c-35 a^3 d\right) (a+b x)^{n+5}}{b^8 (n+5)}+\frac{21 a^2 d^2 (a+b x)^{n+6}}{b^8 (n+6)}-\frac{7 a d^2 (a+b x)^{n+7}}{b^8 (n+7)}+\frac{d^2 (a+b x)^{n+8}}{b^8 (n+8)}",1,"-((a*(b^3*c - a^3*d)^2*(a + b*x)^(1 + n))/(b^8*(1 + n))) + ((b^3*c - 7*a^3*d)*(b^3*c - a^3*d)*(a + b*x)^(2 + n))/(b^8*(2 + n)) + (3*a^2*d*(4*b^3*c - 7*a^3*d)*(a + b*x)^(3 + n))/(b^8*(3 + n)) - (a*d*(8*b^3*c - 35*a^3*d)*(a + b*x)^(4 + n))/(b^8*(4 + n)) + (d*(2*b^3*c - 35*a^3*d)*(a + b*x)^(5 + n))/(b^8*(5 + n)) + (21*a^2*d^2*(a + b*x)^(6 + n))/(b^8*(6 + n)) - (7*a*d^2*(a + b*x)^(7 + n))/(b^8*(7 + n)) + (d^2*(a + b*x)^(8 + n))/(b^8*(8 + n))","A",2,1,18,0.05556,1,"{1620}"
180,1,203,0,0.1148446,"\int (a+b x)^n \left(c+d x^3\right)^2 \, dx","Int[(a + b*x)^n*(c + d*x^3)^2,x]","\frac{\left(b^3 c-a^3 d\right)^2 (a+b x)^{n+1}}{b^7 (n+1)}+\frac{6 a^2 d \left(b^3 c-a^3 d\right) (a+b x)^{n+2}}{b^7 (n+2)}-\frac{3 a d \left(2 b^3 c-5 a^3 d\right) (a+b x)^{n+3}}{b^7 (n+3)}+\frac{2 d \left(b^3 c-10 a^3 d\right) (a+b x)^{n+4}}{b^7 (n+4)}+\frac{15 a^2 d^2 (a+b x)^{n+5}}{b^7 (n+5)}-\frac{6 a d^2 (a+b x)^{n+6}}{b^7 (n+6)}+\frac{d^2 (a+b x)^{n+7}}{b^7 (n+7)}","\frac{\left(b^3 c-a^3 d\right)^2 (a+b x)^{n+1}}{b^7 (n+1)}+\frac{6 a^2 d \left(b^3 c-a^3 d\right) (a+b x)^{n+2}}{b^7 (n+2)}-\frac{3 a d \left(2 b^3 c-5 a^3 d\right) (a+b x)^{n+3}}{b^7 (n+3)}+\frac{2 d \left(b^3 c-10 a^3 d\right) (a+b x)^{n+4}}{b^7 (n+4)}+\frac{15 a^2 d^2 (a+b x)^{n+5}}{b^7 (n+5)}-\frac{6 a d^2 (a+b x)^{n+6}}{b^7 (n+6)}+\frac{d^2 (a+b x)^{n+7}}{b^7 (n+7)}",1,"((b^3*c - a^3*d)^2*(a + b*x)^(1 + n))/(b^7*(1 + n)) + (6*a^2*d*(b^3*c - a^3*d)*(a + b*x)^(2 + n))/(b^7*(2 + n)) - (3*a*d*(2*b^3*c - 5*a^3*d)*(a + b*x)^(3 + n))/(b^7*(3 + n)) + (2*d*(b^3*c - 10*a^3*d)*(a + b*x)^(4 + n))/(b^7*(4 + n)) + (15*a^2*d^2*(a + b*x)^(5 + n))/(b^7*(5 + n)) - (6*a*d^2*(a + b*x)^(6 + n))/(b^7*(6 + n)) + (d^2*(a + b*x)^(7 + n))/(b^7*(7 + n))","A",2,1,17,0.05882,1,"{1850}"
181,1,209,0,0.1268257,"\int \frac{(a+b x)^n \left(c+d x^3\right)^2}{x} \, dx","Int[((a + b*x)^n*(c + d*x^3)^2)/x,x]","\frac{a^2 d \left(2 b^3 c-a^3 d\right) (a+b x)^{n+1}}{b^6 (n+1)}-\frac{a d \left(4 b^3 c-5 a^3 d\right) (a+b x)^{n+2}}{b^6 (n+2)}+\frac{2 d \left(b^3 c-5 a^3 d\right) (a+b x)^{n+3}}{b^6 (n+3)}+\frac{10 a^2 d^2 (a+b x)^{n+4}}{b^6 (n+4)}-\frac{5 a d^2 (a+b x)^{n+5}}{b^6 (n+5)}+\frac{d^2 (a+b x)^{n+6}}{b^6 (n+6)}-\frac{c^2 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}","\frac{a^2 d \left(2 b^3 c-a^3 d\right) (a+b x)^{n+1}}{b^6 (n+1)}-\frac{a d \left(4 b^3 c-5 a^3 d\right) (a+b x)^{n+2}}{b^6 (n+2)}+\frac{2 d \left(b^3 c-5 a^3 d\right) (a+b x)^{n+3}}{b^6 (n+3)}+\frac{10 a^2 d^2 (a+b x)^{n+4}}{b^6 (n+4)}-\frac{5 a d^2 (a+b x)^{n+5}}{b^6 (n+5)}+\frac{d^2 (a+b x)^{n+6}}{b^6 (n+6)}-\frac{c^2 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"(a^2*d*(2*b^3*c - a^3*d)*(a + b*x)^(1 + n))/(b^6*(1 + n)) - (a*d*(4*b^3*c - 5*a^3*d)*(a + b*x)^(2 + n))/(b^6*(2 + n)) + (2*d*(b^3*c - 5*a^3*d)*(a + b*x)^(3 + n))/(b^6*(3 + n)) + (10*a^2*d^2*(a + b*x)^(4 + n))/(b^6*(4 + n)) - (5*a*d^2*(a + b*x)^(5 + n))/(b^6*(5 + n)) + (d^2*(a + b*x)^(6 + n))/(b^6*(6 + n)) - (c^2*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n))","A",3,2,20,0.1000,1,"{1620, 65}"
182,1,459,0,0.3166985,"\int x^2 (a+b x)^n \left(c+d x^3\right)^3 \, dx","Int[x^2*(a + b*x)^n*(c + d*x^3)^3,x]","\frac{\left(b^3 c-a^3 d\right) \left(-29 a^3 b^3 c d+55 a^6 d^2+b^6 c^2\right) (a+b x)^{n+3}}{b^{12} (n+3)}+\frac{3 a^2 d \left(-56 a^3 b^3 c d+55 a^6 d^2+10 b^6 c^2\right) (a+b x)^{n+4}}{b^{12} (n+4)}-\frac{15 a d \left(-14 a^3 b^3 c d+22 a^6 d^2+b^6 c^2\right) (a+b x)^{n+5}}{b^{12} (n+5)}+\frac{3 d \left(-56 a^3 b^3 c d+154 a^6 d^2+b^6 c^2\right) (a+b x)^{n+6}}{b^{12} (n+6)}+\frac{42 a^2 d^2 \left(2 b^3 c-11 a^3 d\right) (a+b x)^{n+7}}{b^{12} (n+7)}-\frac{6 a d^2 \left(4 b^3 c-55 a^3 d\right) (a+b x)^{n+8}}{b^{12} (n+8)}+\frac{3 d^2 \left(b^3 c-55 a^3 d\right) (a+b x)^{n+9}}{b^{12} (n+9)}+\frac{a^2 \left(b^3 c-a^3 d\right)^3 (a+b x)^{n+1}}{b^{12} (n+1)}-\frac{a \left(2 b^3 c-11 a^3 d\right) \left(b^3 c-a^3 d\right)^2 (a+b x)^{n+2}}{b^{12} (n+2)}+\frac{55 a^2 d^3 (a+b x)^{n+10}}{b^{12} (n+10)}-\frac{11 a d^3 (a+b x)^{n+11}}{b^{12} (n+11)}+\frac{d^3 (a+b x)^{n+12}}{b^{12} (n+12)}","\frac{\left(b^3 c-a^3 d\right) \left(-29 a^3 b^3 c d+55 a^6 d^2+b^6 c^2\right) (a+b x)^{n+3}}{b^{12} (n+3)}+\frac{3 a^2 d \left(-56 a^3 b^3 c d+55 a^6 d^2+10 b^6 c^2\right) (a+b x)^{n+4}}{b^{12} (n+4)}-\frac{15 a d \left(-14 a^3 b^3 c d+22 a^6 d^2+b^6 c^2\right) (a+b x)^{n+5}}{b^{12} (n+5)}+\frac{3 d \left(-56 a^3 b^3 c d+154 a^6 d^2+b^6 c^2\right) (a+b x)^{n+6}}{b^{12} (n+6)}+\frac{42 a^2 d^2 \left(2 b^3 c-11 a^3 d\right) (a+b x)^{n+7}}{b^{12} (n+7)}-\frac{6 a d^2 \left(4 b^3 c-55 a^3 d\right) (a+b x)^{n+8}}{b^{12} (n+8)}+\frac{3 d^2 \left(b^3 c-55 a^3 d\right) (a+b x)^{n+9}}{b^{12} (n+9)}+\frac{a^2 \left(b^3 c-a^3 d\right)^3 (a+b x)^{n+1}}{b^{12} (n+1)}-\frac{a \left(2 b^3 c-11 a^3 d\right) \left(b^3 c-a^3 d\right)^2 (a+b x)^{n+2}}{b^{12} (n+2)}+\frac{55 a^2 d^3 (a+b x)^{n+10}}{b^{12} (n+10)}-\frac{11 a d^3 (a+b x)^{n+11}}{b^{12} (n+11)}+\frac{d^3 (a+b x)^{n+12}}{b^{12} (n+12)}",1,"(a^2*(b^3*c - a^3*d)^3*(a + b*x)^(1 + n))/(b^12*(1 + n)) - (a*(2*b^3*c - 11*a^3*d)*(b^3*c - a^3*d)^2*(a + b*x)^(2 + n))/(b^12*(2 + n)) + ((b^3*c - a^3*d)*(b^6*c^2 - 29*a^3*b^3*c*d + 55*a^6*d^2)*(a + b*x)^(3 + n))/(b^12*(3 + n)) + (3*a^2*d*(10*b^6*c^2 - 56*a^3*b^3*c*d + 55*a^6*d^2)*(a + b*x)^(4 + n))/(b^12*(4 + n)) - (15*a*d*(b^6*c^2 - 14*a^3*b^3*c*d + 22*a^6*d^2)*(a + b*x)^(5 + n))/(b^12*(5 + n)) + (3*d*(b^6*c^2 - 56*a^3*b^3*c*d + 154*a^6*d^2)*(a + b*x)^(6 + n))/(b^12*(6 + n)) + (42*a^2*d^2*(2*b^3*c - 11*a^3*d)*(a + b*x)^(7 + n))/(b^12*(7 + n)) - (6*a*d^2*(4*b^3*c - 55*a^3*d)*(a + b*x)^(8 + n))/(b^12*(8 + n)) + (3*d^2*(b^3*c - 55*a^3*d)*(a + b*x)^(9 + n))/(b^12*(9 + n)) + (55*a^2*d^3*(a + b*x)^(10 + n))/(b^12*(10 + n)) - (11*a*d^3*(a + b*x)^(11 + n))/(b^12*(11 + n)) + (d^3*(a + b*x)^(12 + n))/(b^12*(12 + n))","A",2,1,20,0.05000,1,"{1620}"
183,1,396,0,0.2642326,"\int x (a+b x)^n \left(c+d x^3\right)^3 \, dx","Int[x*(a + b*x)^n*(c + d*x^3)^3,x]","-\frac{3 a d \left(-35 a^3 b^3 c d+40 a^6 d^2+4 b^6 c^2\right) (a+b x)^{n+4}}{b^{11} (n+4)}+\frac{3 d \left(-35 a^3 b^3 c d+70 a^6 d^2+b^6 c^2\right) (a+b x)^{n+5}}{b^{11} (n+5)}+\frac{63 a^2 d^2 \left(b^3 c-4 a^3 d\right) (a+b x)^{n+6}}{b^{11} (n+6)}-\frac{21 a d^2 \left(b^3 c-10 a^3 d\right) (a+b x)^{n+7}}{b^{11} (n+7)}+\frac{3 d^2 \left(b^3 c-40 a^3 d\right) (a+b x)^{n+8}}{b^{11} (n+8)}-\frac{a \left(b^3 c-a^3 d\right)^3 (a+b x)^{n+1}}{b^{11} (n+1)}+\frac{\left(b^3 c-10 a^3 d\right) \left(b^3 c-a^3 d\right)^2 (a+b x)^{n+2}}{b^{11} (n+2)}+\frac{9 a^2 d \left(2 b^3 c-5 a^3 d\right) \left(b^3 c-a^3 d\right) (a+b x)^{n+3}}{b^{11} (n+3)}+\frac{45 a^2 d^3 (a+b x)^{n+9}}{b^{11} (n+9)}-\frac{10 a d^3 (a+b x)^{n+10}}{b^{11} (n+10)}+\frac{d^3 (a+b x)^{n+11}}{b^{11} (n+11)}","-\frac{3 a d \left(-35 a^3 b^3 c d+40 a^6 d^2+4 b^6 c^2\right) (a+b x)^{n+4}}{b^{11} (n+4)}+\frac{3 d \left(-35 a^3 b^3 c d+70 a^6 d^2+b^6 c^2\right) (a+b x)^{n+5}}{b^{11} (n+5)}+\frac{63 a^2 d^2 \left(b^3 c-4 a^3 d\right) (a+b x)^{n+6}}{b^{11} (n+6)}-\frac{21 a d^2 \left(b^3 c-10 a^3 d\right) (a+b x)^{n+7}}{b^{11} (n+7)}+\frac{3 d^2 \left(b^3 c-40 a^3 d\right) (a+b x)^{n+8}}{b^{11} (n+8)}-\frac{a \left(b^3 c-a^3 d\right)^3 (a+b x)^{n+1}}{b^{11} (n+1)}+\frac{\left(b^3 c-10 a^3 d\right) \left(b^3 c-a^3 d\right)^2 (a+b x)^{n+2}}{b^{11} (n+2)}+\frac{9 a^2 d \left(2 b^3 c-5 a^3 d\right) \left(b^3 c-a^3 d\right) (a+b x)^{n+3}}{b^{11} (n+3)}+\frac{45 a^2 d^3 (a+b x)^{n+9}}{b^{11} (n+9)}-\frac{10 a d^3 (a+b x)^{n+10}}{b^{11} (n+10)}+\frac{d^3 (a+b x)^{n+11}}{b^{11} (n+11)}",1,"-((a*(b^3*c - a^3*d)^3*(a + b*x)^(1 + n))/(b^11*(1 + n))) + ((b^3*c - 10*a^3*d)*(b^3*c - a^3*d)^2*(a + b*x)^(2 + n))/(b^11*(2 + n)) + (9*a^2*d*(2*b^3*c - 5*a^3*d)*(b^3*c - a^3*d)*(a + b*x)^(3 + n))/(b^11*(3 + n)) - (3*a*d*(4*b^6*c^2 - 35*a^3*b^3*c*d + 40*a^6*d^2)*(a + b*x)^(4 + n))/(b^11*(4 + n)) + (3*d*(b^6*c^2 - 35*a^3*b^3*c*d + 70*a^6*d^2)*(a + b*x)^(5 + n))/(b^11*(5 + n)) + (63*a^2*d^2*(b^3*c - 4*a^3*d)*(a + b*x)^(6 + n))/(b^11*(6 + n)) - (21*a*d^2*(b^3*c - 10*a^3*d)*(a + b*x)^(7 + n))/(b^11*(7 + n)) + (3*d^2*(b^3*c - 40*a^3*d)*(a + b*x)^(8 + n))/(b^11*(8 + n)) + (45*a^2*d^3*(a + b*x)^(9 + n))/(b^11*(9 + n)) - (10*a*d^3*(a + b*x)^(10 + n))/(b^11*(10 + n)) + (d^3*(a + b*x)^(11 + n))/(b^11*(11 + n))","A",2,1,18,0.05556,1,"{1620}"
184,1,337,0,0.2085947,"\int (a+b x)^n \left(c+d x^3\right)^3 \, dx","Int[(a + b*x)^n*(c + d*x^3)^3,x]","\frac{3 d \left(-20 a^3 b^3 c d+28 a^6 d^2+b^6 c^2\right) (a+b x)^{n+4}}{b^{10} (n+4)}+\frac{9 a^2 d^2 \left(5 b^3 c-14 a^3 d\right) (a+b x)^{n+5}}{b^{10} (n+5)}-\frac{18 a d^2 \left(b^3 c-7 a^3 d\right) (a+b x)^{n+6}}{b^{10} (n+6)}+\frac{3 d^2 \left(b^3 c-28 a^3 d\right) (a+b x)^{n+7}}{b^{10} (n+7)}+\frac{\left(b^3 c-a^3 d\right)^3 (a+b x)^{n+1}}{b^{10} (n+1)}+\frac{9 a^2 d \left(b^3 c-a^3 d\right)^2 (a+b x)^{n+2}}{b^{10} (n+2)}-\frac{9 a d \left(b^3 c-4 a^3 d\right) \left(b^3 c-a^3 d\right) (a+b x)^{n+3}}{b^{10} (n+3)}+\frac{36 a^2 d^3 (a+b x)^{n+8}}{b^{10} (n+8)}-\frac{9 a d^3 (a+b x)^{n+9}}{b^{10} (n+9)}+\frac{d^3 (a+b x)^{n+10}}{b^{10} (n+10)}","\frac{3 d \left(-20 a^3 b^3 c d+28 a^6 d^2+b^6 c^2\right) (a+b x)^{n+4}}{b^{10} (n+4)}+\frac{9 a^2 d^2 \left(5 b^3 c-14 a^3 d\right) (a+b x)^{n+5}}{b^{10} (n+5)}-\frac{18 a d^2 \left(b^3 c-7 a^3 d\right) (a+b x)^{n+6}}{b^{10} (n+6)}+\frac{3 d^2 \left(b^3 c-28 a^3 d\right) (a+b x)^{n+7}}{b^{10} (n+7)}+\frac{\left(b^3 c-a^3 d\right)^3 (a+b x)^{n+1}}{b^{10} (n+1)}+\frac{9 a^2 d \left(b^3 c-a^3 d\right)^2 (a+b x)^{n+2}}{b^{10} (n+2)}-\frac{9 a d \left(b^3 c-4 a^3 d\right) \left(b^3 c-a^3 d\right) (a+b x)^{n+3}}{b^{10} (n+3)}+\frac{36 a^2 d^3 (a+b x)^{n+8}}{b^{10} (n+8)}-\frac{9 a d^3 (a+b x)^{n+9}}{b^{10} (n+9)}+\frac{d^3 (a+b x)^{n+10}}{b^{10} (n+10)}",1,"((b^3*c - a^3*d)^3*(a + b*x)^(1 + n))/(b^10*(1 + n)) + (9*a^2*d*(b^3*c - a^3*d)^2*(a + b*x)^(2 + n))/(b^10*(2 + n)) - (9*a*d*(b^3*c - 4*a^3*d)*(b^3*c - a^3*d)*(a + b*x)^(3 + n))/(b^10*(3 + n)) + (3*d*(b^6*c^2 - 20*a^3*b^3*c*d + 28*a^6*d^2)*(a + b*x)^(4 + n))/(b^10*(4 + n)) + (9*a^2*d^2*(5*b^3*c - 14*a^3*d)*(a + b*x)^(5 + n))/(b^10*(5 + n)) - (18*a*d^2*(b^3*c - 7*a^3*d)*(a + b*x)^(6 + n))/(b^10*(6 + n)) + (3*d^2*(b^3*c - 28*a^3*d)*(a + b*x)^(7 + n))/(b^10*(7 + n)) + (36*a^2*d^3*(a + b*x)^(8 + n))/(b^10*(8 + n)) - (9*a*d^3*(a + b*x)^(9 + n))/(b^10*(9 + n)) + (d^3*(a + b*x)^(10 + n))/(b^10*(10 + n))","A",2,1,17,0.05882,1,"{1850}"
185,1,358,0,0.2242144,"\int \frac{(a+b x)^n \left(c+d x^3\right)^3}{x} \, dx","Int[((a + b*x)^n*(c + d*x^3)^3)/x,x]","\frac{a^2 d \left(-3 a^3 b^3 c d+a^6 d^2+3 b^6 c^2\right) (a+b x)^{n+1}}{b^9 (n+1)}-\frac{a d \left(-15 a^3 b^3 c d+8 a^6 d^2+6 b^6 c^2\right) (a+b x)^{n+2}}{b^9 (n+2)}+\frac{d \left(-30 a^3 b^3 c d+28 a^6 d^2+3 b^6 c^2\right) (a+b x)^{n+3}}{b^9 (n+3)}+\frac{2 a^2 d^2 \left(15 b^3 c-28 a^3 d\right) (a+b x)^{n+4}}{b^9 (n+4)}-\frac{5 a d^2 \left(3 b^3 c-14 a^3 d\right) (a+b x)^{n+5}}{b^9 (n+5)}+\frac{d^2 \left(3 b^3 c-56 a^3 d\right) (a+b x)^{n+6}}{b^9 (n+6)}+\frac{28 a^2 d^3 (a+b x)^{n+7}}{b^9 (n+7)}-\frac{8 a d^3 (a+b x)^{n+8}}{b^9 (n+8)}+\frac{d^3 (a+b x)^{n+9}}{b^9 (n+9)}-\frac{c^3 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}","\frac{a^2 d \left(-3 a^3 b^3 c d+a^6 d^2+3 b^6 c^2\right) (a+b x)^{n+1}}{b^9 (n+1)}-\frac{a d \left(-15 a^3 b^3 c d+8 a^6 d^2+6 b^6 c^2\right) (a+b x)^{n+2}}{b^9 (n+2)}+\frac{d \left(-30 a^3 b^3 c d+28 a^6 d^2+3 b^6 c^2\right) (a+b x)^{n+3}}{b^9 (n+3)}+\frac{2 a^2 d^2 \left(15 b^3 c-28 a^3 d\right) (a+b x)^{n+4}}{b^9 (n+4)}-\frac{5 a d^2 \left(3 b^3 c-14 a^3 d\right) (a+b x)^{n+5}}{b^9 (n+5)}+\frac{d^2 \left(3 b^3 c-56 a^3 d\right) (a+b x)^{n+6}}{b^9 (n+6)}+\frac{28 a^2 d^3 (a+b x)^{n+7}}{b^9 (n+7)}-\frac{8 a d^3 (a+b x)^{n+8}}{b^9 (n+8)}+\frac{d^3 (a+b x)^{n+9}}{b^9 (n+9)}-\frac{c^3 (a+b x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b x}{a}+1\right)}{a (n+1)}",1,"(a^2*d*(3*b^6*c^2 - 3*a^3*b^3*c*d + a^6*d^2)*(a + b*x)^(1 + n))/(b^9*(1 + n)) - (a*d*(6*b^6*c^2 - 15*a^3*b^3*c*d + 8*a^6*d^2)*(a + b*x)^(2 + n))/(b^9*(2 + n)) + (d*(3*b^6*c^2 - 30*a^3*b^3*c*d + 28*a^6*d^2)*(a + b*x)^(3 + n))/(b^9*(3 + n)) + (2*a^2*d^2*(15*b^3*c - 28*a^3*d)*(a + b*x)^(4 + n))/(b^9*(4 + n)) - (5*a*d^2*(3*b^3*c - 14*a^3*d)*(a + b*x)^(5 + n))/(b^9*(5 + n)) + (d^2*(3*b^3*c - 56*a^3*d)*(a + b*x)^(6 + n))/(b^9*(6 + n)) + (28*a^2*d^3*(a + b*x)^(7 + n))/(b^9*(7 + n)) - (8*a*d^3*(a + b*x)^(8 + n))/(b^9*(8 + n)) + (d^3*(a + b*x)^(9 + n))/(b^9*(9 + n)) - (c^3*(a + b*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (b*x)/a])/(a*(1 + n))","A",3,2,20,0.1000,1,"{1620, 65}"
186,1,324,0,0.8645488,"\int \frac{x^5 (e+f x)^n}{a+b x^3} \, dx","Int[(x^5*(e + f*x)^n)/(a + b*x^3),x]","\frac{a (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b^{5/3} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{a (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e+\sqrt[3]{-1} \sqrt[3]{a} f}\right)}{3 b^{5/3} (n+1) \left(\sqrt[3]{-1} \sqrt[3]{a} f+\sqrt[3]{b} e\right)}+\frac{a (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f}\right)}{3 b^{5/3} (n+1) \left(\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f\right)}+\frac{e^2 (e+f x)^{n+1}}{b f^3 (n+1)}-\frac{2 e (e+f x)^{n+2}}{b f^3 (n+2)}+\frac{(e+f x)^{n+3}}{b f^3 (n+3)}","\frac{a (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b^{5/3} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{a (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e+\sqrt[3]{-1} \sqrt[3]{a} f}\right)}{3 b^{5/3} (n+1) \left(\sqrt[3]{-1} \sqrt[3]{a} f+\sqrt[3]{b} e\right)}+\frac{a (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f}\right)}{3 b^{5/3} (n+1) \left(\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f\right)}+\frac{e^2 (e+f x)^{n+1}}{b f^3 (n+1)}-\frac{2 e (e+f x)^{n+2}}{b f^3 (n+2)}+\frac{(e+f x)^{n+3}}{b f^3 (n+3)}",1,"(e^2*(e + f*x)^(1 + n))/(b*f^3*(1 + n)) - (2*e*(e + f*x)^(2 + n))/(b*f^3*(2 + n)) + (e + f*x)^(3 + n)/(b*f^3*(3 + n)) + (a*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e - a^(1/3)*f)])/(3*b^(5/3)*(b^(1/3)*e - a^(1/3)*f)*(1 + n)) + (a*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e + (-1)^(1/3)*a^(1/3)*f)])/(3*b^(5/3)*(b^(1/3)*e + (-1)^(1/3)*a^(1/3)*f)*(1 + n)) + (a*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e - (-1)^(2/3)*a^(1/3)*f)])/(3*b^(5/3)*(b^(1/3)*e - (-1)^(2/3)*a^(1/3)*f)*(1 + n))","A",7,2,20,0.1000,1,"{6725, 68}"
187,1,332,0,0.8623764,"\int \frac{x^4 (e+f x)^n}{a+b x^3} \, dx","Int[(x^4*(e + f*x)^n)/(a + b*x^3),x]","-\frac{a^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b^{4/3} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{\sqrt[3]{-1} a^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{(-1)^{2/3} \sqrt[3]{b} (e+f x)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b^{4/3} (n+1) \left((-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{(-1)^{2/3} a^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{-1} \sqrt[3]{b} (e+f x)}{\sqrt[3]{-1} \sqrt[3]{b} e+\sqrt[3]{a} f}\right)}{3 b^{4/3} (n+1) \left(\sqrt[3]{a} f+\sqrt[3]{-1} \sqrt[3]{b} e\right)}-\frac{e (e+f x)^{n+1}}{b f^2 (n+1)}+\frac{(e+f x)^{n+2}}{b f^2 (n+2)}","-\frac{a^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b^{4/3} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{\sqrt[3]{-1} a^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{(-1)^{2/3} \sqrt[3]{b} (e+f x)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b^{4/3} (n+1) \left((-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{(-1)^{2/3} a^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{-1} \sqrt[3]{b} (e+f x)}{\sqrt[3]{-1} \sqrt[3]{b} e+\sqrt[3]{a} f}\right)}{3 b^{4/3} (n+1) \left(\sqrt[3]{a} f+\sqrt[3]{-1} \sqrt[3]{b} e\right)}-\frac{e (e+f x)^{n+1}}{b f^2 (n+1)}+\frac{(e+f x)^{n+2}}{b f^2 (n+2)}",1,"-((e*(e + f*x)^(1 + n))/(b*f^2*(1 + n))) + (e + f*x)^(2 + n)/(b*f^2*(2 + n)) - (a^(2/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e - a^(1/3)*f)])/(3*b^(4/3)*(b^(1/3)*e - a^(1/3)*f)*(1 + n)) + ((-1)^(1/3)*a^(2/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, ((-1)^(2/3)*b^(1/3)*(e + f*x))/((-1)^(2/3)*b^(1/3)*e - a^(1/3)*f)])/(3*b^(4/3)*((-1)^(2/3)*b^(1/3)*e - a^(1/3)*f)*(1 + n)) + ((-1)^(2/3)*a^(2/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, ((-1)^(1/3)*b^(1/3)*(e + f*x))/((-1)^(1/3)*b^(1/3)*e + a^(1/3)*f)])/(3*b^(4/3)*((-1)^(1/3)*b^(1/3)*e + a^(1/3)*f)*(1 + n))","A",7,2,20,0.1000,1,"{6725, 68}"
188,1,293,0,0.4761779,"\int \frac{x^3 (e+f x)^n}{a+b x^3} \, dx","Int[(x^3*(e + f*x)^n)/(a + b*x^3),x]","\frac{\sqrt[3]{a} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{\sqrt[3]{a} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{(-1)^{2/3} \sqrt[3]{b} (e+f x)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b (n+1) \left((-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f\right)}-\frac{\sqrt[3]{a} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{-1} \sqrt[3]{b} (e+f x)}{\sqrt[3]{-1} \sqrt[3]{b} e+\sqrt[3]{a} f}\right)}{3 b (n+1) \left(\sqrt[3]{a} f+\sqrt[3]{-1} \sqrt[3]{b} e\right)}+\frac{(e+f x)^{n+1}}{b f (n+1)}","\frac{\sqrt[3]{a} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{\sqrt[3]{a} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{(-1)^{2/3} \sqrt[3]{b} (e+f x)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b (n+1) \left((-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f\right)}-\frac{\sqrt[3]{a} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{-1} \sqrt[3]{b} (e+f x)}{\sqrt[3]{-1} \sqrt[3]{b} e+\sqrt[3]{a} f}\right)}{3 b (n+1) \left(\sqrt[3]{a} f+\sqrt[3]{-1} \sqrt[3]{b} e\right)}+\frac{(e+f x)^{n+1}}{b f (n+1)}",1,"(e + f*x)^(1 + n)/(b*f*(1 + n)) + (a^(1/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e - a^(1/3)*f)])/(3*b*(b^(1/3)*e - a^(1/3)*f)*(1 + n)) + (a^(1/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, ((-1)^(2/3)*b^(1/3)*(e + f*x))/((-1)^(2/3)*b^(1/3)*e - a^(1/3)*f)])/(3*b*((-1)^(2/3)*b^(1/3)*e - a^(1/3)*f)*(1 + n)) - (a^(1/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, ((-1)^(1/3)*b^(1/3)*(e + f*x))/((-1)^(1/3)*b^(1/3)*e + a^(1/3)*f)])/(3*b*((-1)^(1/3)*b^(1/3)*e + a^(1/3)*f)*(1 + n))","A",7,2,20,0.1000,1,"{6725, 68}"
189,1,253,0,0.2780069,"\int \frac{x^2 (e+f x)^n}{a+b x^3} \, dx","Int[(x^2*(e + f*x)^n)/(a + b*x^3),x]","-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b^{2/3} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e+\sqrt[3]{-1} \sqrt[3]{a} f}\right)}{3 b^{2/3} (n+1) \left(\sqrt[3]{-1} \sqrt[3]{a} f+\sqrt[3]{b} e\right)}-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f}\right)}{3 b^{2/3} (n+1) \left(\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f\right)}","-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 b^{2/3} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e+\sqrt[3]{-1} \sqrt[3]{a} f}\right)}{3 b^{2/3} (n+1) \left(\sqrt[3]{-1} \sqrt[3]{a} f+\sqrt[3]{b} e\right)}-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f}\right)}{3 b^{2/3} (n+1) \left(\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f\right)}",1,"-((e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e - a^(1/3)*f)])/(3*b^(2/3)*(b^(1/3)*e - a^(1/3)*f)*(1 + n)) - ((e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e + (-1)^(1/3)*a^(1/3)*f)])/(3*b^(2/3)*(b^(1/3)*e + (-1)^(1/3)*a^(1/3)*f)*(1 + n)) - ((e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e - (-1)^(2/3)*a^(1/3)*f)])/(3*b^(2/3)*(b^(1/3)*e - (-1)^(2/3)*a^(1/3)*f)*(1 + n))","A",5,2,20,0.1000,1,"{6725, 68}"
190,1,288,0,0.2833695,"\int \frac{x (e+f x)^n}{a+b x^3} \, dx","Int[(x*(e + f*x)^n)/(a + b*x^3),x]","\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}-\frac{\sqrt[3]{-1} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{(-1)^{2/3} \sqrt[3]{b} (e+f x)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} (n+1) \left((-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f\right)}-\frac{(-1)^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{-1} \sqrt[3]{b} (e+f x)}{\sqrt[3]{-1} \sqrt[3]{b} e+\sqrt[3]{a} f}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} (n+1) \left(\sqrt[3]{a} f+\sqrt[3]{-1} \sqrt[3]{b} e\right)}","\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}-\frac{\sqrt[3]{-1} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{(-1)^{2/3} \sqrt[3]{b} (e+f x)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} (n+1) \left((-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f\right)}-\frac{(-1)^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{-1} \sqrt[3]{b} (e+f x)}{\sqrt[3]{-1} \sqrt[3]{b} e+\sqrt[3]{a} f}\right)}{3 \sqrt[3]{a} \sqrt[3]{b} (n+1) \left(\sqrt[3]{a} f+\sqrt[3]{-1} \sqrt[3]{b} e\right)}",1,"((e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e - a^(1/3)*f)])/(3*a^(1/3)*b^(1/3)*(b^(1/3)*e - a^(1/3)*f)*(1 + n)) - ((-1)^(1/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, ((-1)^(2/3)*b^(1/3)*(e + f*x))/((-1)^(2/3)*b^(1/3)*e - a^(1/3)*f)])/(3*a^(1/3)*b^(1/3)*((-1)^(2/3)*b^(1/3)*e - a^(1/3)*f)*(1 + n)) - ((-1)^(2/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, ((-1)^(1/3)*b^(1/3)*(e + f*x))/((-1)^(1/3)*b^(1/3)*e + a^(1/3)*f)])/(3*a^(1/3)*b^(1/3)*((-1)^(1/3)*b^(1/3)*e + a^(1/3)*f)*(1 + n))","A",5,2,18,0.1111,1,"{6725, 68}"
191,1,263,0,0.1581922,"\int \frac{(e+f x)^n}{a+b x^3} \, dx","Int[(e + f*x)^n/(a + b*x^3),x]","-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 a^{2/3} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{(-1)^{2/3} \sqrt[3]{b} (e+f x)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 a^{2/3} (n+1) \left((-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{-1} \sqrt[3]{b} (e+f x)}{\sqrt[3]{-1} \sqrt[3]{b} e+\sqrt[3]{a} f}\right)}{3 a^{2/3} (n+1) \left(\sqrt[3]{a} f+\sqrt[3]{-1} \sqrt[3]{b} e\right)}","-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 a^{2/3} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{(-1)^{2/3} \sqrt[3]{b} (e+f x)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 a^{2/3} (n+1) \left((-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{-1} \sqrt[3]{b} (e+f x)}{\sqrt[3]{-1} \sqrt[3]{b} e+\sqrt[3]{a} f}\right)}{3 a^{2/3} (n+1) \left(\sqrt[3]{a} f+\sqrt[3]{-1} \sqrt[3]{b} e\right)}",1,"-((e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e - a^(1/3)*f)])/(3*a^(2/3)*(b^(1/3)*e - a^(1/3)*f)*(1 + n)) - ((e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, ((-1)^(2/3)*b^(1/3)*(e + f*x))/((-1)^(2/3)*b^(1/3)*e - a^(1/3)*f)])/(3*a^(2/3)*((-1)^(2/3)*b^(1/3)*e - a^(1/3)*f)*(1 + n)) + ((e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, ((-1)^(1/3)*b^(1/3)*(e + f*x))/((-1)^(1/3)*b^(1/3)*e + a^(1/3)*f)])/(3*a^(2/3)*((-1)^(1/3)*b^(1/3)*e + a^(1/3)*f)*(1 + n))","A",5,2,17,0.1176,1,"{6725, 68}"
192,1,300,0,0.5591433,"\int \frac{(e+f x)^n}{x \left(a+b x^3\right)} \, dx","Int[(e + f*x)^n/(x*(a + b*x^3)),x]","\frac{\sqrt[3]{b} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 a (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{\sqrt[3]{b} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e+\sqrt[3]{-1} \sqrt[3]{a} f}\right)}{3 a (n+1) \left(\sqrt[3]{-1} \sqrt[3]{a} f+\sqrt[3]{b} e\right)}+\frac{\sqrt[3]{b} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f}\right)}{3 a (n+1) \left(\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f\right)}-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{f x}{e}+1\right)}{a e (n+1)}","\frac{\sqrt[3]{b} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 a (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{\sqrt[3]{b} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e+\sqrt[3]{-1} \sqrt[3]{a} f}\right)}{3 a (n+1) \left(\sqrt[3]{-1} \sqrt[3]{a} f+\sqrt[3]{b} e\right)}+\frac{\sqrt[3]{b} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f}\right)}{3 a (n+1) \left(\sqrt[3]{b} e-(-1)^{2/3} \sqrt[3]{a} f\right)}-\frac{(e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{f x}{e}+1\right)}{a e (n+1)}",1,"(b^(1/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e - a^(1/3)*f)])/(3*a*(b^(1/3)*e - a^(1/3)*f)*(1 + n)) + (b^(1/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e + (-1)^(1/3)*a^(1/3)*f)])/(3*a*(b^(1/3)*e + (-1)^(1/3)*a^(1/3)*f)*(1 + n)) + (b^(1/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e - (-1)^(2/3)*a^(1/3)*f)])/(3*a*(b^(1/3)*e - (-1)^(2/3)*a^(1/3)*f)*(1 + n)) - ((e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + (f*x)/e])/(a*e*(1 + n))","A",8,3,20,0.1500,1,"{6725, 65, 68}"
193,1,326,0,0.611083,"\int \frac{(e+f x)^n}{x^2 \left(a+b x^3\right)} \, dx","Int[(e + f*x)^n/(x^2*(a + b*x^3)),x]","-\frac{b^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 a^{4/3} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{\sqrt[3]{-1} b^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{(-1)^{2/3} \sqrt[3]{b} (e+f x)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 a^{4/3} (n+1) \left((-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{(-1)^{2/3} b^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{-1} \sqrt[3]{b} (e+f x)}{\sqrt[3]{-1} \sqrt[3]{b} e+\sqrt[3]{a} f}\right)}{3 a^{4/3} (n+1) \left(\sqrt[3]{a} f+\sqrt[3]{-1} \sqrt[3]{b} e\right)}+\frac{f (e+f x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{f x}{e}+1\right)}{a e^2 (n+1)}","-\frac{b^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{b} (e+f x)}{\sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 a^{4/3} (n+1) \left(\sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{\sqrt[3]{-1} b^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{(-1)^{2/3} \sqrt[3]{b} (e+f x)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f}\right)}{3 a^{4/3} (n+1) \left((-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} f\right)}+\frac{(-1)^{2/3} b^{2/3} (e+f x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[3]{-1} \sqrt[3]{b} (e+f x)}{\sqrt[3]{-1} \sqrt[3]{b} e+\sqrt[3]{a} f}\right)}{3 a^{4/3} (n+1) \left(\sqrt[3]{a} f+\sqrt[3]{-1} \sqrt[3]{b} e\right)}+\frac{f (e+f x)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{f x}{e}+1\right)}{a e^2 (n+1)}",1,"-(b^(2/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/3)*(e + f*x))/(b^(1/3)*e - a^(1/3)*f)])/(3*a^(4/3)*(b^(1/3)*e - a^(1/3)*f)*(1 + n)) + ((-1)^(1/3)*b^(2/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, ((-1)^(2/3)*b^(1/3)*(e + f*x))/((-1)^(2/3)*b^(1/3)*e - a^(1/3)*f)])/(3*a^(4/3)*((-1)^(2/3)*b^(1/3)*e - a^(1/3)*f)*(1 + n)) + ((-1)^(2/3)*b^(2/3)*(e + f*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, ((-1)^(1/3)*b^(1/3)*(e + f*x))/((-1)^(1/3)*b^(1/3)*e + a^(1/3)*f)])/(3*a^(4/3)*((-1)^(1/3)*b^(1/3)*e + a^(1/3)*f)*(1 + n)) + (f*(e + f*x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, 1 + (f*x)/e])/(a*e^2*(1 + n))","A",8,3,20,0.1500,1,"{6725, 65, 68}"
194,1,253,0,0.5851194,"\int \frac{x^2 (c+d x)^{1+n}}{a+b x^3} \, dx","Int[(x^2*(c + d*x)^(1 + n))/(a + b*x^3),x]","-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{2/3} (n+2) \left(\sqrt[3]{b} c-\sqrt[3]{a} d\right)}-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c+\sqrt[3]{-1} \sqrt[3]{a} d}\right)}{3 b^{2/3} (n+2) \left(\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c\right)}-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 b^{2/3} (n+2) \left(\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d\right)}","-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-\sqrt[3]{a} d}\right)}{3 b^{2/3} (n+2) \left(\sqrt[3]{b} c-\sqrt[3]{a} d\right)}-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c+\sqrt[3]{-1} \sqrt[3]{a} d}\right)}{3 b^{2/3} (n+2) \left(\sqrt[3]{-1} \sqrt[3]{a} d+\sqrt[3]{b} c\right)}-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[3]{b} (c+d x)}{\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d}\right)}{3 b^{2/3} (n+2) \left(\sqrt[3]{b} c-(-1)^{2/3} \sqrt[3]{a} d\right)}",1,"-((c + d*x)^(2 + n)*Hypergeometric2F1[1, 2 + n, 3 + n, (b^(1/3)*(c + d*x))/(b^(1/3)*c - a^(1/3)*d)])/(3*b^(2/3)*(b^(1/3)*c - a^(1/3)*d)*(2 + n)) - ((c + d*x)^(2 + n)*Hypergeometric2F1[1, 2 + n, 3 + n, (b^(1/3)*(c + d*x))/(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)])/(3*b^(2/3)*(b^(1/3)*c + (-1)^(1/3)*a^(1/3)*d)*(2 + n)) - ((c + d*x)^(2 + n)*Hypergeometric2F1[1, 2 + n, 3 + n, (b^(1/3)*(c + d*x))/(b^(1/3)*c - (-1)^(2/3)*a^(1/3)*d)])/(3*b^(2/3)*(b^(1/3)*c - (-1)^(2/3)*a^(1/3)*d)*(2 + n))","A",5,2,22,0.09091,1,"{6725, 68}"
195,1,211,0,0.462599,"\int \frac{x^m (e+f x)^n}{a+b x^3} \, dx","Int[(x^m*(e + f*x)^n)/(a + b*x^3),x]","\frac{x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{\sqrt[3]{b} x}{\sqrt[3]{a}}\right)}{3 a (m+1)}+\frac{x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},\frac{\sqrt[3]{-1} \sqrt[3]{b} x}{\sqrt[3]{a}}\right)}{3 a (m+1)}+\frac{x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{(-1)^{2/3} \sqrt[3]{b} x}{\sqrt[3]{a}}\right)}{3 a (m+1)}","\frac{x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{\sqrt[3]{b} x}{\sqrt[3]{a}}\right)}{3 a (m+1)}+\frac{x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},\frac{\sqrt[3]{-1} \sqrt[3]{b} x}{\sqrt[3]{a}}\right)}{3 a (m+1)}+\frac{x^{m+1} (e+f x)^n \left(\frac{f x}{e}+1\right)^{-n} F_1\left(m+1;-n,1;m+2;-\frac{f x}{e},-\frac{(-1)^{2/3} \sqrt[3]{b} x}{\sqrt[3]{a}}\right)}{3 a (m+1)}",1,"(x^(1 + m)*(e + f*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((f*x)/e), -((b^(1/3)*x)/a^(1/3))])/(3*a*(1 + m)*(1 + (f*x)/e)^n) + (x^(1 + m)*(e + f*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((f*x)/e), ((-1)^(1/3)*b^(1/3)*x)/a^(1/3)])/(3*a*(1 + m)*(1 + (f*x)/e)^n) + (x^(1 + m)*(e + f*x)^n*AppellF1[1 + m, -n, 1, 2 + m, -((f*x)/e), -(((-1)^(2/3)*b^(1/3)*x)/a^(1/3))])/(3*a*(1 + m)*(1 + (f*x)/e)^n)","A",8,3,20,0.1500,1,"{6725, 135, 133}"
196,1,1482,0,2.8145805,"\int \frac{\sqrt{c+d x^3}}{a+b x} \, dx","Int[Sqrt[c + d*x^3]/(a + b*x),x]","\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \sqrt[3]{d} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right) \sqrt{\frac{d^{2/3} x^2-\sqrt[3]{c} \sqrt[3]{d} x+c^{2/3}}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right) a}{b^2 \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \sqrt{d x^3+c}}+\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d} a+\left(1-\sqrt{3}\right) b \sqrt[3]{c}\right) \sqrt[3]{d} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right) \sqrt{\frac{d^{2/3} x^2-\sqrt[3]{c} \sqrt[3]{d} x+c^{2/3}}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right) a}{\sqrt[4]{3} b^3 \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \sqrt{d x^3+c}}-\frac{2 \sqrt[3]{d} \sqrt{d x^3+c} a}{b^2 \left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)}-\frac{\sqrt[6]{c} \sqrt{b \sqrt[3]{c}-a \sqrt[3]{d}} \sqrt{d^{2/3} a^2+b \sqrt[3]{c} \sqrt[3]{d} a+b^2 c^{2/3}} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right) \sqrt{\frac{c^{2/3} \left(\frac{d^{2/3} x^2}{c^{2/3}}-\frac{\sqrt[3]{d} x}{\sqrt[3]{c}}+1\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{3}} \sqrt{d^{2/3} a^2+b \sqrt[3]{c} \sqrt[3]{d} a+b^2 c^{2/3}} \sqrt{1-\frac{\left(\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}\right)^2}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}}}{\sqrt[4]{3} \sqrt{b} \sqrt[6]{c} \sqrt{b \sqrt[3]{c}-a \sqrt[3]{d}} \sqrt{\frac{\left(\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}\right)^2}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}-4 \sqrt{3}+7}}\right)}{b^{5/2} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \sqrt{d x^3+c}}-\frac{2 \sqrt{2+\sqrt{3}} \left(b^3 c-a^3 d\right) \left(\sqrt[3]{d} x+\sqrt[3]{c}\right) \sqrt{\frac{d^{2/3} x^2-\sqrt[3]{c} \sqrt[3]{d} x+c^{2/3}}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^3 \left(\left(1+\sqrt{3}\right) b \sqrt[3]{c}-a \sqrt[3]{d}\right) \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \sqrt{d x^3+c}}-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{c} \left(b^3 c-a^3 d\right) \left(\sqrt[3]{d} x+\sqrt[3]{c}\right) \sqrt{\frac{c^{2/3} \left(\frac{d^{2/3} x^2}{c^{2/3}}-\frac{\sqrt[3]{d} x}{\sqrt[3]{c}}+1\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \Pi \left(\frac{\left(\left(1+\sqrt{3}\right) b \sqrt[3]{c}-a \sqrt[3]{d}\right)^2}{\left(\left(1-\sqrt{3}\right) b \sqrt[3]{c}-a \sqrt[3]{d}\right)^2};-\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{b^2 \left(-d^{2/3} a^2+2 b \sqrt[3]{c} \sqrt[3]{d} a+2 b^2 c^{2/3}\right) \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \sqrt{d x^3+c}}+\frac{2 \sqrt{d x^3+c}}{3 b}","\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \sqrt[3]{d} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right) \sqrt{\frac{d^{2/3} x^2-\sqrt[3]{c} \sqrt[3]{d} x+c^{2/3}}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right) a}{b^2 \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \sqrt{d x^3+c}}+\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{d} a+\left(1-\sqrt{3}\right) b \sqrt[3]{c}\right) \sqrt[3]{d} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right) \sqrt{\frac{d^{2/3} x^2-\sqrt[3]{c} \sqrt[3]{d} x+c^{2/3}}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right) a}{\sqrt[4]{3} b^3 \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \sqrt{d x^3+c}}-\frac{2 \sqrt[3]{d} \sqrt{d x^3+c} a}{b^2 \left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)}-\frac{\sqrt[6]{c} \sqrt{b \sqrt[3]{c}-a \sqrt[3]{d}} \sqrt{d^{2/3} a^2+b \sqrt[3]{c} \sqrt[3]{d} a+b^2 c^{2/3}} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right) \sqrt{\frac{c^{2/3} \left(\frac{d^{2/3} x^2}{c^{2/3}}-\frac{\sqrt[3]{d} x}{\sqrt[3]{c}}+1\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \tanh ^{-1}\left(\frac{\sqrt{2-\sqrt{3}} \sqrt{d^{2/3} a^2+b \sqrt[3]{c} \sqrt[3]{d} a+b^2 c^{2/3}} \sqrt{1-\frac{\left(\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}\right)^2}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}}}{\sqrt[4]{3} \sqrt{b} \sqrt[6]{c} \sqrt{b \sqrt[3]{c}-a \sqrt[3]{d}} \sqrt{\frac{\left(\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}\right)^2}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}-4 \sqrt{3}+7}}\right)}{b^{5/2} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \sqrt{d x^3+c}}-\frac{2 \sqrt{2+\sqrt{3}} \left(b^3 c-a^3 d\right) \left(\sqrt[3]{d} x+\sqrt[3]{c}\right) \sqrt{\frac{d^{2/3} x^2-\sqrt[3]{c} \sqrt[3]{d} x+c^{2/3}}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^3 \left(\left(1+\sqrt{3}\right) b \sqrt[3]{c}-a \sqrt[3]{d}\right) \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \sqrt{d x^3+c}}-\frac{4 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{c} \left(b^3 c-a^3 d\right) \left(\sqrt[3]{d} x+\sqrt[3]{c}\right) \sqrt{\frac{c^{2/3} \left(\frac{d^{2/3} x^2}{c^{2/3}}-\frac{\sqrt[3]{d} x}{\sqrt[3]{c}}+1\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \Pi \left(\frac{\left(\left(1+\sqrt{3}\right) b \sqrt[3]{c}-a \sqrt[3]{d}\right)^2}{\left(\left(1-\sqrt{3}\right) b \sqrt[3]{c}-a \sqrt[3]{d}\right)^2};-\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{b^2 \left(-d^{2/3} a^2+2 b \sqrt[3]{c} \sqrt[3]{d} a+2 b^2 c^{2/3}\right) \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{d} x+\sqrt[3]{c}\right)}{\left(\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}\right)^2}} \sqrt{d x^3+c}}+\frac{2 \sqrt{d x^3+c}}{3 b}",1,"(2*Sqrt[c + d*x^3])/(3*b) - (2*a*d^(1/3)*Sqrt[c + d*x^3])/(b^2*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (c^(1/6)*Sqrt[b*c^(1/3) - a*d^(1/3)]*Sqrt[b^2*c^(2/3) + a*b*c^(1/3)*d^(1/3) + a^2*d^(2/3)]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3)*(1 - (d^(1/3)*x)/c^(1/3) + (d^(2/3)*x^2)/c^(2/3)))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*ArcTanh[(Sqrt[2 - Sqrt[3]]*Sqrt[b^2*c^(2/3) + a*b*c^(1/3)*d^(1/3) + a^2*d^(2/3)]*Sqrt[1 - ((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)^2/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2])/(3^(1/4)*Sqrt[b]*c^(1/6)*Sqrt[b*c^(1/3) - a*d^(1/3)]*Sqrt[7 - 4*Sqrt[3] + ((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)^2/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2])])/(b^(5/2)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*a*c^(1/3)*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^2*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (2*Sqrt[2 + Sqrt[3]]*a*((1 - Sqrt[3])*b*c^(1/3) + a*d^(1/3))*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^3*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (2*Sqrt[2 + Sqrt[3]]*(b^3*c - a^3*d)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^3*((1 + Sqrt[3])*b*c^(1/3) - a*d^(1/3))*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (4*3^(1/4)*Sqrt[2 + Sqrt[3]]*c^(1/3)*(b^3*c - a^3*d)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3)*(1 - (d^(1/3)*x)/c^(1/3) + (d^(2/3)*x^2)/c^(2/3)))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticPi[((1 + Sqrt[3])*b*c^(1/3) - a*d^(1/3))^2/((1 - Sqrt[3])*b*c^(1/3) - a*d^(1/3))^2, -ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^2*(2*b^2*c^(2/3) + 2*a*b*c^(1/3)*d^(1/3) - a^2*d^(2/3))*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",13,12,19,0.6316,1,"{2147, 261, 1878, 218, 1877, 2136, 2142, 2113, 537, 571, 93, 208}"
197,0,0,0,0.0856207,"\int \frac{\left(d^3+e^3 x^3\right)^p}{d+e x} \, dx","Int[(d^3 + e^3*x^3)^p/(d + e*x),x]","\int \frac{\left(d^3+e^3 x^3\right)^p}{d+e x} \, dx","\frac{\left(d^3+e^3 x^3\right)^p \left(1+\frac{2 (d+e x)}{\left(-3+i \sqrt{3}\right) d}\right)^{-p} \left(1-\frac{2 (d+e x)}{\left(3+i \sqrt{3}\right) d}\right)^{-p} F_1\left(p;-p,-p;p+1;-\frac{2 (d+e x)}{\left(-3+i \sqrt{3}\right) d},\frac{2 (d+e x)}{\left(3+i \sqrt{3}\right) d}\right)}{e p}",1,"Defer[Int][(d^3 + e^3*x^3)^p/(d + e*x), x]","F",0,0,0,0,-1,"{}"
198,1,16,0,0.0767319,"\int \frac{2-2 x-x^2}{\left(2+x^2\right) \sqrt{1+x^3}} \, dx","Int[(2 - 2*x - x^2)/((2 + x^2)*Sqrt[1 + x^3]),x]","2 \tan ^{-1}\left(\frac{x+1}{\sqrt{x^3+1}}\right)","2 \tan ^{-1}\left(\frac{x+1}{\sqrt{x^3+1}}\right)",1,"2*ArcTan[(1 + x)/Sqrt[1 + x^3]]","A",2,2,27,0.07407,1,"{2146, 203}"
199,1,20,0,0.0850639,"\int \frac{2+2 x-x^2}{\left(2+x^2\right) \sqrt{1-x^3}} \, dx","Int[(2 + 2*x - x^2)/((2 + x^2)*Sqrt[1 - x^3]),x]","-2 \tan ^{-1}\left(\frac{1-x}{\sqrt{1-x^3}}\right)","-2 \tan ^{-1}\left(\frac{1-x}{\sqrt{1-x^3}}\right)",1,"-2*ArcTan[(1 - x)/Sqrt[1 - x^3]]","A",2,2,29,0.06897,1,"{2146, 203}"
200,1,18,0,0.0792075,"\int \frac{2+2 x-x^2}{\left(2+x^2\right) \sqrt{-1+x^3}} \, dx","Int[(2 + 2*x - x^2)/((2 + x^2)*Sqrt[-1 + x^3]),x]","-2 \tanh ^{-1}\left(\frac{1-x}{\sqrt{x^3-1}}\right)","-2 \tanh ^{-1}\left(\frac{1-x}{\sqrt{x^3-1}}\right)",1,"-2*ArcTanh[(1 - x)/Sqrt[-1 + x^3]]","A",2,2,27,0.07407,1,"{2146, 206}"
201,1,18,0,0.0829336,"\int \frac{2-2 x-x^2}{\left(2+x^2\right) \sqrt{-1-x^3}} \, dx","Int[(2 - 2*x - x^2)/((2 + x^2)*Sqrt[-1 - x^3]),x]","2 \tanh ^{-1}\left(\frac{x+1}{\sqrt{-x^3-1}}\right)","2 \tanh ^{-1}\left(\frac{x+1}{\sqrt{-x^3-1}}\right)",1,"2*ArcTanh[(1 + x)/Sqrt[-1 - x^3]]","A",2,2,29,0.06897,1,"{2146, 206}"
202,1,30,0,0.0930462,"\int \frac{2-2 x-x^2}{\left(2+d+d x+x^2\right) \sqrt{1+x^3}} \, dx","Int[(2 - 2*x - x^2)/((2 + d + d*x + x^2)*Sqrt[1 + x^3]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{d+1} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{d+1}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{d+1} (x+1)}{\sqrt{x^3+1}}\right)}{\sqrt{d+1}}",1,"(2*ArcTan[(Sqrt[1 + d]*(1 + x))/Sqrt[1 + x^3]])/Sqrt[1 + d]","A",2,2,31,0.06452,1,"{2145, 204}"
203,1,38,0,0.1077121,"\int \frac{2+2 x-x^2}{\left(2-d+d x+x^2\right) \sqrt{1-x^3}} \, dx","Int[(2 + 2*x - x^2)/((2 - d + d*x + x^2)*Sqrt[1 - x^3]),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-d} (1-x)}{\sqrt{1-x^3}}\right)}{\sqrt{1-d}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{1-d} (1-x)}{\sqrt{1-x^3}}\right)}{\sqrt{1-d}}",1,"(-2*ArcTan[(Sqrt[1 - d]*(1 - x))/Sqrt[1 - x^3]])/Sqrt[1 - d]","A",2,2,35,0.05714,1,"{2145, 204}"
204,1,36,0,0.0930514,"\int \frac{2+2 x-x^2}{\left(2-d+d x+x^2\right) \sqrt{-1+x^3}} \, dx","Int[(2 + 2*x - x^2)/((2 - d + d*x + x^2)*Sqrt[-1 + x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{1-d} (1-x)}{\sqrt{x^3-1}}\right)}{\sqrt{1-d}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{1-d} (1-x)}{\sqrt{x^3-1}}\right)}{\sqrt{1-d}}",1,"(-2*ArcTanh[(Sqrt[1 - d]*(1 - x))/Sqrt[-1 + x^3]])/Sqrt[1 - d]","A",2,2,33,0.06061,1,"{2145, 207}"
205,1,32,0,0.0926577,"\int \frac{2-2 x-x^2}{\left(2+d+d x+x^2\right) \sqrt{-1-x^3}} \, dx","Int[(2 - 2*x - x^2)/((2 + d + d*x + x^2)*Sqrt[-1 - x^3]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+1} (x+1)}{\sqrt{-x^3-1}}\right)}{\sqrt{d+1}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d+1} (x+1)}{\sqrt{-x^3-1}}\right)}{\sqrt{d+1}}",1,"(2*ArcTanh[(Sqrt[1 + d]*(1 + x))/Sqrt[-1 - x^3]])/Sqrt[1 + d]","A",2,2,33,0.06061,1,"{2145, 207}"
206,1,355,0,0.2326138,"\int (d+e x)^3 \sqrt{a+c x^4} \, dx","Int[(d + e*x)^3*Sqrt[a + c*x^4],x]","\frac{a^{3/4} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(9 \sqrt{a} e^2+5 \sqrt{c} d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{a+c x^4}}-\frac{6 a^{5/4} d e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{a+c x^4}}+\frac{1}{15} d x \sqrt{a+c x^4} \left(5 d^2+9 e^2 x^2\right)+\frac{3}{4} d^2 e x^2 \sqrt{a+c x^4}+\frac{3 a d^2 e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{4 \sqrt{c}}+\frac{6 a d e^2 x \sqrt{a+c x^4}}{5 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{e^3 \left(a+c x^4\right)^{3/2}}{6 c}","\frac{a^{3/4} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(9 \sqrt{a} e^2+5 \sqrt{c} d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{a+c x^4}}-\frac{6 a^{5/4} d e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{a+c x^4}}+\frac{1}{15} d x \sqrt{a+c x^4} \left(5 d^2+9 e^2 x^2\right)+\frac{3}{4} d^2 e x^2 \sqrt{a+c x^4}+\frac{3 a d^2 e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{4 \sqrt{c}}+\frac{6 a d e^2 x \sqrt{a+c x^4}}{5 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{e^3 \left(a+c x^4\right)^{3/2}}{6 c}",1,"(3*d^2*e*x^2*Sqrt[a + c*x^4])/4 + (6*a*d*e^2*x*Sqrt[a + c*x^4])/(5*Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) + (d*x*(5*d^2 + 9*e^2*x^2)*Sqrt[a + c*x^4])/15 + (e^3*(a + c*x^4)^(3/2))/(6*c) + (3*a*d^2*e*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/(4*Sqrt[c]) - (6*a^(5/4)*d*e^2*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(5*c^(3/4)*Sqrt[a + c*x^4]) + (a^(3/4)*d*(5*Sqrt[c]*d^2 + 9*Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(15*c^(3/4)*Sqrt[a + c*x^4])","A",11,10,19,0.5263,1,"{1885, 1177, 1198, 220, 1196, 1248, 641, 195, 217, 206}"
207,1,326,0,0.1890135,"\int (d+e x)^2 \sqrt{a+c x^4} \, dx","Int[(d + e*x)^2*Sqrt[a + c*x^4],x]","\frac{a^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(3 \sqrt{a} e^2+5 \sqrt{c} d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{a+c x^4}}-\frac{2 a^{5/4} e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{a+c x^4}}+\frac{1}{15} x \sqrt{a+c x^4} \left(5 d^2+3 e^2 x^2\right)+\frac{1}{2} d e x^2 \sqrt{a+c x^4}+\frac{a d e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{2 \sqrt{c}}+\frac{2 a e^2 x \sqrt{a+c x^4}}{5 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}","\frac{a^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(3 \sqrt{a} e^2+5 \sqrt{c} d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{a+c x^4}}-\frac{2 a^{5/4} e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{a+c x^4}}+\frac{1}{15} x \sqrt{a+c x^4} \left(5 d^2+3 e^2 x^2\right)+\frac{1}{2} d e x^2 \sqrt{a+c x^4}+\frac{a d e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{2 \sqrt{c}}+\frac{2 a e^2 x \sqrt{a+c x^4}}{5 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"(d*e*x^2*Sqrt[a + c*x^4])/2 + (2*a*e^2*x*Sqrt[a + c*x^4])/(5*Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) + (x*(5*d^2 + 3*e^2*x^2)*Sqrt[a + c*x^4])/15 + (a*d*e*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/(2*Sqrt[c]) - (2*a^(5/4)*e^2*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(5*c^(3/4)*Sqrt[a + c*x^4]) + (a^(3/4)*(5*Sqrt[c]*d^2 + 3*Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(15*c^(3/4)*Sqrt[a + c*x^4])","A",10,9,19,0.4737,1,"{1885, 275, 195, 217, 206, 1177, 1198, 220, 1196}"
208,1,158,0,0.0890388,"\int (d+e x) \sqrt{a+c x^4} \, dx","Int[(d + e*x)*Sqrt[a + c*x^4],x]","\frac{a^{3/4} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{1}{3} d x \sqrt{a+c x^4}+\frac{1}{4} e x^2 \sqrt{a+c x^4}+\frac{a e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{4 \sqrt{c}}","\frac{a^{3/4} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{1}{3} d x \sqrt{a+c x^4}+\frac{1}{4} e x^2 \sqrt{a+c x^4}+\frac{a e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{4 \sqrt{c}}",1,"(d*x*Sqrt[a + c*x^4])/3 + (e*x^2*Sqrt[a + c*x^4])/4 + (a*e*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/(4*Sqrt[c]) + (a^(3/4)*d*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(3*c^(1/4)*Sqrt[a + c*x^4])","A",8,6,17,0.3529,1,"{1885, 195, 220, 275, 217, 206}"
209,1,105,0,0.0194917,"\int \sqrt{a+c x^4} \, dx","Int[Sqrt[a + c*x^4],x]","\frac{a^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{1}{3} x \sqrt{a+c x^4}","\frac{a^{3/4} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{1}{3} x \sqrt{a+c x^4}",1,"(x*Sqrt[a + c*x^4])/3 + (a^(3/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(3*c^(1/4)*Sqrt[a + c*x^4])","A",2,2,11,0.1818,1,"{195, 220}"
210,1,730,0,0.7252507,"\int \frac{\sqrt{a+c x^4}}{d+e x} \, dx","Int[Sqrt[a + c*x^4]/(d + e*x),x]","-\frac{\sqrt{-a e^4-c d^4} \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{2 e^3}+\frac{\sqrt{c} d^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{2 e^3}-\frac{\sqrt{a e^4+c d^4} \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{2 e^3}-\frac{\sqrt[4]{a} \sqrt[4]{c} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\frac{\sqrt{c} d^2}{\sqrt{a}}+e^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 e^4 \sqrt{a+c x^4}}+\frac{\sqrt[4]{c} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(a e^4+c d^4\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} e^4 \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(a e^4+c d^4\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{c} d e^4 \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\sqrt{c} d x \sqrt{a+c x^4}}{e^2 \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{\sqrt[4]{a} \sqrt[4]{c} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{e^2 \sqrt{a+c x^4}}+\frac{\sqrt{a+c x^4}}{2 e}","-\frac{\sqrt{-a e^4-c d^4} \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{2 e^3}+\frac{\sqrt{c} d^2 \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{2 e^3}-\frac{\sqrt{a e^4+c d^4} \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{2 e^3}-\frac{\sqrt[4]{a} \sqrt[4]{c} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\frac{\sqrt{c} d^2}{\sqrt{a}}+e^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 e^4 \sqrt{a+c x^4}}+\frac{\sqrt[4]{c} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(a e^4+c d^4\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} e^4 \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(a e^4+c d^4\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{c} d e^4 \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\sqrt{c} d x \sqrt{a+c x^4}}{e^2 \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{\sqrt[4]{a} \sqrt[4]{c} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{e^2 \sqrt{a+c x^4}}+\frac{\sqrt{a+c x^4}}{2 e}",1,"Sqrt[a + c*x^4]/(2*e) - (Sqrt[c]*d*x*Sqrt[a + c*x^4])/(e^2*(Sqrt[a] + Sqrt[c]*x^2)) - (Sqrt[-(c*d^4) - a*e^4]*ArcTan[(Sqrt[-(c*d^4) - a*e^4]*x)/(d*e*Sqrt[a + c*x^4])])/(2*e^3) + (Sqrt[c]*d^2*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/(2*e^3) - (Sqrt[c*d^4 + a*e^4]*ArcTanh[(a*e^2 + c*d^2*x^2)/(Sqrt[c*d^4 + a*e^4]*Sqrt[a + c*x^4])])/(2*e^3) + (a^(1/4)*c^(1/4)*d*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(e^2*Sqrt[a + c*x^4]) - (a^(1/4)*c^(1/4)*d*((Sqrt[c]*d^2)/Sqrt[a] + e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*e^4*Sqrt[a + c*x^4]) + (c^(1/4)*d*(c*d^4 + a*e^4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*e^4*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4]) - ((Sqrt[c]*d^2 - Sqrt[a]*e^2)*(c*d^4 + a*e^4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[(Sqrt[c]*d^2 + Sqrt[a]*e^2)^2/(4*Sqrt[a]*Sqrt[c]*d^2*e^2), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*c^(1/4)*d*e^4*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4])","A",15,13,19,0.6842,1,"{1729, 1209, 1198, 220, 1196, 1217, 1707, 1248, 735, 844, 217, 206, 725}"
211,1,1221,0,1.799706,"\int \frac{\sqrt{a+c x^4}}{(d+e x)^2} \, dx","Int[Sqrt[a + c*x^4]/(d + e*x)^2,x]","\frac{c \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{c d^4+a e^4} \sqrt{c x^4+a}}\right) d^3}{e^3 \sqrt{c d^4+a e^4}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{c x^4+a}}\right) d}{e^3}-\frac{\sqrt{c x^4+a} d}{e \left(d^2-e^2 x^2\right)}-\frac{2 \sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{e^2 \sqrt{c x^4+a}}+\frac{3 \sqrt[4]{a} \sqrt[4]{c} \left(\frac{\sqrt{c} d^2}{\sqrt{a}}+e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 e^4 \sqrt{c x^4+a}}-\frac{\sqrt[4]{c} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} e^4 \sqrt{c x^4+a}}+\frac{\sqrt[4]{c} \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} e^4 \sqrt{c x^4+a}}-\frac{\sqrt[4]{c} \left(c d^4+a e^4\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} e^4 \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \sqrt{c x^4+a}}+\frac{2 \sqrt{c} x \sqrt{c x^4+a}}{e^2 \left(\sqrt{c} x^2+\sqrt{a}\right)}+\frac{x \sqrt{c x^4+a}}{d^2-e^2 x^2}-\frac{\left(c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{-c d^4-a e^4} x}{d e \sqrt{c x^4+a}}\right)}{2 e^3 \sqrt{-c d^4-a e^4} d}+\frac{\sqrt{-c d^4-a e^4} \tan ^{-1}\left(\frac{\sqrt{-c d^4-a e^4} x}{d e \sqrt{c x^4+a}}\right)}{2 e^3 d}+\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right)^2 \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{c} e^4 \sqrt{c x^4+a} d^2}+\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(c d^4+a e^4\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{c} e^4 \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \sqrt{c x^4+a} d^2}","\frac{c \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{c d^4+a e^4} \sqrt{c x^4+a}}\right) d^3}{e^3 \sqrt{c d^4+a e^4}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{c x^4+a}}\right) d}{e^3}-\frac{\sqrt{c x^4+a} d}{e \left(d^2-e^2 x^2\right)}-\frac{2 \sqrt[4]{a} \sqrt[4]{c} \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{e^2 \sqrt{c x^4+a}}+\frac{3 \sqrt[4]{a} \sqrt[4]{c} \left(\frac{\sqrt{c} d^2}{\sqrt{a}}+e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 e^4 \sqrt{c x^4+a}}-\frac{\sqrt[4]{c} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} e^4 \sqrt{c x^4+a}}+\frac{\sqrt[4]{c} \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} e^4 \sqrt{c x^4+a}}-\frac{\sqrt[4]{c} \left(c d^4+a e^4\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} e^4 \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \sqrt{c x^4+a}}+\frac{2 \sqrt{c} x \sqrt{c x^4+a}}{e^2 \left(\sqrt{c} x^2+\sqrt{a}\right)}+\frac{x \sqrt{c x^4+a}}{d^2-e^2 x^2}-\frac{\left(c d^4-a e^4\right) \tan ^{-1}\left(\frac{\sqrt{-c d^4-a e^4} x}{d e \sqrt{c x^4+a}}\right)}{2 e^3 \sqrt{-c d^4-a e^4} d}+\frac{\sqrt{-c d^4-a e^4} \tan ^{-1}\left(\frac{\sqrt{-c d^4-a e^4} x}{d e \sqrt{c x^4+a}}\right)}{2 e^3 d}+\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right)^2 \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{c} e^4 \sqrt{c x^4+a} d^2}+\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(c d^4+a e^4\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{c} e^4 \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \sqrt{c x^4+a} d^2}",1,"(2*Sqrt[c]*x*Sqrt[a + c*x^4])/(e^2*(Sqrt[a] + Sqrt[c]*x^2)) - (d*Sqrt[a + c*x^4])/(e*(d^2 - e^2*x^2)) + (x*Sqrt[a + c*x^4])/(d^2 - e^2*x^2) + (Sqrt[-(c*d^4) - a*e^4]*ArcTan[(Sqrt[-(c*d^4) - a*e^4]*x)/(d*e*Sqrt[a + c*x^4])])/(2*d*e^3) - ((c*d^4 - a*e^4)*ArcTan[(Sqrt[-(c*d^4) - a*e^4]*x)/(d*e*Sqrt[a + c*x^4])])/(2*d*e^3*Sqrt[-(c*d^4) - a*e^4]) - (Sqrt[c]*d*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/e^3 + (c*d^3*ArcTanh[(a*e^2 + c*d^2*x^2)/(Sqrt[c*d^4 + a*e^4]*Sqrt[a + c*x^4])])/(e^3*Sqrt[c*d^4 + a*e^4]) - (2*a^(1/4)*c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(e^2*Sqrt[a + c*x^4]) + (3*a^(1/4)*c^(1/4)*((Sqrt[c]*d^2)/Sqrt[a] + e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*e^4*Sqrt[a + c*x^4]) - (c^(1/4)*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*e^4*Sqrt[a + c*x^4]) + (c^(1/4)*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*e^4*Sqrt[a + c*x^4]) - (c^(1/4)*(c*d^4 + a*e^4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*e^4*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4]) + ((Sqrt[c]*d^2 - Sqrt[a]*e^2)^2*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[(Sqrt[c]*d^2 + Sqrt[a]*e^2)^2/(4*Sqrt[a]*Sqrt[c]*d^2*e^2), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*c^(1/4)*d^2*e^4*Sqrt[a + c*x^4]) + ((Sqrt[c]*d^2 - Sqrt[a]*e^2)*(c*d^4 + a*e^4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[(Sqrt[c]*d^2 + Sqrt[a]*e^2)^2/(4*Sqrt[a]*Sqrt[c]*d^2*e^2), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*c^(1/4)*d^2*e^4*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4])","A",32,15,19,0.7895,1,"{2153, 1227, 1198, 220, 1196, 1217, 1707, 1248, 733, 844, 217, 206, 725, 1336, 1209}"
212,1,295,0,0.1600571,"\int \frac{(d+e x)^3}{\sqrt{a+c x^4}} \, dx","Int[(d + e*x)^3/Sqrt[a + c*x^4],x]","\frac{d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(3 \sqrt{a} e^2+\sqrt{c} d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} c^{3/4} \sqrt{a+c x^4}}-\frac{3 \sqrt[4]{a} d e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{a+c x^4}}+\frac{3 d^2 e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{2 \sqrt{c}}+\frac{3 d e^2 x \sqrt{a+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{e^3 \sqrt{a+c x^4}}{2 c}","\frac{d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(3 \sqrt{a} e^2+\sqrt{c} d^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} c^{3/4} \sqrt{a+c x^4}}-\frac{3 \sqrt[4]{a} d e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{a+c x^4}}+\frac{3 d^2 e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{2 \sqrt{c}}+\frac{3 d e^2 x \sqrt{a+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}+\frac{e^3 \sqrt{a+c x^4}}{2 c}",1,"(e^3*Sqrt[a + c*x^4])/(2*c) + (3*d*e^2*x*Sqrt[a + c*x^4])/(Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) + (3*d^2*e*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/(2*Sqrt[c]) - (3*a^(1/4)*d*e^2*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(c^(3/4)*Sqrt[a + c*x^4]) + (d*(Sqrt[c]*d^2 + 3*Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*c^(3/4)*Sqrt[a + c*x^4])","A",9,8,19,0.4211,1,"{1885, 1198, 220, 1196, 1248, 641, 217, 206}"
213,1,263,0,0.1235059,"\int \frac{(d+e x)^2}{\sqrt{a+c x^4}} \, dx","Int[(d + e*x)^2/Sqrt[a + c*x^4],x]","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\frac{\sqrt{c} d^2}{\sqrt{a}}+e^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 c^{3/4} \sqrt{a+c x^4}}-\frac{\sqrt[4]{a} e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{a+c x^4}}+\frac{d e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{\sqrt{c}}+\frac{e^2 x \sqrt{a+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}","\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\frac{\sqrt{c} d^2}{\sqrt{a}}+e^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 c^{3/4} \sqrt{a+c x^4}}-\frac{\sqrt[4]{a} e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{a+c x^4}}+\frac{d e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{\sqrt{c}}+\frac{e^2 x \sqrt{a+c x^4}}{\sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"(e^2*x*Sqrt[a + c*x^4])/(Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) + (d*e*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/Sqrt[c] - (a^(1/4)*e^2*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(c^(3/4)*Sqrt[a + c*x^4]) + (a^(1/4)*((Sqrt[c]*d^2)/Sqrt[a] + e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*c^(3/4)*Sqrt[a + c*x^4])","A",8,7,19,0.3684,1,"{1885, 275, 217, 206, 1198, 220, 1196}"
214,1,121,0,0.062415,"\int \frac{d+e x}{\sqrt{a+c x^4}} \, dx","Int[(d + e*x)/Sqrt[a + c*x^4],x]","\frac{d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{2 \sqrt{c}}","\frac{d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{a+c x^4}}\right)}{2 \sqrt{c}}",1,"(e*ArcTanh[(Sqrt[c]*x^2)/Sqrt[a + c*x^4]])/(2*Sqrt[c]) + (d*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*c^(1/4)*Sqrt[a + c*x^4])","A",6,5,17,0.2941,1,"{1885, 220, 275, 217, 206}"
215,1,88,0,0.0095494,"\int \frac{1}{\sqrt{a+c x^4}} \, dx","Int[1/Sqrt[a + c*x^4],x]","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+c x^4}}","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{c} \sqrt{a+c x^4}}",1,"((Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*c^(1/4)*Sqrt[a + c*x^4])","A",1,1,11,0.09091,1,"{220}"
216,1,405,0,0.2724372,"\int \frac{1}{(d+e x) \sqrt{a+c x^4}} \, dx","Int[1/((d + e*x)*Sqrt[a + c*x^4]),x]","\frac{e \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{2 \sqrt{-a e^4-c d^4}}-\frac{e \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{2 \sqrt{a e^4+c d^4}}+\frac{\sqrt[4]{c} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{c} d \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}","\frac{e \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{2 \sqrt{-a e^4-c d^4}}-\frac{e \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{2 \sqrt{a e^4+c d^4}}+\frac{\sqrt[4]{c} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt[4]{c} d \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}",1,"(e*ArcTan[(Sqrt[-(c*d^4) - a*e^4]*x)/(d*e*Sqrt[a + c*x^4])])/(2*Sqrt[-(c*d^4) - a*e^4]) - (e*ArcTanh[(a*e^2 + c*d^2*x^2)/(Sqrt[c*d^4 + a*e^4]*Sqrt[a + c*x^4])])/(2*Sqrt[c*d^4 + a*e^4]) + (c^(1/4)*d*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4]) - ((Sqrt[c]*d^2 - Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[(Sqrt[c]*d^2 + Sqrt[a]*e^2)^2/(4*Sqrt[a]*Sqrt[c]*d^2*e^2), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*c^(1/4)*d*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4])","A",7,7,19,0.3684,1,"{1725, 1217, 220, 1707, 1248, 725, 206}"
217,1,610,0,0.7601911,"\int \frac{1}{(d+e x)^2 \sqrt{a+c x^4}} \, dx","Int[1/((d + e*x)^2*Sqrt[a + c*x^4]),x]","-\frac{c^{3/4} d^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \left(a e^4+c d^4\right)}-\frac{e^3 \sqrt{a+c x^4}}{(d+e x) \left(a e^4+c d^4\right)}+\frac{\sqrt{c} e^2 x \sqrt{a+c x^4}}{\left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^4+c d^4\right)}-\frac{c d^3 e \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{\left(-a e^4-c d^4\right)^{3/2}}-\frac{c d^3 e \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{\left(a e^4+c d^4\right)^{3/2}}+\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\sqrt[4]{a} \sqrt[4]{c} e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+c x^4} \left(a e^4+c d^4\right)}","-\frac{c^{3/4} d^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right) \left(a e^4+c d^4\right)}-\frac{e^3 \sqrt{a+c x^4}}{(d+e x) \left(a e^4+c d^4\right)}+\frac{\sqrt{c} e^2 x \sqrt{a+c x^4}}{\left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^4+c d^4\right)}-\frac{c d^3 e \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{\left(-a e^4-c d^4\right)^{3/2}}-\frac{c d^3 e \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{\left(a e^4+c d^4\right)^{3/2}}+\frac{\sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt{a+c x^4} \left(\sqrt{a} e^2+\sqrt{c} d^2\right)}-\frac{\sqrt[4]{a} \sqrt[4]{c} e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+c x^4} \left(a e^4+c d^4\right)}",1,"-((e^3*Sqrt[a + c*x^4])/((c*d^4 + a*e^4)*(d + e*x))) + (Sqrt[c]*e^2*x*Sqrt[a + c*x^4])/((c*d^4 + a*e^4)*(Sqrt[a] + Sqrt[c]*x^2)) - (c*d^3*e*ArcTan[(Sqrt[-(c*d^4) - a*e^4]*x)/(d*e*Sqrt[a + c*x^4])])/(-(c*d^4) - a*e^4)^(3/2) - (c*d^3*e*ArcTanh[(a*e^2 + c*d^2*x^2)/(Sqrt[c*d^4 + a*e^4]*Sqrt[a + c*x^4])])/(c*d^4 + a*e^4)^(3/2) - (a^(1/4)*c^(1/4)*e^2*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/((c*d^4 + a*e^4)*Sqrt[a + c*x^4]) + (c^(1/4)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*Sqrt[a + c*x^4]) - (c^(3/4)*d^2*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[(Sqrt[c]*d^2 + Sqrt[a]*e^2)^2/(4*Sqrt[a]*Sqrt[c]*d^2*e^2), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*(c*d^4 + a*e^4)*Sqrt[a + c*x^4])","A",11,11,19,0.5789,1,"{1727, 1742, 12, 1248, 725, 206, 1715, 1196, 1709, 220, 1707}"
218,1,659,0,1.1570172,"\int \frac{1}{(d+e x)^3 \sqrt{a+c x^4}} \, dx","Int[1/((d + e*x)^3*Sqrt[a + c*x^4]),x]","\frac{3 c^{3/2} d^3 e^2 x \sqrt{a+c x^4}}{\left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^4+c d^4\right)^2}+\frac{c^{3/4} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt{a+c x^4} \left(a e^4+c d^4\right)}-\frac{3 \sqrt[4]{a} c^{5/4} d^3 e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+c x^4} \left(a e^4+c d^4\right)^2}-\frac{3 c^{3/4} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right)^2 \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt{a+c x^4} \left(a e^4+c d^4\right)^2}-\frac{3 c d^3 e^3 \sqrt{a+c x^4}}{(d+e x) \left(a e^4+c d^4\right)^2}-\frac{e^3 \sqrt{a+c x^4}}{2 (d+e x)^2 \left(a e^4+c d^4\right)}+\frac{3 c d^2 e \left(c d^4-a e^4\right) \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{2 \left(-a e^4-c d^4\right)^{5/2}}-\frac{3 c d^2 e \left(c d^4-a e^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{2 \left(a e^4+c d^4\right)^{5/2}}","\frac{3 c^{3/2} d^3 e^2 x \sqrt{a+c x^4}}{\left(\sqrt{a}+\sqrt{c} x^2\right) \left(a e^4+c d^4\right)^2}+\frac{c^{3/4} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt{a+c x^4} \left(a e^4+c d^4\right)}-\frac{3 \sqrt[4]{a} c^{5/4} d^3 e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{\sqrt{a+c x^4} \left(a e^4+c d^4\right)^2}-\frac{3 c^{3/4} d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right)^2 \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{a} \sqrt{a+c x^4} \left(a e^4+c d^4\right)^2}-\frac{3 c d^3 e^3 \sqrt{a+c x^4}}{(d+e x) \left(a e^4+c d^4\right)^2}-\frac{e^3 \sqrt{a+c x^4}}{2 (d+e x)^2 \left(a e^4+c d^4\right)}+\frac{3 c d^2 e \left(c d^4-a e^4\right) \tan ^{-1}\left(\frac{x \sqrt{-a e^4-c d^4}}{d e \sqrt{a+c x^4}}\right)}{2 \left(-a e^4-c d^4\right)^{5/2}}-\frac{3 c d^2 e \left(c d^4-a e^4\right) \tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{a+c x^4} \sqrt{a e^4+c d^4}}\right)}{2 \left(a e^4+c d^4\right)^{5/2}}",1,"-(e^3*Sqrt[a + c*x^4])/(2*(c*d^4 + a*e^4)*(d + e*x)^2) - (3*c*d^3*e^3*Sqrt[a + c*x^4])/((c*d^4 + a*e^4)^2*(d + e*x)) + (3*c^(3/2)*d^3*e^2*x*Sqrt[a + c*x^4])/((c*d^4 + a*e^4)^2*(Sqrt[a] + Sqrt[c]*x^2)) + (3*c*d^2*e*(c*d^4 - a*e^4)*ArcTan[(Sqrt[-(c*d^4) - a*e^4]*x)/(d*e*Sqrt[a + c*x^4])])/(2*(-(c*d^4) - a*e^4)^(5/2)) - (3*c*d^2*e*(c*d^4 - a*e^4)*ArcTanh[(a*e^2 + c*d^2*x^2)/(Sqrt[c*d^4 + a*e^4]*Sqrt[a + c*x^4])])/(2*(c*d^4 + a*e^4)^(5/2)) - (3*a^(1/4)*c^(5/4)*d^3*e^2*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/((c*d^4 + a*e^4)^2*Sqrt[a + c*x^4]) + (c^(3/4)*d*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*(c*d^4 + a*e^4)*Sqrt[a + c*x^4]) - (3*c^(3/4)*d*(Sqrt[c]*d^2 - Sqrt[a]*e^2)^2*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[(Sqrt[c]*d^2 + Sqrt[a]*e^2)^2/(4*Sqrt[a]*Sqrt[c]*d^2*e^2), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*(c*d^4 + a*e^4)^2*Sqrt[a + c*x^4])","A",12,12,19,0.6316,1,"{1727, 1739, 1742, 12, 1248, 725, 206, 1715, 1196, 1709, 220, 1707}"
219,1,298,0,0.1357609,"\int \frac{(d+e x)^3}{\left(a+c x^4\right)^{3/2}} \, dx","Int[(d + e*x)^3/(a + c*x^4)^(3/2),x]","\frac{d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-3 \sqrt{a} e^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} c^{3/4} \sqrt{a+c x^4}}+\frac{3 d e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} c^{3/4} \sqrt{a+c x^4}}-\frac{a e^3-c x \left(3 d^2 e x+d^3+3 d e^2 x^2\right)}{2 a c \sqrt{a+c x^4}}-\frac{3 d e^2 x \sqrt{a+c x^4}}{2 a \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}","\frac{d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-3 \sqrt{a} e^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} c^{3/4} \sqrt{a+c x^4}}+\frac{3 d e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} c^{3/4} \sqrt{a+c x^4}}-\frac{a e^3-c x \left(3 d^2 e x+d^3+3 d e^2 x^2\right)}{2 a c \sqrt{a+c x^4}}-\frac{3 d e^2 x \sqrt{a+c x^4}}{2 a \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"(-3*d*e^2*x*Sqrt[a + c*x^4])/(2*a*Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) - (a*e^3 - c*x*(d^3 + 3*d^2*e*x + 3*d*e^2*x^2))/(2*a*c*Sqrt[a + c*x^4]) + (3*d*e^2*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*c^(3/4)*Sqrt[a + c*x^4]) + (d*(Sqrt[c]*d^2 - 3*Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(5/4)*c^(3/4)*Sqrt[a + c*x^4])","A",4,4,19,0.2105,1,"{1854, 1198, 220, 1196}"
220,1,270,0,0.1173858,"\int \frac{(d+e x)^2}{\left(a+c x^4\right)^{3/2}} \, dx","Int[(d + e*x)^2/(a + c*x^4)^(3/2),x]","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} c^{3/4} \sqrt{a+c x^4}}+\frac{e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} c^{3/4} \sqrt{a+c x^4}}+\frac{x (d+e x)^2}{2 a \sqrt{a+c x^4}}-\frac{e^2 x \sqrt{a+c x^4}}{2 a \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} \left(\sqrt{c} d^2-\sqrt{a} e^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} c^{3/4} \sqrt{a+c x^4}}+\frac{e^2 \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} c^{3/4} \sqrt{a+c x^4}}+\frac{x (d+e x)^2}{2 a \sqrt{a+c x^4}}-\frac{e^2 x \sqrt{a+c x^4}}{2 a \sqrt{c} \left(\sqrt{a}+\sqrt{c} x^2\right)}",1,"(x*(d + e*x)^2)/(2*a*Sqrt[a + c*x^4]) - (e^2*x*Sqrt[a + c*x^4])/(2*a*Sqrt[c]*(Sqrt[a] + Sqrt[c]*x^2)) + (e^2*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*c^(3/4)*Sqrt[a + c*x^4]) + ((Sqrt[c]*d^2 - Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(5/4)*c^(3/4)*Sqrt[a + c*x^4])","A",4,4,19,0.2105,1,"{1855, 1198, 220, 1196}"
221,1,114,0,0.0474485,"\int \frac{d+e x}{\left(a+c x^4\right)^{3/2}} \, dx","Int[(d + e*x)/(a + c*x^4)^(3/2),x]","\frac{d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{x (d+e x)}{2 a \sqrt{a+c x^4}}","\frac{d \left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{x (d+e x)}{2 a \sqrt{a+c x^4}}",1,"(x*(d + e*x))/(2*a*Sqrt[a + c*x^4]) + (d*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(5/4)*c^(1/4)*Sqrt[a + c*x^4])","A",3,3,17,0.1765,1,"{1855, 12, 220}"
222,1,108,0,0.0190018,"\int \frac{1}{\left(a+c x^4\right)^{3/2}} \, dx","Int[(a + c*x^4)^(-3/2),x]","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{x}{2 a \sqrt{a+c x^4}}","\frac{\left(\sqrt{a}+\sqrt{c} x^2\right) \sqrt{\frac{a+c x^4}{\left(\sqrt{a}+\sqrt{c} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} \sqrt[4]{c} \sqrt{a+c x^4}}+\frac{x}{2 a \sqrt{a+c x^4}}",1,"x/(2*a*Sqrt[a + c*x^4]) + ((Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(5/4)*c^(1/4)*Sqrt[a + c*x^4])","A",2,2,11,0.1818,1,"{199, 220}"
223,1,818,0,0.6008125,"\int \frac{1}{(d+e x) \left(a+c x^4\right)^{3/2}} \, dx","Int[1/((d + e*x)*(a + c*x^4)^(3/2)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{-c d^4-a e^4} x}{d e \sqrt{c x^4+a}}\right) e^5}{2 \left(-c d^4-a e^4\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{c d^4+a e^4} \sqrt{c x^4+a}}\right) e^5}{2 \left(c d^4+a e^4\right)^{3/2}}+\frac{\sqrt[4]{c} d \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e^4}{2 \sqrt[4]{a} \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \left(c d^4+a e^4\right) \sqrt{c x^4+a}}-\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e^4}{4 \sqrt[4]{a} \sqrt[4]{c} d \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \left(c d^4+a e^4\right) \sqrt{c x^4+a}}+\frac{\sqrt[4]{c} d \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e^2}{2 a^{3/4} \left(c d^4+a e^4\right) \sqrt{c x^4+a}}-\frac{\sqrt{c} d x \sqrt{c x^4+a} e^2}{2 a \left(c d^4+a e^4\right) \left(\sqrt{c} x^2+\sqrt{a}\right)}+\frac{\left(a e^2-c d^2 x^2\right) e}{2 a \left(c d^4+a e^4\right) \sqrt{c x^4+a}}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} \left(c d^4+a e^4\right) \sqrt{c x^4+a}}+\frac{c d x \left(d^2+e^2 x^2\right)}{2 a \left(c d^4+a e^4\right) \sqrt{c x^4+a}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{-c d^4-a e^4} x}{d e \sqrt{c x^4+a}}\right) e^5}{2 \left(-c d^4-a e^4\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{a e^2+c d^2 x^2}{\sqrt{c d^4+a e^4} \sqrt{c x^4+a}}\right) e^5}{2 \left(c d^4+a e^4\right)^{3/2}}+\frac{\sqrt[4]{c} d \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e^4}{2 \sqrt[4]{a} \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \left(c d^4+a e^4\right) \sqrt{c x^4+a}}-\frac{\left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(\sqrt{c} d^2+\sqrt{a} e^2\right)^2}{4 \sqrt{a} \sqrt{c} d^2 e^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e^4}{4 \sqrt[4]{a} \sqrt[4]{c} d \left(\sqrt{c} d^2+\sqrt{a} e^2\right) \left(c d^4+a e^4\right) \sqrt{c x^4+a}}+\frac{\sqrt[4]{c} d \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e^2}{2 a^{3/4} \left(c d^4+a e^4\right) \sqrt{c x^4+a}}-\frac{\sqrt{c} d x \sqrt{c x^4+a} e^2}{2 a \left(c d^4+a e^4\right) \left(\sqrt{c} x^2+\sqrt{a}\right)}+\frac{\left(a e^2-c d^2 x^2\right) e}{2 a \left(c d^4+a e^4\right) \sqrt{c x^4+a}}+\frac{\sqrt[4]{c} d \left(\sqrt{c} d^2-\sqrt{a} e^2\right) \left(\sqrt{c} x^2+\sqrt{a}\right) \sqrt{\frac{c x^4+a}{\left(\sqrt{c} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{5/4} \left(c d^4+a e^4\right) \sqrt{c x^4+a}}+\frac{c d x \left(d^2+e^2 x^2\right)}{2 a \left(c d^4+a e^4\right) \sqrt{c x^4+a}}",1,"(e*(a*e^2 - c*d^2*x^2))/(2*a*(c*d^4 + a*e^4)*Sqrt[a + c*x^4]) + (c*d*x*(d^2 + e^2*x^2))/(2*a*(c*d^4 + a*e^4)*Sqrt[a + c*x^4]) - (Sqrt[c]*d*e^2*x*Sqrt[a + c*x^4])/(2*a*(c*d^4 + a*e^4)*(Sqrt[a] + Sqrt[c]*x^2)) - (e^5*ArcTan[(Sqrt[-(c*d^4) - a*e^4]*x)/(d*e*Sqrt[a + c*x^4])])/(2*(-(c*d^4) - a*e^4)^(3/2)) - (e^5*ArcTanh[(a*e^2 + c*d^2*x^2)/(Sqrt[c*d^4 + a*e^4]*Sqrt[a + c*x^4])])/(2*(c*d^4 + a*e^4)^(3/2)) + (c^(1/4)*d*e^2*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticE[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(3/4)*(c*d^4 + a*e^4)*Sqrt[a + c*x^4]) + (c^(1/4)*d*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(5/4)*(c*d^4 + a*e^4)*Sqrt[a + c*x^4]) + (c^(1/4)*d*e^4*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticF[2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*(c*d^4 + a*e^4)*Sqrt[a + c*x^4]) - (e^4*(Sqrt[c]*d^2 - Sqrt[a]*e^2)*(Sqrt[a] + Sqrt[c]*x^2)*Sqrt[(a + c*x^4)/(Sqrt[a] + Sqrt[c]*x^2)^2]*EllipticPi[(Sqrt[c]*d^2 + Sqrt[a]*e^2)^2/(4*Sqrt[a]*Sqrt[c]*d^2*e^2), 2*ArcTan[(c^(1/4)*x)/a^(1/4)], 1/2])/(4*a^(1/4)*c^(1/4)*d*(Sqrt[c]*d^2 + Sqrt[a]*e^2)*(c*d^4 + a*e^4)*Sqrt[a + c*x^4])","A",14,13,19,0.6842,1,"{1729, 1222, 1179, 1198, 220, 1196, 1217, 1707, 1248, 741, 12, 725, 206}"
224,1,349,0,0.7292578,"\int \frac{x^3 (c+d x)^n}{a+b x^4} \, dx","Int[(x^3*(c + d*x)^n)/(a + b*x^4),x]","-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/4} (n+1) \left(\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d\right)}-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/4} (n+1) \left(\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c\right)}-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{3/4} (n+1) \left(\sqrt[4]{b} c-\sqrt[4]{-a} d\right)}-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)}{4 b^{3/4} (n+1) \left(\sqrt[4]{-a} d+\sqrt[4]{b} c\right)}","-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/4} (n+1) \left(\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d\right)}-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/4} (n+1) \left(\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c\right)}-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{3/4} (n+1) \left(\sqrt[4]{b} c-\sqrt[4]{-a} d\right)}-\frac{(c+d x)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)}{4 b^{3/4} (n+1) \left(\sqrt[4]{-a} d+\sqrt[4]{b} c\right)}",1,"-((c + d*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)])/(4*b^(3/4)*(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)*(1 + n)) - ((c + d*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)])/(4*b^(3/4)*(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)*(1 + n)) - ((c + d*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)])/(4*b^(3/4)*(b^(1/4)*c - (-a)^(1/4)*d)*(1 + n)) - ((c + d*x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*b^(3/4)*(b^(1/4)*c + (-a)^(1/4)*d)*(1 + n))","A",10,3,20,0.1500,1,"{6725, 831, 68}"
225,1,349,0,0.5706323,"\int \frac{x^3 (c+d x)^{1+n}}{a+b x^4} \, dx","Int[(x^3*(c + d*x)^(1 + n))/(a + b*x^4),x]","-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/4} (n+2) \left(\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d\right)}-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/4} (n+2) \left(\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c\right)}-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{3/4} (n+2) \left(\sqrt[4]{b} c-\sqrt[4]{-a} d\right)}-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)}{4 b^{3/4} (n+2) \left(\sqrt[4]{-a} d+\sqrt[4]{b} c\right)}","-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/4} (n+2) \left(\sqrt[4]{b} c-\sqrt{-\sqrt{-a}} d\right)}-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt{-\sqrt{-a}} d}\right)}{4 b^{3/4} (n+2) \left(\sqrt{-\sqrt{-a}} d+\sqrt[4]{b} c\right)}-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c-\sqrt[4]{-a} d}\right)}{4 b^{3/4} (n+2) \left(\sqrt[4]{b} c-\sqrt[4]{-a} d\right)}-\frac{(c+d x)^{n+2} \, _2F_1\left(1,n+2;n+3;\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{b} c+\sqrt[4]{-a} d}\right)}{4 b^{3/4} (n+2) \left(\sqrt[4]{-a} d+\sqrt[4]{b} c\right)}",1,"-((c + d*x)^(2 + n)*Hypergeometric2F1[1, 2 + n, 3 + n, (b^(1/4)*(c + d*x))/(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)])/(4*b^(3/4)*(b^(1/4)*c - Sqrt[-Sqrt[-a]]*d)*(2 + n)) - ((c + d*x)^(2 + n)*Hypergeometric2F1[1, 2 + n, 3 + n, (b^(1/4)*(c + d*x))/(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)])/(4*b^(3/4)*(b^(1/4)*c + Sqrt[-Sqrt[-a]]*d)*(2 + n)) - ((c + d*x)^(2 + n)*Hypergeometric2F1[1, 2 + n, 3 + n, (b^(1/4)*(c + d*x))/(b^(1/4)*c - (-a)^(1/4)*d)])/(4*b^(3/4)*(b^(1/4)*c - (-a)^(1/4)*d)*(2 + n)) - ((c + d*x)^(2 + n)*Hypergeometric2F1[1, 2 + n, 3 + n, (b^(1/4)*(c + d*x))/(b^(1/4)*c + (-a)^(1/4)*d)])/(4*b^(3/4)*(b^(1/4)*c + (-a)^(1/4)*d)*(2 + n))","A",10,3,22,0.1364,1,"{6725, 831, 68}"
226,1,1605,0,9.6796174,"\int \frac{1}{\left(c+d x+e x^2\right) \sqrt{a+b x^4}} \, dx","Int[1/((c + d*x + e*x^2)*Sqrt[a + b*x^4]),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{-b d^4+4 b c e d^2-b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d-2 a e^4-2 b c^2 e^2} x}{e \left(d+\sqrt{d^2-4 c e}\right) \sqrt{b x^4+a}}\right) e^2}{\sqrt{2} \sqrt{d^2-4 c e} \sqrt{-2 a e^4-b \left(d^4+\sqrt{d^2-4 c e} d^3-4 c e d^2-2 c e \sqrt{d^2-4 c e} d+2 c^2 e^2\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{-b d^4+4 b c e d^2+b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d-2 a e^4-2 b c^2 e^2} x}{e \left(d-\sqrt{d^2-4 c e}\right) \sqrt{b x^4+a}}\right) e^2}{\sqrt{2} \sqrt{d^2-4 c e} \sqrt{-2 a e^4-b \left(d^4-\sqrt{d^2-4 c e} d^3-4 c e d^2+2 c e \sqrt{d^2-4 c e} d+2 c^2 e^2\right)}}-\frac{\tanh ^{-1}\left(\frac{4 a e^2+b \left(d-\sqrt{d^2-4 c e}\right)^2 x^2}{2 \sqrt{2} \sqrt{b d^4-4 b c e d^2-b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d+2 a e^4+2 b c^2 e^2} \sqrt{b x^4+a}}\right) e^2}{\sqrt{2} \sqrt{d^2-4 c e} \sqrt{b d^4-4 b c e d^2-b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d+2 a e^4+2 b c^2 e^2}}+\frac{\tanh ^{-1}\left(\frac{4 a e^2+b \left(d+\sqrt{d^2-4 c e}\right)^2 x^2}{2 \sqrt{2} \sqrt{b d^4-4 b c e d^2+b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d+2 a e^4+2 b c^2 e^2} \sqrt{b x^4+a}}\right) e^2}{\sqrt{2} \sqrt{d^2-4 c e} \sqrt{b d^4-4 b c e d^2+b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d+2 a e^4+2 b c^2 e^2}}+\frac{\sqrt[4]{b} \left(d-\sqrt{d^2-4 c e}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e}{2 \sqrt[4]{a} \sqrt{d^2-4 c e} \left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2-\sqrt{d^2-4 c e} d-2 c e\right)\right) \sqrt{b x^4+a}}-\frac{\sqrt[4]{b} \left(d+\sqrt{d^2-4 c e}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e}{2 \sqrt[4]{a} \sqrt{d^2-4 c e} \left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2+\sqrt{d^2-4 c e} d-2 c e\right)\right) \sqrt{b x^4+a}}+\frac{\left(2 \sqrt{a} e^2-\sqrt{b} \left(d^2-\sqrt{d^2-4 c e} d-2 c e\right)\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2-\sqrt{d^2-4 c e} d-2 c e\right)\right)^2}{4 \sqrt{a} \sqrt{b} e^2 \left(d-\sqrt{d^2-4 c e}\right)^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{d^2-4 c e} \left(d-\sqrt{d^2-4 c e}\right) \left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2-\sqrt{d^2-4 c e} d-2 c e\right)\right) \sqrt{b x^4+a}}-\frac{\left(2 \sqrt{a} e^2-\sqrt{b} \left(d^2+\sqrt{d^2-4 c e} d-2 c e\right)\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2+\sqrt{d^2-4 c e} d-2 c e\right)\right)^2}{4 \sqrt{a} \sqrt{b} e^2 \left(d+\sqrt{d^2-4 c e}\right)^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{d^2-4 c e} \left(d+\sqrt{d^2-4 c e}\right) \left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2+\sqrt{d^2-4 c e} d-2 c e\right)\right) \sqrt{b x^4+a}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{-b d^4+4 b c e d^2-b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d-2 a e^4-2 b c^2 e^2} x}{e \left(d+\sqrt{d^2-4 c e}\right) \sqrt{b x^4+a}}\right) e^2}{\sqrt{2} \sqrt{d^2-4 c e} \sqrt{-2 a e^4-b \left(d^4+\sqrt{d^2-4 c e} d^3-4 c e d^2-2 c e \sqrt{d^2-4 c e} d+2 c^2 e^2\right)}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{-b d^4+4 b c e d^2+b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d-2 a e^4-2 b c^2 e^2} x}{e \left(d-\sqrt{d^2-4 c e}\right) \sqrt{b x^4+a}}\right) e^2}{\sqrt{2} \sqrt{d^2-4 c e} \sqrt{-2 a e^4-b \left(d^4-\sqrt{d^2-4 c e} d^3-4 c e d^2+2 c e \sqrt{d^2-4 c e} d+2 c^2 e^2\right)}}-\frac{\tanh ^{-1}\left(\frac{4 a e^2+b \left(d-\sqrt{d^2-4 c e}\right)^2 x^2}{2 \sqrt{2} \sqrt{b d^4-4 b c e d^2-b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d+2 a e^4+2 b c^2 e^2} \sqrt{b x^4+a}}\right) e^2}{\sqrt{2} \sqrt{d^2-4 c e} \sqrt{b d^4-4 b c e d^2-b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d+2 a e^4+2 b c^2 e^2}}+\frac{\tanh ^{-1}\left(\frac{4 a e^2+b \left(d+\sqrt{d^2-4 c e}\right)^2 x^2}{2 \sqrt{2} \sqrt{b d^4-4 b c e d^2+b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d+2 a e^4+2 b c^2 e^2} \sqrt{b x^4+a}}\right) e^2}{\sqrt{2} \sqrt{d^2-4 c e} \sqrt{b d^4-4 b c e d^2+b \sqrt{d^2-4 c e} \left(d^2-2 c e\right) d+2 a e^4+2 b c^2 e^2}}+\frac{\sqrt[4]{b} \left(d-\sqrt{d^2-4 c e}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e}{2 \sqrt[4]{a} \sqrt{d^2-4 c e} \left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2-\sqrt{d^2-4 c e} d-2 c e\right)\right) \sqrt{b x^4+a}}-\frac{\sqrt[4]{b} \left(d+\sqrt{d^2-4 c e}\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e}{2 \sqrt[4]{a} \sqrt{d^2-4 c e} \left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2+\sqrt{d^2-4 c e} d-2 c e\right)\right) \sqrt{b x^4+a}}+\frac{\left(2 \sqrt{a} e^2-\sqrt{b} \left(d^2-\sqrt{d^2-4 c e} d-2 c e\right)\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2-\sqrt{d^2-4 c e} d-2 c e\right)\right)^2}{4 \sqrt{a} \sqrt{b} e^2 \left(d-\sqrt{d^2-4 c e}\right)^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{d^2-4 c e} \left(d-\sqrt{d^2-4 c e}\right) \left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2-\sqrt{d^2-4 c e} d-2 c e\right)\right) \sqrt{b x^4+a}}-\frac{\left(2 \sqrt{a} e^2-\sqrt{b} \left(d^2+\sqrt{d^2-4 c e} d-2 c e\right)\right) \left(\sqrt{b} x^2+\sqrt{a}\right) \sqrt{\frac{b x^4+a}{\left(\sqrt{b} x^2+\sqrt{a}\right)^2}} \Pi \left(\frac{\left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2+\sqrt{d^2-4 c e} d-2 c e\right)\right)^2}{4 \sqrt{a} \sqrt{b} e^2 \left(d+\sqrt{d^2-4 c e}\right)^2};2 \tan ^{-1}\left(\frac{\sqrt[4]{b} x}{\sqrt[4]{a}}\right)|\frac{1}{2}\right) e}{2 \sqrt[4]{a} \sqrt[4]{b} \sqrt{d^2-4 c e} \left(d+\sqrt{d^2-4 c e}\right) \left(2 \sqrt{a} e^2+\sqrt{b} \left(d^2+\sqrt{d^2-4 c e} d-2 c e\right)\right) \sqrt{b x^4+a}}",1,"-((e^2*ArcTan[(Sqrt[2]*Sqrt[-(b*d^4) + 4*b*c*d^2*e - 2*b*c^2*e^2 - 2*a*e^4 - b*d*Sqrt[d^2 - 4*c*e]*(d^2 - 2*c*e)]*x)/(e*(d + Sqrt[d^2 - 4*c*e])*Sqrt[a + b*x^4])])/(Sqrt[2]*Sqrt[d^2 - 4*c*e]*Sqrt[-2*a*e^4 - b*(d^4 - 4*c*d^2*e + 2*c^2*e^2 + d^3*Sqrt[d^2 - 4*c*e] - 2*c*d*e*Sqrt[d^2 - 4*c*e])])) + (e^2*ArcTan[(Sqrt[2]*Sqrt[-(b*d^4) + 4*b*c*d^2*e - 2*b*c^2*e^2 - 2*a*e^4 + b*d*Sqrt[d^2 - 4*c*e]*(d^2 - 2*c*e)]*x)/(e*(d - Sqrt[d^2 - 4*c*e])*Sqrt[a + b*x^4])])/(Sqrt[2]*Sqrt[d^2 - 4*c*e]*Sqrt[-2*a*e^4 - b*(d^4 - 4*c*d^2*e + 2*c^2*e^2 - d^3*Sqrt[d^2 - 4*c*e] + 2*c*d*e*Sqrt[d^2 - 4*c*e])]) - (e^2*ArcTanh[(4*a*e^2 + b*(d - Sqrt[d^2 - 4*c*e])^2*x^2)/(2*Sqrt[2]*Sqrt[b*d^4 - 4*b*c*d^2*e + 2*b*c^2*e^2 + 2*a*e^4 - b*d*Sqrt[d^2 - 4*c*e]*(d^2 - 2*c*e)]*Sqrt[a + b*x^4])])/(Sqrt[2]*Sqrt[d^2 - 4*c*e]*Sqrt[b*d^4 - 4*b*c*d^2*e + 2*b*c^2*e^2 + 2*a*e^4 - b*d*Sqrt[d^2 - 4*c*e]*(d^2 - 2*c*e)]) + (e^2*ArcTanh[(4*a*e^2 + b*(d + Sqrt[d^2 - 4*c*e])^2*x^2)/(2*Sqrt[2]*Sqrt[b*d^4 - 4*b*c*d^2*e + 2*b*c^2*e^2 + 2*a*e^4 + b*d*Sqrt[d^2 - 4*c*e]*(d^2 - 2*c*e)]*Sqrt[a + b*x^4])])/(Sqrt[2]*Sqrt[d^2 - 4*c*e]*Sqrt[b*d^4 - 4*b*c*d^2*e + 2*b*c^2*e^2 + 2*a*e^4 + b*d*Sqrt[d^2 - 4*c*e]*(d^2 - 2*c*e)]) + (b^(1/4)*e*(d - Sqrt[d^2 - 4*c*e])*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*Sqrt[d^2 - 4*c*e]*(2*Sqrt[a]*e^2 + Sqrt[b]*(d^2 - 2*c*e - d*Sqrt[d^2 - 4*c*e]))*Sqrt[a + b*x^4]) - (b^(1/4)*e*(d + Sqrt[d^2 - 4*c*e])*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*Sqrt[d^2 - 4*c*e]*(2*Sqrt[a]*e^2 + Sqrt[b]*(d^2 - 2*c*e + d*Sqrt[d^2 - 4*c*e]))*Sqrt[a + b*x^4]) + (e*(2*Sqrt[a]*e^2 - Sqrt[b]*(d^2 - 2*c*e - d*Sqrt[d^2 - 4*c*e]))*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[(2*Sqrt[a]*e^2 + Sqrt[b]*(d^2 - 2*c*e - d*Sqrt[d^2 - 4*c*e]))^2/(4*Sqrt[a]*Sqrt[b]*e^2*(d - Sqrt[d^2 - 4*c*e])^2), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*Sqrt[d^2 - 4*c*e]*(d - Sqrt[d^2 - 4*c*e])*(2*Sqrt[a]*e^2 + Sqrt[b]*(d^2 - 2*c*e - d*Sqrt[d^2 - 4*c*e]))*Sqrt[a + b*x^4]) - (e*(2*Sqrt[a]*e^2 - Sqrt[b]*(d^2 - 2*c*e + d*Sqrt[d^2 - 4*c*e]))*(Sqrt[a] + Sqrt[b]*x^2)*Sqrt[(a + b*x^4)/(Sqrt[a] + Sqrt[b]*x^2)^2]*EllipticPi[(2*Sqrt[a]*e^2 + Sqrt[b]*(d^2 - 2*c*e + d*Sqrt[d^2 - 4*c*e]))^2/(4*Sqrt[a]*Sqrt[b]*e^2*(d + Sqrt[d^2 - 4*c*e])^2), 2*ArcTan[(b^(1/4)*x)/a^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*Sqrt[d^2 - 4*c*e]*(d + Sqrt[d^2 - 4*c*e])*(2*Sqrt[a]*e^2 + Sqrt[b]*(d^2 - 2*c*e + d*Sqrt[d^2 - 4*c*e]))*Sqrt[a + b*x^4])","A",16,8,24,0.3333,1,"{6728, 1725, 1217, 220, 1707, 1248, 725, 206}"
227,1,205,0,0.127775,"\int x^m \left(c \left(a+b x^2\right)^2\right)^{3/2} \, dx","Int[x^m*(c*(a + b*x^2)^2)^(3/2),x]","\frac{a^3 c x^{m+1} \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{(m+1) \left(a+b x^2\right)}+\frac{3 a^2 b c x^{m+3} \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{(m+3) \left(a+b x^2\right)}+\frac{3 a b^2 c x^{m+5} \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{(m+5) \left(a+b x^2\right)}+\frac{b^3 c x^{m+7} \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{(m+7) \left(a+b x^2\right)}","\frac{a^3 c x^{m+1} \sqrt{c \left(a+b x^2\right)^2}}{(m+1) \left(a+b x^2\right)}+\frac{3 a^2 b c x^{m+3} \sqrt{c \left(a+b x^2\right)^2}}{(m+3) \left(a+b x^2\right)}+\frac{3 a b^2 c x^{m+5} \sqrt{c \left(a+b x^2\right)^2}}{(m+5) \left(a+b x^2\right)}+\frac{b^3 c x^{m+7} \sqrt{c \left(a+b x^2\right)^2}}{(m+7) \left(a+b x^2\right)}",1,"(a^3*c*x^(1 + m)*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/((1 + m)*(a + b*x^2)) + (3*a^2*b*c*x^(3 + m)*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/((3 + m)*(a + b*x^2)) + (3*a*b^2*c*x^(5 + m)*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/((5 + m)*(a + b*x^2)) + (b^3*c*x^(7 + m)*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/((7 + m)*(a + b*x^2))","A",4,3,19,0.1579,1,"{1989, 1112, 270}"
228,1,134,0,0.1618527,"\int x^5 \left(c \left(a+b x^2\right)^2\right)^{3/2} \, dx","Int[x^5*(c*(a + b*x^2)^2)^(3/2),x]","\frac{c \left(a+b x^2\right)^5 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{12 b^3}-\frac{a c \left(a+b x^2\right)^4 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{5 b^3}+\frac{a^2 c \left(a+b x^2\right)^3 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{8 b^3}","\frac{3 a^2 b c x^8 \sqrt{c \left(a+b x^2\right)^2}}{8 \left(a+b x^2\right)}+\frac{a^3 c x^6 \sqrt{c \left(a+b x^2\right)^2}}{6 \left(a+b x^2\right)}+\frac{b^3 c x^{12} \sqrt{c \left(a+b x^2\right)^2}}{12 \left(a+b x^2\right)}+\frac{3 a b^2 c x^{10} \sqrt{c \left(a+b x^2\right)^2}}{10 \left(a+b x^2\right)}",1,"(a^2*c*(a + b*x^2)^3*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(8*b^3) - (a*c*(a + b*x^2)^4*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(5*b^3) + (c*(a + b*x^2)^5*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(12*b^3)","A",4,3,19,0.1579,1,"{1989, 1111, 645}"
229,1,187,0,0.1053895,"\int x^4 \left(c \left(a+b x^2\right)^2\right)^{3/2} \, dx","Int[x^4*(c*(a + b*x^2)^2)^(3/2),x]","\frac{b^3 c x^{11} \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{11 \left(a+b x^2\right)}+\frac{a b^2 c x^9 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{3 \left(a+b x^2\right)}+\frac{3 a^2 b c x^7 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{7 \left(a+b x^2\right)}+\frac{a^3 c x^5 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{5 \left(a+b x^2\right)}","\frac{3 a^2 b c x^7 \sqrt{c \left(a+b x^2\right)^2}}{7 \left(a+b x^2\right)}+\frac{a^3 c x^5 \sqrt{c \left(a+b x^2\right)^2}}{5 \left(a+b x^2\right)}+\frac{b^3 c x^{11} \sqrt{c \left(a+b x^2\right)^2}}{11 \left(a+b x^2\right)}+\frac{a b^2 c x^9 \sqrt{c \left(a+b x^2\right)^2}}{3 \left(a+b x^2\right)}",1,"(a^3*c*x^5*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(5*(a + b*x^2)) + (3*a^2*b*c*x^7*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(7*(a + b*x^2)) + (a*b^2*c*x^9*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(3*(a + b*x^2)) + (b^3*c*x^11*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(11*(a + b*x^2))","A",4,3,19,0.1579,1,"{1989, 1112, 270}"
230,1,78,0,0.113314,"\int x^3 \left(c \left(a+b x^2\right)^2\right)^{3/2} \, dx","Int[x^3*(c*(a + b*x^2)^2)^(3/2),x]","\frac{\left(a^2 c+2 a b c x^2+b^2 c x^4\right)^{5/2}}{10 b^2 c}-\frac{a \left(a+b x^2\right) \left(a^2 c+2 a b c x^2+b^2 c x^4\right)^{3/2}}{8 b^2}","\frac{c \left(a+b x^2\right)^4 \sqrt{c \left(a+b x^2\right)^2}}{10 b^2}-\frac{a c \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^2}}{8 b^2}",1,"-(a*(a + b*x^2)*(a^2*c + 2*a*b*c*x^2 + b^2*c*x^4)^(3/2))/(8*b^2) + (a^2*c + 2*a*b*c*x^2 + b^2*c*x^4)^(5/2)/(10*b^2*c)","A",4,4,19,0.2105,1,"{1989, 1111, 640, 609}"
231,1,187,0,0.1021804,"\int x^2 \left(c \left(a+b x^2\right)^2\right)^{3/2} \, dx","Int[x^2*(c*(a + b*x^2)^2)^(3/2),x]","\frac{b^3 c x^9 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{9 \left(a+b x^2\right)}+\frac{3 a b^2 c x^7 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{7 \left(a+b x^2\right)}+\frac{3 a^2 b c x^5 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{5 \left(a+b x^2\right)}+\frac{a^3 c x^3 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{3 \left(a+b x^2\right)}","\frac{3 a^2 b c x^5 \sqrt{c \left(a+b x^2\right)^2}}{5 \left(a+b x^2\right)}+\frac{a^3 c x^3 \sqrt{c \left(a+b x^2\right)^2}}{3 \left(a+b x^2\right)}+\frac{b^3 c x^9 \sqrt{c \left(a+b x^2\right)^2}}{9 \left(a+b x^2\right)}+\frac{3 a b^2 c x^7 \sqrt{c \left(a+b x^2\right)^2}}{7 \left(a+b x^2\right)}",1,"(a^3*c*x^3*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(3*(a + b*x^2)) + (3*a^2*b*c*x^5*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(5*(a + b*x^2)) + (3*a*b^2*c*x^7*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(7*(a + b*x^2)) + (b^3*c*x^9*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(9*(a + b*x^2))","A",4,3,19,0.1579,1,"{1989, 1112, 270}"
232,1,32,0,0.0223109,"\int x \left(c \left(a+b x^2\right)^2\right)^{3/2} \, dx","Int[x*(c*(a + b*x^2)^2)^(3/2),x]","\frac{c \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^2}}{8 b}","\frac{c \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^2}}{8 b}",1,"(c*(a + b*x^2)^3*Sqrt[c*(a + b*x^2)^2])/(8*b)","A",3,3,17,0.1765,1,"{1591, 15, 30}"
233,1,175,0,0.0530723,"\int \left(c \left(a+b x^2\right)^2\right)^{3/2} \, dx","Int[(c*(a + b*x^2)^2)^(3/2),x]","\frac{b^3 x^7 \left(a^2 c+2 a b c x^2+b^2 c x^4\right)^{3/2}}{7 \left(a+b x^2\right)^3}+\frac{3 a b^2 x^5 \left(a^2 c+2 a b c x^2+b^2 c x^4\right)^{3/2}}{5 \left(a+b x^2\right)^3}+\frac{a^2 b x^3 \left(a^2 c+2 a b c x^2+b^2 c x^4\right)^{3/2}}{\left(a+b x^2\right)^3}+\frac{a^3 x \left(a^2 c+2 a b c x^2+b^2 c x^4\right)^{3/2}}{\left(a+b x^2\right)^3}","\frac{a^2 b c x^3 \sqrt{c \left(a+b x^2\right)^2}}{a+b x^2}+\frac{a^3 c x \sqrt{c \left(a+b x^2\right)^2}}{a+b x^2}+\frac{b^3 c x^7 \sqrt{c \left(a+b x^2\right)^2}}{7 \left(a+b x^2\right)}+\frac{3 a b^2 c x^5 \sqrt{c \left(a+b x^2\right)^2}}{5 \left(a+b x^2\right)}",1,"(a^3*x*(a^2*c + 2*a*b*c*x^2 + b^2*c*x^4)^(3/2))/(a + b*x^2)^3 + (a^2*b*x^3*(a^2*c + 2*a*b*c*x^2 + b^2*c*x^4)^(3/2))/(a + b*x^2)^3 + (3*a*b^2*x^5*(a^2*c + 2*a*b*c*x^2 + b^2*c*x^4)^(3/2))/(5*(a + b*x^2)^3) + (b^3*x^7*(a^2*c + 2*a*b*c*x^2 + b^2*c*x^4)^(3/2))/(7*(a + b*x^2)^3)","A",4,3,15,0.2000,1,"{1988, 1088, 194}"
234,1,183,0,0.1033521,"\int \frac{\left(c \left(a+b x^2\right)^2\right)^{3/2}}{x} \, dx","Int[(c*(a + b*x^2)^2)^(3/2)/x,x]","\frac{b^3 c x^6 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{6 \left(a+b x^2\right)}+\frac{3 a b^2 c x^4 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{4 \left(a+b x^2\right)}+\frac{3 a^2 b c x^2 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{2 \left(a+b x^2\right)}+\frac{a^3 c \log (x) \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{a+b x^2}","\frac{3 a^2 b c x^2 \sqrt{c \left(a+b x^2\right)^2}}{2 \left(a+b x^2\right)}+\frac{a^3 c \log (x) \sqrt{c \left(a+b x^2\right)^2}}{a+b x^2}+\frac{b^3 c x^6 \sqrt{c \left(a+b x^2\right)^2}}{6 \left(a+b x^2\right)}+\frac{3 a b^2 c x^4 \sqrt{c \left(a+b x^2\right)^2}}{4 \left(a+b x^2\right)}",1,"(3*a^2*b*c*x^2*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(2*(a + b*x^2)) + (3*a*b^2*c*x^4*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(4*(a + b*x^2)) + (b^3*c*x^6*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(6*(a + b*x^2)) + (a^3*c*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4]*Log[x])/(a + b*x^2)","A",5,4,19,0.2105,1,"{1989, 1112, 266, 43}"
235,1,178,0,0.0933017,"\int \frac{\left(c \left(a+b x^2\right)^2\right)^{3/2}}{x^2} \, dx","Int[(c*(a + b*x^2)^2)^(3/2)/x^2,x]","\frac{b^3 c x^5 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{5 \left(a+b x^2\right)}+\frac{a b^2 c x^3 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{a+b x^2}+\frac{3 a^2 b c x \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{a+b x^2}-\frac{a^3 c \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{x \left(a+b x^2\right)}","\frac{3 a^2 b c x \sqrt{c \left(a+b x^2\right)^2}}{a+b x^2}-\frac{a^3 c \sqrt{c \left(a+b x^2\right)^2}}{x \left(a+b x^2\right)}+\frac{b^3 c x^5 \sqrt{c \left(a+b x^2\right)^2}}{5 \left(a+b x^2\right)}+\frac{a b^2 c x^3 \sqrt{c \left(a+b x^2\right)^2}}{a+b x^2}",1,"-((a^3*c*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(x*(a + b*x^2))) + (3*a^2*b*c*x*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(a + b*x^2) + (a*b^2*c*x^3*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(a + b*x^2) + (b^3*c*x^5*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(5*(a + b*x^2))","A",4,3,19,0.1579,1,"{1989, 1112, 270}"
236,1,184,0,0.1049835,"\int \frac{\left(c \left(a+b x^2\right)^2\right)^{3/2}}{x^3} \, dx","Int[(c*(a + b*x^2)^2)^(3/2)/x^3,x]","\frac{b^3 c x^4 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{4 \left(a+b x^2\right)}+\frac{3 a b^2 c x^2 \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{2 \left(a+b x^2\right)}-\frac{a^3 c \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{2 x^2 \left(a+b x^2\right)}+\frac{3 a^2 b c \log (x) \sqrt{a^2 c+2 a b c x^2+b^2 c x^4}}{a+b x^2}","-\frac{a^3 c \sqrt{c \left(a+b x^2\right)^2}}{2 x^2 \left(a+b x^2\right)}+\frac{3 a^2 b c \log (x) \sqrt{c \left(a+b x^2\right)^2}}{a+b x^2}+\frac{b^3 c x^4 \sqrt{c \left(a+b x^2\right)^2}}{4 \left(a+b x^2\right)}+\frac{3 a b^2 c x^2 \sqrt{c \left(a+b x^2\right)^2}}{2 \left(a+b x^2\right)}",1,"-(a^3*c*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(2*x^2*(a + b*x^2)) + (3*a*b^2*c*x^2*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(2*(a + b*x^2)) + (b^3*c*x^4*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4])/(4*(a + b*x^2)) + (3*a^2*b*c*Sqrt[a^2*c + 2*a*b*c*x^2 + b^2*c*x^4]*Log[x])/(a + b*x^2)","A",5,4,19,0.2105,1,"{1989, 1112, 266, 43}"
237,1,254,0,0.246433,"\int x^2 \left(c \left(a+b x^2\right)^3\right)^{3/2} \, dx","Int[x^2*(c*(a + b*x^2)^3)^(3/2),x]","-\frac{21 a^6 c \sqrt{c \left(a+b x^2\right)^3} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{1024 b^{3/2} \left(a+b x^2\right)^{3/2}}+\frac{21 a^5 c x \sqrt{c \left(a+b x^2\right)^3}}{1024 b \left(a+b x^2\right)}+\frac{21 a^4 c x^3 \sqrt{c \left(a+b x^2\right)^3}}{512 \left(a+b x^2\right)}+\frac{7}{128} a^3 c x^3 \sqrt{c \left(a+b x^2\right)^3}+\frac{21}{320} a^2 c x^3 \left(a+b x^2\right) \sqrt{c \left(a+b x^2\right)^3}+\frac{3}{40} a c x^3 \left(a+b x^2\right)^2 \sqrt{c \left(a+b x^2\right)^3}+\frac{1}{12} c x^3 \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^3}","-\frac{21 a^{9/2} c \sqrt{c \left(a+b x^2\right)^3} \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{1024 b^{3/2} \left(\frac{b x^2}{a}+1\right)^{3/2}}+\frac{21 a^5 c x \sqrt{c \left(a+b x^2\right)^3}}{1024 b \left(a+b x^2\right)}+\frac{21 a^4 c x^3 \sqrt{c \left(a+b x^2\right)^3}}{512 \left(a+b x^2\right)}+\frac{7}{128} a^3 c x^3 \sqrt{c \left(a+b x^2\right)^3}+\frac{21}{320} a^2 c x^3 \left(a+b x^2\right) \sqrt{c \left(a+b x^2\right)^3}+\frac{3}{40} a c x^3 \left(a+b x^2\right)^2 \sqrt{c \left(a+b x^2\right)^3}+\frac{1}{12} c x^3 \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^3}",1,"(7*a^3*c*x^3*Sqrt[c*(a + b*x^2)^3])/128 + (21*a^5*c*x*Sqrt[c*(a + b*x^2)^3])/(1024*b*(a + b*x^2)) + (21*a^4*c*x^3*Sqrt[c*(a + b*x^2)^3])/(512*(a + b*x^2)) + (21*a^2*c*x^3*(a + b*x^2)*Sqrt[c*(a + b*x^2)^3])/320 + (3*a*c*x^3*(a + b*x^2)^2*Sqrt[c*(a + b*x^2)^3])/40 + (c*x^3*(a + b*x^2)^3*Sqrt[c*(a + b*x^2)^3])/12 - (21*a^6*c*Sqrt[c*(a + b*x^2)^3]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(1024*b^(3/2)*(a + b*x^2)^(3/2))","A",9,5,19,0.2632,1,"{6720, 279, 321, 217, 206}"
238,1,32,0,0.0265127,"\int x \left(c \left(a+b x^2\right)^3\right)^{3/2} \, dx","Int[x*(c*(a + b*x^2)^3)^(3/2),x]","\frac{c \left(a+b x^2\right)^4 \sqrt{c \left(a+b x^2\right)^3}}{11 b}","\frac{c \left(a+b x^2\right)^4 \sqrt{c \left(a+b x^2\right)^3}}{11 b}",1,"(c*(a + b*x^2)^4*Sqrt[c*(a + b*x^2)^3])/(11*b)","A",3,3,17,0.1765,1,"{1591, 15, 30}"
239,1,208,0,0.0733558,"\int \left(c \left(a+b x^2\right)^3\right)^{3/2} \, dx","Int[(c*(a + b*x^2)^3)^(3/2),x]","\frac{63 a^4 c x \sqrt{c \left(a+b x^2\right)^3}}{256 \left(a+b x^2\right)}+\frac{21}{128} a^3 c x \sqrt{c \left(a+b x^2\right)^3}+\frac{21}{160} a^2 c x \left(a+b x^2\right) \sqrt{c \left(a+b x^2\right)^3}+\frac{63 a^5 c \sqrt{c \left(a+b x^2\right)^3} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 \sqrt{b} \left(a+b x^2\right)^{3/2}}+\frac{9}{80} a c x \left(a+b x^2\right)^2 \sqrt{c \left(a+b x^2\right)^3}+\frac{1}{10} c x \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^3}","\frac{63 a^4 c x \sqrt{c \left(a+b x^2\right)^3}}{256 \left(a+b x^2\right)}+\frac{21}{128} a^3 c x \sqrt{c \left(a+b x^2\right)^3}+\frac{21}{160} a^2 c x \left(a+b x^2\right) \sqrt{c \left(a+b x^2\right)^3}+\frac{63 a^{7/2} c \sqrt{c \left(a+b x^2\right)^3} \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{256 \sqrt{b} \left(\frac{b x^2}{a}+1\right)^{3/2}}+\frac{9}{80} a c x \left(a+b x^2\right)^2 \sqrt{c \left(a+b x^2\right)^3}+\frac{1}{10} c x \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^3}",1,"(21*a^3*c*x*Sqrt[c*(a + b*x^2)^3])/128 + (63*a^4*c*x*Sqrt[c*(a + b*x^2)^3])/(256*(a + b*x^2)) + (21*a^2*c*x*(a + b*x^2)*Sqrt[c*(a + b*x^2)^3])/160 + (9*a*c*x*(a + b*x^2)^2*Sqrt[c*(a + b*x^2)^3])/80 + (c*x*(a + b*x^2)^3*Sqrt[c*(a + b*x^2)^3])/10 + (63*a^5*c*Sqrt[c*(a + b*x^2)^3]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(256*Sqrt[b]*(a + b*x^2)^(3/2))","A",8,4,15,0.2667,1,"{6720, 195, 217, 206}"
240,1,194,0,0.2170763,"\int \frac{\left(c \left(a+b x^2\right)^3\right)^{3/2}}{x} \, dx","Int[(c*(a + b*x^2)^3)^(3/2)/x,x]","\frac{a^4 c \sqrt{c \left(a+b x^2\right)^3}}{a+b x^2}+\frac{1}{3} a^3 c \sqrt{c \left(a+b x^2\right)^3}+\frac{1}{5} a^2 c \left(a+b x^2\right) \sqrt{c \left(a+b x^2\right)^3}-\frac{a^{9/2} c \sqrt{c \left(a+b x^2\right)^3} \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\left(a+b x^2\right)^{3/2}}+\frac{1}{7} a c \left(a+b x^2\right)^2 \sqrt{c \left(a+b x^2\right)^3}+\frac{1}{9} c \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^3}","\frac{a^4 c \sqrt{c \left(a+b x^2\right)^3}}{a+b x^2}+\frac{1}{3} a^3 c \sqrt{c \left(a+b x^2\right)^3}+\frac{1}{5} a^2 c \left(a+b x^2\right) \sqrt{c \left(a+b x^2\right)^3}-\frac{a^3 c \sqrt{c \left(a+b x^2\right)^3} \tanh ^{-1}\left(\sqrt{\frac{b x^2}{a}+1}\right)}{\left(\frac{b x^2}{a}+1\right)^{3/2}}+\frac{1}{7} a c \left(a+b x^2\right)^2 \sqrt{c \left(a+b x^2\right)^3}+\frac{1}{9} c \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^3}",1,"(a^3*c*Sqrt[c*(a + b*x^2)^3])/3 + (a^4*c*Sqrt[c*(a + b*x^2)^3])/(a + b*x^2) + (a^2*c*(a + b*x^2)*Sqrt[c*(a + b*x^2)^3])/5 + (a*c*(a + b*x^2)^2*Sqrt[c*(a + b*x^2)^3])/7 + (c*(a + b*x^2)^3*Sqrt[c*(a + b*x^2)^3])/9 - (a^(9/2)*c*Sqrt[c*(a + b*x^2)^3]*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(a + b*x^2)^(3/2)","A",9,5,19,0.2632,1,"{6720, 266, 50, 63, 208}"
241,1,209,0,0.1889596,"\int \frac{\left(c \left(a+b x^2\right)^3\right)^{3/2}}{x^2} \, dx","Int[(c*(a + b*x^2)^3)^(3/2)/x^2,x]","\frac{315 a^3 b c x \sqrt{c \left(a+b x^2\right)^3}}{128 \left(a+b x^2\right)}+\frac{105}{64} a^2 b c x \sqrt{c \left(a+b x^2\right)^3}+\frac{315 a^4 \sqrt{b} c \sqrt{c \left(a+b x^2\right)^3} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 \left(a+b x^2\right)^{3/2}}+\frac{21}{16} a b c x \left(a+b x^2\right) \sqrt{c \left(a+b x^2\right)^3}-\frac{c \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^3}}{x}+\frac{9}{8} b c x \left(a+b x^2\right)^2 \sqrt{c \left(a+b x^2\right)^3}","\frac{315 a^3 b c x \sqrt{c \left(a+b x^2\right)^3}}{128 \left(a+b x^2\right)}+\frac{105}{64} a^2 b c x \sqrt{c \left(a+b x^2\right)^3}+\frac{315 a^{5/2} \sqrt{b} c \sqrt{c \left(a+b x^2\right)^3} \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{128 \left(\frac{b x^2}{a}+1\right)^{3/2}}+\frac{21}{16} a b c x \left(a+b x^2\right) \sqrt{c \left(a+b x^2\right)^3}-\frac{c \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^3}}{x}+\frac{9}{8} b c x \left(a+b x^2\right)^2 \sqrt{c \left(a+b x^2\right)^3}",1,"(105*a^2*b*c*x*Sqrt[c*(a + b*x^2)^3])/64 + (315*a^3*b*c*x*Sqrt[c*(a + b*x^2)^3])/(128*(a + b*x^2)) + (21*a*b*c*x*(a + b*x^2)*Sqrt[c*(a + b*x^2)^3])/16 + (9*b*c*x*(a + b*x^2)^2*Sqrt[c*(a + b*x^2)^3])/8 - (c*(a + b*x^2)^3*Sqrt[c*(a + b*x^2)^3])/x + (315*a^4*Sqrt[b]*c*Sqrt[c*(a + b*x^2)^3]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*(a + b*x^2)^(3/2))","A",8,5,19,0.2632,1,"{6720, 277, 195, 217, 206}"
242,1,204,0,0.2159505,"\int \frac{\left(c \left(a+b x^2\right)^3\right)^{3/2}}{x^3} \, dx","Int[(c*(a + b*x^2)^3)^(3/2)/x^3,x]","\frac{9 a^3 b c \sqrt{c \left(a+b x^2\right)^3}}{2 \left(a+b x^2\right)}+\frac{3}{2} a^2 b c \sqrt{c \left(a+b x^2\right)^3}-\frac{9 a^{7/2} b c \sqrt{c \left(a+b x^2\right)^3} \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 \left(a+b x^2\right)^{3/2}}+\frac{9}{10} a b c \left(a+b x^2\right) \sqrt{c \left(a+b x^2\right)^3}-\frac{c \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^3}}{2 x^2}+\frac{9}{14} b c \left(a+b x^2\right)^2 \sqrt{c \left(a+b x^2\right)^3}","\frac{9 a^3 b c \sqrt{c \left(a+b x^2\right)^3}}{2 \left(a+b x^2\right)}+\frac{3}{2} a^2 b c \sqrt{c \left(a+b x^2\right)^3}-\frac{9 a^2 b c \sqrt{c \left(a+b x^2\right)^3} \tanh ^{-1}\left(\sqrt{\frac{b x^2}{a}+1}\right)}{2 \left(\frac{b x^2}{a}+1\right)^{3/2}}+\frac{9}{10} a b c \left(a+b x^2\right) \sqrt{c \left(a+b x^2\right)^3}-\frac{c \left(a+b x^2\right)^3 \sqrt{c \left(a+b x^2\right)^3}}{2 x^2}+\frac{9}{14} b c \left(a+b x^2\right)^2 \sqrt{c \left(a+b x^2\right)^3}",1,"(3*a^2*b*c*Sqrt[c*(a + b*x^2)^3])/2 + (9*a^3*b*c*Sqrt[c*(a + b*x^2)^3])/(2*(a + b*x^2)) + (9*a*b*c*(a + b*x^2)*Sqrt[c*(a + b*x^2)^3])/10 + (9*b*c*(a + b*x^2)^2*Sqrt[c*(a + b*x^2)^3])/14 - (c*(a + b*x^2)^3*Sqrt[c*(a + b*x^2)^3])/(2*x^2) - (9*a^(7/2)*b*c*Sqrt[c*(a + b*x^2)^3]*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*(a + b*x^2)^(3/2))","A",9,6,19,0.3158,1,"{6720, 266, 47, 50, 63, 208}"
243,1,75,0,0.1426503,"\int x^2 \left(\frac{c}{a+b x^2}\right)^{3/2} \, dx","Int[x^2*(c/(a + b*x^2))^(3/2),x]","\frac{c \sqrt{a+b x^2} \sqrt{\frac{c}{a+b x^2}} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{3/2}}-\frac{c x \sqrt{\frac{c}{a+b x^2}}}{b}","\frac{\sqrt{a} c \sqrt{\frac{b x^2}{a}+1} \sqrt{\frac{c}{a+b x^2}} \sinh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}-\frac{c x \sqrt{\frac{c}{a+b x^2}}}{b}",1,"-((c*x*Sqrt[c/(a + b*x^2)])/b) + (c*Sqrt[c/(a + b*x^2)]*Sqrt[a + b*x^2]*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/b^(3/2)","A",4,4,19,0.2105,1,"{6720, 288, 217, 206}"
244,1,21,0,0.0175141,"\int x \left(\frac{c}{a+b x^2}\right)^{3/2} \, dx","Int[x*(c/(a + b*x^2))^(3/2),x]","-\frac{c \sqrt{\frac{c}{a+b x^2}}}{b}","-\frac{c \sqrt{\frac{c}{a+b x^2}}}{b}",1,"-((c*Sqrt[c/(a + b*x^2)])/b)","A",3,3,17,0.1765,1,"{1591, 15, 30}"
245,1,21,0,0.017496,"\int \left(\frac{c}{a+b x^2}\right)^{3/2} \, dx","Int[(c/(a + b*x^2))^(3/2),x]","\frac{c x \sqrt{\frac{c}{a+b x^2}}}{a}","\frac{c x \sqrt{\frac{c}{a+b x^2}}}{a}",1,"(c*x*Sqrt[c/(a + b*x^2)])/a","A",2,2,15,0.1333,1,"{6720, 191}"
246,1,73,0,0.1357926,"\int \frac{\left(\frac{c}{a+b x^2}\right)^{3/2}}{x} \, dx","Int[(c/(a + b*x^2))^(3/2)/x,x]","\frac{c \sqrt{\frac{c}{a+b x^2}}}{a}-\frac{c \sqrt{a+b x^2} \sqrt{\frac{c}{a+b x^2}} \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{3/2}}","\frac{c \sqrt{\frac{c}{a+b x^2}}}{a}-\frac{c \sqrt{\frac{b x^2}{a}+1} \sqrt{\frac{c}{a+b x^2}} \tanh ^{-1}\left(\sqrt{\frac{b x^2}{a}+1}\right)}{a}",1,"(c*Sqrt[c/(a + b*x^2)])/a - (c*Sqrt[c/(a + b*x^2)]*Sqrt[a + b*x^2]*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/a^(3/2)","A",5,5,19,0.2632,1,"{6720, 266, 51, 63, 208}"
247,1,48,0,0.1141109,"\int \frac{\left(\frac{c}{a+b x^2}\right)^{3/2}}{x^2} \, dx","Int[(c/(a + b*x^2))^(3/2)/x^2,x]","-\frac{2 b c x \sqrt{\frac{c}{a+b x^2}}}{a^2}-\frac{c \sqrt{\frac{c}{a+b x^2}}}{a x}","-\frac{2 b c x \sqrt{\frac{c}{a+b x^2}}}{a^2}-\frac{c \sqrt{\frac{c}{a+b x^2}}}{a x}",1,"-((c*Sqrt[c/(a + b*x^2)])/(a*x)) - (2*b*c*x*Sqrt[c/(a + b*x^2)])/a^2","A",3,3,19,0.1579,1,"{6720, 271, 191}"
248,1,112,0,0.1525991,"\int \frac{\left(\frac{c}{a+b x^2}\right)^{3/2}}{x^3} \, dx","Int[(c/(a + b*x^2))^(3/2)/x^3,x]","-\frac{3 c \left(a+b x^2\right) \sqrt{\frac{c}{a+b x^2}}}{2 a^2 x^2}+\frac{3 b c \sqrt{a+b x^2} \sqrt{\frac{c}{a+b x^2}} \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}+\frac{c \sqrt{\frac{c}{a+b x^2}}}{a x^2}","-\frac{3 b c \sqrt{\frac{c}{a+b x^2}}}{2 a^2}+\frac{3 b c \sqrt{\frac{b x^2}{a}+1} \sqrt{\frac{c}{a+b x^2}} \tanh ^{-1}\left(\sqrt{\frac{b x^2}{a}+1}\right)}{2 a^2}-\frac{c \sqrt{\frac{c}{a+b x^2}}}{2 a x^2}",1,"(c*Sqrt[c/(a + b*x^2)])/(a*x^2) - (3*c*Sqrt[c/(a + b*x^2)]*(a + b*x^2))/(2*a^2*x^2) + (3*b*c*Sqrt[c/(a + b*x^2)]*Sqrt[a + b*x^2]*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(5/2))","A",6,5,19,0.2632,1,"{6720, 266, 51, 63, 208}"
249,1,152,0,0.1878997,"\int x^7 \left(c \sqrt{a+b x^2}\right)^{3/2} \, dx","Int[x^7*(c*Sqrt[a + b*x^2])^(3/2),x]","\frac{6 a^2 c \left(a+b x^2\right)^{5/2} \sqrt{c \sqrt{a+b x^2}}}{11 b^4}-\frac{2 a^3 c \left(a+b x^2\right)^{3/2} \sqrt{c \sqrt{a+b x^2}}}{7 b^4}+\frac{2 c \left(a+b x^2\right)^{9/2} \sqrt{c \sqrt{a+b x^2}}}{19 b^4}-\frac{2 a c \left(a+b x^2\right)^{7/2} \sqrt{c \sqrt{a+b x^2}}}{5 b^4}","\frac{6 a^2 \left(a+b x^2\right)^2 \left(c \sqrt{a+b x^2}\right)^{3/2}}{11 b^4}-\frac{2 a^3 \left(a+b x^2\right) \left(c \sqrt{a+b x^2}\right)^{3/2}}{7 b^4}+\frac{2 \left(a+b x^2\right)^4 \left(c \sqrt{a+b x^2}\right)^{3/2}}{19 b^4}-\frac{2 a \left(a+b x^2\right)^3 \left(c \sqrt{a+b x^2}\right)^{3/2}}{5 b^4}",1,"(-2*a^3*c*Sqrt[c*Sqrt[a + b*x^2]]*(a + b*x^2)^(3/2))/(7*b^4) + (6*a^2*c*Sqrt[c*Sqrt[a + b*x^2]]*(a + b*x^2)^(5/2))/(11*b^4) - (2*a*c*Sqrt[c*Sqrt[a + b*x^2]]*(a + b*x^2)^(7/2))/(5*b^4) + (2*c*Sqrt[c*Sqrt[a + b*x^2]]*(a + b*x^2)^(9/2))/(19*b^4)","A",4,3,21,0.1429,1,"{6720, 266, 43}"
250,1,113,0,0.157332,"\int x^5 \left(c \sqrt{a+b x^2}\right)^{3/2} \, dx","Int[x^5*(c*Sqrt[a + b*x^2])^(3/2),x]","\frac{2 a^2 c \left(a+b x^2\right)^{3/2} \sqrt{c \sqrt{a+b x^2}}}{7 b^3}+\frac{2 c \left(a+b x^2\right)^{7/2} \sqrt{c \sqrt{a+b x^2}}}{15 b^3}-\frac{4 a c \left(a+b x^2\right)^{5/2} \sqrt{c \sqrt{a+b x^2}}}{11 b^3}","\frac{2 a^2 \left(a+b x^2\right) \left(c \sqrt{a+b x^2}\right)^{3/2}}{7 b^3}+\frac{2 \left(a+b x^2\right)^3 \left(c \sqrt{a+b x^2}\right)^{3/2}}{15 b^3}-\frac{4 a \left(a+b x^2\right)^2 \left(c \sqrt{a+b x^2}\right)^{3/2}}{11 b^3}",1,"(2*a^2*c*Sqrt[c*Sqrt[a + b*x^2]]*(a + b*x^2)^(3/2))/(7*b^3) - (4*a*c*Sqrt[c*Sqrt[a + b*x^2]]*(a + b*x^2)^(5/2))/(11*b^3) + (2*c*Sqrt[c*Sqrt[a + b*x^2]]*(a + b*x^2)^(7/2))/(15*b^3)","A",4,3,21,0.1429,1,"{6720, 266, 43}"
251,1,74,0,0.1368214,"\int x^3 \left(c \sqrt{a+b x^2}\right)^{3/2} \, dx","Int[x^3*(c*Sqrt[a + b*x^2])^(3/2),x]","\frac{2 c \left(a+b x^2\right)^{5/2} \sqrt{c \sqrt{a+b x^2}}}{11 b^2}-\frac{2 a c \left(a+b x^2\right)^{3/2} \sqrt{c \sqrt{a+b x^2}}}{7 b^2}","\frac{2 \left(a+b x^2\right)^2 \left(c \sqrt{a+b x^2}\right)^{3/2}}{11 b^2}-\frac{2 a \left(a+b x^2\right) \left(c \sqrt{a+b x^2}\right)^{3/2}}{7 b^2}",1,"(-2*a*c*Sqrt[c*Sqrt[a + b*x^2]]*(a + b*x^2)^(3/2))/(7*b^2) + (2*c*Sqrt[c*Sqrt[a + b*x^2]]*(a + b*x^2)^(5/2))/(11*b^2)","A",4,3,21,0.1429,1,"{6720, 266, 43}"
252,1,36,0,0.0195566,"\int x \left(c \sqrt{a+b x^2}\right)^{3/2} \, dx","Int[x*(c*Sqrt[a + b*x^2])^(3/2),x]","\frac{2 c \left(a+b x^2\right)^{3/2} \sqrt{c \sqrt{a+b x^2}}}{7 b}","\frac{2 c \left(a+b x^2\right)^{3/2} \sqrt{c \sqrt{a+b x^2}}}{7 b}",1,"(2*c*Sqrt[c*Sqrt[a + b*x^2]]*(a + b*x^2)^(3/2))/(7*b)","A",3,3,19,0.1579,1,"{1591, 15, 30}"
253,1,141,0,0.1579421,"\int \frac{\left(c \sqrt{a+b x^2}\right)^{3/2}}{x} \, dx","Int[(c*Sqrt[a + b*x^2])^(3/2)/x,x]","\frac{a^{3/4} c \sqrt{c \sqrt{a+b x^2}} \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^2}}{\sqrt[4]{a}}\right)}{\sqrt[4]{a+b x^2}}-\frac{a^{3/4} c \sqrt{c \sqrt{a+b x^2}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^2}}{\sqrt[4]{a}}\right)}{\sqrt[4]{a+b x^2}}+\frac{2}{3} c \sqrt{a+b x^2} \sqrt{c \sqrt{a+b x^2}}","\frac{2}{3} \left(c \sqrt{a+b x^2}\right)^{3/2}+\frac{\left(c \sqrt{a+b x^2}\right)^{3/2} \tan ^{-1}\left(\sqrt[4]{\frac{b x^2}{a}+1}\right)}{\left(\frac{b x^2}{a}+1\right)^{3/4}}-\frac{\left(c \sqrt{a+b x^2}\right)^{3/2} \tanh ^{-1}\left(\sqrt[4]{\frac{b x^2}{a}+1}\right)}{\left(\frac{b x^2}{a}+1\right)^{3/4}}",1,"(2*c*Sqrt[c*Sqrt[a + b*x^2]]*Sqrt[a + b*x^2])/3 + (a^(3/4)*c*Sqrt[c*Sqrt[a + b*x^2]]*ArcTan[(a + b*x^2)^(1/4)/a^(1/4)])/(a + b*x^2)^(1/4) - (a^(3/4)*c*Sqrt[c*Sqrt[a + b*x^2]]*ArcTanh[(a + b*x^2)^(1/4)/a^(1/4)])/(a + b*x^2)^(1/4)","A",7,7,21,0.3333,1,"{6720, 266, 50, 63, 298, 203, 206}"
254,1,151,0,0.1628663,"\int \frac{\left(c \sqrt{a+b x^2}\right)^{3/2}}{x^3} \, dx","Int[(c*Sqrt[a + b*x^2])^(3/2)/x^3,x]","-\frac{c \sqrt{a+b x^2} \sqrt{c \sqrt{a+b x^2}}}{2 x^2}+\frac{3 b c \sqrt{c \sqrt{a+b x^2}} \tan ^{-1}\left(\frac{\sqrt[4]{a+b x^2}}{\sqrt[4]{a}}\right)}{4 \sqrt[4]{a} \sqrt[4]{a+b x^2}}-\frac{3 b c \sqrt{c \sqrt{a+b x^2}} \tanh ^{-1}\left(\frac{\sqrt[4]{a+b x^2}}{\sqrt[4]{a}}\right)}{4 \sqrt[4]{a} \sqrt[4]{a+b x^2}}","-\frac{\left(c \sqrt{a+b x^2}\right)^{3/2}}{2 x^2}+\frac{3 b \left(c \sqrt{a+b x^2}\right)^{3/2} \tan ^{-1}\left(\sqrt[4]{\frac{b x^2}{a}+1}\right)}{4 a \left(\frac{b x^2}{a}+1\right)^{3/4}}-\frac{3 b \left(c \sqrt{a+b x^2}\right)^{3/2} \tanh ^{-1}\left(\sqrt[4]{\frac{b x^2}{a}+1}\right)}{4 a \left(\frac{b x^2}{a}+1\right)^{3/4}}",1,"-(c*Sqrt[c*Sqrt[a + b*x^2]]*Sqrt[a + b*x^2])/(2*x^2) + (3*b*c*Sqrt[c*Sqrt[a + b*x^2]]*ArcTan[(a + b*x^2)^(1/4)/a^(1/4)])/(4*a^(1/4)*(a + b*x^2)^(1/4)) - (3*b*c*Sqrt[c*Sqrt[a + b*x^2]]*ArcTanh[(a + b*x^2)^(1/4)/a^(1/4)])/(4*a^(1/4)*(a + b*x^2)^(1/4))","A",7,7,21,0.3333,1,"{6720, 266, 47, 63, 298, 203, 206}"
255,1,191,0,0.1655058,"\int x^2 \left(c \sqrt{a+b x^2}\right)^{3/2} \, dx","Int[x^2*(c*Sqrt[a + b*x^2])^(3/2),x]","\frac{4 a^{5/2} c \sqrt[4]{\frac{b x^2}{a}+1} \sqrt{c \sqrt{a+b x^2}} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 b^{3/2} \sqrt{a+b x^2}}-\frac{4 a^2 c x \sqrt{c \sqrt{a+b x^2}}}{15 b \sqrt{a+b x^2}}+\frac{2}{9} c x^3 \sqrt{a+b x^2} \sqrt{c \sqrt{a+b x^2}}+\frac{2 a c x \sqrt{a+b x^2} \sqrt{c \sqrt{a+b x^2}}}{15 b}","\frac{4 a^{3/2} \left(c \sqrt{a+b x^2}\right)^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 b^{3/2} \left(\frac{b x^2}{a}+1\right)^{3/4}}-\frac{4 a^2 x \left(c \sqrt{a+b x^2}\right)^{3/2}}{15 b \left(a+b x^2\right)}+\frac{2}{9} x^3 \left(c \sqrt{a+b x^2}\right)^{3/2}+\frac{2 a x \left(c \sqrt{a+b x^2}\right)^{3/2}}{15 b}",1,"(-4*a^2*c*x*Sqrt[c*Sqrt[a + b*x^2]])/(15*b*Sqrt[a + b*x^2]) + (2*a*c*x*Sqrt[c*Sqrt[a + b*x^2]]*Sqrt[a + b*x^2])/(15*b) + (2*c*x^3*Sqrt[c*Sqrt[a + b*x^2]]*Sqrt[a + b*x^2])/9 + (4*a^(5/2)*c*Sqrt[c*Sqrt[a + b*x^2]]*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(15*b^(3/2)*Sqrt[a + b*x^2])","A",6,6,21,0.2857,1,"{6720, 279, 321, 229, 227, 196}"
256,1,146,0,0.0522481,"\int \left(c \sqrt{a+b x^2}\right)^{3/2} \, dx","Int[(c*Sqrt[a + b*x^2])^(3/2),x]","-\frac{6 a^{3/2} c \sqrt[4]{\frac{b x^2}{a}+1} \sqrt{c \sqrt{a+b x^2}} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{b} \sqrt{a+b x^2}}+\frac{6 a c x \sqrt{c \sqrt{a+b x^2}}}{5 \sqrt{a+b x^2}}+\frac{2}{5} c x \sqrt{a+b x^2} \sqrt{c \sqrt{a+b x^2}}","\frac{2}{5} x \left(c \sqrt{a+b x^2}\right)^{3/2}+\frac{6 a x \left(c \sqrt{a+b x^2}\right)^{3/2}}{5 \left(a+b x^2\right)}-\frac{6 \sqrt{a} \left(c \sqrt{a+b x^2}\right)^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{b} \left(\frac{b x^2}{a}+1\right)^{3/4}}",1,"(6*a*c*x*Sqrt[c*Sqrt[a + b*x^2]])/(5*Sqrt[a + b*x^2]) + (2*c*x*Sqrt[c*Sqrt[a + b*x^2]]*Sqrt[a + b*x^2])/5 - (6*a^(3/2)*c*Sqrt[c*Sqrt[a + b*x^2]]*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*Sqrt[b]*Sqrt[a + b*x^2])","A",5,5,17,0.2941,1,"{6720, 195, 229, 227, 196}"
257,1,142,0,0.1374109,"\int \frac{\left(c \sqrt{a+b x^2}\right)^{3/2}}{x^2} \, dx","Int[(c*Sqrt[a + b*x^2])^(3/2)/x^2,x]","-\frac{c \sqrt{a+b x^2} \sqrt{c \sqrt{a+b x^2}}}{x}+\frac{3 b c x \sqrt{c \sqrt{a+b x^2}}}{\sqrt{a+b x^2}}-\frac{3 \sqrt{a} \sqrt{b} c \sqrt[4]{\frac{b x^2}{a}+1} \sqrt{c \sqrt{a+b x^2}} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a+b x^2}}","-\frac{\left(c \sqrt{a+b x^2}\right)^{3/2}}{x}+\frac{3 b x \left(c \sqrt{a+b x^2}\right)^{3/2}}{a+b x^2}-\frac{3 \sqrt{b} \left(c \sqrt{a+b x^2}\right)^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \left(\frac{b x^2}{a}+1\right)^{3/4}}",1,"(3*b*c*x*Sqrt[c*Sqrt[a + b*x^2]])/Sqrt[a + b*x^2] - (c*Sqrt[c*Sqrt[a + b*x^2]]*Sqrt[a + b*x^2])/x - (3*Sqrt[a]*Sqrt[b]*c*Sqrt[c*Sqrt[a + b*x^2]]*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/Sqrt[a + b*x^2]","A",5,5,21,0.2381,1,"{6720, 277, 229, 227, 196}"
258,1,193,0,0.1578014,"\int \frac{\left(c \sqrt{a+b x^2}\right)^{3/2}}{x^4} \, dx","Int[(c*Sqrt[a + b*x^2])^(3/2)/x^4,x]","\frac{b^2 c x \sqrt{c \sqrt{a+b x^2}}}{2 a \sqrt{a+b x^2}}-\frac{b^{3/2} c \sqrt[4]{\frac{b x^2}{a}+1} \sqrt{c \sqrt{a+b x^2}} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 \sqrt{a} \sqrt{a+b x^2}}-\frac{b c \sqrt{a+b x^2} \sqrt{c \sqrt{a+b x^2}}}{2 a x}-\frac{c \sqrt{a+b x^2} \sqrt{c \sqrt{a+b x^2}}}{3 x^3}","-\frac{b^{3/2} \left(c \sqrt{a+b x^2}\right)^{3/2} E\left(\left.\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 a^{3/2} \left(\frac{b x^2}{a}+1\right)^{3/4}}+\frac{b^2 x \left(c \sqrt{a+b x^2}\right)^{3/2}}{2 a \left(a+b x^2\right)}-\frac{b \left(c \sqrt{a+b x^2}\right)^{3/2}}{2 a x}-\frac{\left(c \sqrt{a+b x^2}\right)^{3/2}}{3 x^3}",1,"(b^2*c*x*Sqrt[c*Sqrt[a + b*x^2]])/(2*a*Sqrt[a + b*x^2]) - (c*Sqrt[c*Sqrt[a + b*x^2]]*Sqrt[a + b*x^2])/(3*x^3) - (b*c*Sqrt[c*Sqrt[a + b*x^2]]*Sqrt[a + b*x^2])/(2*a*x) - (b^(3/2)*c*Sqrt[c*Sqrt[a + b*x^2]]*(1 + (b*x^2)/a)^(1/4)*EllipticE[ArcTan[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(2*Sqrt[a]*Sqrt[a + b*x^2])","A",6,6,21,0.2857,1,"{6720, 277, 325, 229, 227, 196}"
259,1,71,0,0.0254128,"\int \sqrt{(b-x) (-a+x)} \, dx","Int[Sqrt[(b - x)*(-a + x)],x]","-\frac{1}{4} (a+b-2 x) \sqrt{x (a+b)-a b-x^2}-\frac{1}{8} (a-b)^2 \tan ^{-1}\left(\frac{a+b-2 x}{2 \sqrt{x (a+b)-a b-x^2}}\right)","-\frac{1}{4} (a+b-2 x) \sqrt{x (a+b)-a b-x^2}-\frac{1}{8} (a-b)^2 \tan ^{-1}\left(\frac{a+b-2 x}{2 \sqrt{x (a+b)-a b-x^2}}\right)",1,"-((a + b - 2*x)*Sqrt[-(a*b) + (a + b)*x - x^2])/4 - ((a - b)^2*ArcTan[(a + b - 2*x)/(2*Sqrt[-(a*b) + (a + b)*x - x^2])])/8","A",4,4,15,0.2667,1,"{1981, 612, 621, 204}"
260,1,48,0,0.0428554,"\int \sqrt{\left(1-x^2\right) \left(3+x^2\right)} \, dx","Int[Sqrt[(1 - x^2)*(3 + x^2)],x]","\frac{1}{3} \sqrt{-x^4-2 x^2+3} x+\frac{4 F\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}-\frac{2 E\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}","\frac{1}{3} \sqrt{-x^4-2 x^2+3} x+\frac{4 F\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}-\frac{2 E\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}",1,"(x*Sqrt[3 - 2*x^2 - x^4])/3 - (2*EllipticE[ArcSin[x], -1/3])/Sqrt[3] + (4*EllipticF[ArcSin[x], -1/3])/Sqrt[3]","A",6,6,17,0.3529,1,"{1988, 1091, 1180, 524, 424, 419}"
261,1,32,0,0.0130767,"\int \frac{1}{\sqrt{(b-x) (-a+x)}} \, dx","Int[1/Sqrt[(b - x)*(-a + x)],x]","-\tan ^{-1}\left(\frac{a+b-2 x}{2 \sqrt{x (a+b)-a b-x^2}}\right)","-\tan ^{-1}\left(\frac{a+b-2 x}{2 \sqrt{x (a+b)-a b-x^2}}\right)",1,"-ArcTan[(a + b - 2*x)/(2*Sqrt[-(a*b) + (a + b)*x - x^2])]","A",3,3,15,0.2000,1,"{1981, 621, 204}"
262,1,12,0,0.0131315,"\int \frac{1}{\sqrt{\left(1-x^2\right) \left(3+x^2\right)}} \, dx","Int[1/Sqrt[(1 - x^2)*(3 + x^2)],x]","\frac{F\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}","\frac{F\left(\sin ^{-1}(x)|-\frac{1}{3}\right)}{\sqrt{3}}",1,"EllipticF[ArcSin[x], -1/3]/Sqrt[3]","A",3,3,17,0.1765,1,"{1988, 1095, 419}"
263,1,244,0,0.3325081,"\int x^5 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} \, dx","Int[x^5*Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","\frac{\left(c+d x^2\right) \left(-a^2 d^2-2 a b c d+11 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{16 b^2 d^3}-\frac{\sqrt{e} (b c-a d) \left(a^2 d^2+2 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{16 b^{5/2} d^{7/2}}+\frac{\left(c+d x^2\right)^3 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{6 b d^2 e}-\frac{\left(c+d x^2\right)^2 (a d+3 b c) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 b d^3}","\frac{\left(c+d x^2\right) \left(-a^2 d^2-2 a b c d+11 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{16 b^2 d^3}-\frac{\sqrt{e} (b c-a d) \left(a^2 d^2+2 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{16 b^{5/2} d^{7/2}}+\frac{\left(c+d x^2\right)^3 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{6 b d^2 e}-\frac{\left(c+d x^2\right)^2 (a d+3 b c) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 b d^3}",1,"((11*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(16*b^2*d^3) - ((3*b*c + a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)^2)/(8*b*d^3) + (((e*(a + b*x^2))/(c + d*x^2))^(3/2)*(c + d*x^2)^3)/(6*b*d^2*e) - ((b*c - a*d)*(5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*Sqrt[e]*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(16*b^(5/2)*d^(7/2))","A",5,5,26,0.1923,1,"{1960, 463, 455, 385, 208}"
264,1,161,0,0.1629426,"\int x^3 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} \, dx","Int[x^3*Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","\frac{\sqrt{e} (b c-a d) (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{8 b^{3/2} d^{5/2}}+\frac{\left(c+d x^2\right)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 d^2}-\frac{\left(c+d x^2\right) (5 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 b d^2}","\frac{\sqrt{e} (b c-a d) (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{8 b^{3/2} d^{5/2}}+\frac{\left(c+d x^2\right)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 d^2}-\frac{\left(c+d x^2\right) (5 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 b d^2}",1,"-((5*b*c - a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(8*b*d^2) + (Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)^2)/(4*d^2) + ((b*c - a*d)*(3*b*c + a*d)*Sqrt[e]*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(8*b^(3/2)*d^(5/2))","A",4,4,26,0.1538,1,"{1960, 455, 385, 208}"
265,1,103,0,0.0698071,"\int x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} \, dx","Int[x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","\frac{\left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 d}-\frac{\sqrt{e} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{2 \sqrt{b} d^{3/2}}","\frac{\left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 d}-\frac{\sqrt{e} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{2 \sqrt{b} d^{3/2}}",1,"(Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(2*d) - ((b*c - a*d)*Sqrt[e]*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(2*Sqrt[b]*d^(3/2))","A",3,3,24,0.1250,1,"{1960, 288, 208}"
266,1,112,0,0.1277906,"\int \frac{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{x} \, dx","Int[Sqrt[(e*(a + b*x^2))/(c + d*x^2)]/x,x]","\frac{\sqrt{b} \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{\sqrt{d}}-\frac{\sqrt{a} \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{\sqrt{c}}","\frac{\sqrt{b} \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{\sqrt{d}}-\frac{\sqrt{a} \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{\sqrt{c}}",1,"-((Sqrt[a]*Sqrt[e]*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/Sqrt[c]) + (Sqrt[b]*Sqrt[e]*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/Sqrt[d]","A",4,3,26,0.1154,1,"{1960, 481, 208}"
267,1,127,0,0.086561,"\int \frac{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{x^3} \, dx","Int[Sqrt[(e*(a + b*x^2))/(c + d*x^2)]/x^3,x]","\frac{(b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 c \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)}-\frac{\sqrt{e} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{2 \sqrt{a} c^{3/2}}","\frac{(b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 c \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)}-\frac{\sqrt{e} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{2 \sqrt{a} c^{3/2}}",1,"((b*c - a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(2*c*(a - (c*(a + b*x^2))/(c + d*x^2))) - ((b*c - a*d)*Sqrt[e]*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(2*Sqrt[a]*c^(3/2))","A",3,3,26,0.1154,1,"{1960, 288, 208}"
268,1,208,0,0.1695091,"\int \frac{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{x^5} \, dx","Int[Sqrt[(e*(a + b*x^2))/(c + d*x^2)]/x^5,x]","\frac{\sqrt{e} (3 a d+b c) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{8 a^{3/2} c^{5/2}}-\frac{(b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 c^2 \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)^2}+\frac{(b c-5 a d) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 a c^2 \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)}","\frac{\sqrt{e} (3 a d+b c) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{8 a^{3/2} c^{5/2}}-\frac{(b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 c^2 \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)^2}+\frac{(b c-5 a d) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 a c^2 \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)}",1,"-((b*c - a*d)^2*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(4*c^2*(a - (c*(a + b*x^2))/(c + d*x^2))^2) + ((b*c - 5*a*d)*(b*c - a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(8*a*c^2*(a - (c*(a + b*x^2))/(c + d*x^2))) + ((b*c - a*d)*(b*c + 3*a*d)*Sqrt[e]*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(8*a^(3/2)*c^(5/2))","A",4,4,26,0.1538,1,"{1960, 455, 385, 208}"
269,1,318,0,0.3115221,"\int \frac{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{x^7} \, dx","Int[Sqrt[(e*(a + b*x^2))/(c + d*x^2)]/x^7,x]","-\frac{\left(-11 a^2 d^2+2 a b c d+b^2 c^2\right) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{16 a^2 c^3 \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)}-\frac{\sqrt{e} \left(5 a^2 d^2+2 a b c d+b^2 c^2\right) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{16 a^{5/2} c^{7/2}}+\frac{e^2 (b c-a d)^3 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{6 a c^2 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^3}+\frac{(3 a d+b c) (b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 a c^3 \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)^2}","-\frac{\left(-11 a^2 d^2+2 a b c d+b^2 c^2\right) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{16 a^2 c^3 \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)}-\frac{\sqrt{e} \left(5 a^2 d^2+2 a b c d+b^2 c^2\right) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{16 a^{5/2} c^{7/2}}+\frac{e^2 (b c-a d)^3 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{6 a c^2 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^3}+\frac{(3 a d+b c) (b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 a c^3 \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)^2}",1,"((b*c - a*d)^2*(b*c + 3*a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(8*a*c^3*(a - (c*(a + b*x^2))/(c + d*x^2))^2) - ((b*c - a*d)*(b^2*c^2 + 2*a*b*c*d - 11*a^2*d^2)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(16*a^2*c^3*(a - (c*(a + b*x^2))/(c + d*x^2))) + ((b*c - a*d)^3*e^2*((e*(a + b*x^2))/(c + d*x^2))^(3/2))/(6*a*c^2*(a*e - (c*e*(a + b*x^2))/(c + d*x^2))^3) - ((b*c - a*d)*(b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*Sqrt[e]*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(16*a^(5/2)*c^(7/2))","A",5,5,26,0.1923,1,"{1960, 463, 455, 385, 208}"
270,1,357,0,0.5199544,"\int x^4 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} \, dx","Int[x^4*Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","\frac{x \left(-2 a^2 d^2-3 a b c d+8 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{15 b^2 d^2}-\frac{\sqrt{c} \left(-2 a^2 d^2-3 a b c d+8 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^2 d^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{c^{3/2} (4 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b d^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{x \left(c+d x^2\right) (4 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{15 b d^2}+\frac{x^3 \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 d}","\frac{x \left(-2 a^2 d^2-3 a b c d+8 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{15 b^2 d^2}-\frac{\sqrt{c} \left(-2 a^2 d^2-3 a b c d+8 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^2 d^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{c^{3/2} (4 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b d^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{x \left(c+d x^2\right) (4 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{15 b d^2}+\frac{x^3 \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 d}",1,"((8*b^2*c^2 - 3*a*b*c*d - 2*a^2*d^2)*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(15*b^2*d^2) - ((4*b*c - a*d)*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(15*b*d^2) + (x^3*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(5*d) - (Sqrt[c]*(8*b^2*c^2 - 3*a*b*c*d - 2*a^2*d^2)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*b^2*d^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) + (c^(3/2)*(4*b*c - a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*b*d^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",7,7,26,0.2692,1,"{6719, 478, 582, 531, 418, 492, 411}"
271,1,266,0,0.3378441,"\int x^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} \, dx","Int[x^2*Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","-\frac{c^{3/2} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 d^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{\sqrt{c} (2 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b d^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{x \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 d}-\frac{x (2 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 b d}","-\frac{c^{3/2} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 d^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{\sqrt{c} (2 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b d^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{x \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 d}-\frac{x (2 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 b d}",1,"-((2*b*c - a*d)*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(3*b*d) + (x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(3*d) + (Sqrt[c]*(2*b*c - a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*b*d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) - (c^(3/2)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",6,6,26,0.2308,1,"{6719, 478, 531, 418, 492, 411}"
272,1,194,0,0.122526,"\int \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} \, dx","Int[Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}+\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}","x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}+\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}",1,"x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)] - (Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) + (Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",5,5,22,0.2273,1,"{6719, 422, 418, 492, 411}"
273,1,239,0,0.3138694,"\int \frac{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{x^2} \, dx","Int[Sqrt[(e*(a + b*x^2))/(c + d*x^2)]/x^2,x]","\frac{d x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c}-\frac{\left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c x}+\frac{b \sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}","\frac{d x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c}-\frac{\left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c x}+\frac{b \sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}",1,"(d*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/c - (Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(c*x) - (Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(Sqrt[c]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) + (b*Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(a*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",7,7,26,0.2692,1,"{6719, 475, 21, 422, 418, 492, 411}"
274,1,321,0,0.4446541,"\int \frac{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{x^4} \, dx","Int[Sqrt[(e*(a + b*x^2))/(c + d*x^2)]/x^4,x]","\frac{d x (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 a c^2}-\frac{\left(c+d x^2\right) (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 a c^2 x}-\frac{\sqrt{d} (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a c^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 c x^3}-\frac{b \sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a \sqrt{c} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}","\frac{d x (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 a c^2}-\frac{\left(c+d x^2\right) (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 a c^2 x}-\frac{\sqrt{d} (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a c^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 c x^3}-\frac{b \sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a \sqrt{c} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}",1,"(d*(b*c - 2*a*d)*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(3*a*c^2) - (Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(3*c*x^3) - ((b*c - 2*a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(3*a*c^2*x) - (Sqrt[d]*(b*c - 2*a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a*c^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) - (b*Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a*Sqrt[c]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",7,7,26,0.2692,1,"{6719, 475, 583, 531, 418, 492, 411}"
275,1,424,0,0.6335797,"\int \frac{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{x^6} \, dx","Int[Sqrt[(e*(a + b*x^2))/(c + d*x^2)]/x^6,x]","-\frac{d x \left(-8 a^2 d^2+3 a b c d+2 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{15 a^2 c^3}+\frac{\left(c+d x^2\right) \left(-8 a^2 d^2+3 a b c d+2 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{15 a^2 c^3 x}+\frac{\sqrt{d} \left(-8 a^2 d^2+3 a b c d+2 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 a^2 c^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{b \sqrt{d} (b c-4 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 a^2 c^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\left(c+d x^2\right) (b c-4 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{15 a c^2 x^3}-\frac{\left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 c x^5}","-\frac{d x \left(-8 a^2 d^2+3 a b c d+2 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{15 a^2 c^3}+\frac{\left(c+d x^2\right) \left(-8 a^2 d^2+3 a b c d+2 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{15 a^2 c^3 x}+\frac{\sqrt{d} \left(-8 a^2 d^2+3 a b c d+2 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 a^2 c^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{b \sqrt{d} (b c-4 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 a^2 c^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\left(c+d x^2\right) (b c-4 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{15 a c^2 x^3}-\frac{\left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 c x^5}",1,"-(d*(2*b^2*c^2 + 3*a*b*c*d - 8*a^2*d^2)*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(15*a^2*c^3) - (Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(5*c*x^5) - ((b*c - 4*a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(15*a*c^2*x^3) + ((2*b^2*c^2 + 3*a*b*c*d - 8*a^2*d^2)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(15*a^2*c^3*x) + (Sqrt[d]*(2*b^2*c^2 + 3*a*b*c*d - 8*a^2*d^2)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*a^2*c^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) - (b*Sqrt[d]*(b*c - 4*a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*a^2*c^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",8,7,26,0.2692,1,"{6719, 475, 583, 531, 418, 492, 411}"
276,1,282,0,0.3832426,"\int x^5 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2} \, dx","Int[x^5*((e*(a + b*x^2))/(c + d*x^2))^(3/2),x]","-\frac{e^{3/2} (b c-a d) \left(-a^2 d^2-10 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{16 b^{3/2} d^{9/2}}+\frac{e \left(c+d x^2\right) \left(-5 a^2 d^2-50 a b c d+79 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{48 b d^4}+\frac{c^2 e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{d^4}+\frac{\left(c+d x^2\right)^3 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{5/2}}{6 b d^2 e}-\frac{e \left(c+d x^2\right)^2 (a d+11 b c) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{24 d^4}","-\frac{e^{3/2} (b c-a d) \left(-a^2 d^2-10 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{16 b^{3/2} d^{9/2}}+\frac{e \left(c+d x^2\right) \left(-5 a^2 d^2-50 a b c d+79 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{48 b d^4}+\frac{c^2 e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{d^4}+\frac{\left(c+d x^2\right)^3 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{5/2}}{6 b d^2 e}-\frac{e \left(c+d x^2\right)^2 (a d+11 b c) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{24 d^4}",1,"(c^2*(b*c - a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/d^4 + ((79*b^2*c^2 - 50*a*b*c*d - 5*a^2*d^2)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(48*b*d^4) - ((11*b*c + a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)^2)/(24*d^4) + (((e*(a + b*x^2))/(c + d*x^2))^(5/2)*(c + d*x^2)^3)/(6*b*d^2*e) - ((b*c - a*d)*(35*b^2*c^2 - 10*a*b*c*d - a^2*d^2)*e^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(16*b^(3/2)*d^(9/2))","A",6,6,26,0.2308,1,"{1960, 463, 455, 1157, 388, 208}"
277,1,199,0,0.2205375,"\int x^3 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2} \, dx","Int[x^3*((e*(a + b*x^2))/(c + d*x^2))^(3/2),x]","\frac{3 e^{3/2} (b c-a d) (5 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{8 \sqrt{b} d^{7/2}}+\frac{b e \left(c+d x^2\right)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 d^3}-\frac{e \left(c+d x^2\right) (9 b c-5 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 d^3}-\frac{c e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{d^3}","\frac{3 e^{3/2} (b c-a d) (5 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{8 \sqrt{b} d^{7/2}}+\frac{b e \left(c+d x^2\right)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 d^3}-\frac{e \left(c+d x^2\right) (9 b c-5 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 d^3}-\frac{c e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{d^3}",1,"-((c*(b*c - a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/d^3) - ((9*b*c - 5*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(8*d^3) + (b*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)^2)/(4*d^3) + (3*(b*c - a*d)*(5*b*c - a*d)*e^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(8*Sqrt[b]*d^(7/2))","A",5,5,26,0.1923,1,"{1960, 455, 1157, 388, 208}"
278,1,141,0,0.0899479,"\int x \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2} \, dx","Int[x*((e*(a + b*x^2))/(c + d*x^2))^(3/2),x]","-\frac{3 \sqrt{b} e^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{2 d^{5/2}}+\frac{3 e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 d^2}+\frac{\left(c+d x^2\right) \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{2 d}","-\frac{3 \sqrt{b} e^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{2 d^{5/2}}+\frac{3 e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 d^2}+\frac{\left(c+d x^2\right) \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{2 d}",1,"(3*(b*c - a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(2*d^2) + (((e*(a + b*x^2))/(c + d*x^2))^(3/2)*(c + d*x^2))/(2*d) - (3*Sqrt[b]*(b*c - a*d)*e^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(2*d^(5/2))","A",4,4,24,0.1667,1,"{1960, 288, 321, 208}"
279,1,151,0,0.1918904,"\int \frac{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{x} \, dx","Int[((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x,x]","-\frac{a^{3/2} e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{c^{3/2}}+\frac{b^{3/2} e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{d^{3/2}}-\frac{e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d}","-\frac{a^{3/2} e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{c^{3/2}}+\frac{b^{3/2} e^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{d^{3/2}}-\frac{e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d}",1,"-(((b*c - a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(c*d)) - (a^(3/2)*e^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/c^(3/2) + (b^(3/2)*e^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/d^(3/2)","A",5,4,26,0.1538,1,"{1960, 479, 522, 208}"
280,1,165,0,0.1037182,"\int \frac{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{x^3} \, dx","Int[((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^3,x]","-\frac{3 \sqrt{a} e^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{2 c^{5/2}}+\frac{3 e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 c^2}+\frac{(b c-a d) \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{2 c \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)}","-\frac{3 \sqrt{a} e^{3/2} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{2 c^{5/2}}+\frac{3 e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 c^2}+\frac{(b c-a d) \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{2 c \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right)}",1,"(3*(b*c - a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(2*c^2) + ((b*c - a*d)*((e*(a + b*x^2))/(c + d*x^2))^(3/2))/(2*c*(a - (c*(a + b*x^2))/(c + d*x^2))) - (3*Sqrt[a]*(b*c - a*d)*e^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(2*c^(5/2))","A",4,4,26,0.1538,1,"{1960, 288, 321, 208}"
281,1,256,0,0.2179226,"\int \frac{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{x^5} \, dx","Int[((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^5,x]","-\frac{a e^3 (b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 c^3 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^2}+\frac{e^2 (5 b c-9 a d) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 c^3 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)}-\frac{3 e^{3/2} (b c-5 a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{8 \sqrt{a} c^{7/2}}-\frac{d e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c^3}","-\frac{a e^3 (b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 c^3 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^2}+\frac{e^2 (5 b c-9 a d) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 c^3 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)}-\frac{3 e^{3/2} (b c-5 a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{8 \sqrt{a} c^{7/2}}-\frac{d e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c^3}",1,"-((d*(b*c - a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/c^3) - (a*(b*c - a*d)^2*e^3*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(4*c^3*(a*e - (c*e*(a + b*x^2))/(c + d*x^2))^2) + ((5*b*c - 9*a*d)*(b*c - a*d)*e^2*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(8*c^3*(a*e - (c*e*(a + b*x^2))/(c + d*x^2))) - (3*(b*c - 5*a*d)*(b*c - a*d)*e^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(8*Sqrt[a]*c^(7/2))","A",5,5,26,0.1923,1,"{1960, 455, 1157, 388, 208}"
282,1,366,0,0.3689816,"\int \frac{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{x^7} \, dx","Int[((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^7,x]","-\frac{e^2 \left(-79 a^2 d^2+50 a b c d+5 b^2 c^2\right) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{48 a c^4 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)}+\frac{e^{3/2} \left(-35 a^2 d^2+10 a b c d+b^2 c^2\right) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{16 a^{3/2} c^{9/2}}+\frac{d^2 e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c^4}+\frac{e^2 (b c-a d)^3 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{5/2}}{6 a c^2 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^3}+\frac{e^3 (11 a d+b c) (b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{24 c^4 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^2}","-\frac{e^2 \left(-79 a^2 d^2+50 a b c d+5 b^2 c^2\right) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{48 a c^4 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)}+\frac{e^{3/2} \left(-35 a^2 d^2+10 a b c d+b^2 c^2\right) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{16 a^{3/2} c^{9/2}}+\frac{d^2 e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c^4}+\frac{e^2 (b c-a d)^3 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{5/2}}{6 a c^2 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^3}+\frac{e^3 (11 a d+b c) (b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{24 c^4 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^2}",1,"(d^2*(b*c - a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/c^4 + ((b*c - a*d)^3*e^2*((e*(a + b*x^2))/(c + d*x^2))^(5/2))/(6*a*c^2*(a*e - (c*e*(a + b*x^2))/(c + d*x^2))^3) + ((b*c - a*d)^2*(b*c + 11*a*d)*e^3*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(24*c^4*(a*e - (c*e*(a + b*x^2))/(c + d*x^2))^2) - ((b*c - a*d)*(5*b^2*c^2 + 50*a*b*c*d - 79*a^2*d^2)*e^2*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(48*a*c^4*(a*e - (c*e*(a + b*x^2))/(c + d*x^2))) + ((b*c - a*d)*(b^2*c^2 + 10*a*b*c*d - 35*a^2*d^2)*e^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(16*a^(3/2)*c^(9/2))","A",6,6,26,0.2308,1,"{1960, 463, 455, 1157, 388, 208}"
283,1,391,0,0.6780752,"\int x^4 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2} \, dx","Int[x^4*((e*(a + b*x^2))/(c + d*x^2))^(3/2),x]","-\frac{\sqrt{c} e \left(a^2 d^2-16 a b c d+16 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 b d^{7/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e x \left(-\frac{a^2 d}{b}+16 a c-\frac{16 b c^2}{d}\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 d^2}+\frac{c^{3/2} e (8 b c-7 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 d^{7/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{6 b e x^3 \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 d^2}-\frac{e x \left(c+d x^2\right) (8 b c-7 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 d^3}-\frac{e x^3 \left(a+b x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{d}","-\frac{\sqrt{c} e \left(a^2 d^2-16 a b c d+16 b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 b d^{7/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e x \left(-\frac{a^2 d}{b}+16 a c-\frac{16 b c^2}{d}\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 d^2}+\frac{c^{3/2} e (8 b c-7 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 d^{7/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{6 b e x^3 \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 d^2}-\frac{e x \left(c+d x^2\right) (8 b c-7 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 d^3}-\frac{e x^3 \left(a+b x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{d}",1,"-((16*a*c - (16*b*c^2)/d - (a^2*d)/b)*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(5*d^2) - (e*x^3*(a + b*x^2)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/d - ((8*b*c - 7*a*d)*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(5*d^3) + (6*b*e*x^3*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(5*d^2) - (Sqrt[c]*(16*b^2*c^2 - 16*a*b*c*d + a^2*d^2)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(5*b*d^(7/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) + (c^(3/2)*(8*b*c - 7*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(5*d^(7/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",8,8,26,0.3077,1,"{6719, 467, 581, 582, 531, 418, 492, 411}"
284,1,310,0,0.4381665,"\int x^2 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2} \, dx","Int[x^2*((e*(a + b*x^2))/(c + d*x^2))^(3/2),x]","\frac{4 b e x \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 d^2}-\frac{e x (8 b c-7 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 d^2}-\frac{\sqrt{c} e (4 b c-3 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 d^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{\sqrt{c} e (8 b c-7 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 d^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e x \left(a+b x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{d}","\frac{4 b e x \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 d^2}-\frac{e x (8 b c-7 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 d^2}-\frac{\sqrt{c} e (4 b c-3 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 d^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{\sqrt{c} e (8 b c-7 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 d^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e x \left(a+b x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{d}",1,"-((8*b*c - 7*a*d)*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(3*d^2) - (e*x*(a + b*x^2)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/d + (4*b*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(3*d^2) + (Sqrt[c]*(8*b*c - 7*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*d^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) - (Sqrt[c]*(4*b*c - 3*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*d^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",7,7,26,0.2692,1,"{6719, 467, 528, 531, 418, 492, 411}"
285,1,262,0,0.2021388,"\int \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2} \, dx","Int[((e*(a + b*x^2))/(c + d*x^2))^(3/2),x]","\frac{b \sqrt{c} e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{d^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e (2 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} d^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e x (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d}+\frac{e x (2 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d}","\frac{b \sqrt{c} e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{d^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e (2 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} d^{3/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e x (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d}+\frac{e x (2 b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d}",1,"-(((b*c - a*d)*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(c*d)) + ((2*b*c - a*d)*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(c*d) - ((2*b*c - a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(Sqrt[c]*d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) + (b*Sqrt[c]*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",6,6,22,0.2727,1,"{6719, 413, 531, 418, 492, 411}"
286,1,307,0,0.4497279,"\int \frac{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{x^2} \, dx","Int[((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^2,x]","\frac{e \left(c+d x^2\right) (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c^2 d x}-\frac{e x (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c^2}+\frac{e (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{c^{3/2} \sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d x}+\frac{b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} \sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}","\frac{e \left(c+d x^2\right) (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c^2 d x}-\frac{e x (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c^2}+\frac{e (b c-2 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{c^{3/2} \sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d x}+\frac{b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} \sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}",1,"-(((b*c - a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(c*d*x)) - ((b*c - 2*a*d)*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/c^2 + ((b*c - 2*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(c^2*d*x) + ((b*c - 2*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(c^(3/2)*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) + (b*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(Sqrt[c]*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",7,7,26,0.2692,1,"{6719, 468, 583, 531, 418, 492, 411}"
287,1,383,0,0.6317838,"\int \frac{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{x^4} \, dx","Int[((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^4,x]","-\frac{e \left(c+d x^2\right) (7 b c-8 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 c^3 x}+\frac{e \left(c+d x^2\right) (3 b c-4 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 c^2 d x^3}+\frac{d e x (7 b c-8 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 c^3}+\frac{b e (3 b c-4 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a c^{3/2} \sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{d} e (7 b c-8 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 c^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d x^3}","-\frac{e \left(c+d x^2\right) (7 b c-8 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 c^3 x}+\frac{e \left(c+d x^2\right) (3 b c-4 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 c^2 d x^3}+\frac{d e x (7 b c-8 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{3 c^3}+\frac{b e (3 b c-4 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a c^{3/2} \sqrt{d} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{d} e (7 b c-8 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 c^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d x^3}",1,"-(((b*c - a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(c*d*x^3)) + (d*(7*b*c - 8*a*d)*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(3*c^3) + ((3*b*c - 4*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(3*c^2*d*x^3) - ((7*b*c - 8*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(3*c^3*x) - (Sqrt[d]*(7*b*c - 8*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*c^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) + (b*(3*b*c - 4*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a*c^(3/2)*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",8,7,26,0.2692,1,"{6719, 468, 583, 531, 418, 492, 411}"
288,1,480,0,0.8085825,"\int \frac{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}}{x^6} \, dx","Int[((e*(a + b*x^2))/(c + d*x^2))^(3/2)/x^6,x]","-\frac{e \left(c+d x^2\right) \left(16 a^2 d^2-16 a b c d+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 a c^4 x}+\frac{d e x \left(16 a^2 d^2-16 a b c d+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 a c^4}-\frac{\sqrt{d} e \left(16 a^2 d^2-16 a b c d+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 a c^{7/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e \left(c+d x^2\right) (7 b c-8 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 c^3 x^3}+\frac{e \left(c+d x^2\right) (5 b c-6 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 c^2 d x^5}-\frac{b \sqrt{d} e (7 b c-8 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 a c^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d x^5}","-\frac{e \left(c+d x^2\right) \left(16 a^2 d^2-16 a b c d+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 a c^4 x}+\frac{d e x \left(16 a^2 d^2-16 a b c d+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 a c^4}-\frac{\sqrt{d} e \left(16 a^2 d^2-16 a b c d+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 a c^{7/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e \left(c+d x^2\right) (7 b c-8 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 c^3 x^3}+\frac{e \left(c+d x^2\right) (5 b c-6 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{5 c^2 d x^5}-\frac{b \sqrt{d} e (7 b c-8 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 a c^{5/2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{e (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{c d x^5}",1,"-(((b*c - a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(c*d*x^5)) + (d*(b^2*c^2 - 16*a*b*c*d + 16*a^2*d^2)*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(5*a*c^4) + ((5*b*c - 6*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(5*c^2*d*x^5) - ((7*b*c - 8*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(5*c^3*x^3) - ((b^2*c^2 - 16*a*b*c*d + 16*a^2*d^2)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(5*a*c^4*x) - (Sqrt[d]*(b^2*c^2 - 16*a*b*c*d + 16*a^2*d^2)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(5*a*c^(7/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]) - (b*Sqrt[d]*(7*b*c - 8*a*d)*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(5*a*c^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))])","A",9,7,26,0.2692,1,"{6719, 468, 583, 531, 418, 492, 411}"
289,1,51,0,0.0233902,"\int x \sqrt{\frac{1-x^2}{1+x^2}} \, dx","Int[x*Sqrt[(1 - x^2)/(1 + x^2)],x]","\frac{1}{2} \sqrt{\frac{1-x^2}{x^2+1}} \left(x^2+1\right)-\tan ^{-1}\left(\sqrt{\frac{1-x^2}{x^2+1}}\right)","\frac{1}{2} \sqrt{\frac{1-x^2}{x^2+1}} \left(x^2+1\right)-\tan ^{-1}\left(\sqrt{\frac{1-x^2}{x^2+1}}\right)",1,"(Sqrt[(1 - x^2)/(1 + x^2)]*(1 + x^2))/2 - ArcTan[Sqrt[(1 - x^2)/(1 + x^2)]]","A",3,3,21,0.1429,1,"{1960, 288, 204}"
290,1,72,0,0.0321963,"\int x \sqrt{\frac{5-7 x^2}{7+5 x^2}} \, dx","Int[x*Sqrt[(5 - 7*x^2)/(7 + 5*x^2)],x]","\frac{1}{10} \sqrt{\frac{5-7 x^2}{5 x^2+7}} \left(5 x^2+7\right)-\frac{37 \tan ^{-1}\left(\sqrt{\frac{5}{7}} \sqrt{\frac{5-7 x^2}{5 x^2+7}}\right)}{5 \sqrt{35}}","\frac{1}{10} \sqrt{\frac{5-7 x^2}{5 x^2+7}} \left(5 x^2+7\right)-\frac{37 \tan ^{-1}\left(\sqrt{\frac{5}{7}} \sqrt{\frac{5-7 x^2}{5 x^2+7}}\right)}{5 \sqrt{35}}",1,"(Sqrt[(5 - 7*x^2)/(7 + 5*x^2)]*(7 + 5*x^2))/10 - (37*ArcTan[Sqrt[5/7]*Sqrt[(5 - 7*x^2)/(7 + 5*x^2)]])/(5*Sqrt[35])","A",3,3,23,0.1304,1,"{1960, 288, 204}"
291,1,53,0,0.0291266,"\int x^2 \sqrt{\frac{1-x^3}{1+x^3}} \, dx","Int[x^2*Sqrt[(1 - x^3)/(1 + x^3)],x]","\frac{1}{3} \sqrt{\frac{1-x^3}{x^3+1}} \left(x^3+1\right)-\frac{2}{3} \tan ^{-1}\left(\sqrt{\frac{1-x^3}{x^3+1}}\right)","\frac{1}{3} \sqrt{\frac{1-x^3}{x^3+1}} \left(x^3+1\right)-\frac{2}{3} \tan ^{-1}\left(\sqrt{\frac{1-x^3}{x^3+1}}\right)",1,"(Sqrt[(1 - x^3)/(1 + x^3)]*(1 + x^3))/3 - (2*ArcTan[Sqrt[(1 - x^3)/(1 + x^3)]])/3","A",3,3,23,0.1304,1,"{1960, 288, 204}"
292,1,113,0,0.0635612,"\int x^8 \sqrt{\frac{1-x^3}{1+x^3}} \, dx","Int[x^8*Sqrt[(1 - x^3)/(1 + x^3)],x]","-\frac{1}{9} \left(\frac{1-x^3}{x^3+1}\right)^{3/2} \left(x^3+1\right)^3-\frac{1}{6} \sqrt{\frac{1-x^3}{x^3+1}} \left(x^3+1\right)^2+\frac{1}{2} \sqrt{\frac{1-x^3}{x^3+1}} \left(x^3+1\right)-\frac{1}{3} \tan ^{-1}\left(\sqrt{\frac{1-x^3}{x^3+1}}\right)","-\frac{1}{9} \left(\frac{1-x^3}{x^3+1}\right)^{3/2} \left(x^3+1\right)^3-\frac{1}{6} \sqrt{\frac{1-x^3}{x^3+1}} \left(x^3+1\right)^2+\frac{1}{2} \sqrt{\frac{1-x^3}{x^3+1}} \left(x^3+1\right)-\frac{1}{3} \tan ^{-1}\left(\sqrt{\frac{1-x^3}{x^3+1}}\right)",1,"(Sqrt[(1 - x^3)/(1 + x^3)]*(1 + x^3))/2 - (Sqrt[(1 - x^3)/(1 + x^3)]*(1 + x^3)^2)/6 - (((1 - x^3)/(1 + x^3))^(3/2)*(1 + x^3)^3)/9 - ArcTan[Sqrt[(1 - x^3)/(1 + x^3)]]/3","A",5,5,23,0.2174,1,"{1960, 463, 455, 385, 204}"
293,1,106,0,0.0557393,"\int x^9 \sqrt{\frac{5-7 x^5}{7+5 x^5}} \, dx","Int[x^9*Sqrt[(5 - 7*x^5)/(7 + 5*x^5)],x]","\frac{1}{250} \sqrt{\frac{5-7 x^5}{5 x^5+7}} \left(5 x^5+7\right)^2-\frac{27}{350} \sqrt{\frac{5-7 x^5}{5 x^5+7}} \left(5 x^5+7\right)+\frac{2257 \tan ^{-1}\left(\sqrt{\frac{5}{7}} \sqrt{\frac{5-7 x^5}{5 x^5+7}}\right)}{875 \sqrt{35}}","\frac{1}{250} \sqrt{\frac{5-7 x^5}{5 x^5+7}} \left(5 x^5+7\right)^2-\frac{27}{350} \sqrt{\frac{5-7 x^5}{5 x^5+7}} \left(5 x^5+7\right)+\frac{2257 \tan ^{-1}\left(\sqrt{\frac{5}{7}} \sqrt{\frac{5-7 x^5}{5 x^5+7}}\right)}{875 \sqrt{35}}",1,"(-27*Sqrt[(5 - 7*x^5)/(7 + 5*x^5)]*(7 + 5*x^5))/350 + (Sqrt[(5 - 7*x^5)/(7 + 5*x^5)]*(7 + 5*x^5)^2)/250 + (2257*ArcTan[Sqrt[5/7]*Sqrt[(5 - 7*x^5)/(7 + 5*x^5)]])/(875*Sqrt[35])","A",4,4,25,0.1600,1,"{1960, 455, 385, 204}"
294,1,52,0,0.0989364,"\int \frac{\sqrt{\frac{x^2}{-1+x^2}}}{1+x^2} \, dx","Int[Sqrt[x^2/(-1 + x^2)]/(1 + x^2),x]","\frac{\sqrt{-\frac{x^2}{1-x^2}} \sqrt{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x^2-1}}{\sqrt{2}}\right)}{\sqrt{2} x}","\frac{\sqrt{-\frac{x^2}{1-x^2}} \sqrt{x^2-1} \tan ^{-1}\left(\frac{\sqrt{x^2-1}}{\sqrt{2}}\right)}{\sqrt{2} x}",1,"(Sqrt[-(x^2/(1 - x^2))]*Sqrt[-1 + x^2]*ArcTan[Sqrt[-1 + x^2]/Sqrt[2]])/(Sqrt[2]*x)","A",4,4,23,0.1739,1,"{6719, 444, 63, 203}"
295,1,68,0,0.1910464,"\int \frac{\sqrt{\frac{x^2}{-1+a+(1+a) x^2}}}{1+x^2} \, dx","Int[Sqrt[x^2/(-1 + a + (1 + a)*x^2)]/(1 + x^2),x]","\frac{\sqrt{-\frac{x^2}{-(a+1) x^2-a+1}} \sqrt{(a+1) x^2+a-1} \tan ^{-1}\left(\frac{\sqrt{(a+1) x^2+a-1}}{\sqrt{2}}\right)}{\sqrt{2} x}","\frac{\sqrt{-\frac{x^2}{-(a+1) x^2-a+1}} \sqrt{(a+1) x^2+a-1} \tan ^{-1}\left(\frac{\sqrt{(a+1) x^2+a-1}}{\sqrt{2}}\right)}{\sqrt{2} x}",1,"(Sqrt[-(x^2/(1 - a - (1 + a)*x^2))]*Sqrt[-1 + a + (1 + a)*x^2]*ArcTan[Sqrt[-1 + a + (1 + a)*x^2]/Sqrt[2]])/(Sqrt[2]*x)","A",4,4,28,0.1429,1,"{6719, 444, 63, 205}"
296,1,281,0,0.2902424,"\int \frac{x^5}{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}} \, dx","Int[x^5/Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","\frac{\left(c+d x^2\right) \left(5 a^2 d^2+2 a b c d+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{16 b^3 d^2 e}+\frac{(b c-a d) \left(5 a^2 d^2+2 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{16 b^{7/2} d^{5/2} \sqrt{e}}-\frac{\left(c+d x^2\right)^2 (5 a d+3 b c) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{24 b^2 d^2 e}-\frac{\left(c+d x^2\right)^3 \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{6 b d e (b c-a d)}","\frac{\left(c+d x^2\right) \left(5 a^2 d^2+2 a b c d+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{16 b^3 d^2 e}+\frac{(b c-a d) \left(5 a^2 d^2+2 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{16 b^{7/2} d^{5/2} \sqrt{e}}-\frac{\left(c+d x^2\right)^2 (5 a d+3 b c) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{24 b^2 d^2 e}-\frac{\left(c+d x^2\right)^3 \left(a-\frac{c \left(a+b x^2\right)}{c+d x^2}\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{6 b d e (b c-a d)}",1,"((b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(16*b^3*d^2*e) - ((3*b*c + 5*a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)^2)/(24*b^2*d^2*e) - (Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)^3*(a - (c*(a + b*x^2))/(c + d*x^2)))/(6*b*d*(b*c - a*d)*e) + ((b*c - a*d)*(b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(16*b^(7/2)*d^(5/2)*Sqrt[e])","A",5,5,26,0.1923,1,"{1960, 413, 385, 199, 208}"
297,1,169,0,0.1346348,"\int \frac{x^3}{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}} \, dx","Int[x^3/Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","-\frac{(b c-a d) (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{8 b^{5/2} d^{3/2} \sqrt{e}}-\frac{\left(c+d x^2\right) (3 a d+b c) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 b^2 d e}+\frac{\left(c+d x^2\right)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 b d e}","-\frac{(b c-a d) (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{8 b^{5/2} d^{3/2} \sqrt{e}}-\frac{\left(c+d x^2\right) (3 a d+b c) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 b^2 d e}+\frac{\left(c+d x^2\right)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 b d e}",1,"-((b*c + 3*a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(8*b^2*d*e) + (Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)^2)/(4*b*d*e) - ((b*c - a*d)*(b*c + 3*a*d)*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(8*b^(5/2)*d^(3/2)*Sqrt[e])","A",4,4,26,0.1538,1,"{1960, 385, 199, 208}"
298,1,106,0,0.0682991,"\int \frac{x}{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}} \, dx","Int[x/Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{2 b^{3/2} \sqrt{d} \sqrt{e}}+\frac{\left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 b e}","\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{2 b^{3/2} \sqrt{d} \sqrt{e}}+\frac{\left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 b e}",1,"(Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(2*b*e) + ((b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(2*b^(3/2)*Sqrt[d]*Sqrt[e])","A",3,3,24,0.1250,1,"{1960, 199, 208}"
299,1,112,0,0.1058199,"\int \frac{1}{x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}} \, dx","Int[1/(x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]),x]","\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{\sqrt{b} \sqrt{e}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{\sqrt{a} \sqrt{e}}","\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{\sqrt{b} \sqrt{e}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{\sqrt{a} \sqrt{e}}",1,"-((Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(Sqrt[a]*Sqrt[e])) + (Sqrt[d]*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(Sqrt[b]*Sqrt[e])","A",4,3,26,0.1154,1,"{1960, 391, 208}"
300,1,130,0,0.08368,"\int \frac{1}{x^3 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}} \, dx","Int[1/(x^3*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]),x]","\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{2 a^{3/2} \sqrt{c} \sqrt{e}}+\frac{(b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 a \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)}","\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{2 a^{3/2} \sqrt{c} \sqrt{e}}+\frac{(b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{2 a \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)}",1,"((b*c - a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(2*a*(a*e - (c*e*(a + b*x^2))/(c + d*x^2))) + ((b*c - a*d)*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(2*a^(3/2)*Sqrt[c]*Sqrt[e])","A",3,3,26,0.1154,1,"{1960, 199, 208}"
301,1,218,0,0.1354213,"\int \frac{1}{x^5 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}} \, dx","Int[1/(x^5*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]),x]","-\frac{(a d+3 b c) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{8 a^{5/2} c^{3/2} \sqrt{e}}-\frac{(a d+3 b c) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 a^2 c \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)}-\frac{e (b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 a c \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^2}","-\frac{(a d+3 b c) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{8 a^{5/2} c^{3/2} \sqrt{e}}-\frac{(a d+3 b c) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 a^2 c \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)}-\frac{e (b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 a c \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^2}",1,"-((b*c - a*d)^2*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(4*a*c*(a*e - (c*e*(a + b*x^2))/(c + d*x^2))^2) - ((b*c - a*d)*(3*b*c + a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(8*a^2*c*(a*e - (c*e*(a + b*x^2))/(c + d*x^2))) - ((b*c - a*d)*(3*b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(8*a^(5/2)*c^(3/2)*Sqrt[e])","A",4,4,26,0.1538,1,"{1960, 385, 199, 208}"
302,1,403,0,0.522041,"\int \frac{x^4}{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}} \, dx","Int[x^4/Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","-\frac{x \left(a+b x^2\right) \left(-8 a^2 d^2+3 a b c d+2 b^2 c^2\right)}{15 b^3 d \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{\sqrt{c} \left(a+b x^2\right) \left(-8 a^2 d^2+3 a b c d+2 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^3 d^{3/2} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{c^{3/2} \left(a+b x^2\right) (b c-4 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^2 d^{3/2} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{x \left(a+b x^2\right) (b c-4 a d)}{15 b^2 d \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{x^3 \left(a+b x^2\right)}{5 b \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","-\frac{x \left(a+b x^2\right) \left(-8 a^2 d^2+3 a b c d+2 b^2 c^2\right)}{15 b^3 d \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{\sqrt{c} \left(a+b x^2\right) \left(-8 a^2 d^2+3 a b c d+2 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^3 d^{3/2} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{c^{3/2} \left(a+b x^2\right) (b c-4 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^2 d^{3/2} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{x \left(a+b x^2\right) (b c-4 a d)}{15 b^2 d \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{x^3 \left(a+b x^2\right)}{5 b \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"((b*c - 4*a*d)*x*(a + b*x^2))/(15*b^2*d*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + (x^3*(a + b*x^2))/(5*b*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) - ((2*b^2*c^2 + 3*a*b*c*d - 8*a^2*d^2)*x*(a + b*x^2))/(15*b^3*d*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) + (Sqrt[c]*(2*b^2*c^2 + 3*a*b*c*d - 8*a^2*d^2)*(a + b*x^2)*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*b^3*d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) - (c^(3/2)*(b*c - 4*a*d)*(a + b*x^2)*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*b^2*d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))","A",7,7,26,0.2692,1,"{6719, 478, 582, 531, 418, 492, 411}"
303,1,312,0,0.3381064,"\int \frac{x^2}{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}} \, dx","Int[x^2/Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","\frac{x \left(a+b x^2\right) (b c-2 a d)}{3 b^2 \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \left(a+b x^2\right) (b c-2 a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b^2 \sqrt{d} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{c^{3/2} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b \sqrt{d} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{x \left(a+b x^2\right)}{3 b \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","\frac{x \left(a+b x^2\right) (b c-2 a d)}{3 b^2 \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \left(a+b x^2\right) (b c-2 a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b^2 \sqrt{d} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{c^{3/2} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b \sqrt{d} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{x \left(a+b x^2\right)}{3 b \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"(x*(a + b*x^2))/(3*b*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + ((b*c - 2*a*d)*x*(a + b*x^2))/(3*b^2*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) - (Sqrt[c]*(b*c - 2*a*d)*(a + b*x^2)*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*b^2*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) - (c^(3/2)*(a + b*x^2)*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*b*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))","A",6,6,26,0.2308,1,"{6719, 478, 531, 418, 492, 411}"
304,1,252,0,0.1301017,"\int \frac{1}{\sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}} \, dx","Int[1/Sqrt[(e*(a + b*x^2))/(c + d*x^2)],x]","\frac{c^{3/2} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{d} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{d x \left(a+b x^2\right)}{b \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{b \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","\frac{c^{3/2} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{d} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{d x \left(a+b x^2\right)}{b \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{b \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"(d*x*(a + b*x^2))/(b*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) - (Sqrt[c]*Sqrt[d]*(a + b*x^2)*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(b*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) + (c^(3/2)*(a + b*x^2)*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(a*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))","A",5,5,22,0.2273,1,"{6719, 422, 418, 492, 411}"
305,1,289,0,0.311714,"\int \frac{1}{x^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}} \, dx","Int[1/(x^2*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]),x]","-\frac{a+b x^2}{a x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{d x \left(a+b x^2\right)}{a \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","-\frac{a+b x^2}{a x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{d x \left(a+b x^2\right)}{a \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"-((a + b*x^2)/(a*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])) + (d*x*(a + b*x^2))/(a*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) - (Sqrt[c]*Sqrt[d]*(a + b*x^2)*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(a*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) + (Sqrt[c]*Sqrt[d]*(a + b*x^2)*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(a*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))","A",7,7,26,0.2692,1,"{6719, 475, 21, 422, 418, 492, 411}"
306,1,372,0,0.453529,"\int \frac{1}{x^4 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}} \, dx","Int[1/(x^4*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]),x]","\frac{\left(a+b x^2\right) (2 b c-a d)}{3 a^2 c x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{d x \left(a+b x^2\right) (2 b c-a d)}{3 a^2 c \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{b \sqrt{c} \sqrt{d} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^2 \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{\sqrt{d} \left(a+b x^2\right) (2 b c-a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^2 \sqrt{c} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{a+b x^2}{3 a x^3 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","\frac{\left(a+b x^2\right) (2 b c-a d)}{3 a^2 c x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{d x \left(a+b x^2\right) (2 b c-a d)}{3 a^2 c \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{b \sqrt{c} \sqrt{d} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^2 \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{\sqrt{d} \left(a+b x^2\right) (2 b c-a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^2 \sqrt{c} \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{a+b x^2}{3 a x^3 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"-(a + b*x^2)/(3*a*x^3*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + ((2*b*c - a*d)*(a + b*x^2))/(3*a^2*c*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) - (d*(2*b*c - a*d)*x*(a + b*x^2))/(3*a^2*c*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) + (Sqrt[d]*(2*b*c - a*d)*(a + b*x^2)*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a^2*Sqrt[c]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) - (b*Sqrt[c]*Sqrt[d]*(a + b*x^2)*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a^2*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))","A",7,7,26,0.2692,1,"{6719, 475, 583, 531, 418, 492, 411}"
307,1,348,0,0.3785983,"\int \frac{x^5}{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}} \, dx","Int[x^5/((e*(a + b*x^2))/(c + d*x^2))^(3/2),x]","-\frac{a^2 \left(c+d x^2\right)^3}{b e (b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{(b c-a d) \left(5 a d (2 b c-7 a d)+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{16 b^{9/2} d^{3/2} e^{3/2}}+\frac{\left(c+d x^2\right)^3 \left(\frac{c^2}{d}-\frac{a (2 b c-7 a d)}{b^2}\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{6 e^2 (b c-a d)^2}-\frac{\left(c+d x^2\right)^2 \left(\frac{5 a (2 b c-7 a d)}{b^2}+\frac{c^2}{d}\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{24 b e^2 (b c-a d)}-\frac{\left(c+d x^2\right) \left(5 a d (2 b c-7 a d)+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{16 b^4 d e^2}","\frac{\left(c+d x^2\right)^3 \left(7 a^2 d^2-2 a b c d+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{6 b^2 d e^2 (b c-a d)^2}-\frac{a^2 \left(c+d x^2\right)^3}{b e (b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{(b c-a d) \left(5 a d (2 b c-7 a d)+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{16 b^{9/2} d^{3/2} e^{3/2}}-\frac{\left(c+d x^2\right)^2 \left(5 a d (2 b c-7 a d)+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{24 b^3 d e^2 (b c-a d)}-\frac{\left(c+d x^2\right) \left(5 a d (2 b c-7 a d)+b^2 c^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{16 b^4 d e^2}",1,"-((b^2*c^2 + 5*a*d*(2*b*c - 7*a*d))*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(16*b^4*d*e^2) - ((c^2/d + (5*a*(2*b*c - 7*a*d))/b^2)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)^2)/(24*b*(b*c - a*d)*e^2) - (a^2*(c + d*x^2)^3)/(b*(b*c - a*d)^2*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + ((c^2/d - (a*(2*b*c - 7*a*d))/b^2)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)^3)/(6*(b*c - a*d)^2*e^2) - ((b*c - a*d)*(b^2*c^2 + 5*a*d*(2*b*c - 7*a*d))*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(16*b^(9/2)*d^(3/2)*e^(3/2))","A",6,5,26,0.1923,1,"{1960, 462, 385, 199, 208}"
308,1,202,0,0.2386686,"\int \frac{x^3}{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}} \, dx","Int[x^3/((e*(a + b*x^2))/(c + d*x^2))^(3/2),x]","\frac{\left(c+d x^2\right)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 b^2 e^2}+\frac{\left(c+d x^2\right) (3 b c-7 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 b^3 e^2}+\frac{3 (b c-5 a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{8 b^{7/2} \sqrt{d} e^{3/2}}+\frac{a (b c-a d)}{b^3 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","\frac{\left(c+d x^2\right)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 b^2 e^2}+\frac{\left(c+d x^2\right) (3 b c-7 a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 b^3 e^2}+\frac{3 (b c-5 a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{8 b^{7/2} \sqrt{d} e^{3/2}}+\frac{a (b c-a d)}{b^3 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"(a*(b*c - a*d))/(b^3*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + ((3*b*c - 7*a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))/(8*b^3*e^2) + (Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)^2)/(4*b^2*e^2) + (3*(b*c - 5*a*d)*(b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(8*b^(7/2)*Sqrt[d]*e^(3/2))","A",5,4,26,0.1538,1,"{1960, 456, 453, 208}"
309,1,146,0,0.0983798,"\int \frac{x}{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}} \, dx","Int[x/((e*(a + b*x^2))/(c + d*x^2))^(3/2),x]","\frac{3 \sqrt{d} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{2 b^{5/2} e^{3/2}}-\frac{3 (b c-a d)}{2 b^2 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{c+d x^2}{2 b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","\frac{3 \sqrt{d} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{2 b^{5/2} e^{3/2}}-\frac{3 (b c-a d)}{2 b^2 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{c+d x^2}{2 b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"(-3*(b*c - a*d))/(2*b^2*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + (c + d*x^2)/(2*b*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + (3*Sqrt[d]*(b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(2*b^(5/2)*e^(3/2))","A",4,4,24,0.1667,1,"{1960, 290, 325, 208}"
310,1,152,0,0.1961131,"\int \frac{1}{x \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}} \, dx","Int[1/(x*((e*(a + b*x^2))/(c + d*x^2))^(3/2)),x]","-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{a^{3/2} e^{3/2}}+\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{b^{3/2} e^{3/2}}+\frac{b c-a d}{a b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{a^{3/2} e^{3/2}}+\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{b} \sqrt{e}}\right)}{b^{3/2} e^{3/2}}+\frac{b c-a d}{a b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"(b*c - a*d)/(a*b*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) - (c^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(a^(3/2)*e^(3/2)) + (d^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[b]*Sqrt[e])])/(b^(3/2)*e^(3/2))","A",5,4,26,0.1538,1,"{1960, 480, 522, 208}"
311,1,170,0,0.1114818,"\int \frac{1}{x^3 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}} \, dx","Int[1/(x^3*((e*(a + b*x^2))/(c + d*x^2))^(3/2)),x]","\frac{3 \sqrt{c} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{2 a^{5/2} e^{3/2}}-\frac{3 (b c-a d)}{2 a^2 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{b c-a d}{2 a \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)}","\frac{3 \sqrt{c} (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{2 a^{5/2} e^{3/2}}-\frac{3 (b c-a d)}{2 a^2 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{b c-a d}{2 a \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}} \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)}",1,"(-3*(b*c - a*d))/(2*a^2*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + (b*c - a*d)/(2*a*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(a*e - (c*e*(a + b*x^2))/(c + d*x^2))) + (3*Sqrt[c]*(b*c - a*d)*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(2*a^(5/2)*e^(3/2))","A",4,4,26,0.1538,1,"{1960, 290, 325, 208}"
312,1,255,0,0.2282799,"\int \frac{1}{x^5 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}} \, dx","Int[1/(x^5*((e*(a + b*x^2))/(c + d*x^2))^(3/2)),x]","-\frac{(7 b c-3 a d) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 a^3 \left(a e^2-\frac{c e^2 \left(a+b x^2\right)}{c+d x^2}\right)}-\frac{3 (5 b c-a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{8 a^{7/2} \sqrt{c} e^{3/2}}-\frac{(b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 a^2 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^2}+\frac{b (b c-a d)}{a^3 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","-\frac{(7 b c-3 a d) (b c-a d) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{8 a^3 \left(a e^2-\frac{c e^2 \left(a+b x^2\right)}{c+d x^2}\right)}-\frac{3 (5 b c-a d) (b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{\sqrt{a} \sqrt{e}}\right)}{8 a^{7/2} \sqrt{c} e^{3/2}}-\frac{(b c-a d)^2 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}{4 a^2 \left(a e-\frac{c e \left(a+b x^2\right)}{c+d x^2}\right)^2}+\frac{b (b c-a d)}{a^3 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"(b*(b*c - a*d))/(a^3*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) - ((b*c - a*d)^2*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(4*a^2*(a*e - (c*e*(a + b*x^2))/(c + d*x^2))^2) - ((7*b*c - 3*a*d)*(b*c - a*d)*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(8*a^3*(a*e^2 - (c*e^2*(a + b*x^2))/(c + d*x^2))) - (3*(b*c - a*d)*(5*b*c - a*d)*ArcTanh[(Sqrt[c]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)])/(Sqrt[a]*Sqrt[e])])/(8*a^(7/2)*Sqrt[c]*e^(3/2))","A",5,4,26,0.1538,1,"{1960, 456, 453, 208}"
313,1,453,0,0.6751779,"\int \frac{x^4}{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}} \, dx","Int[x^4/((e*(a + b*x^2))/(c + d*x^2))^(3/2),x]","\frac{x \left(a+b x^2\right) \left(16 a^2 d^2-16 a b c d+b^2 c^2\right)}{5 b^4 e \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \left(a+b x^2\right) \left(16 a^2 d^2-16 a b c d+b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 b^4 \sqrt{d} e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{c^{3/2} \left(a+b x^2\right) (7 b c-8 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 b^3 \sqrt{d} e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{6 d x^3 \left(a+b x^2\right)}{5 b^2 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{x \left(a+b x^2\right) (7 b c-8 a d)}{5 b^3 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{x^3 \left(c+d x^2\right)}{b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","\frac{x \left(a+b x^2\right) \left(16 a^2 d^2-16 a b c d+b^2 c^2\right)}{5 b^4 e \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \left(a+b x^2\right) \left(16 a^2 d^2-16 a b c d+b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 b^4 \sqrt{d} e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{c^{3/2} \left(a+b x^2\right) (7 b c-8 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{5 b^3 \sqrt{d} e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{6 d x^3 \left(a+b x^2\right)}{5 b^2 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{x \left(a+b x^2\right) (7 b c-8 a d)}{5 b^3 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{x^3 \left(c+d x^2\right)}{b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"((7*b*c - 8*a*d)*x*(a + b*x^2))/(5*b^3*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + (6*d*x^3*(a + b*x^2))/(5*b^2*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + ((b^2*c^2 - 16*a*b*c*d + 16*a^2*d^2)*x*(a + b*x^2))/(5*b^4*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) - (x^3*(c + d*x^2))/(b*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) - (Sqrt[c]*(b^2*c^2 - 16*a*b*c*d + 16*a^2*d^2)*(a + b*x^2)*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(5*b^4*Sqrt[d]*e*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) - (c^(3/2)*(7*b*c - 8*a*d)*(a + b*x^2)*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(5*b^3*Sqrt[d]*e*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))","A",8,8,26,0.3077,1,"{6719, 467, 581, 582, 531, 418, 492, 411}"
314,1,378,0,0.4419611,"\int \frac{x^2}{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}} \, dx","Int[x^2/((e*(a + b*x^2))/(c + d*x^2))^(3/2),x]","\frac{c^{3/2} \left(a+b x^2\right) (3 b c-4 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a b^2 \sqrt{d} e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{4 d x \left(a+b x^2\right)}{3 b^2 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{d x \left(a+b x^2\right) (7 b c-8 a d)}{3 b^3 e \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) (7 b c-8 a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b^3 e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{x \left(c+d x^2\right)}{b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","\frac{c^{3/2} \left(a+b x^2\right) (3 b c-4 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a b^2 \sqrt{d} e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{4 d x \left(a+b x^2\right)}{3 b^2 e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{d x \left(a+b x^2\right) (7 b c-8 a d)}{3 b^3 e \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) (7 b c-8 a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b^3 e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{x \left(c+d x^2\right)}{b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"(4*d*x*(a + b*x^2))/(3*b^2*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + (d*(7*b*c - 8*a*d)*x*(a + b*x^2))/(3*b^3*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) - (x*(c + d*x^2))/(b*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) - (Sqrt[c]*Sqrt[d]*(7*b*c - 8*a*d)*(a + b*x^2)*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*b^3*e*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) + (c^(3/2)*(3*b*c - 4*a*d)*(a + b*x^2)*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a*b^2*Sqrt[d]*e*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))","A",7,7,26,0.2692,1,"{6719, 467, 528, 531, 418, 492, 411}"
315,1,327,0,0.2197196,"\int \frac{1}{\left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}} \, dx","Int[((e*(a + b*x^2))/(c + d*x^2))^(-3/2),x]","-\frac{d x \left(a+b x^2\right) (b c-2 a d)}{a b^2 e \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) (b c-2 a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a b^2 e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{c^{3/2} \sqrt{d} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a b e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{x (b c-a d)}{a b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","-\frac{d x \left(a+b x^2\right) (b c-2 a d)}{a b^2 e \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) (b c-2 a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a b^2 e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{c^{3/2} \sqrt{d} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a b e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{x (b c-a d)}{a b e \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"((b*c - a*d)*x)/(a*b*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) - (d*(b*c - 2*a*d)*x*(a + b*x^2))/(a*b^2*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) + (Sqrt[c]*Sqrt[d]*(b*c - 2*a*d)*(a + b*x^2)*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(a*b^2*e*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) + (c^(3/2)*Sqrt[d]*(a + b*x^2)*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(a*b*e*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))","A",6,6,22,0.2727,1,"{6719, 413, 531, 418, 492, 411}"
316,1,380,0,0.4701592,"\int \frac{1}{x^2 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}} \, dx","Int[1/(x^2*((e*(a + b*x^2))/(c + d*x^2))^(3/2)),x]","\frac{c^{3/2} \sqrt{d} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a^2 e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\left(a+b x^2\right) (2 b c-a d)}{a^2 b e x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{d x \left(a+b x^2\right) (2 b c-a d)}{a^2 b e \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) (2 b c-a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a^2 b e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{b c-a d}{a b e x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","\frac{c^{3/2} \sqrt{d} \left(a+b x^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a^2 e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\left(a+b x^2\right) (2 b c-a d)}{a^2 b e x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{d x \left(a+b x^2\right) (2 b c-a d)}{a^2 b e \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) (2 b c-a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a^2 b e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{b c-a d}{a b e x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"(b*c - a*d)/(a*b*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) - ((2*b*c - a*d)*(a + b*x^2))/(a^2*b*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + (d*(2*b*c - a*d)*x*(a + b*x^2))/(a^2*b*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) - (Sqrt[c]*Sqrt[d]*(2*b*c - a*d)*(a + b*x^2)*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(a^2*b*e*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) + (c^(3/2)*Sqrt[d]*(a + b*x^2)*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(a^2*e*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))","A",7,7,26,0.2692,1,"{6719, 468, 583, 531, 418, 492, 411}"
317,1,444,0,0.6493314,"\int \frac{1}{x^4 \left(\frac{e \left(a+b x^2\right)}{c+d x^2}\right)^{3/2}} \, dx","Int[1/(x^4*((e*(a + b*x^2))/(c + d*x^2))^(3/2)),x]","\frac{\left(a+b x^2\right) (8 b c-7 a d)}{3 a^3 e x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\left(a+b x^2\right) (4 b c-3 a d)}{3 a^2 b e x^3 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{d x \left(a+b x^2\right) (8 b c-7 a d)}{3 a^3 e \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) (4 b c-3 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^3 e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) (8 b c-7 a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^3 e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{b c-a d}{a b e x^3 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}","\frac{\left(a+b x^2\right) (8 b c-7 a d)}{3 a^3 e x \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\left(a+b x^2\right) (4 b c-3 a d)}{3 a^2 b e x^3 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{d x \left(a+b x^2\right) (8 b c-7 a d)}{3 a^3 e \left(c+d x^2\right) \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) (4 b c-3 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^3 e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{\sqrt{c} \sqrt{d} \left(a+b x^2\right) (8 b c-7 a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^3 e \left(c+d x^2\right) \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}} \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}+\frac{b c-a d}{a b e x^3 \sqrt{\frac{e \left(a+b x^2\right)}{c+d x^2}}}",1,"(b*c - a*d)/(a*b*e*x^3*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) - ((4*b*c - 3*a*d)*(a + b*x^2))/(3*a^2*b*e*x^3*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) + ((8*b*c - 7*a*d)*(a + b*x^2))/(3*a^3*e*x*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]) - (d*(8*b*c - 7*a*d)*x*(a + b*x^2))/(3*a^3*e*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) + (Sqrt[c]*Sqrt[d]*(8*b*c - 7*a*d)*(a + b*x^2)*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a^3*e*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2)) - (Sqrt[c]*Sqrt[d]*(4*b*c - 3*a*d)*(a + b*x^2)*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a^3*e*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[(e*(a + b*x^2))/(c + d*x^2)]*(c + d*x^2))","A",8,7,26,0.2692,1,"{6719, 468, 583, 531, 418, 492, 411}"
318,1,259,0,0.6203208,"\int x^5 \sqrt{a+\frac{b}{c+d x^2}} \, dx","Int[x^5*Sqrt[a + b/(c + d*x^2)],x]","\frac{\left(8 a^2 c^2+4 a b c+b^2\right) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{16 a^2 d^3}+\frac{b \left(8 a^2 c^2+4 a b c+b^2\right) \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{16 a^{5/2} d^3 \sqrt{a \left(c+d x^2\right)+b}}-\frac{(8 a c+3 b) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)}{24 a^2 d^3}+\frac{x^2 \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)}{6 a d^2}","-\frac{\left(-8 a^2 c^2+4 a b c+b^2\right) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{16 a^2 d^3}+\frac{b \left(8 a^2 c^2+4 a b c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)}{16 a^{5/2} d^3}+\frac{\left(c+d x^2\right)^3 \left(\frac{a c+a d x^2+b}{c+d x^2}\right)^{3/2}}{6 a d^3}-\frac{(4 a c+b) \left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{8 a d^3}",1,"((b^2 + 4*a*b*c + 8*a^2*c^2)*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(16*a^2*d^3) - ((3*b + 8*a*c)*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2)))/(24*a^2*d^3) + (x^2*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2)))/(6*a*d^2) + (b*(b^2 + 4*a*b*c + 8*a^2*c^2)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/(16*a^(5/2)*d^3*Sqrt[b + a*(c + d*x^2)])","A",9,9,21,0.4286,1,"{6722, 1975, 446, 90, 80, 50, 63, 217, 206}"
319,1,181,0,0.4668954,"\int x^3 \sqrt{a+\frac{b}{c+d x^2}} \, dx","Int[x^3*Sqrt[a + b/(c + d*x^2)],x]","-\frac{b (4 a c+b) \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{8 a^{3/2} d^2 \sqrt{a \left(c+d x^2\right)+b}}+\frac{\left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)}{4 a d^2}-\frac{(4 a c+b) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{8 a d^2}","-\frac{b (4 a c+b) \tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)}{8 a^{3/2} d^2}+\frac{\left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{4 d^2}+\frac{(b-4 a c) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{8 a d^2}",1,"-((b + 4*a*c)*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(8*a*d^2) + ((c + d*x^2)*Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2)))/(4*a*d^2) - (b*(b + 4*a*c)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/(8*a^(3/2)*d^2*Sqrt[b + a*(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 446, 80, 50, 63, 217, 206}"
320,1,69,0,0.0539107,"\int x \sqrt{a+\frac{b}{c+d x^2}} \, dx","Int[x*Sqrt[a + b/(c + d*x^2)],x]","\frac{\left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{2 d}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{c+d x^2}}}{\sqrt{a}}\right)}{2 \sqrt{a} d}","\frac{\left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{2 d}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{c+d x^2}}}{\sqrt{a}}\right)}{2 \sqrt{a} d}",1,"((c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(2*d) + (b*ArcTanh[Sqrt[a + b/(c + d*x^2)]/Sqrt[a]])/(2*Sqrt[a]*d)","A",5,5,19,0.2632,1,"{1591, 242, 47, 63, 208}"
321,1,184,0,0.4328684,"\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x} \, dx","Int[Sqrt[a + b/(c + d*x^2)]/x,x]","\frac{\sqrt{a} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{\sqrt{a \left(c+d x^2\right)+b}}-\frac{\sqrt{a c+b} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}","\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)-\frac{\sqrt{a c+b} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{\sqrt{c}}",1,"(Sqrt[a]*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/Sqrt[b + a*(c + d*x^2)] - (Sqrt[b + a*c]*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])","A",9,9,21,0.4286,1,"{6722, 1975, 446, 105, 63, 217, 206, 93, 208}"
322,1,140,0,0.3858749,"\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^3} \, dx","Int[Sqrt[a + b/(c + d*x^2)]/x^3,x]","\frac{b d \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{2 c^{3/2} \sqrt{a c+b} \sqrt{a \left(c+d x^2\right)+b}}-\frac{\left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{2 c x^2}","\frac{b d \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{2 c^{3/2} \sqrt{a c+b}}-\frac{\left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{2 c x^2}",1,"-((c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(2*c*x^2) + (b*d*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(2*c^(3/2)*Sqrt[b + a*c]*Sqrt[b + a*(c + d*x^2)])","A",6,6,21,0.2857,1,"{6722, 1975, 446, 94, 93, 208}"
323,1,218,0,0.5072667,"\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^5} \, dx","Int[Sqrt[a + b/(c + d*x^2)]/x^5,x]","-\frac{b d^2 (4 a c+3 b) \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{8 c^{5/2} (a c+b)^{3/2} \sqrt{a \left(c+d x^2\right)+b}}+\frac{d (4 a c+3 b) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{8 c^2 x^2 (a c+b)}-\frac{\left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)}{4 c x^4 (a c+b)}","-\frac{b d^2 (4 a c+3 b) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{8 c^{5/2} (a c+b)^{3/2}}+\frac{d (4 a c+5 b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{8 c^2 x^2 (a c+b)}-\frac{\left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{4 c^2 x^4}",1,"((3*b + 4*a*c)*d*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(8*c^2*(b + a*c)*x^2) - ((c + d*x^2)*Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2)))/(4*c*(b + a*c)*x^4) - (b*(3*b + 4*a*c)*d^2*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(8*c^(5/2)*(b + a*c)^(3/2)*Sqrt[b + a*(c + d*x^2)])","A",7,7,21,0.3333,1,"{6722, 1975, 446, 96, 94, 93, 208}"
324,1,271,0,0.6069027,"\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^7} \, dx","Int[Sqrt[a + b/(c + d*x^2)]/x^7,x]","\frac{b d^3 \left(8 a^2 c^2+12 a b c+5 b^2\right) \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{16 c^{7/2} (a c+b)^{5/2} \sqrt{a \left(c+d x^2\right)+b}}-\frac{d^2 (2 a c+5 b) (4 a c+3 b) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{48 c^3 x^2 (a c+b)^2}+\frac{d (4 a c+5 b) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{24 c^2 x^4 (a c+b)}-\frac{\left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{6 c x^6}","-\frac{d^2 \left(8 a^2 c^2+20 a b c+11 b^2\right) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{16 c^3 x^2 (a c+b)^2}+\frac{b d^3 \left(8 a^2 c^2+12 a b c+5 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{16 c^{7/2} (a c+b)^{5/2}}+\frac{d (4 a c+3 b) \left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{8 c^3 x^4 (a c+b)}-\frac{\left(c+d x^2\right)^3 \left(\frac{a c+a d x^2+b}{c+d x^2}\right)^{3/2}}{6 c^2 x^6 (a c+b)}",1,"-((c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(6*c*x^6) + ((5*b + 4*a*c)*d*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(24*c^2*(b + a*c)*x^4) - ((5*b + 2*a*c)*(3*b + 4*a*c)*d^2*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(48*c^3*(b + a*c)^2*x^2) + (b*(5*b^2 + 12*a*b*c + 8*a^2*c^2)*d^3*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(16*c^(7/2)*(b + a*c)^(5/2)*Sqrt[b + a*(c + d*x^2)])","A",9,8,21,0.3810,1,"{6722, 1975, 446, 99, 151, 12, 93, 208}"
325,1,478,0,0.7180723,"\int x^4 \sqrt{a+\frac{b}{c+d x^2}} \, dx","Int[x^4*Sqrt[a + b/(c + d*x^2)],x]","-\frac{x \left(-3 a^2 c^2+7 a b c+2 b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{15 a^2 d^2 \sqrt{a \left(c+d x^2\right)+b}}+\frac{\sqrt{c} \left(-3 a^2 c^2+7 a b c+2 b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 a^2 d^{5/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}-\frac{c^{3/2} (b-3 a c) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 a d^{5/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{x (b-3 a c) \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{15 a d^2 \sqrt{a \left(c+d x^2\right)+b}}+\frac{x^3 \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{5 d \sqrt{a \left(c+d x^2\right)+b}}","-\frac{x \left(-3 a^2 c^2+7 a b c+2 b^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{15 a^2 d^2}+\frac{\sqrt{c} \left(-3 a^2 c^2+7 a b c+2 b^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 a^2 d^{5/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{c^{3/2} (b-3 a c) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 a d^{5/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{x (b-3 a c) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{15 a d^2}+\frac{x^3 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{5 d}",1,"-((2*b^2 + 7*a*b*c - 3*a^2*c^2)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(15*a^2*d^2*Sqrt[b + a*(c + d*x^2)]) + ((b - 3*a*c)*x*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(15*a*d^2*Sqrt[b + a*(c + d*x^2)]) + (x^3*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(5*d*Sqrt[b + a*(c + d*x^2)]) + (Sqrt[c]*(2*b^2 + 7*a*b*c - 3*a^2*c^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(15*a^2*d^(5/2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) - (c^(3/2)*(b - 3*a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(15*a*d^(5/2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 478, 582, 531, 418, 492, 411}"
326,1,370,0,0.5171835,"\int x^2 \sqrt{a+\frac{b}{c+d x^2}} \, dx","Int[x^2*Sqrt[a + b/(c + d*x^2)],x]","-\frac{c^{3/2} \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 d^{3/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}-\frac{\sqrt{c} (b-a c) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 a d^{3/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{x (b-a c) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{3 a d \sqrt{a \left(c+d x^2\right)+b}}+\frac{x \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{3 d \sqrt{a \left(c+d x^2\right)+b}}","-\frac{c^{3/2} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 d^{3/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{\sqrt{c} (b-a c) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 a d^{3/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{x (b-a c) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{3 a d}+\frac{x \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{3 d}",1,"((b - a*c)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(3*a*d*Sqrt[b + a*(c + d*x^2)]) + (x*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(3*d*Sqrt[b + a*(c + d*x^2)]) - (Sqrt[c]*(b - a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*a*d^(3/2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) - (c^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*d^(3/2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",7,7,21,0.3333,1,"{6722, 1975, 478, 531, 418, 492, 411}"
327,1,279,0,0.2031566,"\int \sqrt{a+\frac{b}{c+d x^2}} \, dx","Int[Sqrt[a + b/(c + d*x^2)],x]","\frac{x \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{\sqrt{a \left(c+d x^2\right)+b}}+\frac{\sqrt{c} \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{d} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}-\frac{\sqrt{c} \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{d} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}","x \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}+\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{d} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{d} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}",1,"(x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/Sqrt[b + a*(c + d*x^2)] - (Sqrt[c]*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(Sqrt[d]*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) + (Sqrt[c]*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(Sqrt[d]*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",6,6,17,0.3529,1,"{6722, 1974, 422, 418, 492, 411}"
328,1,353,0,0.5095943,"\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^2} \, dx","Int[Sqrt[a + b/(c + d*x^2)]/x^2,x]","\frac{d x \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{c \sqrt{a \left(c+d x^2\right)+b}}-\frac{\left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{c x \sqrt{a \left(c+d x^2\right)+b}}+\frac{a \sqrt{c} \sqrt{d} \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{(a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}-\frac{\sqrt{d} \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{c} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}","\frac{d x \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c}-\frac{\left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c x}+\frac{a \sqrt{c} \sqrt{d} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{(a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{\sqrt{d} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{c} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}",1,"(d*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(c*Sqrt[b + a*(c + d*x^2)]) - ((c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(c*x*Sqrt[b + a*(c + d*x^2)]) - (Sqrt[d]*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(Sqrt[c]*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) + (a*Sqrt[c]*Sqrt[d]*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/((b + a*c)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 475, 21, 422, 418, 492, 411}"
329,1,472,0,0.6301718,"\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^4} \, dx","Int[Sqrt[a + b/(c + d*x^2)]/x^4,x]","-\frac{d^2 x (a c+2 b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{3 c^2 (a c+b) \sqrt{a \left(c+d x^2\right)+b}}+\frac{d^{3/2} (a c+2 b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 c^{3/2} (a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{d (a c+2 b) \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{3 c^2 x (a c+b) \sqrt{a \left(c+d x^2\right)+b}}-\frac{a d^{3/2} \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 \sqrt{c} (a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}-\frac{\left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{3 c x^3 \sqrt{a \left(c+d x^2\right)+b}}","-\frac{d^2 x (a c+2 b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{3 c^2 (a c+b)}+\frac{d^{3/2} (a c+2 b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 c^{3/2} (a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{d (a c+2 b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{3 c^2 x (a c+b)}-\frac{a d^{3/2} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 \sqrt{c} (a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{\left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{3 c x^3}",1,"-((2*b + a*c)*d^2*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(3*c^2*(b + a*c)*Sqrt[b + a*(c + d*x^2)]) - ((c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(3*c*x^3*Sqrt[b + a*(c + d*x^2)]) + ((2*b + a*c)*d*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(3*c^2*(b + a*c)*x*Sqrt[b + a*(c + d*x^2)]) + ((2*b + a*c)*d^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*c^(3/2)*(b + a*c)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) - (a*d^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*Sqrt[c]*(b + a*c)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 475, 583, 531, 418, 492, 411}"
330,1,598,0,0.8119808,"\int \frac{\sqrt{a+\frac{b}{c+d x^2}}}{x^6} \, dx","Int[Sqrt[a + b/(c + d*x^2)]/x^6,x]","\frac{d^3 x \left(3 a^2 c^2+13 a b c+8 b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{15 c^3 (a c+b)^2 \sqrt{a \left(c+d x^2\right)+b}}-\frac{d^2 \left(3 a^2 c^2+13 a b c+8 b^2\right) \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{15 c^3 x (a c+b)^2 \sqrt{a \left(c+d x^2\right)+b}}-\frac{d^{5/2} \left(3 a^2 c^2+13 a b c+8 b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 c^{5/2} (a c+b)^2 \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{a d^{5/2} (3 a c+4 b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 c^{3/2} (a c+b)^2 \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{d (3 a c+4 b) \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{15 c^2 x^3 (a c+b) \sqrt{a \left(c+d x^2\right)+b}}-\frac{\left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{5 c x^5 \sqrt{a \left(c+d x^2\right)+b}}","\frac{d^3 x \left(3 a^2 c^2+13 a b c+8 b^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{15 c^3 (a c+b)^2}-\frac{d^2 \left(3 a^2 c^2+13 a b c+8 b^2\right) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{15 c^3 x (a c+b)^2}-\frac{d^{5/2} \left(3 a^2 c^2+13 a b c+8 b^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 c^{5/2} (a c+b)^2 \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{a d^{5/2} (3 a c+4 b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 c^{3/2} (a c+b)^2 \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{d (3 a c+4 b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{15 c^2 x^3 (a c+b)}-\frac{\left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{5 c x^5}",1,"((8*b^2 + 13*a*b*c + 3*a^2*c^2)*d^3*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(15*c^3*(b + a*c)^2*Sqrt[b + a*(c + d*x^2)]) - ((c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(5*c*x^5*Sqrt[b + a*(c + d*x^2)]) + ((4*b + 3*a*c)*d*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(15*c^2*(b + a*c)*x^3*Sqrt[b + a*(c + d*x^2)]) - ((8*b^2 + 13*a*b*c + 3*a^2*c^2)*d^2*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(15*c^3*(b + a*c)^2*x*Sqrt[b + a*(c + d*x^2)]) - ((8*b^2 + 13*a*b*c + 3*a^2*c^2)*d^(5/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(15*c^(5/2)*(b + a*c)^2*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) + (a*(4*b + 3*a*c)*d^(5/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(15*c^(3/2)*(b + a*c)^2*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",9,8,21,0.3810,1,"{6722, 1975, 475, 583, 531, 418, 492, 411}"
331,1,311,0,0.7301465,"\int x^5 \left(a+\frac{b}{c+d x^2}\right)^{3/2} \, dx","Int[x^5*(a + b/(c + d*x^2))^(3/2),x]","-\frac{\left(-24 a^2 c^2+12 a b c+b^2\right) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)}{24 a b d^3}-\frac{\left(-24 a^2 c^2+12 a b c+b^2\right) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{16 a d^3}-\frac{b \left(-24 a^2 c^2+12 a b c+b^2\right) \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{16 a^{3/2} d^3 \sqrt{a \left(c+d x^2\right)+b}}-\frac{c^2 \sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)^2}{b d^3}+\frac{\left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)^2}{6 a d^3}","-\frac{\left(-24 a^2 c^2+60 a b c+5 b^2\right) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{48 a d^3}-\frac{b \left(-24 a^2 c^2+12 a b c+b^2\right) \tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)}{16 a^{3/2} d^3}-\frac{b c^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{d^3}+\frac{\left(c+d x^2\right)^3 \left(\frac{a c+a d x^2+b}{c+d x^2}\right)^{5/2}}{6 a d^3}-\frac{(12 a c+b) \left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{24 d^3}",1,"-((b^2 + 12*a*b*c - 24*a^2*c^2)*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(16*a*d^3) - ((b^2 + 12*a*b*c - 24*a^2*c^2)*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2)))/(24*a*b*d^3) - (c^2*Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2))^2)/(b*d^3) + ((c + d*x^2)*Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2))^2)/(6*a*d^3) - (b*(b^2 + 12*a*b*c - 24*a^2*c^2)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/(16*a^(3/2)*d^3*Sqrt[b + a*(c + d*x^2)])","A",10,9,21,0.4286,1,"{6722, 1975, 446, 89, 80, 50, 63, 217, 206}"
332,1,222,0,0.5357147,"\int x^3 \left(a+\frac{b}{c+d x^2}\right)^{3/2} \, dx","Int[x^3*(a + b/(c + d*x^2))^(3/2),x]","\frac{c \sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)^2}{b d^2}+\frac{(b-4 a c) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)}{4 b d^2}+\frac{3 (b-4 a c) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{8 d^2}+\frac{3 b (b-4 a c) \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{8 \sqrt{a} d^2 \sqrt{a \left(c+d x^2\right)+b}}","\frac{a \left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{4 d^2}+\frac{(5 b-4 a c) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{8 d^2}+\frac{b c \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{d^2}+\frac{3 b (b-4 a c) \tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)}{8 \sqrt{a} d^2}",1,"(3*(b - 4*a*c)*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(8*d^2) + ((b - 4*a*c)*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2)))/(4*b*d^2) + (c*Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2))^2)/(b*d^2) + (3*b*(b - 4*a*c)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/(8*Sqrt[a]*d^2*Sqrt[b + a*(c + d*x^2)])","A",9,8,21,0.3810,1,"{6722, 1975, 446, 78, 50, 63, 217, 206}"
333,1,94,0,0.0659592,"\int x \left(a+\frac{b}{c+d x^2}\right)^{3/2} \, dx","Int[x*(a + b/(c + d*x^2))^(3/2),x]","\frac{\left(c+d x^2\right) \left(a+\frac{b}{c+d x^2}\right)^{3/2}}{2 d}-\frac{3 b \sqrt{a+\frac{b}{c+d x^2}}}{2 d}+\frac{3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{c+d x^2}}}{\sqrt{a}}\right)}{2 d}","\frac{\left(c+d x^2\right) \left(a+\frac{b}{c+d x^2}\right)^{3/2}}{2 d}-\frac{3 b \sqrt{a+\frac{b}{c+d x^2}}}{2 d}+\frac{3 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{c+d x^2}}}{\sqrt{a}}\right)}{2 d}",1,"(-3*b*Sqrt[a + b/(c + d*x^2)])/(2*d) + ((c + d*x^2)*(a + b/(c + d*x^2))^(3/2))/(2*d) + (3*Sqrt[a]*b*ArcTanh[Sqrt[a + b/(c + d*x^2)]/Sqrt[a]])/(2*d)","A",6,6,19,0.3158,1,"{1591, 242, 47, 50, 63, 208}"
334,1,206,0,0.490115,"\int \frac{\left(a+\frac{b}{c+d x^2}\right)^{3/2}}{x} \, dx","Int[(a + b/(c + d*x^2))^(3/2)/x,x]","\frac{a^{3/2} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{\sqrt{a \left(c+d x^2\right)+b}}-\frac{(a c+b)^{3/2} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{c^{3/2} \sqrt{a \left(c+d x^2\right)+b}}+\frac{b \sqrt{a+\frac{b}{c+d x^2}}}{c}","a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)-\frac{(a c+b)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{c^{3/2}}+\frac{b \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c}",1,"(b*Sqrt[a + b/(c + d*x^2)])/c + (a^(3/2)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/Sqrt[b + a*(c + d*x^2)] - ((b + a*c)^(3/2)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(c^(3/2)*Sqrt[b + a*(c + d*x^2)])","A",10,10,21,0.4762,1,"{6722, 1975, 446, 98, 157, 63, 217, 206, 93, 208}"
335,1,170,0,0.5256024,"\int \frac{\left(a+\frac{b}{c+d x^2}\right)^{3/2}}{x^3} \, dx","Int[(a + b/(c + d*x^2))^(3/2)/x^3,x]","-\frac{3 b d \sqrt{a+\frac{b}{c+d x^2}}}{2 c^2}+\frac{3 b d \sqrt{a c+b} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{2 c^{5/2} \sqrt{a \left(c+d x^2\right)+b}}-\frac{\sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)}{2 c x^2}","-\frac{3 b d \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{2 c^2}+\frac{3 b d \sqrt{a c+b} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{2 c^{5/2}}-\frac{\left(c+d x^2\right) \left(\frac{a c+a d x^2+b}{c+d x^2}\right)^{3/2}}{2 c x^2}",1,"(-3*b*d*Sqrt[a + b/(c + d*x^2)])/(2*c^2) - (Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2)))/(2*c*x^2) + (3*b*Sqrt[b + a*c]*d*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(2*c^(5/2)*Sqrt[b + a*(c + d*x^2)])","A",7,6,21,0.2857,1,"{6722, 1975, 446, 94, 93, 208}"
336,1,260,0,0.5913977,"\int \frac{\left(a+\frac{b}{c+d x^2}\right)^{3/2}}{x^5} \, dx","Int[(a + b/(c + d*x^2))^(3/2)/x^5,x]","\frac{3 b d^2 (4 a c+5 b) \sqrt{a+\frac{b}{c+d x^2}}}{8 c^3 (a c+b)}-\frac{3 b d^2 (4 a c+5 b) \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{8 c^{7/2} \sqrt{a c+b} \sqrt{a \left(c+d x^2\right)+b}}+\frac{d (4 a c+5 b) \sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)}{8 c^2 x^2 (a c+b)}-\frac{\sqrt{a+\frac{b}{c+d x^2}} \left(a \left(c+d x^2\right)+b\right)^2}{4 c x^4 (a c+b)}","\frac{b d^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c^3}-\frac{3 b d^2 (4 a c+5 b) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{8 c^{7/2} \sqrt{a c+b}}+\frac{d (4 a c+9 b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{8 c^3 x^2}-\frac{(a c+b) \left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{4 c^3 x^4}",1,"(3*b*(5*b + 4*a*c)*d^2*Sqrt[a + b/(c + d*x^2)])/(8*c^3*(b + a*c)) + ((5*b + 4*a*c)*d*Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2)))/(8*c^2*(b + a*c)*x^2) - (Sqrt[a + b/(c + d*x^2)]*(b + a*(c + d*x^2))^2)/(4*c*(b + a*c)*x^4) - (3*b*(5*b + 4*a*c)*d^2*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(8*c^(7/2)*Sqrt[b + a*c]*Sqrt[b + a*(c + d*x^2)])","A",8,7,21,0.3333,1,"{6722, 1975, 446, 96, 94, 93, 208}"
337,1,287,0,0.7254554,"\int \frac{\left(a+\frac{b}{c+d x^2}\right)^{3/2}}{x^7} \, dx","Int[(a + b/(c + d*x^2))^(3/2)/x^7,x]","-\frac{d^3 \left(8 a^2 c^2+110 a b c+105 b^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{48 c^4 (a c+b)}+\frac{b d^3 \left(24 a^2 c^2+60 a b c+35 b^2\right) \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{16 c^{9/2} (a c+b)^{3/2} \sqrt{a \left(c+d x^2\right)+b}}-\frac{b d^2 (32 a c+35 b) \sqrt{a+\frac{b}{c+d x^2}}}{48 c^3 x^2 (a c+b)}+\frac{7 b d \sqrt{a+\frac{b}{c+d x^2}}}{24 c^2 x^4}-\frac{(a c+b) \sqrt{a+\frac{b}{c+d x^2}}}{6 c x^6}","-\frac{d^2 \left(24 a^2 c^2+108 a b c+79 b^2\right) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{48 c^4 x^2 (a c+b)}+\frac{b d^3 \left(24 a^2 c^2+60 a b c+35 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{16 c^{9/2} (a c+b)^{3/2}}-\frac{b d^3 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c^4}+\frac{d (12 a c+11 b) \left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{24 c^4 x^4}-\frac{\left(c+d x^2\right)^3 \left(\frac{a c+a d x^2+b}{c+d x^2}\right)^{5/2}}{6 c^2 x^6 (a c+b)}",1,"-((105*b^2 + 110*a*b*c + 8*a^2*c^2)*d^3*Sqrt[a + b/(c + d*x^2)])/(48*c^4*(b + a*c)) - ((b + a*c)*Sqrt[a + b/(c + d*x^2)])/(6*c*x^6) + (7*b*d*Sqrt[a + b/(c + d*x^2)])/(24*c^2*x^4) - (b*(35*b + 32*a*c)*d^2*Sqrt[a + b/(c + d*x^2)])/(48*c^3*(b + a*c)*x^2) + (b*(35*b^2 + 60*a*b*c + 24*a^2*c^2)*d^3*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(16*c^(9/2)*(b + a*c)^(3/2)*Sqrt[b + a*(c + d*x^2)])","A",10,9,21,0.4286,1,"{6722, 1975, 446, 98, 151, 152, 12, 93, 208}"
338,1,526,0,0.8760413,"\int x^4 \left(a+\frac{b}{c+d x^2}\right)^{3/2} \, dx","Int[x^4*(a + b/(c + d*x^2))^(3/2),x]","\frac{x \left(a^2 c^2-14 a b c+b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{5 a d^2 \sqrt{a \left(c+d x^2\right)+b}}-\frac{\sqrt{c} \left(a^2 c^2-14 a b c+b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 a d^{5/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}-\frac{c^{3/2} (7 b-a c) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 d^{5/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{x (7 b-a c) \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{5 d^2 \sqrt{a \left(c+d x^2\right)+b}}-\frac{x^3 \left(a c+a d x^2+b\right)^{3/2} \sqrt{a+\frac{b}{c+d x^2}}}{d \sqrt{a \left(c+d x^2\right)+b}}+\frac{6 a x^3 \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{5 d \sqrt{a \left(c+d x^2\right)+b}}","\frac{x \left(a^2 c^2-14 a b c+b^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{5 a d^2}-\frac{\sqrt{c} \left(a^2 c^2-14 a b c+b^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 a d^{5/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{c^{3/2} (7 b-a c) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 d^{5/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{x (7 b-a c) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{5 d^2}+\frac{6 a x^3 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{5 d}-\frac{x^3 \left(a c+a d x^2+b\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{d}",1,"((b^2 - 14*a*b*c + a^2*c^2)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(5*a*d^2*Sqrt[b + a*(c + d*x^2)]) + ((7*b - a*c)*x*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(5*d^2*Sqrt[b + a*(c + d*x^2)]) + (6*a*x^3*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(5*d*Sqrt[b + a*(c + d*x^2)]) - (x^3*(b + a*c + a*d*x^2)^(3/2)*Sqrt[a + b/(c + d*x^2)])/(d*Sqrt[b + a*(c + d*x^2)]) - (Sqrt[c]*(b^2 - 14*a*b*c + a^2*c^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(5*a*d^(5/2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) - (c^(3/2)*(7*b - a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(5*d^(5/2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",9,9,21,0.4286,1,"{6722, 1975, 467, 581, 582, 531, 418, 492, 411}"
339,1,430,0,0.634819,"\int x^2 \left(a+\frac{b}{c+d x^2}\right)^{3/2} \, dx","Int[x^2*(a + b/(c + d*x^2))^(3/2),x]","\frac{\sqrt{c} (3 b-a c) \sqrt{a+\frac{b}{c+d x^2}} \sqrt{a c+a d x^2+b} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 d^{3/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}-\frac{\sqrt{c} (7 b-a c) \sqrt{a+\frac{b}{c+d x^2}} \sqrt{a c+a d x^2+b} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 d^{3/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}-\frac{x \sqrt{a+\frac{b}{c+d x^2}} \left(a c+a d x^2+b\right)^{3/2}}{d \sqrt{a \left(c+d x^2\right)+b}}+\frac{x (7 b-a c) \sqrt{a+\frac{b}{c+d x^2}} \sqrt{a c+a d x^2+b}}{3 d \sqrt{a \left(c+d x^2\right)+b}}+\frac{4 a x \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}} \sqrt{a c+a d x^2+b}}{3 d \sqrt{a \left(c+d x^2\right)+b}}","\frac{\sqrt{c} (3 b-a c) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 d^{3/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{\sqrt{c} (7 b-a c) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 d^{3/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{4 a x \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{3 d}-\frac{x \left(a c+a d x^2+b\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{d}+\frac{x (7 b-a c) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{3 d}",1,"((7*b - a*c)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(3*d*Sqrt[b + a*(c + d*x^2)]) + (4*a*x*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(3*d*Sqrt[b + a*(c + d*x^2)]) - (x*(b + a*c + a*d*x^2)^(3/2)*Sqrt[a + b/(c + d*x^2)])/(d*Sqrt[b + a*(c + d*x^2)]) - (Sqrt[c]*(7*b - a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*d^(3/2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) + (Sqrt[c]*(3*b - a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*d^(3/2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 467, 528, 531, 418, 492, 411}"
340,1,348,0,0.2914172,"\int \left(a+\frac{b}{c+d x^2}\right)^{3/2} \, dx","Int[(a + b/(c + d*x^2))^(3/2),x]","-\frac{x (b-a c) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{c \sqrt{a \left(c+d x^2\right)+b}}+\frac{b x \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{c \sqrt{a \left(c+d x^2\right)+b}}+\frac{a \sqrt{c} \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{d} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{(b-a c) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{c} \sqrt{d} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}","-\frac{x (b-a c) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c}+\frac{b x \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c}+\frac{a \sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{d} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{(b-a c) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{c} \sqrt{d} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}",1,"(b*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(c*Sqrt[b + a*(c + d*x^2)]) - ((b - a*c)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(c*Sqrt[b + a*(c + d*x^2)]) + ((b - a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(Sqrt[c]*Sqrt[d]*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) + (a*Sqrt[c]*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(Sqrt[d]*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",7,7,17,0.4118,1,"{6722, 1974, 413, 531, 418, 492, 411}"
341,1,422,0,0.6635756,"\int \frac{\left(a+\frac{b}{c+d x^2}\right)^{3/2}}{x^2} \, dx","Int[(a + b/(c + d*x^2))^(3/2)/x^2,x]","\frac{d x (a c+2 b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{c^2 \sqrt{a \left(c+d x^2\right)+b}}-\frac{(a c+2 b) \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{c^2 x \sqrt{a \left(c+d x^2\right)+b}}-\frac{\sqrt{d} (a c+2 b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{c^{3/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{b \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{c x \sqrt{a \left(c+d x^2\right)+b}}+\frac{a \sqrt{d} \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{c} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}","\frac{d x (a c+2 b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c^2}-\frac{(a c+2 b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c^2 x}-\frac{\sqrt{d} (a c+2 b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{c^{3/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{b \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c x}+\frac{a \sqrt{d} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{c} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}",1,"(b*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(c*x*Sqrt[b + a*(c + d*x^2)]) + ((2*b + a*c)*d*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(c^2*Sqrt[b + a*(c + d*x^2)]) - ((2*b + a*c)*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(c^2*x*Sqrt[b + a*(c + d*x^2)]) - ((2*b + a*c)*Sqrt[d]*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(c^(3/2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) + (a*Sqrt[d]*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(Sqrt[c]*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 468, 583, 531, 418, 492, 411}"
342,1,520,0,0.8685766,"\int \frac{\left(a+\frac{b}{c+d x^2}\right)^{3/2}}{x^4} \, dx","Int[(a + b/(c + d*x^2))^(3/2)/x^4,x]","-\frac{d^2 x (a c+8 b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{3 c^3 \sqrt{a \left(c+d x^2\right)+b}}-\frac{a d^{3/2} (a c+4 b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 c^{3/2} (a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{d^{3/2} (a c+8 b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 c^{5/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{d (a c+8 b) \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{3 c^3 x \sqrt{a \left(c+d x^2\right)+b}}-\frac{(a c+4 b) \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{3 c^2 x^3 \sqrt{a \left(c+d x^2\right)+b}}+\frac{b \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{c x^3 \sqrt{a \left(c+d x^2\right)+b}}","-\frac{d^2 x (a c+8 b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{3 c^3}-\frac{a d^{3/2} (a c+4 b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 c^{3/2} (a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{d^{3/2} (a c+8 b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 c^{5/2} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{d (a c+8 b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{3 c^3 x}-\frac{(a c+4 b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{3 c^2 x^3}+\frac{b \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c x^3}",1,"(b*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(c*x^3*Sqrt[b + a*(c + d*x^2)]) - ((8*b + a*c)*d^2*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(3*c^3*Sqrt[b + a*(c + d*x^2)]) - ((4*b + a*c)*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(3*c^2*x^3*Sqrt[b + a*(c + d*x^2)]) + ((8*b + a*c)*d*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(3*c^3*x*Sqrt[b + a*(c + d*x^2)]) + ((8*b + a*c)*d^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*c^(5/2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) - (a*(4*b + a*c)*d^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*c^(3/2)*(b + a*c)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",9,8,21,0.3810,1,"{6722, 1975, 468, 583, 531, 418, 492, 411}"
343,1,648,0,1.0751796,"\int \frac{\left(a+\frac{b}{c+d x^2}\right)^{3/2}}{x^6} \, dx","Int[(a + b/(c + d*x^2))^(3/2)/x^6,x]","\frac{d^3 x \left(a^2 c^2+16 a b c+16 b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{5 c^4 (a c+b) \sqrt{a \left(c+d x^2\right)+b}}-\frac{d^2 \left(a^2 c^2+16 a b c+16 b^2\right) \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{5 c^4 x (a c+b) \sqrt{a \left(c+d x^2\right)+b}}-\frac{d^{5/2} \left(a^2 c^2+16 a b c+16 b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 c^{7/2} (a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{a d^{5/2} (a c+8 b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 c^{5/2} (a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a \left(c+d x^2\right)+b}}+\frac{d (a c+8 b) \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{5 c^3 x^3 \sqrt{a \left(c+d x^2\right)+b}}-\frac{(a c+6 b) \left(c+d x^2\right) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{5 c^2 x^5 \sqrt{a \left(c+d x^2\right)+b}}+\frac{b \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}{c x^5 \sqrt{a \left(c+d x^2\right)+b}}","\frac{d^3 x \left(a^2 c^2+16 a b c+16 b^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{5 c^4 (a c+b)}-\frac{d^2 \left(a^2 c^2+16 a b c+16 b^2\right) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{5 c^4 x (a c+b)}-\frac{d^{5/2} \left(a^2 c^2+16 a b c+16 b^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 c^{7/2} (a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{a d^{5/2} (a c+8 b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 c^{5/2} (a c+b) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{d (a c+8 b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{5 c^3 x^3}-\frac{(a c+6 b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{5 c^2 x^5}+\frac{b \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{c x^5}",1,"(b*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(c*x^5*Sqrt[b + a*(c + d*x^2)]) + ((16*b^2 + 16*a*b*c + a^2*c^2)*d^3*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(5*c^4*(b + a*c)*Sqrt[b + a*(c + d*x^2)]) - ((6*b + a*c)*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(5*c^2*x^5*Sqrt[b + a*(c + d*x^2)]) + ((8*b + a*c)*d*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(5*c^3*x^3*Sqrt[b + a*(c + d*x^2)]) - ((16*b^2 + 16*a*b*c + a^2*c^2)*d^2*(c + d*x^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])/(5*c^4*(b + a*c)*x*Sqrt[b + a*(c + d*x^2)]) - ((16*b^2 + 16*a*b*c + a^2*c^2)*d^(5/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(5*c^(7/2)*(b + a*c)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)]) + (a*(8*b + a*c)*d^(5/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(5*c^(5/2)*(b + a*c)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[b + a*(c + d*x^2)])","A",10,8,21,0.3810,1,"{6722, 1975, 468, 583, 531, 418, 492, 411}"
344,1,267,0,0.6221001,"\int \frac{x^5}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx","Int[x^5/Sqrt[a + b/(c + d*x^2)],x]","\frac{\left(8 a^2 c^2+12 a b c+5 b^2\right) \left(a \left(c+d x^2\right)+b\right)}{16 a^3 d^3 \sqrt{a+\frac{b}{c+d x^2}}}-\frac{b \left(8 a^2 c^2+12 a b c+5 b^2\right) \sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{16 a^{7/2} d^3 \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{(8 a c+5 b) \left(c+d x^2\right) \left(a \left(c+d x^2\right)+b\right)}{24 a^2 d^3 \sqrt{a+\frac{b}{c+d x^2}}}+\frac{x^2 \left(c+d x^2\right) \left(a \left(c+d x^2\right)+b\right)}{6 a d^2 \sqrt{a+\frac{b}{c+d x^2}}}","\frac{\left(8 a^2 c^2+12 a b c+5 b^2\right) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{16 a^3 d^3}-\frac{b \left(8 a^2 c^2+12 a b c+5 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)}{16 a^{7/2} d^3}-\frac{(8 a c+5 b) \left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{24 a^2 d^3}+\frac{x^2 \left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{6 a d^2}",1,"((5*b^2 + 12*a*b*c + 8*a^2*c^2)*(b + a*(c + d*x^2)))/(16*a^3*d^3*Sqrt[a + b/(c + d*x^2)]) - ((5*b + 8*a*c)*(c + d*x^2)*(b + a*(c + d*x^2)))/(24*a^2*d^3*Sqrt[a + b/(c + d*x^2)]) + (x^2*(c + d*x^2)*(b + a*(c + d*x^2)))/(6*a*d^2*Sqrt[a + b/(c + d*x^2)]) - (b*(5*b^2 + 12*a*b*c + 8*a^2*c^2)*Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/(16*a^(7/2)*d^3*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)])","A",9,9,21,0.4286,1,"{6722, 1975, 446, 90, 80, 50, 63, 217, 206}"
345,1,189,0,0.4648037,"\int \frac{x^3}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx","Int[x^3/Sqrt[a + b/(c + d*x^2)],x]","-\frac{(4 a c+3 b) \left(a \left(c+d x^2\right)+b\right)}{8 a^2 d^2 \sqrt{a+\frac{b}{c+d x^2}}}+\frac{b (4 a c+3 b) \sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{8 a^{5/2} d^2 \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{\left(c+d x^2\right) \left(a \left(c+d x^2\right)+b\right)}{4 a d^2 \sqrt{a+\frac{b}{c+d x^2}}}","-\frac{(4 a c+3 b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{8 a^2 d^2}+\frac{b (4 a c+3 b) \tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)}{8 a^{5/2} d^2}+\frac{\left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{4 a d^2}",1,"-((3*b + 4*a*c)*(b + a*(c + d*x^2)))/(8*a^2*d^2*Sqrt[a + b/(c + d*x^2)]) + ((c + d*x^2)*(b + a*(c + d*x^2)))/(4*a*d^2*Sqrt[a + b/(c + d*x^2)]) + (b*(3*b + 4*a*c)*Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/(8*a^(5/2)*d^2*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 446, 80, 50, 63, 217, 206}"
346,1,72,0,0.0520451,"\int \frac{x}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx","Int[x/Sqrt[a + b/(c + d*x^2)],x]","\frac{\left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{2 a d}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{c+d x^2}}}{\sqrt{a}}\right)}{2 a^{3/2} d}","\frac{\left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{2 a d}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{c+d x^2}}}{\sqrt{a}}\right)}{2 a^{3/2} d}",1,"((c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(2*a*d) - (b*ArcTanh[Sqrt[a + b/(c + d*x^2)]/Sqrt[a]])/(2*a^(3/2)*d)","A",5,5,19,0.2632,1,"{1591, 242, 51, 63, 208}"
347,1,184,0,0.4144772,"\int \frac{1}{x \sqrt{a+\frac{b}{c+d x^2}}} \, dx","Int[1/(x*Sqrt[a + b/(c + d*x^2)]),x]","\frac{\sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{\sqrt{a} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{\sqrt{a c+b} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{\sqrt{a c+b}}",1,"(Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/(Sqrt[a]*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]) - (Sqrt[c]*Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(Sqrt[b + a*c]*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)])","A",9,9,21,0.4286,1,"{6722, 1975, 446, 105, 63, 217, 206, 93, 208}"
348,1,148,0,0.3872779,"\int \frac{1}{x^3 \sqrt{a+\frac{b}{c+d x^2}}} \, dx","Int[1/(x^3*Sqrt[a + b/(c + d*x^2)]),x]","-\frac{a \left(c+d x^2\right)+b}{2 x^2 (a c+b) \sqrt{a+\frac{b}{c+d x^2}}}-\frac{b d \sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{2 \sqrt{c} (a c+b)^{3/2} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}","-\frac{\left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{2 x^2 (a c+b)}-\frac{b d \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{2 \sqrt{c} (a c+b)^{3/2}}",1,"-(b + a*(c + d*x^2))/(2*(b + a*c)*x^2*Sqrt[a + b/(c + d*x^2)]) - (b*d*Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(2*Sqrt[c]*(b + a*c)^(3/2)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)])","A",6,6,21,0.2857,1,"{6722, 1975, 446, 94, 93, 208}"
349,1,218,0,0.4721565,"\int \frac{1}{x^5 \sqrt{a+\frac{b}{c+d x^2}}} \, dx","Int[1/(x^5*Sqrt[a + b/(c + d*x^2)]),x]","\frac{b d^2 (4 a c+b) \sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{8 c^{3/2} (a c+b)^{5/2} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{d (4 a c+b) \left(a \left(c+d x^2\right)+b\right)}{8 c x^2 (a c+b)^2 \sqrt{a+\frac{b}{c+d x^2}}}-\frac{\left(c+d x^2\right) \left(a \left(c+d x^2\right)+b\right)}{4 c x^4 (a c+b) \sqrt{a+\frac{b}{c+d x^2}}}","\frac{b d^2 (4 a c+b) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{8 c^{3/2} (a c+b)^{5/2}}+\frac{d (4 a c+b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{8 c x^2 (a c+b)^2}-\frac{\left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{4 c x^4 (a c+b)}",1,"((b + 4*a*c)*d*(b + a*(c + d*x^2)))/(8*c*(b + a*c)^2*x^2*Sqrt[a + b/(c + d*x^2)]) - ((c + d*x^2)*(b + a*(c + d*x^2)))/(4*c*(b + a*c)*x^4*Sqrt[a + b/(c + d*x^2)]) + (b*(b + 4*a*c)*d^2*Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(8*c^(3/2)*(b + a*c)^(5/2)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)])","A",7,7,21,0.3333,1,"{6722, 1975, 446, 96, 94, 93, 208}"
350,1,498,0,0.708877,"\int \frac{x^4}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx","Int[x^4/Sqrt[a + b/(c + d*x^2)],x]","\frac{x \left(3 a^2 c^2+13 a b c+8 b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{15 a^3 d^2 \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}-\frac{\sqrt{c} \left(3 a^2 c^2+13 a b c+8 b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 a^3 d^{5/2} \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{c^{3/2} (3 a c+4 b) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 a^2 d^{5/2} \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{x (3 a c+4 b) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{15 a^2 d^2 \sqrt{a+\frac{b}{c+d x^2}}}+\frac{x^3 \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{5 a d \sqrt{a+\frac{b}{c+d x^2}}}","\frac{x \left(3 a^2 c^2+13 a b c+8 b^2\right) \left(a c+a d x^2+b\right)}{15 a^3 d^2 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{\sqrt{c} \left(3 a^2 c^2+13 a b c+8 b^2\right) \left(a c+a d x^2+b\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 a^3 d^{5/2} \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{c^{3/2} (3 a c+4 b) \left(a c+a d x^2+b\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{15 a^2 d^{5/2} \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{x (3 a c+4 b) \left(a c+a d x^2+b\right)}{15 a^2 d^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}+\frac{x^3 \left(a c+a d x^2+b\right)}{5 a d \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}",1,"-((4*b + 3*a*c)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(15*a^2*d^2*Sqrt[a + b/(c + d*x^2)]) + (x^3*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(5*a*d*Sqrt[a + b/(c + d*x^2)]) + ((8*b^2 + 13*a*b*c + 3*a^2*c^2)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(15*a^3*d^2*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]) - (Sqrt[c]*(8*b^2 + 13*a*b*c + 3*a^2*c^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(15*a^3*d^(5/2)*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)]) + (c^(3/2)*(4*b + 3*a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(15*a^2*d^(5/2)*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 478, 582, 531, 418, 492, 411}"
351,1,398,0,0.5206232,"\int \frac{x^2}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx","Int[x^2/Sqrt[a + b/(c + d*x^2)],x]","\frac{\sqrt{c} (a c+2 b) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 a^2 d^{3/2} \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{x (a c+2 b) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{3 a^2 d \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}-\frac{c^{3/2} \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 a d^{3/2} \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{x \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{3 a d \sqrt{a+\frac{b}{c+d x^2}}}","\frac{\sqrt{c} (a c+2 b) \left(a c+a d x^2+b\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 a^2 d^{3/2} \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{x (a c+2 b) \left(a c+a d x^2+b\right)}{3 a^2 d \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{c^{3/2} \left(a c+a d x^2+b\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 a d^{3/2} \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{x \left(a c+a d x^2+b\right)}{3 a d \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}",1,"(x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(3*a*d*Sqrt[a + b/(c + d*x^2)]) - ((2*b + a*c)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(3*a^2*d*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]) + (Sqrt[c]*(2*b + a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*a^2*d^(3/2)*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)]) - (c^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*a*d^(3/2)*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)])","A",7,7,21,0.3333,1,"{6722, 1975, 478, 531, 418, 492, 411}"
352,1,319,0,0.208576,"\int \frac{1}{\sqrt{a+\frac{b}{c+d x^2}}} \, dx","Int[1/Sqrt[a + b/(c + d*x^2)],x]","\frac{c^{3/2} \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{d} (a c+b) \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{x \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{a \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{a \sqrt{d} \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}","\frac{c^{3/2} \left(a c+a d x^2+b\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{\sqrt{d} (a c+b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{x \left(a c+a d x^2+b\right)}{a \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{\sqrt{c} \left(a c+a d x^2+b\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{a \sqrt{d} \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}",1,"(x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(a*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]) - (Sqrt[c]*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(a*Sqrt[d]*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)]) + (c^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/((b + a*c)*Sqrt[d]*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)])","A",6,6,17,0.3529,1,"{6722, 1974, 422, 418, 492, 411}"
353,1,387,0,0.4833609,"\int \frac{1}{x^2 \sqrt{a+\frac{b}{c+d x^2}}} \, dx","Int[1/(x^2*Sqrt[a + b/(c + d*x^2)]),x]","\frac{d x \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{(a c+b) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}-\frac{\sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{x (a c+b) \sqrt{a+\frac{b}{c+d x^2}}}+\frac{\sqrt{c} \sqrt{d} \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{(a c+b) \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{\sqrt{c} \sqrt{d} \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{(a c+b) \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}","-\frac{a c+a d x^2+b}{x (a c+b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}+\frac{d x \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}+\frac{\sqrt{c} \sqrt{d} \left(a c+a d x^2+b\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{(a c+b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{\sqrt{c} \sqrt{d} \left(a c+a d x^2+b\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{(a c+b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}",1,"-((Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/((b + a*c)*x*Sqrt[a + b/(c + d*x^2)])) + (d*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/((b + a*c)*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]) - (Sqrt[c]*Sqrt[d]*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/((b + a*c)*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)]) + (Sqrt[c]*Sqrt[d]*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/((b + a*c)*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 475, 21, 422, 418, 492, 411}"
354,1,486,0,0.6370866,"\int \frac{1}{x^4 \sqrt{a+\frac{b}{c+d x^2}}} \, dx","Int[1/(x^4*Sqrt[a + b/(c + d*x^2)]),x]","\frac{d^2 x (b-a c) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{3 c (a c+b)^2 \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}-\frac{a \sqrt{c} d^{3/2} \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 (a c+b)^2 \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{d^{3/2} (b-a c) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 \sqrt{c} (a c+b)^2 \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{d (b-a c) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{3 c x (a c+b)^2 \sqrt{a+\frac{b}{c+d x^2}}}-\frac{\sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{3 x^3 (a c+b) \sqrt{a+\frac{b}{c+d x^2}}}","\frac{d^2 x (b-a c) \left(a c+a d x^2+b\right)}{3 c (a c+b)^2 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{a \sqrt{c} d^{3/2} \left(a c+a d x^2+b\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 (a c+b)^2 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{d^{3/2} (b-a c) \left(a c+a d x^2+b\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 \sqrt{c} (a c+b)^2 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{d (b-a c) \left(a c+a d x^2+b\right)}{3 c x (a c+b)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{a c+a d x^2+b}{3 x^3 (a c+b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}",1,"-(Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(3*(b + a*c)*x^3*Sqrt[a + b/(c + d*x^2)]) - ((b - a*c)*d*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(3*c*(b + a*c)^2*x*Sqrt[a + b/(c + d*x^2)]) + ((b - a*c)*d^2*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(3*c*(b + a*c)^2*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]) - ((b - a*c)*d^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*Sqrt[c]*(b + a*c)^2*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)]) - (a*Sqrt[c]*d^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*(b + a*c)^2*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 475, 583, 531, 418, 492, 411}"
355,1,323,0,0.7829442,"\int \frac{x^5}{\left(a+\frac{b}{c+d x^2}\right)^{3/2}} \, dx","Int[x^5/(a + b/(c + d*x^2))^(3/2),x]","-\frac{\left(24 a^2 c^2+60 a b c+35 b^2\right) \left(c+d x^2\right) \left(a \left(c+d x^2\right)+b\right)}{24 a^3 b d^3 \sqrt{a+\frac{b}{c+d x^2}}}+\frac{\left(24 a^2 c^2+60 a b c+35 b^2\right) \left(a \left(c+d x^2\right)+b\right)}{16 a^4 d^3 \sqrt{a+\frac{b}{c+d x^2}}}-\frac{b \left(24 a^2 c^2+60 a b c+35 b^2\right) \sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{16 a^{9/2} d^3 \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{\left(c+d x^2\right)^2 \left(a \left(c+d x^2\right)+b\right)}{6 a^2 d^3 \sqrt{a+\frac{b}{c+d x^2}}}+\frac{(a c+b)^2 \left(c+d x^2\right)^2}{a^2 b d^3 \sqrt{a+\frac{b}{c+d x^2}}}","\frac{\left(6 a^2 c^2+12 a b c+7 b^2\right) \left(c+d x^2\right)^3 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{6 a^2 b^2 d^3}-\frac{\left(24 a^2 c^2+60 a b c+35 b^2\right) \left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{24 a^3 b d^3}+\frac{\left(24 a^2 c^2+60 a b c+35 b^2\right) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{16 a^4 d^3}-\frac{b \left(24 a^2 c^2+60 a b c+35 b^2\right) \tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)}{16 a^{9/2} d^3}-\frac{(a c+b)^2 \left(c+d x^2\right)^3}{a b^2 d^3 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}",1,"((b + a*c)^2*(c + d*x^2)^2)/(a^2*b*d^3*Sqrt[a + b/(c + d*x^2)]) + ((35*b^2 + 60*a*b*c + 24*a^2*c^2)*(b + a*(c + d*x^2)))/(16*a^4*d^3*Sqrt[a + b/(c + d*x^2)]) - ((35*b^2 + 60*a*b*c + 24*a^2*c^2)*(c + d*x^2)*(b + a*(c + d*x^2)))/(24*a^3*b*d^3*Sqrt[a + b/(c + d*x^2)]) + ((c + d*x^2)^2*(b + a*(c + d*x^2)))/(6*a^2*d^3*Sqrt[a + b/(c + d*x^2)]) - (b*(35*b^2 + 60*a*b*c + 24*a^2*c^2)*Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/(16*a^(9/2)*d^3*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)])","A",10,9,21,0.4286,1,"{6722, 1975, 446, 89, 80, 50, 63, 217, 206}"
356,1,242,0,0.5738659,"\int \frac{x^3}{\left(a+\frac{b}{c+d x^2}\right)^{3/2}} \, dx","Int[x^3/(a + b/(c + d*x^2))^(3/2),x]","\frac{(4 a c+5 b) \left(c+d x^2\right) \left(a \left(c+d x^2\right)+b\right)}{4 a^2 b d^2 \sqrt{a+\frac{b}{c+d x^2}}}-\frac{3 (4 a c+5 b) \left(a \left(c+d x^2\right)+b\right)}{8 a^3 d^2 \sqrt{a+\frac{b}{c+d x^2}}}+\frac{3 b (4 a c+5 b) \sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{8 a^{7/2} d^2 \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{(a c+b) \left(c+d x^2\right)^2}{a b d^2 \sqrt{a+\frac{b}{c+d x^2}}}","\frac{\left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{4 a^2 d^2}-\frac{(4 a c+7 b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{8 a^3 d^2}-\frac{b (a c+b)}{a^3 d^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}+\frac{3 b (4 a c+5 b) \tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)}{8 a^{7/2} d^2}",1,"-(((b + a*c)*(c + d*x^2)^2)/(a*b*d^2*Sqrt[a + b/(c + d*x^2)])) - (3*(5*b + 4*a*c)*(b + a*(c + d*x^2)))/(8*a^3*d^2*Sqrt[a + b/(c + d*x^2)]) + ((5*b + 4*a*c)*(c + d*x^2)*(b + a*(c + d*x^2)))/(4*a^2*b*d^2*Sqrt[a + b/(c + d*x^2)]) + (3*b*(5*b + 4*a*c)*Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/(8*a^(7/2)*d^2*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)])","A",9,8,21,0.3810,1,"{6722, 1975, 446, 78, 50, 63, 217, 206}"
357,1,104,0,0.0733392,"\int \frac{x}{\left(a+\frac{b}{c+d x^2}\right)^{3/2}} \, dx","Int[x/(a + b/(c + d*x^2))^(3/2),x]","\frac{3 \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}{2 a^2 d}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{c+d x^2}}}{\sqrt{a}}\right)}{2 a^{5/2} d}-\frac{c+d x^2}{a d \sqrt{a+\frac{b}{c+d x^2}}}","\frac{3 b}{2 a^2 d \sqrt{a+\frac{b}{c+d x^2}}}-\frac{3 b \tanh ^{-1}\left(\frac{\sqrt{a+\frac{b}{c+d x^2}}}{\sqrt{a}}\right)}{2 a^{5/2} d}+\frac{c+d x^2}{2 a d \sqrt{a+\frac{b}{c+d x^2}}}",1,"-((c + d*x^2)/(a*d*Sqrt[a + b/(c + d*x^2)])) + (3*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)])/(2*a^2*d) - (3*b*ArcTanh[Sqrt[a + b/(c + d*x^2)]/Sqrt[a]])/(2*a^(5/2)*d)","A",6,5,19,0.2632,1,"{1591, 242, 51, 63, 208}"
358,1,214,0,0.51397,"\int \frac{1}{x \left(a+\frac{b}{c+d x^2}\right)^{3/2}} \, dx","Int[1/(x*(a + b/(c + d*x^2))^(3/2)),x]","\frac{\sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{c+d x^2}}{\sqrt{a \left(c+d x^2\right)+b}}\right)}{a^{3/2} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{c^{3/2} \sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{(a c+b)^{3/2} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{b}{a (a c+b) \sqrt{a+\frac{b}{c+d x^2}}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a}}\right)}{a^{3/2}}-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{(a c+b)^{3/2}}-\frac{b}{a (a c+b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}",1,"-(b/(a*(b + a*c)*Sqrt[a + b/(c + d*x^2)])) + (Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[a]*Sqrt[c + d*x^2])/Sqrt[b + a*(c + d*x^2)]])/(a^(3/2)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)]) - (c^(3/2)*Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/((b + a*c)^(3/2)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)])","A",10,10,21,0.4762,1,"{6722, 1975, 446, 98, 157, 63, 217, 206, 93, 208}"
359,1,174,0,0.449395,"\int \frac{1}{x^3 \left(a+\frac{b}{c+d x^2}\right)^{3/2}} \, dx","Int[1/(x^3*(a + b/(c + d*x^2))^(3/2)),x]","\frac{3 b d}{2 (a c+b)^2 \sqrt{a+\frac{b}{c+d x^2}}}-\frac{c+d x^2}{2 x^2 (a c+b) \sqrt{a+\frac{b}{c+d x^2}}}-\frac{3 b \sqrt{c} d \sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{2 (a c+b)^{5/2} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}","\frac{3 b d}{2 (a c+b)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{c+d x^2}{2 x^2 (a c+b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{3 b \sqrt{c} d \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{2 (a c+b)^{5/2}}",1,"(3*b*d)/(2*(b + a*c)^2*Sqrt[a + b/(c + d*x^2)]) - (c + d*x^2)/(2*(b + a*c)*x^2*Sqrt[a + b/(c + d*x^2)]) - (3*b*Sqrt[c]*d*Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(2*(b + a*c)^(5/2)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)])","A",7,6,21,0.2857,1,"{6722, 1975, 446, 94, 93, 208}"
360,1,246,0,0.5843974,"\int \frac{1}{x^5 \left(a+\frac{b}{c+d x^2}\right)^{3/2}} \, dx","Int[1/(x^5*(a + b/(c + d*x^2))^(3/2)),x]","\frac{3 b d^2 (b-4 a c)}{8 c (a c+b)^3 \sqrt{a+\frac{b}{c+d x^2}}}-\frac{3 b d^2 (b-4 a c) \sqrt{a \left(c+d x^2\right)+b} \tanh ^{-1}\left(\frac{\sqrt{a c+b} \sqrt{c+d x^2}}{\sqrt{c} \sqrt{a \left(c+d x^2\right)+b}}\right)}{8 \sqrt{c} (a c+b)^{7/2} \sqrt{c+d x^2} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{d (b-4 a c) \left(c+d x^2\right)}{8 c x^2 (a c+b)^2 \sqrt{a+\frac{b}{c+d x^2}}}-\frac{\left(c+d x^2\right)^2}{4 c x^4 (a c+b) \sqrt{a+\frac{b}{c+d x^2}}}","-\frac{a b d^2}{(a c+b)^3 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{3 b d^2 (b-4 a c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{\sqrt{a c+b}}\right)}{8 \sqrt{c} (a c+b)^{7/2}}-\frac{d (3 b-4 a c) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{8 x^2 (a c+b)^3}-\frac{\left(c+d x^2\right)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}{4 x^4 (a c+b)^2}",1,"(3*b*(b - 4*a*c)*d^2)/(8*c*(b + a*c)^3*Sqrt[a + b/(c + d*x^2)]) - ((b - 4*a*c)*d*(c + d*x^2))/(8*c*(b + a*c)^2*x^2*Sqrt[a + b/(c + d*x^2)]) - (c + d*x^2)^2/(4*c*(b + a*c)*x^4*Sqrt[a + b/(c + d*x^2)]) - (3*b*(b - 4*a*c)*d^2*Sqrt[b + a*(c + d*x^2)]*ArcTanh[(Sqrt[b + a*c]*Sqrt[c + d*x^2])/(Sqrt[c]*Sqrt[b + a*(c + d*x^2)])])/(8*Sqrt[c]*(b + a*c)^(7/2)*Sqrt[c + d*x^2]*Sqrt[a + b/(c + d*x^2)])","A",8,7,21,0.3333,1,"{6722, 1975, 446, 96, 94, 93, 208}"
361,1,559,0,0.9062938,"\int \frac{x^4}{\left(a+\frac{b}{c+d x^2}\right)^{3/2}} \, dx","Int[x^4/(a + b/(c + d*x^2))^(3/2),x]","\frac{x \left(a^2 c^2+16 a b c+16 b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{5 a^4 d^2 \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}-\frac{\sqrt{c} \left(a^2 c^2+16 a b c+16 b^2\right) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 a^4 d^{5/2} \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{c^{3/2} (a c+8 b) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 a^3 d^{5/2} \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{x (a c+8 b) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{5 a^3 d^2 \sqrt{a+\frac{b}{c+d x^2}}}+\frac{6 x^3 \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{5 a^2 d \sqrt{a+\frac{b}{c+d x^2}}}-\frac{x^3 \left(c+d x^2\right) \sqrt{a \left(c+d x^2\right)+b}}{a d \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}","\frac{x \left(a^2 c^2+16 a b c+16 b^2\right) \left(a c+a d x^2+b\right)}{5 a^4 d^2 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{\sqrt{c} \left(a^2 c^2+16 a b c+16 b^2\right) \left(a c+a d x^2+b\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 a^4 d^{5/2} \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{c^{3/2} (a c+8 b) \left(a c+a d x^2+b\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{5 a^3 d^{5/2} \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{x (a c+8 b) \left(a c+a d x^2+b\right)}{5 a^3 d^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}+\frac{6 x^3 \left(a c+a d x^2+b\right)}{5 a^2 d \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{x^3 \left(c+d x^2\right)}{a d \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}",1,"-((x^3*(c + d*x^2)*Sqrt[b + a*(c + d*x^2)])/(a*d*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])) - ((8*b + a*c)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(5*a^3*d^2*Sqrt[a + b/(c + d*x^2)]) + (6*x^3*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(5*a^2*d*Sqrt[a + b/(c + d*x^2)]) + ((16*b^2 + 16*a*b*c + a^2*c^2)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(5*a^4*d^2*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]) - (Sqrt[c]*(16*b^2 + 16*a*b*c + a^2*c^2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(5*a^4*d^(5/2)*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)]) + (c^(3/2)*(8*b + a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(5*a^3*d^(5/2)*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)])","A",9,9,21,0.4286,1,"{6722, 1975, 467, 581, 582, 531, 418, 492, 411}"
362,1,475,0,0.6606147,"\int \frac{x^2}{\left(a+\frac{b}{c+d x^2}\right)^{3/2}} \, dx","Int[x^2/(a + b/(c + d*x^2))^(3/2),x]","-\frac{c^{3/2} (a c+4 b) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 a^2 d^{3/2} (a c+b) \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{\sqrt{c} (a c+8 b) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 a^3 d^{3/2} \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{4 x \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{3 a^2 d \sqrt{a+\frac{b}{c+d x^2}}}-\frac{x (a c+8 b) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{3 a^3 d \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}-\frac{x \left(c+d x^2\right) \sqrt{a \left(c+d x^2\right)+b}}{a d \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}","-\frac{c^{3/2} (a c+4 b) \left(a c+a d x^2+b\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 a^2 d^{3/2} (a c+b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{\sqrt{c} (a c+8 b) \left(a c+a d x^2+b\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 a^3 d^{3/2} \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{4 x \left(a c+a d x^2+b\right)}{3 a^2 d \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{x (a c+8 b) \left(a c+a d x^2+b\right)}{3 a^3 d \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{x \left(c+d x^2\right)}{a d \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}",1,"-((x*(c + d*x^2)*Sqrt[b + a*(c + d*x^2)])/(a*d*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])) + (4*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(3*a^2*d*Sqrt[a + b/(c + d*x^2)]) - ((8*b + a*c)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(3*a^3*d*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]) + (Sqrt[c]*(8*b + a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*a^3*d^(3/2)*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)]) - (c^(3/2)*(4*b + a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*a^2*(b + a*c)*d^(3/2)*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 467, 528, 531, 418, 492, 411}"
363,1,411,0,0.3093552,"\int \frac{1}{\left(a+\frac{b}{c+d x^2}\right)^{3/2}} \, dx","Int[(a + b/(c + d*x^2))^(-3/2),x]","\frac{x (a c+2 b) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{a^2 (a c+b) \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}-\frac{\sqrt{c} (a c+2 b) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{a^2 \sqrt{d} (a c+b) \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{c^{3/2} \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{a \sqrt{d} (a c+b) \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{b x \sqrt{a \left(c+d x^2\right)+b}}{a (a c+b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}","\frac{x (a c+2 b) \left(a c+a d x^2+b\right)}{a^2 (a c+b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{\sqrt{c} (a c+2 b) \left(a c+a d x^2+b\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{a^2 \sqrt{d} (a c+b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{c^{3/2} \left(a c+a d x^2+b\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{a \sqrt{d} (a c+b) \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{b x}{a (a c+b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}",1,"-((b*x*Sqrt[b + a*(c + d*x^2)])/(a*(b + a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])) + ((2*b + a*c)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(a^2*(b + a*c)*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]) - (Sqrt[c]*(2*b + a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(a^2*(b + a*c)*Sqrt[d]*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)]) + (c^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(a*(b + a*c)*Sqrt[d]*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)])","A",7,7,17,0.4118,1,"{6722, 1974, 413, 531, 418, 492, 411}"
364,1,476,0,0.680291,"\int \frac{1}{x^2 \left(a+\frac{b}{c+d x^2}\right)^{3/2}} \, dx","Int[1/(x^2*(a + b/(c + d*x^2))^(3/2)),x]","\frac{c^{3/2} \sqrt{d} \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{(a c+b)^2 \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{(b-a c) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{a x (a c+b)^2 \sqrt{a+\frac{b}{c+d x^2}}}-\frac{d x (b-a c) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{a (a c+b)^2 \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}-\frac{b \sqrt{a \left(c+d x^2\right)+b}}{a x (a c+b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}+\frac{\sqrt{c} \sqrt{d} (b-a c) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{a (a c+b)^2 \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}","\frac{c^{3/2} \sqrt{d} \left(a c+a d x^2+b\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{(a c+b)^2 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}+\frac{(b-a c) \left(a c+a d x^2+b\right)}{a x (a c+b)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{d x (b-a c) \left(a c+a d x^2+b\right)}{a (a c+b)^2 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{b}{a x (a c+b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}+\frac{\sqrt{c} \sqrt{d} (b-a c) \left(a c+a d x^2+b\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{a (a c+b)^2 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}",1,"-((b*Sqrt[b + a*(c + d*x^2)])/(a*(b + a*c)*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])) + ((b - a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(a*(b + a*c)^2*x*Sqrt[a + b/(c + d*x^2)]) - ((b - a*c)*d*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(a*(b + a*c)^2*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]) + (Sqrt[c]*(b - a*c)*Sqrt[d]*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(a*(b + a*c)^2*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)]) + (c^(3/2)*Sqrt[d]*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/((b + a*c)^2*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)])","A",8,8,21,0.3810,1,"{6722, 1975, 468, 583, 531, 418, 492, 411}"
365,1,567,0,0.8667208,"\int \frac{1}{x^4 \left(a+\frac{b}{c+d x^2}\right)^{3/2}} \, dx","Int[1/(x^4*(a + b/(c + d*x^2))^(3/2)),x]","\frac{d^2 x (7 b-a c) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{3 (a c+b)^3 \left(c+d x^2\right) \sqrt{a+\frac{b}{c+d x^2}}}+\frac{\sqrt{c} d^{3/2} (3 b-a c) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 (a c+b)^3 \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{\sqrt{c} d^{3/2} (7 b-a c) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 (a c+b)^3 \left(c+d x^2\right) \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}} \sqrt{a+\frac{b}{c+d x^2}}}-\frac{d (7 b-a c) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{3 x (a c+b)^3 \sqrt{a+\frac{b}{c+d x^2}}}+\frac{(3 b-a c) \sqrt{a c+a d x^2+b} \sqrt{a \left(c+d x^2\right)+b}}{3 a x^3 (a c+b)^2 \sqrt{a+\frac{b}{c+d x^2}}}-\frac{b \sqrt{a \left(c+d x^2\right)+b}}{a x^3 (a c+b) \sqrt{a c+a d x^2+b} \sqrt{a+\frac{b}{c+d x^2}}}","\frac{d^2 x (7 b-a c) \left(a c+a d x^2+b\right)}{3 (a c+b)^3 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}+\frac{\sqrt{c} d^{3/2} (3 b-a c) \left(a c+a d x^2+b\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 (a c+b)^3 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{\sqrt{c} d^{3/2} (7 b-a c) \left(a c+a d x^2+b\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|\frac{b}{b+a c}\right)}{3 (a c+b)^3 \left(c+d x^2\right) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}} \sqrt{\frac{c \left(a c+a d x^2+b\right)}{(a c+b) \left(c+d x^2\right)}}}-\frac{d (7 b-a c) \left(a c+a d x^2+b\right)}{3 x (a c+b)^3 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}+\frac{(3 b-a c) \left(a c+a d x^2+b\right)}{3 a x^3 (a c+b)^2 \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}-\frac{b}{a x^3 (a c+b) \sqrt{\frac{a c+a d x^2+b}{c+d x^2}}}",1,"-((b*Sqrt[b + a*(c + d*x^2)])/(a*(b + a*c)*x^3*Sqrt[b + a*c + a*d*x^2]*Sqrt[a + b/(c + d*x^2)])) + ((3*b - a*c)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(3*a*(b + a*c)^2*x^3*Sqrt[a + b/(c + d*x^2)]) - ((7*b - a*c)*d*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(3*(b + a*c)^3*x*Sqrt[a + b/(c + d*x^2)]) + ((7*b - a*c)*d^2*x*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)])/(3*(b + a*c)^3*(c + d*x^2)*Sqrt[a + b/(c + d*x^2)]) - (Sqrt[c]*(7*b - a*c)*d^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*(b + a*c)^3*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)]) + (Sqrt[c]*(3*b - a*c)*d^(3/2)*Sqrt[b + a*c + a*d*x^2]*Sqrt[b + a*(c + d*x^2)]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], b/(b + a*c)])/(3*(b + a*c)^3*(c + d*x^2)*Sqrt[(c*(b + a*c + a*d*x^2))/((b + a*c)*(c + d*x^2))]*Sqrt[a + b/(c + d*x^2)])","A",9,8,21,0.3810,1,"{6722, 1975, 468, 583, 531, 418, 492, 411}"
366,1,75,0,0.0174213,"\int \frac{\sqrt{a x^{23}}}{\sqrt{1+x^5}} \, dx","Int[Sqrt[a*x^23]/Sqrt[1 + x^5],x]","\frac{\sqrt{x^5+1} \sqrt{a x^{23}}}{10 x^4}-\frac{3 \sqrt{x^5+1} \sqrt{a x^{23}}}{20 x^9}+\frac{3 \sqrt{a x^{23}} \sinh ^{-1}\left(x^{5/2}\right)}{20 x^{23/2}}","\frac{\sqrt{x^5+1} \sqrt{a x^{23}}}{10 x^4}-\frac{3 \sqrt{x^5+1} \sqrt{a x^{23}}}{20 x^9}+\frac{3 \sqrt{a x^{23}} \sinh ^{-1}\left(x^{5/2}\right)}{20 x^{23/2}}",1,"(-3*Sqrt[a*x^23]*Sqrt[1 + x^5])/(20*x^9) + (Sqrt[a*x^23]*Sqrt[1 + x^5])/(10*x^4) + (3*Sqrt[a*x^23]*ArcSinh[x^(5/2)])/(20*x^(23/2))","A",6,5,19,0.2632,1,"{15, 321, 329, 275, 215}"
367,1,50,0,0.012267,"\int \frac{\sqrt{a x^{13}}}{\sqrt{1+x^5}} \, dx","Int[Sqrt[a*x^13]/Sqrt[1 + x^5],x]","\frac{\sqrt{x^5+1} \sqrt{a x^{13}}}{5 x^4}-\frac{\sqrt{a x^{13}} \sinh ^{-1}\left(x^{5/2}\right)}{5 x^{13/2}}","\frac{\sqrt{x^5+1} \sqrt{a x^{13}}}{5 x^4}-\frac{\sqrt{a x^{13}} \sinh ^{-1}\left(x^{5/2}\right)}{5 x^{13/2}}",1,"(Sqrt[a*x^13]*Sqrt[1 + x^5])/(5*x^4) - (Sqrt[a*x^13]*ArcSinh[x^(5/2)])/(5*x^(13/2))","A",5,5,19,0.2632,1,"{15, 321, 329, 275, 215}"
368,1,24,0,0.0078643,"\int \frac{\sqrt{a x^3}}{\sqrt{1+x^5}} \, dx","Int[Sqrt[a*x^3]/Sqrt[1 + x^5],x]","\frac{2 \sqrt{a x^3} \sinh ^{-1}\left(x^{5/2}\right)}{5 x^{3/2}}","\frac{2 \sqrt{a x^3} \sinh ^{-1}\left(x^{5/2}\right)}{5 x^{3/2}}",1,"(2*Sqrt[a*x^3]*ArcSinh[x^(5/2)])/(5*x^(3/2))","A",4,4,19,0.2105,1,"{15, 329, 275, 215}"
369,1,23,0,0.0043128,"\int \frac{\sqrt{\frac{a}{x^7}}}{\sqrt{1+x^5}} \, dx","Int[Sqrt[a/x^7]/Sqrt[1 + x^5],x]","-\frac{2}{5} x \sqrt{x^5+1} \sqrt{\frac{a}{x^7}}","-\frac{2}{5} x \sqrt{x^5+1} \sqrt{\frac{a}{x^7}}",1,"(-2*Sqrt[a/x^7]*x*Sqrt[1 + x^5])/5","A",2,2,19,0.1053,1,"{15, 264}"
370,1,49,0,0.0093764,"\int \frac{\sqrt{\frac{a}{x^{17}}}}{\sqrt{1+x^5}} \, dx","Int[Sqrt[a/x^17]/Sqrt[1 + x^5],x]","\frac{4}{15} x^6 \sqrt{x^5+1} \sqrt{\frac{a}{x^{17}}}-\frac{2}{15} x \sqrt{x^5+1} \sqrt{\frac{a}{x^{17}}}","\frac{4}{15} x^6 \sqrt{x^5+1} \sqrt{\frac{a}{x^{17}}}-\frac{2}{15} x \sqrt{x^5+1} \sqrt{\frac{a}{x^{17}}}",1,"(-2*Sqrt[a/x^17]*x*Sqrt[1 + x^5])/15 + (4*Sqrt[a/x^17]*x^6*Sqrt[1 + x^5])/15","A",3,3,19,0.1579,1,"{15, 271, 264}"
371,1,37,0,0.0077202,"\int \frac{\sqrt{a x^6}}{x \left(1-x^4\right)} \, dx","Int[Sqrt[a*x^6]/(x*(1 - x^4)),x]","\frac{\sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}-\frac{\sqrt{a x^6} \tan ^{-1}(x)}{2 x^3}","\frac{\sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}-\frac{\sqrt{a x^6} \tan ^{-1}(x)}{2 x^3}",1,"-(Sqrt[a*x^6]*ArcTan[x])/(2*x^3) + (Sqrt[a*x^6]*ArcTanh[x])/(2*x^3)","A",4,4,22,0.1818,1,"{15, 298, 203, 206}"
372,1,37,0,0.012713,"\int \frac{\sqrt{a x^6}}{x-x^5} \, dx","Int[Sqrt[a*x^6]/(x - x^5),x]","\frac{\sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}-\frac{\sqrt{a x^6} \tan ^{-1}(x)}{2 x^3}","\frac{\sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}-\frac{\sqrt{a x^6} \tan ^{-1}(x)}{2 x^3}",1,"-(Sqrt[a*x^6]*ArcTan[x])/(2*x^3) + (Sqrt[a*x^6]*ArcTanh[x])/(2*x^3)","A",5,5,19,0.2632,1,"{15, 1584, 298, 203, 206}"
373,1,71,0,0.0146736,"\int \frac{\left(a x^6\right)^{3/2}}{x \left(1-x^4\right)} \, dx","Int[(a*x^6)^(3/2)/(x*(1 - x^4)),x]","-\frac{1}{5} a x^2 \sqrt{a x^6}-\frac{a \sqrt{a x^6}}{x^2}+\frac{a \sqrt{a x^6} \tan ^{-1}(x)}{2 x^3}+\frac{a \sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}","-\frac{1}{5} a x^2 \sqrt{a x^6}-\frac{a \sqrt{a x^6}}{x^2}+\frac{a \sqrt{a x^6} \tan ^{-1}(x)}{2 x^3}+\frac{a \sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}",1,"-((a*Sqrt[a*x^6])/x^2) - (a*x^2*Sqrt[a*x^6])/5 + (a*Sqrt[a*x^6]*ArcTan[x])/(2*x^3) + (a*Sqrt[a*x^6]*ArcTanh[x])/(2*x^3)","A",6,5,22,0.2273,1,"{15, 302, 212, 206, 203}"
374,1,49,0,0.0133674,"\int \left(\frac{1}{1-x^4}-\frac{\sqrt{a x^6}}{x \left(1-x^4\right)}\right) \, dx","Int[(1 - x^4)^(-1) - Sqrt[a*x^6]/(x*(1 - x^4)),x]","\frac{\sqrt{a x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)","\frac{\sqrt{a x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)",1,"ArcTan[x]/2 + (Sqrt[a*x^6]*ArcTan[x])/(2*x^3) + ArcTanh[x]/2 - (Sqrt[a*x^6]*ArcTanh[x])/(2*x^3)","A",8,5,33,0.1515,1,"{212, 206, 203, 15, 298}"
375,1,49,0,0.0177482,"\int \left(\frac{1}{1-x^4}-\frac{\sqrt{a x^6}}{x-x^5}\right) \, dx","Int[(1 - x^4)^(-1) - Sqrt[a*x^6]/(x - x^5),x]","\frac{\sqrt{a x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)","\frac{\sqrt{a x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{a x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)",1,"ArcTan[x]/2 + (Sqrt[a*x^6]*ArcTan[x])/(2*x^3) + ArcTanh[x]/2 - (Sqrt[a*x^6]*ArcTanh[x])/(2*x^3)","A",9,6,30,0.2000,1,"{212, 206, 203, 15, 1584, 298}"
376,1,44,0,0.0148215,"\int \frac{\sqrt{a x^3}}{x-x^3} \, dx","Int[Sqrt[a*x^3]/(x - x^3),x]","\frac{\sqrt{a x^3} \tanh ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}-\frac{\sqrt{a x^3} \tan ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}","\frac{\sqrt{a x^3} \tanh ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}-\frac{\sqrt{a x^3} \tan ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}",1,"-((Sqrt[a*x^3]*ArcTan[Sqrt[x]])/x^(3/2)) + (Sqrt[a*x^3]*ArcTanh[Sqrt[x]])/x^(3/2)","A",6,6,19,0.3158,1,"{15, 1584, 329, 298, 203, 206}"
377,1,44,0,0.0064502,"\int \frac{\sqrt{a x^4}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[a*x^4]/Sqrt[1 + x^2],x]","\frac{\sqrt{x^2+1} \sqrt{a x^4}}{2 x}-\frac{\sqrt{a x^4} \sinh ^{-1}(x)}{2 x^2}","\frac{\sqrt{x^2+1} \sqrt{a x^4}}{2 x}-\frac{\sqrt{a x^4} \sinh ^{-1}(x)}{2 x^2}",1,"(Sqrt[a*x^4]*Sqrt[1 + x^2])/(2*x) - (Sqrt[a*x^4]*ArcSinh[x])/(2*x^2)","A",3,3,19,0.1579,1,"{15, 321, 215}"
378,1,83,0,0.0258057,"\int \frac{\sqrt{a x^3}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[a*x^3]/Sqrt[1 + x^2],x]","\frac{2 \sqrt{x^2+1} \sqrt{a x^3}}{3 x}-\frac{(x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{a x^3} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{3 x^{3/2} \sqrt{x^2+1}}","\frac{2 \sqrt{x^2+1} \sqrt{a x^3}}{3 x}-\frac{(x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{a x^3} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{3 x^{3/2} \sqrt{x^2+1}}",1,"(2*Sqrt[a*x^3]*Sqrt[1 + x^2])/(3*x) - (Sqrt[a*x^3]*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/(3*x^(3/2)*Sqrt[1 + x^2])","A",4,4,19,0.2105,1,"{15, 321, 329, 220}"
379,1,22,0,0.0031639,"\int \frac{\sqrt{a x^2}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[a*x^2]/Sqrt[1 + x^2],x]","\frac{\sqrt{x^2+1} \sqrt{a x^2}}{x}","\frac{\sqrt{x^2+1} \sqrt{a x^2}}{x}",1,"(Sqrt[a*x^2]*Sqrt[1 + x^2])/x","A",2,2,19,0.1053,1,"{15, 261}"
380,1,131,0,0.0818356,"\int \frac{\sqrt{a x}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[a*x]/Sqrt[1 + x^2],x]","\frac{2 \sqrt{x^2+1} \sqrt{a x}}{x+1}+\frac{\sqrt{a} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a x}}{\sqrt{a}}\right)|\frac{1}{2}\right)}{\sqrt{x^2+1}}-\frac{2 \sqrt{a} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{a x}}{\sqrt{a}}\right)|\frac{1}{2}\right)}{\sqrt{x^2+1}}","\frac{2 \sqrt{x^2+1} \sqrt{a x}}{x+1}+\frac{\sqrt{a} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt{a x}}{\sqrt{a}}\right)|\frac{1}{2}\right)}{\sqrt{x^2+1}}-\frac{2 \sqrt{a} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt{a x}}{\sqrt{a}}\right)|\frac{1}{2}\right)}{\sqrt{x^2+1}}",1,"(2*Sqrt[a*x]*Sqrt[1 + x^2])/(1 + x) - (2*Sqrt[a]*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticE[2*ArcTan[Sqrt[a*x]/Sqrt[a]], 1/2])/Sqrt[1 + x^2] + (Sqrt[a]*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[a*x]/Sqrt[a]], 1/2])/Sqrt[1 + x^2]","A",4,4,17,0.2353,1,"{329, 305, 220, 1196}"
381,1,54,0,0.0206193,"\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[a/x]/Sqrt[1 + x^2],x]","\frac{\sqrt{x} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{\frac{a}{x}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{\sqrt{x^2+1}}","\frac{\sqrt{x} (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} \sqrt{\frac{a}{x}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{\sqrt{x^2+1}}",1,"(Sqrt[a/x]*Sqrt[x]*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/Sqrt[1 + x^2]","A",3,3,19,0.1579,1,"{15, 329, 220}"
382,1,22,0,0.0085699,"\int \frac{\sqrt{\frac{a}{x^2}}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[a/x^2]/Sqrt[1 + x^2],x]","x \left(-\sqrt{\frac{a}{x^2}}\right) \tanh ^{-1}\left(\sqrt{x^2+1}\right)","x \left(-\sqrt{\frac{a}{x^2}}\right) \tanh ^{-1}\left(\sqrt{x^2+1}\right)",1,"-(Sqrt[a/x^2]*x*ArcTanh[Sqrt[1 + x^2]])","A",4,4,19,0.2105,1,"{15, 266, 63, 207}"
383,1,159,0,0.0518476,"\int \frac{\sqrt{\frac{a}{x^3}}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[a/x^3]/Sqrt[1 + x^2],x]","\frac{2 \sqrt{x^2+1} x^2 \sqrt{\frac{a}{x^3}}}{x+1}-2 \sqrt{x^2+1} x \sqrt{\frac{a}{x^3}}+\frac{(x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} x^{3/2} \sqrt{\frac{a}{x^3}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{\sqrt{x^2+1}}-\frac{2 (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} x^{3/2} \sqrt{\frac{a}{x^3}} E\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{\sqrt{x^2+1}}","\frac{2 \sqrt{x^2+1} x^2 \sqrt{\frac{a}{x^3}}}{x+1}-2 \sqrt{x^2+1} x \sqrt{\frac{a}{x^3}}+\frac{(x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} x^{3/2} \sqrt{\frac{a}{x^3}} F\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{\sqrt{x^2+1}}-\frac{2 (x+1) \sqrt{\frac{x^2+1}{(x+1)^2}} x^{3/2} \sqrt{\frac{a}{x^3}} E\left(2 \tan ^{-1}\left(\sqrt{x}\right)|\frac{1}{2}\right)}{\sqrt{x^2+1}}",1,"-2*Sqrt[a/x^3]*x*Sqrt[1 + x^2] + (2*Sqrt[a/x^3]*x^2*Sqrt[1 + x^2])/(1 + x) - (2*Sqrt[a/x^3]*x^(3/2)*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticE[2*ArcTan[Sqrt[x]], 1/2])/Sqrt[1 + x^2] + (Sqrt[a/x^3]*x^(3/2)*(1 + x)*Sqrt[(1 + x^2)/(1 + x)^2]*EllipticF[2*ArcTan[Sqrt[x]], 1/2])/Sqrt[1 + x^2]","A",6,6,19,0.3158,1,"{15, 325, 329, 305, 220, 1196}"
384,1,21,0,0.0042075,"\int \frac{\sqrt{\frac{a}{x^4}}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[a/x^4]/Sqrt[1 + x^2],x]","x \sqrt{x^2+1} \left(-\sqrt{\frac{a}{x^4}}\right)","x \sqrt{x^2+1} \left(-\sqrt{\frac{a}{x^4}}\right)",1,"-(Sqrt[a/x^4]*x*Sqrt[1 + x^2])","A",2,2,19,0.1053,1,"{15, 264}"
385,1,25,0,0.0040289,"\int \frac{\sqrt{a x^4}}{\sqrt{1+x^3}} \, dx","Int[Sqrt[a*x^4]/Sqrt[1 + x^3],x]","\frac{2 \sqrt{x^3+1} \sqrt{a x^4}}{3 x^2}","\frac{2 \sqrt{x^3+1} \sqrt{a x^4}}{3 x^2}",1,"(2*Sqrt[a*x^4]*Sqrt[1 + x^3])/(3*x^2)","A",2,2,19,0.1053,1,"{15, 261}"
386,1,292,0,0.2316848,"\int \frac{\sqrt{a x^3}}{\sqrt{1+x^3}} \, dx","Int[Sqrt[a*x^3]/Sqrt[1 + x^3],x]","\frac{\left(1+\sqrt{3}\right) \sqrt{x^3+1} \sqrt{a x^3}}{x \left(\left(1+\sqrt{3}\right) x+1\right)}-\frac{\left(1-\sqrt{3}\right) (x+1) \sqrt{\frac{x^2-x+1}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{a x^3} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x+1}{\left(1+\sqrt{3}\right) x+1}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} x \sqrt{\frac{x (x+1)}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{a x^3} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x+1}{\left(1+\sqrt{3}\right) x+1}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{x \sqrt{\frac{x (x+1)}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{x^3+1}}","\frac{\left(1+\sqrt{3}\right) \sqrt{x^3+1} \sqrt{a x^3}}{x \left(\left(1+\sqrt{3}\right) x+1\right)}-\frac{\left(1-\sqrt{3}\right) (x+1) \sqrt{\frac{x^2-x+1}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{a x^3} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x+1}{\left(1+\sqrt{3}\right) x+1}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} x \sqrt{\frac{x (x+1)}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{a x^3} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x+1}{\left(1+\sqrt{3}\right) x+1}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{x \sqrt{\frac{x (x+1)}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{x^3+1}}",1,"((1 + Sqrt[3])*Sqrt[a*x^3]*Sqrt[1 + x^3])/(x*(1 + (1 + Sqrt[3])*x)) - (3^(1/4)*Sqrt[a*x^3]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticE[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(x*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[1 + x^3]) - ((1 - Sqrt[3])*Sqrt[a*x^3]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(2*3^(1/4)*x*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[1 + x^3])","A",5,5,19,0.2632,1,"{15, 329, 308, 225, 1881}"
387,1,260,0,0.0607094,"\int \frac{\sqrt{a x^2}}{\sqrt{1+x^3}} \, dx","Int[Sqrt[a*x^2]/Sqrt[1 + x^3],x]","\frac{2 \sqrt{x^3+1} \sqrt{a x^2}}{x \left(x+\sqrt{3}+1\right)}+\frac{2 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{a x^2} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} x \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{a x^2} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{x \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{2 \sqrt{x^3+1} \sqrt{a x^2}}{x \left(x+\sqrt{3}+1\right)}+\frac{2 \sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{a x^2} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} x \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{a x^2} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{x \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"(2*Sqrt[a*x^2]*Sqrt[1 + x^3])/(x*(1 + Sqrt[3] + x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*Sqrt[a*x^2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(x*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (2*Sqrt[2]*Sqrt[a*x^2]*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*x*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",4,4,19,0.2105,1,"{15, 303, 218, 1877}"
388,1,23,0,0.015498,"\int \frac{\sqrt{a x}}{\sqrt{1+x^3}} \, dx","Int[Sqrt[a*x]/Sqrt[1 + x^3],x]","\frac{2}{3} \sqrt{a} \sinh ^{-1}\left(\frac{(a x)^{3/2}}{a^{3/2}}\right)","\frac{2}{3} \sqrt{a} \sinh ^{-1}\left(\frac{(a x)^{3/2}}{a^{3/2}}\right)",1,"(2*Sqrt[a]*ArcSinh[(a*x)^(3/2)/a^(3/2)])/3","A",3,3,17,0.1765,1,"{329, 275, 215}"
389,1,116,0,0.073026,"\int \frac{\sqrt{\frac{a}{x}}}{\sqrt{1+x^3}} \, dx","Int[Sqrt[a/x]/Sqrt[1 + x^3],x]","\frac{x (x+1) \sqrt{\frac{x^2-x+1}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{\frac{a}{x}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x+1}{\left(1+\sqrt{3}\right) x+1}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt{\frac{x (x+1)}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{x^3+1}}","\frac{x (x+1) \sqrt{\frac{x^2-x+1}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{\frac{a}{x}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x+1}{\left(1+\sqrt{3}\right) x+1}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt{\frac{x (x+1)}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{x^3+1}}",1,"(Sqrt[a/x]*x*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[1 + x^3])","A",3,3,19,0.1579,1,"{15, 329, 225}"
390,1,24,0,0.0087115,"\int \frac{\sqrt{\frac{a}{x^2}}}{\sqrt{1+x^3}} \, dx","Int[Sqrt[a/x^2]/Sqrt[1 + x^3],x]","-\frac{2}{3} x \sqrt{\frac{a}{x^2}} \tanh ^{-1}\left(\sqrt{x^3+1}\right)","-\frac{2}{3} x \sqrt{\frac{a}{x^2}} \tanh ^{-1}\left(\sqrt{x^3+1}\right)",1,"(-2*Sqrt[a/x^2]*x*ArcTanh[Sqrt[1 + x^3]])/3","A",4,4,19,0.2105,1,"{15, 266, 63, 207}"
391,1,312,0,0.2277963,"\int \frac{\sqrt{\frac{a}{x^3}}}{\sqrt{1+x^3}} \, dx","Int[Sqrt[a/x^3]/Sqrt[1 + x^3],x]","\frac{2 \left(1+\sqrt{3}\right) \sqrt{x^3+1} x^2 \sqrt{\frac{a}{x^3}}}{\left(1+\sqrt{3}\right) x+1}-2 \sqrt{x^3+1} x \sqrt{\frac{a}{x^3}}-\frac{\left(1-\sqrt{3}\right) (x+1) \sqrt{\frac{x^2-x+1}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} x^2 \sqrt{\frac{a}{x^3}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x+1}{\left(1+\sqrt{3}\right) x+1}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt{\frac{x (x+1)}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{x^3+1}}-\frac{2 \sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} x^2 \sqrt{\frac{a}{x^3}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x+1}{\left(1+\sqrt{3}\right) x+1}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt{\frac{x (x+1)}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{x^3+1}}","\frac{2 \left(1+\sqrt{3}\right) \sqrt{x^3+1} x^2 \sqrt{\frac{a}{x^3}}}{\left(1+\sqrt{3}\right) x+1}-2 \sqrt{x^3+1} x \sqrt{\frac{a}{x^3}}-\frac{\left(1-\sqrt{3}\right) (x+1) \sqrt{\frac{x^2-x+1}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} x^2 \sqrt{\frac{a}{x^3}} F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x+1}{\left(1+\sqrt{3}\right) x+1}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt[4]{3} \sqrt{\frac{x (x+1)}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{x^3+1}}-\frac{2 \sqrt[4]{3} (x+1) \sqrt{\frac{x^2-x+1}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} x^2 \sqrt{\frac{a}{x^3}} E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) x+1}{\left(1+\sqrt{3}\right) x+1}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{\sqrt{\frac{x (x+1)}{\left(\left(1+\sqrt{3}\right) x+1\right)^2}} \sqrt{x^3+1}}",1,"-2*Sqrt[a/x^3]*x*Sqrt[1 + x^3] + (2*(1 + Sqrt[3])*Sqrt[a/x^3]*x^2*Sqrt[1 + x^3])/(1 + (1 + Sqrt[3])*x) - (2*3^(1/4)*Sqrt[a/x^3]*x^2*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticE[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[1 + x^3]) - ((1 - Sqrt[3])*Sqrt[a/x^3]*x^2*(1 + x)*Sqrt[(1 - x + x^2)/(1 + (1 + Sqrt[3])*x)^2]*EllipticF[ArcCos[(1 + (1 - Sqrt[3])*x)/(1 + (1 + Sqrt[3])*x)], (2 + Sqrt[3])/4])/(3^(1/4)*Sqrt[(x*(1 + x))/(1 + (1 + Sqrt[3])*x)^2]*Sqrt[1 + x^3])","A",6,6,19,0.3158,1,"{15, 325, 329, 308, 225, 1881}"
392,1,281,0,0.0730181,"\int \frac{\sqrt{\frac{a}{x^4}}}{\sqrt{1+x^3}} \, dx","Int[Sqrt[a/x^4]/Sqrt[1 + x^3],x]","\frac{\sqrt{x^3+1} x^2 \sqrt{\frac{a}{x^4}}}{x+\sqrt{3}+1}-\sqrt{x^3+1} x \sqrt{\frac{a}{x^4}}+\frac{\sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} x^2 \sqrt{\frac{a}{x^4}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} x^2 \sqrt{\frac{a}{x^4}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}","\frac{\sqrt{x^3+1} x^2 \sqrt{\frac{a}{x^4}}}{x+\sqrt{3}+1}-\sqrt{x^3+1} x \sqrt{\frac{a}{x^4}}+\frac{\sqrt{2} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} x^2 \sqrt{\frac{a}{x^4}} F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} (x+1) \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} x^2 \sqrt{\frac{a}{x^4}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^3+1}}",1,"-(Sqrt[a/x^4]*x*Sqrt[1 + x^3]) + (Sqrt[a/x^4]*x^2*Sqrt[1 + x^3])/(1 + Sqrt[3] + x) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*Sqrt[a/x^4]*x^2*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(2*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3]) + (Sqrt[2]*Sqrt[a/x^4]*x^2*(1 + x)*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 + x^3])","A",5,5,19,0.2632,1,"{15, 325, 303, 218, 1877}"
393,1,37,0,0.0122416,"\int \frac{\sqrt{a x^{2 n}}}{\sqrt{1+x^n}} \, dx","Int[Sqrt[a*x^(2*n)]/Sqrt[1 + x^n],x]","\frac{x \sqrt{a x^{2 n}} \, _2F_1\left(\frac{1}{2},1+\frac{1}{n};2+\frac{1}{n};-x^n\right)}{n+1}","\frac{x \sqrt{a x^{2 n}} \, _2F_1\left(\frac{1}{2},1+\frac{1}{n};2+\frac{1}{n};-x^n\right)}{n+1}",1,"(x*Sqrt[a*x^(2*n)]*Hypergeometric2F1[1/2, 1 + n^(-1), 2 + n^(-1), -x^n])/(1 + n)","A",2,2,21,0.09524,1,"{15, 364}"
394,1,48,0,0.0141593,"\int \frac{\sqrt{a x^n}}{\sqrt{1+x^n}} \, dx","Int[Sqrt[a*x^n]/Sqrt[1 + x^n],x]","\frac{2 x \sqrt{a x^n} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(1+\frac{2}{n}\right);\frac{1}{2} \left(3+\frac{2}{n}\right);-x^n\right)}{n+2}","\frac{2 x \sqrt{a x^n} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(1+\frac{2}{n}\right);\frac{1}{2} \left(3+\frac{2}{n}\right);-x^n\right)}{n+2}",1,"(2*x*Sqrt[a*x^n]*Hypergeometric2F1[1/2, (1 + 2/n)/2, (3 + 2/n)/2, -x^n])/(2 + n)","A",2,2,19,0.1053,1,"{15, 364}"
395,1,52,0,0.0148895,"\int \frac{\sqrt{a x^{n/2}}}{\sqrt{1+x^n}} \, dx","Int[Sqrt[a*x^(n/2)]/Sqrt[1 + x^n],x]","\frac{4 x \sqrt{a x^{n/2}} \, _2F_1\left(\frac{1}{2},\frac{1}{4} \left(1+\frac{4}{n}\right);\frac{1}{4} \left(5+\frac{4}{n}\right);-x^n\right)}{n+4}","\frac{4 x \sqrt{a x^{n/2}} \, _2F_1\left(\frac{1}{2},\frac{1}{4} \left(1+\frac{4}{n}\right);\frac{1}{4} \left(5+\frac{4}{n}\right);-x^n\right)}{n+4}",1,"(4*x*Sqrt[a*x^(n/2)]*Hypergeometric2F1[1/2, (1 + 4/n)/4, (5 + 4/n)/4, -x^n])/(4 + n)","A",2,2,23,0.08696,1,"{15, 364}"
396,1,80,0,0.0295837,"\int \left(\frac{\sqrt{a x^{2 n}}}{\sqrt{1+x^n}}+\frac{2 x^{-n} \sqrt{a x^{2 n}}}{(2+n) \sqrt{1+x^n}}\right) \, dx","Int[Sqrt[a*x^(2*n)]/Sqrt[1 + x^n] + (2*Sqrt[a*x^(2*n)])/((2 + n)*x^n*Sqrt[1 + x^n]),x]","\frac{2 x^{1-n} \sqrt{a x^{2 n}} \, _2F_1\left(\frac{1}{2},\frac{1}{n};1+\frac{1}{n};-x^n\right)}{n+2}+\frac{x \sqrt{a x^{2 n}} \, _2F_1\left(\frac{1}{2},1+\frac{1}{n};2+\frac{1}{n};-x^n\right)}{n+1}","\frac{2 x^{1-n} \sqrt{x^n+1} \sqrt{a x^{2 n}}}{n+2}",1,"(x*Sqrt[a*x^(2*n)]*Hypergeometric2F1[1/2, 1 + n^(-1), 2 + n^(-1), -x^n])/(1 + n) + (2*x^(1 - n)*Sqrt[a*x^(2*n)]*Hypergeometric2F1[1/2, n^(-1), 1 + n^(-1), -x^n])/(2 + n)","C",5,3,54,0.05556,1,"{15, 364, 245}"
397,1,114,0,0.0561957,"\int \frac{\sqrt{a x}}{\sqrt{d+e x} \sqrt{e+f x}} \, dx","Int[Sqrt[a*x]/(Sqrt[d + e*x]*Sqrt[e + f*x]),x]","\frac{2 \sqrt{a x} \sqrt{d f-e^2} \sqrt{\frac{e (e+f x)}{e^2-d f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{d+e x}}{\sqrt{d f-e^2}}\right)|1-\frac{e^2}{d f}\right)}{e \sqrt{f} \sqrt{-\frac{e x}{d}} \sqrt{e+f x}}","\frac{2 \sqrt{a x} \sqrt{d f-e^2} \sqrt{\frac{e (e+f x)}{e^2-d f}} E\left(\sin ^{-1}\left(\frac{\sqrt{f} \sqrt{d+e x}}{\sqrt{d f-e^2}}\right)|1-\frac{e^2}{d f}\right)}{e \sqrt{f} \sqrt{-\frac{e x}{d}} \sqrt{e+f x}}",1,"(2*Sqrt[-e^2 + d*f]*Sqrt[a*x]*Sqrt[(e*(e + f*x))/(e^2 - d*f)]*EllipticE[ArcSin[(Sqrt[f]*Sqrt[d + e*x])/Sqrt[-e^2 + d*f]], 1 - e^2/(d*f)])/(e*Sqrt[f]*Sqrt[-((e*x)/d)]*Sqrt[e + f*x])","A",2,2,26,0.07692,1,"{114, 113}"
398,1,16,0,0.0046085,"\int \left(a x^m\right)^r \, dx","Int[(a*x^m)^r,x]","\frac{x \left(a x^m\right)^r}{m r+1}","\frac{x \left(a x^m\right)^r}{m r+1}",1,"(x*(a*x^m)^r)/(1 + m*r)","A",2,2,7,0.2857,1,"{15, 30}"
399,1,26,0,0.0091378,"\int \left(a x^m\right)^r \left(b x^n\right)^s \, dx","Int[(a*x^m)^r*(b*x^n)^s,x]","\frac{x \left(a x^m\right)^r \left(b x^n\right)^s}{m r+n s+1}","\frac{x \left(a x^m\right)^r \left(b x^n\right)^s}{m r+n s+1}",1,"(x*(a*x^m)^r*(b*x^n)^s)/(1 + m*r + n*s)","A",3,2,15,0.1333,1,"{15, 30}"
400,1,36,0,0.0155787,"\int \left(a x^m\right)^r \left(b x^n\right)^s \left(c x^p\right)^t \, dx","Int[(a*x^m)^r*(b*x^n)^s*(c*x^p)^t,x]","\frac{x \left(a x^m\right)^r \left(b x^n\right)^s \left(c x^p\right)^t}{m r+n s+p t+1}","\frac{x \left(a x^m\right)^r \left(b x^n\right)^s \left(c x^p\right)^t}{m r+n s+p t+1}",1,"(x*(a*x^m)^r*(b*x^n)^s*(c*x^p)^t)/(1 + m*r + n*s + p*t)","A",4,2,22,0.09091,1,"{15, 30}"
401,1,147,0,0.1323431,"\int \frac{x^2}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx","Int[x^2/(Sqrt[a + b*x] + Sqrt[c + b*x]),x]","\frac{2 a^2 (a+b x)^{3/2}}{3 b^3 (a-c)}-\frac{2 c^2 (b x+c)^{3/2}}{3 b^3 (a-c)}+\frac{2 (a+b x)^{7/2}}{7 b^3 (a-c)}-\frac{4 a (a+b x)^{5/2}}{5 b^3 (a-c)}-\frac{2 (b x+c)^{7/2}}{7 b^3 (a-c)}+\frac{4 c (b x+c)^{5/2}}{5 b^3 (a-c)}","\frac{2 a^2 (a+b x)^{3/2}}{3 b^3 (a-c)}-\frac{2 c^2 (b x+c)^{3/2}}{3 b^3 (a-c)}+\frac{2 (a+b x)^{7/2}}{7 b^3 (a-c)}-\frac{4 a (a+b x)^{5/2}}{5 b^3 (a-c)}-\frac{2 (b x+c)^{7/2}}{7 b^3 (a-c)}+\frac{4 c (b x+c)^{5/2}}{5 b^3 (a-c)}",1,"(2*a^2*(a + b*x)^(3/2))/(3*b^3*(a - c)) - (4*a*(a + b*x)^(5/2))/(5*b^3*(a - c)) + (2*(a + b*x)^(7/2))/(7*b^3*(a - c)) - (2*c^2*(c + b*x)^(3/2))/(3*b^3*(a - c)) + (4*c*(c + b*x)^(5/2))/(5*b^3*(a - c)) - (2*(c + b*x)^(7/2))/(7*b^3*(a - c))","A",5,2,25,0.08000,1,"{2104, 43}"
402,1,95,0,0.0812099,"\int \frac{x}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx","Int[x/(Sqrt[a + b*x] + Sqrt[c + b*x]),x]","\frac{2 (a+b x)^{5/2}}{5 b^2 (a-c)}-\frac{2 a (a+b x)^{3/2}}{3 b^2 (a-c)}-\frac{2 (b x+c)^{5/2}}{5 b^2 (a-c)}+\frac{2 c (b x+c)^{3/2}}{3 b^2 (a-c)}","\frac{2 (a+b x)^{5/2}}{5 b^2 (a-c)}-\frac{2 a (a+b x)^{3/2}}{3 b^2 (a-c)}-\frac{2 (b x+c)^{5/2}}{5 b^2 (a-c)}+\frac{2 c (b x+c)^{3/2}}{3 b^2 (a-c)}",1,"(-2*a*(a + b*x)^(3/2))/(3*b^2*(a - c)) + (2*(a + b*x)^(5/2))/(5*b^2*(a - c)) + (2*c*(c + b*x)^(3/2))/(3*b^2*(a - c)) - (2*(c + b*x)^(5/2))/(5*b^2*(a - c))","A",5,2,23,0.08696,1,"{2104, 43}"
403,1,47,0,0.0466709,"\int \frac{1}{\sqrt{a+b x}+\sqrt{c+b x}} \, dx","Int[(Sqrt[a + b*x] + Sqrt[c + b*x])^(-1),x]","\frac{2 (a+b x)^{3/2}}{3 b (a-c)}-\frac{2 (b x+c)^{3/2}}{3 b (a-c)}","\frac{2 (a+b x)^{3/2}}{3 b (a-c)}-\frac{2 (b x+c)^{3/2}}{3 b (a-c)}",1,"(2*(a + b*x)^(3/2))/(3*b*(a - c)) - (2*(c + b*x)^(3/2))/(3*b*(a - c))","A",2,1,21,0.04762,1,"{6689}"
404,1,97,0,0.1039544,"\int \frac{1}{x \left(\sqrt{a+b x}+\sqrt{c+b x}\right)} \, dx","Int[1/(x*(Sqrt[a + b*x] + Sqrt[c + b*x])),x]","\frac{2 \sqrt{a+b x}}{a-c}-\frac{2 \sqrt{b x+c}}{a-c}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a-c}+\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{b x+c}}{\sqrt{c}}\right)}{a-c}","\frac{2 \sqrt{a+b x}}{a-c}-\frac{2 \sqrt{b x+c}}{a-c}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{a-c}+\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{b x+c}}{\sqrt{c}}\right)}{a-c}",1,"(2*Sqrt[a + b*x])/(a - c) - (2*Sqrt[c + b*x])/(a - c) - (2*Sqrt[a]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(a - c) + (2*Sqrt[c]*ArcTanh[Sqrt[c + b*x]/Sqrt[c]])/(a - c)","A",7,4,25,0.1600,1,"{2104, 50, 63, 208}"
405,1,103,0,0.1021214,"\int \frac{1}{x^2 \left(\sqrt{a+b x}+\sqrt{c+b x}\right)} \, dx","Int[1/(x^2*(Sqrt[a + b*x] + Sqrt[c + b*x])),x]","-\frac{\sqrt{a+b x}}{x (a-c)}+\frac{\sqrt{b x+c}}{x (a-c)}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a} (a-c)}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{b x+c}}{\sqrt{c}}\right)}{\sqrt{c} (a-c)}","-\frac{\sqrt{a+b x}}{x (a-c)}+\frac{\sqrt{b x+c}}{x (a-c)}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a} (a-c)}+\frac{b \tanh ^{-1}\left(\frac{\sqrt{b x+c}}{\sqrt{c}}\right)}{\sqrt{c} (a-c)}",1,"-(Sqrt[a + b*x]/((a - c)*x)) + Sqrt[c + b*x]/((a - c)*x) - (b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(Sqrt[a]*(a - c)) + (b*ArcTanh[Sqrt[c + b*x]/Sqrt[c]])/((a - c)*Sqrt[c])","A",7,4,25,0.1600,1,"{2104, 47, 63, 208}"
406,1,228,0,0.3733962,"\int \frac{x^2}{\left(\sqrt{a+b x}+\sqrt{c+b x}\right)^2} \, dx","Int[x^2/(Sqrt[a + b*x] + Sqrt[c + b*x])^2,x]","-\frac{x (a+b x)^{3/2} (b x+c)^{3/2}}{2 b^2 (a-c)^2}+\frac{5 (a+c) (a+b x)^{3/2} (b x+c)^{3/2}}{12 b^3 (a-c)^2}+\frac{\left(4 a c-5 (a+c)^2\right) (a+b x)^{3/2} \sqrt{b x+c}}{16 b^3 (a-c)^2}-\frac{\left(4 a c-5 (a+c)^2\right) \sqrt{a+b x} \sqrt{b x+c}}{32 b^3 (a-c)}-\frac{\left(4 a c-5 (a+c)^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{b x+c}}\right)}{32 b^3}+\frac{b x^4}{2 (a-c)^2}+\frac{x^3 (a+c)}{3 (a-c)^2}","-\frac{x (a+b x)^{3/2} (b x+c)^{3/2}}{2 b^2 (a-c)^2}+\frac{5 (a+c) (a+b x)^{3/2} (b x+c)^{3/2}}{12 b^3 (a-c)^2}+\frac{\left(4 a c-5 (a+c)^2\right) (a+b x)^{3/2} \sqrt{b x+c}}{16 b^3 (a-c)^2}-\frac{\left(4 a c-5 (a+c)^2\right) \sqrt{a+b x} \sqrt{b x+c}}{32 b^3 (a-c)}-\frac{\left(4 a c-5 (a+c)^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{b x+c}}\right)}{32 b^3}+\frac{b x^4}{2 (a-c)^2}+\frac{x^3 (a+c)}{3 (a-c)^2}",1,"((a + c)*x^3)/(3*(a - c)^2) + (b*x^4)/(2*(a - c)^2) - ((4*a*c - 5*(a + c)^2)*Sqrt[a + b*x]*Sqrt[c + b*x])/(32*b^3*(a - c)) + ((4*a*c - 5*(a + c)^2)*(a + b*x)^(3/2)*Sqrt[c + b*x])/(16*b^3*(a - c)^2) + (5*(a + c)*(a + b*x)^(3/2)*(c + b*x)^(3/2))/(12*b^3*(a - c)^2) - (x*(a + b*x)^(3/2)*(c + b*x)^(3/2))/(2*b^2*(a - c)^2) - ((4*a*c - 5*(a + c)^2)*ArcTanh[Sqrt[a + b*x]/Sqrt[c + b*x]])/(32*b^3)","A",9,7,25,0.2800,1,"{6689, 90, 80, 50, 63, 217, 206}"
407,1,165,0,0.2100098,"\int \frac{x}{\left(\sqrt{a+b x}+\sqrt{c+b x}\right)^2} \, dx","Int[x/(Sqrt[a + b*x] + Sqrt[c + b*x])^2,x]","-\frac{2 (a+b x)^{3/2} (b x+c)^{3/2}}{3 b^2 (a-c)^2}+\frac{(a+c) (a+b x)^{3/2} \sqrt{b x+c}}{2 b^2 (a-c)^2}-\frac{(a+c) \sqrt{a+b x} \sqrt{b x+c}}{4 b^2 (a-c)}-\frac{(a+c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{b x+c}}\right)}{4 b^2}+\frac{2 b x^3}{3 (a-c)^2}+\frac{x^2 (a+c)}{2 (a-c)^2}","-\frac{2 (a+b x)^{3/2} (b x+c)^{3/2}}{3 b^2 (a-c)^2}+\frac{(a+c) (a+b x)^{3/2} \sqrt{b x+c}}{2 b^2 (a-c)^2}-\frac{(a+c) \sqrt{a+b x} \sqrt{b x+c}}{4 b^2 (a-c)}-\frac{(a+c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{b x+c}}\right)}{4 b^2}+\frac{2 b x^3}{3 (a-c)^2}+\frac{x^2 (a+c)}{2 (a-c)^2}",1,"((a + c)*x^2)/(2*(a - c)^2) + (2*b*x^3)/(3*(a - c)^2) - ((a + c)*Sqrt[a + b*x]*Sqrt[c + b*x])/(4*b^2*(a - c)) + ((a + c)*(a + b*x)^(3/2)*Sqrt[c + b*x])/(2*b^2*(a - c)^2) - (2*(a + b*x)^(3/2)*(c + b*x)^(3/2))/(3*b^2*(a - c)^2) - ((a + c)*ArcTanh[Sqrt[a + b*x]/Sqrt[c + b*x]])/(4*b^2)","A",8,6,23,0.2609,1,"{6689, 80, 50, 63, 217, 206}"
408,1,114,0,0.0985642,"\int \frac{1}{\left(\sqrt{a+b x}+\sqrt{c+b x}\right)^2} \, dx","Int[(Sqrt[a + b*x] + Sqrt[c + b*x])^(-2),x]","\frac{b x^2}{(a-c)^2}-\frac{(a+b x)^{3/2} \sqrt{b x+c}}{b (a-c)^2}+\frac{\sqrt{a+b x} \sqrt{b x+c}}{2 b (a-c)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{b x+c}}\right)}{2 b}+\frac{x (a+c)}{(a-c)^2}","\frac{(a-c)^2}{8 b \left(\sqrt{a+b x}+\sqrt{b x+c}\right)^4}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{b x+c}}\right)}{2 b}",1,"((a + c)*x)/(a - c)^2 + (b*x^2)/(a - c)^2 + (Sqrt[a + b*x]*Sqrt[c + b*x])/(2*b*(a - c)) - ((a + b*x)^(3/2)*Sqrt[c + b*x])/(b*(a - c)^2) + ArcTanh[Sqrt[a + b*x]/Sqrt[c + b*x]]/(2*b)","A",7,5,21,0.2381,1,"{6689, 50, 63, 217, 206}"
409,1,133,0,0.2296976,"\int \frac{1}{x \left(\sqrt{a+b x}+\sqrt{c+b x}\right)^2} \, dx","Int[1/(x*(Sqrt[a + b*x] + Sqrt[c + b*x])^2),x]","\frac{2 b x}{(a-c)^2}-\frac{2 \sqrt{a+b x} \sqrt{b x+c}}{(a-c)^2}-\frac{2 (a+c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{b x+c}}\right)}{(a-c)^2}+\frac{4 \sqrt{a} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{b x+c}}\right)}{(a-c)^2}+\frac{(a+c) \log (x)}{(a-c)^2}","\frac{2 b x}{(a-c)^2}-\frac{2 \sqrt{a+b x} \sqrt{b x+c}}{(a-c)^2}-\frac{2 (a+c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{b x+c}}\right)}{(a-c)^2}+\frac{4 \sqrt{a} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{b x+c}}\right)}{(a-c)^2}+\frac{(a+c) \log (x)}{(a-c)^2}",1,"(2*b*x)/(a - c)^2 - (2*Sqrt[a + b*x]*Sqrt[c + b*x])/(a - c)^2 - (2*(a + c)*ArcTanh[Sqrt[a + b*x]/Sqrt[c + b*x]])/(a - c)^2 + (4*Sqrt[a]*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + b*x])])/(a - c)^2 + ((a + c)*Log[x])/(a - c)^2","A",9,8,25,0.3200,1,"{6689, 101, 157, 63, 217, 206, 93, 208}"
410,1,141,0,0.215897,"\int \frac{1}{x^2 \left(\sqrt{a+b x}+\sqrt{c+b x}\right)^2} \, dx","Int[1/(x^2*(Sqrt[a + b*x] + Sqrt[c + b*x])^2),x]","\frac{2 \sqrt{a+b x} \sqrt{b x+c}}{x (a-c)^2}+\frac{2 b \log (x)}{(a-c)^2}+\frac{2 b (a+c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{b x+c}}\right)}{\sqrt{a} \sqrt{c} (a-c)^2}-\frac{4 b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{b x+c}}\right)}{(a-c)^2}-\frac{a+c}{x (a-c)^2}","\frac{2 \sqrt{a+b x} \sqrt{b x+c}}{x (a-c)^2}+\frac{2 b \log (x)}{(a-c)^2}+\frac{2 b (a+c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{a} \sqrt{b x+c}}\right)}{\sqrt{a} \sqrt{c} (a-c)^2}-\frac{4 b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{b x+c}}\right)}{(a-c)^2}-\frac{a+c}{x (a-c)^2}",1,"-((a + c)/((a - c)^2*x)) + (2*Sqrt[a + b*x]*Sqrt[c + b*x])/((a - c)^2*x) - (4*b*ArcTanh[Sqrt[a + b*x]/Sqrt[c + b*x]])/(a - c)^2 + (2*b*(a + c)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[a]*Sqrt[c + b*x])])/(Sqrt[a]*(a - c)^2*Sqrt[c]) + (2*b*Log[x])/(a - c)^2","A",9,8,25,0.3200,1,"{6689, 97, 157, 63, 217, 206, 93, 208}"
411,1,375,0,0.3716401,"\int \frac{x^2}{\left(\sqrt{a+b x}+\sqrt{c+b x}\right)^3} \, dx","Int[x^2/(Sqrt[a + b*x] + Sqrt[c + b*x])^3,x]","\frac{24 a^2 (a+b x)^{5/2}}{5 b^3 (a-c)^3}+\frac{2 a^2 (a+3 c) (a+b x)^{3/2}}{3 b^3 (a-c)^3}-\frac{8 a^3 (a+b x)^{3/2}}{3 b^3 (a-c)^3}-\frac{24 c^2 (b x+c)^{5/2}}{5 b^3 (a-c)^3}+\frac{8 c^3 (b x+c)^{3/2}}{3 b^3 (a-c)^3}-\frac{2 c^2 (3 a+c) (b x+c)^{3/2}}{3 b^3 (a-c)^3}+\frac{8 (a+b x)^{9/2}}{9 b^3 (a-c)^3}+\frac{2 (a+3 c) (a+b x)^{7/2}}{7 b^3 (a-c)^3}-\frac{24 a (a+b x)^{7/2}}{7 b^3 (a-c)^3}-\frac{4 a (a+3 c) (a+b x)^{5/2}}{5 b^3 (a-c)^3}-\frac{8 (b x+c)^{9/2}}{9 b^3 (a-c)^3}+\frac{24 c (b x+c)^{7/2}}{7 b^3 (a-c)^3}-\frac{2 (3 a+c) (b x+c)^{7/2}}{7 b^3 (a-c)^3}+\frac{4 c (3 a+c) (b x+c)^{5/2}}{5 b^3 (a-c)^3}","\frac{24 a^2 (a+b x)^{5/2}}{5 b^3 (a-c)^3}+\frac{2 a^2 (a+3 c) (a+b x)^{3/2}}{3 b^3 (a-c)^3}-\frac{8 a^3 (a+b x)^{3/2}}{3 b^3 (a-c)^3}-\frac{24 c^2 (b x+c)^{5/2}}{5 b^3 (a-c)^3}+\frac{8 c^3 (b x+c)^{3/2}}{3 b^3 (a-c)^3}-\frac{2 c^2 (3 a+c) (b x+c)^{3/2}}{3 b^3 (a-c)^3}+\frac{8 (a+b x)^{9/2}}{9 b^3 (a-c)^3}+\frac{2 (a+3 c) (a+b x)^{7/2}}{7 b^3 (a-c)^3}-\frac{24 a (a+b x)^{7/2}}{7 b^3 (a-c)^3}-\frac{4 a (a+3 c) (a+b x)^{5/2}}{5 b^3 (a-c)^3}-\frac{8 (b x+c)^{9/2}}{9 b^3 (a-c)^3}+\frac{24 c (b x+c)^{7/2}}{7 b^3 (a-c)^3}-\frac{2 (3 a+c) (b x+c)^{7/2}}{7 b^3 (a-c)^3}+\frac{4 c (3 a+c) (b x+c)^{5/2}}{5 b^3 (a-c)^3}",1,"(-8*a^3*(a + b*x)^(3/2))/(3*b^3*(a - c)^3) + (2*a^2*(a + 3*c)*(a + b*x)^(3/2))/(3*b^3*(a - c)^3) + (24*a^2*(a + b*x)^(5/2))/(5*b^3*(a - c)^3) - (4*a*(a + 3*c)*(a + b*x)^(5/2))/(5*b^3*(a - c)^3) - (24*a*(a + b*x)^(7/2))/(7*b^3*(a - c)^3) + (2*(a + 3*c)*(a + b*x)^(7/2))/(7*b^3*(a - c)^3) + (8*(a + b*x)^(9/2))/(9*b^3*(a - c)^3) + (8*c^3*(c + b*x)^(3/2))/(3*b^3*(a - c)^3) - (2*c^2*(3*a + c)*(c + b*x)^(3/2))/(3*b^3*(a - c)^3) - (24*c^2*(c + b*x)^(5/2))/(5*b^3*(a - c)^3) + (4*c*(3*a + c)*(c + b*x)^(5/2))/(5*b^3*(a - c)^3) + (24*c*(c + b*x)^(7/2))/(7*b^3*(a - c)^3) - (2*(3*a + c)*(c + b*x)^(7/2))/(7*b^3*(a - c)^3) - (8*(c + b*x)^(9/2))/(9*b^3*(a - c)^3)","A",10,2,25,0.08000,1,"{6689, 43}"
412,1,261,0,0.2363457,"\int \frac{x}{\left(\sqrt{a+b x}+\sqrt{c+b x}\right)^3} \, dx","Int[x/(Sqrt[a + b*x] + Sqrt[c + b*x])^3,x]","\frac{8 a^2 (a+b x)^{3/2}}{3 b^2 (a-c)^3}-\frac{8 c^2 (b x+c)^{3/2}}{3 b^2 (a-c)^3}+\frac{8 (a+b x)^{7/2}}{7 b^2 (a-c)^3}+\frac{2 (a+3 c) (a+b x)^{5/2}}{5 b^2 (a-c)^3}-\frac{16 a (a+b x)^{5/2}}{5 b^2 (a-c)^3}-\frac{2 a (a+3 c) (a+b x)^{3/2}}{3 b^2 (a-c)^3}-\frac{8 (b x+c)^{7/2}}{7 b^2 (a-c)^3}+\frac{16 c (b x+c)^{5/2}}{5 b^2 (a-c)^3}-\frac{2 (3 a+c) (b x+c)^{5/2}}{5 b^2 (a-c)^3}+\frac{2 c (3 a+c) (b x+c)^{3/2}}{3 b^2 (a-c)^3}","\frac{8 a^2 (a+b x)^{3/2}}{3 b^2 (a-c)^3}-\frac{8 c^2 (b x+c)^{3/2}}{3 b^2 (a-c)^3}+\frac{8 (a+b x)^{7/2}}{7 b^2 (a-c)^3}+\frac{2 (a+3 c) (a+b x)^{5/2}}{5 b^2 (a-c)^3}-\frac{16 a (a+b x)^{5/2}}{5 b^2 (a-c)^3}-\frac{2 a (a+3 c) (a+b x)^{3/2}}{3 b^2 (a-c)^3}-\frac{8 (b x+c)^{7/2}}{7 b^2 (a-c)^3}+\frac{16 c (b x+c)^{5/2}}{5 b^2 (a-c)^3}-\frac{2 (3 a+c) (b x+c)^{5/2}}{5 b^2 (a-c)^3}+\frac{2 c (3 a+c) (b x+c)^{3/2}}{3 b^2 (a-c)^3}",1,"(8*a^2*(a + b*x)^(3/2))/(3*b^2*(a - c)^3) - (2*a*(a + 3*c)*(a + b*x)^(3/2))/(3*b^2*(a - c)^3) - (16*a*(a + b*x)^(5/2))/(5*b^2*(a - c)^3) + (2*(a + 3*c)*(a + b*x)^(5/2))/(5*b^2*(a - c)^3) + (8*(a + b*x)^(7/2))/(7*b^2*(a - c)^3) - (8*c^2*(c + b*x)^(3/2))/(3*b^2*(a - c)^3) + (2*c*(3*a + c)*(c + b*x)^(3/2))/(3*b^2*(a - c)^3) + (16*c*(c + b*x)^(5/2))/(5*b^2*(a - c)^3) - (2*(3*a + c)*(c + b*x)^(5/2))/(5*b^2*(a - c)^3) - (8*(c + b*x)^(7/2))/(7*b^2*(a - c)^3)","A",10,2,23,0.08696,1,"{6689, 43}"
413,1,151,0,0.0946979,"\int \frac{1}{\left(\sqrt{a+b x}+\sqrt{c+b x}\right)^3} \, dx","Int[(Sqrt[a + b*x] + Sqrt[c + b*x])^(-3),x]","\frac{8 (a+b x)^{5/2}}{5 b (a-c)^3}+\frac{2 (a+3 c) (a+b x)^{3/2}}{3 b (a-c)^3}-\frac{8 a (a+b x)^{3/2}}{3 b (a-c)^3}-\frac{8 (b x+c)^{5/2}}{5 b (a-c)^3}+\frac{8 c (b x+c)^{3/2}}{3 b (a-c)^3}-\frac{2 (3 a+c) (b x+c)^{3/2}}{3 b (a-c)^3}","\frac{(a-c)^2}{10 b \left(\sqrt{a+b x}+\sqrt{b x+c}\right)^5}-\frac{1}{2 b \left(\sqrt{a+b x}+\sqrt{b x+c}\right)}",1,"(-8*a*(a + b*x)^(3/2))/(3*b*(a - c)^3) + (2*(a + 3*c)*(a + b*x)^(3/2))/(3*b*(a - c)^3) + (8*(a + b*x)^(5/2))/(5*b*(a - c)^3) + (8*c*(c + b*x)^(3/2))/(3*b*(a - c)^3) - (2*(3*a + c)*(c + b*x)^(3/2))/(3*b*(a - c)^3) - (8*(c + b*x)^(5/2))/(5*b*(a - c)^3)","B",6,2,21,0.09524,1,"{6689, 43}"
414,1,157,0,0.2327904,"\int \frac{1}{x \left(\sqrt{a+b x}+\sqrt{c+b x}\right)^3} \, dx","Int[1/(x*(Sqrt[a + b*x] + Sqrt[c + b*x])^3),x]","\frac{8 (a+b x)^{3/2}}{3 (a-c)^3}+\frac{2 (a+3 c) \sqrt{a+b x}}{(a-c)^3}-\frac{8 (b x+c)^{3/2}}{3 (a-c)^3}-\frac{2 (3 a+c) \sqrt{b x+c}}{(a-c)^3}-\frac{2 \sqrt{a} (a+3 c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{(a-c)^3}+\frac{2 \sqrt{c} (3 a+c) \tanh ^{-1}\left(\frac{\sqrt{b x+c}}{\sqrt{c}}\right)}{(a-c)^3}","\frac{8 (a+b x)^{3/2}}{3 (a-c)^3}+\frac{2 (a+3 c) \sqrt{a+b x}}{(a-c)^3}-\frac{8 (b x+c)^{3/2}}{3 (a-c)^3}-\frac{2 (3 a+c) \sqrt{b x+c}}{(a-c)^3}-\frac{2 \sqrt{a} (a+3 c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{(a-c)^3}+\frac{2 \sqrt{c} (3 a+c) \tanh ^{-1}\left(\frac{\sqrt{b x+c}}{\sqrt{c}}\right)}{(a-c)^3}",1,"(2*(a + 3*c)*Sqrt[a + b*x])/(a - c)^3 + (8*(a + b*x)^(3/2))/(3*(a - c)^3) - (2*(3*a + c)*Sqrt[c + b*x])/(a - c)^3 - (8*(c + b*x)^(3/2))/(3*(a - c)^3) - (2*Sqrt[a]*(a + 3*c)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(a - c)^3 + (2*Sqrt[c]*(3*a + c)*ArcTanh[Sqrt[c + b*x]/Sqrt[c]])/(a - c)^3","A",8,4,25,0.1600,1,"{6689, 50, 63, 208}"
415,1,223,0,0.2733173,"\int \frac{1}{x^2 \left(\sqrt{a+b x}+\sqrt{c+b x}\right)^3} \, dx","Int[1/(x^2*(Sqrt[a + b*x] + Sqrt[c + b*x])^3),x]","\frac{8 b \sqrt{a+b x}}{(a-c)^3}-\frac{8 b \sqrt{b x+c}}{(a-c)^3}-\frac{(a+3 c) \sqrt{a+b x}}{x (a-c)^3}+\frac{(3 a+c) \sqrt{b x+c}}{x (a-c)^3}-\frac{b (a+3 c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a} (a-c)^3}-\frac{8 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{(a-c)^3}+\frac{b (3 a+c) \tanh ^{-1}\left(\frac{\sqrt{b x+c}}{\sqrt{c}}\right)}{\sqrt{c} (a-c)^3}+\frac{8 b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{b x+c}}{\sqrt{c}}\right)}{(a-c)^3}","\frac{8 b \sqrt{a+b x}}{(a-c)^3}-\frac{8 b \sqrt{b x+c}}{(a-c)^3}-\frac{(a+3 c) \sqrt{a+b x}}{x (a-c)^3}+\frac{(3 a+c) \sqrt{b x+c}}{x (a-c)^3}-\frac{3 b (3 a+c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a} (a-c)^3}-\frac{3 b (a+3 c) \tanh ^{-1}\left(\frac{\sqrt{b x+c}}{\sqrt{c}}\right)}{\sqrt{c} (c-a)^3}",1,"(8*b*Sqrt[a + b*x])/(a - c)^3 - ((a + 3*c)*Sqrt[a + b*x])/((a - c)^3*x) - (8*b*Sqrt[c + b*x])/(a - c)^3 + ((3*a + c)*Sqrt[c + b*x])/((a - c)^3*x) - (8*Sqrt[a]*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(a - c)^3 - (b*(a + 3*c)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(Sqrt[a]*(a - c)^3) + (8*b*Sqrt[c]*ArcTanh[Sqrt[c + b*x]/Sqrt[c]])/(a - c)^3 + (b*(3*a + c)*ArcTanh[Sqrt[c + b*x]/Sqrt[c]])/((a - c)^3*Sqrt[c])","A",14,5,25,0.2000,1,"{6689, 47, 63, 208, 50}"
416,1,21,0,0.0059096,"\int \frac{1}{\sqrt{x}+\sqrt{1+x}} \, dx","Int[(Sqrt[x] + Sqrt[1 + x])^(-1),x]","\frac{2}{3} (x+1)^{3/2}-\frac{2 x^{3/2}}{3}","\frac{2}{3} (x+1)^{3/2}-\frac{2 x^{3/2}}{3}",1,"(-2*x^(3/2))/3 + (2*(1 + x)^(3/2))/3","A",3,3,15,0.2000,1,"{2106, 30, 32}"
417,1,21,0,0.00695,"\int \frac{1}{\sqrt{-1+x}+\sqrt{x}} \, dx","Int[(Sqrt[-1 + x] + Sqrt[x])^(-1),x]","\frac{2 x^{3/2}}{3}-\frac{2}{3} (x-1)^{3/2}","\frac{2 x^{3/2}}{3}-\frac{2}{3} (x-1)^{3/2}",1,"(-2*(-1 + x)^(3/2))/3 + (2*x^(3/2))/3","A",3,3,15,0.2000,1,"{2106, 30, 32}"
418,1,23,0,0.0225083,"\int \frac{1}{\sqrt{-1+x}+\sqrt{1+x}} \, dx","Int[(Sqrt[-1 + x] + Sqrt[1 + x])^(-1),x]","\frac{1}{3} (x+1)^{3/2}-\frac{1}{3} (x-1)^{3/2}","\frac{1}{3} (x+1)^{3/2}-\frac{1}{3} (x-1)^{3/2}",1,"-(-1 + x)^(3/2)/3 + (1 + x)^(3/2)/3","A",2,1,17,0.05882,1,"{6689}"
419,1,38,0,0.1136236,"\int x^3 \left(\sqrt{1-x}+\sqrt{1+x}\right)^2 \, dx","Int[x^3*(Sqrt[1 - x] + Sqrt[1 + x])^2,x]","\frac{x^4}{2}+\frac{2}{5} \left(1-x^2\right)^{5/2}-\frac{2}{3} \left(1-x^2\right)^{3/2}","\frac{x^4}{2}+\frac{2}{5} \left(1-x^2\right)^{5/2}-\frac{2}{3} \left(1-x^2\right)^{3/2}",1,"x^4/2 - (2*(1 - x^2)^(3/2))/3 + (2*(1 - x^2)^(5/2))/5","A",5,3,23,0.1304,1,"{6742, 266, 43}"
420,1,48,0,0.0895353,"\int x^2 \left(\sqrt{1-x}+\sqrt{1+x}\right)^2 \, dx","Int[x^2*(Sqrt[1 - x] + Sqrt[1 + x])^2,x]","\frac{1}{2} \sqrt{1-x^2} x^3+\frac{2 x^3}{3}-\frac{1}{4} \sqrt{1-x^2} x+\frac{1}{4} \sin ^{-1}(x)","\frac{1}{2} \sqrt{1-x^2} x^3+\frac{2 x^3}{3}-\frac{1}{4} \sqrt{1-x^2} x+\frac{1}{4} \sin ^{-1}(x)",1,"(2*x^3)/3 - (x*Sqrt[1 - x^2])/4 + (x^3*Sqrt[1 - x^2])/2 + ArcSin[x]/4","A",5,4,23,0.1739,1,"{6742, 279, 321, 216}"
421,1,19,0,0.0541514,"\int x \left(\sqrt{1-x}+\sqrt{1+x}\right)^2 \, dx","Int[x*(Sqrt[1 - x] + Sqrt[1 + x])^2,x]","x^2-\frac{2}{3} \left(1-x^2\right)^{3/2}","x^2-\frac{2}{3} \left(1-x^2\right)^{3/2}",1,"x^2 - (2*(1 - x^2)^(3/2))/3","A",3,2,21,0.09524,1,"{6742, 261}"
422,1,19,0,0.0249363,"\int \left(\sqrt{1-x}+\sqrt{1+x}\right)^2 \, dx","Int[(Sqrt[1 - x] + Sqrt[1 + x])^2,x]","\sqrt{1-x^2} x+2 x+\sin ^{-1}(x)","\sqrt{1-x^2} x+2 x+\sin ^{-1}(x)",1,"2*x + x*Sqrt[1 - x^2] + ArcSin[x]","A",4,3,19,0.1579,1,"{6742, 195, 216}"
423,1,32,0,0.0887197,"\int \frac{\left(\sqrt{1-x}+\sqrt{1+x}\right)^2}{x} \, dx","Int[(Sqrt[1 - x] + Sqrt[1 + x])^2/x,x]","2 \sqrt{1-x^2}-2 \tanh ^{-1}\left(\sqrt{1-x^2}\right)+2 \log (x)","2 \sqrt{1-x^2}-2 \tanh ^{-1}\left(\sqrt{1-x^2}\right)+2 \log (x)",1,"2*Sqrt[1 - x^2] - 2*ArcTanh[Sqrt[1 - x^2]] + 2*Log[x]","A",6,5,23,0.2174,1,"{6742, 266, 50, 63, 206}"
424,1,26,0,0.080425,"\int \frac{\left(\sqrt{1-x}+\sqrt{1+x}\right)^2}{x^2} \, dx","Int[(Sqrt[1 - x] + Sqrt[1 + x])^2/x^2,x]","-\frac{2 \sqrt{1-x^2}}{x}-\frac{2}{x}-2 \sin ^{-1}(x)","-\frac{2 \sqrt{1-x^2}}{x}-\frac{2}{x}-2 \sin ^{-1}(x)",1,"-2/x - (2*Sqrt[1 - x^2])/x - 2*ArcSin[x]","A",4,3,23,0.1304,1,"{6742, 277, 216}"
425,1,34,0,0.0911825,"\int \frac{\left(\sqrt{1-x}+\sqrt{1+x}\right)^2}{x^3} \, dx","Int[(Sqrt[1 - x] + Sqrt[1 + x])^2/x^3,x]","-\frac{\sqrt{1-x^2}}{x^2}-\frac{1}{x^2}+\tanh ^{-1}\left(\sqrt{1-x^2}\right)","-\frac{\sqrt{1-x^2}}{x^2}-\frac{1}{x^2}+\tanh ^{-1}\left(\sqrt{1-x^2}\right)",1,"-x^(-2) - Sqrt[1 - x^2]/x^2 + ArcTanh[Sqrt[1 - x^2]]","A",6,5,23,0.2174,1,"{6742, 266, 47, 63, 206}"
426,1,147,0,0.1218376,"\int \frac{x^3}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx","Int[x^3/(Sqrt[a + b*x] + Sqrt[a + c*x]),x]","\frac{2 a^2 (a+b x)^{3/2}}{3 b^3 (b-c)}-\frac{2 a^2 (a+c x)^{3/2}}{3 c^3 (b-c)}+\frac{2 (a+b x)^{7/2}}{7 b^3 (b-c)}-\frac{4 a (a+b x)^{5/2}}{5 b^3 (b-c)}-\frac{2 (a+c x)^{7/2}}{7 c^3 (b-c)}+\frac{4 a (a+c x)^{5/2}}{5 c^3 (b-c)}","\frac{2 a^2 (a+b x)^{3/2}}{3 b^3 (b-c)}-\frac{2 a^2 (a+c x)^{3/2}}{3 c^3 (b-c)}+\frac{2 (a+b x)^{7/2}}{7 b^3 (b-c)}-\frac{4 a (a+b x)^{5/2}}{5 b^3 (b-c)}-\frac{2 (a+c x)^{7/2}}{7 c^3 (b-c)}+\frac{4 a (a+c x)^{5/2}}{5 c^3 (b-c)}",1,"(2*a^2*(a + b*x)^(3/2))/(3*b^3*(b - c)) - (4*a*(a + b*x)^(5/2))/(5*b^3*(b - c)) + (2*(a + b*x)^(7/2))/(7*b^3*(b - c)) - (2*a^2*(a + c*x)^(3/2))/(3*(b - c)*c^3) + (4*a*(a + c*x)^(5/2))/(5*(b - c)*c^3) - (2*(a + c*x)^(7/2))/(7*(b - c)*c^3)","A",5,2,25,0.08000,1,"{2103, 43}"
427,1,95,0,0.1005339,"\int \frac{x^2}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx","Int[x^2/(Sqrt[a + b*x] + Sqrt[a + c*x]),x]","\frac{2 (a+b x)^{5/2}}{5 b^2 (b-c)}-\frac{2 a (a+b x)^{3/2}}{3 b^2 (b-c)}-\frac{2 (a+c x)^{5/2}}{5 c^2 (b-c)}+\frac{2 a (a+c x)^{3/2}}{3 c^2 (b-c)}","\frac{2 (a+b x)^{5/2}}{5 b^2 (b-c)}-\frac{2 a (a+b x)^{3/2}}{3 b^2 (b-c)}-\frac{2 (a+c x)^{5/2}}{5 c^2 (b-c)}+\frac{2 a (a+c x)^{3/2}}{3 c^2 (b-c)}",1,"(-2*a*(a + b*x)^(3/2))/(3*b^2*(b - c)) + (2*(a + b*x)^(5/2))/(5*b^2*(b - c)) + (2*a*(a + c*x)^(3/2))/(3*(b - c)*c^2) - (2*(a + c*x)^(5/2))/(5*(b - c)*c^2)","A",5,2,25,0.08000,1,"{2103, 43}"
428,1,47,0,0.0550301,"\int \frac{x}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx","Int[x/(Sqrt[a + b*x] + Sqrt[a + c*x]),x]","\frac{2 (a+b x)^{3/2}}{3 b (b-c)}-\frac{2 (a+c x)^{3/2}}{3 c (b-c)}","\frac{2 (a+b x)^{3/2}}{3 b (b-c)}-\frac{2 (a+c x)^{3/2}}{3 c (b-c)}",1,"(2*(a + b*x)^(3/2))/(3*b*(b - c)) - (2*(a + c*x)^(3/2))/(3*(b - c)*c)","A",3,2,23,0.08696,1,"{2103, 32}"
429,1,97,0,0.0708231,"\int \frac{1}{\sqrt{a+b x}+\sqrt{a+c x}} \, dx","Int[(Sqrt[a + b*x] + Sqrt[a + c*x])^(-1),x]","\frac{2 \sqrt{a+b x}}{b-c}-\frac{2 \sqrt{a+c x}}{b-c}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{b-c}+\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{b-c}","\frac{2 \sqrt{a+b x}}{b-c}-\frac{2 \sqrt{a+c x}}{b-c}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{b-c}+\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{b-c}",1,"(2*Sqrt[a + b*x])/(b - c) - (2*Sqrt[a + c*x])/(b - c) - (2*Sqrt[a]*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(b - c) + (2*Sqrt[a]*ArcTanh[Sqrt[a + c*x]/Sqrt[a]])/(b - c)","A",8,4,21,0.1905,1,"{6690, 50, 63, 208}"
430,1,103,0,0.0945461,"\int \frac{1}{x \left(\sqrt{a+b x}+\sqrt{a+c x}\right)} \, dx","Int[1/(x*(Sqrt[a + b*x] + Sqrt[a + c*x])),x]","-\frac{\sqrt{a+b x}}{x (b-c)}+\frac{\sqrt{a+c x}}{x (b-c)}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a} (b-c)}+\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{\sqrt{a} (b-c)}","-\frac{\sqrt{a+b x}}{x (b-c)}+\frac{\sqrt{a+c x}}{x (b-c)}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a} (b-c)}+\frac{c \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{\sqrt{a} (b-c)}",1,"-(Sqrt[a + b*x]/((b - c)*x)) + Sqrt[a + c*x]/((b - c)*x) - (b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(Sqrt[a]*(b - c)) + (c*ArcTanh[Sqrt[a + c*x]/Sqrt[a]])/(Sqrt[a]*(b - c))","A",7,4,25,0.1600,1,"{2103, 47, 63, 208}"
431,1,171,0,0.112481,"\int \frac{1}{x^2 \left(\sqrt{a+b x}+\sqrt{a+c x}\right)} \, dx","Int[1/(x^2*(Sqrt[a + b*x] + Sqrt[a + c*x])),x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{3/2} (b-c)}-\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{4 a^{3/2} (b-c)}-\frac{\sqrt{a+b x}}{2 x^2 (b-c)}+\frac{\sqrt{a+c x}}{2 x^2 (b-c)}-\frac{b \sqrt{a+b x}}{4 a x (b-c)}+\frac{c \sqrt{a+c x}}{4 a x (b-c)}","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{4 a^{3/2} (b-c)}-\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{4 a^{3/2} (b-c)}-\frac{\sqrt{a+b x}}{2 x^2 (b-c)}+\frac{\sqrt{a+c x}}{2 x^2 (b-c)}-\frac{b \sqrt{a+b x}}{4 a x (b-c)}+\frac{c \sqrt{a+c x}}{4 a x (b-c)}",1,"-Sqrt[a + b*x]/(2*(b - c)*x^2) - (b*Sqrt[a + b*x])/(4*a*(b - c)*x) + Sqrt[a + c*x]/(2*(b - c)*x^2) + (c*Sqrt[a + c*x])/(4*a*(b - c)*x) + (b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(4*a^(3/2)*(b - c)) - (c^2*ArcTanh[Sqrt[a + c*x]/Sqrt[a]])/(4*a^(3/2)*(b - c))","A",9,5,25,0.2000,1,"{2103, 47, 51, 63, 208}"
432,1,195,0,0.3493,"\int \frac{x^3}{\left(\sqrt{a+b x}+\sqrt{a+c x}\right)^2} \, dx","Int[x^3/(Sqrt[a + b*x] + Sqrt[a + c*x])^2,x]","\frac{a^2 (b+c) \sqrt{a+b x} \sqrt{a+c x}}{4 b^2 c^2 (b-c)}-\frac{a^3 (b+c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{b} \sqrt{a+c x}}\right)}{4 b^{5/2} c^{5/2}}+\frac{a (b+c) (a+b x)^{3/2} \sqrt{a+c x}}{2 b^2 c (b-c)^2}+\frac{a x^2}{(b-c)^2}-\frac{2 (a+b x)^{3/2} (a+c x)^{3/2}}{3 b c (b-c)^2}+\frac{x^3 (b+c)}{3 (b-c)^2}","\frac{a^2 (b+c) \sqrt{a+b x} \sqrt{a+c x}}{4 b^2 c^2 (b-c)}-\frac{a^3 (b+c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{b} \sqrt{a+c x}}\right)}{4 b^{5/2} c^{5/2}}+\frac{a (b+c) (a+b x)^{3/2} \sqrt{a+c x}}{2 b^2 c (b-c)^2}+\frac{a x^2}{(b-c)^2}-\frac{2 (a+b x)^{3/2} (a+c x)^{3/2}}{3 b c (b-c)^2}+\frac{x^3 (b+c)}{3 (b-c)^2}",1,"(a*x^2)/(b - c)^2 + ((b + c)*x^3)/(3*(b - c)^2) + (a^2*(b + c)*Sqrt[a + b*x]*Sqrt[a + c*x])/(4*b^2*(b - c)*c^2) + (a*(b + c)*(a + b*x)^(3/2)*Sqrt[a + c*x])/(2*b^2*(b - c)^2*c) - (2*(a + b*x)^(3/2)*(a + c*x)^(3/2))/(3*b*(b - c)^2*c) - (a^3*(b + c)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[a + c*x])])/(4*b^(5/2)*c^(5/2))","A",8,6,25,0.2400,1,"{6690, 80, 50, 63, 217, 206}"
433,1,142,0,0.2277586,"\int \frac{x^2}{\left(\sqrt{a+b x}+\sqrt{a+c x}\right)^2} \, dx","Int[x^2/(Sqrt[a + b*x] + Sqrt[a + c*x])^2,x]","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{b} \sqrt{a+c x}}\right)}{2 b^{3/2} c^{3/2}}+\frac{2 a x}{(b-c)^2}-\frac{a \sqrt{a+b x} \sqrt{a+c x}}{2 b c (b-c)}-\frac{(a+b x)^{3/2} \sqrt{a+c x}}{b (b-c)^2}+\frac{x^2 (b+c)}{2 (b-c)^2}","\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{b} \sqrt{a+c x}}\right)}{2 b^{3/2} c^{3/2}}+\frac{2 a x}{(b-c)^2}-\frac{a \sqrt{a+b x} \sqrt{a+c x}}{2 b c (b-c)}-\frac{(a+b x)^{3/2} \sqrt{a+c x}}{b (b-c)^2}+\frac{x^2 (b+c)}{2 (b-c)^2}",1,"(2*a*x)/(b - c)^2 + ((b + c)*x^2)/(2*(b - c)^2) - (a*Sqrt[a + b*x]*Sqrt[a + c*x])/(2*b*(b - c)*c) - ((a + b*x)^(3/2)*Sqrt[a + c*x])/(b*(b - c)^2) + (a^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[a + c*x])])/(2*b^(3/2)*c^(3/2))","A",7,5,25,0.2000,1,"{6690, 50, 63, 217, 206}"
434,1,135,0,0.1814477,"\int \frac{x}{\left(\sqrt{a+b x}+\sqrt{a+c x}\right)^2} \, dx","Int[x/(Sqrt[a + b*x] + Sqrt[a + c*x])^2,x]","-\frac{2 \sqrt{a+b x} \sqrt{a+c x}}{(b-c)^2}+\frac{2 a \log (x)}{(b-c)^2}+\frac{4 a \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a+c x}}\right)}{(b-c)^2}-\frac{2 a (b+c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{b} \sqrt{a+c x}}\right)}{\sqrt{b} \sqrt{c} (b-c)^2}+\frac{x (b+c)}{(b-c)^2}","-\frac{2 \sqrt{a+b x} \sqrt{a+c x}}{(b-c)^2}+\frac{2 a \log (x)}{(b-c)^2}+\frac{4 a \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a+c x}}\right)}{(b-c)^2}-\frac{2 a (b+c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{b} \sqrt{a+c x}}\right)}{\sqrt{b} \sqrt{c} (b-c)^2}+\frac{x (b+c)}{(b-c)^2}",1,"((b + c)*x)/(b - c)^2 - (2*Sqrt[a + b*x]*Sqrt[a + c*x])/(b - c)^2 + (4*a*ArcTanh[Sqrt[a + b*x]/Sqrt[a + c*x]])/(b - c)^2 - (2*a*(b + c)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[a + c*x])])/(Sqrt[b]*(b - c)^2*Sqrt[c]) + (2*a*Log[x])/(b - c)^2","A",9,8,23,0.3478,1,"{6690, 101, 157, 63, 217, 206, 93, 208}"
435,1,138,0,0.1136647,"\int \frac{1}{\left(\sqrt{a+b x}+\sqrt{a+c x}\right)^2} \, dx","Int[(Sqrt[a + b*x] + Sqrt[a + c*x])^(-2),x]","-\frac{2 a}{x (b-c)^2}+\frac{2 \sqrt{a+b x} \sqrt{a+c x}}{x (b-c)^2}+\frac{2 (b+c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a+c x}}\right)}{(b-c)^2}-\frac{4 \sqrt{b} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{b} \sqrt{a+c x}}\right)}{(b-c)^2}+\frac{(b+c) \log (x)}{(b-c)^2}","-\frac{2 a}{x (b-c)^2}+\frac{2 \sqrt{a+b x} \sqrt{a+c x}}{x (b-c)^2}+\frac{2 (b+c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a+c x}}\right)}{(b-c)^2}-\frac{4 \sqrt{b} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x}}{\sqrt{b} \sqrt{a+c x}}\right)}{(b-c)^2}+\frac{(b+c) \log (x)}{(b-c)^2}",1,"(-2*a)/((b - c)^2*x) + (2*Sqrt[a + b*x]*Sqrt[a + c*x])/((b - c)^2*x) + (2*(b + c)*ArcTanh[Sqrt[a + b*x]/Sqrt[a + c*x]])/(b - c)^2 - (4*Sqrt[b]*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x])/(Sqrt[b]*Sqrt[a + c*x])])/(b - c)^2 + ((b + c)*Log[x])/(b - c)^2","A",9,8,21,0.3810,1,"{6690, 97, 157, 63, 217, 206, 93, 208}"
436,1,123,0,0.2014472,"\int \frac{1}{x \left(\sqrt{a+b x}+\sqrt{a+c x}\right)^2} \, dx","Int[1/(x*(Sqrt[a + b*x] + Sqrt[a + c*x])^2),x]","\frac{\sqrt{a+b x} (a+c x)^{3/2}}{a x^2 (b-c)^2}-\frac{a}{x^2 (b-c)^2}+\frac{\sqrt{a+b x} \sqrt{a+c x}}{2 a x (b-c)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a+c x}}\right)}{2 a}-\frac{b+c}{x (b-c)^2}","\frac{\sqrt{a+b x} (a+c x)^{3/2}}{a x^2 (b-c)^2}-\frac{a}{x^2 (b-c)^2}+\frac{\sqrt{a+b x} \sqrt{a+c x}}{2 a x (b-c)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a+c x}}\right)}{2 a}-\frac{b+c}{x (b-c)^2}",1,"-(a/((b - c)^2*x^2)) - (b + c)/((b - c)^2*x) + (Sqrt[a + b*x]*Sqrt[a + c*x])/(2*a*(b - c)*x) + (Sqrt[a + b*x]*(a + c*x)^(3/2))/(a*(b - c)^2*x^2) - ArcTanh[Sqrt[a + b*x]/Sqrt[a + c*x]]/(2*a)","A",6,4,25,0.1600,1,"{6690, 94, 93, 208}"
437,1,174,0,0.2232445,"\int \frac{1}{x^2 \left(\sqrt{a+b x}+\sqrt{a+c x}\right)^2} \, dx","Int[1/(x^2*(Sqrt[a + b*x] + Sqrt[a + c*x])^2),x]","\frac{2 (a+b x)^{3/2} (a+c x)^{3/2}}{3 a^2 x^3 (b-c)^2}-\frac{(b+c) \sqrt{a+b x} (a+c x)^{3/2}}{2 a^2 x^2 (b-c)^2}-\frac{(b+c) \sqrt{a+b x} \sqrt{a+c x}}{4 a^2 x (b-c)}+\frac{(b+c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a+c x}}\right)}{4 a^2}-\frac{2 a}{3 x^3 (b-c)^2}-\frac{b+c}{2 x^2 (b-c)^2}","\frac{2 (a+b x)^{3/2} (a+c x)^{3/2}}{3 a^2 x^3 (b-c)^2}-\frac{(b+c) \sqrt{a+b x} (a+c x)^{3/2}}{2 a^2 x^2 (b-c)^2}-\frac{(b+c) \sqrt{a+b x} \sqrt{a+c x}}{4 a^2 x (b-c)}+\frac{(b+c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a+c x}}\right)}{4 a^2}-\frac{2 a}{3 x^3 (b-c)^2}-\frac{b+c}{2 x^2 (b-c)^2}",1,"(-2*a)/(3*(b - c)^2*x^3) - (b + c)/(2*(b - c)^2*x^2) - ((b + c)*Sqrt[a + b*x]*Sqrt[a + c*x])/(4*a^2*(b - c)*x) - ((b + c)*Sqrt[a + b*x]*(a + c*x)^(3/2))/(2*a^2*(b - c)^2*x^2) + (2*(a + b*x)^(3/2)*(a + c*x)^(3/2))/(3*a^2*(b - c)^2*x^3) + ((b + c)*ArcTanh[Sqrt[a + b*x]/Sqrt[a + c*x]])/(4*a^2)","A",7,5,25,0.2000,1,"{6690, 96, 94, 93, 208}"
438,1,277,0,0.3192161,"\int \frac{x^4}{\left(\sqrt{a+b x}+\sqrt{a+c x}\right)^3} \, dx","Int[x^4/(Sqrt[a + b*x] + Sqrt[a + c*x])^3,x]","\frac{2 a^2 (b+3 c) (a+b x)^{3/2}}{3 b^3 (b-c)^3}-\frac{8 a^2 (a+b x)^{3/2}}{3 b^2 (b-c)^3}-\frac{2 a^2 (3 b+c) (a+c x)^{3/2}}{3 c^3 (b-c)^3}+\frac{8 a^2 (a+c x)^{3/2}}{3 c^2 (b-c)^3}+\frac{2 (b+3 c) (a+b x)^{7/2}}{7 b^3 (b-c)^3}-\frac{4 a (b+3 c) (a+b x)^{5/2}}{5 b^3 (b-c)^3}+\frac{8 a (a+b x)^{5/2}}{5 b^2 (b-c)^3}-\frac{2 (3 b+c) (a+c x)^{7/2}}{7 c^3 (b-c)^3}+\frac{4 a (3 b+c) (a+c x)^{5/2}}{5 c^3 (b-c)^3}-\frac{8 a (a+c x)^{5/2}}{5 c^2 (b-c)^3}","\frac{2 a^2 (b+3 c) (a+b x)^{3/2}}{3 b^3 (b-c)^3}-\frac{8 a^2 (a+b x)^{3/2}}{3 b^2 (b-c)^3}-\frac{2 a^2 (3 b+c) (a+c x)^{3/2}}{3 c^3 (b-c)^3}+\frac{8 a^2 (a+c x)^{3/2}}{3 c^2 (b-c)^3}+\frac{2 (b+3 c) (a+b x)^{7/2}}{7 b^3 (b-c)^3}-\frac{4 a (b+3 c) (a+b x)^{5/2}}{5 b^3 (b-c)^3}+\frac{8 a (a+b x)^{5/2}}{5 b^2 (b-c)^3}-\frac{2 (3 b+c) (a+c x)^{7/2}}{7 c^3 (b-c)^3}+\frac{4 a (3 b+c) (a+c x)^{5/2}}{5 c^3 (b-c)^3}-\frac{8 a (a+c x)^{5/2}}{5 c^2 (b-c)^3}",1,"(-8*a^2*(a + b*x)^(3/2))/(3*b^2*(b - c)^3) + (2*a^2*(b + 3*c)*(a + b*x)^(3/2))/(3*b^3*(b - c)^3) + (8*a*(a + b*x)^(5/2))/(5*b^2*(b - c)^3) - (4*a*(b + 3*c)*(a + b*x)^(5/2))/(5*b^3*(b - c)^3) + (2*(b + 3*c)*(a + b*x)^(7/2))/(7*b^3*(b - c)^3) + (8*a^2*(a + c*x)^(3/2))/(3*(b - c)^3*c^2) - (2*a^2*(3*b + c)*(a + c*x)^(3/2))/(3*(b - c)^3*c^3) - (8*a*(a + c*x)^(5/2))/(5*(b - c)^3*c^2) + (4*a*(3*b + c)*(a + c*x)^(5/2))/(5*(b - c)^3*c^3) - (2*(3*b + c)*(a + c*x)^(7/2))/(7*(b - c)^3*c^3)","A",10,2,25,0.08000,1,"{6690, 43}"
439,1,163,0,0.2175493,"\int \frac{x^3}{\left(\sqrt{a+b x}+\sqrt{a+c x}\right)^3} \, dx","Int[x^3/(Sqrt[a + b*x] + Sqrt[a + c*x])^3,x]","\frac{2 (b+3 c) (a+b x)^{5/2}}{5 b^2 (b-c)^3}-\frac{2 a (b+3 c) (a+b x)^{3/2}}{3 b^2 (b-c)^3}-\frac{2 (3 b+c) (a+c x)^{5/2}}{5 c^2 (b-c)^3}+\frac{2 a (3 b+c) (a+c x)^{3/2}}{3 c^2 (b-c)^3}+\frac{8 a (a+b x)^{3/2}}{3 b (b-c)^3}-\frac{8 a (a+c x)^{3/2}}{3 c (b-c)^3}","\frac{2 (b+3 c) (a+b x)^{5/2}}{5 b^2 (b-c)^3}-\frac{2 a (b+3 c) (a+b x)^{3/2}}{3 b^2 (b-c)^3}-\frac{2 (3 b+c) (a+c x)^{5/2}}{5 c^2 (b-c)^3}+\frac{2 a (3 b+c) (a+c x)^{3/2}}{3 c^2 (b-c)^3}+\frac{8 a (a+b x)^{3/2}}{3 b (b-c)^3}-\frac{8 a (a+c x)^{3/2}}{3 c (b-c)^3}",1,"(8*a*(a + b*x)^(3/2))/(3*b*(b - c)^3) - (2*a*(b + 3*c)*(a + b*x)^(3/2))/(3*b^2*(b - c)^3) + (2*(b + 3*c)*(a + b*x)^(5/2))/(5*b^2*(b - c)^3) - (8*a*(a + c*x)^(3/2))/(3*(b - c)^3*c) + (2*a*(3*b + c)*(a + c*x)^(3/2))/(3*(b - c)^3*c^2) - (2*(3*b + c)*(a + c*x)^(5/2))/(5*(b - c)^3*c^2)","A",6,2,25,0.08000,1,"{6690, 43}"
440,1,155,0,0.2024749,"\int \frac{x^2}{\left(\sqrt{a+b x}+\sqrt{a+c x}\right)^3} \, dx","Int[x^2/(Sqrt[a + b*x] + Sqrt[a + c*x])^3,x]","-\frac{8 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{(b-c)^3}+\frac{8 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{(b-c)^3}+\frac{8 a \sqrt{a+b x}}{(b-c)^3}-\frac{8 a \sqrt{a+c x}}{(b-c)^3}+\frac{2 (b+3 c) (a+b x)^{3/2}}{3 b (b-c)^3}-\frac{2 (3 b+c) (a+c x)^{3/2}}{3 c (b-c)^3}","-\frac{8 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{(b-c)^3}+\frac{8 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{(b-c)^3}+\frac{8 a \sqrt{a+b x}}{(b-c)^3}-\frac{8 a \sqrt{a+c x}}{(b-c)^3}+\frac{2 (b+3 c) (a+b x)^{3/2}}{3 b (b-c)^3}-\frac{2 (3 b+c) (a+c x)^{3/2}}{3 c (b-c)^3}",1,"(8*a*Sqrt[a + b*x])/(b - c)^3 + (2*(b + 3*c)*(a + b*x)^(3/2))/(3*b*(b - c)^3) - (8*a*Sqrt[a + c*x])/(b - c)^3 - (2*(3*b + c)*(a + c*x)^(3/2))/(3*(b - c)^3*c) - (8*a^(3/2)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(b - c)^3 + (8*a^(3/2)*ArcTanh[Sqrt[a + c*x]/Sqrt[a]])/(b - c)^3","A",8,4,25,0.1600,1,"{6690, 50, 63, 208}"
441,1,223,0,0.2172518,"\int \frac{x}{\left(\sqrt{a+b x}+\sqrt{a+c x}\right)^3} \, dx","Int[x/(Sqrt[a + b*x] + Sqrt[a + c*x])^3,x]","-\frac{4 a \sqrt{a+b x}}{x (b-c)^3}+\frac{4 a \sqrt{a+c x}}{x (b-c)^3}+\frac{2 (b+3 c) \sqrt{a+b x}}{(b-c)^3}-\frac{2 (3 b+c) \sqrt{a+c x}}{(b-c)^3}-\frac{2 \sqrt{a} (b+3 c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{(b-c)^3}-\frac{4 \sqrt{a} b \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{(b-c)^3}+\frac{4 \sqrt{a} c \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{(b-c)^3}+\frac{2 \sqrt{a} (3 b+c) \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{(b-c)^3}","-\frac{4 a \sqrt{a+b x}}{x (b-c)^3}+\frac{4 a \sqrt{a+c x}}{x (b-c)^3}+\frac{2 (b+3 c) \sqrt{a+b x}}{(b-c)^3}-\frac{2 (3 b+c) \sqrt{a+c x}}{(b-c)^3}-\frac{6 \sqrt{a} (b+c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{(b-c)^3}+\frac{6 \sqrt{a} (b+c) \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{(b-c)^3}",1,"(2*(b + 3*c)*Sqrt[a + b*x])/(b - c)^3 - (4*a*Sqrt[a + b*x])/((b - c)^3*x) - (2*(3*b + c)*Sqrt[a + c*x])/(b - c)^3 + (4*a*Sqrt[a + c*x])/((b - c)^3*x) - (4*Sqrt[a]*b*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(b - c)^3 - (2*Sqrt[a]*(b + 3*c)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(b - c)^3 + (4*Sqrt[a]*c*ArcTanh[Sqrt[a + c*x]/Sqrt[a]])/(b - c)^3 + (2*Sqrt[a]*(3*b + c)*ArcTanh[Sqrt[a + c*x]/Sqrt[a]])/(b - c)^3","A",14,5,23,0.2174,1,"{6690, 47, 63, 208, 50}"
442,1,275,0,0.1780998,"\int \frac{1}{\left(\sqrt{a+b x}+\sqrt{a+c x}\right)^3} \, dx","Int[(Sqrt[a + b*x] + Sqrt[a + c*x])^(-3),x]","\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a} (b-c)^3}-\frac{c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{\sqrt{a} (b-c)^3}-\frac{2 a \sqrt{a+b x}}{x^2 (b-c)^3}+\frac{2 a \sqrt{a+c x}}{x^2 (b-c)^3}-\frac{b \sqrt{a+b x}}{x (b-c)^3}-\frac{(b+3 c) \sqrt{a+b x}}{x (b-c)^3}+\frac{c \sqrt{a+c x}}{x (b-c)^3}+\frac{(3 b+c) \sqrt{a+c x}}{x (b-c)^3}-\frac{b (b+3 c) \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a} (b-c)^3}+\frac{c (3 b+c) \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{\sqrt{a} (b-c)^3}","-\frac{2 a \sqrt{a+b x}}{x^2 (b-c)^3}+\frac{2 a \sqrt{a+c x}}{x^2 (b-c)^3}-\frac{(2 b+3 c) \sqrt{a+b x}}{x (b-c)^3}+\frac{(3 b+2 c) \sqrt{a+c x}}{x (b-c)^3}-\frac{3 b c \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a} (b-c)^3}+\frac{3 b c \tanh ^{-1}\left(\frac{\sqrt{a+c x}}{\sqrt{a}}\right)}{\sqrt{a} (b-c)^3}",1,"(-2*a*Sqrt[a + b*x])/((b - c)^3*x^2) - (b*Sqrt[a + b*x])/((b - c)^3*x) - ((b + 3*c)*Sqrt[a + b*x])/((b - c)^3*x) + (2*a*Sqrt[a + c*x])/((b - c)^3*x^2) + (c*Sqrt[a + c*x])/((b - c)^3*x) + ((3*b + c)*Sqrt[a + c*x])/((b - c)^3*x) + (b^2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(Sqrt[a]*(b - c)^3) - (b*(b + 3*c)*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/(Sqrt[a]*(b - c)^3) - (c^2*ArcTanh[Sqrt[a + c*x]/Sqrt[a]])/(Sqrt[a]*(b - c)^3) + (c*(3*b + c)*ArcTanh[Sqrt[a + c*x]/Sqrt[a]])/(Sqrt[a]*(b - c)^3)","A",16,5,21,0.2381,1,"{6690, 47, 51, 63, 208}"
443,1,31,0,0.0461493,"\int \sqrt{1-x} \left(\sqrt{1-x}+\sqrt{1+x}\right) \, dx","Int[Sqrt[1 - x]*(Sqrt[1 - x] + Sqrt[1 + x]),x]","-\frac{x^2}{2}+\frac{1}{2} \sqrt{1-x^2} x+x+\frac{1}{2} \sin ^{-1}(x)","-\frac{x^2}{2}+\frac{1}{2} \sqrt{1-x^2} x+x+\frac{1}{2} \sin ^{-1}(x)",1,"x - x^2/2 + (x*Sqrt[1 - x^2])/2 + ArcSin[x]/2","A",4,3,27,0.1111,1,"{6688, 195, 216}"
444,1,38,0,0.324781,"\int x^3 \left(-\sqrt{1-x}-\sqrt{1+x}\right) \left(\sqrt{1-x}+\sqrt{1+x}\right) \, dx","Int[x^3*(-Sqrt[1 - x] - Sqrt[1 + x])*(Sqrt[1 - x] + Sqrt[1 + x]),x]","-\frac{x^4}{2}-\frac{2}{5} \left(1-x^2\right)^{5/2}+\frac{2}{3} \left(1-x^2\right)^{3/2}","-\frac{x^4}{2}-\frac{2}{5} \left(1-x^2\right)^{5/2}+\frac{2}{3} \left(1-x^2\right)^{3/2}",1,"-x^4/2 + (2*(1 - x^2)^(3/2))/3 - (2*(1 - x^2)^(5/2))/5","A",6,4,42,0.09524,1,"{6688, 6742, 266, 43}"
445,1,48,0,0.2419192,"\int x^2 \left(-\sqrt{1-x}-\sqrt{1+x}\right) \left(\sqrt{1-x}+\sqrt{1+x}\right) \, dx","Int[x^2*(-Sqrt[1 - x] - Sqrt[1 + x])*(Sqrt[1 - x] + Sqrt[1 + x]),x]","-\frac{1}{2} \sqrt{1-x^2} x^3-\frac{2 x^3}{3}+\frac{1}{4} \sqrt{1-x^2} x-\frac{1}{4} \sin ^{-1}(x)","-\frac{1}{2} \sqrt{1-x^2} x^3-\frac{2 x^3}{3}+\frac{1}{4} \sqrt{1-x^2} x-\frac{1}{4} \sin ^{-1}(x)",1,"(-2*x^3)/3 + (x*Sqrt[1 - x^2])/4 - (x^3*Sqrt[1 - x^2])/2 - ArcSin[x]/4","A",6,5,42,0.1190,1,"{6688, 6742, 279, 321, 216}"
446,1,21,0,0.1128799,"\int x \left(-\sqrt{1-x}-\sqrt{1+x}\right) \left(\sqrt{1-x}+\sqrt{1+x}\right) \, dx","Int[x*(-Sqrt[1 - x] - Sqrt[1 + x])*(Sqrt[1 - x] + Sqrt[1 + x]),x]","\frac{2}{3} \left(1-x^2\right)^{3/2}-x^2","\frac{2}{3} \left(1-x^2\right)^{3/2}-x^2",1,"-x^2 + (2*(1 - x^2)^(3/2))/3","A",4,3,40,0.07500,1,"{6688, 6742, 261}"
447,1,22,0,0.0545297,"\int \left(-\sqrt{1-x}-\sqrt{1+x}\right) \left(\sqrt{1-x}+\sqrt{1+x}\right) \, dx","Int[(-Sqrt[1 - x] - Sqrt[1 + x])*(Sqrt[1 - x] + Sqrt[1 + x]),x]","-\sqrt{1-x^2} x-2 x-\sin ^{-1}(x)","-\sqrt{1-x^2} x-2 x-\sin ^{-1}(x)",1,"-2*x - x*Sqrt[1 - x^2] - ArcSin[x]","A",5,4,39,0.1026,1,"{6688, 6742, 195, 216}"
448,1,32,0,0.1957861,"\int \frac{\left(-\sqrt{1-x}-\sqrt{1+x}\right) \left(\sqrt{1-x}+\sqrt{1+x}\right)}{x} \, dx","Int[((-Sqrt[1 - x] - Sqrt[1 + x])*(Sqrt[1 - x] + Sqrt[1 + x]))/x,x]","-2 \sqrt{1-x^2}+2 \tanh ^{-1}\left(\sqrt{1-x^2}\right)-2 \log (x)","-2 \sqrt{1-x^2}+2 \tanh ^{-1}\left(\sqrt{1-x^2}\right)-2 \log (x)",1,"-2*Sqrt[1 - x^2] + 2*ArcTanh[Sqrt[1 - x^2]] - 2*Log[x]","A",7,6,42,0.1429,1,"{6688, 6742, 266, 50, 63, 206}"
449,1,26,0,0.205232,"\int \frac{\left(-\sqrt{1-x}-\sqrt{1+x}\right) \left(\sqrt{1-x}+\sqrt{1+x}\right)}{x^2} \, dx","Int[((-Sqrt[1 - x] - Sqrt[1 + x])*(Sqrt[1 - x] + Sqrt[1 + x]))/x^2,x]","\frac{2 \sqrt{1-x^2}}{x}+\frac{2}{x}+2 \sin ^{-1}(x)","\frac{2 \sqrt{1-x^2}}{x}+\frac{2}{x}+2 \sin ^{-1}(x)",1,"2/x + (2*Sqrt[1 - x^2])/x + 2*ArcSin[x]","A",5,4,42,0.09524,1,"{6688, 6742, 277, 216}"
450,1,33,0,0.2154258,"\int \frac{\left(-\sqrt{1-x}-\sqrt{1+x}\right) \left(\sqrt{1-x}+\sqrt{1+x}\right)}{x^3} \, dx","Int[((-Sqrt[1 - x] - Sqrt[1 + x])*(Sqrt[1 - x] + Sqrt[1 + x]))/x^3,x]","\frac{\sqrt{1-x^2}}{x^2}+\frac{1}{x^2}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)","\frac{\sqrt{1-x^2}}{x^2}+\frac{1}{x^2}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)",1,"x^(-2) + Sqrt[1 - x^2]/x^2 - ArcTanh[Sqrt[1 - x^2]]","A",7,6,42,0.1429,1,"{6688, 6742, 266, 47, 63, 206}"
451,1,28,0,0.3209485,"\int \frac{\sqrt{1-x}+\sqrt{1+x}}{-\sqrt{1-x}+\sqrt{1+x}} \, dx","Int[(Sqrt[1 - x] + Sqrt[1 + x])/(-Sqrt[1 - x] + Sqrt[1 + x]),x]","\sqrt{1-x^2}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)+\log (x)","\sqrt{1-x^2}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)+\log (x)",1,"Sqrt[1 - x^2] - ArcTanh[Sqrt[1 - x^2]] + Log[x]","A",15,7,39,0.1795,1,"{2103, 6688, 14, 266, 50, 63, 206}"
452,1,33,0,0.1429815,"\int \frac{-\sqrt{-1+x}+\sqrt{1+x}}{\sqrt{-1+x}+\sqrt{1+x}} \, dx","Int[(-Sqrt[-1 + x] + Sqrt[1 + x])/(Sqrt[-1 + x] + Sqrt[1 + x]),x]","\frac{x^2}{2}-\frac{1}{2} \sqrt{x-1} \sqrt{x+1} x+\frac{1}{2} \cosh ^{-1}(x)","\frac{x^2}{2}-\frac{1}{2} \sqrt{x-1} \sqrt{x+1} x+\frac{1}{2} \cosh ^{-1}(x)",1,"x^2/2 - (Sqrt[-1 + x]*x*Sqrt[1 + x])/2 + ArcCosh[x]/2","A",9,4,35,0.1143,1,"{2104, 6742, 38, 52}"
453,1,121,0,0.1031604,"\int \left(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right)^n \, dx","Int[(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^n,x]","\frac{a f^2 \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+a}}{d}\right)}{2 d^2 e (n+1)}+\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{2 e (n+1)}","\frac{a f^2 \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+a}}{d}\right)}{2 d^2 e (n+1)}+\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{2 e (n+1)}",1,"(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(1 + n)/(2*e*(1 + n)) + (a*f^2*(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, (d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])/d])/(2*d^2*e*(1 + n))","A",4,3,25,0.1200,1,"{2117, 947, 64}"
454,1,175,0,0.133334,"\int \left(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right)^3 \, dx","Int[(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^3,x]","-\frac{a d^3 f^2}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}+\frac{3 a d^2 f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{2 e}+\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^4}{8 e}+\frac{a f^2 \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^2}{4 e}+\frac{a d f^2 \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{e}","-\frac{a d^3 f^2}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}+\frac{3 a d^2 f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{2 e}+\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^4}{8 e}+\frac{a f^2 \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^2}{4 e}+\frac{a d f^2 \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{e}",1,"-(a*d^3*f^2)/(2*e*(e*x + f*Sqrt[a + (e^2*x^2)/f^2])) + (a*d*f^2*(e*x + f*Sqrt[a + (e^2*x^2)/f^2]))/e + (a*f^2*(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^2)/(4*e) + (d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^4/(8*e) + (3*a*d^2*f^2*Log[e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(2*e)","A",3,2,25,0.08000,1,"{2117, 893}"
455,1,136,0,0.1033287,"\int \left(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right)^2 \, dx","Int[(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^2,x]","-\frac{a d^2 f^2}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}+\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^3}{6 e}+\frac{a d f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{e}+\frac{a f^2 \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{2 e}","-\frac{a d^2 f^2}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}+\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^3}{6 e}+\frac{a d f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{e}+\frac{a f^2 \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{2 e}",1,"-(a*d^2*f^2)/(2*e*(e*x + f*Sqrt[a + (e^2*x^2)/f^2])) + (a*f^2*(e*x + f*Sqrt[a + (e^2*x^2)/f^2]))/(2*e) + (d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^3/(6*e) + (a*d*f^2*Log[e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/e","A",3,2,25,0.08000,1,"{2117, 893}"
456,1,68,0,0.0339407,"\int \left(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right) \, dx","Int[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2],x]","\frac{1}{2} f x \sqrt{a+\frac{e^2 x^2}{f^2}}+\frac{a f^2 \tanh ^{-1}\left(\frac{e x}{f \sqrt{a+\frac{e^2 x^2}{f^2}}}\right)}{2 e}+d x+\frac{e x^2}{2}","\frac{1}{2} f x \sqrt{a+\frac{e^2 x^2}{f^2}}+\frac{a f^2 \tanh ^{-1}\left(\frac{e x}{f \sqrt{a+\frac{e^2 x^2}{f^2}}}\right)}{2 e}+d x+\frac{e x^2}{2}",1,"d*x + (e*x^2)/2 + (f*x*Sqrt[a + (e^2*x^2)/f^2])/2 + (a*f^2*ArcTanh[(e*x)/(f*Sqrt[a + (e^2*x^2)/f^2])])/(2*e)","A",4,3,23,0.1304,1,"{195, 217, 206}"
457,1,117,0,0.0941509,"\int \frac{1}{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}} \, dx","Int[(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(-1),x]","-\frac{a f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{2 d^2 e}+\frac{\left(\frac{a f^2}{d^2}+1\right) \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)}{2 e}-\frac{a f^2}{2 d e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}","-\frac{a f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{2 d^2 e}+\frac{\left(\frac{a f^2}{d^2}+1\right) \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)}{2 e}-\frac{a f^2}{2 d e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}",1,"-(a*f^2)/(2*d*e*(e*x + f*Sqrt[a + (e^2*x^2)/f^2])) - (a*f^2*Log[e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(2*d^2*e) + ((1 + (a*f^2)/d^2)*Log[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(2*e)","A",3,2,25,0.08000,1,"{2117, 893}"
458,1,151,0,0.112668,"\int \frac{1}{\left(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right)^2} \, dx","Int[(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(-2),x]","-\frac{a f^2}{2 d^2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{\frac{a f^2}{d^2}+1}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)}-\frac{a f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{d^3 e}+\frac{a f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)}{d^3 e}","-\frac{a f^2}{2 d^2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{\frac{a f^2}{d^2}+1}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)}-\frac{a f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{d^3 e}+\frac{a f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)}{d^3 e}",1,"-(a*f^2)/(2*d^2*e*(e*x + f*Sqrt[a + (e^2*x^2)/f^2])) - (1 + (a*f^2)/d^2)/(2*e*(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])) - (a*f^2*Log[e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(d^3*e) + (a*f^2*Log[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(d^3*e)","A",3,2,25,0.08000,1,"{2117, 893}"
459,1,193,0,0.1274629,"\int \frac{1}{\left(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right)^3} \, dx","Int[(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(-3),x]","-\frac{a f^2}{2 d^3 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{a f^2}{d^3 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)}-\frac{\frac{a f^2}{d^2}+1}{4 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^2}-\frac{3 a f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{2 d^4 e}+\frac{3 a f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)}{2 d^4 e}","-\frac{a f^2}{2 d^3 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{a f^2}{d^3 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)}-\frac{\frac{a f^2}{d^2}+1}{4 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^2}-\frac{3 a f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}{2 d^4 e}+\frac{3 a f^2 \log \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)}{2 d^4 e}",1,"-(a*f^2)/(2*d^3*e*(e*x + f*Sqrt[a + (e^2*x^2)/f^2])) - (1 + (a*f^2)/d^2)/(4*e*(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^2) - (a*f^2)/(d^3*e*(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])) - (3*a*f^2*Log[e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(2*d^4*e) + (3*a*f^2*Log[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(2*d^4*e)","A",3,2,25,0.08000,1,"{2117, 893}"
460,1,225,0,0.1852372,"\int \left(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right)^{5/2} \, dx","Int[(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(5/2),x]","-\frac{a d^2 f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{5 a d^{3/2} f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 e}+\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{7/2}}{7 e}+\frac{a f^2 \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}{3 e}+\frac{2 a d f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{e}","-\frac{a d^2 f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{5 a d^{3/2} f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 e}+\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{7/2}}{7 e}+\frac{a f^2 \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}{3 e}+\frac{2 a d f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{e}",1,"(2*a*d*f^2*Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/e - (a*d^2*f^2*Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(2*e*(e*x + f*Sqrt[a + (e^2*x^2)/f^2])) + (a*f^2*(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(3/2))/(3*e) + (d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(7/2)/(7*e) - (5*a*d^(3/2)*f^2*ArcTanh[Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]]/Sqrt[d]])/(2*e)","A",6,5,27,0.1852,1,"{2117, 897, 1257, 1810, 206}"
461,1,183,0,0.1496871,"\int \left(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right)^{3/2} \, dx","Int[(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(3/2),x]","\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{5/2}}{5 e}+\frac{a f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{e}-\frac{a d f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{3 a \sqrt{d} f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 e}","\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{5/2}}{5 e}+\frac{a f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{e}-\frac{a d f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{3 a \sqrt{d} f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 e}",1,"(a*f^2*Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/e - (a*d*f^2*Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(2*e*(e*x + f*Sqrt[a + (e^2*x^2)/f^2])) + (d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(5/2)/(5*e) - (3*a*Sqrt[d]*f^2*ArcTanh[Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]]/Sqrt[d]])/(2*e)","A",6,5,27,0.1852,1,"{2117, 897, 1257, 1810, 206}"
462,1,147,0,0.1222836,"\int \sqrt{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}} \, dx","Int[Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]],x]","-\frac{a f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}+\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}{3 e}-\frac{a f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 \sqrt{d} e}","-\frac{a f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}+\frac{\left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}{3 e}-\frac{a f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 \sqrt{d} e}",1,"-(a*f^2*Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(2*e*(e*x + f*Sqrt[a + (e^2*x^2)/f^2])) + (d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(3/2)/(3*e) - (a*f^2*ArcTanh[Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]]/Sqrt[d]])/(2*Sqrt[d]*e)","A",6,5,27,0.1852,1,"{2117, 897, 1257, 1153, 206}"
463,1,147,0,0.1086023,"\int \frac{1}{\sqrt{d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}}} \, dx","Int[1/Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]],x]","\frac{a f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 d^{3/2} e}-\frac{a f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 d e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}+\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{e}","\frac{a f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 d^{3/2} e}-\frac{a f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 d e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}+\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{e}",1,"Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]]/e - (a*f^2*Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(2*d*e*(e*x + f*Sqrt[a + (e^2*x^2)/f^2])) + (a*f^2*ArcTanh[Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]]/Sqrt[d]])/(2*d^(3/2)*e)","A",5,5,27,0.1852,1,"{2117, 897, 1157, 388, 206}"
464,1,158,0,0.1558836,"\int \frac{1}{\left(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right)^{3/2}} \, dx","Int[(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(-3/2),x]","-\frac{a f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 d^2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{\frac{a f^2}{d^2}+1}{e \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}+\frac{3 a f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 d^{5/2} e}","-\frac{a f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 d^2 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{\frac{a f^2}{d^2}+1}{e \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}+\frac{3 a f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 d^{5/2} e}",1,"-((1 + (a*f^2)/d^2)/(e*Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])) - (a*f^2*Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(2*d^2*e*(e*x + f*Sqrt[a + (e^2*x^2)/f^2])) + (3*a*f^2*ArcTanh[Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]]/Sqrt[d]])/(2*d^(5/2)*e)","A",5,5,27,0.1852,1,"{2117, 897, 1259, 453, 206}"
465,1,199,0,0.1766845,"\int \frac{1}{\left(d+e x+f \sqrt{a+\frac{e^2 x^2}{f^2}}\right)^{5/2}} \, dx","Int[(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(-5/2),x]","-\frac{a f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 d^3 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{2 a f^2}{d^3 e \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}-\frac{\frac{a f^2}{d^2}+1}{3 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}+\frac{5 a f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 d^{7/2} e}","-\frac{a f^2 \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{2 d^3 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+e x\right)}-\frac{2 a f^2}{d^3 e \sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}-\frac{\frac{a f^2}{d^2}+1}{3 e \left(f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}+\frac{5 a f^2 \tanh ^{-1}\left(\frac{\sqrt{f \sqrt{a+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{d}}\right)}{2 d^{7/2} e}",1,"-(1 + (a*f^2)/d^2)/(3*e*(d + e*x + f*Sqrt[a + (e^2*x^2)/f^2])^(3/2)) - (2*a*f^2)/(d^3*e*Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]]) - (a*f^2*Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]])/(2*d^3*e*(e*x + f*Sqrt[a + (e^2*x^2)/f^2])) + (5*a*f^2*ArcTanh[Sqrt[d + e*x + f*Sqrt[a + (e^2*x^2)/f^2]]/Sqrt[d]])/(2*d^(7/2)*e)","A",6,5,27,0.1852,1,"{2117, 897, 1259, 1261, 206}"
466,1,41,0,0.0163519,"\int \sqrt{x-\sqrt{-4+x^2}} \, dx","Int[Sqrt[x - Sqrt[-4 + x^2]],x]","\frac{1}{3} \left(x-\sqrt{x^2-4}\right)^{3/2}+\frac{4}{\sqrt{x-\sqrt{x^2-4}}}","\frac{1}{3} \left(x-\sqrt{x^2-4}\right)^{3/2}+\frac{4}{\sqrt{x-\sqrt{x^2-4}}}",1,"4/Sqrt[x - Sqrt[-4 + x^2]] + (x - Sqrt[-4 + x^2])^(3/2)/3","A",3,2,17,0.1176,1,"{2117, 14}"
467,1,69,0,0.0570967,"\int \sqrt{a x+b \sqrt{c+\frac{a^2 x^2}{b^2}}} \, dx","Int[Sqrt[a*x + b*Sqrt[c + (a^2*x^2)/b^2]],x]","\frac{\left(b \sqrt{\frac{a^2 x^2}{b^2}+c}+a x\right)^{3/2}}{3 a}-\frac{b^2 c}{a \sqrt{b \sqrt{\frac{a^2 x^2}{b^2}+c}+a x}}","\frac{\left(b \sqrt{\frac{a^2 x^2}{b^2}+c}+a x\right)^{3/2}}{3 a}-\frac{b^2 c}{a \sqrt{b \sqrt{\frac{a^2 x^2}{b^2}+c}+a x}}",1,"-((b^2*c)/(a*Sqrt[a*x + b*Sqrt[c + (a^2*x^2)/b^2]])) + (a*x + b*Sqrt[c + (a^2*x^2)/b^2])^(3/2)/(3*a)","A",3,2,26,0.07692,1,"{2117, 14}"
468,1,45,0,0.009672,"\int \sqrt{1+\sqrt{1-x^2}} \, dx","Int[Sqrt[1 + Sqrt[1 - x^2]],x]","\frac{2 x}{\sqrt{\sqrt{1-x^2}+1}}-\frac{2 x^3}{3 \left(\sqrt{1-x^2}+1\right)^{3/2}}","\frac{2 x}{\sqrt{\sqrt{1-x^2}+1}}-\frac{2 x^3}{3 \left(\sqrt{1-x^2}+1\right)^{3/2}}",1,"(-2*x^3)/(3*(1 + Sqrt[1 - x^2])^(3/2)) + (2*x)/Sqrt[1 + Sqrt[1 - x^2]]","A",1,1,17,0.05882,1,"{2129}"
469,1,41,0,0.0073905,"\int \sqrt{1+\sqrt{1+x^2}} \, dx","Int[Sqrt[1 + Sqrt[1 + x^2]],x]","\frac{2 x^3}{3 \left(\sqrt{x^2+1}+1\right)^{3/2}}+\frac{2 x}{\sqrt{\sqrt{x^2+1}+1}}","\frac{2 x^3}{3 \left(\sqrt{x^2+1}+1\right)^{3/2}}+\frac{2 x}{\sqrt{\sqrt{x^2+1}+1}}",1,"(2*x^3)/(3*(1 + Sqrt[1 + x^2])^(3/2)) + (2*x)/Sqrt[1 + Sqrt[1 + x^2]]","A",1,1,15,0.06667,1,"{2129}"
470,1,41,0,0.0074054,"\int \sqrt{5+\sqrt{25+x^2}} \, dx","Int[Sqrt[5 + Sqrt[25 + x^2]],x]","\frac{2 x^3}{3 \left(\sqrt{x^2+25}+5\right)^{3/2}}+\frac{10 x}{\sqrt{\sqrt{x^2+25}+5}}","\frac{2 x^3}{3 \left(\sqrt{x^2+25}+5\right)^{3/2}}+\frac{10 x}{\sqrt{\sqrt{x^2+25}+5}}",1,"(2*x^3)/(3*(5 + Sqrt[25 + x^2])^(3/2)) + (10*x)/Sqrt[5 + Sqrt[25 + x^2]]","A",1,1,15,0.06667,1,"{2129}"
471,1,66,0,0.0329764,"\int \sqrt{a+b \sqrt{\frac{a^2}{b^2}+c x^2}} \, dx","Int[Sqrt[a + b*Sqrt[a^2/b^2 + c*x^2]],x]","\frac{2 b^2 c x^3}{3 \left(b \sqrt{\frac{a^2}{b^2}+c x^2}+a\right)^{3/2}}+\frac{2 a x}{\sqrt{b \sqrt{\frac{a^2}{b^2}+c x^2}+a}}","\frac{2 b^2 c x^3}{3 \left(b \sqrt{\frac{a^2}{b^2}+c x^2}+a\right)^{3/2}}+\frac{2 a x}{\sqrt{b \sqrt{\frac{a^2}{b^2}+c x^2}+a}}",1,"(2*b^2*c*x^3)/(3*(a + b*Sqrt[a^2/b^2 + c*x^2])^(3/2)) + (2*a*x)/Sqrt[a + b*Sqrt[a^2/b^2 + c*x^2]]","A",1,1,25,0.04000,1,"{2129}"
472,1,166,0,0.1796841,"\int \left(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right)^n \, dx","Int[(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^n,x]","\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{2 e \left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+b x+a}\right)}{2 d e-b f^2}\right)}{2 e (n+1) \left(2 d e-b f^2\right)^2}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{2 e (n+1)}","\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{2 e \left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+b x+a}\right)}{2 d e-b f^2}\right)}{2 e (n+1) \left(2 d e-b f^2\right)^2}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{2 e (n+1)}",1,"(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(1 + n)/(2*e*(1 + n)) + (f^2*(4*a*e^2 - b^2*f^2)*(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, (2*e*(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]))/(2*d*e - b*f^2)])/(2*e*(2*d*e - b*f^2)^2*(1 + n))","A",4,3,28,0.1071,1,"{2116, 947, 64}"
473,1,303,0,0.3843989,"\int \left(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right)^3 \, dx","Int[(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^3,x]","\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^2}{16 e^3}+\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right) \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+e x\right)}{8 e^4}-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right)^3}{32 e^5 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}+\frac{3 f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right)^2 \log \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}{32 e^5}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^4}{8 e}","\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^2}{16 e^3}+\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right) \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+e x\right)}{8 e^4}-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right)^3}{32 e^5 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}+\frac{3 f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right)^2 \log \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}{32 e^5}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^4}{8 e}",1,"(f^2*(2*d*e - b*f^2)*(4*a*e^2 - b^2*f^2)*(e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]))/(8*e^4) + (f^2*(4*a*e^2 - b^2*f^2)*(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^2)/(16*e^3) + (d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^4/(8*e) - (f^2*(2*d*e - b*f^2)^3*(4*a*e^2 - b^2*f^2))/(32*e^5*(b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2]))) + (3*f^2*(2*d*e - b*f^2)^2*(4*a*e^2 - b^2*f^2)*Log[b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2])])/(32*e^5)","A",3,2,28,0.07143,1,"{2116, 893}"
474,1,237,0,0.2393523,"\int \left(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right)^2 \, dx","Int[(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^2,x]","-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right)^2}{16 e^4 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}+\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right) \log \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}{8 e^4}+\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+e x\right)}{8 e^3}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^3}{6 e}","-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right)^2}{16 e^4 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}+\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right) \log \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}{8 e^4}+\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+e x\right)}{8 e^3}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^3}{6 e}",1,"(f^2*(4*a*e^2 - b^2*f^2)*(e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]))/(8*e^3) + (d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^3/(6*e) - (f^2*(2*d*e - b*f^2)^2*(4*a*e^2 - b^2*f^2))/(16*e^4*(b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2]))) + (f^2*(2*d*e - b*f^2)*(4*a*e^2 - b^2*f^2)*Log[b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2])])/(8*e^4)","A",3,2,28,0.07143,1,"{2116, 893}"
475,1,118,0,0.0625189,"\int \left(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right) \, dx","Int[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2],x]","\frac{f^2 \left(4 a e^2-b^2 f^2\right) \tanh ^{-1}\left(\frac{b f^2+2 e^2 x}{2 e f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}}\right)}{8 e^3}+\frac{f \left(b f^2+2 e^2 x\right) \sqrt{a+b x+\frac{e^2 x^2}{f^2}}}{4 e^2}+d x+\frac{e x^2}{2}","\frac{f^2 \left(4 a e^2-b^2 f^2\right) \tanh ^{-1}\left(\frac{b f^2+2 e^2 x}{2 e f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}}\right)}{8 e^3}+\frac{f \left(b f^2+2 e^2 x\right) \sqrt{a+b x+\frac{e^2 x^2}{f^2}}}{4 e^2}+d x+\frac{e x^2}{2}",1,"d*x + (e*x^2)/2 + (f*(b*f^2 + 2*e^2*x)*Sqrt[a + b*x + (e^2*x^2)/f^2])/(4*e^2) + (f^2*(4*a*e^2 - b^2*f^2)*ArcTanh[(b*f^2 + 2*e^2*x)/(2*e*f*Sqrt[a + b*x + (e^2*x^2)/f^2])])/(8*e^3)","A",4,3,26,0.1154,1,"{612, 621, 206}"
476,1,215,0,0.1929013,"\int \frac{1}{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}} \, dx","Int[(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(-1),x]","-\frac{f^2 \left(4 a e^2-b^2 f^2\right)}{2 e \left(2 d e-b f^2\right) \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \log \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}{2 e \left(2 d e-b f^2\right)^2}+\frac{2 \left(a e f^2-b d f^2+d^2 e\right) \log \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)}{\left(2 d e-b f^2\right)^2}","-\frac{f^2 \left(4 a e^2-b^2 f^2\right)}{2 e \left(2 d e-b f^2\right) \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \log \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}{2 e \left(2 d e-b f^2\right)^2}+\frac{2 \left(a e f^2-b d f^2+d^2 e\right) \log \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)}{\left(2 d e-b f^2\right)^2}",1,"-(f^2*(4*a*e^2 - b^2*f^2))/(2*e*(2*d*e - b*f^2)*(b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2]))) + (2*(d^2*e - b*d*f^2 + a*e*f^2)*Log[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/(2*d*e - b*f^2)^2 - (f^2*(4*a*e^2 - b^2*f^2)*Log[b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2])])/(2*e*(2*d*e - b*f^2)^2)","A",3,2,28,0.07143,1,"{2116, 893}"
477,1,266,0,0.2320462,"\int \frac{1}{\left(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right)^2} \, dx","Int[(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(-2),x]","\frac{2 f^2 \left(4 a e^2-b^2 f^2\right) \log \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)}{\left(2 d e-b f^2\right)^3}-\frac{f^2 \left(4 a e^2-b^2 f^2\right)}{\left(2 d e-b f^2\right)^2 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{2 f^2 \left(4 a e^2-b^2 f^2\right) \log \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}{\left(2 d e-b f^2\right)^3}-\frac{2 \left(a e f^2-b d f^2+d^2 e\right)}{\left(2 d e-b f^2\right)^2 \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)}","\frac{2 f^2 \left(4 a e^2-b^2 f^2\right) \log \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)}{\left(2 d e-b f^2\right)^3}-\frac{f^2 \left(4 a e^2-b^2 f^2\right)}{\left(2 d e-b f^2\right)^2 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{2 f^2 \left(4 a e^2-b^2 f^2\right) \log \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}{\left(2 d e-b f^2\right)^3}-\frac{2 \left(a e f^2-b d f^2+d^2 e\right)}{\left(2 d e-b f^2\right)^2 \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)}",1,"(-2*(d^2*e - b*d*f^2 + a*e*f^2))/((2*d*e - b*f^2)^2*(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])) - (f^2*(4*a*e^2 - b^2*f^2))/((2*d*e - b*f^2)^2*(b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2]))) + (2*f^2*(4*a*e^2 - b^2*f^2)*Log[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/(2*d*e - b*f^2)^3 - (2*f^2*(4*a*e^2 - b^2*f^2)*Log[b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2])])/(2*d*e - b*f^2)^3","A",3,2,28,0.07143,1,"{2116, 893}"
478,1,330,0,0.2894725,"\int \frac{1}{\left(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right)^3} \, dx","Int[(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(-3),x]","-\frac{2 f^2 \left(4 a e^2-b^2 f^2\right)}{\left(2 d e-b f^2\right)^3 \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)}+\frac{6 e f^2 \left(4 a e^2-b^2 f^2\right) \log \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)}{\left(2 d e-b f^2\right)^4}-\frac{2 e f^2 \left(4 a e^2-b^2 f^2\right)}{\left(2 d e-b f^2\right)^3 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{6 e f^2 \left(4 a e^2-b^2 f^2\right) \log \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}{\left(2 d e-b f^2\right)^4}-\frac{a e f^2-b d f^2+d^2 e}{\left(2 d e-b f^2\right)^2 \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^2}","-\frac{2 f^2 \left(4 a e^2-b^2 f^2\right)}{\left(2 d e-b f^2\right)^3 \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)}+\frac{6 e f^2 \left(4 a e^2-b^2 f^2\right) \log \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)}{\left(2 d e-b f^2\right)^4}-\frac{2 e f^2 \left(4 a e^2-b^2 f^2\right)}{\left(2 d e-b f^2\right)^3 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{6 e f^2 \left(4 a e^2-b^2 f^2\right) \log \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}{\left(2 d e-b f^2\right)^4}-\frac{a e f^2-b d f^2+d^2 e}{\left(2 d e-b f^2\right)^2 \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^2}",1,"-((d^2*e - b*d*f^2 + a*e*f^2)/((2*d*e - b*f^2)^2*(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^2)) - (2*f^2*(4*a*e^2 - b^2*f^2))/((2*d*e - b*f^2)^3*(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])) - (2*e*f^2*(4*a*e^2 - b^2*f^2))/((2*d*e - b*f^2)^3*(b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2]))) + (6*e*f^2*(4*a*e^2 - b^2*f^2)*Log[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/(2*d*e - b*f^2)^4 - (6*e*f^2*(4*a*e^2 - b^2*f^2)*Log[b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2])])/(2*d*e - b*f^2)^4","A",3,2,28,0.07143,1,"{2116, 893}"
479,1,370,0,0.600375,"\int \left(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right)^{5/2} \, dx","Int[(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(5/2),x]","\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}{12 e^3}+\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{4 e^4}-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right)^2 \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{16 e^4 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{5 f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{16 \sqrt{2} e^{9/2}}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{7/2}}{7 e}","\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}{12 e^3}+\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{4 e^4}-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right)^2 \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{16 e^4 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{5 f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{16 \sqrt{2} e^{9/2}}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{7/2}}{7 e}",1,"(f^2*(2*d*e - b*f^2)*(4*a*e^2 - b^2*f^2)*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/(4*e^4) + (f^2*(4*a*e^2 - b^2*f^2)*(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(3/2))/(12*e^3) + (d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(7/2)/(7*e) - (f^2*(2*d*e - b*f^2)^2*(4*a*e^2 - b^2*f^2)*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/(16*e^4*(b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2]))) - (5*f^2*(2*d*e - b*f^2)^(3/2)*(4*a*e^2 - b^2*f^2)*ArcTanh[(Sqrt[2]*Sqrt[e]*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/Sqrt[2*d*e - b*f^2]])/(16*Sqrt[2]*e^(9/2))","A",6,5,30,0.1667,1,"{2116, 897, 1257, 1810, 208}"
480,1,302,0,0.4146196,"\int \left(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right)^{3/2} \, dx","Int[(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(3/2),x]","\frac{f^2 \left(4 a e^2-b^2 f^2\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{4 e^3}-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{8 e^3 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{3 f^2 \left(4 a e^2-b^2 f^2\right) \sqrt{2 d e-b f^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{8 \sqrt{2} e^{7/2}}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{5/2}}{5 e}","\frac{f^2 \left(4 a e^2-b^2 f^2\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{4 e^3}-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \left(2 d e-b f^2\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{8 e^3 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{3 f^2 \left(4 a e^2-b^2 f^2\right) \sqrt{2 d e-b f^2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{8 \sqrt{2} e^{7/2}}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{5/2}}{5 e}",1,"(f^2*(4*a*e^2 - b^2*f^2)*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/(4*e^3) + (d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(5/2)/(5*e) - (f^2*(2*d*e - b*f^2)*(4*a*e^2 - b^2*f^2)*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/(8*e^3*(b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2]))) - (3*f^2*Sqrt[2*d*e - b*f^2]*(4*a*e^2 - b^2*f^2)*ArcTanh[(Sqrt[2]*Sqrt[e]*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/Sqrt[2*d*e - b*f^2]])/(8*Sqrt[2]*e^(7/2))","A",6,5,30,0.1667,1,"{2116, 897, 1257, 1810, 208}"
481,1,233,0,0.3045876,"\int \sqrt{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}} \, dx","Int[Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]],x]","-\frac{f^2 \left(4 a-\frac{b^2 f^2}{e^2}\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{4 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{4 \sqrt{2} e^{5/2} \sqrt{2 d e-b f^2}}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}{3 e}","-\frac{f^2 \left(4 a-\frac{b^2 f^2}{e^2}\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{4 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{4 \sqrt{2} e^{5/2} \sqrt{2 d e-b f^2}}+\frac{\left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}{3 e}",1,"(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(3/2)/(3*e) - (f^2*(4*a - (b^2*f^2)/e^2)*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/(4*(b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2]))) - (f^2*(4*a*e^2 - b^2*f^2)*ArcTanh[(Sqrt[2]*Sqrt[e]*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/Sqrt[2*d*e - b*f^2]])/(4*Sqrt[2]*e^(5/2)*Sqrt[2*d*e - b*f^2])","A",6,5,30,0.1667,1,"{2116, 897, 1257, 1153, 208}"
482,1,244,0,0.2916527,"\int \frac{1}{\sqrt{d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}}} \, dx","Int[1/Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]],x]","-\frac{f^2 \left(4 a e-\frac{b^2 f^2}{e}\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{2 \left(2 d e-b f^2\right) \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}+\frac{f^2 \left(4 a e^2-b^2 f^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{2 \sqrt{2} e^{3/2} \left(2 d e-b f^2\right)^{3/2}}+\frac{\sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{e}","-\frac{f^2 \left(4 a e-\frac{b^2 f^2}{e}\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{2 \left(2 d e-b f^2\right) \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}+\frac{f^2 \left(4 a e^2-b^2 f^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{2 \sqrt{2} e^{3/2} \left(2 d e-b f^2\right)^{3/2}}+\frac{\sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{e}",1,"Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]]/e - (f^2*(4*a*e - (b^2*f^2)/e)*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/(2*(2*d*e - b*f^2)*(b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2]))) + (f^2*(4*a*e^2 - b^2*f^2)*ArcTanh[(Sqrt[2]*Sqrt[e]*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/Sqrt[2*d*e - b*f^2]])/(2*Sqrt[2]*e^(3/2)*(2*d*e - b*f^2)^(3/2))","A",5,5,30,0.1667,1,"{2116, 897, 1157, 388, 208}"
483,1,269,0,0.3676327,"\int \frac{1}{\left(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right)^{3/2}} \, dx","Int[(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(-3/2),x]","-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\left(2 d e-b f^2\right)^2 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}+\frac{3 f^2 \left(4 a e^2-b^2 f^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{\sqrt{2} \sqrt{e} \left(2 d e-b f^2\right)^{5/2}}-\frac{4 \left(a e f^2-b d f^2+d^2 e\right)}{\left(2 d e-b f^2\right)^2 \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}","-\frac{f^2 \left(4 a e^2-b^2 f^2\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\left(2 d e-b f^2\right)^2 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}+\frac{3 f^2 \left(4 a e^2-b^2 f^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{\sqrt{2} \sqrt{e} \left(2 d e-b f^2\right)^{5/2}}-\frac{4 \left(a e f^2-b d f^2+d^2 e\right)}{\left(2 d e-b f^2\right)^2 \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}",1,"(-4*(d^2*e - b*d*f^2 + a*e*f^2))/((2*d*e - b*f^2)^2*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]]) - (f^2*(4*a*e^2 - b^2*f^2)*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/((2*d*e - b*f^2)^2*(b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2]))) + (3*f^2*(4*a*e^2 - b^2*f^2)*ArcTanh[(Sqrt[2]*Sqrt[e]*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/Sqrt[2*d*e - b*f^2]])/(Sqrt[2]*Sqrt[e]*(2*d*e - b*f^2)^(5/2))","A",5,5,30,0.1667,1,"{2116, 897, 1259, 453, 208}"
484,1,335,0,0.5002625,"\int \frac{1}{\left(d+e x+f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}\right)^{5/2}} \, dx","Int[(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(-5/2),x]","-\frac{4 f^2 \left(4 a e^2-b^2 f^2\right)}{\left(2 d e-b f^2\right)^3 \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}-\frac{2 e f^2 \left(4 a e^2-b^2 f^2\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\left(2 d e-b f^2\right)^3 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}+\frac{5 \sqrt{2} \sqrt{e} f^2 \left(4 a e^2-b^2 f^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{\left(2 d e-b f^2\right)^{7/2}}-\frac{4 \left(a e f^2-b d f^2+d^2 e\right)}{3 \left(2 d e-b f^2\right)^2 \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}","-\frac{4 f^2 \left(4 a e^2-b^2 f^2\right)}{\left(2 d e-b f^2\right)^3 \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}-\frac{2 e f^2 \left(4 a e^2-b^2 f^2\right) \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\left(2 d e-b f^2\right)^3 \left(2 e \left(f \sqrt{a+\frac{x \left(b f^2+e^2 x\right)}{f^2}}+e x\right)+b f^2\right)}+\frac{5 \sqrt{2} \sqrt{e} f^2 \left(4 a e^2-b^2 f^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{e} \sqrt{f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x}}{\sqrt{2 d e-b f^2}}\right)}{\left(2 d e-b f^2\right)^{7/2}}-\frac{4 \left(a e f^2-b d f^2+d^2 e\right)}{3 \left(2 d e-b f^2\right)^2 \left(f \sqrt{a+b x+\frac{e^2 x^2}{f^2}}+d+e x\right)^{3/2}}",1,"(-4*(d^2*e - b*d*f^2 + a*e*f^2))/(3*(2*d*e - b*f^2)^2*(d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2])^(3/2)) - (4*f^2*(4*a*e^2 - b^2*f^2))/((2*d*e - b*f^2)^3*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]]) - (2*e*f^2*(4*a*e^2 - b^2*f^2)*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/((2*d*e - b*f^2)^3*(b*f^2 + 2*e*(e*x + f*Sqrt[a + (x*(b*f^2 + e^2*x))/f^2]))) + (5*Sqrt[2]*Sqrt[e]*f^2*(4*a*e^2 - b^2*f^2)*ArcTanh[(Sqrt[2]*Sqrt[e]*Sqrt[d + e*x + f*Sqrt[a + b*x + (e^2*x^2)/f^2]])/Sqrt[2*d*e - b*f^2]])/(2*d*e - b*f^2)^(7/2)","A",6,5,30,0.1667,1,"{2116, 897, 1259, 1261, 208}"
485,1,164,0,0.1104973,"\int \left(a+x^2\right)^2 \left(x+\sqrt{a+x^2}\right)^n \, dx","Int[(a + x^2)^2*(x + Sqrt[a + x^2])^n,x]","-\frac{a^5 \left(\sqrt{a+x^2}+x\right)^{n-5}}{32 (5-n)}-\frac{5 a^4 \left(\sqrt{a+x^2}+x\right)^{n-3}}{32 (3-n)}-\frac{5 a^3 \left(\sqrt{a+x^2}+x\right)^{n-1}}{16 (1-n)}+\frac{5 a^2 \left(\sqrt{a+x^2}+x\right)^{n+1}}{16 (n+1)}+\frac{5 a \left(\sqrt{a+x^2}+x\right)^{n+3}}{32 (n+3)}+\frac{\left(\sqrt{a+x^2}+x\right)^{n+5}}{32 (n+5)}","-\frac{a^5 \left(\sqrt{a+x^2}+x\right)^{n-5}}{32 (5-n)}-\frac{5 a^4 \left(\sqrt{a+x^2}+x\right)^{n-3}}{32 (3-n)}-\frac{5 a^3 \left(\sqrt{a+x^2}+x\right)^{n-1}}{16 (1-n)}+\frac{5 a^2 \left(\sqrt{a+x^2}+x\right)^{n+1}}{16 (n+1)}+\frac{5 a \left(\sqrt{a+x^2}+x\right)^{n+3}}{32 (n+3)}+\frac{\left(\sqrt{a+x^2}+x\right)^{n+5}}{32 (n+5)}",1,"-(a^5*(x + Sqrt[a + x^2])^(-5 + n))/(32*(5 - n)) - (5*a^4*(x + Sqrt[a + x^2])^(-3 + n))/(32*(3 - n)) - (5*a^3*(x + Sqrt[a + x^2])^(-1 + n))/(16*(1 - n)) + (5*a^2*(x + Sqrt[a + x^2])^(1 + n))/(16*(1 + n)) + (5*a*(x + Sqrt[a + x^2])^(3 + n))/(32*(3 + n)) + (x + Sqrt[a + x^2])^(5 + n)/(32*(5 + n))","A",3,2,21,0.09524,1,"{2122, 270}"
486,1,108,0,0.0626827,"\int \left(a+x^2\right) \left(x+\sqrt{a+x^2}\right)^n \, dx","Int[(a + x^2)*(x + Sqrt[a + x^2])^n,x]","-\frac{a^3 \left(\sqrt{a+x^2}+x\right)^{n-3}}{8 (3-n)}-\frac{3 a^2 \left(\sqrt{a+x^2}+x\right)^{n-1}}{8 (1-n)}+\frac{3 a \left(\sqrt{a+x^2}+x\right)^{n+1}}{8 (n+1)}+\frac{\left(\sqrt{a+x^2}+x\right)^{n+3}}{8 (n+3)}","-\frac{a^3 \left(\sqrt{a+x^2}+x\right)^{n-3}}{8 (3-n)}-\frac{3 a^2 \left(\sqrt{a+x^2}+x\right)^{n-1}}{8 (1-n)}+\frac{3 a \left(\sqrt{a+x^2}+x\right)^{n+1}}{8 (n+1)}+\frac{\left(\sqrt{a+x^2}+x\right)^{n+3}}{8 (n+3)}",1,"-(a^3*(x + Sqrt[a + x^2])^(-3 + n))/(8*(3 - n)) - (3*a^2*(x + Sqrt[a + x^2])^(-1 + n))/(8*(1 - n)) + (3*a*(x + Sqrt[a + x^2])^(1 + n))/(8*(1 + n)) + (x + Sqrt[a + x^2])^(3 + n)/(8*(3 + n))","A",3,2,19,0.1053,1,"{2122, 270}"
487,1,52,0,0.0211651,"\int \left(x+\sqrt{a+x^2}\right)^n \, dx","Int[(x + Sqrt[a + x^2])^n,x]","\frac{\left(\sqrt{a+x^2}+x\right)^{n+1}}{2 (n+1)}-\frac{a \left(\sqrt{a+x^2}+x\right)^{n-1}}{2 (1-n)}","\frac{\left(\sqrt{a+x^2}+x\right)^{n+1}}{2 (n+1)}-\frac{a \left(\sqrt{a+x^2}+x\right)^{n-1}}{2 (1-n)}",1,"-(a*(x + Sqrt[a + x^2])^(-1 + n))/(2*(1 - n)) + (x + Sqrt[a + x^2])^(1 + n)/(2*(1 + n))","A",3,2,13,0.1538,1,"{2117, 14}"
488,1,59,0,0.0679521,"\int \frac{\left(x+\sqrt{a+x^2}\right)^n}{a+x^2} \, dx","Int[(x + Sqrt[a + x^2])^n/(a + x^2),x]","\frac{2 \left(\sqrt{a+x^2}+x\right)^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\frac{\left(x+\sqrt{x^2+a}\right)^2}{a}\right)}{a (n+1)}","\frac{2 \left(\sqrt{a+x^2}+x\right)^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\frac{\left(x+\sqrt{x^2+a}\right)^2}{a}\right)}{a (n+1)}",1,"(2*(x + Sqrt[a + x^2])^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -((x + Sqrt[a + x^2])^2/a)])/(a*(1 + n))","A",2,2,21,0.09524,1,"{2122, 364}"
489,1,59,0,0.0661979,"\int \frac{\left(x+\sqrt{a+x^2}\right)^n}{\left(a+x^2\right)^2} \, dx","Int[(x + Sqrt[a + x^2])^n/(a + x^2)^2,x]","\frac{8 \left(\sqrt{a+x^2}+x\right)^{n+3} \, _2F_1\left(3,\frac{n+3}{2};\frac{n+5}{2};-\frac{\left(x+\sqrt{x^2+a}\right)^2}{a}\right)}{a^3 (n+3)}","\frac{8 \left(\sqrt{a+x^2}+x\right)^{n+3} \, _2F_1\left(3,\frac{n+3}{2};\frac{n+5}{2};-\frac{\left(x+\sqrt{x^2+a}\right)^2}{a}\right)}{a^3 (n+3)}",1,"(8*(x + Sqrt[a + x^2])^(3 + n)*Hypergeometric2F1[3, (3 + n)/2, (5 + n)/2, -((x + Sqrt[a + x^2])^2/a)])/(a^3*(3 + n))","A",2,2,21,0.09524,1,"{2122, 364}"
490,1,176,0,0.1088881,"\int \left(a+x^2\right)^2 \left(x-\sqrt{a+x^2}\right)^n \, dx","Int[(a + x^2)^2*(x - Sqrt[a + x^2])^n,x]","-\frac{a^5 \left(x-\sqrt{a+x^2}\right)^{n-5}}{32 (5-n)}-\frac{5 a^4 \left(x-\sqrt{a+x^2}\right)^{n-3}}{32 (3-n)}-\frac{5 a^3 \left(x-\sqrt{a+x^2}\right)^{n-1}}{16 (1-n)}+\frac{5 a^2 \left(x-\sqrt{a+x^2}\right)^{n+1}}{16 (n+1)}+\frac{5 a \left(x-\sqrt{a+x^2}\right)^{n+3}}{32 (n+3)}+\frac{\left(x-\sqrt{a+x^2}\right)^{n+5}}{32 (n+5)}","-\frac{a^5 \left(x-\sqrt{a+x^2}\right)^{n-5}}{32 (5-n)}-\frac{5 a^4 \left(x-\sqrt{a+x^2}\right)^{n-3}}{32 (3-n)}-\frac{5 a^3 \left(x-\sqrt{a+x^2}\right)^{n-1}}{16 (1-n)}+\frac{5 a^2 \left(x-\sqrt{a+x^2}\right)^{n+1}}{16 (n+1)}+\frac{5 a \left(x-\sqrt{a+x^2}\right)^{n+3}}{32 (n+3)}+\frac{\left(x-\sqrt{a+x^2}\right)^{n+5}}{32 (n+5)}",1,"-(a^5*(x - Sqrt[a + x^2])^(-5 + n))/(32*(5 - n)) - (5*a^4*(x - Sqrt[a + x^2])^(-3 + n))/(32*(3 - n)) - (5*a^3*(x - Sqrt[a + x^2])^(-1 + n))/(16*(1 - n)) + (5*a^2*(x - Sqrt[a + x^2])^(1 + n))/(16*(1 + n)) + (5*a*(x - Sqrt[a + x^2])^(3 + n))/(32*(3 + n)) + (x - Sqrt[a + x^2])^(5 + n)/(32*(5 + n))","A",3,2,23,0.08696,1,"{2122, 270}"
491,1,116,0,0.0638217,"\int \left(a+x^2\right) \left(x-\sqrt{a+x^2}\right)^n \, dx","Int[(a + x^2)*(x - Sqrt[a + x^2])^n,x]","-\frac{a^3 \left(x-\sqrt{a+x^2}\right)^{n-3}}{8 (3-n)}-\frac{3 a^2 \left(x-\sqrt{a+x^2}\right)^{n-1}}{8 (1-n)}+\frac{3 a \left(x-\sqrt{a+x^2}\right)^{n+1}}{8 (n+1)}+\frac{\left(x-\sqrt{a+x^2}\right)^{n+3}}{8 (n+3)}","-\frac{a^3 \left(x-\sqrt{a+x^2}\right)^{n-3}}{8 (3-n)}-\frac{3 a^2 \left(x-\sqrt{a+x^2}\right)^{n-1}}{8 (1-n)}+\frac{3 a \left(x-\sqrt{a+x^2}\right)^{n+1}}{8 (n+1)}+\frac{\left(x-\sqrt{a+x^2}\right)^{n+3}}{8 (n+3)}",1,"-(a^3*(x - Sqrt[a + x^2])^(-3 + n))/(8*(3 - n)) - (3*a^2*(x - Sqrt[a + x^2])^(-1 + n))/(8*(1 - n)) + (3*a*(x - Sqrt[a + x^2])^(1 + n))/(8*(1 + n)) + (x - Sqrt[a + x^2])^(3 + n)/(8*(3 + n))","A",3,2,21,0.09524,1,"{2122, 270}"
492,1,56,0,0.0228994,"\int \left(x-\sqrt{a+x^2}\right)^n \, dx","Int[(x - Sqrt[a + x^2])^n,x]","\frac{\left(x-\sqrt{a+x^2}\right)^{n+1}}{2 (n+1)}-\frac{a \left(x-\sqrt{a+x^2}\right)^{n-1}}{2 (1-n)}","\frac{\left(x-\sqrt{a+x^2}\right)^{n+1}}{2 (n+1)}-\frac{a \left(x-\sqrt{a+x^2}\right)^{n-1}}{2 (1-n)}",1,"-(a*(x - Sqrt[a + x^2])^(-1 + n))/(2*(1 - n)) + (x - Sqrt[a + x^2])^(1 + n)/(2*(1 + n))","A",3,2,15,0.1333,1,"{2117, 14}"
493,1,63,0,0.0721823,"\int \frac{\left(x-\sqrt{a+x^2}\right)^n}{a+x^2} \, dx","Int[(x - Sqrt[a + x^2])^n/(a + x^2),x]","\frac{2 \left(x-\sqrt{a+x^2}\right)^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\frac{\left(x-\sqrt{x^2+a}\right)^2}{a}\right)}{a (n+1)}","\frac{2 \left(x-\sqrt{a+x^2}\right)^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};-\frac{\left(x-\sqrt{x^2+a}\right)^2}{a}\right)}{a (n+1)}",1,"(2*(x - Sqrt[a + x^2])^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, -((x - Sqrt[a + x^2])^2/a)])/(a*(1 + n))","A",2,2,23,0.08696,1,"{2122, 364}"
494,1,63,0,0.0650891,"\int \frac{\left(x-\sqrt{a+x^2}\right)^n}{\left(a+x^2\right)^2} \, dx","Int[(x - Sqrt[a + x^2])^n/(a + x^2)^2,x]","\frac{8 \left(x-\sqrt{a+x^2}\right)^{n+3} \, _2F_1\left(3,\frac{n+3}{2};\frac{n+5}{2};-\frac{\left(x-\sqrt{x^2+a}\right)^2}{a}\right)}{a^3 (n+3)}","\frac{8 \left(x-\sqrt{a+x^2}\right)^{n+3} \, _2F_1\left(3,\frac{n+3}{2};\frac{n+5}{2};-\frac{\left(x-\sqrt{x^2+a}\right)^2}{a}\right)}{a^3 (n+3)}",1,"(8*(x - Sqrt[a + x^2])^(3 + n)*Hypergeometric2F1[3, (3 + n)/2, (5 + n)/2, -((x - Sqrt[a + x^2])^2/a)])/(a^3*(3 + n))","A",2,2,23,0.08696,1,"{2122, 364}"
495,1,187,0,0.1171777,"\int \left(a+x^2\right)^{5/2} \left(x+\sqrt{a+x^2}\right)^n \, dx","Int[(a + x^2)^(5/2)*(x + Sqrt[a + x^2])^n,x]","-\frac{a^6 \left(\sqrt{a+x^2}+x\right)^{n-6}}{64 (6-n)}-\frac{3 a^5 \left(\sqrt{a+x^2}+x\right)^{n-4}}{32 (4-n)}-\frac{15 a^4 \left(\sqrt{a+x^2}+x\right)^{n-2}}{64 (2-n)}+\frac{5 a^3 \left(\sqrt{a+x^2}+x\right)^n}{16 n}+\frac{15 a^2 \left(\sqrt{a+x^2}+x\right)^{n+2}}{64 (n+2)}+\frac{3 a \left(\sqrt{a+x^2}+x\right)^{n+4}}{32 (n+4)}+\frac{\left(\sqrt{a+x^2}+x\right)^{n+6}}{64 (n+6)}","-\frac{a^6 \left(\sqrt{a+x^2}+x\right)^{n-6}}{64 (6-n)}-\frac{3 a^5 \left(\sqrt{a+x^2}+x\right)^{n-4}}{32 (4-n)}-\frac{15 a^4 \left(\sqrt{a+x^2}+x\right)^{n-2}}{64 (2-n)}+\frac{5 a^3 \left(\sqrt{a+x^2}+x\right)^n}{16 n}+\frac{15 a^2 \left(\sqrt{a+x^2}+x\right)^{n+2}}{64 (n+2)}+\frac{3 a \left(\sqrt{a+x^2}+x\right)^{n+4}}{32 (n+4)}+\frac{\left(\sqrt{a+x^2}+x\right)^{n+6}}{64 (n+6)}",1,"-(a^6*(x + Sqrt[a + x^2])^(-6 + n))/(64*(6 - n)) - (3*a^5*(x + Sqrt[a + x^2])^(-4 + n))/(32*(4 - n)) - (15*a^4*(x + Sqrt[a + x^2])^(-2 + n))/(64*(2 - n)) + (5*a^3*(x + Sqrt[a + x^2])^n)/(16*n) + (15*a^2*(x + Sqrt[a + x^2])^(2 + n))/(64*(2 + n)) + (3*a*(x + Sqrt[a + x^2])^(4 + n))/(32*(4 + n)) + (x + Sqrt[a + x^2])^(6 + n)/(64*(6 + n))","A",3,2,23,0.08696,1,"{2122, 270}"
496,1,131,0,0.094264,"\int \left(a+x^2\right)^{3/2} \left(x+\sqrt{a+x^2}\right)^n \, dx","Int[(a + x^2)^(3/2)*(x + Sqrt[a + x^2])^n,x]","-\frac{a^4 \left(\sqrt{a+x^2}+x\right)^{n-4}}{16 (4-n)}-\frac{a^3 \left(\sqrt{a+x^2}+x\right)^{n-2}}{4 (2-n)}+\frac{3 a^2 \left(\sqrt{a+x^2}+x\right)^n}{8 n}+\frac{a \left(\sqrt{a+x^2}+x\right)^{n+2}}{4 (n+2)}+\frac{\left(\sqrt{a+x^2}+x\right)^{n+4}}{16 (n+4)}","-\frac{a^4 \left(\sqrt{a+x^2}+x\right)^{n-4}}{16 (4-n)}-\frac{a^3 \left(\sqrt{a+x^2}+x\right)^{n-2}}{4 (2-n)}+\frac{3 a^2 \left(\sqrt{a+x^2}+x\right)^n}{8 n}+\frac{a \left(\sqrt{a+x^2}+x\right)^{n+2}}{4 (n+2)}+\frac{\left(\sqrt{a+x^2}+x\right)^{n+4}}{16 (n+4)}",1,"-(a^4*(x + Sqrt[a + x^2])^(-4 + n))/(16*(4 - n)) - (a^3*(x + Sqrt[a + x^2])^(-2 + n))/(4*(2 - n)) + (3*a^2*(x + Sqrt[a + x^2])^n)/(8*n) + (a*(x + Sqrt[a + x^2])^(2 + n))/(4*(2 + n)) + (x + Sqrt[a + x^2])^(4 + n)/(16*(4 + n))","A",3,2,23,0.08696,1,"{2122, 270}"
497,1,75,0,0.0755965,"\int \sqrt{a+x^2} \left(x+\sqrt{a+x^2}\right)^n \, dx","Int[Sqrt[a + x^2]*(x + Sqrt[a + x^2])^n,x]","-\frac{a^2 \left(\sqrt{a+x^2}+x\right)^{n-2}}{4 (2-n)}+\frac{a \left(\sqrt{a+x^2}+x\right)^n}{2 n}+\frac{\left(\sqrt{a+x^2}+x\right)^{n+2}}{4 (n+2)}","-\frac{a^2 \left(\sqrt{a+x^2}+x\right)^{n-2}}{4 (2-n)}+\frac{a \left(\sqrt{a+x^2}+x\right)^n}{2 n}+\frac{\left(\sqrt{a+x^2}+x\right)^{n+2}}{4 (n+2)}",1,"-(a^2*(x + Sqrt[a + x^2])^(-2 + n))/(4*(2 - n)) + (a*(x + Sqrt[a + x^2])^n)/(2*n) + (x + Sqrt[a + x^2])^(2 + n)/(4*(2 + n))","A",3,2,23,0.08696,1,"{2122, 270}"
498,1,17,0,0.0536436,"\int \frac{\left(x+\sqrt{a+x^2}\right)^n}{\sqrt{a+x^2}} \, dx","Int[(x + Sqrt[a + x^2])^n/Sqrt[a + x^2],x]","\frac{\left(\sqrt{a+x^2}+x\right)^n}{n}","\frac{\left(\sqrt{a+x^2}+x\right)^n}{n}",1,"(x + Sqrt[a + x^2])^n/n","A",2,2,23,0.08696,1,"{2122, 30}"
499,1,59,0,0.0717657,"\int \frac{\left(x+\sqrt{a+x^2}\right)^n}{\left(a+x^2\right)^{3/2}} \, dx","Int[(x + Sqrt[a + x^2])^n/(a + x^2)^(3/2),x]","\frac{4 \left(\sqrt{a+x^2}+x\right)^{n+2} \, _2F_1\left(2,\frac{n+2}{2};\frac{n+4}{2};-\frac{\left(x+\sqrt{x^2+a}\right)^2}{a}\right)}{a^2 (n+2)}","\frac{4 \left(\sqrt{a+x^2}+x\right)^{n+2} \, _2F_1\left(2,\frac{n+2}{2};\frac{n+4}{2};-\frac{\left(x+\sqrt{x^2+a}\right)^2}{a}\right)}{a^2 (n+2)}",1,"(4*(x + Sqrt[a + x^2])^(2 + n)*Hypergeometric2F1[2, (2 + n)/2, (4 + n)/2, -((x + Sqrt[a + x^2])^2/a)])/(a^2*(2 + n))","A",2,2,23,0.08696,1,"{2122, 364}"
500,1,59,0,0.0715277,"\int \frac{\left(x+\sqrt{a+x^2}\right)^n}{\left(a+x^2\right)^{5/2}} \, dx","Int[(x + Sqrt[a + x^2])^n/(a + x^2)^(5/2),x]","\frac{16 \left(\sqrt{a+x^2}+x\right)^{n+4} \, _2F_1\left(4,\frac{n+4}{2};\frac{n+6}{2};-\frac{\left(x+\sqrt{x^2+a}\right)^2}{a}\right)}{a^4 (n+4)}","\frac{16 \left(\sqrt{a+x^2}+x\right)^{n+4} \, _2F_1\left(4,\frac{n+4}{2};\frac{n+6}{2};-\frac{\left(x+\sqrt{x^2+a}\right)^2}{a}\right)}{a^4 (n+4)}",1,"(16*(x + Sqrt[a + x^2])^(4 + n)*Hypergeometric2F1[4, (4 + n)/2, (6 + n)/2, -((x + Sqrt[a + x^2])^2/a)])/(a^4*(4 + n))","A",2,2,23,0.08696,1,"{2122, 364}"
501,1,201,0,0.1121335,"\int \left(a+x^2\right)^{5/2} \left(x-\sqrt{a+x^2}\right)^n \, dx","Int[(a + x^2)^(5/2)*(x - Sqrt[a + x^2])^n,x]","\frac{a^6 \left(x-\sqrt{a+x^2}\right)^{n-6}}{64 (6-n)}+\frac{3 a^5 \left(x-\sqrt{a+x^2}\right)^{n-4}}{32 (4-n)}+\frac{15 a^4 \left(x-\sqrt{a+x^2}\right)^{n-2}}{64 (2-n)}-\frac{5 a^3 \left(x-\sqrt{a+x^2}\right)^n}{16 n}-\frac{15 a^2 \left(x-\sqrt{a+x^2}\right)^{n+2}}{64 (n+2)}-\frac{3 a \left(x-\sqrt{a+x^2}\right)^{n+4}}{32 (n+4)}-\frac{\left(x-\sqrt{a+x^2}\right)^{n+6}}{64 (n+6)}","\frac{a^6 \left(x-\sqrt{a+x^2}\right)^{n-6}}{64 (6-n)}+\frac{3 a^5 \left(x-\sqrt{a+x^2}\right)^{n-4}}{32 (4-n)}+\frac{15 a^4 \left(x-\sqrt{a+x^2}\right)^{n-2}}{64 (2-n)}-\frac{5 a^3 \left(x-\sqrt{a+x^2}\right)^n}{16 n}-\frac{15 a^2 \left(x-\sqrt{a+x^2}\right)^{n+2}}{64 (n+2)}-\frac{3 a \left(x-\sqrt{a+x^2}\right)^{n+4}}{32 (n+4)}-\frac{\left(x-\sqrt{a+x^2}\right)^{n+6}}{64 (n+6)}",1,"(a^6*(x - Sqrt[a + x^2])^(-6 + n))/(64*(6 - n)) + (3*a^5*(x - Sqrt[a + x^2])^(-4 + n))/(32*(4 - n)) + (15*a^4*(x - Sqrt[a + x^2])^(-2 + n))/(64*(2 - n)) - (5*a^3*(x - Sqrt[a + x^2])^n)/(16*n) - (15*a^2*(x - Sqrt[a + x^2])^(2 + n))/(64*(2 + n)) - (3*a*(x - Sqrt[a + x^2])^(4 + n))/(32*(4 + n)) - (x - Sqrt[a + x^2])^(6 + n)/(64*(6 + n))","A",3,2,25,0.08000,1,"{2122, 270}"
502,1,141,0,0.0948329,"\int \left(a+x^2\right)^{3/2} \left(x-\sqrt{a+x^2}\right)^n \, dx","Int[(a + x^2)^(3/2)*(x - Sqrt[a + x^2])^n,x]","\frac{a^4 \left(x-\sqrt{a+x^2}\right)^{n-4}}{16 (4-n)}+\frac{a^3 \left(x-\sqrt{a+x^2}\right)^{n-2}}{4 (2-n)}-\frac{3 a^2 \left(x-\sqrt{a+x^2}\right)^n}{8 n}-\frac{a \left(x-\sqrt{a+x^2}\right)^{n+2}}{4 (n+2)}-\frac{\left(x-\sqrt{a+x^2}\right)^{n+4}}{16 (n+4)}","\frac{a^4 \left(x-\sqrt{a+x^2}\right)^{n-4}}{16 (4-n)}+\frac{a^3 \left(x-\sqrt{a+x^2}\right)^{n-2}}{4 (2-n)}-\frac{3 a^2 \left(x-\sqrt{a+x^2}\right)^n}{8 n}-\frac{a \left(x-\sqrt{a+x^2}\right)^{n+2}}{4 (n+2)}-\frac{\left(x-\sqrt{a+x^2}\right)^{n+4}}{16 (n+4)}",1,"(a^4*(x - Sqrt[a + x^2])^(-4 + n))/(16*(4 - n)) + (a^3*(x - Sqrt[a + x^2])^(-2 + n))/(4*(2 - n)) - (3*a^2*(x - Sqrt[a + x^2])^n)/(8*n) - (a*(x - Sqrt[a + x^2])^(2 + n))/(4*(2 + n)) - (x - Sqrt[a + x^2])^(4 + n)/(16*(4 + n))","A",3,2,25,0.08000,1,"{2122, 270}"
503,1,81,0,0.0750473,"\int \sqrt{a+x^2} \left(x-\sqrt{a+x^2}\right)^n \, dx","Int[Sqrt[a + x^2]*(x - Sqrt[a + x^2])^n,x]","\frac{a^2 \left(x-\sqrt{a+x^2}\right)^{n-2}}{4 (2-n)}-\frac{a \left(x-\sqrt{a+x^2}\right)^n}{2 n}-\frac{\left(x-\sqrt{a+x^2}\right)^{n+2}}{4 (n+2)}","\frac{a^2 \left(x-\sqrt{a+x^2}\right)^{n-2}}{4 (2-n)}-\frac{a \left(x-\sqrt{a+x^2}\right)^n}{2 n}-\frac{\left(x-\sqrt{a+x^2}\right)^{n+2}}{4 (n+2)}",1,"(a^2*(x - Sqrt[a + x^2])^(-2 + n))/(4*(2 - n)) - (a*(x - Sqrt[a + x^2])^n)/(2*n) - (x - Sqrt[a + x^2])^(2 + n)/(4*(2 + n))","A",3,2,25,0.08000,1,"{2122, 270}"
504,1,20,0,0.0565753,"\int \frac{\left(x-\sqrt{a+x^2}\right)^n}{\sqrt{a+x^2}} \, dx","Int[(x - Sqrt[a + x^2])^n/Sqrt[a + x^2],x]","-\frac{\left(x-\sqrt{a+x^2}\right)^n}{n}","-\frac{\left(x-\sqrt{a+x^2}\right)^n}{n}",1,"-((x - Sqrt[a + x^2])^n/n)","A",2,2,25,0.08000,1,"{2122, 30}"
505,1,63,0,0.0724693,"\int \frac{\left(x-\sqrt{a+x^2}\right)^n}{\left(a+x^2\right)^{3/2}} \, dx","Int[(x - Sqrt[a + x^2])^n/(a + x^2)^(3/2),x]","-\frac{4 \left(x-\sqrt{a+x^2}\right)^{n+2} \, _2F_1\left(2,\frac{n+2}{2};\frac{n+4}{2};-\frac{\left(x-\sqrt{x^2+a}\right)^2}{a}\right)}{a^2 (n+2)}","-\frac{4 \left(x-\sqrt{a+x^2}\right)^{n+2} \, _2F_1\left(2,\frac{n+2}{2};\frac{n+4}{2};-\frac{\left(x-\sqrt{x^2+a}\right)^2}{a}\right)}{a^2 (n+2)}",1,"(-4*(x - Sqrt[a + x^2])^(2 + n)*Hypergeometric2F1[2, (2 + n)/2, (4 + n)/2, -((x - Sqrt[a + x^2])^2/a)])/(a^2*(2 + n))","A",2,2,25,0.08000,1,"{2122, 364}"
506,1,63,0,0.07218,"\int \frac{\left(x-\sqrt{a+x^2}\right)^n}{\left(a+x^2\right)^{5/2}} \, dx","Int[(x - Sqrt[a + x^2])^n/(a + x^2)^(5/2),x]","-\frac{16 \left(x-\sqrt{a+x^2}\right)^{n+4} \, _2F_1\left(4,\frac{n+4}{2};\frac{n+6}{2};-\frac{\left(x-\sqrt{x^2+a}\right)^2}{a}\right)}{a^4 (n+4)}","-\frac{16 \left(x-\sqrt{a+x^2}\right)^{n+4} \, _2F_1\left(4,\frac{n+4}{2};\frac{n+6}{2};-\frac{\left(x-\sqrt{x^2+a}\right)^2}{a}\right)}{a^4 (n+4)}",1,"(-16*(x - Sqrt[a + x^2])^(4 + n)*Hypergeometric2F1[4, (4 + n)/2, (6 + n)/2, -((x - Sqrt[a + x^2])^2/a)])/(a^4*(4 + n))","A",2,2,25,0.08000,1,"{2122, 364}"
507,1,365,0,0.4737595,"\int \left(a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right)^2 \left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n \, dx","Int[(a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2)^2*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n,x]","\frac{\left(d^2-a f^2\right)^5 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-5}}{32 e f^4 (5-n)}-\frac{5 \left(d^2-a f^2\right)^4 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-3}}{32 e f^4 (3-n)}+\frac{5 \left(d^2-a f^2\right)^3 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-1}}{16 e f^4 (1-n)}+\frac{5 \left(d^2-a f^2\right)^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{16 e f^4 (n+1)}-\frac{5 \left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+3}}{32 e f^4 (n+3)}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+5}}{32 e f^4 (n+5)}","\frac{\left(d^2-a f^2\right)^5 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-5}}{32 e f^4 (5-n)}-\frac{5 \left(d^2-a f^2\right)^4 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-3}}{32 e f^4 (3-n)}+\frac{5 \left(d^2-a f^2\right)^3 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-1}}{16 e f^4 (1-n)}+\frac{5 \left(d^2-a f^2\right)^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{16 e f^4 (n+1)}-\frac{5 \left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+3}}{32 e f^4 (n+3)}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+5}}{32 e f^4 (n+5)}",1,"((d^2 - a*f^2)^5*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(-5 + n))/(32*e*f^4*(5 - n)) - (5*(d^2 - a*f^2)^4*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(-3 + n))/(32*e*f^4*(3 - n)) + (5*(d^2 - a*f^2)^3*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(-1 + n))/(16*e*f^4*(1 - n)) + (5*(d^2 - a*f^2)^2*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(1 + n))/(16*e*f^4*(1 + n)) - (5*(d^2 - a*f^2)*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(3 + n))/(32*e*f^4*(3 + n)) + (d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(5 + n)/(32*e*f^4*(5 + n))","A",4,3,56,0.05357,1,"{2121, 12, 270}"
508,1,239,0,0.2500618,"\int \left(a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right) \left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n \, dx","Int[(a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2)*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n,x]","\frac{\left(d^2-a f^2\right)^3 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-3}}{8 e f^2 (3-n)}-\frac{3 \left(d^2-a f^2\right)^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-1}}{8 e f^2 (1-n)}-\frac{3 \left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{8 e f^2 (n+1)}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+3}}{8 e f^2 (n+3)}","\frac{\left(d^2-a f^2\right)^3 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-3}}{8 e f^2 (3-n)}-\frac{3 \left(d^2-a f^2\right)^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-1}}{8 e f^2 (1-n)}-\frac{3 \left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{8 e f^2 (n+1)}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+3}}{8 e f^2 (n+3)}",1,"((d^2 - a*f^2)^3*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(-3 + n))/(8*e*f^2*(3 - n)) - (3*(d^2 - a*f^2)^2*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(-1 + n))/(8*e*f^2*(1 - n)) - (3*(d^2 - a*f^2)*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(1 + n))/(8*e*f^2*(1 + n)) + (d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(3 + n)/(8*e*f^2*(3 + n))","A",4,3,54,0.05556,1,"{2121, 12, 270}"
509,1,107,0,0.089253,"\int \left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n \, dx","Int[(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n,x]","\frac{\left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-1}}{2 e (1-n)}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{2 e (n+1)}","\frac{\left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-1}}{2 e (1-n)}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{2 e (n+1)}",1,"((d^2 - a*f^2)*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(-1 + n))/(2*e*(1 - n)) + (d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(1 + n)/(2*e*(1 + n))","A",4,3,33,0.09091,1,"{2116, 12, 14}"
510,1,122,0,0.2926692,"\int \frac{\left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n}{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \, dx","Int[(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n/(a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2),x]","-\frac{2 f^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\frac{\left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+\frac{2 d e x}{f^2}+a}\right)^2}{d^2-a f^2}\right)}{e (n+1) \left(d^2-a f^2\right)}","-\frac{2 f^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\frac{\left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+\frac{2 d e x}{f^2}+a}\right)^2}{d^2-a f^2}\right)}{e (n+1) \left(d^2-a f^2\right)}",1,"(-2*f^2*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, (d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^2/(d^2 - a*f^2)])/(e*(d^2 - a*f^2)*(1 + n))","A",2,2,56,0.03571,1,"{2121, 364}"
511,1,122,0,0.267613,"\int \frac{\left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n}{\left(a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right)^2} \, dx","Int[(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n/(a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2)^2,x]","-\frac{8 f^4 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+3} \, _2F_1\left(3,\frac{n+3}{2};\frac{n+5}{2};\frac{\left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+\frac{2 d e x}{f^2}+a}\right)^2}{d^2-a f^2}\right)}{e (n+3) \left(d^2-a f^2\right)^3}","-\frac{8 f^4 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+3} \, _2F_1\left(3,\frac{n+3}{2};\frac{n+5}{2};\frac{\left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+\frac{2 d e x}{f^2}+a}\right)^2}{d^2-a f^2}\right)}{e (n+3) \left(d^2-a f^2\right)^3}",1,"(-8*f^4*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(3 + n)*Hypergeometric2F1[3, (3 + n)/2, (5 + n)/2, (d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^2/(d^2 - a*f^2)])/(e*(d^2 - a*f^2)^3*(3 + n))","A",3,3,56,0.05357,1,"{2121, 12, 364}"
512,1,107,0,0.1325549,"\int \left(d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right)^n \, dx","Int[(d + e*x + f*Sqrt[(a*f^2 + e*x*(2*d + e*x))/f^2])^n,x]","\frac{\left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-1}}{2 e (1-n)}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{2 e (n+1)}","\frac{\left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-1}}{2 e (1-n)}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1}}{2 e (n+1)}",1,"((d^2 - a*f^2)*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(-1 + n))/(2*e*(1 - n)) + (d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(1 + n)/(2*e*(1 + n))","A",5,4,33,0.1212,1,"{2118, 2116, 12, 14}"
513,1,122,0,0.4984522,"\int \frac{\left(d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right)^n}{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \, dx","Int[(d + e*x + f*Sqrt[(a*f^2 + e*x*(2*d + e*x))/f^2])^n/(a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2),x]","-\frac{2 f^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\frac{\left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+\frac{2 d e x}{f^2}+a}\right)^2}{d^2-a f^2}\right)}{e (n+1) \left(d^2-a f^2\right)}","-\frac{2 f^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+1} \, _2F_1\left(1,\frac{n+1}{2};\frac{n+3}{2};\frac{\left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+\frac{2 d e x}{f^2}+a}\right)^2}{d^2-a f^2}\right)}{e (n+1) \left(d^2-a f^2\right)}",1,"(-2*f^2*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(1 + n)*Hypergeometric2F1[1, (1 + n)/2, (3 + n)/2, (d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^2/(d^2 - a*f^2)])/(e*(d^2 - a*f^2)*(1 + n))","A",3,3,56,0.05357,1,"{2127, 2121, 364}"
514,1,297,0,0.4194562,"\int \left(a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right)^{3/2} \left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n \, dx","Int[(a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2)^(3/2)*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n,x]","-\frac{\left(d^2-a f^2\right)^4 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-4}}{16 e f^3 (4-n)}+\frac{\left(d^2-a f^2\right)^3 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-2}}{4 e f^3 (2-n)}+\frac{3 \left(d^2-a f^2\right)^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{8 e f^3 n}-\frac{\left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+2}}{4 e f^3 (n+2)}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+4}}{16 e f^3 (n+4)}","-\frac{\left(d^2-a f^2\right)^4 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-4}}{16 e f^3 (4-n)}+\frac{\left(d^2-a f^2\right)^3 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-2}}{4 e f^3 (2-n)}+\frac{3 \left(d^2-a f^2\right)^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{8 e f^3 n}-\frac{\left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+2}}{4 e f^3 (n+2)}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+4}}{16 e f^3 (n+4)}",1,"-((d^2 - a*f^2)^4*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(-4 + n))/(16*e*f^3*(4 - n)) + ((d^2 - a*f^2)^3*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(-2 + n))/(4*e*f^3*(2 - n)) + (3*(d^2 - a*f^2)^2*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n)/(8*e*f^3*n) - ((d^2 - a*f^2)*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(2 + n))/(4*e*f^3*(2 + n)) + (d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(4 + n)/(16*e*f^3*(4 + n))","A",4,3,58,0.05172,1,"{2121, 12, 270}"
515,1,171,0,0.3249753,"\int \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n \, dx","Int[Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2]*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n,x]","-\frac{\left(d^2-a f^2\right)^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-2}}{4 e f (2-n)}-\frac{\left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{2 e f n}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+2}}{4 e f (n+2)}","-\frac{\left(d^2-a f^2\right)^2 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-2}}{4 e f (2-n)}-\frac{\left(d^2-a f^2\right) \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{2 e f n}+\frac{\left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+2}}{4 e f (n+2)}",1,"-((d^2 - a*f^2)^2*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(-2 + n))/(4*e*f*(2 - n)) - ((d^2 - a*f^2)*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n)/(2*e*f*n) + (d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(2 + n)/(4*e*f*(2 + n))","A",4,3,58,0.05172,1,"{2121, 12, 270}"
516,1,41,0,0.2544298,"\int \frac{\left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n}{\sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}} \, dx","Int[(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n/Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2],x]","\frac{f \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{e n}","\frac{f \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{e n}",1,"(f*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n)/(e*n)","A",3,3,58,0.05172,1,"{2121, 12, 30}"
517,1,122,0,0.3021764,"\int \frac{\left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n}{\left(a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}\right)^{3/2}} \, dx","Int[(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n/(a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2)^(3/2),x]","\frac{4 f^3 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+2} \, _2F_1\left(2,\frac{n+2}{2};\frac{n+4}{2};\frac{\left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+\frac{2 d e x}{f^2}+a}\right)^2}{d^2-a f^2}\right)}{e (n+2) \left(d^2-a f^2\right)^2}","\frac{4 f^3 \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+2} \, _2F_1\left(2,\frac{n+2}{2};\frac{n+4}{2};\frac{\left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+\frac{2 d e x}{f^2}+a}\right)^2}{d^2-a f^2}\right)}{e (n+2) \left(d^2-a f^2\right)^2}",1,"(4*f^3*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(2 + n)*Hypergeometric2F1[2, (2 + n)/2, (4 + n)/2, (d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^2/(d^2 - a*f^2)])/(e*(d^2 - a*f^2)^2*(2 + n))","A",3,3,58,0.05172,1,"{2121, 12, 364}"
518,1,41,0,0.4442356,"\int \frac{\left(d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right)^n}{\sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}} \, dx","Int[(d + e*x + f*Sqrt[(a*f^2 + e*x*(2*d + e*x))/f^2])^n/Sqrt[(a*f^2 + e*x*(2*d + e*x))/f^2],x]","\frac{f \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{e n}","\frac{f \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{e n}",1,"(f*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n)/(e*n)","A",4,4,58,0.06897,1,"{2127, 2121, 12, 30}"
519,1,327,0,0.6169852,"\int \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}} \left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n \, dx","Int[Sqrt[a*g + (2*d*e*g*x)/f^2 + (e^2*g*x^2)/f^2]*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n,x]","-\frac{\left(d^2-a f^2\right)^2 \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-2}}{4 e f (2-n) \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}}-\frac{\left(d^2-a f^2\right) \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{2 e f n \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}}+\frac{\sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+2}}{4 e f (n+2) \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}}","-\frac{\left(d^2-a f^2\right)^2 \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n-2}}{4 e f (2-n) \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}}-\frac{\left(d^2-a f^2\right) \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{2 e f n \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}}+\frac{\sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+2}}{4 e f (n+2) \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}}",1,"-((d^2 - a*f^2)^2*Sqrt[a*g + (2*d*e*g*x)/f^2 + (e^2*g*x^2)/f^2]*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(-2 + n))/(4*e*f*(2 - n)*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2]) - ((d^2 - a*f^2)*Sqrt[a*g + (2*d*e*g*x)/f^2 + (e^2*g*x^2)/f^2]*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n)/(2*e*f*n*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2]) + (Sqrt[a*g + (2*d*e*g*x)/f^2 + (e^2*g*x^2)/f^2]*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(2 + n))/(4*e*f*(2 + n)*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])","A",5,4,62,0.06452,1,"{2123, 2121, 12, 270}"
520,1,93,0,0.5290086,"\int \frac{\left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n}{\sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}}} \, dx","Int[(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n/Sqrt[a*g + (2*d*e*g*x)/f^2 + (e^2*g*x^2)/f^2],x]","\frac{f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{e n \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}}}","\frac{f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{e n \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}}}",1,"(f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2]*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n)/(e*n*Sqrt[a*g + (2*d*e*g*x)/f^2 + (e^2*g*x^2)/f^2])","A",4,4,62,0.06452,1,"{2125, 2121, 12, 30}"
521,1,177,0,0.5861961,"\int \frac{\left(d+e x+f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}\right)^n}{\left(a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}\right)^{3/2}} \, dx","Int[(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n/(a*g + (2*d*e*g*x)/f^2 + (e^2*g*x^2)/f^2)^(3/2),x]","\frac{4 f^3 \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+2} \, _2F_1\left(2,\frac{n+2}{2};\frac{n+4}{2};\frac{\left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+\frac{2 d e x}{f^2}+a}\right)^2}{d^2-a f^2}\right)}{e g (n+2) \left(d^2-a f^2\right)^2 \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}}}","\frac{4 f^3 \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^{n+2} \, _2F_1\left(2,\frac{n+2}{2};\frac{n+4}{2};\frac{\left(d+e x+f \sqrt{\frac{e^2 x^2}{f^2}+\frac{2 d e x}{f^2}+a}\right)^2}{d^2-a f^2}\right)}{e g (n+2) \left(d^2-a f^2\right)^2 \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}}}",1,"(4*f^3*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2]*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^(2 + n)*Hypergeometric2F1[2, (2 + n)/2, (4 + n)/2, (d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^2/(d^2 - a*f^2)])/(e*(d^2 - a*f^2)^2*g*(2 + n)*Sqrt[a*g + (2*d*e*g*x)/f^2 + (e^2*g*x^2)/f^2])","A",4,4,62,0.06452,1,"{2125, 2121, 12, 364}"
522,1,93,0,0.7354194,"\int \frac{\left(d+e x+f \sqrt{\frac{a f^2+e x (2 d+e x)}{f^2}}\right)^n}{\sqrt{\frac{a f^2 g+e g x (2 d+e x)}{f^2}}} \, dx","Int[(d + e*x + f*Sqrt[(a*f^2 + e*x*(2*d + e*x))/f^2])^n/Sqrt[(a*f^2*g + e*g*x*(2*d + e*x))/f^2],x]","\frac{f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{e n \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}}}","\frac{f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}} \left(f \sqrt{a+\frac{2 d e x}{f^2}+\frac{e^2 x^2}{f^2}}+d+e x\right)^n}{e n \sqrt{a g+\frac{2 d e g x}{f^2}+\frac{e^2 g x^2}{f^2}}}",1,"(f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2]*(d + e*x + f*Sqrt[a + (2*d*e*x)/f^2 + (e^2*x^2)/f^2])^n)/(e*n*Sqrt[a*g + (2*d*e*g*x)/f^2 + (e^2*g*x^2)/f^2])","A",5,5,60,0.08333,1,"{2127, 2125, 2121, 12, 30}"
523,1,191,0,0.5129835,"\int \frac{1}{(a+b x) \sqrt{c+d x^2} \sqrt{e+f x^2}} \, dx","Int[1/((a + b*x)*Sqrt[c + d*x^2]*Sqrt[e + f*x^2]),x]","\frac{\sqrt{-c} \sqrt{\frac{d x^2}{c}+1} \sqrt{\frac{f x^2}{e}+1} \Pi \left(-\frac{b^2 c}{a^2 d};\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{-c}}\right)|\frac{c f}{d e}\right)}{a \sqrt{d} \sqrt{c+d x^2} \sqrt{e+f x^2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{c+d x^2} \sqrt{a^2 f+b^2 e}}{\sqrt{e+f x^2} \sqrt{a^2 d+b^2 c}}\right)}{\sqrt{a^2 d+b^2 c} \sqrt{a^2 f+b^2 e}}","\frac{\sqrt{-c} \sqrt{\frac{d x^2}{c}+1} \sqrt{\frac{f x^2}{e}+1} \Pi \left(-\frac{b^2 c}{a^2 d};\sin ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{-c}}\right)|\frac{c f}{d e}\right)}{a \sqrt{d} \sqrt{c+d x^2} \sqrt{e+f x^2}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{c+d x^2} \sqrt{a^2 f+b^2 e}}{\sqrt{e+f x^2} \sqrt{a^2 d+b^2 c}}\right)}{\sqrt{a^2 d+b^2 c} \sqrt{a^2 f+b^2 e}}",1,"-((b*ArcTanh[(Sqrt[b^2*e + a^2*f]*Sqrt[c + d*x^2])/(Sqrt[b^2*c + a^2*d]*Sqrt[e + f*x^2])])/(Sqrt[b^2*c + a^2*d]*Sqrt[b^2*e + a^2*f])) + (Sqrt[-c]*Sqrt[1 + (d*x^2)/c]*Sqrt[1 + (f*x^2)/e]*EllipticPi[-((b^2*c)/(a^2*d)), ArcSin[(Sqrt[d]*x)/Sqrt[-c]], (c*f)/(d*e)])/(a*Sqrt[d]*Sqrt[c + d*x^2]*Sqrt[e + f*x^2])","A",7,6,30,0.2000,1,"{2113, 538, 537, 571, 93, 208}"
524,1,81,0,0.0583478,"\int \frac{e-2 f x^2}{e^2+4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx","Int[(e - 2*f*x^2)/(e^2 + 4*d*f*x^2 + 4*e*f*x^2 + 4*f^2*x^4),x]","\frac{\log \left(2 \sqrt{-d} \sqrt{f} x+e+2 f x^2\right)}{4 \sqrt{-d} \sqrt{f}}-\frac{\log \left(-2 \sqrt{-d} \sqrt{f} x+e+2 f x^2\right)}{4 \sqrt{-d} \sqrt{f}}","\frac{\log \left(2 \sqrt{-d} \sqrt{f} x+e+2 f x^2\right)}{4 \sqrt{-d} \sqrt{f}}-\frac{\log \left(-2 \sqrt{-d} \sqrt{f} x+e+2 f x^2\right)}{4 \sqrt{-d} \sqrt{f}}",1,"-Log[e - 2*Sqrt[-d]*Sqrt[f]*x + 2*f*x^2]/(4*Sqrt[-d]*Sqrt[f]) + Log[e + 2*Sqrt[-d]*Sqrt[f]*x + 2*f*x^2]/(4*Sqrt[-d]*Sqrt[f])","A",4,3,37,0.08108,1,"{6, 1164, 628}"
525,1,73,0,0.0445108,"\int \frac{e-2 f x^2}{e^2-4 d f x^2+4 e f x^2+4 f^2 x^4} \, dx","Int[(e - 2*f*x^2)/(e^2 - 4*d*f*x^2 + 4*e*f*x^2 + 4*f^2*x^4),x]","\frac{\log \left(2 \sqrt{d} \sqrt{f} x+e+2 f x^2\right)}{4 \sqrt{d} \sqrt{f}}-\frac{\log \left(-2 \sqrt{d} \sqrt{f} x+e+2 f x^2\right)}{4 \sqrt{d} \sqrt{f}}","\frac{\log \left(2 \sqrt{d} \sqrt{f} x+e+2 f x^2\right)}{4 \sqrt{d} \sqrt{f}}-\frac{\log \left(-2 \sqrt{d} \sqrt{f} x+e+2 f x^2\right)}{4 \sqrt{d} \sqrt{f}}",1,"-Log[e - 2*Sqrt[d]*Sqrt[f]*x + 2*f*x^2]/(4*Sqrt[d]*Sqrt[f]) + Log[e + 2*Sqrt[d]*Sqrt[f]*x + 2*f*x^2]/(4*Sqrt[d]*Sqrt[f])","A",4,3,37,0.08108,1,"{6, 1164, 628}"
526,1,38,0,0.0627856,"\int \frac{e-4 f x^3}{e^2+4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx","Int[(e - 4*f*x^3)/(e^2 + 4*d*f*x^2 + 4*e*f*x^3 + 4*f^2*x^6),x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTan[(2*Sqrt[d]*Sqrt[f]*x)/(e + 2*f*x^3)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,37,0.05405,1,"{2093, 205}"
527,1,38,0,0.0615178,"\int \frac{e-4 f x^3}{e^2-4 d f x^2+4 e f x^3+4 f^2 x^6} \, dx","Int[(e - 4*f*x^3)/(e^2 - 4*d*f*x^2 + 4*e*f*x^3 + 4*f^2*x^6),x]","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTanh[(2*Sqrt[d]*Sqrt[f]*x)/(e + 2*f*x^3)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,37,0.05405,1,"{2093, 208}"
528,1,38,0,0.0955535,"\int \frac{e-2 f (-1+n) x^n}{e^2+4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx","Int[(e - 2*f*(-1 + n)*x^n)/(e^2 + 4*d*f*x^2 + 4*e*f*x^n + 4*f^2*x^(2*n)),x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x}{e+2 f x^n}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x}{e+2 f x^n}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTan[(2*Sqrt[d]*Sqrt[f]*x)/(e + 2*f*x^n)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,42,0.04762,1,"{2093, 205}"
529,1,38,0,0.0950575,"\int \frac{e-2 f (-1+n) x^n}{e^2-4 d f x^2+4 e f x^n+4 f^2 x^{2 n}} \, dx","Int[(e - 2*f*(-1 + n)*x^n)/(e^2 - 4*d*f*x^2 + 4*e*f*x^n + 4*f^2*x^(2*n)),x]","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x}{e+2 f x^n}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x}{e+2 f x^n}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTanh[(2*Sqrt[d]*Sqrt[f]*x)/(e + 2*f*x^n)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,42,0.04762,1,"{2093, 208}"
530,1,42,0,0.0661598,"\int \frac{x}{e^2+4 e f x^2+4 d f x^4+4 f^2 x^4} \, dx","Int[x/(e^2 + 4*e*f*x^2 + 4*d*f*x^4 + 4*f^2*x^4),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{f} \left(2 x^2 (d+f)+e\right)}{\sqrt{d} e}\right)}{4 \sqrt{d} e \sqrt{f}}","\frac{\tan ^{-1}\left(\frac{\sqrt{f} \left(2 x^2 (d+f)+e\right)}{\sqrt{d} e}\right)}{4 \sqrt{d} e \sqrt{f}}",1,"ArcTan[(Sqrt[f]*(e + 2*(d + f)*x^2))/(Sqrt[d]*e)]/(4*Sqrt[d]*e*Sqrt[f])","A",4,4,30,0.1333,1,"{6, 1107, 618, 204}"
531,1,44,0,0.0674179,"\int \frac{x}{e^2+4 e f x^2-4 d f x^4+4 f^2 x^4} \, dx","Int[x/(e^2 + 4*e*f*x^2 - 4*d*f*x^4 + 4*f^2*x^4),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \left(e-2 x^2 (d-f)\right)}{\sqrt{d} e}\right)}{4 \sqrt{d} e \sqrt{f}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \left(e-2 x^2 (d-f)\right)}{\sqrt{d} e}\right)}{4 \sqrt{d} e \sqrt{f}}",1,"-ArcTanh[(Sqrt[f]*(e - 2*(d - f)*x^2))/(Sqrt[d]*e)]/(4*Sqrt[d]*e*Sqrt[f])","A",4,4,30,0.1333,1,"{6, 1107, 618, 206}"
532,1,40,0,0.1299585,"\int \frac{x^2 \left(3 e+2 f x^2\right)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^6} \, dx","Int[(x^2*(3*e + 2*f*x^2))/(e^2 + 4*e*f*x^2 + 4*f^2*x^4 + 4*d*f*x^6),x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^3}{e+2 f x^2}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^3}{e+2 f x^2}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTan[(2*Sqrt[d]*Sqrt[f]*x^3)/(e + 2*f*x^2)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,42,0.04762,1,"{2094, 205}"
533,1,40,0,0.1276745,"\int \frac{x^2 \left(3 e+2 f x^2\right)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^6} \, dx","Int[(x^2*(3*e + 2*f*x^2))/(e^2 + 4*e*f*x^2 + 4*f^2*x^4 - 4*d*f*x^6),x]","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^3}{e+2 f x^2}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^3}{e+2 f x^2}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTanh[(2*Sqrt[d]*Sqrt[f]*x^3)/(e + 2*f*x^2)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,42,0.04762,1,"{2094, 208}"
534,1,61,0,0.2190732,"\int \frac{x^m \left(e (1+m)+2 f (-1+m) x^2\right)}{e^2+4 e f x^2+4 f^2 x^4+4 d f x^{2+2 m}} \, dx","Int[(x^m*(e*(1 + m) + 2*f*(-1 + m)*x^2))/(e^2 + 4*e*f*x^2 + 4*f^2*x^4 + 4*d*f*x^(2 + 2*m)),x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} \left(1-m^2\right) x^{m+1}}{(1-m) (m+1) \left(e+2 f x^2\right)}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^{m+1}}{e+2 f x^2}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTan[(2*Sqrt[d]*Sqrt[f]*(1 - m^2)*x^(1 + m))/((1 - m)*(1 + m)*(e + 2*f*x^2))]/(2*Sqrt[d]*Sqrt[f])","A",2,2,51,0.03922,1,"{2094, 205}"
535,1,61,0,0.2180339,"\int \frac{x^m \left(e (1+m)+2 f (-1+m) x^2\right)}{e^2+4 e f x^2+4 f^2 x^4-4 d f x^{2+2 m}} \, dx","Int[(x^m*(e*(1 + m) + 2*f*(-1 + m)*x^2))/(e^2 + 4*e*f*x^2 + 4*f^2*x^4 - 4*d*f*x^(2 + 2*m)),x]","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} \left(1-m^2\right) x^{m+1}}{(1-m) (m+1) \left(e+2 f x^2\right)}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^{m+1}}{e+2 f x^2}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTanh[(2*Sqrt[d]*Sqrt[f]*(1 - m^2)*x^(1 + m))/((1 - m)*(1 + m)*(e + 2*f*x^2))]/(2*Sqrt[d]*Sqrt[f])","A",2,2,51,0.03922,1,"{2094, 208}"
536,1,40,0,0.089305,"\int \frac{x \left(2 e-2 f x^3\right)}{e^2+4 e f x^3+4 d f x^4+4 f^2 x^6} \, dx","Int[(x*(2*e - 2*f*x^3))/(e^2 + 4*e*f*x^3 + 4*d*f*x^4 + 4*f^2*x^6),x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^2}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^2}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTan[(2*Sqrt[d]*Sqrt[f]*x^2)/(e + 2*f*x^3)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,40,0.05000,1,"{2094, 205}"
537,1,40,0,0.0891171,"\int \frac{x \left(2 e-2 f x^3\right)}{e^2+4 e f x^3-4 d f x^4+4 f^2 x^6} \, dx","Int[(x*(2*e - 2*f*x^3))/(e^2 + 4*e*f*x^3 - 4*d*f*x^4 + 4*f^2*x^6),x]","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^2}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^2}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTanh[(2*Sqrt[d]*Sqrt[f]*x^2)/(e + 2*f*x^3)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,40,0.05000,1,"{2094, 208}"
538,1,42,0,0.0589649,"\int \frac{x^2}{e^2+4 e f x^3+4 d f x^6+4 f^2 x^6} \, dx","Int[x^2/(e^2 + 4*e*f*x^3 + 4*d*f*x^6 + 4*f^2*x^6),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{f} \left(2 x^3 (d+f)+e\right)}{\sqrt{d} e}\right)}{6 \sqrt{d} e \sqrt{f}}","\frac{\tan ^{-1}\left(\frac{\sqrt{f} \left(2 x^3 (d+f)+e\right)}{\sqrt{d} e}\right)}{6 \sqrt{d} e \sqrt{f}}",1,"ArcTan[(Sqrt[f]*(e + 2*(d + f)*x^3))/(Sqrt[d]*e)]/(6*Sqrt[d]*e*Sqrt[f])","A",4,4,32,0.1250,1,"{6, 1352, 618, 204}"
539,1,44,0,0.0616221,"\int \frac{x^2}{e^2+4 e f x^3-4 d f x^6+4 f^2 x^6} \, dx","Int[x^2/(e^2 + 4*e*f*x^3 - 4*d*f*x^6 + 4*f^2*x^6),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \left(e-2 x^3 (d-f)\right)}{\sqrt{d} e}\right)}{6 \sqrt{d} e \sqrt{f}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{f} \left(e-2 x^3 (d-f)\right)}{\sqrt{d} e}\right)}{6 \sqrt{d} e \sqrt{f}}",1,"-ArcTanh[(Sqrt[f]*(e - 2*(d - f)*x^3))/(Sqrt[d]*e)]/(6*Sqrt[d]*e*Sqrt[f])","A",4,4,32,0.1250,1,"{6, 1352, 618, 206}"
540,1,42,0,0.2230095,"\int \frac{x^m \left(e (1+m)+2 f (-2+m) x^3\right)}{e^2+4 e f x^3+4 f^2 x^6+4 d f x^{2+2 m}} \, dx","Int[(x^m*(e*(1 + m) + 2*f*(-2 + m)*x^3))/(e^2 + 4*e*f*x^3 + 4*f^2*x^6 + 4*d*f*x^(2 + 2*m)),x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^{m+1}}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^{m+1}}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTan[(2*Sqrt[d]*Sqrt[f]*x^(1 + m))/(e + 2*f*x^3)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,51,0.03922,1,"{2094, 205}"
541,1,42,0,0.2159924,"\int \frac{x^m \left(e (1+m)+2 f (-2+m) x^3\right)}{e^2+4 e f x^3+4 f^2 x^6-4 d f x^{2+2 m}} \, dx","Int[(x^m*(e*(1 + m) + 2*f*(-2 + m)*x^3))/(e^2 + 4*e*f*x^3 + 4*f^2*x^6 - 4*d*f*x^(2 + 2*m)),x]","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^{m+1}}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^{m+1}}{e+2 f x^3}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTanh[(2*Sqrt[d]*Sqrt[f]*x^(1 + m))/(e + 2*f*x^3)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,51,0.03922,1,"{2094, 208}"
542,1,42,0,0.2493034,"\int \frac{x^m \left(e (1+m)+2 f (1+m-n) x^n\right)}{e^2+4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx","Int[(x^m*(e*(1 + m) + 2*f*(1 + m - n)*x^n))/(e^2 + 4*d*f*x^(2 + 2*m) + 4*e*f*x^n + 4*f^2*x^(2*n)),x]","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^{m+1}}{e+2 f x^n}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tan ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^{m+1}}{e+2 f x^n}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTan[(2*Sqrt[d]*Sqrt[f]*x^(1 + m))/(e + 2*f*x^n)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,56,0.03571,1,"{2094, 205}"
543,1,42,0,0.2426562,"\int \frac{x^m \left(e (1+m)+2 f (1+m-n) x^n\right)}{e^2-4 d f x^{2+2 m}+4 e f x^n+4 f^2 x^{2 n}} \, dx","Int[(x^m*(e*(1 + m) + 2*f*(1 + m - n)*x^n))/(e^2 - 4*d*f*x^(2 + 2*m) + 4*e*f*x^n + 4*f^2*x^(2*n)),x]","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^{m+1}}{e+2 f x^n}\right)}{2 \sqrt{d} \sqrt{f}}","\frac{\tanh ^{-1}\left(\frac{2 \sqrt{d} \sqrt{f} x^{m+1}}{e+2 f x^n}\right)}{2 \sqrt{d} \sqrt{f}}",1,"ArcTanh[(2*Sqrt[d]*Sqrt[f]*x^(1 + m))/(e + 2*f*x^n)]/(2*Sqrt[d]*Sqrt[f])","A",2,2,56,0.03571,1,"{2094, 208}"
544,1,134,0,0.3728873,"\int \frac{x^5}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx","Int[x^5/(a*c + b*c*x^2 + d*Sqrt[a + b*x^2]),x]","-\frac{x^2 \left(2 a c^2-d^2\right)}{2 b^2 c^3}+\frac{d \sqrt{a+b x^2} \left(2 a c^2-d^2\right)}{b^3 c^4}+\frac{\left(a c^2-d^2\right)^2 \log \left(c \sqrt{a+b x^2}+d\right)}{b^3 c^5}-\frac{d \left(a+b x^2\right)^{3/2}}{3 b^3 c^2}+\frac{\left(a+b x^2\right)^2}{4 b^3 c}","-\frac{x^2 \left(2 a c^2-d^2\right)}{2 b^2 c^3}+\frac{d \sqrt{a+b x^2} \left(2 a c^2-d^2\right)}{b^3 c^4}+\frac{\left(a c^2-d^2\right)^2 \log \left(c \sqrt{a+b x^2}+d\right)}{b^3 c^5}-\frac{d \left(a+b x^2\right)^{3/2}}{3 b^3 c^2}+\frac{\left(a+b x^2\right)^2}{4 b^3 c}",1,"-((2*a*c^2 - d^2)*x^2)/(2*b^2*c^3) + (d*(2*a*c^2 - d^2)*Sqrt[a + b*x^2])/(b^3*c^4) - (d*(a + b*x^2)^(3/2))/(3*b^3*c^2) + (a + b*x^2)^2/(4*b^3*c) + ((a*c^2 - d^2)^2*Log[d + c*Sqrt[a + b*x^2]])/(b^3*c^5)","A",4,2,29,0.06897,1,"{2155, 697}"
545,1,69,0,0.2146005,"\int \frac{x^3}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx","Int[x^3/(a*c + b*c*x^2 + d*Sqrt[a + b*x^2]),x]","-\frac{\left(a c^2-d^2\right) \log \left(c \sqrt{a+b x^2}+d\right)}{b^2 c^3}-\frac{d \sqrt{a+b x^2}}{b^2 c^2}+\frac{x^2}{2 b c}","-\frac{\left(a c^2-d^2\right) \log \left(c \sqrt{a+b x^2}+d\right)}{b^2 c^3}-\frac{d \sqrt{a+b x^2}}{b^2 c^2}+\frac{x^2}{2 b c}",1,"x^2/(2*b*c) - (d*Sqrt[a + b*x^2])/(b^2*c^2) - ((a*c^2 - d^2)*Log[d + c*Sqrt[a + b*x^2]])/(b^2*c^3)","A",4,2,29,0.06897,1,"{2155, 697}"
546,1,23,0,0.085703,"\int \frac{x}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx","Int[x/(a*c + b*c*x^2 + d*Sqrt[a + b*x^2]),x]","\frac{\log \left(c \sqrt{a+b x^2}+d\right)}{b c}","\frac{\log \left(c \sqrt{a+b x^2}+d\right)}{b c}",1,"Log[d + c*Sqrt[a + b*x^2]]/(b*c)","A",3,2,27,0.07407,1,"{2155, 31}"
547,1,88,0,0.2471731,"\int \frac{1}{x \left(a c+b c x^2+d \sqrt{a+b x^2}\right)} \, dx","Int[1/(x*(a*c + b*c*x^2 + d*Sqrt[a + b*x^2])),x]","-\frac{c \log \left(c \sqrt{a+b x^2}+d\right)}{a c^2-d^2}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a} \left(a c^2-d^2\right)}+\frac{c \log (x)}{a c^2-d^2}","-\frac{c \log \left(c \sqrt{a+b x^2}+d\right)}{a c^2-d^2}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a} \left(a c^2-d^2\right)}+\frac{c \log (x)}{a c^2-d^2}",1,"(d*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(Sqrt[a]*(a*c^2 - d^2)) + (c*Log[x])/(a*c^2 - d^2) - (c*Log[d + c*Sqrt[a + b*x^2]])/(a*c^2 - d^2)","A",7,6,29,0.2069,1,"{2155, 706, 31, 635, 207, 260}"
548,1,151,0,0.352349,"\int \frac{1}{x^3 \left(a c+b c x^2+d \sqrt{a+b x^2}\right)} \, dx","Int[1/(x^3*(a*c + b*c*x^2 + d*Sqrt[a + b*x^2])),x]","-\frac{b d \left(3 a c^2-d^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2} \left(a c^2-d^2\right)^2}-\frac{a c-d \sqrt{a+b x^2}}{2 a x^2 \left(a c^2-d^2\right)}+\frac{b c^3 \log \left(c \sqrt{a+b x^2}+d\right)}{\left(a c^2-d^2\right)^2}-\frac{b c^3 \log (x)}{\left(a c^2-d^2\right)^2}","-\frac{b d \left(3 a c^2-d^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2} \left(a c^2-d^2\right)^2}-\frac{a c-d \sqrt{a+b x^2}}{2 a x^2 \left(a c^2-d^2\right)}+\frac{b c^3 \log \left(c \sqrt{a+b x^2}+d\right)}{\left(a c^2-d^2\right)^2}-\frac{b c^3 \log (x)}{\left(a c^2-d^2\right)^2}",1,"-(a*c - d*Sqrt[a + b*x^2])/(2*a*(a*c^2 - d^2)*x^2) - (b*d*(3*a*c^2 - d^2)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(3/2)*(a*c^2 - d^2)^2) - (b*c^3*Log[x])/(a*c^2 - d^2)^2 + (b*c^3*Log[d + c*Sqrt[a + b*x^2]])/(a*c^2 - d^2)^2","A",8,6,29,0.2069,1,"{2155, 741, 801, 635, 206, 260}"
549,1,147,0,0.2394225,"\int \frac{x^2}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx","Int[x^2/(a*c + b*c*x^2 + d*Sqrt[a + b*x^2]),x]","\frac{\sqrt{a c^2-d^2} \tan ^{-1}\left(\frac{\sqrt{b} d x}{\sqrt{a+b x^2} \sqrt{a c^2-d^2}}\right)}{b^{3/2} c^2}-\frac{\sqrt{a c^2-d^2} \tan ^{-1}\left(\frac{\sqrt{b} c x}{\sqrt{a c^2-d^2}}\right)}{b^{3/2} c^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{3/2} c^2}+\frac{x}{b c}","\frac{\sqrt{a c^2-d^2} \tan ^{-1}\left(\frac{\sqrt{b} d x}{\sqrt{a+b x^2} \sqrt{a c^2-d^2}}\right)}{b^{3/2} c^2}-\frac{\sqrt{a c^2-d^2} \tan ^{-1}\left(\frac{\sqrt{b} c x}{\sqrt{a c^2-d^2}}\right)}{b^{3/2} c^2}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{3/2} c^2}+\frac{x}{b c}",1,"x/(b*c) - (Sqrt[a*c^2 - d^2]*ArcTan[(Sqrt[b]*c*x)/Sqrt[a*c^2 - d^2]])/(b^(3/2)*c^2) + (Sqrt[a*c^2 - d^2]*ArcTan[(Sqrt[b]*d*x)/(Sqrt[a*c^2 - d^2]*Sqrt[a + b*x^2])])/(b^(3/2)*c^2) - (d*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(b^(3/2)*c^2)","A",8,7,29,0.2414,1,"{2156, 321, 205, 483, 217, 206, 377}"
550,1,103,0,0.0674658,"\int \frac{1}{a c+b c x^2+d \sqrt{a+b x^2}} \, dx","Int[(a*c + b*c*x^2 + d*Sqrt[a + b*x^2])^(-1),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} c x}{\sqrt{a c^2-d^2}}\right)}{\sqrt{b} \sqrt{a c^2-d^2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} d x}{\sqrt{a+b x^2} \sqrt{a c^2-d^2}}\right)}{\sqrt{b} \sqrt{a c^2-d^2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} c x}{\sqrt{a c^2-d^2}}\right)}{\sqrt{b} \sqrt{a c^2-d^2}}-\frac{\tan ^{-1}\left(\frac{\sqrt{b} d x}{\sqrt{a+b x^2} \sqrt{a c^2-d^2}}\right)}{\sqrt{b} \sqrt{a c^2-d^2}}",1,"ArcTan[(Sqrt[b]*c*x)/Sqrt[a*c^2 - d^2]]/(Sqrt[b]*Sqrt[a*c^2 - d^2]) - ArcTan[(Sqrt[b]*d*x)/(Sqrt[a*c^2 - d^2]*Sqrt[a + b*x^2])]/(Sqrt[b]*Sqrt[a*c^2 - d^2])","A",4,3,25,0.1200,1,"{2156, 205, 377}"
551,1,160,0,0.2401005,"\int \frac{1}{x^2 \left(a c+b c x^2+d \sqrt{a+b x^2}\right)} \, dx","Int[1/(x^2*(a*c + b*c*x^2 + d*Sqrt[a + b*x^2])),x]","\frac{d \sqrt{a+b x^2}}{a x \left(a c^2-d^2\right)}+\frac{\sqrt{b} c^2 \tan ^{-1}\left(\frac{\sqrt{b} d x}{\sqrt{a+b x^2} \sqrt{a c^2-d^2}}\right)}{\left(a c^2-d^2\right)^{3/2}}-\frac{\sqrt{b} c^2 \tan ^{-1}\left(\frac{\sqrt{b} c x}{\sqrt{a c^2-d^2}}\right)}{\left(a c^2-d^2\right)^{3/2}}-\frac{c}{x \left(a c^2-d^2\right)}","\frac{d \sqrt{a+b x^2}}{a x \left(a c^2-d^2\right)}+\frac{\sqrt{b} c^2 \tan ^{-1}\left(\frac{\sqrt{b} d x}{\sqrt{a+b x^2} \sqrt{a c^2-d^2}}\right)}{\left(a c^2-d^2\right)^{3/2}}-\frac{\sqrt{b} c^2 \tan ^{-1}\left(\frac{\sqrt{b} c x}{\sqrt{a c^2-d^2}}\right)}{\left(a c^2-d^2\right)^{3/2}}-\frac{c}{x \left(a c^2-d^2\right)}",1,"-(c/((a*c^2 - d^2)*x)) + (d*Sqrt[a + b*x^2])/(a*(a*c^2 - d^2)*x) - (Sqrt[b]*c^2*ArcTan[(Sqrt[b]*c*x)/Sqrt[a*c^2 - d^2]])/(a*c^2 - d^2)^(3/2) + (Sqrt[b]*c^2*ArcTan[(Sqrt[b]*d*x)/(Sqrt[a*c^2 - d^2]*Sqrt[a + b*x^2])])/(a*c^2 - d^2)^(3/2)","A",7,6,29,0.2069,1,"{2156, 325, 205, 480, 12, 377}"
552,1,140,0,0.2991068,"\int \frac{x^8}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx","Int[x^8/(a*c + b*c*x^3 + d*Sqrt[a + b*x^3]),x]","-\frac{x^3 \left(2 a c^2-d^2\right)}{3 b^2 c^3}+\frac{2 d \sqrt{a+b x^3} \left(2 a c^2-d^2\right)}{3 b^3 c^4}+\frac{2 \left(a c^2-d^2\right)^2 \log \left(c \sqrt{a+b x^3}+d\right)}{3 b^3 c^5}-\frac{2 d \left(a+b x^3\right)^{3/2}}{9 b^3 c^2}+\frac{\left(a+b x^3\right)^2}{6 b^3 c}","-\frac{x^3 \left(2 a c^2-d^2\right)}{3 b^2 c^3}+\frac{2 d \sqrt{a+b x^3} \left(2 a c^2-d^2\right)}{3 b^3 c^4}+\frac{2 \left(a c^2-d^2\right)^2 \log \left(c \sqrt{a+b x^3}+d\right)}{3 b^3 c^5}-\frac{2 d \left(a+b x^3\right)^{3/2}}{9 b^3 c^2}+\frac{\left(a+b x^3\right)^2}{6 b^3 c}",1,"-((2*a*c^2 - d^2)*x^3)/(3*b^2*c^3) + (2*d*(2*a*c^2 - d^2)*Sqrt[a + b*x^3])/(3*b^3*c^4) - (2*d*(a + b*x^3)^(3/2))/(9*b^3*c^2) + (a + b*x^3)^2/(6*b^3*c) + (2*(a*c^2 - d^2)^2*Log[d + c*Sqrt[a + b*x^3]])/(3*b^3*c^5)","A",4,2,29,0.06897,1,"{2155, 697}"
553,1,73,0,0.201527,"\int \frac{x^5}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx","Int[x^5/(a*c + b*c*x^3 + d*Sqrt[a + b*x^3]),x]","-\frac{2 \left(a c^2-d^2\right) \log \left(c \sqrt{a+b x^3}+d\right)}{3 b^2 c^3}-\frac{2 d \sqrt{a+b x^3}}{3 b^2 c^2}+\frac{x^3}{3 b c}","-\frac{2 \left(a c^2-d^2\right) \log \left(c \sqrt{a+b x^3}+d\right)}{3 b^2 c^3}-\frac{2 d \sqrt{a+b x^3}}{3 b^2 c^2}+\frac{x^3}{3 b c}",1,"x^3/(3*b*c) - (2*d*Sqrt[a + b*x^3])/(3*b^2*c^2) - (2*(a*c^2 - d^2)*Log[d + c*Sqrt[a + b*x^3]])/(3*b^2*c^3)","A",4,2,29,0.06897,1,"{2155, 697}"
554,1,26,0,0.1105287,"\int \frac{x^2}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx","Int[x^2/(a*c + b*c*x^3 + d*Sqrt[a + b*x^3]),x]","\frac{2 \log \left(c \sqrt{a+b x^3}+d\right)}{3 b c}","\frac{2 \log \left(c \sqrt{a+b x^3}+d\right)}{3 b c}",1,"(2*Log[d + c*Sqrt[a + b*x^3]])/(3*b*c)","A",3,2,29,0.06897,1,"{2155, 31}"
555,1,93,0,0.2227041,"\int \frac{1}{x \left(a c+b c x^3+d \sqrt{a+b x^3}\right)} \, dx","Int[1/(x*(a*c + b*c*x^3 + d*Sqrt[a + b*x^3])),x]","-\frac{2 c \log \left(c \sqrt{a+b x^3}+d\right)}{3 \left(a c^2-d^2\right)}+\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a} \left(a c^2-d^2\right)}+\frac{c \log (x)}{a c^2-d^2}","-\frac{2 c \log \left(c \sqrt{a+b x^3}+d\right)}{3 \left(a c^2-d^2\right)}+\frac{2 d \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a} \left(a c^2-d^2\right)}+\frac{c \log (x)}{a c^2-d^2}",1,"(2*d*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a]*(a*c^2 - d^2)) + (c*Log[x])/(a*c^2 - d^2) - (2*c*Log[d + c*Sqrt[a + b*x^3]])/(3*(a*c^2 - d^2))","A",7,6,29,0.2069,1,"{2155, 706, 31, 635, 207, 260}"
556,1,154,0,0.2980764,"\int \frac{1}{x^4 \left(a c+b c x^3+d \sqrt{a+b x^3}\right)} \, dx","Int[1/(x^4*(a*c + b*c*x^3 + d*Sqrt[a + b*x^3])),x]","-\frac{b d \left(3 a c^2-d^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2} \left(a c^2-d^2\right)^2}-\frac{a c-d \sqrt{a+b x^3}}{3 a x^3 \left(a c^2-d^2\right)}+\frac{2 b c^3 \log \left(c \sqrt{a+b x^3}+d\right)}{3 \left(a c^2-d^2\right)^2}-\frac{b c^3 \log (x)}{\left(a c^2-d^2\right)^2}","-\frac{b d \left(3 a c^2-d^2\right) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2} \left(a c^2-d^2\right)^2}-\frac{a c-d \sqrt{a+b x^3}}{3 a x^3 \left(a c^2-d^2\right)}+\frac{2 b c^3 \log \left(c \sqrt{a+b x^3}+d\right)}{3 \left(a c^2-d^2\right)^2}-\frac{b c^3 \log (x)}{\left(a c^2-d^2\right)^2}",1,"-(a*c - d*Sqrt[a + b*x^3])/(3*a*(a*c^2 - d^2)*x^3) - (b*d*(3*a*c^2 - d^2)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*a^(3/2)*(a*c^2 - d^2)^2) - (b*c^3*Log[x])/(a*c^2 - d^2)^2 + (2*b*c^3*Log[d + c*Sqrt[a + b*x^3]])/(3*(a*c^2 - d^2)^2)","A",8,6,29,0.2069,1,"{2155, 741, 801, 635, 206, 260}"
557,1,311,0,0.5038033,"\int \frac{x^3}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx","Int[x^3/(a*c + b*c*x^3 + d*Sqrt[a + b*x^3]),x]","-\frac{d x^4 \sqrt{\frac{b x^3}{a}+1} F_1\left(\frac{4}{3};\frac{1}{2},1;\frac{7}{3};-\frac{b x^3}{a},-\frac{b c^2 x^3}{a c^2-d^2}\right)}{4 \sqrt{a+b x^3} \left(a c^2-d^2\right)}+\frac{\sqrt[3]{a c^2-d^2} \log \left(-\sqrt[3]{b} c^{2/3} x \sqrt[3]{a c^2-d^2}+\left(a c^2-d^2\right)^{2/3}+b^{2/3} c^{4/3} x^2\right)}{6 b^{4/3} c^{5/3}}-\frac{\sqrt[3]{a c^2-d^2} \log \left(\sqrt[3]{a c^2-d^2}+\sqrt[3]{b} c^{2/3} x\right)}{3 b^{4/3} c^{5/3}}+\frac{\sqrt[3]{a c^2-d^2} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} c^{2/3} x}{\sqrt[3]{a c^2-d^2}}}{\sqrt{3}}\right)}{\sqrt{3} b^{4/3} c^{5/3}}+\frac{x}{b c}","-\frac{d x^4 \sqrt{\frac{b x^3}{a}+1} F_1\left(\frac{4}{3};\frac{1}{2},1;\frac{7}{3};-\frac{b x^3}{a},-\frac{b c^2 x^3}{a c^2-d^2}\right)}{4 \sqrt{a+b x^3} \left(a c^2-d^2\right)}+\frac{\sqrt[3]{a c^2-d^2} \log \left(-\sqrt[3]{b} c^{2/3} x \sqrt[3]{a c^2-d^2}+\left(a c^2-d^2\right)^{2/3}+b^{2/3} c^{4/3} x^2\right)}{6 b^{4/3} c^{5/3}}-\frac{\sqrt[3]{a c^2-d^2} \log \left(\sqrt[3]{a c^2-d^2}+\sqrt[3]{b} c^{2/3} x\right)}{3 b^{4/3} c^{5/3}}+\frac{\sqrt[3]{a c^2-d^2} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} c^{2/3} x}{\sqrt[3]{a c^2-d^2}}}{\sqrt{3}}\right)}{\sqrt{3} b^{4/3} c^{5/3}}+\frac{x}{b c}",1,"x/(b*c) - (d*x^4*Sqrt[1 + (b*x^3)/a]*AppellF1[4/3, 1/2, 1, 7/3, -((b*x^3)/a), -((b*c^2*x^3)/(a*c^2 - d^2))])/(4*(a*c^2 - d^2)*Sqrt[a + b*x^3]) + ((a*c^2 - d^2)^(1/3)*ArcTan[(1 - (2*b^(1/3)*c^(2/3)*x)/(a*c^2 - d^2)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(4/3)*c^(5/3)) - ((a*c^2 - d^2)^(1/3)*Log[(a*c^2 - d^2)^(1/3) + b^(1/3)*c^(2/3)*x])/(3*b^(4/3)*c^(5/3)) + ((a*c^2 - d^2)^(1/3)*Log[(a*c^2 - d^2)^(2/3) - b^(1/3)*c^(2/3)*(a*c^2 - d^2)^(1/3)*x + b^(2/3)*c^(4/3)*x^2])/(6*b^(4/3)*c^(5/3))","A",10,10,29,0.3448,1,"{2156, 321, 200, 31, 634, 617, 204, 628, 511, 510}"
558,1,304,0,0.2993333,"\int \frac{x}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx","Int[x/(a*c + b*c*x^3 + d*Sqrt[a + b*x^3]),x]","-\frac{d x^2 \sqrt{\frac{b x^3}{a}+1} F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};-\frac{b x^3}{a},-\frac{b c^2 x^3}{a c^2-d^2}\right)}{2 \sqrt{a+b x^3} \left(a c^2-d^2\right)}+\frac{\log \left(-\sqrt[3]{b} c^{2/3} x \sqrt[3]{a c^2-d^2}+\left(a c^2-d^2\right)^{2/3}+b^{2/3} c^{4/3} x^2\right)}{6 b^{2/3} \sqrt[3]{c} \sqrt[3]{a c^2-d^2}}-\frac{\log \left(\sqrt[3]{a c^2-d^2}+\sqrt[3]{b} c^{2/3} x\right)}{3 b^{2/3} \sqrt[3]{c} \sqrt[3]{a c^2-d^2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} c^{2/3} x}{\sqrt[3]{a c^2-d^2}}}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3} \sqrt[3]{c} \sqrt[3]{a c^2-d^2}}","-\frac{d x^2 \sqrt{\frac{b x^3}{a}+1} F_1\left(\frac{2}{3};\frac{1}{2},1;\frac{5}{3};-\frac{b x^3}{a},-\frac{b c^2 x^3}{a c^2-d^2}\right)}{2 \sqrt{a+b x^3} \left(a c^2-d^2\right)}+\frac{\log \left(-\sqrt[3]{b} c^{2/3} x \sqrt[3]{a c^2-d^2}+\left(a c^2-d^2\right)^{2/3}+b^{2/3} c^{4/3} x^2\right)}{6 b^{2/3} \sqrt[3]{c} \sqrt[3]{a c^2-d^2}}-\frac{\log \left(\sqrt[3]{a c^2-d^2}+\sqrt[3]{b} c^{2/3} x\right)}{3 b^{2/3} \sqrt[3]{c} \sqrt[3]{a c^2-d^2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} c^{2/3} x}{\sqrt[3]{a c^2-d^2}}}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3} \sqrt[3]{c} \sqrt[3]{a c^2-d^2}}",1,"-(d*x^2*Sqrt[1 + (b*x^3)/a]*AppellF1[2/3, 1/2, 1, 5/3, -((b*x^3)/a), -((b*c^2*x^3)/(a*c^2 - d^2))])/(2*(a*c^2 - d^2)*Sqrt[a + b*x^3]) - ArcTan[(1 - (2*b^(1/3)*c^(2/3)*x)/(a*c^2 - d^2)^(1/3))/Sqrt[3]]/(Sqrt[3]*b^(2/3)*c^(1/3)*(a*c^2 - d^2)^(1/3)) - Log[(a*c^2 - d^2)^(1/3) + b^(1/3)*c^(2/3)*x]/(3*b^(2/3)*c^(1/3)*(a*c^2 - d^2)^(1/3)) + Log[(a*c^2 - d^2)^(2/3) - b^(1/3)*c^(2/3)*(a*c^2 - d^2)^(1/3)*x + b^(2/3)*c^(4/3)*x^2]/(6*b^(2/3)*c^(1/3)*(a*c^2 - d^2)^(1/3))","A",9,9,27,0.3333,1,"{2156, 292, 31, 634, 617, 204, 628, 511, 510}"
559,1,300,0,0.2590668,"\int \frac{1}{a c+b c x^3+d \sqrt{a+b x^3}} \, dx","Int[(a*c + b*c*x^3 + d*Sqrt[a + b*x^3])^(-1),x]","-\frac{d x \sqrt{\frac{b x^3}{a}+1} F_1\left(\frac{1}{3};\frac{1}{2},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{b c^2 x^3}{a c^2-d^2}\right)}{\sqrt{a+b x^3} \left(a c^2-d^2\right)}-\frac{\sqrt[3]{c} \log \left(-\sqrt[3]{b} c^{2/3} x \sqrt[3]{a c^2-d^2}+\left(a c^2-d^2\right)^{2/3}+b^{2/3} c^{4/3} x^2\right)}{6 \sqrt[3]{b} \left(a c^2-d^2\right)^{2/3}}+\frac{\sqrt[3]{c} \log \left(\sqrt[3]{a c^2-d^2}+\sqrt[3]{b} c^{2/3} x\right)}{3 \sqrt[3]{b} \left(a c^2-d^2\right)^{2/3}}-\frac{\sqrt[3]{c} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} c^{2/3} x}{\sqrt[3]{a c^2-d^2}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b} \left(a c^2-d^2\right)^{2/3}}","-\frac{d x \sqrt{\frac{b x^3}{a}+1} F_1\left(\frac{1}{3};\frac{1}{2},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{b c^2 x^3}{a c^2-d^2}\right)}{\sqrt{a+b x^3} \left(a c^2-d^2\right)}-\frac{\sqrt[3]{c} \log \left(-\sqrt[3]{b} c^{2/3} x \sqrt[3]{a c^2-d^2}+\left(a c^2-d^2\right)^{2/3}+b^{2/3} c^{4/3} x^2\right)}{6 \sqrt[3]{b} \left(a c^2-d^2\right)^{2/3}}+\frac{\sqrt[3]{c} \log \left(\sqrt[3]{a c^2-d^2}+\sqrt[3]{b} c^{2/3} x\right)}{3 \sqrt[3]{b} \left(a c^2-d^2\right)^{2/3}}-\frac{\sqrt[3]{c} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} c^{2/3} x}{\sqrt[3]{a c^2-d^2}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b} \left(a c^2-d^2\right)^{2/3}}",1,"-((d*x*Sqrt[1 + (b*x^3)/a]*AppellF1[1/3, 1/2, 1, 4/3, -((b*x^3)/a), -((b*c^2*x^3)/(a*c^2 - d^2))])/((a*c^2 - d^2)*Sqrt[a + b*x^3])) - (c^(1/3)*ArcTan[(1 - (2*b^(1/3)*c^(2/3)*x)/(a*c^2 - d^2)^(1/3))/Sqrt[3]])/(Sqrt[3]*b^(1/3)*(a*c^2 - d^2)^(2/3)) + (c^(1/3)*Log[(a*c^2 - d^2)^(1/3) + b^(1/3)*c^(2/3)*x])/(3*b^(1/3)*(a*c^2 - d^2)^(2/3)) - (c^(1/3)*Log[(a*c^2 - d^2)^(2/3) - b^(1/3)*c^(2/3)*(a*c^2 - d^2)^(1/3)*x + b^(2/3)*c^(4/3)*x^2])/(6*b^(1/3)*(a*c^2 - d^2)^(2/3))","A",9,9,25,0.3600,1,"{2156, 200, 31, 634, 617, 204, 628, 430, 429}"
560,1,319,0,0.407952,"\int \frac{1}{x^2 \left(a c+b c x^3+d \sqrt{a+b x^3}\right)} \, dx","Int[1/(x^2*(a*c + b*c*x^3 + d*Sqrt[a + b*x^3])),x]","\frac{d \sqrt{\frac{b x^3}{a}+1} F_1\left(-\frac{1}{3};\frac{1}{2},1;\frac{2}{3};-\frac{b x^3}{a},-\frac{b c^2 x^3}{a c^2-d^2}\right)}{x \sqrt{a+b x^3} \left(a c^2-d^2\right)}-\frac{\sqrt[3]{b} c^{5/3} \log \left(-\sqrt[3]{b} c^{2/3} x \sqrt[3]{a c^2-d^2}+\left(a c^2-d^2\right)^{2/3}+b^{2/3} c^{4/3} x^2\right)}{6 \left(a c^2-d^2\right)^{4/3}}+\frac{\sqrt[3]{b} c^{5/3} \log \left(\sqrt[3]{a c^2-d^2}+\sqrt[3]{b} c^{2/3} x\right)}{3 \left(a c^2-d^2\right)^{4/3}}+\frac{\sqrt[3]{b} c^{5/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} c^{2/3} x}{\sqrt[3]{a c^2-d^2}}}{\sqrt{3}}\right)}{\sqrt{3} \left(a c^2-d^2\right)^{4/3}}-\frac{c}{x \left(a c^2-d^2\right)}","\frac{d \sqrt{\frac{b x^3}{a}+1} F_1\left(-\frac{1}{3};\frac{1}{2},1;\frac{2}{3};-\frac{b x^3}{a},-\frac{b c^2 x^3}{a c^2-d^2}\right)}{x \sqrt{a+b x^3} \left(a c^2-d^2\right)}-\frac{\sqrt[3]{b} c^{5/3} \log \left(-\sqrt[3]{b} c^{2/3} x \sqrt[3]{a c^2-d^2}+\left(a c^2-d^2\right)^{2/3}+b^{2/3} c^{4/3} x^2\right)}{6 \left(a c^2-d^2\right)^{4/3}}+\frac{\sqrt[3]{b} c^{5/3} \log \left(\sqrt[3]{a c^2-d^2}+\sqrt[3]{b} c^{2/3} x\right)}{3 \left(a c^2-d^2\right)^{4/3}}+\frac{\sqrt[3]{b} c^{5/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} c^{2/3} x}{\sqrt[3]{a c^2-d^2}}}{\sqrt{3}}\right)}{\sqrt{3} \left(a c^2-d^2\right)^{4/3}}-\frac{c}{x \left(a c^2-d^2\right)}",1,"-(c/((a*c^2 - d^2)*x)) + (d*Sqrt[1 + (b*x^3)/a]*AppellF1[-1/3, 1/2, 1, 2/3, -((b*x^3)/a), -((b*c^2*x^3)/(a*c^2 - d^2))])/((a*c^2 - d^2)*x*Sqrt[a + b*x^3]) + (b^(1/3)*c^(5/3)*ArcTan[(1 - (2*b^(1/3)*c^(2/3)*x)/(a*c^2 - d^2)^(1/3))/Sqrt[3]])/(Sqrt[3]*(a*c^2 - d^2)^(4/3)) + (b^(1/3)*c^(5/3)*Log[(a*c^2 - d^2)^(1/3) + b^(1/3)*c^(2/3)*x])/(3*(a*c^2 - d^2)^(4/3)) - (b^(1/3)*c^(5/3)*Log[(a*c^2 - d^2)^(2/3) - b^(1/3)*c^(2/3)*(a*c^2 - d^2)^(1/3)*x + b^(2/3)*c^(4/3)*x^2])/(6*(a*c^2 - d^2)^(4/3))","A",10,10,29,0.3448,1,"{2156, 325, 292, 31, 634, 617, 204, 628, 511, 510}"
561,1,324,0,0.4132338,"\int \frac{1}{x^3 \left(a c+b c x^3+d \sqrt{a+b x^3}\right)} \, dx","Int[1/(x^3*(a*c + b*c*x^3 + d*Sqrt[a + b*x^3])),x]","\frac{d \sqrt{\frac{b x^3}{a}+1} F_1\left(-\frac{2}{3};\frac{1}{2},1;\frac{1}{3};-\frac{b x^3}{a},-\frac{b c^2 x^3}{a c^2-d^2}\right)}{2 x^2 \sqrt{a+b x^3} \left(a c^2-d^2\right)}+\frac{b^{2/3} c^{7/3} \log \left(-\sqrt[3]{b} c^{2/3} x \sqrt[3]{a c^2-d^2}+\left(a c^2-d^2\right)^{2/3}+b^{2/3} c^{4/3} x^2\right)}{6 \left(a c^2-d^2\right)^{5/3}}-\frac{b^{2/3} c^{7/3} \log \left(\sqrt[3]{a c^2-d^2}+\sqrt[3]{b} c^{2/3} x\right)}{3 \left(a c^2-d^2\right)^{5/3}}+\frac{b^{2/3} c^{7/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} c^{2/3} x}{\sqrt[3]{a c^2-d^2}}}{\sqrt{3}}\right)}{\sqrt{3} \left(a c^2-d^2\right)^{5/3}}-\frac{c}{2 x^2 \left(a c^2-d^2\right)}","\frac{d \sqrt{\frac{b x^3}{a}+1} F_1\left(-\frac{2}{3};\frac{1}{2},1;\frac{1}{3};-\frac{b x^3}{a},-\frac{b c^2 x^3}{a c^2-d^2}\right)}{2 x^2 \sqrt{a+b x^3} \left(a c^2-d^2\right)}+\frac{b^{2/3} c^{7/3} \log \left(-\sqrt[3]{b} c^{2/3} x \sqrt[3]{a c^2-d^2}+\left(a c^2-d^2\right)^{2/3}+b^{2/3} c^{4/3} x^2\right)}{6 \left(a c^2-d^2\right)^{5/3}}-\frac{b^{2/3} c^{7/3} \log \left(\sqrt[3]{a c^2-d^2}+\sqrt[3]{b} c^{2/3} x\right)}{3 \left(a c^2-d^2\right)^{5/3}}+\frac{b^{2/3} c^{7/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} c^{2/3} x}{\sqrt[3]{a c^2-d^2}}}{\sqrt{3}}\right)}{\sqrt{3} \left(a c^2-d^2\right)^{5/3}}-\frac{c}{2 x^2 \left(a c^2-d^2\right)}",1,"-c/(2*(a*c^2 - d^2)*x^2) + (d*Sqrt[1 + (b*x^3)/a]*AppellF1[-2/3, 1/2, 1, 1/3, -((b*x^3)/a), -((b*c^2*x^3)/(a*c^2 - d^2))])/(2*(a*c^2 - d^2)*x^2*Sqrt[a + b*x^3]) + (b^(2/3)*c^(7/3)*ArcTan[(1 - (2*b^(1/3)*c^(2/3)*x)/(a*c^2 - d^2)^(1/3))/Sqrt[3]])/(Sqrt[3]*(a*c^2 - d^2)^(5/3)) - (b^(2/3)*c^(7/3)*Log[(a*c^2 - d^2)^(1/3) + b^(1/3)*c^(2/3)*x])/(3*(a*c^2 - d^2)^(5/3)) + (b^(2/3)*c^(7/3)*Log[(a*c^2 - d^2)^(2/3) - b^(1/3)*c^(2/3)*(a*c^2 - d^2)^(1/3)*x + b^(2/3)*c^(4/3)*x^2])/(6*(a*c^2 - d^2)^(5/3))","A",10,10,29,0.3448,1,"{2156, 325, 200, 31, 634, 617, 204, 628, 511, 510}"
562,1,135,0,0.0938964,"\int \frac{1}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx","Int[(a*c + b*c*x^n + d*Sqrt[a + b*x^n])^(-1),x]","\frac{c x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b c^2 x^n}{a c^2-d^2}\right)}{a c^2-d^2}-\frac{d x \sqrt{\frac{b x^n}{a}+1} F_1\left(\frac{1}{n};\frac{1}{2},1;1+\frac{1}{n};-\frac{b x^n}{a},-\frac{b c^2 x^n}{a c^2-d^2}\right)}{\left(a c^2-d^2\right) \sqrt{a+b x^n}}","\frac{c x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b c^2 x^n}{a c^2-d^2}\right)}{a c^2-d^2}-\frac{d x \sqrt{\frac{b x^n}{a}+1} F_1\left(\frac{1}{n};\frac{1}{2},1;1+\frac{1}{n};-\frac{b x^n}{a},-\frac{b c^2 x^n}{a c^2-d^2}\right)}{\left(a c^2-d^2\right) \sqrt{a+b x^n}}",1,"-((d*x*Sqrt[1 + (b*x^n)/a]*AppellF1[n^(-1), 1/2, 1, 1 + n^(-1), -((b*x^n)/a), -((b*c^2*x^n)/(a*c^2 - d^2))])/((a*c^2 - d^2)*Sqrt[a + b*x^n])) + (c*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*c^2*x^n)/(a*c^2 - d^2))])/(a*c^2 - d^2)","A",4,4,25,0.1600,1,"{2156, 245, 430, 429}"
563,1,167,0,0.1969848,"\int \frac{x^m}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx","Int[x^m/(a*c + b*c*x^n + d*Sqrt[a + b*x^n]),x]","\frac{c x^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b c^2 x^n}{a c^2-d^2}\right)}{(m+1) \left(a c^2-d^2\right)}-\frac{d x^{m+1} \sqrt{\frac{b x^n}{a}+1} F_1\left(\frac{m+1}{n};\frac{1}{2},1;\frac{m+n+1}{n};-\frac{b x^n}{a},-\frac{b c^2 x^n}{a c^2-d^2}\right)}{(m+1) \left(a c^2-d^2\right) \sqrt{a+b x^n}}","\frac{c x^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b c^2 x^n}{a c^2-d^2}\right)}{(m+1) \left(a c^2-d^2\right)}-\frac{d x^{m+1} \sqrt{\frac{b x^n}{a}+1} F_1\left(\frac{m+1}{n};\frac{1}{2},1;\frac{m+n+1}{n};-\frac{b x^n}{a},-\frac{b c^2 x^n}{a c^2-d^2}\right)}{(m+1) \left(a c^2-d^2\right) \sqrt{a+b x^n}}",1,"-((d*x^(1 + m)*Sqrt[1 + (b*x^n)/a]*AppellF1[(1 + m)/n, 1/2, 1, (1 + m + n)/n, -((b*x^n)/a), -((b*c^2*x^n)/(a*c^2 - d^2))])/((a*c^2 - d^2)*(1 + m)*Sqrt[a + b*x^n])) + (c*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*c^2*x^n)/(a*c^2 - d^2))])/((a*c^2 - d^2)*(1 + m))","A",4,4,29,0.1379,1,"{2156, 364, 511, 510}"
564,1,27,0,0.1099101,"\int \frac{x^{-1+n}}{a c+b c x^n+d \sqrt{a+b x^n}} \, dx","Int[x^(-1 + n)/(a*c + b*c*x^n + d*Sqrt[a + b*x^n]),x]","\frac{2 \log \left(c \sqrt{a+b x^n}+d\right)}{b c n}","\frac{2 \log \left(c \sqrt{a+b x^n}+d\right)}{b c n}",1,"(2*Log[d + c*Sqrt[a + b*x^n]])/(b*c*n)","A",3,2,31,0.06452,1,"{2155, 31}"
565,1,8,0,0.0057815,"\int \frac{1}{\sqrt{x}+4 x^{3/2}} \, dx","Int[(Sqrt[x] + 4*x^(3/2))^(-1),x]","\tan ^{-1}\left(2 \sqrt{x}\right)","\tan ^{-1}\left(2 \sqrt{x}\right)",1,"ArcTan[2*Sqrt[x]]","A",3,3,15,0.2000,1,"{1593, 63, 203}"
566,1,13,0,0.0084578,"\int \frac{1}{\sqrt{x}-x^{5/2}} \, dx","Int[(Sqrt[x] - x^(5/2))^(-1),x]","\tan ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}\left(\sqrt{x}\right)","\tan ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}\left(\sqrt{x}\right)",1,"ArcTan[Sqrt[x]] + ArcTanh[Sqrt[x]]","A",5,5,15,0.3333,1,"{1593, 329, 212, 206, 203}"
567,1,27,0,0.0116985,"\int \frac{1}{-\sqrt[4]{x}+\sqrt{x}} \, dx","Int[(-x^(1/4) + Sqrt[x])^(-1),x]","2 \sqrt{x}+4 \sqrt[4]{x}+4 \log \left(1-\sqrt[4]{x}\right)","2 \sqrt{x}+4 \sqrt[4]{x}+4 \log \left(1-\sqrt[4]{x}\right)",1,"4*x^(1/4) + 2*Sqrt[x] + 4*Log[1 - x^(1/4)]","A",4,3,15,0.2000,1,"{1593, 266, 43}"
568,1,32,0,0.0142512,"\int \frac{1}{\sqrt[3]{x}+\sqrt{x}} \, dx","Int[(x^(1/3) + Sqrt[x])^(-1),x]","2 \sqrt{x}-3 \sqrt[3]{x}+6 \sqrt[6]{x}-6 \log \left(\sqrt[6]{x}+1\right)","2 \sqrt{x}-3 \sqrt[3]{x}+6 \sqrt[6]{x}-6 \log \left(\sqrt[6]{x}+1\right)",1,"6*x^(1/6) - 3*x^(1/3) + 2*Sqrt[x] - 6*Log[1 + x^(1/6)]","A",4,3,13,0.2308,1,"{1593, 266, 43}"
569,1,25,0,0.0112607,"\int \frac{1}{\sqrt[4]{x}+\sqrt{x}} \, dx","Int[(x^(1/4) + Sqrt[x])^(-1),x]","2 \sqrt{x}-4 \sqrt[4]{x}+4 \log \left(\sqrt[4]{x}+1\right)","2 \sqrt{x}-4 \sqrt[4]{x}+4 \log \left(\sqrt[4]{x}+1\right)",1,"-4*x^(1/4) + 2*Sqrt[x] + 4*Log[1 + x^(1/4)]","A",4,3,13,0.2308,1,"{1593, 266, 43}"
570,1,20,0,0.0091215,"\int \frac{1}{-\sqrt[3]{x}+x^{2/3}} \, dx","Int[(-x^(1/3) + x^(2/3))^(-1),x]","3 \sqrt[3]{x}+3 \log \left(1-\sqrt[3]{x}\right)","3 \sqrt[3]{x}+3 \log \left(1-\sqrt[3]{x}\right)",1,"3*x^(1/3) + 3*Log[1 - x^(1/3)]","A",4,3,15,0.2000,1,"{1593, 266, 43}"
571,1,62,0,0.0374304,"\int \frac{1}{\frac{1}{\sqrt[4]{x}}+\sqrt{x}} \, dx","Int[(x^(-1/4) + Sqrt[x])^(-1),x]","2 \sqrt{x}+\frac{4}{3} \log \left(\sqrt[4]{x}+1\right)-\frac{2}{3} \log \left(\sqrt{x}-\sqrt[4]{x}+1\right)+\frac{4 \tan ^{-1}\left(\frac{1-2 \sqrt[4]{x}}{\sqrt{3}}\right)}{\sqrt{3}}","2 \sqrt{x}+\frac{4}{3} \log \left(\sqrt[4]{x}+1\right)-\frac{2}{3} \log \left(\sqrt{x}-\sqrt[4]{x}+1\right)+\frac{4 \tan ^{-1}\left(\frac{1-2 \sqrt[4]{x}}{\sqrt{3}}\right)}{\sqrt{3}}",1,"2*Sqrt[x] + (4*ArcTan[(1 - 2*x^(1/4))/Sqrt[3]])/Sqrt[3] + (4*Log[1 + x^(1/4)])/3 - (2*Log[1 - x^(1/4) + Sqrt[x]])/3","A",9,9,13,0.6923,1,"{1593, 341, 321, 292, 31, 634, 618, 204, 628}"
572,1,73,0,0.0282093,"\int \frac{1}{\sqrt[4]{x}+\sqrt[3]{x}} \, dx","Int[(x^(1/4) + x^(1/3))^(-1),x]","\frac{3 x^{2/3}}{2}-\frac{12 x^{7/12}}{7}-\frac{12 x^{5/12}}{5}+2 \sqrt{x}+3 \sqrt[3]{x}-4 \sqrt[4]{x}+6 \sqrt[6]{x}-12 \sqrt[12]{x}+12 \log \left(\sqrt[12]{x}+1\right)","\frac{3 x^{2/3}}{2}-\frac{12 x^{7/12}}{7}-\frac{12 x^{5/12}}{5}+2 \sqrt{x}+3 \sqrt[3]{x}-4 \sqrt[4]{x}+6 \sqrt[6]{x}-12 \sqrt[12]{x}+12 \log \left(\sqrt[12]{x}+1\right)",1,"-12*x^(1/12) + 6*x^(1/6) - 4*x^(1/4) + 3*x^(1/3) - (12*x^(5/12))/5 + 2*Sqrt[x] - (12*x^(7/12))/7 + (3*x^(2/3))/2 + 12*Log[1 + x^(1/12)]","A",4,3,13,0.2308,1,"{1593, 266, 43}"
573,1,130,0,0.045854,"\int \frac{1}{\frac{1}{\sqrt[3]{x}}+\frac{1}{\sqrt[4]{x}}} \, dx","Int[(x^(-1/3) + x^(-1/4))^(-1),x]","\frac{4 x^{5/4}}{5}-\frac{6 x^{7/6}}{7}+\frac{12 x^{13/12}}{13}+\frac{12 x^{11/12}}{11}-\frac{6 x^{5/6}}{5}+\frac{4 x^{3/4}}{3}-\frac{3 x^{2/3}}{2}+\frac{12 x^{7/12}}{7}+\frac{12 x^{5/12}}{5}-x-2 \sqrt{x}-3 \sqrt[3]{x}+4 \sqrt[4]{x}-6 \sqrt[6]{x}+12 \sqrt[12]{x}-12 \log \left(\sqrt[12]{x}+1\right)","\frac{4 x^{5/4}}{5}-\frac{6 x^{7/6}}{7}+\frac{12 x^{13/12}}{13}+\frac{12 x^{11/12}}{11}-\frac{6 x^{5/6}}{5}+\frac{4 x^{3/4}}{3}-\frac{3 x^{2/3}}{2}+\frac{12 x^{7/12}}{7}+\frac{12 x^{5/12}}{5}-x-2 \sqrt{x}-3 \sqrt[3]{x}+4 \sqrt[4]{x}-6 \sqrt[6]{x}+12 \sqrt[12]{x}-12 \log \left(\sqrt[12]{x}+1\right)",1,"12*x^(1/12) - 6*x^(1/6) + 4*x^(1/4) - 3*x^(1/3) + (12*x^(5/12))/5 - 2*Sqrt[x] + (12*x^(7/12))/7 - (3*x^(2/3))/2 + (4*x^(3/4))/3 - (6*x^(5/6))/5 + (12*x^(11/12))/11 - x + (12*x^(13/12))/13 - (6*x^(7/6))/7 + (4*x^(5/4))/5 - 12*Log[1 + x^(1/12)]","A",4,3,13,0.2308,1,"{1593, 266, 43}"
574,1,200,0,0.3955987,"\int \frac{1}{-\frac{1}{\sqrt[3]{x}}+\sqrt{x}} \, dx","Int[(-x^(-1/3) + Sqrt[x])^(-1),x]","2 \sqrt{x}+\frac{6}{5} \log \left(1-\sqrt[6]{x}\right)-\frac{3}{10} \left(1+\sqrt{5}\right) \log \left(2 \sqrt[3]{x}-\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)-\frac{3}{10} \left(1-\sqrt{5}\right) \log \left(2 \sqrt[3]{x}+\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)+\frac{3}{5} \sqrt{2 \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 \sqrt[6]{x}-\sqrt{5}+1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)-\frac{3}{5} \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(4 \sqrt[6]{x}+\sqrt{5}+1\right)\right)","2 \sqrt{x}+\frac{6}{5} \log \left(1-\sqrt[6]{x}\right)-\frac{3}{10} \left(1+\sqrt{5}\right) \log \left(2 \sqrt[3]{x}-\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)-\frac{3}{10} \left(1-\sqrt{5}\right) \log \left(2 \sqrt[3]{x}+\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)+\frac{3}{5} \sqrt{2 \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 \sqrt[6]{x}-\sqrt{5}+1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)-\frac{3}{5} \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(4 \sqrt[6]{x}+\sqrt{5}+1\right)\right)",1,"2*Sqrt[x] + (3*Sqrt[2*(5 - Sqrt[5])]*ArcTan[(1 - Sqrt[5] + 4*x^(1/6))/Sqrt[2*(5 + Sqrt[5])]])/5 - (3*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*(1 + Sqrt[5] + 4*x^(1/6)))/2])/5 + (6*Log[1 - x^(1/6)])/5 - (3*(1 + Sqrt[5])*Log[2 + x^(1/6) - Sqrt[5]*x^(1/6) + 2*x^(1/3)])/10 - (3*(1 - Sqrt[5])*Log[2 + x^(1/6) + Sqrt[5]*x^(1/6) + 2*x^(1/3)])/10","A",9,9,15,0.6000,1,"{1593, 341, 321, 294, 634, 618, 204, 628, 31}"
575,1,8,0,0.0047993,"\int \frac{\sqrt{x}}{x+x^2} \, dx","Int[Sqrt[x]/(x + x^2),x]","2 \tan ^{-1}\left(\sqrt{x}\right)","2 \tan ^{-1}\left(\sqrt{x}\right)",1,"2*ArcTan[Sqrt[x]]","A",3,3,13,0.2308,1,"{647, 63, 203}"
576,1,19,0,0.0143723,"\int \frac{x}{4 \sqrt{x}+x} \, dx","Int[x/(4*Sqrt[x] + x),x]","x-8 \sqrt{x}+32 \log \left(\sqrt{x}+4\right)","x-8 \sqrt{x}+32 \log \left(\sqrt{x}+4\right)",1,"-8*Sqrt[x] + x + 32*Log[4 + Sqrt[x]]","A",4,3,13,0.2308,1,"{1584, 266, 43}"
577,1,108,0,0.0827125,"\int \frac{\sqrt{x}}{\sqrt[3]{x}+x} \, dx","Int[Sqrt[x]/(x^(1/3) + x),x]","2 \sqrt{x}-\frac{3 \log \left(\sqrt[3]{x}-\sqrt{2} \sqrt[6]{x}+1\right)}{2 \sqrt{2}}+\frac{3 \log \left(\sqrt[3]{x}+\sqrt{2} \sqrt[6]{x}+1\right)}{2 \sqrt{2}}+\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt[6]{x}\right)}{\sqrt{2}}-\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt[6]{x}+1\right)}{\sqrt{2}}","2 \sqrt{x}-\frac{3 \log \left(\sqrt[3]{x}-\sqrt{2} \sqrt[6]{x}+1\right)}{2 \sqrt{2}}+\frac{3 \log \left(\sqrt[3]{x}+\sqrt{2} \sqrt[6]{x}+1\right)}{2 \sqrt{2}}+\frac{3 \tan ^{-1}\left(1-\sqrt{2} \sqrt[6]{x}\right)}{\sqrt{2}}-\frac{3 \tan ^{-1}\left(\sqrt{2} \sqrt[6]{x}+1\right)}{\sqrt{2}}",1,"2*Sqrt[x] + (3*ArcTan[1 - Sqrt[2]*x^(1/6)])/Sqrt[2] - (3*ArcTan[1 + Sqrt[2]*x^(1/6)])/Sqrt[2] - (3*Log[1 - Sqrt[2]*x^(1/6) + x^(1/3)])/(2*Sqrt[2]) + (3*Log[1 + Sqrt[2]*x^(1/6) + x^(1/3)])/(2*Sqrt[2])","A",13,10,15,0.6667,1,"{1584, 341, 321, 329, 297, 1162, 617, 204, 1165, 628}"
578,1,76,0,0.0344146,"\int \frac{\sqrt[3]{x}}{\sqrt[4]{x}+\sqrt{x}} \, dx","Int[x^(1/3)/(x^(1/4) + Sqrt[x]),x]","\frac{6 x^{5/6}}{5}-\frac{12 x^{7/12}}{7}+3 \sqrt[3]{x}-12 \sqrt[12]{x}+6 \log \left(\sqrt[12]{x}+1\right)-2 \log \left(\sqrt[4]{x}+1\right)-4 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[12]{x}}{\sqrt{3}}\right)","\frac{6 x^{5/6}}{5}-\frac{12 x^{7/12}}{7}+3 \sqrt[3]{x}-12 \sqrt[12]{x}+6 \log \left(\sqrt[12]{x}+1\right)-2 \log \left(\sqrt[4]{x}+1\right)-4 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[12]{x}}{\sqrt{3}}\right)",1,"-12*x^(1/12) + 3*x^(1/3) - (12*x^(7/12))/7 + (6*x^(5/6))/5 - 4*Sqrt[3]*ArcTan[(1 - 2*x^(1/12))/Sqrt[3]] + 6*Log[1 + x^(1/12)] - 2*Log[1 + x^(1/4)]","A",10,7,19,0.3684,1,"{1584, 341, 50, 58, 618, 204, 31}"
579,1,119,0,0.0493564,"\int \frac{\sqrt{x}}{\sqrt[4]{x}+\sqrt[3]{x}} \, dx","Int[Sqrt[x]/(x^(1/4) + x^(1/3)),x]","\frac{6 x^{7/6}}{7}-\frac{12 x^{13/12}}{13}-\frac{12 x^{11/12}}{11}+\frac{6 x^{5/6}}{5}-\frac{4 x^{3/4}}{3}+\frac{3 x^{2/3}}{2}-\frac{12 x^{7/12}}{7}-\frac{12 x^{5/12}}{5}+x+2 \sqrt{x}+3 \sqrt[3]{x}-4 \sqrt[4]{x}+6 \sqrt[6]{x}-12 \sqrt[12]{x}+12 \log \left(\sqrt[12]{x}+1\right)","\frac{6 x^{7/6}}{7}-\frac{12 x^{13/12}}{13}-\frac{12 x^{11/12}}{11}+\frac{6 x^{5/6}}{5}-\frac{4 x^{3/4}}{3}+\frac{3 x^{2/3}}{2}-\frac{12 x^{7/12}}{7}-\frac{12 x^{5/12}}{5}+x+2 \sqrt{x}+3 \sqrt[3]{x}-4 \sqrt[4]{x}+6 \sqrt[6]{x}-12 \sqrt[12]{x}+12 \log \left(\sqrt[12]{x}+1\right)",1,"-12*x^(1/12) + 6*x^(1/6) - 4*x^(1/4) + 3*x^(1/3) - (12*x^(5/12))/5 + 2*Sqrt[x] - (12*x^(7/12))/7 + (3*x^(2/3))/2 - (4*x^(3/4))/3 + (6*x^(5/6))/5 - (12*x^(11/12))/11 + x - (12*x^(13/12))/13 + (6*x^(7/6))/7 + 12*Log[1 + x^(1/12)]","A",4,3,19,0.1579,1,"{1584, 266, 43}"
580,1,201,0,0.2239255,"\int \frac{\sqrt{x}}{-\frac{1}{\sqrt[3]{x}}+\sqrt{x}} \, dx","Int[Sqrt[x]/(-x^(-1/3) + Sqrt[x]),x]","x+6 \sqrt[6]{x}+\frac{6}{5} \log \left(1-\sqrt[6]{x}\right)-\frac{3}{10} \left(1-\sqrt{5}\right) \log \left(2 \sqrt[3]{x}-\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)-\frac{3}{10} \left(1+\sqrt{5}\right) \log \left(2 \sqrt[3]{x}+\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)-\frac{3}{5} \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 \sqrt[6]{x}-\sqrt{5}+1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)-\frac{3}{5} \sqrt{2 \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(4 \sqrt[6]{x}+\sqrt{5}+1\right)\right)","x+6 \sqrt[6]{x}+\frac{6}{5} \log \left(1-\sqrt[6]{x}\right)-\frac{3}{10} \left(1-\sqrt{5}\right) \log \left(2 \sqrt[3]{x}-\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)-\frac{3}{10} \left(1+\sqrt{5}\right) \log \left(2 \sqrt[3]{x}+\sqrt{5} \sqrt[6]{x}+\sqrt[6]{x}+2\right)-\frac{3}{5} \sqrt{2 \left(5+\sqrt{5}\right)} \tan ^{-1}\left(\frac{4 \sqrt[6]{x}-\sqrt{5}+1}{\sqrt{2 \left(5+\sqrt{5}\right)}}\right)-\frac{3}{5} \sqrt{2 \left(5-\sqrt{5}\right)} \tan ^{-1}\left(\frac{1}{2} \sqrt{\frac{1}{10} \left(5+\sqrt{5}\right)} \left(4 \sqrt[6]{x}+\sqrt{5}+1\right)\right)",1,"6*x^(1/6) + x - (3*Sqrt[2*(5 + Sqrt[5])]*ArcTan[(1 - Sqrt[5] + 4*x^(1/6))/Sqrt[2*(5 + Sqrt[5])]])/5 - (3*Sqrt[2*(5 - Sqrt[5])]*ArcTan[(Sqrt[(5 + Sqrt[5])/10]*(1 + Sqrt[5] + 4*x^(1/6)))/2])/5 + (6*Log[1 - x^(1/6)])/5 - (3*(1 - Sqrt[5])*Log[2 + x^(1/6) - Sqrt[5]*x^(1/6) + 2*x^(1/3)])/10 - (3*(1 + Sqrt[5])*Log[2 + x^(1/6) + Sqrt[5]*x^(1/6) + 2*x^(1/3)])/10","A",10,9,21,0.4286,1,"{1584, 341, 302, 202, 634, 618, 204, 628, 31}"
581,1,36,0,0.036967,"\int \frac{\sqrt{b-\frac{a}{x}} x^m}{\sqrt{a-b x}} \, dx","Int[(Sqrt[b - a/x]*x^m)/Sqrt[a - b*x],x]","\frac{2 x^{m+1} \sqrt{b-\frac{a}{x}}}{(2 m+1) \sqrt{a-b x}}","\frac{2 x^{m+1} \sqrt{b-\frac{a}{x}}}{(2 m+1) \sqrt{a-b x}}",1,"(2*Sqrt[b - a/x]*x^(1 + m))/((1 + 2*m)*Sqrt[a - b*x])","A",3,3,26,0.1154,1,"{515, 23, 30}"
582,1,29,0,0.0342811,"\int \frac{\sqrt{b-\frac{a}{x}} x^2}{\sqrt{a-b x}} \, dx","Int[(Sqrt[b - a/x]*x^2)/Sqrt[a - b*x],x]","\frac{2 x^3 \sqrt{b-\frac{a}{x}}}{5 \sqrt{a-b x}}","\frac{2 x^3 \sqrt{b-\frac{a}{x}}}{5 \sqrt{a-b x}}",1,"(2*Sqrt[b - a/x]*x^3)/(5*Sqrt[a - b*x])","A",3,3,26,0.1154,1,"{515, 23, 30}"
583,1,29,0,0.023956,"\int \frac{\sqrt{b-\frac{a}{x}} x}{\sqrt{a-b x}} \, dx","Int[(Sqrt[b - a/x]*x)/Sqrt[a - b*x],x]","\frac{2 x^2 \sqrt{b-\frac{a}{x}}}{3 \sqrt{a-b x}}","\frac{2 x^2 \sqrt{b-\frac{a}{x}}}{3 \sqrt{a-b x}}",1,"(2*Sqrt[b - a/x]*x^2)/(3*Sqrt[a - b*x])","A",3,3,24,0.1250,1,"{515, 23, 30}"
584,1,25,0,0.014152,"\int \frac{\sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}} \, dx","Int[Sqrt[b - a/x]/Sqrt[a - b*x],x]","\frac{2 x \sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}}","\frac{2 x \sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}}",1,"(2*Sqrt[b - a/x]*x)/Sqrt[a - b*x]","A",3,3,23,0.1304,1,"{435, 23, 30}"
585,1,24,0,0.0343887,"\int \frac{\sqrt{b-\frac{a}{x}}}{x \sqrt{a-b x}} \, dx","Int[Sqrt[b - a/x]/(x*Sqrt[a - b*x]),x]","-\frac{2 \sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}}","-\frac{2 \sqrt{b-\frac{a}{x}}}{\sqrt{a-b x}}",1,"(-2*Sqrt[b - a/x])/Sqrt[a - b*x]","A",3,3,26,0.1154,1,"{515, 23, 30}"
586,1,29,0,0.0330215,"\int \frac{\sqrt{b-\frac{a}{x}}}{x^2 \sqrt{a-b x}} \, dx","Int[Sqrt[b - a/x]/(x^2*Sqrt[a - b*x]),x]","-\frac{2 \sqrt{b-\frac{a}{x}}}{3 x \sqrt{a-b x}}","-\frac{2 \sqrt{b-\frac{a}{x}}}{3 x \sqrt{a-b x}}",1,"(-2*Sqrt[b - a/x])/(3*x*Sqrt[a - b*x])","A",3,3,26,0.1154,1,"{515, 23, 30}"
587,1,80,0,0.0591799,"\int \left(a+\frac{b}{x}\right)^m (c+d x)^n \, dx","Int[(a + b/x)^m*(c + d*x)^n,x]","\frac{x \left(a+\frac{b}{x}\right)^m \left(\frac{a x}{b}+1\right)^{-m} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} F_1\left(1-m;-m,-n;2-m;-\frac{a x}{b},-\frac{d x}{c}\right)}{1-m}","\frac{x \left(a+\frac{b}{x}\right)^m \left(\frac{a x}{b}+1\right)^{-m} (c+d x)^n \left(\frac{d x}{c}+1\right)^{-n} F_1\left(1-m;-m,-n;2-m;-\frac{a x}{b},-\frac{d x}{c}\right)}{1-m}",1,"((a + b/x)^m*x*(c + d*x)^n*AppellF1[1 - m, -m, -n, 2 - m, -((a*x)/b), -((d*x)/c)])/((1 - m)*(1 + (a*x)/b)^m*(1 + (d*x)/c)^n)","A",4,3,17,0.1765,1,"{435, 135, 133}"
588,1,138,0,0.1167168,"\int \left(a+\frac{b}{x}\right)^m (c+d x)^2 \, dx","Int[(a + b/x)^m*(c + d*x)^2,x]","-\frac{b \left(a+\frac{b}{x}\right)^{m+1} \left(6 a^2 c^2-6 a b c d (1-m)+b^2 d^2 \left(m^2-3 m+2\right)\right) \, _2F_1\left(2,m+1;m+2;\frac{b}{a x}+1\right)}{6 a^4 (m+1)}+\frac{d x^2 \left(a+\frac{b}{x}\right)^{m+1} (6 a c-b d (2-m))}{6 a^2}+\frac{d^2 x^3 \left(a+\frac{b}{x}\right)^{m+1}}{3 a}","-\frac{b \left(a+\frac{b}{x}\right)^{m+1} \left(6 a^2 c^2-6 a b c d (1-m)+b^2 d^2 \left(m^2-3 m+2\right)\right) \, _2F_1\left(2,m+1;m+2;\frac{b}{a x}+1\right)}{6 a^4 (m+1)}+\frac{d x^2 \left(a+\frac{b}{x}\right)^{m+1} (6 a c-b d (2-m))}{6 a^2}+\frac{d^2 x^3 \left(a+\frac{b}{x}\right)^{m+1}}{3 a}",1,"(d*(6*a*c - b*d*(2 - m))*(a + b/x)^(1 + m)*x^2)/(6*a^2) + (d^2*(a + b/x)^(1 + m)*x^3)/(3*a) - (b*(6*a^2*c^2 - 6*a*b*c*d*(1 - m) + b^2*d^2*(2 - 3*m + m^2))*(a + b/x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, 1 + b/(a*x)])/(6*a^4*(1 + m))","A",5,5,17,0.2941,1,"{434, 446, 89, 78, 65}"
589,1,79,0,0.0378231,"\int \left(a+\frac{b}{x}\right)^m (c+d x) \, dx","Int[(a + b/x)^m*(c + d*x),x]","\frac{d x^2 \left(a+\frac{b}{x}\right)^{m+1}}{2 a}-\frac{b \left(a+\frac{b}{x}\right)^{m+1} (2 a c-b d (1-m)) \, _2F_1\left(2,m+1;m+2;\frac{b}{a x}+1\right)}{2 a^3 (m+1)}","\frac{d x^2 \left(a+\frac{b}{x}\right)^{m+1}}{2 a}-\frac{b \left(a+\frac{b}{x}\right)^{m+1} (2 a c-b d (1-m)) \, _2F_1\left(2,m+1;m+2;\frac{b}{a x}+1\right)}{2 a^3 (m+1)}",1,"(d*(a + b/x)^(1 + m)*x^2)/(2*a) - (b*(2*a*c - b*d*(1 - m))*(a + b/x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, 1 + b/(a*x)])/(2*a^3*(1 + m))","A",4,4,15,0.2667,1,"{434, 446, 78, 65}"
590,1,40,0,0.0101131,"\int \left(a+\frac{b}{x}\right)^m \, dx","Int[(a + b/x)^m,x]","-\frac{b \left(a+\frac{b}{x}\right)^{m+1} \, _2F_1\left(2,m+1;m+2;\frac{b}{a x}+1\right)}{a^2 (m+1)}","-\frac{b \left(a+\frac{b}{x}\right)^{m+1} \, _2F_1\left(2,m+1;m+2;\frac{b}{a x}+1\right)}{a^2 (m+1)}",1,"-((b*(a + b/x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, 1 + b/(a*x)])/(a^2*(1 + m)))","A",2,2,9,0.2222,1,"{242, 65}"
591,1,101,0,0.0684855,"\int \frac{\left(a+\frac{b}{x}\right)^m}{c+d x} \, dx","Int[(a + b/x)^m/(c + d*x),x]","\frac{\left(a+\frac{b}{x}\right)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b}{a x}+1\right)}{a d (m+1)}-\frac{c \left(a+\frac{b}{x}\right)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d (m+1) (a c-b d)}","\frac{\left(a+\frac{b}{x}\right)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b}{a x}+1\right)}{a d (m+1)}-\frac{c \left(a+\frac{b}{x}\right)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d (m+1) (a c-b d)}",1,"-((c*(a + b/x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (c*(a + b/x))/(a*c - b*d)])/(d*(a*c - b*d)*(1 + m))) + ((a + b/x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, 1 + b/(a*x)])/(a*d*(1 + m))","A",5,5,17,0.2941,1,"{434, 446, 86, 65, 68}"
592,1,56,0,0.0340559,"\int \frac{\left(a+\frac{b}{x}\right)^m}{(c+d x)^2} \, dx","Int[(a + b/x)^m/(c + d*x)^2,x]","-\frac{b \left(a+\frac{b}{x}\right)^{m+1} \, _2F_1\left(2,m+1;m+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{(m+1) (a c-b d)^2}","-\frac{b \left(a+\frac{b}{x}\right)^{m+1} \, _2F_1\left(2,m+1;m+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{(m+1) (a c-b d)^2}",1,"-((b*(a + b/x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, (c*(a + b/x))/(a*c - b*d)])/((a*c - b*d)^2*(1 + m)))","A",3,3,17,0.1765,1,"{434, 444, 68}"
593,1,112,0,0.0680983,"\int \frac{\left(a+\frac{b}{x}\right)^m}{(c+d x)^3} \, dx","Int[(a + b/x)^m/(c + d*x)^3,x]","-\frac{b \left(a+\frac{b}{x}\right)^{m+1} (2 a c-b d (m+1)) \, _2F_1\left(2,m+1;m+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{2 c (m+1) (a c-b d)^3}-\frac{d \left(a+\frac{b}{x}\right)^{m+1}}{2 c \left(\frac{c}{x}+d\right)^2 (a c-b d)}","-\frac{b \left(a+\frac{b}{x}\right)^{m+1} (2 a c-b d (m+1)) \, _2F_1\left(2,m+1;m+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{2 c (m+1) (a c-b d)^3}-\frac{d \left(a+\frac{b}{x}\right)^{m+1}}{2 c \left(\frac{c}{x}+d\right)^2 (a c-b d)}",1,"-(d*(a + b/x)^(1 + m))/(2*c*(a*c - b*d)*(d + c/x)^2) - (b*(2*a*c - b*d*(1 + m))*(a + b/x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, (c*(a + b/x))/(a*c - b*d)])/(2*c*(a*c - b*d)^3*(1 + m))","A",4,4,17,0.2353,1,"{434, 446, 78, 68}"
594,1,185,0,0.18285,"\int \frac{\left(a+\frac{b}{x}\right)^m}{(c+d x)^4} \, dx","Int[(a + b/x)^m/(c + d*x)^4,x]","-\frac{b \left(a+\frac{b}{x}\right)^{m+1} \left(6 a^2 c^2-6 a b c d (m+1)+b^2 d^2 \left(m^2+3 m+2\right)\right) \, _2F_1\left(2,m+1;m+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{6 c^2 (m+1) (a c-b d)^4}+\frac{d^2 \left(a+\frac{b}{x}\right)^{m+1}}{3 c^2 \left(\frac{c}{x}+d\right)^3 (a c-b d)}-\frac{d \left(a+\frac{b}{x}\right)^{m+1} (6 a c-b d (m+4))}{6 c^2 \left(\frac{c}{x}+d\right)^2 (a c-b d)^2}","-\frac{b \left(a+\frac{b}{x}\right)^{m+1} \left(6 a^2 c^2-6 a b c d (m+1)+b^2 d^2 \left(m^2+3 m+2\right)\right) \, _2F_1\left(2,m+1;m+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{6 c^2 (m+1) (a c-b d)^4}+\frac{d^2 \left(a+\frac{b}{x}\right)^{m+1}}{3 c^2 \left(\frac{c}{x}+d\right)^3 (a c-b d)}-\frac{d \left(a+\frac{b}{x}\right)^{m+1} (6 a c-b d (m+4))}{6 c^2 \left(\frac{c}{x}+d\right)^2 (a c-b d)^2}",1,"(d^2*(a + b/x)^(1 + m))/(3*c^2*(a*c - b*d)*(d + c/x)^3) - (d*(6*a*c - b*d*(4 + m))*(a + b/x)^(1 + m))/(6*c^2*(a*c - b*d)^2*(d + c/x)^2) - (b*(6*a^2*c^2 - 6*a*b*c*d*(1 + m) + b^2*d^2*(2 + 3*m + m^2))*(a + b/x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, (c*(a + b/x))/(a*c - b*d)])/(6*c^2*(a*c - b*d)^4*(1 + m))","A",5,5,17,0.2941,1,"{434, 446, 89, 78, 68}"
595,1,33,0,0.0314056,"\int \frac{\sqrt{b-\frac{a}{x^2}} x^m}{\sqrt{a-b x^2}} \, dx","Int[(Sqrt[b - a/x^2]*x^m)/Sqrt[a - b*x^2],x]","\frac{x^{m+1} \sqrt{b-\frac{a}{x^2}}}{m \sqrt{a-b x^2}}","\frac{x^{m+1} \sqrt{b-\frac{a}{x^2}}}{m \sqrt{a-b x^2}}",1,"(Sqrt[b - a/x^2]*x^(1 + m))/(m*Sqrt[a - b*x^2])","A",3,3,28,0.1071,1,"{515, 23, 30}"
596,1,31,0,0.0351915,"\int \frac{\sqrt{b-\frac{a}{x^2}} x^2}{\sqrt{a-b x^2}} \, dx","Int[(Sqrt[b - a/x^2]*x^2)/Sqrt[a - b*x^2],x]","\frac{x^3 \sqrt{b-\frac{a}{x^2}}}{2 \sqrt{a-b x^2}}","\frac{x^3 \sqrt{b-\frac{a}{x^2}}}{2 \sqrt{a-b x^2}}",1,"(Sqrt[b - a/x^2]*x^3)/(2*Sqrt[a - b*x^2])","A",3,3,28,0.1071,1,"{515, 23, 30}"
597,1,28,0,0.0260666,"\int \frac{\sqrt{b-\frac{a}{x^2}} x}{\sqrt{a-b x^2}} \, dx","Int[(Sqrt[b - a/x^2]*x)/Sqrt[a - b*x^2],x]","\frac{x^2 \sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}}","\frac{x^2 \sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}}",1,"(Sqrt[b - a/x^2]*x^2)/Sqrt[a - b*x^2]","A",3,3,26,0.1154,1,"{515, 23, 8}"
598,1,28,0,0.0186658,"\int \frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}} \, dx","Int[Sqrt[b - a/x^2]/Sqrt[a - b*x^2],x]","\frac{x \log (x) \sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}}","\frac{x \log (x) \sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}}",1,"(Sqrt[b - a/x^2]*x*Log[x])/Sqrt[a - b*x^2]","A",3,3,25,0.1200,1,"{435, 23, 29}"
599,1,26,0,0.0319128,"\int \frac{\sqrt{b-\frac{a}{x^2}}}{x \sqrt{a-b x^2}} \, dx","Int[Sqrt[b - a/x^2]/(x*Sqrt[a - b*x^2]),x]","-\frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}}","-\frac{\sqrt{b-\frac{a}{x^2}}}{\sqrt{a-b x^2}}",1,"-(Sqrt[b - a/x^2]/Sqrt[a - b*x^2])","A",3,3,28,0.1071,1,"{515, 23, 30}"
600,1,31,0,0.0344175,"\int \frac{\sqrt{b-\frac{a}{x^2}}}{x^2 \sqrt{a-b x^2}} \, dx","Int[Sqrt[b - a/x^2]/(x^2*Sqrt[a - b*x^2]),x]","-\frac{\sqrt{b-\frac{a}{x^2}}}{2 x \sqrt{a-b x^2}}","-\frac{\sqrt{b-\frac{a}{x^2}}}{2 x \sqrt{a-b x^2}}",1,"-Sqrt[b - a/x^2]/(2*x*Sqrt[a - b*x^2])","A",3,3,28,0.1071,1,"{515, 23, 30}"
601,1,406,0,0.4636811,"\int \frac{(c+d x)^{3/2}}{\sqrt{a+\frac{b}{x^2}}} \, dx","Int[(c + d*x)^(3/2)/Sqrt[a + b/x^2],x]","-\frac{2 \sqrt{b} c \sqrt{\frac{a x^2}{b}+1} \left(a c^2+b d^2\right) \sqrt{\frac{a (c+d x)}{a c-\sqrt{-a} \sqrt{b} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{-a} x}{\sqrt{b}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-a} \sqrt{b} d}{a c-\sqrt{-a} \sqrt{b} d}\right)}{5 (-a)^{3/2} d x \sqrt{a+\frac{b}{x^2}} \sqrt{c+d x}}+\frac{2 \sqrt{b} \sqrt{\frac{a x^2}{b}+1} \sqrt{c+d x} \left(a c^2-3 b d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{-a} x}{\sqrt{b}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-a} \sqrt{b} d}{a c-\sqrt{-a} \sqrt{b} d}\right)}{5 (-a)^{3/2} d x \sqrt{a+\frac{b}{x^2}} \sqrt{\frac{a (c+d x)}{a c-\sqrt{-a} \sqrt{b} d}}}+\frac{2 \left(a x^2+b\right) (c+d x)^{3/2}}{5 a x \sqrt{a+\frac{b}{x^2}}}+\frac{2 c \left(a x^2+b\right) \sqrt{c+d x}}{5 a x \sqrt{a+\frac{b}{x^2}}}","-\frac{2 \sqrt{b} c \sqrt{\frac{a x^2}{b}+1} \left(a c^2+b d^2\right) \sqrt{\frac{a (c+d x)}{a c-\sqrt{-a} \sqrt{b} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{-a} x}{\sqrt{b}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-a} \sqrt{b} d}{a c-\sqrt{-a} \sqrt{b} d}\right)}{5 (-a)^{3/2} d x \sqrt{a+\frac{b}{x^2}} \sqrt{c+d x}}+\frac{2 \sqrt{b} \sqrt{\frac{a x^2}{b}+1} \sqrt{c+d x} \left(a c^2-3 b d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{-a} x}{\sqrt{b}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{-a} \sqrt{b} d}{a c-\sqrt{-a} \sqrt{b} d}\right)}{5 (-a)^{3/2} d x \sqrt{a+\frac{b}{x^2}} \sqrt{\frac{a (c+d x)}{a c-\sqrt{-a} \sqrt{b} d}}}+\frac{2 \left(a x^2+b\right) (c+d x)^{3/2}}{5 a x \sqrt{a+\frac{b}{x^2}}}+\frac{2 c \left(a x^2+b\right) \sqrt{c+d x}}{5 a x \sqrt{a+\frac{b}{x^2}}}",1,"(2*c*Sqrt[c + d*x]*(b + a*x^2))/(5*a*Sqrt[a + b/x^2]*x) + (2*(c + d*x)^(3/2)*(b + a*x^2))/(5*a*Sqrt[a + b/x^2]*x) + (2*Sqrt[b]*(a*c^2 - 3*b*d^2)*Sqrt[c + d*x]*Sqrt[1 + (a*x^2)/b]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[-a]*x)/Sqrt[b]]/Sqrt[2]], (-2*Sqrt[-a]*Sqrt[b]*d)/(a*c - Sqrt[-a]*Sqrt[b]*d)])/(5*(-a)^(3/2)*d*Sqrt[a + b/x^2]*x*Sqrt[(a*(c + d*x))/(a*c - Sqrt[-a]*Sqrt[b]*d)]) - (2*Sqrt[b]*c*(a*c^2 + b*d^2)*Sqrt[(a*(c + d*x))/(a*c - Sqrt[-a]*Sqrt[b]*d)]*Sqrt[1 + (a*x^2)/b]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[-a]*x)/Sqrt[b]]/Sqrt[2]], (-2*Sqrt[-a]*Sqrt[b]*d)/(a*c - Sqrt[-a]*Sqrt[b]*d)])/(5*(-a)^(3/2)*d*Sqrt[a + b/x^2]*x*Sqrt[c + d*x])","A",8,6,21,0.2857,1,"{1450, 833, 844, 719, 424, 419}"
602,1,15,0,0.0093661,"\int \frac{-1+x^3}{\left(-4 x+x^4\right)^{2/3}} \, dx","Int[(-1 + x^3)/(-4*x + x^4)^(2/3),x]","\frac{3}{4} \sqrt[3]{x^4-4 x}","\frac{3}{4} \sqrt[3]{x^4-4 x}",1,"(3*(-4*x + x^4)^(1/3))/4","A",1,1,17,0.05882,1,"{1588}"
603,1,17,0,0.0087056,"\int \left(2-x^2\right) \sqrt[4]{6 x-x^3} \, dx","Int[(2 - x^2)*(6*x - x^3)^(1/4),x]","\frac{4}{15} \left(6 x-x^3\right)^{5/4}","\frac{4}{15} \left(6 x-x^3\right)^{5/4}",1,"(4*(6*x - x^3)^(5/4))/15","A",1,1,21,0.04762,1,"{1588}"
604,1,15,0,0.008289,"\int \left(1+x^4\right) \sqrt{5 x+x^5} \, dx","Int[(1 + x^4)*Sqrt[5*x + x^5],x]","\frac{2}{15} \left(x^5+5 x\right)^{3/2}","\frac{2}{15} \left(x^5+5 x\right)^{3/2}",1,"(2*(5*x + x^5)^(3/2))/15","A",1,1,17,0.05882,1,"{1588}"
605,1,15,0,0.0083743,"\int \left(2+5 x^4\right) \sqrt{2 x+x^5} \, dx","Int[(2 + 5*x^4)*Sqrt[2*x + x^5],x]","\frac{2}{3} \left(x^5+2 x\right)^{3/2}","\frac{2}{3} \left(x^5+2 x\right)^{3/2}",1,"(2*(2*x + x^5)^(3/2))/3","A",1,1,19,0.05263,1,"{1588}"
606,1,13,0,0.0097622,"\int \frac{x+3 x^2}{\sqrt{x^2+2 x^3}} \, dx","Int[(x + 3*x^2)/Sqrt[x^2 + 2*x^3],x]","\sqrt{2 x^3+x^2}","\sqrt{2 x^3+x^2}",1,"Sqrt[x^2 + 2*x^3]","A",1,1,21,0.04762,1,"{1588}"
607,1,44,0,0.0243852,"\int \frac{2+\sqrt[3]{1-5 x}}{3+\sqrt[3]{1-5 x}} \, dx","Int[(2 + (1 - 5*x)^(1/3))/(3 + (1 - 5*x)^(1/3)),x]","x+\frac{3}{10} (1-5 x)^{2/3}-\frac{9}{5} \sqrt[3]{1-5 x}+\frac{27}{5} \log \left(\sqrt[3]{1-5 x}+3\right)","x+\frac{3}{10} (1-5 x)^{2/3}-\frac{9}{5} \sqrt[3]{1-5 x}+\frac{27}{5} \log \left(\sqrt[3]{1-5 x}+3\right)",1,"(-9*(1 - 5*x)^(1/3))/5 + (3*(1 - 5*x)^(2/3))/10 + x + (27*Log[3 + (1 - 5*x)^(1/3)])/5","A",4,3,25,0.1200,1,"{431, 376, 77}"
608,1,21,0,0.01262,"\int \frac{1+\sqrt{x}}{-1+\sqrt{x}} \, dx","Int[(1 + Sqrt[x])/(-1 + Sqrt[x]),x]","x+4 \sqrt{x}+4 \log \left(1-\sqrt{x}\right)","x+4 \sqrt{x}+4 \log \left(1-\sqrt{x}\right)",1,"4*Sqrt[x] + x + 4*Log[1 - Sqrt[x]]","A",3,2,17,0.1176,1,"{376, 77}"
609,1,33,0,0.0216975,"\int \frac{1-\sqrt{2+3 x}}{1+\sqrt{2+3 x}} \, dx","Int[(1 - Sqrt[2 + 3*x])/(1 + Sqrt[2 + 3*x]),x]","-x+\frac{4}{3} \sqrt{3 x+2}-\frac{4}{3} \log \left(\sqrt{3 x+2}+1\right)","-x+\frac{4}{3} \sqrt{3 x+2}-\frac{4}{3} \log \left(\sqrt{3 x+2}+1\right)",1,"-x + (4*Sqrt[2 + 3*x])/3 - (4*Log[1 + Sqrt[2 + 3*x]])/3","A",4,3,27,0.1111,1,"{431, 376, 77}"
610,1,33,0,0.020707,"\int \frac{-1+\sqrt{a+b x}}{1+\sqrt{a+b x}} \, dx","Int[(-1 + Sqrt[a + b*x])/(1 + Sqrt[a + b*x]),x]","-\frac{4 \sqrt{a+b x}}{b}+\frac{4 \log \left(\sqrt{a+b x}+1\right)}{b}+x","-\frac{4 \sqrt{a+b x}}{b}+\frac{4 \log \left(\sqrt{a+b x}+1\right)}{b}+x",1,"x - (4*Sqrt[a + b*x])/b + (4*Log[1 + Sqrt[a + b*x]])/b","A",4,3,25,0.1200,1,"{431, 376, 77}"
611,1,17,0,0.0523407,"\int \frac{a+b n x^{-1+n}}{a x+b x^n} \, dx","Int[(a + b*n*x^(-1 + n))/(a*x + b*x^n),x]","\log \left(a x^{1-n}+b\right)+n \log (x)","\log \left(a x+b x^n\right)",1,"n*Log[x] + Log[b + a*x^(1 - n)]","A",5,4,22,0.1818,1,"{1593, 514, 446, 72}"
612,1,17,0,0.0377438,"\int \frac{x^{-n} \left(a+b n x^{-1+n}\right)}{b+a x^{1-n}} \, dx","Int[(a + b*n*x^(-1 + n))/(x^n*(b + a*x^(1 - n))),x]","\log \left(a x^{1-n}+b\right)+n \log (x)","\log \left(a x^{1-n}+b\right)+n \log (x)",1,"n*Log[x] + Log[b + a*x^(1 - n)]","A",4,3,29,0.1034,1,"{514, 446, 72}"
613,1,37,0,0.0923031,"\int x \left(a+b x+c x^2\right)^m \left(d+e x+f x^2+g x^3\right)^n \left(2 a d+(3 b d+3 a e+b d m+a e n) x+(4 c d+4 b e+4 a f+2 c d m+b e m+b e n+2 a f n) x^2+(5 c e+5 b f+5 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(6 c f+6 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (7+2 m+3 n) x^5\right) \, dx","Int[x*(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(2*a*d + (3*b*d + 3*a*e + b*d*m + a*e*n)*x + (4*c*d + 4*b*e + 4*a*f + 2*c*d*m + b*e*m + b*e*n + 2*a*f*n)*x^2 + (5*c*e + 5*b*f + 5*a*g + 2*c*e*m + b*f*m + c*e*n + 2*b*f*n + 3*a*g*n)*x^3 + (6*c*f + 6*b*g + 2*c*f*m + b*g*m + 2*c*f*n + 3*b*g*n)*x^4 + c*g*(7 + 2*m + 3*n)*x^5),x]","x^2 \left(a+b x+c x^2\right)^{m+1} \left(d+e x+f x^2+g x^3\right)^{n+1}","x^2 \left(a+b x+c x^2\right)^{m+1} \left(d+e x+f x^2+g x^3\right)^{n+1}",1,"x^2*(a + b*x + c*x^2)^(1 + m)*(d + e*x + f*x^2 + g*x^3)^(1 + n)","A",1,1,176,0.005682,1,"{1590}"
614,1,35,0,0.0972397,"\int \left(a+b x+c x^2\right)^m \left(d+e x+f x^2+g x^3\right)^n \left(a d+(2 b d+2 a e+b d m+a e n) x+(3 c d+3 b e+3 a f+2 c d m+b e m+b e n+2 a f n) x^2+(4 c e+4 b f+4 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(5 c f+5 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (6+2 m+3 n) x^5\right) \, dx","Int[(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(a*d + (2*b*d + 2*a*e + b*d*m + a*e*n)*x + (3*c*d + 3*b*e + 3*a*f + 2*c*d*m + b*e*m + b*e*n + 2*a*f*n)*x^2 + (4*c*e + 4*b*f + 4*a*g + 2*c*e*m + b*f*m + c*e*n + 2*b*f*n + 3*a*g*n)*x^3 + (5*c*f + 5*b*g + 2*c*f*m + b*g*m + 2*c*f*n + 3*b*g*n)*x^4 + c*g*(6 + 2*m + 3*n)*x^5),x]","x \left(a+b x+c x^2\right)^{m+1} \left(d+e x+f x^2+g x^3\right)^{n+1}","x \left(a+b x+c x^2\right)^{m+1} \left(d+e x+f x^2+g x^3\right)^{n+1}",1,"x*(a + b*x + c*x^2)^(1 + m)*(d + e*x + f*x^2 + g*x^3)^(1 + n)","A",1,1,174,0.005747,1,"{1590}"
615,1,34,0,0.11651,"\int \left(a+b x+c x^2\right)^m \left(d+e x+f x^2+g x^3\right)^n \left(b d+a e+b d m+a e n+(2 c d+2 b e+2 a f+2 c d m+b e m+b e n+2 a f n) x+(3 c e+3 b f+3 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^2+(4 c f+4 b g+2 c f m+b g m+2 c f n+3 b g n) x^3+c g (5+2 m+3 n) x^4\right) \, dx","Int[(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(b*d + a*e + b*d*m + a*e*n + (2*c*d + 2*b*e + 2*a*f + 2*c*d*m + b*e*m + b*e*n + 2*a*f*n)*x + (3*c*e + 3*b*f + 3*a*g + 2*c*e*m + b*f*m + c*e*n + 2*b*f*n + 3*a*g*n)*x^2 + (4*c*f + 4*b*g + 2*c*f*m + b*g*m + 2*c*f*n + 3*b*g*n)*x^3 + c*g*(5 + 2*m + 3*n)*x^4),x]","\left(a+b x+c x^2\right)^{m+1} \left(d+e x+f x^2+g x^3\right)^{n+1}","\left(a+b x+c x^2\right)^{m+1} \left(d+e x+f x^2+g x^3\right)^{n+1}",1,"(a + b*x + c*x^2)^(1 + m)*(d + e*x + f*x^2 + g*x^3)^(1 + n)","A",1,1,164,0.006098,1,"{1590}"
616,0,0,0,3.3743199,"\int \frac{\left(a+b x+c x^2\right)^m \left(d+e x+f x^2+g x^3\right)^n \left(-a d+(b d m+a e n) x+(c d+b e+a f+2 c d m+b e m+b e n+2 a f n) x^2+(2 c e+2 b f+2 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(3 c f+3 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (4+2 m+3 n) x^5\right)}{x^2} \, dx","Int[((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(-(a*d) + (b*d*m + a*e*n)*x + (c*d + b*e + a*f + 2*c*d*m + b*e*m + b*e*n + 2*a*f*n)*x^2 + (2*c*e + 2*b*f + 2*a*g + 2*c*e*m + b*f*m + c*e*n + 2*b*f*n + 3*a*g*n)*x^3 + (3*c*f + 3*b*g + 2*c*f*m + b*g*m + 2*c*f*n + 3*b*g*n)*x^4 + c*g*(4 + 2*m + 3*n)*x^5))/x^2,x]","\int \frac{\left(a+b x+c x^2\right)^m \left(d+e x+f x^2+g x^3\right)^n \left(-a d+(b d m+a e n) x+(c d+b e+a f+2 c d m+b e m+b e n+2 a f n) x^2+(2 c e+2 b f+2 a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(3 c f+3 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (4+2 m+3 n) x^5\right)}{x^2} \, dx","\frac{\left(a+b x+c x^2\right)^{m+1} \left(d+e x+f x^2+g x^3\right)^{n+1}}{x}",1,"(c*(d + 2*d*m) + b*e*(1 + m + n) + a*f*(1 + 2*n))*Defer[Int][(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n, x] - a*d*Defer[Int][((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n)/x^2, x] + (b*d*m + a*e*n)*Defer[Int][((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n)/x, x] + (c*e*(2 + 2*m + n) + b*f*(2 + m + 2*n) + a*g*(2 + 3*n))*Defer[Int][x*(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n, x] + (c*f*(3 + 2*m + 2*n) + b*g*(3 + m + 3*n))*Defer[Int][x^2*(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n, x] + c*g*(4 + 2*m + 3*n)*Defer[Int][x^3*(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n, x]","F",0,0,0,0,-1,"{}"
617,0,0,0,2.99845,"\int \frac{\left(a+b x+c x^2\right)^m \left(d+e x+f x^2+g x^3\right)^n \left(-2 a d+(-b d-a e+b d m+a e n) x+(2 c d m+b e m+b e n+2 a f n) x^2+(c e+b f+a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(2 c f+2 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (3+2 m+3 n) x^5\right)}{x^3} \, dx","Int[((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n*(-2*a*d + (-(b*d) - a*e + b*d*m + a*e*n)*x + (2*c*d*m + b*e*m + b*e*n + 2*a*f*n)*x^2 + (c*e + b*f + a*g + 2*c*e*m + b*f*m + c*e*n + 2*b*f*n + 3*a*g*n)*x^3 + (2*c*f + 2*b*g + 2*c*f*m + b*g*m + 2*c*f*n + 3*b*g*n)*x^4 + c*g*(3 + 2*m + 3*n)*x^5))/x^3,x]","\int \frac{\left(a+b x+c x^2\right)^m \left(d+e x+f x^2+g x^3\right)^n \left(-2 a d+(-b d-a e+b d m+a e n) x+(2 c d m+b e m+b e n+2 a f n) x^2+(c e+b f+a g+2 c e m+b f m+c e n+2 b f n+3 a g n) x^3+(2 c f+2 b g+2 c f m+b g m+2 c f n+3 b g n) x^4+c g (3+2 m+3 n) x^5\right)}{x^3} \, dx","\frac{\left(a+b x+c x^2\right)^{m+1} \left(d+e x+f x^2+g x^3\right)^{n+1}}{x^2}",1,"(c*e*(1 + 2*m + n) + b*f*(1 + m + 2*n) + a*g*(1 + 3*n))*Defer[Int][(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n, x] - 2*a*d*Defer[Int][((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n)/x^3, x] - (b*d*(1 - m) + a*e*(1 - n))*Defer[Int][((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n)/x^2, x] + (2*c*d*m + 2*a*f*n + b*e*(m + n))*Defer[Int][((a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n)/x, x] + (2*c*f*(1 + m + n) + b*g*(2 + m + 3*n))*Defer[Int][x*(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n, x] + c*g*(3 + 2*m + 3*n)*Defer[Int][x^2*(a + b*x + c*x^2)^m*(d + e*x + f*x^2 + g*x^3)^n, x]","F",0,0,0,0,-1,"{}"
618,1,185,0,0.2547699,"\int x^3 \left(a+b \sqrt{c+d x}\right)^2 \, dx","Int[x^3*(a + b*Sqrt[c + d*x])^2,x]","\frac{c^2 \left(3 a^2-b^2 c\right) (c+d x)^2}{2 d^4}+\frac{\left(a^2-3 b^2 c\right) (c+d x)^4}{4 d^4}-\frac{c \left(a^2-b^2 c\right) (c+d x)^3}{d^4}-\frac{a^2 c^3 x}{d^3}+\frac{12 a b c^2 (c+d x)^{5/2}}{5 d^4}-\frac{4 a b c^3 (c+d x)^{3/2}}{3 d^4}+\frac{4 a b (c+d x)^{9/2}}{9 d^4}-\frac{12 a b c (c+d x)^{7/2}}{7 d^4}+\frac{b^2 (c+d x)^5}{5 d^4}","\frac{c^2 \left(3 a^2-b^2 c\right) (c+d x)^2}{2 d^4}+\frac{\left(a^2-3 b^2 c\right) (c+d x)^4}{4 d^4}-\frac{c \left(a^2-b^2 c\right) (c+d x)^3}{d^4}-\frac{a^2 c^3 x}{d^3}+\frac{12 a b c^2 (c+d x)^{5/2}}{5 d^4}-\frac{4 a b c^3 (c+d x)^{3/2}}{3 d^4}+\frac{4 a b (c+d x)^{9/2}}{9 d^4}-\frac{12 a b c (c+d x)^{7/2}}{7 d^4}+\frac{b^2 (c+d x)^5}{5 d^4}",1,"-((a^2*c^3*x)/d^3) - (4*a*b*c^3*(c + d*x)^(3/2))/(3*d^4) + (c^2*(3*a^2 - b^2*c)*(c + d*x)^2)/(2*d^4) + (12*a*b*c^2*(c + d*x)^(5/2))/(5*d^4) - (c*(a^2 - b^2*c)*(c + d*x)^3)/d^4 - (12*a*b*c*(c + d*x)^(7/2))/(7*d^4) + ((a^2 - 3*b^2*c)*(c + d*x)^4)/(4*d^4) + (4*a*b*(c + d*x)^(9/2))/(9*d^4) + (b^2*(c + d*x)^5)/(5*d^4)","A",4,3,19,0.1579,1,"{371, 1398, 772}"
619,1,138,0,0.1663297,"\int x^2 \left(a+b \sqrt{c+d x}\right)^2 \, dx","Int[x^2*(a + b*Sqrt[c + d*x])^2,x]","\frac{\left(a^2-2 b^2 c\right) (c+d x)^3}{3 d^3}-\frac{c \left(2 a^2-b^2 c\right) (c+d x)^2}{2 d^3}+\frac{a^2 c^2 x}{d^2}+\frac{4 a b c^2 (c+d x)^{3/2}}{3 d^3}+\frac{4 a b (c+d x)^{7/2}}{7 d^3}-\frac{8 a b c (c+d x)^{5/2}}{5 d^3}+\frac{b^2 (c+d x)^4}{4 d^3}","\frac{\left(a^2-2 b^2 c\right) (c+d x)^3}{3 d^3}-\frac{c \left(2 a^2-b^2 c\right) (c+d x)^2}{2 d^3}+\frac{a^2 c^2 x}{d^2}+\frac{4 a b c^2 (c+d x)^{3/2}}{3 d^3}+\frac{4 a b (c+d x)^{7/2}}{7 d^3}-\frac{8 a b c (c+d x)^{5/2}}{5 d^3}+\frac{b^2 (c+d x)^4}{4 d^3}",1,"(a^2*c^2*x)/d^2 + (4*a*b*c^2*(c + d*x)^(3/2))/(3*d^3) - (c*(2*a^2 - b^2*c)*(c + d*x)^2)/(2*d^3) - (8*a*b*c*(c + d*x)^(5/2))/(5*d^3) + ((a^2 - 2*b^2*c)*(c + d*x)^3)/(3*d^3) + (4*a*b*(c + d*x)^(7/2))/(7*d^3) + (b^2*(c + d*x)^4)/(4*d^3)","A",4,3,19,0.1579,1,"{371, 1398, 772}"
620,1,89,0,0.090381,"\int x \left(a+b \sqrt{c+d x}\right)^2 \, dx","Int[x*(a + b*Sqrt[c + d*x])^2,x]","\frac{\left(a^2-b^2 c\right) (c+d x)^2}{2 d^2}-\frac{a^2 c x}{d}+\frac{4 a b (c+d x)^{5/2}}{5 d^2}-\frac{4 a b c (c+d x)^{3/2}}{3 d^2}+\frac{b^2 (c+d x)^3}{3 d^2}","\frac{\left(a^2-b^2 c\right) (c+d x)^2}{2 d^2}-\frac{a^2 c x}{d}+\frac{4 a b (c+d x)^{5/2}}{5 d^2}-\frac{4 a b c (c+d x)^{3/2}}{3 d^2}+\frac{b^2 (c+d x)^3}{3 d^2}",1,"-((a^2*c*x)/d) - (4*a*b*c*(c + d*x)^(3/2))/(3*d^2) + ((a^2 - b^2*c)*(c + d*x)^2)/(2*d^2) + (4*a*b*(c + d*x)^(5/2))/(5*d^2) + (b^2*(c + d*x)^3)/(3*d^2)","A",4,3,17,0.1765,1,"{371, 1398, 772}"
621,1,41,0,0.0303472,"\int \left(a+b \sqrt{c+d x}\right)^2 \, dx","Int[(a + b*Sqrt[c + d*x])^2,x]","a^2 x+\frac{4 a b (c+d x)^{3/2}}{3 d}+\frac{b^2 (c+d x)^2}{2 d}","a^2 x+\frac{4 a b (c+d x)^{3/2}}{3 d}+\frac{b^2 (c+d x)^2}{2 d}",1,"a^2*x + (4*a*b*(c + d*x)^(3/2))/(3*d) + (b^2*(c + d*x)^2)/(2*d)","A",4,3,15,0.2000,1,"{247, 190, 43}"
622,1,57,0,0.0655491,"\int \frac{\left(a+b \sqrt{c+d x}\right)^2}{x} \, dx","Int[(a + b*Sqrt[c + d*x])^2/x,x]","\log (x) \left(a^2+b^2 c\right)+4 a b \sqrt{c+d x}-4 a b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)+b^2 d x","\log (x) \left(a^2+b^2 c\right)+4 a b \sqrt{c+d x}-4 a b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)+b^2 d x",1,"b^2*d*x + 4*a*b*Sqrt[c + d*x] - 4*a*b*Sqrt[c]*ArcTanh[Sqrt[c + d*x]/Sqrt[c]] + (a^2 + b^2*c)*Log[x]","A",7,6,19,0.3158,1,"{371, 1398, 801, 635, 207, 260}"
623,1,54,0,0.0659866,"\int \frac{\left(a+b \sqrt{c+d x}\right)^2}{x^2} \, dx","Int[(a + b*Sqrt[c + d*x])^2/x^2,x]","-\frac{\left(a+b \sqrt{c+d x}\right)^2}{x}-\frac{2 a b d \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{\sqrt{c}}+b^2 d \log (x)","-\frac{\left(a+b \sqrt{c+d x}\right)^2}{x}-\frac{2 a b d \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{\sqrt{c}}+b^2 d \log (x)",1,"-((a + b*Sqrt[c + d*x])^2/x) - (2*a*b*d*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/Sqrt[c] + b^2*d*Log[x]","A",6,6,19,0.3158,1,"{371, 1398, 819, 635, 207, 260}"
624,1,80,0,0.073545,"\int \frac{\left(a+b \sqrt{c+d x}\right)^2}{x^3} \, dx","Int[(a + b*Sqrt[c + d*x])^2/x^3,x]","\frac{a b d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{2 c^{3/2}}-\frac{\left(a+b \sqrt{c+d x}\right)^2}{2 x^2}-\frac{b d \left(a \sqrt{c+d x}+b c\right)}{2 c x}","\frac{a b d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{2 c^{3/2}}-\frac{\left(a+b \sqrt{c+d x}\right)^2}{2 x^2}-\frac{b d \left(a \sqrt{c+d x}+b c\right)}{2 c x}",1,"-(b*d*(b*c + a*Sqrt[c + d*x]))/(2*c*x) - (a + b*Sqrt[c + d*x])^2/(2*x^2) + (a*b*d^2*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(2*c^(3/2))","A",6,6,19,0.3158,1,"{371, 1398, 821, 12, 639, 207}"
625,1,326,0,0.242677,"\int x^3 \sqrt{a+b \sqrt{c+d x}} \, dx","Int[x^3*Sqrt[a + b*Sqrt[c + d*x]],x]","\frac{4 \left(-30 a^2 b^2 c+35 a^4+3 b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{9/2}}{9 b^8 d^4}+\frac{12 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{13/2}}{13 b^8 d^4}-\frac{20 a \left(7 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{11/2}}{11 b^8 d^4}-\frac{12 a \left(7 a^2-3 b^2 c\right) \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^8 d^4}+\frac{4 \left(a^2-b^2 c\right)^2 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^8 d^4}-\frac{4 a \left(a^2-b^2 c\right)^3 \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^8 d^4}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{17/2}}{17 b^8 d^4}-\frac{28 a \left(a+b \sqrt{c+d x}\right)^{15/2}}{15 b^8 d^4}","\frac{4 \left(-30 a^2 b^2 c+35 a^4+3 b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{9/2}}{9 b^8 d^4}+\frac{12 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{13/2}}{13 b^8 d^4}-\frac{20 a \left(7 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{11/2}}{11 b^8 d^4}-\frac{12 a \left(7 a^2-3 b^2 c\right) \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^8 d^4}+\frac{4 \left(a^2-b^2 c\right)^2 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^8 d^4}-\frac{4 a \left(a^2-b^2 c\right)^3 \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^8 d^4}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{17/2}}{17 b^8 d^4}-\frac{28 a \left(a+b \sqrt{c+d x}\right)^{15/2}}{15 b^8 d^4}",1,"(-4*a*(a^2 - b^2*c)^3*(a + b*Sqrt[c + d*x])^(3/2))/(3*b^8*d^4) + (4*(a^2 - b^2*c)^2*(7*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(5/2))/(5*b^8*d^4) - (12*a*(7*a^2 - 3*b^2*c)*(a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(7/2))/(7*b^8*d^4) + (4*(35*a^4 - 30*a^2*b^2*c + 3*b^4*c^2)*(a + b*Sqrt[c + d*x])^(9/2))/(9*b^8*d^4) - (20*a*(7*a^2 - 3*b^2*c)*(a + b*Sqrt[c + d*x])^(11/2))/(11*b^8*d^4) + (12*(7*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(13/2))/(13*b^8*d^4) - (28*a*(a + b*Sqrt[c + d*x])^(15/2))/(15*b^8*d^4) + (4*(a + b*Sqrt[c + d*x])^(17/2))/(17*b^8*d^4)","A",4,3,21,0.1429,1,"{371, 1398, 772}"
626,1,224,0,0.1563355,"\int x^2 \sqrt{a+b \sqrt{c+d x}} \, dx","Int[x^2*Sqrt[a + b*Sqrt[c + d*x]],x]","\frac{4 \left(-6 a^2 b^2 c+5 a^4+b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^6 d^3}+\frac{8 \left(5 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{9/2}}{9 b^6 d^3}-\frac{8 a \left(5 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^6 d^3}-\frac{4 a \left(a^2-b^2 c\right)^2 \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^6 d^3}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{13/2}}{13 b^6 d^3}-\frac{20 a \left(a+b \sqrt{c+d x}\right)^{11/2}}{11 b^6 d^3}","\frac{4 \left(-6 a^2 b^2 c+5 a^4+b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^6 d^3}+\frac{8 \left(5 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{9/2}}{9 b^6 d^3}-\frac{8 a \left(5 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^6 d^3}-\frac{4 a \left(a^2-b^2 c\right)^2 \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^6 d^3}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{13/2}}{13 b^6 d^3}-\frac{20 a \left(a+b \sqrt{c+d x}\right)^{11/2}}{11 b^6 d^3}",1,"(-4*a*(a^2 - b^2*c)^2*(a + b*Sqrt[c + d*x])^(3/2))/(3*b^6*d^3) + (4*(5*a^4 - 6*a^2*b^2*c + b^4*c^2)*(a + b*Sqrt[c + d*x])^(5/2))/(5*b^6*d^3) - (8*a*(5*a^2 - 3*b^2*c)*(a + b*Sqrt[c + d*x])^(7/2))/(7*b^6*d^3) + (8*(5*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(9/2))/(9*b^6*d^3) - (20*a*(a + b*Sqrt[c + d*x])^(11/2))/(11*b^6*d^3) + (4*(a + b*Sqrt[c + d*x])^(13/2))/(13*b^6*d^3)","A",4,3,21,0.1429,1,"{371, 1398, 772}"
627,1,133,0,0.0958616,"\int x \sqrt{a+b \sqrt{c+d x}} \, dx","Int[x*Sqrt[a + b*Sqrt[c + d*x]],x]","\frac{4 \left(3 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^4 d^2}-\frac{4 a \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^4 d^2}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{9/2}}{9 b^4 d^2}-\frac{12 a \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^4 d^2}","\frac{4 \left(3 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^4 d^2}-\frac{4 a \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^4 d^2}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{9/2}}{9 b^4 d^2}-\frac{12 a \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^4 d^2}",1,"(-4*a*(a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(3/2))/(3*b^4*d^2) + (4*(3*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(5/2))/(5*b^4*d^2) - (12*a*(a + b*Sqrt[c + d*x])^(7/2))/(7*b^4*d^2) + (4*(a + b*Sqrt[c + d*x])^(9/2))/(9*b^4*d^2)","A",4,3,19,0.1579,1,"{371, 1398, 772}"
628,1,56,0,0.0327106,"\int \sqrt{a+b \sqrt{c+d x}} \, dx","Int[Sqrt[a + b*Sqrt[c + d*x]],x]","\frac{4 \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^2 d}-\frac{4 a \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^2 d}","\frac{4 \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^2 d}-\frac{4 a \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^2 d}",1,"(-4*a*(a + b*Sqrt[c + d*x])^(3/2))/(3*b^2*d) + (4*(a + b*Sqrt[c + d*x])^(5/2))/(5*b^2*d)","A",4,3,17,0.1765,1,"{247, 190, 43}"
629,1,116,0,0.1559356,"\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x} \, dx","Int[Sqrt[a + b*Sqrt[c + d*x]]/x,x]","4 \sqrt{a+b \sqrt{c+d x}}-2 \sqrt{a-b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)-2 \sqrt{a+b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)","4 \sqrt{a+b \sqrt{c+d x}}-2 \sqrt{a-b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)-2 \sqrt{a+b \sqrt{c}} \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)",1,"4*Sqrt[a + b*Sqrt[c + d*x]] - 2*Sqrt[a - b*Sqrt[c]]*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a - b*Sqrt[c]]] - 2*Sqrt[a + b*Sqrt[c]]*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a + b*Sqrt[c]]]","A",7,6,21,0.2857,1,"{371, 1398, 825, 827, 1166, 207}"
630,1,137,0,0.1688793,"\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x^2} \, dx","Int[Sqrt[a + b*Sqrt[c + d*x]]/x^2,x]","-\frac{\sqrt{a+b \sqrt{c+d x}}}{x}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)}{2 \sqrt{c} \sqrt{a-b \sqrt{c}}}-\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)}{2 \sqrt{c} \sqrt{a+b \sqrt{c}}}","-\frac{\sqrt{a+b \sqrt{c+d x}}}{x}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)}{2 \sqrt{c} \sqrt{a-b \sqrt{c}}}-\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)}{2 \sqrt{c} \sqrt{a+b \sqrt{c}}}",1,"-(Sqrt[a + b*Sqrt[c + d*x]]/x) + (b*d*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a - b*Sqrt[c]]])/(2*Sqrt[a - b*Sqrt[c]]*Sqrt[c]) - (b*d*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a + b*Sqrt[c]]])/(2*Sqrt[a + b*Sqrt[c]]*Sqrt[c])","A",8,7,21,0.3333,1,"{371, 1398, 821, 12, 708, 1093, 207}"
631,1,224,0,0.4288745,"\int \frac{\sqrt{a+b \sqrt{c+d x}}}{x^3} \, dx","Int[Sqrt[a + b*Sqrt[c + d*x]]/x^3,x]","\frac{b d \left(b c-a \sqrt{c+d x}\right) \sqrt{a+b \sqrt{c+d x}}}{8 c x \left(a^2-b^2 c\right)}-\frac{b d^2 \left(2 a-3 b \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)}{16 c^{3/2} \left(a-b \sqrt{c}\right)^{3/2}}+\frac{b d^2 \left(2 a+3 b \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)}{16 c^{3/2} \left(a+b \sqrt{c}\right)^{3/2}}-\frac{\sqrt{a+b \sqrt{c+d x}}}{2 x^2}","\frac{b d \left(b c-a \sqrt{c+d x}\right) \sqrt{a+b \sqrt{c+d x}}}{8 c x \left(a^2-b^2 c\right)}-\frac{b d^2 \left(2 a-3 b \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)}{16 c^{3/2} \left(a-b \sqrt{c}\right)^{3/2}}+\frac{b d^2 \left(2 a+3 b \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)}{16 c^{3/2} \left(a+b \sqrt{c}\right)^{3/2}}-\frac{\sqrt{a+b \sqrt{c+d x}}}{2 x^2}",1,"-Sqrt[a + b*Sqrt[c + d*x]]/(2*x^2) + (b*d*(b*c - a*Sqrt[c + d*x])*Sqrt[a + b*Sqrt[c + d*x]])/(8*c*(a^2 - b^2*c)*x) - (b*(2*a - 3*b*Sqrt[c])*d^2*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a - b*Sqrt[c]]])/(16*(a - b*Sqrt[c])^(3/2)*c^(3/2)) + (b*(2*a + 3*b*Sqrt[c])*d^2*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a + b*Sqrt[c]]])/(16*(a + b*Sqrt[c])^(3/2)*c^(3/2))","A",9,8,21,0.3810,1,"{371, 1398, 821, 12, 741, 827, 1166, 207}"
632,1,230,0,0.2585774,"\int \frac{x^3}{a+b \sqrt{c+d x}} \, dx","Int[x^3/(a + b*Sqrt[c + d*x]),x]","\frac{2 \left(-3 a^2 b^2 c+a^4+3 b^4 c^2\right) (c+d x)^{3/2}}{3 b^5 d^4}-\frac{a x \left(-3 a^2 b^2 c+a^4+3 b^4 c^2\right)}{b^6 d^3}+\frac{2 \left(a^2-3 b^2 c\right) (c+d x)^{5/2}}{5 b^3 d^4}-\frac{a \left(a^2-3 b^2 c\right) (c+d x)^2}{2 b^4 d^4}+\frac{2 \left(a^2-b^2 c\right)^3 \sqrt{c+d x}}{b^7 d^4}-\frac{2 a \left(a^2-b^2 c\right)^3 \log \left(a+b \sqrt{c+d x}\right)}{b^8 d^4}-\frac{a (c+d x)^3}{3 b^2 d^4}+\frac{2 (c+d x)^{7/2}}{7 b d^4}","\frac{2 \left(-3 a^2 b^2 c+a^4+3 b^4 c^2\right) (c+d x)^{3/2}}{3 b^5 d^4}-\frac{a x \left(-3 a^2 b^2 c+a^4+3 b^4 c^2\right)}{b^6 d^3}+\frac{2 \left(a^2-3 b^2 c\right) (c+d x)^{5/2}}{5 b^3 d^4}-\frac{a \left(a^2-3 b^2 c\right) (c+d x)^2}{2 b^4 d^4}+\frac{2 \left(a^2-b^2 c\right)^3 \sqrt{c+d x}}{b^7 d^4}-\frac{2 a \left(a^2-b^2 c\right)^3 \log \left(a+b \sqrt{c+d x}\right)}{b^8 d^4}-\frac{a (c+d x)^3}{3 b^2 d^4}+\frac{2 (c+d x)^{7/2}}{7 b d^4}",1,"-((a*(a^4 - 3*a^2*b^2*c + 3*b^4*c^2)*x)/(b^6*d^3)) + (2*(a^2 - b^2*c)^3*Sqrt[c + d*x])/(b^7*d^4) + (2*(a^4 - 3*a^2*b^2*c + 3*b^4*c^2)*(c + d*x)^(3/2))/(3*b^5*d^4) - (a*(a^2 - 3*b^2*c)*(c + d*x)^2)/(2*b^4*d^4) + (2*(a^2 - 3*b^2*c)*(c + d*x)^(5/2))/(5*b^3*d^4) - (a*(c + d*x)^3)/(3*b^2*d^4) + (2*(c + d*x)^(7/2))/(7*b*d^4) - (2*a*(a^2 - b^2*c)^3*Log[a + b*Sqrt[c + d*x]])/(b^8*d^4)","A",4,3,19,0.1579,1,"{371, 1398, 772}"
633,1,151,0,0.1574751,"\int \frac{x^2}{a+b \sqrt{c+d x}} \, dx","Int[x^2/(a + b*Sqrt[c + d*x]),x]","\frac{2 \left(a^2-2 b^2 c\right) (c+d x)^{3/2}}{3 b^3 d^3}+\frac{2 \left(a^2-b^2 c\right)^2 \sqrt{c+d x}}{b^5 d^3}-\frac{a x \left(a^2-2 b^2 c\right)}{b^4 d^2}-\frac{2 a \left(a^2-b^2 c\right)^2 \log \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}-\frac{a (c+d x)^2}{2 b^2 d^3}+\frac{2 (c+d x)^{5/2}}{5 b d^3}","\frac{2 \left(a^2-2 b^2 c\right) (c+d x)^{3/2}}{3 b^3 d^3}+\frac{2 \left(a^2-b^2 c\right)^2 \sqrt{c+d x}}{b^5 d^3}-\frac{a x \left(a^2-2 b^2 c\right)}{b^4 d^2}-\frac{2 a \left(a^2-b^2 c\right)^2 \log \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}-\frac{a (c+d x)^2}{2 b^2 d^3}+\frac{2 (c+d x)^{5/2}}{5 b d^3}",1,"-((a*(a^2 - 2*b^2*c)*x)/(b^4*d^2)) + (2*(a^2 - b^2*c)^2*Sqrt[c + d*x])/(b^5*d^3) + (2*(a^2 - 2*b^2*c)*(c + d*x)^(3/2))/(3*b^3*d^3) - (a*(c + d*x)^2)/(2*b^2*d^3) + (2*(c + d*x)^(5/2))/(5*b*d^3) - (2*a*(a^2 - b^2*c)^2*Log[a + b*Sqrt[c + d*x]])/(b^6*d^3)","A",4,3,19,0.1579,1,"{371, 1398, 772}"
634,1,90,0,0.0803427,"\int \frac{x}{a+b \sqrt{c+d x}} \, dx","Int[x/(a + b*Sqrt[c + d*x]),x]","\frac{2 \left(a^2-b^2 c\right) \sqrt{c+d x}}{b^3 d^2}-\frac{2 a \left(a^2-b^2 c\right) \log \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}-\frac{a x}{b^2 d}+\frac{2 (c+d x)^{3/2}}{3 b d^2}","\frac{2 \left(a^2-b^2 c\right) \sqrt{c+d x}}{b^3 d^2}-\frac{2 a \left(a^2-b^2 c\right) \log \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}-\frac{a x}{b^2 d}+\frac{2 (c+d x)^{3/2}}{3 b d^2}",1,"-((a*x)/(b^2*d)) + (2*(a^2 - b^2*c)*Sqrt[c + d*x])/(b^3*d^2) + (2*(c + d*x)^(3/2))/(3*b*d^2) - (2*a*(a^2 - b^2*c)*Log[a + b*Sqrt[c + d*x]])/(b^4*d^2)","A",4,3,17,0.1765,1,"{371, 1398, 772}"
635,1,41,0,0.0241772,"\int \frac{1}{a+b \sqrt{c+d x}} \, dx","Int[(a + b*Sqrt[c + d*x])^(-1),x]","\frac{2 \sqrt{c+d x}}{b d}-\frac{2 a \log \left(a+b \sqrt{c+d x}\right)}{b^2 d}","\frac{2 \sqrt{c+d x}}{b d}-\frac{2 a \log \left(a+b \sqrt{c+d x}\right)}{b^2 d}",1,"(2*Sqrt[c + d*x])/(b*d) - (2*a*Log[a + b*Sqrt[c + d*x]])/(b^2*d)","A",4,3,15,0.2000,1,"{247, 190, 43}"
636,1,82,0,0.0791696,"\int \frac{1}{x \left(a+b \sqrt{c+d x}\right)} \, dx","Int[1/(x*(a + b*Sqrt[c + d*x])),x]","-\frac{2 a \log \left(a+b \sqrt{c+d x}\right)}{a^2-b^2 c}+\frac{2 b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2-b^2 c}+\frac{a \log (x)}{a^2-b^2 c}","-\frac{2 a \log \left(a+b \sqrt{c+d x}\right)}{a^2-b^2 c}+\frac{2 b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{a^2-b^2 c}+\frac{a \log (x)}{a^2-b^2 c}",1,"(2*b*Sqrt[c]*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(a^2 - b^2*c) + (a*Log[x])/(a^2 - b^2*c) - (2*a*Log[a + b*Sqrt[c + d*x]])/(a^2 - b^2*c)","A",7,6,19,0.3158,1,"{371, 1398, 801, 635, 206, 260}"
637,1,130,0,0.1783042,"\int \frac{1}{x^2 \left(a+b \sqrt{c+d x}\right)} \, dx","Int[1/(x^2*(a + b*Sqrt[c + d*x])),x]","-\frac{a-b \sqrt{c+d x}}{x \left(a^2-b^2 c\right)}+\frac{a b^2 d \log (x)}{\left(a^2-b^2 c\right)^2}-\frac{2 a b^2 d \log \left(a+b \sqrt{c+d x}\right)}{\left(a^2-b^2 c\right)^2}+\frac{b d \left(a^2+b^2 c\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{\sqrt{c} \left(a^2-b^2 c\right)^2}","-\frac{a-b \sqrt{c+d x}}{x \left(a^2-b^2 c\right)}+\frac{a b^2 d \log (x)}{\left(a^2-b^2 c\right)^2}-\frac{2 a b^2 d \log \left(a+b \sqrt{c+d x}\right)}{\left(a^2-b^2 c\right)^2}+\frac{b d \left(a^2+b^2 c\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{\sqrt{c} \left(a^2-b^2 c\right)^2}",1,"-((a - b*Sqrt[c + d*x])/((a^2 - b^2*c)*x)) + (b*(a^2 + b^2*c)*d*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(Sqrt[c]*(a^2 - b^2*c)^2) + (a*b^2*d*Log[x])/(a^2 - b^2*c)^2 - (2*a*b^2*d*Log[a + b*Sqrt[c + d*x]])/(a^2 - b^2*c)^2","A",8,7,19,0.3684,1,"{371, 1398, 823, 801, 635, 206, 260}"
638,1,204,0,0.2775075,"\int \frac{1}{x^3 \left(a+b \sqrt{c+d x}\right)} \, dx","Int[1/(x^3*(a + b*Sqrt[c + d*x])),x]","-\frac{b d^2 \left(-6 a^2 b^2 c+a^4-3 b^4 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{4 c^{3/2} \left(a^2-b^2 c\right)^3}+\frac{a b^4 d^2 \log (x)}{\left(a^2-b^2 c\right)^3}-\frac{2 a b^4 d^2 \log \left(a+b \sqrt{c+d x}\right)}{\left(a^2-b^2 c\right)^3}-\frac{a-b \sqrt{c+d x}}{2 x^2 \left(a^2-b^2 c\right)}-\frac{b d \left(4 a b c-\left(a^2+3 b^2 c\right) \sqrt{c+d x}\right)}{4 c x \left(a^2-b^2 c\right)^2}","-\frac{b d^2 \left(-6 a^2 b^2 c+a^4-3 b^4 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{4 c^{3/2} \left(a^2-b^2 c\right)^3}+\frac{a b^4 d^2 \log (x)}{\left(a^2-b^2 c\right)^3}-\frac{2 a b^4 d^2 \log \left(a+b \sqrt{c+d x}\right)}{\left(a^2-b^2 c\right)^3}-\frac{a-b \sqrt{c+d x}}{2 x^2 \left(a^2-b^2 c\right)}-\frac{b d \left(4 a b c-\left(a^2+3 b^2 c\right) \sqrt{c+d x}\right)}{4 c x \left(a^2-b^2 c\right)^2}",1,"-(a - b*Sqrt[c + d*x])/(2*(a^2 - b^2*c)*x^2) - (b*d*(4*a*b*c - (a^2 + 3*b^2*c)*Sqrt[c + d*x]))/(4*c*(a^2 - b^2*c)^2*x) - (b*(a^4 - 6*a^2*b^2*c - 3*b^4*c^2)*d^2*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(4*c^(3/2)*(a^2 - b^2*c)^3) + (a*b^4*d^2*Log[x])/(a^2 - b^2*c)^3 - (2*a*b^4*d^2*Log[a + b*Sqrt[c + d*x]])/(a^2 - b^2*c)^3","A",9,7,19,0.3684,1,"{371, 1398, 823, 801, 635, 206, 260}"
639,1,240,0,0.2795229,"\int \frac{x^3}{\left(a+b \sqrt{c+d x}\right)^2} \, dx","Int[x^3/(a + b*Sqrt[c + d*x])^2,x]","\frac{x \left(-9 a^2 b^2 c+5 a^4+3 b^4 c^2\right)}{b^6 d^3}+\frac{2 a \left(a^2-b^2 c\right)^3}{b^8 d^4 \left(a+b \sqrt{c+d x}\right)}-\frac{12 a \left(a^2-b^2 c\right)^2 \sqrt{c+d x}}{b^7 d^4}+\frac{3 \left(a^2-b^2 c\right) (c+d x)^2}{2 b^4 d^4}-\frac{4 a \left(2 a^2-3 b^2 c\right) (c+d x)^{3/2}}{3 b^5 d^4}+\frac{2 \left(7 a^2-b^2 c\right) \left(a^2-b^2 c\right)^2 \log \left(a+b \sqrt{c+d x}\right)}{b^8 d^4}-\frac{4 a (c+d x)^{5/2}}{5 b^3 d^4}+\frac{(c+d x)^3}{3 b^2 d^4}","\frac{x \left(-9 a^2 b^2 c+5 a^4+3 b^4 c^2\right)}{b^6 d^3}+\frac{2 a \left(a^2-b^2 c\right)^3}{b^8 d^4 \left(a+b \sqrt{c+d x}\right)}-\frac{12 a \left(a^2-b^2 c\right)^2 \sqrt{c+d x}}{b^7 d^4}+\frac{3 \left(a^2-b^2 c\right) (c+d x)^2}{2 b^4 d^4}-\frac{4 a \left(2 a^2-3 b^2 c\right) (c+d x)^{3/2}}{3 b^5 d^4}+\frac{2 \left(7 a^2-b^2 c\right) \left(a^2-b^2 c\right)^2 \log \left(a+b \sqrt{c+d x}\right)}{b^8 d^4}-\frac{4 a (c+d x)^{5/2}}{5 b^3 d^4}+\frac{(c+d x)^3}{3 b^2 d^4}",1,"((5*a^4 - 9*a^2*b^2*c + 3*b^4*c^2)*x)/(b^6*d^3) - (12*a*(a^2 - b^2*c)^2*Sqrt[c + d*x])/(b^7*d^4) - (4*a*(2*a^2 - 3*b^2*c)*(c + d*x)^(3/2))/(3*b^5*d^4) + (3*(a^2 - b^2*c)*(c + d*x)^2)/(2*b^4*d^4) - (4*a*(c + d*x)^(5/2))/(5*b^3*d^4) + (c + d*x)^3/(3*b^2*d^4) + (2*a*(a^2 - b^2*c)^3)/(b^8*d^4*(a + b*Sqrt[c + d*x])) + (2*(a^2 - b^2*c)^2*(7*a^2 - b^2*c)*Log[a + b*Sqrt[c + d*x]])/(b^8*d^4)","A",4,3,19,0.1579,1,"{371, 1398, 772}"
640,1,166,0,0.1720169,"\int \frac{x^2}{\left(a+b \sqrt{c+d x}\right)^2} \, dx","Int[x^2/(a + b*Sqrt[c + d*x])^2,x]","\frac{2 \left(-6 a^2 b^2 c+5 a^4+b^4 c^2\right) \log \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}+\frac{2 a \left(a^2-b^2 c\right)^2}{b^6 d^3 \left(a+b \sqrt{c+d x}\right)}-\frac{8 a \left(a^2-b^2 c\right) \sqrt{c+d x}}{b^5 d^3}+\frac{x \left(3 a^2-2 b^2 c\right)}{b^4 d^2}-\frac{4 a (c+d x)^{3/2}}{3 b^3 d^3}+\frac{(c+d x)^2}{2 b^2 d^3}","\frac{2 \left(-6 a^2 b^2 c+5 a^4+b^4 c^2\right) \log \left(a+b \sqrt{c+d x}\right)}{b^6 d^3}+\frac{2 a \left(a^2-b^2 c\right)^2}{b^6 d^3 \left(a+b \sqrt{c+d x}\right)}-\frac{8 a \left(a^2-b^2 c\right) \sqrt{c+d x}}{b^5 d^3}+\frac{x \left(3 a^2-2 b^2 c\right)}{b^4 d^2}-\frac{4 a (c+d x)^{3/2}}{3 b^3 d^3}+\frac{(c+d x)^2}{2 b^2 d^3}",1,"((3*a^2 - 2*b^2*c)*x)/(b^4*d^2) - (8*a*(a^2 - b^2*c)*Sqrt[c + d*x])/(b^5*d^3) - (4*a*(c + d*x)^(3/2))/(3*b^3*d^3) + (c + d*x)^2/(2*b^2*d^3) + (2*a*(a^2 - b^2*c)^2)/(b^6*d^3*(a + b*Sqrt[c + d*x])) + (2*(5*a^4 - 6*a^2*b^2*c + b^4*c^2)*Log[a + b*Sqrt[c + d*x]])/(b^6*d^3)","A",4,3,19,0.1579,1,"{371, 1398, 772}"
641,1,95,0,0.0898834,"\int \frac{x}{\left(a+b \sqrt{c+d x}\right)^2} \, dx","Int[x/(a + b*Sqrt[c + d*x])^2,x]","\frac{2 a \left(a^2-b^2 c\right)}{b^4 d^2 \left(a+b \sqrt{c+d x}\right)}+\frac{2 \left(3 a^2-b^2 c\right) \log \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}-\frac{4 a \sqrt{c+d x}}{b^3 d^2}+\frac{x}{b^2 d}","\frac{2 a \left(a^2-b^2 c\right)}{b^4 d^2 \left(a+b \sqrt{c+d x}\right)}+\frac{2 \left(3 a^2-b^2 c\right) \log \left(a+b \sqrt{c+d x}\right)}{b^4 d^2}-\frac{4 a \sqrt{c+d x}}{b^3 d^2}+\frac{x}{b^2 d}",1,"x/(b^2*d) - (4*a*Sqrt[c + d*x])/(b^3*d^2) + (2*a*(a^2 - b^2*c))/(b^4*d^2*(a + b*Sqrt[c + d*x])) + (2*(3*a^2 - b^2*c)*Log[a + b*Sqrt[c + d*x]])/(b^4*d^2)","A",4,3,17,0.1765,1,"{371, 1398, 772}"
642,1,47,0,0.0327996,"\int \frac{1}{\left(a+b \sqrt{c+d x}\right)^2} \, dx","Int[(a + b*Sqrt[c + d*x])^(-2),x]","\frac{2 a}{b^2 d \left(a+b \sqrt{c+d x}\right)}+\frac{2 \log \left(a+b \sqrt{c+d x}\right)}{b^2 d}","\frac{2 a}{b^2 d \left(a+b \sqrt{c+d x}\right)}+\frac{2 \log \left(a+b \sqrt{c+d x}\right)}{b^2 d}",1,"(2*a)/(b^2*d*(a + b*Sqrt[c + d*x])) + (2*Log[a + b*Sqrt[c + d*x]])/(b^2*d)","A",4,3,15,0.2000,1,"{247, 190, 43}"
643,1,129,0,0.1194836,"\int \frac{1}{x \left(a+b \sqrt{c+d x}\right)^2} \, dx","Int[1/(x*(a + b*Sqrt[c + d*x])^2),x]","\frac{2 a}{\left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)}-\frac{2 \left(a^2+b^2 c\right) \log \left(a+b \sqrt{c+d x}\right)}{\left(a^2-b^2 c\right)^2}+\frac{4 a b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{\left(a^2-b^2 c\right)^2}+\frac{\log (x) \left(a^2+b^2 c\right)}{\left(a^2-b^2 c\right)^2}","\frac{2 a}{\left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)}-\frac{2 \left(a^2+b^2 c\right) \log \left(a+b \sqrt{c+d x}\right)}{\left(a^2-b^2 c\right)^2}+\frac{4 a b \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{\left(a^2-b^2 c\right)^2}+\frac{\log (x) \left(a^2+b^2 c\right)}{\left(a^2-b^2 c\right)^2}",1,"(2*a)/((a^2 - b^2*c)*(a + b*Sqrt[c + d*x])) + (4*a*b*Sqrt[c]*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(a^2 - b^2*c)^2 + ((a^2 + b^2*c)*Log[x])/(a^2 - b^2*c)^2 - (2*(a^2 + b^2*c)*Log[a + b*Sqrt[c + d*x]])/(a^2 - b^2*c)^2","A",7,6,19,0.3158,1,"{371, 1398, 801, 635, 206, 260}"
644,1,202,0,0.2451049,"\int \frac{1}{x^2 \left(a+b \sqrt{c+d x}\right)^2} \, dx","Int[1/(x^2*(a + b*Sqrt[c + d*x])^2),x]","\frac{4 a b^2 d}{\left(a^2-b^2 c\right)^2 \left(a+b \sqrt{c+d x}\right)}-\frac{a-b \sqrt{c+d x}}{x \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)}+\frac{b^2 d \log (x) \left(3 a^2+b^2 c\right)}{\left(a^2-b^2 c\right)^3}-\frac{2 b^2 d \left(3 a^2+b^2 c\right) \log \left(a+b \sqrt{c+d x}\right)}{\left(a^2-b^2 c\right)^3}+\frac{2 a b d \left(a^2+3 b^2 c\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{\sqrt{c} \left(a^2-b^2 c\right)^3}","\frac{4 a b^2 d}{\left(a^2-b^2 c\right)^2 \left(a+b \sqrt{c+d x}\right)}-\frac{a-b \sqrt{c+d x}}{x \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)}+\frac{b^2 d \log (x) \left(3 a^2+b^2 c\right)}{\left(a^2-b^2 c\right)^3}-\frac{2 b^2 d \left(3 a^2+b^2 c\right) \log \left(a+b \sqrt{c+d x}\right)}{\left(a^2-b^2 c\right)^3}+\frac{2 a b d \left(a^2+3 b^2 c\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{\sqrt{c} \left(a^2-b^2 c\right)^3}",1,"(4*a*b^2*d)/((a^2 - b^2*c)^2*(a + b*Sqrt[c + d*x])) - (a - b*Sqrt[c + d*x])/((a^2 - b^2*c)*x*(a + b*Sqrt[c + d*x])) + (2*a*b*(a^2 + 3*b^2*c)*d*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(Sqrt[c]*(a^2 - b^2*c)^3) + (b^2*(3*a^2 + b^2*c)*d*Log[x])/(a^2 - b^2*c)^3 - (2*b^2*(3*a^2 + b^2*c)*d*Log[a + b*Sqrt[c + d*x]])/(a^2 - b^2*c)^3","A",8,7,19,0.3684,1,"{371, 1398, 823, 801, 635, 206, 260}"
645,1,306,0,0.4029821,"\int \frac{1}{x^3 \left(a+b \sqrt{c+d x}\right)^2} \, dx","Int[1/(x^3*(a + b*Sqrt[c + d*x])^2),x]","-\frac{a b d^2 \left(-10 a^2 b^2 c+a^4-15 b^4 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{2 c^{3/2} \left(a^2-b^2 c\right)^4}+\frac{a b^2 d^2 \left(a^2+11 b^2 c\right)}{2 c \left(a^2-b^2 c\right)^3 \left(a+b \sqrt{c+d x}\right)}+\frac{b^4 d^2 \log (x) \left(5 a^2+b^2 c\right)}{\left(a^2-b^2 c\right)^4}-\frac{2 b^4 d^2 \left(5 a^2+b^2 c\right) \log \left(a+b \sqrt{c+d x}\right)}{\left(a^2-b^2 c\right)^4}-\frac{a-b \sqrt{c+d x}}{2 x^2 \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)}-\frac{b d \left(3 a b c-\left(a^2+2 b^2 c\right) \sqrt{c+d x}\right)}{2 c x \left(a^2-b^2 c\right)^2 \left(a+b \sqrt{c+d x}\right)}","-\frac{a b d^2 \left(-10 a^2 b^2 c+a^4-15 b^4 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x}}{\sqrt{c}}\right)}{2 c^{3/2} \left(a^2-b^2 c\right)^4}+\frac{a b^2 d^2 \left(a^2+11 b^2 c\right)}{2 c \left(a^2-b^2 c\right)^3 \left(a+b \sqrt{c+d x}\right)}+\frac{b^4 d^2 \log (x) \left(5 a^2+b^2 c\right)}{\left(a^2-b^2 c\right)^4}-\frac{2 b^4 d^2 \left(5 a^2+b^2 c\right) \log \left(a+b \sqrt{c+d x}\right)}{\left(a^2-b^2 c\right)^4}-\frac{a-b \sqrt{c+d x}}{2 x^2 \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)}-\frac{b d \left(3 a b c-\left(a^2+2 b^2 c\right) \sqrt{c+d x}\right)}{2 c x \left(a^2-b^2 c\right)^2 \left(a+b \sqrt{c+d x}\right)}",1,"(a*b^2*(a^2 + 11*b^2*c)*d^2)/(2*c*(a^2 - b^2*c)^3*(a + b*Sqrt[c + d*x])) - (a - b*Sqrt[c + d*x])/(2*(a^2 - b^2*c)*x^2*(a + b*Sqrt[c + d*x])) - (b*d*(3*a*b*c - (a^2 + 2*b^2*c)*Sqrt[c + d*x]))/(2*c*(a^2 - b^2*c)^2*x*(a + b*Sqrt[c + d*x])) - (a*b*(a^4 - 10*a^2*b^2*c - 15*b^4*c^2)*d^2*ArcTanh[Sqrt[c + d*x]/Sqrt[c]])/(2*c^(3/2)*(a^2 - b^2*c)^4) + (b^4*(5*a^2 + b^2*c)*d^2*Log[x])/(a^2 - b^2*c)^4 - (2*b^4*(5*a^2 + b^2*c)*d^2*Log[a + b*Sqrt[c + d*x]])/(a^2 - b^2*c)^4","A",9,7,19,0.3684,1,"{371, 1398, 823, 801, 635, 206, 260}"
646,1,324,0,0.2299573,"\int \frac{x^3}{\sqrt{a+b \sqrt{c+d x}}} \, dx","Int[x^3/Sqrt[a + b*Sqrt[c + d*x]],x]","\frac{4 \left(-30 a^2 b^2 c+35 a^4+3 b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^8 d^4}+\frac{12 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{11/2}}{11 b^8 d^4}-\frac{20 a \left(7 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{9/2}}{9 b^8 d^4}-\frac{12 a \left(7 a^2-3 b^2 c\right) \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^8 d^4}+\frac{4 \left(a^2-b^2 c\right)^2 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^8 d^4}-\frac{4 a \left(a^2-b^2 c\right)^3 \sqrt{a+b \sqrt{c+d x}}}{b^8 d^4}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{15/2}}{15 b^8 d^4}-\frac{28 a \left(a+b \sqrt{c+d x}\right)^{13/2}}{13 b^8 d^4}","\frac{4 \left(-30 a^2 b^2 c+35 a^4+3 b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^8 d^4}+\frac{12 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{11/2}}{11 b^8 d^4}-\frac{20 a \left(7 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{9/2}}{9 b^8 d^4}-\frac{12 a \left(7 a^2-3 b^2 c\right) \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^8 d^4}+\frac{4 \left(a^2-b^2 c\right)^2 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^8 d^4}-\frac{4 a \left(a^2-b^2 c\right)^3 \sqrt{a+b \sqrt{c+d x}}}{b^8 d^4}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{15/2}}{15 b^8 d^4}-\frac{28 a \left(a+b \sqrt{c+d x}\right)^{13/2}}{13 b^8 d^4}",1,"(-4*a*(a^2 - b^2*c)^3*Sqrt[a + b*Sqrt[c + d*x]])/(b^8*d^4) + (4*(a^2 - b^2*c)^2*(7*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(3/2))/(3*b^8*d^4) - (12*a*(7*a^2 - 3*b^2*c)*(a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(5/2))/(5*b^8*d^4) + (4*(35*a^4 - 30*a^2*b^2*c + 3*b^4*c^2)*(a + b*Sqrt[c + d*x])^(7/2))/(7*b^8*d^4) - (20*a*(7*a^2 - 3*b^2*c)*(a + b*Sqrt[c + d*x])^(9/2))/(9*b^8*d^4) + (12*(7*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(11/2))/(11*b^8*d^4) - (28*a*(a + b*Sqrt[c + d*x])^(13/2))/(13*b^8*d^4) + (4*(a + b*Sqrt[c + d*x])^(15/2))/(15*b^8*d^4)","A",4,3,21,0.1429,1,"{371, 1398, 772}"
647,1,222,0,0.1581268,"\int \frac{x^2}{\sqrt{a+b \sqrt{c+d x}}} \, dx","Int[x^2/Sqrt[a + b*Sqrt[c + d*x]],x]","\frac{4 \left(-6 a^2 b^2 c+5 a^4+b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^6 d^3}+\frac{8 \left(5 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^6 d^3}-\frac{8 a \left(5 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^6 d^3}-\frac{4 a \left(a^2-b^2 c\right)^2 \sqrt{a+b \sqrt{c+d x}}}{b^6 d^3}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{11/2}}{11 b^6 d^3}-\frac{20 a \left(a+b \sqrt{c+d x}\right)^{9/2}}{9 b^6 d^3}","\frac{4 \left(-6 a^2 b^2 c+5 a^4+b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^6 d^3}+\frac{8 \left(5 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^6 d^3}-\frac{8 a \left(5 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^6 d^3}-\frac{4 a \left(a^2-b^2 c\right)^2 \sqrt{a+b \sqrt{c+d x}}}{b^6 d^3}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{11/2}}{11 b^6 d^3}-\frac{20 a \left(a+b \sqrt{c+d x}\right)^{9/2}}{9 b^6 d^3}",1,"(-4*a*(a^2 - b^2*c)^2*Sqrt[a + b*Sqrt[c + d*x]])/(b^6*d^3) + (4*(5*a^4 - 6*a^2*b^2*c + b^4*c^2)*(a + b*Sqrt[c + d*x])^(3/2))/(3*b^6*d^3) - (8*a*(5*a^2 - 3*b^2*c)*(a + b*Sqrt[c + d*x])^(5/2))/(5*b^6*d^3) + (8*(5*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(7/2))/(7*b^6*d^3) - (20*a*(a + b*Sqrt[c + d*x])^(9/2))/(9*b^6*d^3) + (4*(a + b*Sqrt[c + d*x])^(11/2))/(11*b^6*d^3)","A",4,3,21,0.1429,1,"{371, 1398, 772}"
648,1,131,0,0.0939594,"\int \frac{x}{\sqrt{a+b \sqrt{c+d x}}} \, dx","Int[x/Sqrt[a + b*Sqrt[c + d*x]],x]","\frac{4 \left(3 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^4 d^2}-\frac{4 a \left(a^2-b^2 c\right) \sqrt{a+b \sqrt{c+d x}}}{b^4 d^2}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^4 d^2}-\frac{12 a \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^4 d^2}","\frac{4 \left(3 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^4 d^2}-\frac{4 a \left(a^2-b^2 c\right) \sqrt{a+b \sqrt{c+d x}}}{b^4 d^2}+\frac{4 \left(a+b \sqrt{c+d x}\right)^{7/2}}{7 b^4 d^2}-\frac{12 a \left(a+b \sqrt{c+d x}\right)^{5/2}}{5 b^4 d^2}",1,"(-4*a*(a^2 - b^2*c)*Sqrt[a + b*Sqrt[c + d*x]])/(b^4*d^2) + (4*(3*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(3/2))/(3*b^4*d^2) - (12*a*(a + b*Sqrt[c + d*x])^(5/2))/(5*b^4*d^2) + (4*(a + b*Sqrt[c + d*x])^(7/2))/(7*b^4*d^2)","A",4,3,19,0.1579,1,"{371, 1398, 772}"
649,1,54,0,0.0314209,"\int \frac{1}{\sqrt{a+b \sqrt{c+d x}}} \, dx","Int[1/Sqrt[a + b*Sqrt[c + d*x]],x]","\frac{4 \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^2 d}-\frac{4 a \sqrt{a+b \sqrt{c+d x}}}{b^2 d}","\frac{4 \left(a+b \sqrt{c+d x}\right)^{3/2}}{3 b^2 d}-\frac{4 a \sqrt{a+b \sqrt{c+d x}}}{b^2 d}",1,"(-4*a*Sqrt[a + b*Sqrt[c + d*x]])/(b^2*d) + (4*(a + b*Sqrt[c + d*x])^(3/2))/(3*b^2*d)","A",4,3,17,0.1765,1,"{247, 190, 43}"
650,1,97,0,0.0850731,"\int \frac{1}{x \sqrt{a+b \sqrt{c+d x}}} \, dx","Int[1/(x*Sqrt[a + b*Sqrt[c + d*x]]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)}{\sqrt{a-b \sqrt{c}}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)}{\sqrt{a+b \sqrt{c}}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)}{\sqrt{a-b \sqrt{c}}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)}{\sqrt{a+b \sqrt{c}}}",1,"(-2*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a - b*Sqrt[c]]])/Sqrt[a - b*Sqrt[c]] - (2*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a + b*Sqrt[c]]])/Sqrt[a + b*Sqrt[c]]","A",6,5,21,0.2381,1,"{371, 1398, 827, 1166, 207}"
651,1,163,0,0.2034339,"\int \frac{1}{x^2 \sqrt{a+b \sqrt{c+d x}}} \, dx","Int[1/(x^2*Sqrt[a + b*Sqrt[c + d*x]]),x]","-\frac{\sqrt{a+b \sqrt{c+d x}} \left(a-b \sqrt{c+d x}\right)}{x \left(a^2-b^2 c\right)}-\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)}{2 \sqrt{c} \left(a-b \sqrt{c}\right)^{3/2}}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)}{2 \sqrt{c} \left(a+b \sqrt{c}\right)^{3/2}}","-\frac{\sqrt{a+b \sqrt{c+d x}} \left(a-b \sqrt{c+d x}\right)}{x \left(a^2-b^2 c\right)}-\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)}{2 \sqrt{c} \left(a-b \sqrt{c}\right)^{3/2}}+\frac{b d \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)}{2 \sqrt{c} \left(a+b \sqrt{c}\right)^{3/2}}",1,"-(((a - b*Sqrt[c + d*x])*Sqrt[a + b*Sqrt[c + d*x]])/((a^2 - b^2*c)*x)) - (b*d*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a - b*Sqrt[c]]])/(2*(a - b*Sqrt[c])^(3/2)*Sqrt[c]) + (b*d*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a + b*Sqrt[c]]])/(2*(a + b*Sqrt[c])^(3/2)*Sqrt[c])","A",7,6,21,0.2857,1,"{371, 1398, 823, 827, 1166, 207}"
652,1,261,0,0.4814359,"\int \frac{1}{x^3 \sqrt{a+b \sqrt{c+d x}}} \, dx","Int[1/(x^3*Sqrt[a + b*Sqrt[c + d*x]]),x]","-\frac{\left(a-b \sqrt{c+d x}\right) \sqrt{a+b \sqrt{c+d x}}}{2 x^2 \left(a^2-b^2 c\right)}-\frac{b d \sqrt{a+b \sqrt{c+d x}} \left(6 a b c-\left(a^2+5 b^2 c\right) \sqrt{c+d x}\right)}{8 c x \left(a^2-b^2 c\right)^2}+\frac{b d^2 \left(2 a-5 b \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)}{16 c^{3/2} \left(a-b \sqrt{c}\right)^{5/2}}-\frac{b d^2 \left(2 a+5 b \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)}{16 c^{3/2} \left(a+b \sqrt{c}\right)^{5/2}}","-\frac{\left(a-b \sqrt{c+d x}\right) \sqrt{a+b \sqrt{c+d x}}}{2 x^2 \left(a^2-b^2 c\right)}-\frac{b d \sqrt{a+b \sqrt{c+d x}} \left(6 a b c-\left(a^2+5 b^2 c\right) \sqrt{c+d x}\right)}{8 c x \left(a^2-b^2 c\right)^2}+\frac{b d^2 \left(2 a-5 b \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a-b \sqrt{c}}}\right)}{16 c^{3/2} \left(a-b \sqrt{c}\right)^{5/2}}-\frac{b d^2 \left(2 a+5 b \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt{a+b \sqrt{c+d x}}}{\sqrt{a+b \sqrt{c}}}\right)}{16 c^{3/2} \left(a+b \sqrt{c}\right)^{5/2}}",1,"-((a - b*Sqrt[c + d*x])*Sqrt[a + b*Sqrt[c + d*x]])/(2*(a^2 - b^2*c)*x^2) - (b*d*Sqrt[a + b*Sqrt[c + d*x]]*(6*a*b*c - (a^2 + 5*b^2*c)*Sqrt[c + d*x]))/(8*c*(a^2 - b^2*c)^2*x) + (b*(2*a - 5*b*Sqrt[c])*d^2*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a - b*Sqrt[c]]])/(16*(a - b*Sqrt[c])^(5/2)*c^(3/2)) - (b*(2*a + 5*b*Sqrt[c])*d^2*ArcTanh[Sqrt[a + b*Sqrt[c + d*x]]/Sqrt[a + b*Sqrt[c]]])/(16*(a + b*Sqrt[c])^(5/2)*c^(3/2))","A",8,6,21,0.2857,1,"{371, 1398, 823, 827, 1166, 207}"
653,1,350,0,0.2787581,"\int x^3 \left(a+b \sqrt{c+d x}\right)^p \, dx","Int[x^3*(a + b*Sqrt[c + d*x])^p,x]","\frac{2 \left(-30 a^2 b^2 c+35 a^4+3 b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{p+4}}{b^8 d^4 (p+4)}-\frac{2 a \left(a^2-b^2 c\right)^3 \left(a+b \sqrt{c+d x}\right)^{p+1}}{b^8 d^4 (p+1)}+\frac{2 \left(a^2-b^2 c\right)^2 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+2}}{b^8 d^4 (p+2)}-\frac{6 a \left(7 a^2-3 b^2 c\right) \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+3}}{b^8 d^4 (p+3)}-\frac{10 a \left(7 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+5}}{b^8 d^4 (p+5)}+\frac{6 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+6}}{b^8 d^4 (p+6)}-\frac{14 a \left(a+b \sqrt{c+d x}\right)^{p+7}}{b^8 d^4 (p+7)}+\frac{2 \left(a+b \sqrt{c+d x}\right)^{p+8}}{b^8 d^4 (p+8)}","\frac{2 \left(-30 a^2 b^2 c+35 a^4+3 b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{p+4}}{b^8 d^4 (p+4)}-\frac{2 a \left(a^2-b^2 c\right)^3 \left(a+b \sqrt{c+d x}\right)^{p+1}}{b^8 d^4 (p+1)}+\frac{2 \left(a^2-b^2 c\right)^2 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+2}}{b^8 d^4 (p+2)}-\frac{6 a \left(7 a^2-3 b^2 c\right) \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+3}}{b^8 d^4 (p+3)}-\frac{10 a \left(7 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+5}}{b^8 d^4 (p+5)}+\frac{6 \left(7 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+6}}{b^8 d^4 (p+6)}-\frac{14 a \left(a+b \sqrt{c+d x}\right)^{p+7}}{b^8 d^4 (p+7)}+\frac{2 \left(a+b \sqrt{c+d x}\right)^{p+8}}{b^8 d^4 (p+8)}",1,"(-2*a*(a^2 - b^2*c)^3*(a + b*Sqrt[c + d*x])^(1 + p))/(b^8*d^4*(1 + p)) + (2*(a^2 - b^2*c)^2*(7*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(2 + p))/(b^8*d^4*(2 + p)) - (6*a*(7*a^2 - 3*b^2*c)*(a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(3 + p))/(b^8*d^4*(3 + p)) + (2*(35*a^4 - 30*a^2*b^2*c + 3*b^4*c^2)*(a + b*Sqrt[c + d*x])^(4 + p))/(b^8*d^4*(4 + p)) - (10*a*(7*a^2 - 3*b^2*c)*(a + b*Sqrt[c + d*x])^(5 + p))/(b^8*d^4*(5 + p)) + (6*(7*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(6 + p))/(b^8*d^4*(6 + p)) - (14*a*(a + b*Sqrt[c + d*x])^(7 + p))/(b^8*d^4*(7 + p)) + (2*(a + b*Sqrt[c + d*x])^(8 + p))/(b^8*d^4*(8 + p))","A",4,3,19,0.1579,1,"{371, 1398, 772}"
654,1,242,0,0.1824399,"\int x^2 \left(a+b \sqrt{c+d x}\right)^p \, dx","Int[x^2*(a + b*Sqrt[c + d*x])^p,x]","\frac{2 \left(-6 a^2 b^2 c+5 a^4+b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{p+2}}{b^6 d^3 (p+2)}-\frac{2 a \left(a^2-b^2 c\right)^2 \left(a+b \sqrt{c+d x}\right)^{p+1}}{b^6 d^3 (p+1)}-\frac{4 a \left(5 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+3}}{b^6 d^3 (p+3)}+\frac{4 \left(5 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+4}}{b^6 d^3 (p+4)}-\frac{10 a \left(a+b \sqrt{c+d x}\right)^{p+5}}{b^6 d^3 (p+5)}+\frac{2 \left(a+b \sqrt{c+d x}\right)^{p+6}}{b^6 d^3 (p+6)}","\frac{2 \left(-6 a^2 b^2 c+5 a^4+b^4 c^2\right) \left(a+b \sqrt{c+d x}\right)^{p+2}}{b^6 d^3 (p+2)}-\frac{2 a \left(a^2-b^2 c\right)^2 \left(a+b \sqrt{c+d x}\right)^{p+1}}{b^6 d^3 (p+1)}-\frac{4 a \left(5 a^2-3 b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+3}}{b^6 d^3 (p+3)}+\frac{4 \left(5 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+4}}{b^6 d^3 (p+4)}-\frac{10 a \left(a+b \sqrt{c+d x}\right)^{p+5}}{b^6 d^3 (p+5)}+\frac{2 \left(a+b \sqrt{c+d x}\right)^{p+6}}{b^6 d^3 (p+6)}",1,"(-2*a*(a^2 - b^2*c)^2*(a + b*Sqrt[c + d*x])^(1 + p))/(b^6*d^3*(1 + p)) + (2*(5*a^4 - 6*a^2*b^2*c + b^4*c^2)*(a + b*Sqrt[c + d*x])^(2 + p))/(b^6*d^3*(2 + p)) - (4*a*(5*a^2 - 3*b^2*c)*(a + b*Sqrt[c + d*x])^(3 + p))/(b^6*d^3*(3 + p)) + (4*(5*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(4 + p))/(b^6*d^3*(4 + p)) - (10*a*(a + b*Sqrt[c + d*x])^(5 + p))/(b^6*d^3*(5 + p)) + (2*(a + b*Sqrt[c + d*x])^(6 + p))/(b^6*d^3*(6 + p))","A",4,3,19,0.1579,1,"{371, 1398, 772}"
655,1,145,0,0.1083891,"\int x \left(a+b \sqrt{c+d x}\right)^p \, dx","Int[x*(a + b*Sqrt[c + d*x])^p,x]","-\frac{2 a \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+1}}{b^4 d^2 (p+1)}+\frac{2 \left(3 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+2}}{b^4 d^2 (p+2)}-\frac{6 a \left(a+b \sqrt{c+d x}\right)^{p+3}}{b^4 d^2 (p+3)}+\frac{2 \left(a+b \sqrt{c+d x}\right)^{p+4}}{b^4 d^2 (p+4)}","-\frac{2 a \left(a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+1}}{b^4 d^2 (p+1)}+\frac{2 \left(3 a^2-b^2 c\right) \left(a+b \sqrt{c+d x}\right)^{p+2}}{b^4 d^2 (p+2)}-\frac{6 a \left(a+b \sqrt{c+d x}\right)^{p+3}}{b^4 d^2 (p+3)}+\frac{2 \left(a+b \sqrt{c+d x}\right)^{p+4}}{b^4 d^2 (p+4)}",1,"(-2*a*(a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(1 + p))/(b^4*d^2*(1 + p)) + (2*(3*a^2 - b^2*c)*(a + b*Sqrt[c + d*x])^(2 + p))/(b^4*d^2*(2 + p)) - (6*a*(a + b*Sqrt[c + d*x])^(3 + p))/(b^4*d^2*(3 + p)) + (2*(a + b*Sqrt[c + d*x])^(4 + p))/(b^4*d^2*(4 + p))","A",4,3,17,0.1765,1,"{371, 1398, 772}"
656,1,62,0,0.0401228,"\int \left(a+b \sqrt{c+d x}\right)^p \, dx","Int[(a + b*Sqrt[c + d*x])^p,x]","\frac{2 \left(a+b \sqrt{c+d x}\right)^{p+2}}{b^2 d (p+2)}-\frac{2 a \left(a+b \sqrt{c+d x}\right)^{p+1}}{b^2 d (p+1)}","\frac{2 \left(a+b \sqrt{c+d x}\right)^{p+2}}{b^2 d (p+2)}-\frac{2 a \left(a+b \sqrt{c+d x}\right)^{p+1}}{b^2 d (p+1)}",1,"(-2*a*(a + b*Sqrt[c + d*x])^(1 + p))/(b^2*d*(1 + p)) + (2*(a + b*Sqrt[c + d*x])^(2 + p))/(b^2*d*(2 + p))","A",4,3,15,0.2000,1,"{247, 190, 43}"
657,1,139,0,0.1305404,"\int \frac{\left(a+b \sqrt{c+d x}\right)^p}{x} \, dx","Int[(a + b*Sqrt[c + d*x])^p/x,x]","-\frac{\left(a+b \sqrt{c+d x}\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{a+b \sqrt{c+d x}}{a-b \sqrt{c}}\right)}{(p+1) \left(a-b \sqrt{c}\right)}-\frac{\left(a+b \sqrt{c+d x}\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{a+b \sqrt{c+d x}}{a+b \sqrt{c}}\right)}{(p+1) \left(a+b \sqrt{c}\right)}","-\frac{\left(a+b \sqrt{c+d x}\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{a+b \sqrt{c+d x}}{a-b \sqrt{c}}\right)}{(p+1) \left(a-b \sqrt{c}\right)}-\frac{\left(a+b \sqrt{c+d x}\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{a+b \sqrt{c+d x}}{a+b \sqrt{c}}\right)}{(p+1) \left(a+b \sqrt{c}\right)}",1,"-(((a + b*Sqrt[c + d*x])^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (a + b*Sqrt[c + d*x])/(a - b*Sqrt[c])])/((a - b*Sqrt[c])*(1 + p))) - ((a + b*Sqrt[c + d*x])^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, (a + b*Sqrt[c + d*x])/(a + b*Sqrt[c])])/((a + b*Sqrt[c])*(1 + p))","A",6,4,19,0.2105,1,"{371, 1398, 831, 68}"
658,1,93,0,0.0752527,"\int \frac{\left(a+b (c x)^n\right)^{5/2}}{x} \, dx","Int[(a + b*(c*x)^n)^(5/2)/x,x]","\frac{2 a^2 \sqrt{a+b (c x)^n}}{n}-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{n}+\frac{2 a \left(a+b (c x)^n\right)^{3/2}}{3 n}+\frac{2 \left(a+b (c x)^n\right)^{5/2}}{5 n}","\frac{2 a^2 \sqrt{a+b (c x)^n}}{n}-\frac{2 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{n}+\frac{2 a \left(a+b (c x)^n\right)^{3/2}}{3 n}+\frac{2 \left(a+b (c x)^n\right)^{5/2}}{5 n}",1,"(2*a^2*Sqrt[a + b*(c*x)^n])/n + (2*a*(a + b*(c*x)^n)^(3/2))/(3*n) + (2*(a + b*(c*x)^n)^(5/2))/(5*n) - (2*a^(5/2)*ArcTanh[Sqrt[a + b*(c*x)^n]/Sqrt[a]])/n","A",8,6,17,0.3529,1,"{367, 12, 266, 50, 63, 208}"
659,1,70,0,0.0572577,"\int \frac{\left(a+b (c x)^n\right)^{3/2}}{x} \, dx","Int[(a + b*(c*x)^n)^(3/2)/x,x]","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{n}+\frac{2 a \sqrt{a+b (c x)^n}}{n}+\frac{2 \left(a+b (c x)^n\right)^{3/2}}{3 n}","-\frac{2 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{n}+\frac{2 a \sqrt{a+b (c x)^n}}{n}+\frac{2 \left(a+b (c x)^n\right)^{3/2}}{3 n}",1,"(2*a*Sqrt[a + b*(c*x)^n])/n + (2*(a + b*(c*x)^n)^(3/2))/(3*n) - (2*a^(3/2)*ArcTanh[Sqrt[a + b*(c*x)^n]/Sqrt[a]])/n","A",7,6,17,0.3529,1,"{367, 12, 266, 50, 63, 208}"
660,1,49,0,0.0415735,"\int \frac{\sqrt{a+b (c x)^n}}{x} \, dx","Int[Sqrt[a + b*(c*x)^n]/x,x]","\frac{2 \sqrt{a+b (c x)^n}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{n}","\frac{2 \sqrt{a+b (c x)^n}}{n}-\frac{2 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{n}",1,"(2*Sqrt[a + b*(c*x)^n])/n - (2*Sqrt[a]*ArcTanh[Sqrt[a + b*(c*x)^n]/Sqrt[a]])/n","A",6,6,17,0.3529,1,"{367, 12, 266, 50, 63, 208}"
661,1,30,0,0.0315944,"\int \frac{1}{x \sqrt{a+b (c x)^n}} \, dx","Int[1/(x*Sqrt[a + b*(c*x)^n]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{\sqrt{a} n}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{\sqrt{a} n}",1,"(-2*ArcTanh[Sqrt[a + b*(c*x)^n]/Sqrt[a]])/(Sqrt[a]*n)","A",5,5,17,0.2941,1,"{367, 12, 266, 63, 208}"
662,1,52,0,0.046182,"\int \frac{1}{x \left(a+b (c x)^n\right)^{3/2}} \, dx","Int[1/(x*(a + b*(c*x)^n)^(3/2)),x]","\frac{2}{a n \sqrt{a+b (c x)^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{a^{3/2} n}","\frac{2}{a n \sqrt{a+b (c x)^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{a^{3/2} n}",1,"2/(a*n*Sqrt[a + b*(c*x)^n]) - (2*ArcTanh[Sqrt[a + b*(c*x)^n]/Sqrt[a]])/(a^(3/2)*n)","A",6,6,17,0.3529,1,"{367, 12, 266, 51, 63, 208}"
663,1,75,0,0.0642267,"\int \frac{1}{x \left(a+b (c x)^n\right)^{5/2}} \, dx","Int[1/(x*(a + b*(c*x)^n)^(5/2)),x]","\frac{2}{a^2 n \sqrt{a+b (c x)^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{a^{5/2} n}+\frac{2}{3 a n \left(a+b (c x)^n\right)^{3/2}}","\frac{2}{a^2 n \sqrt{a+b (c x)^n}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^n}}{\sqrt{a}}\right)}{a^{5/2} n}+\frac{2}{3 a n \left(a+b (c x)^n\right)^{3/2}}",1,"2/(3*a*n*(a + b*(c*x)^n)^(3/2)) + 2/(a^2*n*Sqrt[a + b*(c*x)^n]) - (2*ArcTanh[Sqrt[a + b*(c*x)^n]/Sqrt[a]])/(a^(5/2)*n)","A",7,6,17,0.3529,1,"{367, 12, 266, 51, 63, 208}"
664,1,101,0,0.0730843,"\int \frac{\left(-a+b (c x)^n\right)^{5/2}}{x} \, dx","Int[(-a + b*(c*x)^n)^(5/2)/x,x]","\frac{2 a^2 \sqrt{b (c x)^n-a}}{n}-\frac{2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{n}-\frac{2 a \left(b (c x)^n-a\right)^{3/2}}{3 n}+\frac{2 \left(b (c x)^n-a\right)^{5/2}}{5 n}","\frac{2 a^2 \sqrt{b (c x)^n-a}}{n}-\frac{2 a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{n}-\frac{2 a \left(b (c x)^n-a\right)^{3/2}}{3 n}+\frac{2 \left(b (c x)^n-a\right)^{5/2}}{5 n}",1,"(2*a^2*Sqrt[-a + b*(c*x)^n])/n - (2*a*(-a + b*(c*x)^n)^(3/2))/(3*n) + (2*(-a + b*(c*x)^n)^(5/2))/(5*n) - (2*a^(5/2)*ArcTan[Sqrt[-a + b*(c*x)^n]/Sqrt[a]])/n","A",8,6,19,0.3158,1,"{367, 12, 266, 50, 63, 205}"
665,1,76,0,0.0570967,"\int \frac{\left(-a+b (c x)^n\right)^{3/2}}{x} \, dx","Int[(-a + b*(c*x)^n)^(3/2)/x,x]","\frac{2 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{n}-\frac{2 a \sqrt{b (c x)^n-a}}{n}+\frac{2 \left(b (c x)^n-a\right)^{3/2}}{3 n}","\frac{2 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{n}-\frac{2 a \sqrt{b (c x)^n-a}}{n}+\frac{2 \left(b (c x)^n-a\right)^{3/2}}{3 n}",1,"(-2*a*Sqrt[-a + b*(c*x)^n])/n + (2*(-a + b*(c*x)^n)^(3/2))/(3*n) + (2*a^(3/2)*ArcTan[Sqrt[-a + b*(c*x)^n]/Sqrt[a]])/n","A",7,6,19,0.3158,1,"{367, 12, 266, 50, 63, 205}"
666,1,53,0,0.0414853,"\int \frac{\sqrt{-a+b (c x)^n}}{x} \, dx","Int[Sqrt[-a + b*(c*x)^n]/x,x]","\frac{2 \sqrt{b (c x)^n-a}}{n}-\frac{2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{n}","\frac{2 \sqrt{b (c x)^n-a}}{n}-\frac{2 \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{n}",1,"(2*Sqrt[-a + b*(c*x)^n])/n - (2*Sqrt[a]*ArcTan[Sqrt[-a + b*(c*x)^n]/Sqrt[a]])/n","A",6,6,19,0.3158,1,"{367, 12, 266, 50, 63, 205}"
667,1,32,0,0.031478,"\int \frac{1}{x \sqrt{-a+b (c x)^n}} \, dx","Int[1/(x*Sqrt[-a + b*(c*x)^n]),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{\sqrt{a} n}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{\sqrt{a} n}",1,"(2*ArcTan[Sqrt[-a + b*(c*x)^n]/Sqrt[a]])/(Sqrt[a]*n)","A",5,5,19,0.2632,1,"{367, 12, 266, 63, 205}"
668,1,56,0,0.0442907,"\int \frac{1}{x \left(-a+b (c x)^n\right)^{3/2}} \, dx","Int[1/(x*(-a + b*(c*x)^n)^(3/2)),x]","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{a^{3/2} n}-\frac{2}{a n \sqrt{b (c x)^n-a}}","-\frac{2 \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{a^{3/2} n}-\frac{2}{a n \sqrt{b (c x)^n-a}}",1,"-2/(a*n*Sqrt[-a + b*(c*x)^n]) - (2*ArcTan[Sqrt[-a + b*(c*x)^n]/Sqrt[a]])/(a^(3/2)*n)","A",6,6,19,0.3158,1,"{367, 12, 266, 51, 63, 205}"
669,1,81,0,0.0609469,"\int \frac{1}{x \left(-a+b (c x)^n\right)^{5/2}} \, dx","Int[1/(x*(-a + b*(c*x)^n)^(5/2)),x]","\frac{2}{a^2 n \sqrt{b (c x)^n-a}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{a^{5/2} n}-\frac{2}{3 a n \left(b (c x)^n-a\right)^{3/2}}","\frac{2}{a^2 n \sqrt{b (c x)^n-a}}+\frac{2 \tan ^{-1}\left(\frac{\sqrt{b (c x)^n-a}}{\sqrt{a}}\right)}{a^{5/2} n}-\frac{2}{3 a n \left(b (c x)^n-a\right)^{3/2}}",1,"-2/(3*a*n*(-a + b*(c*x)^n)^(3/2)) + 2/(a^2*n*Sqrt[-a + b*(c*x)^n]) + (2*ArcTan[Sqrt[-a + b*(c*x)^n]/Sqrt[a]])/(a^(5/2)*n)","A",7,6,19,0.3158,1,"{367, 12, 266, 51, 63, 205}"
670,1,23,0,0.0071878,"\int \frac{1}{x \sqrt{a+b x}} \, dx","Int[1/(x*Sqrt[a + b*x]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b x}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(-2*ArcTanh[Sqrt[a + b*x]/Sqrt[a]])/Sqrt[a]","A",2,2,13,0.1538,1,"{63, 208}"
671,1,30,0,0.031459,"\int \frac{1}{x \sqrt{a+b (c x)^m}} \, dx","Int[1/(x*Sqrt[a + b*(c*x)^m]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^m}}{\sqrt{a}}\right)}{\sqrt{a} m}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b (c x)^m}}{\sqrt{a}}\right)}{\sqrt{a} m}",1,"(-2*ArcTanh[Sqrt[a + b*(c*x)^m]/Sqrt[a]])/(Sqrt[a]*m)","A",5,5,17,0.2941,1,"{367, 12, 266, 63, 208}"
672,1,37,0,0.1669274,"\int \frac{1}{x \sqrt{a+b \left(c (d x)^m\right)^n}} \, dx","Int[1/(x*Sqrt[a + b*(c*(d*x)^m)^n]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c (d x)^m\right)^n}}{\sqrt{a}}\right)}{\sqrt{a} m n}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c (d x)^m\right)^n}}{\sqrt{a}}\right)}{\sqrt{a} m n}",1,"(-2*ArcTanh[Sqrt[a + b*(c*(d*x)^m)^n]/Sqrt[a]])/(Sqrt[a]*m*n)","A",6,5,21,0.2381,1,"{367, 12, 266, 63, 208}"
673,1,44,0,0.3727214,"\int \frac{1}{x \sqrt{a+b \left(c \left(d (e x)^m\right)^n\right)^p}} \, dx","Int[1/(x*Sqrt[a + b*(c*(d*(e*x)^m)^n)^p]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c \left(d (e x)^m\right)^n\right)^p}}{\sqrt{a}}\right)}{\sqrt{a} m n p}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c \left(d (e x)^m\right)^n\right)^p}}{\sqrt{a}}\right)}{\sqrt{a} m n p}",1,"(-2*ArcTanh[Sqrt[a + b*(c*(d*(e*x)^m)^n)^p]/Sqrt[a]])/(Sqrt[a]*m*n*p)","A",7,5,25,0.2000,1,"{367, 12, 266, 63, 208}"
674,1,51,0,0.6558746,"\int \frac{1}{x \sqrt{a+b \left(c \left(d \left(e (f x)^m\right)^n\right)^p\right)^q}} \, dx","Int[1/(x*Sqrt[a + b*(c*(d*(e*(f*x)^m)^n)^p)^q]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c \left(d \left(e (f x)^m\right)^n\right)^p\right)^q}}{\sqrt{a}}\right)}{\sqrt{a} m n p q}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{a+b \left(c \left(d \left(e (f x)^m\right)^n\right)^p\right)^q}}{\sqrt{a}}\right)}{\sqrt{a} m n p q}",1,"(-2*ArcTanh[Sqrt[a + b*(c*(d*(e*(f*x)^m)^n)^p)^q]/Sqrt[a]])/(Sqrt[a]*m*n*p*q)","A",8,5,29,0.1724,1,"{367, 12, 266, 63, 208}"
675,1,76,0,0.026315,"\int \frac{\sqrt{-1+\frac{1}{x^2}} \left(-1+x^2\right)^3}{x} \, dx","Int[(Sqrt[-1 + x^(-2)]*(-1 + x^2)^3)/x,x]","-\frac{1}{6} \left(\frac{1}{x^2}-1\right)^{7/2} x^6-\frac{7}{24} \left(\frac{1}{x^2}-1\right)^{5/2} x^4-\frac{35}{48} \left(\frac{1}{x^2}-1\right)^{3/2} x^2+\frac{35}{16} \sqrt{\frac{1}{x^2}-1}-\frac{35}{16} \tan ^{-1}\left(\sqrt{\frac{1}{x^2}-1}\right)","-\frac{1}{6} \left(\frac{1}{x^2}-1\right)^{7/2} x^6-\frac{7}{24} \left(\frac{1}{x^2}-1\right)^{5/2} x^4-\frac{35}{48} \left(\frac{1}{x^2}-1\right)^{3/2} x^2+\frac{35}{16} \sqrt{\frac{1}{x^2}-1}-\frac{35}{16} \tan ^{-1}\left(\sqrt{\frac{1}{x^2}-1}\right)",1,"(35*Sqrt[-1 + x^(-2)])/16 - (35*(-1 + x^(-2))^(3/2)*x^2)/48 - (7*(-1 + x^(-2))^(5/2)*x^4)/24 - ((-1 + x^(-2))^(7/2)*x^6)/6 - (35*ArcTan[Sqrt[-1 + x^(-2)]])/16","A",8,6,20,0.3000,1,"{25, 266, 47, 50, 63, 203}"
676,1,60,0,0.0199571,"\int \frac{\sqrt{-1+\frac{1}{x^2}} \left(-1+x^2\right)^2}{x} \, dx","Int[(Sqrt[-1 + x^(-2)]*(-1 + x^2)^2)/x,x]","\frac{1}{4} \left(\frac{1}{x^2}-1\right)^{5/2} x^4+\frac{5}{8} \left(\frac{1}{x^2}-1\right)^{3/2} x^2-\frac{15}{8} \sqrt{\frac{1}{x^2}-1}+\frac{15}{8} \tan ^{-1}\left(\sqrt{\frac{1}{x^2}-1}\right)","\frac{1}{4} \left(\frac{1}{x^2}-1\right)^{5/2} x^4+\frac{5}{8} \left(\frac{1}{x^2}-1\right)^{3/2} x^2-\frac{15}{8} \sqrt{\frac{1}{x^2}-1}+\frac{15}{8} \tan ^{-1}\left(\sqrt{\frac{1}{x^2}-1}\right)",1,"(-15*Sqrt[-1 + x^(-2)])/8 + (5*(-1 + x^(-2))^(3/2)*x^2)/8 + ((-1 + x^(-2))^(5/2)*x^4)/4 + (15*ArcTan[Sqrt[-1 + x^(-2)]])/8","A",7,6,20,0.3000,1,"{25, 266, 47, 50, 63, 203}"
677,1,44,0,0.0138863,"\int \frac{\sqrt{-1+\frac{1}{x^2}} \left(-1+x^2\right)}{x} \, dx","Int[(Sqrt[-1 + x^(-2)]*(-1 + x^2))/x,x]","-\frac{1}{2} \left(\frac{1}{x^2}-1\right)^{3/2} x^2+\frac{3}{2} \sqrt{\frac{1}{x^2}-1}-\frac{3}{2} \tan ^{-1}\left(\sqrt{\frac{1}{x^2}-1}\right)","-\frac{1}{2} \left(\frac{1}{x^2}-1\right)^{3/2} x^2+\frac{3}{2} \sqrt{\frac{1}{x^2}-1}-\frac{3}{2} \tan ^{-1}\left(\sqrt{\frac{1}{x^2}-1}\right)",1,"(3*Sqrt[-1 + x^(-2)])/2 - ((-1 + x^(-2))^(3/2)*x^2)/2 - (3*ArcTan[Sqrt[-1 + x^(-2)]])/2","A",6,6,18,0.3333,1,"{25, 266, 47, 50, 63, 203}"
678,1,9,0,0.0040838,"\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x \left(-1+x^2\right)} \, dx","Int[Sqrt[-1 + x^(-2)]/(x*(-1 + x^2)),x]","\sqrt{\frac{1}{x^2}-1}","\sqrt{\frac{1}{x^2}-1}",1,"Sqrt[-1 + x^(-2)]","A",2,2,20,0.1000,1,"{25, 261}"
679,1,21,0,0.0107285,"\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x \left(-1+x^2\right)^2} \, dx","Int[Sqrt[-1 + x^(-2)]/(x*(-1 + x^2)^2),x]","\frac{1}{\sqrt{\frac{1}{x^2}-1}}-\sqrt{\frac{1}{x^2}-1}","\frac{1}{\sqrt{\frac{1}{x^2}-1}}-\sqrt{\frac{1}{x^2}-1}",1,"1/Sqrt[-1 + x^(-2)] - Sqrt[-1 + x^(-2)]","A",4,3,20,0.1500,1,"{25, 266, 43}"
680,1,34,0,0.0142253,"\int \frac{\sqrt{-1+\frac{1}{x^2}}}{x \left(-1+x^2\right)^3} \, dx","Int[Sqrt[-1 + x^(-2)]/(x*(-1 + x^2)^3),x]","\sqrt{\frac{1}{x^2}-1}-\frac{2}{\sqrt{\frac{1}{x^2}-1}}-\frac{1}{3 \left(\frac{1}{x^2}-1\right)^{3/2}}","\sqrt{\frac{1}{x^2}-1}-\frac{2}{\sqrt{\frac{1}{x^2}-1}}-\frac{1}{3 \left(\frac{1}{x^2}-1\right)^{3/2}}",1,"-1/(3*(-1 + x^(-2))^(3/2)) - 2/Sqrt[-1 + x^(-2)] + Sqrt[-1 + x^(-2)]","A",4,3,20,0.1500,1,"{25, 266, 43}"
681,1,9,0,0.0038201,"\int \frac{\sqrt{1+\frac{1}{x^2}} x}{\left(1+x^2\right)^2} \, dx","Int[(Sqrt[1 + x^(-2)]*x)/(1 + x^2)^2,x]","\frac{1}{\sqrt{\frac{1}{x^2}+1}}","\frac{1}{\sqrt{\frac{1}{x^2}+1}}",1,"1/Sqrt[1 + x^(-2)]","A",2,2,18,0.1111,1,"{25, 261}"
682,1,9,0,0.003854,"\int \frac{1}{\sqrt{1+\frac{1}{x^2}} x \left(1+x^2\right)} \, dx","Int[1/(Sqrt[1 + x^(-2)]*x*(1 + x^2)),x]","\frac{1}{\sqrt{\frac{1}{x^2}+1}}","\frac{1}{\sqrt{\frac{1}{x^2}+1}}",1,"1/Sqrt[1 + x^(-2)]","A",2,2,20,0.1000,1,"{25, 261}"
683,1,18,0,0.0717561,"\int \frac{x}{a+b x^2+\sqrt{a+b x^2}} \, dx","Int[x/(a + b*x^2 + Sqrt[a + b*x^2]),x]","\frac{\log \left(\sqrt{a+b x^2}+1\right)}{b}","\frac{\log \left(\sqrt{a+b x^2}+1\right)}{b}",1,"Log[1 + Sqrt[a + b*x^2]]/b","A",3,2,22,0.09091,1,"{2155, 31}"
684,1,16,0,0.061193,"\int \frac{x}{x^2-\sqrt[3]{x^2}} \, dx","Int[x/(x^2 - (x^2)^(1/3)),x]","\frac{3}{4} \log \left(1-\left(x^2\right)^{2/3}\right)","\frac{3}{4} \log \left(1-\left(x^2\right)^{2/3}\right)",1,"(3*Log[1 - (x^2)^(2/3)])/4","A",3,3,17,0.1765,1,"{6715, 1593, 260}"
685,1,44,0,0.030516,"\int x \left(1+x^2\right)^3 \sqrt{2+2 x^2+x^4} \, dx","Int[x*(1 + x^2)^3*Sqrt[2 + 2*x^2 + x^4],x]","\frac{1}{10} \left(x^2+1\right)^2 \left(x^4+2 x^2+2\right)^{3/2}-\frac{1}{15} \left(x^4+2 x^2+2\right)^{3/2}","\frac{1}{10} \left(x^2+1\right)^2 \left(x^4+2 x^2+2\right)^{3/2}-\frac{1}{15} \left(x^4+2 x^2+2\right)^{3/2}",1,"-(2 + 2*x^2 + x^4)^(3/2)/15 + ((1 + x^2)^2*(2 + 2*x^2 + x^4)^(3/2))/10","A",3,3,23,0.1304,1,"{1247, 692, 629}"
686,1,121,0,0.1113137,"\int x^5 \sqrt{1-x^3} \left(1+x^9\right)^2 \, dx","Int[x^5*Sqrt[1 - x^3]*(1 + x^9)^2,x]","\frac{2}{51} \left(1-x^3\right)^{17/2}-\frac{14}{45} \left(1-x^3\right)^{15/2}+\frac{14}{13} \left(1-x^3\right)^{13/2}-\frac{74}{33} \left(1-x^3\right)^{11/2}+\frac{86}{27} \left(1-x^3\right)^{9/2}-\frac{22}{7} \left(1-x^3\right)^{7/2}+\frac{32}{15} \left(1-x^3\right)^{5/2}-\frac{8}{9} \left(1-x^3\right)^{3/2}","\frac{2}{51} \left(1-x^3\right)^{17/2}-\frac{14}{45} \left(1-x^3\right)^{15/2}+\frac{14}{13} \left(1-x^3\right)^{13/2}-\frac{74}{33} \left(1-x^3\right)^{11/2}+\frac{86}{27} \left(1-x^3\right)^{9/2}-\frac{22}{7} \left(1-x^3\right)^{7/2}+\frac{32}{15} \left(1-x^3\right)^{5/2}-\frac{8}{9} \left(1-x^3\right)^{3/2}",1,"(-8*(1 - x^3)^(3/2))/9 + (32*(1 - x^3)^(5/2))/15 - (22*(1 - x^3)^(7/2))/7 + (86*(1 - x^3)^(9/2))/27 - (74*(1 - x^3)^(11/2))/33 + (14*(1 - x^3)^(13/2))/13 - (14*(1 - x^3)^(15/2))/45 + (2*(1 - x^3)^(17/2))/51","A",3,2,22,0.09091,1,"{1821, 1620}"
687,1,50,0,0.0433835,"\int \left(\frac{x}{\left(a+b x^2\right)^{3/2}}+\frac{x}{\left(1+x^2\right) \sqrt{a+b x^2}}\right) \, dx","Int[x/(a + b*x^2)^(3/2) + x/((1 + x^2)*Sqrt[a + b*x^2]),x]","-\frac{1}{b \sqrt{a+b x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}","-\frac{1}{b \sqrt{a+b x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}",1,"-(1/(b*Sqrt[a + b*x^2])) - ArcTanh[Sqrt[a + b*x^2]/Sqrt[a - b]]/Sqrt[a - b]","A",5,4,34,0.1176,1,"{261, 444, 63, 208}"
688,1,50,0,0.0644341,"\int \frac{x \left(1+a+x^2+b x^2\right)}{\left(1+x^2\right) \left(a+b x^2\right)^{3/2}} \, dx","Int[(x*(1 + a + x^2 + b*x^2))/((1 + x^2)*(a + b*x^2)^(3/2)),x]","-\frac{1}{b \sqrt{a+b x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}","-\frac{1}{b \sqrt{a+b x^2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}",1,"-(1/(b*Sqrt[a + b*x^2])) - ArcTanh[Sqrt[a + b*x^2]/Sqrt[a - b]]/Sqrt[a - b]","A",5,5,31,0.1613,1,"{6, 571, 78, 63, 208}"
689,1,68,0,0.0417059,"\int \left(\frac{x}{\left(a+b x^2\right)^{5/2}}+\frac{x}{\left(a+b x^2\right)^{3/2}}+\frac{x}{\left(1+x^2\right) \sqrt{a+b x^2}}\right) \, dx","Int[x/(a + b*x^2)^(5/2) + x/(a + b*x^2)^(3/2) + x/((1 + x^2)*Sqrt[a + b*x^2]),x]","-\frac{1}{b \sqrt{a+b x^2}}-\frac{1}{3 b \left(a+b x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}","-\frac{1}{b \sqrt{a+b x^2}}-\frac{1}{3 b \left(a+b x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}",1,"-1/(3*b*(a + b*x^2)^(3/2)) - 1/(b*Sqrt[a + b*x^2]) - ArcTanh[Sqrt[a + b*x^2]/Sqrt[a - b]]/Sqrt[a - b]","A",6,4,47,0.08511,1,"{261, 444, 63, 208}"
690,1,68,0,0.509217,"\int \frac{x \left(1+a+a^2+x^2+a x^2+b x^2+2 a b x^2+b x^4+b^2 x^4\right)}{\left(1+x^2\right) \left(a+b x^2\right)^{5/2}} \, dx","Int[(x*(1 + a + a^2 + x^2 + a*x^2 + b*x^2 + 2*a*b*x^2 + b*x^4 + b^2*x^4))/((1 + x^2)*(a + b*x^2)^(5/2)),x]","-\frac{1}{b \sqrt{a+b x^2}}-\frac{1}{3 b \left(a+b x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}","-\frac{1}{b \sqrt{a+b x^2}}-\frac{1}{3 b \left(a+b x^2\right)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}",1,"-1/(3*b*(a + b*x^2)^(3/2)) - 1/(b*Sqrt[a + b*x^2]) - ArcTanh[Sqrt[a + b*x^2]/Sqrt[a - b]]/Sqrt[a - b]","A",9,5,58,0.08621,1,"{6, 6715, 897, 1261, 207}"
691,1,34,0,0.0314615,"\int \frac{1}{\sqrt{\sqrt{x}+x}} \, dx","Int[1/Sqrt[Sqrt[x] + x],x]","2 \sqrt{x+\sqrt{x}}-2 \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x+\sqrt{x}}}\right)","2 \sqrt{x+\sqrt{x}}-2 \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x+\sqrt{x}}}\right)",1,"2*Sqrt[Sqrt[x] + x] - 2*ArcTanh[Sqrt[x]/Sqrt[Sqrt[x] + x]]","A",4,4,11,0.3636,1,"{2010, 2013, 620, 206}"
692,1,74,0,0.0451278,"\int \sqrt{\sqrt{x}+x} \, dx","Int[Sqrt[Sqrt[x] + x],x]","\frac{2}{3} \sqrt{x+\sqrt{x}} x+\frac{1}{6} \sqrt{x+\sqrt{x}} \sqrt{x}-\frac{\sqrt{x+\sqrt{x}}}{4}+\frac{1}{4} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x+\sqrt{x}}}\right)","\frac{2}{3} \sqrt{x+\sqrt{x}} x+\frac{1}{6} \sqrt{x+\sqrt{x}} \sqrt{x}-\frac{\sqrt{x+\sqrt{x}}}{4}+\frac{1}{4} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x+\sqrt{x}}}\right)",1,"-Sqrt[Sqrt[x] + x]/4 + (Sqrt[x]*Sqrt[Sqrt[x] + x])/6 + (2*x*Sqrt[Sqrt[x] + x])/3 + ArcTanh[Sqrt[x]/Sqrt[Sqrt[x] + x]]/4","A",6,6,11,0.5455,1,"{2004, 2018, 670, 640, 620, 206}"
693,1,19,0,0.0047248,"\int \sqrt{-x} \left(\sqrt{-x}+x\right) \, dx","Int[Sqrt[-x]*(Sqrt[-x] + x),x]","\frac{2}{5} (-x)^{5/2}-\frac{x^2}{2}","\frac{2}{5} (-x)^{5/2}-\frac{x^2}{2}",1,"(2*(-x)^(5/2))/5 - x^2/2","A",2,1,17,0.05882,1,"{14}"
694,1,54,0,0.0831094,"\int \frac{5+\sqrt[4]{x}}{-6+x} \, dx","Int[(5 + x^(1/4))/(-6 + x),x]","4 \sqrt[4]{x}+5 \log (6-x)-2 \sqrt[4]{6} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{6}}\right)-2 \sqrt[4]{6} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{6}}\right)","4 \sqrt[4]{x}+5 \log (6-x)-2 \sqrt[4]{6} \tan ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{6}}\right)-2 \sqrt[4]{6} \tanh ^{-1}\left(\frac{\sqrt[4]{x}}{\sqrt[4]{6}}\right)",1,"4*x^(1/4) - 2*6^(1/4)*ArcTan[x^(1/4)/6^(1/4)] - 2*6^(1/4)*ArcTanh[x^(1/4)/6^(1/4)] + 5*Log[6 - x]","A",8,6,13,0.4615,1,"{1831, 260, 321, 212, 206, 203}"
695,1,14,0,0.0185971,"\int \frac{1}{4+\sqrt{4-x}-x} \, dx","Int[(4 + Sqrt[4 - x] - x)^(-1),x]","-2 \log \left(\sqrt{4-x}+1\right)","-2 \log \left(\sqrt{4-x}+1\right)",1,"-2*Log[1 + Sqrt[4 - x]]","A",2,1,16,0.06250,1,"{31}"
696,1,61,0,0.0435459,"\int \frac{1}{1+x-\sqrt{2+x}} \, dx","Int[(1 + x - Sqrt[2 + x])^(-1),x]","\frac{1}{5} \left(5-\sqrt{5}\right) \log \left(-2 \sqrt{x+2}-\sqrt{5}+1\right)+\frac{1}{5} \left(5+\sqrt{5}\right) \log \left(-2 \sqrt{x+2}+\sqrt{5}+1\right)","\frac{1}{5} \left(5-\sqrt{5}\right) \log \left(-2 \sqrt{x+2}-\sqrt{5}+1\right)+\frac{1}{5} \left(5+\sqrt{5}\right) \log \left(-2 \sqrt{x+2}+\sqrt{5}+1\right)",1,"((5 - Sqrt[5])*Log[1 - Sqrt[5] - 2*Sqrt[2 + x]])/5 + ((5 + Sqrt[5])*Log[1 + Sqrt[5] - 2*Sqrt[2 + x]])/5","A",4,2,14,0.1429,1,"{632, 31}"
697,1,37,0,0.0377686,"\int \frac{1}{4+x+\sqrt{1+x}} \, dx","Int[(4 + x + Sqrt[1 + x])^(-1),x]","\log \left(x+\sqrt{x+1}+4\right)-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt{x+1}+1}{\sqrt{11}}\right)}{\sqrt{11}}","\log \left(x+\sqrt{x+1}+4\right)-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt{x+1}+1}{\sqrt{11}}\right)}{\sqrt{11}}",1,"(-2*ArcTan[(1 + 2*Sqrt[1 + x])/Sqrt[11]])/Sqrt[11] + Log[4 + x + Sqrt[1 + x]]","A",5,4,12,0.3333,1,"{634, 618, 204, 628}"
698,1,61,0,0.0311208,"\int \frac{1}{x-\sqrt{1+x}} \, dx","Int[(x - Sqrt[1 + x])^(-1),x]","\frac{1}{5} \left(5-\sqrt{5}\right) \log \left(-2 \sqrt{x+1}-\sqrt{5}+1\right)+\frac{1}{5} \left(5+\sqrt{5}\right) \log \left(-2 \sqrt{x+1}+\sqrt{5}+1\right)","\frac{1}{5} \left(5-\sqrt{5}\right) \log \left(-2 \sqrt{x+1}-\sqrt{5}+1\right)+\frac{1}{5} \left(5+\sqrt{5}\right) \log \left(-2 \sqrt{x+1}+\sqrt{5}+1\right)",1,"((5 - Sqrt[5])*Log[1 - Sqrt[5] - 2*Sqrt[1 + x]])/5 + ((5 + Sqrt[5])*Log[1 + Sqrt[5] - 2*Sqrt[1 + x]])/5","A",4,2,13,0.1538,1,"{632, 31}"
699,1,31,0,0.0211831,"\int \frac{1}{x-\sqrt{2+x}} \, dx","Int[(x - Sqrt[2 + x])^(-1),x]","\frac{4}{3} \log \left(2-\sqrt{x+2}\right)+\frac{2}{3} \log \left(\sqrt{x+2}+1\right)","\frac{4}{3} \log \left(2-\sqrt{x+2}\right)+\frac{2}{3} \log \left(\sqrt{x+2}+1\right)",1,"(4*Log[2 - Sqrt[2 + x]])/3 + (2*Log[1 + Sqrt[2 + x]])/3","A",4,2,13,0.1538,1,"{632, 31}"
700,1,65,0,0.0372839,"\int \frac{1}{-\sqrt{1-x}+x} \, dx","Int[(-Sqrt[1 - x] + x)^(-1),x]","\frac{1}{5} \left(5-\sqrt{5}\right) \log \left(2 \sqrt{1-x}-\sqrt{5}+1\right)+\frac{1}{5} \left(5+\sqrt{5}\right) \log \left(2 \sqrt{1-x}+\sqrt{5}+1\right)","\frac{1}{5} \left(5-\sqrt{5}\right) \log \left(2 \sqrt{1-x}-\sqrt{5}+1\right)+\frac{1}{5} \left(5+\sqrt{5}\right) \log \left(2 \sqrt{1-x}+\sqrt{5}+1\right)",1,"((5 - Sqrt[5])*Log[1 - Sqrt[5] + 2*Sqrt[1 - x]])/5 + ((5 + Sqrt[5])*Log[1 + Sqrt[5] + 2*Sqrt[1 - x]])/5","A",4,2,15,0.1333,1,"{632, 31}"
701,1,62,0,0.0253673,"\int \sqrt{1+\sqrt{x}+x} \, dx","Int[Sqrt[1 + Sqrt[x] + x],x]","\frac{2}{3} \left(x+\sqrt{x}+1\right)^{3/2}-\frac{1}{4} \left(2 \sqrt{x}+1\right) \sqrt{x+\sqrt{x}+1}-\frac{3}{8} \sinh ^{-1}\left(\frac{2 \sqrt{x}+1}{\sqrt{3}}\right)","\frac{2}{3} \left(x+\sqrt{x}+1\right)^{3/2}-\frac{1}{4} \left(2 \sqrt{x}+1\right) \sqrt{x+\sqrt{x}+1}-\frac{3}{8} \sinh ^{-1}\left(\frac{2 \sqrt{x}+1}{\sqrt{3}}\right)",1,"-((1 + 2*Sqrt[x])*Sqrt[1 + Sqrt[x] + x])/4 + (2*(1 + Sqrt[x] + x)^(3/2))/3 - (3*ArcSinh[(1 + 2*Sqrt[x])/Sqrt[3]])/8","A",5,5,12,0.4167,1,"{1341, 640, 612, 619, 215}"
702,1,75,0,0.0440683,"\int \sqrt{1+x+\sqrt{1+x}} \, dx","Int[Sqrt[1 + x + Sqrt[1 + x]],x]","\frac{2}{3} \left(x+\sqrt{x+1}+1\right)^{3/2}-\frac{1}{4} \left(2 \sqrt{x+1}+1\right) \sqrt{x+\sqrt{x+1}+1}+\frac{1}{4} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{x+\sqrt{x+1}+1}}\right)","\frac{2}{3} \left(x+\sqrt{x+1}+1\right)^{3/2}-\frac{1}{4} \left(2 \sqrt{x+1}+1\right) \sqrt{x+\sqrt{x+1}+1}+\frac{1}{4} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{x+\sqrt{x+1}+1}}\right)",1,"(2*(1 + x + Sqrt[1 + x])^(3/2))/3 - (Sqrt[1 + x + Sqrt[1 + x]]*(1 + 2*Sqrt[1 + x]))/4 + ArcTanh[Sqrt[1 + x]/Sqrt[1 + x + Sqrt[1 + x]]]/4","A",6,5,14,0.3571,1,"{1980, 640, 612, 620, 206}"
703,1,68,0,0.0421857,"\int \sqrt{\sqrt{-1+x}+x} \, dx","Int[Sqrt[Sqrt[-1 + x] + x],x]","\frac{2}{3} \left(x+\sqrt{x-1}\right)^{3/2}-\frac{1}{4} \left(2 \sqrt{x-1}+1\right) \sqrt{x+\sqrt{x-1}}-\frac{3}{8} \sinh ^{-1}\left(\frac{2 \sqrt{x-1}+1}{\sqrt{3}}\right)","\frac{2}{3} \left(x+\sqrt{x-1}\right)^{3/2}-\frac{1}{4} \left(2 \sqrt{x-1}+1\right) \sqrt{x+\sqrt{x-1}}-\frac{3}{8} \sinh ^{-1}\left(\frac{2 \sqrt{x-1}+1}{\sqrt{3}}\right)",1,"-((1 + 2*Sqrt[-1 + x])*Sqrt[Sqrt[-1 + x] + x])/4 + (2*(Sqrt[-1 + x] + x)^(3/2))/3 - (3*ArcSinh[(1 + 2*Sqrt[-1 + x])/Sqrt[3]])/8","A",5,4,13,0.3077,1,"{640, 612, 619, 215}"
704,1,80,0,0.0393168,"\int \sqrt{2 x+\sqrt{-1+2 x}} \, dx","Int[Sqrt[2*x + Sqrt[-1 + 2*x]],x]","\frac{1}{3} \left(2 x+\sqrt{2 x-1}\right)^{3/2}-\frac{1}{8} \left(2 \sqrt{2 x-1}+1\right) \sqrt{2 x+\sqrt{2 x-1}}-\frac{3}{16} \sinh ^{-1}\left(\frac{2 \sqrt{2 x-1}+1}{\sqrt{3}}\right)","\frac{1}{3} \left(2 x+\sqrt{2 x-1}\right)^{3/2}-\frac{1}{8} \left(2 \sqrt{2 x-1}+1\right) \sqrt{2 x+\sqrt{2 x-1}}-\frac{3}{16} \sinh ^{-1}\left(\frac{2 \sqrt{2 x-1}+1}{\sqrt{3}}\right)",1,"(2*x + Sqrt[-1 + 2*x])^(3/2)/3 - (Sqrt[2*x + Sqrt[-1 + 2*x]]*(1 + 2*Sqrt[-1 + 2*x]))/8 - (3*ArcSinh[(1 + 2*Sqrt[-1 + 2*x])/Sqrt[3]])/16","A",5,4,17,0.2353,1,"{640, 612, 619, 215}"
705,1,109,0,0.06955,"\int \sqrt{3 x+\sqrt{-7+8 x}} \, dx","Int[Sqrt[3*x + Sqrt[-7 + 8*x]],x]","\frac{\left(-3 (7-8 x)+8 \sqrt{8 x-7}+21\right)^{3/2}}{72 \sqrt{2}}-\frac{\left(3 \sqrt{8 x-7}+4\right) \sqrt{-3 (7-8 x)+8 \sqrt{8 x-7}+21}}{36 \sqrt{2}}-\frac{47 \sinh ^{-1}\left(\frac{3 \sqrt{8 x-7}+4}{\sqrt{47}}\right)}{36 \sqrt{6}}","\frac{\left(-3 (7-8 x)+8 \sqrt{8 x-7}+21\right)^{3/2}}{72 \sqrt{2}}-\frac{\left(3 \sqrt{8 x-7}+4\right) \sqrt{-3 (7-8 x)+8 \sqrt{8 x-7}+21}}{36 \sqrt{2}}-\frac{47 \sinh ^{-1}\left(\frac{3 \sqrt{8 x-7}+4}{\sqrt{47}}\right)}{36 \sqrt{6}}",1,"-((4 + 3*Sqrt[-7 + 8*x])*Sqrt[21 - 3*(7 - 8*x) + 8*Sqrt[-7 + 8*x]])/(36*Sqrt[2]) + (21 - 3*(7 - 8*x) + 8*Sqrt[-7 + 8*x])^(3/2)/(72*Sqrt[2]) - (47*ArcSinh[(4 + 3*Sqrt[-7 + 8*x])/Sqrt[47]])/(36*Sqrt[6])","A",5,4,17,0.2353,1,"{640, 612, 619, 215}"
706,1,47,0,0.0295322,"\int \frac{1}{\sqrt{x+\sqrt{1+x}}} \, dx","Int[1/Sqrt[x + Sqrt[1 + x]],x]","2 \sqrt{x+\sqrt{x+1}}-\tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)","2 \sqrt{x+\sqrt{x+1}}-\tanh ^{-1}\left(\frac{2 \sqrt{x+1}+1}{2 \sqrt{x+\sqrt{x+1}}}\right)",1,"2*Sqrt[x + Sqrt[1 + x]] - ArcTanh[(1 + 2*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])]","A",4,3,13,0.2308,1,"{640, 621, 206}"
707,1,67,0,0.1299459,"\int \frac{1+x}{4+x+\sqrt{-9+6 x}} \, dx","Int[(1 + x)/(4 + x + Sqrt[-9 + 6*x]),x]","x-2 \sqrt{3} \sqrt{2 x-3}+3 \log \left(x+\sqrt{3} \sqrt{2 x-3}+4\right)+4 \sqrt{6} \tan ^{-1}\left(\frac{\sqrt{6 x-9}+3}{2 \sqrt{6}}\right)","x-2 \sqrt{3} \sqrt{2 x-3}+3 \log \left(x+\sqrt{3} \sqrt{2 x-3}+4\right)+4 \sqrt{6} \tan ^{-1}\left(\frac{\sqrt{6 x-9}+3}{2 \sqrt{6}}\right)",1,"x - 2*Sqrt[3]*Sqrt[-3 + 2*x] + 4*Sqrt[6]*ArcTan[(3 + Sqrt[-9 + 6*x])/(2*Sqrt[6])] + 3*Log[4 + x + Sqrt[3]*Sqrt[-3 + 2*x]]","A",7,5,18,0.2778,1,"{1628, 634, 618, 204, 628}"
708,1,71,0,0.1097634,"\int \frac{12-x}{4+x+\sqrt{-9+6 x}} \, dx","Int[(12 - x)/(4 + x + Sqrt[-9 + 6*x]),x]","-x+2 \sqrt{3} \sqrt{2 x-3}+10 \log \left(x+\sqrt{3} \sqrt{2 x-3}+4\right)-21 \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{6 x-9}+3}{2 \sqrt{6}}\right)","-x+2 \sqrt{3} \sqrt{2 x-3}+10 \log \left(x+\sqrt{3} \sqrt{2 x-3}+4\right)-21 \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{6 x-9}+3}{2 \sqrt{6}}\right)",1,"-x + 2*Sqrt[3]*Sqrt[-3 + 2*x] - 21*Sqrt[3/2]*ArcTan[(3 + Sqrt[-9 + 6*x])/(2*Sqrt[6])] + 10*Log[4 + x + Sqrt[3]*Sqrt[-3 + 2*x]]","A",7,5,20,0.2500,1,"{1628, 634, 618, 204, 628}"
709,1,52,0,0.0532846,"\int \frac{-1+x^3}{\sqrt{x} \left(1+x^2\right)} \, dx","Int[(-1 + x^3)/(Sqrt[x]*(1 + x^2)),x]","\frac{2 x^{3/2}}{3}+\sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)-\sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)","\frac{2 x^{3/2}}{3}+\sqrt{2} \tan ^{-1}\left(1-\sqrt{2} \sqrt{x}\right)-\sqrt{2} \tan ^{-1}\left(\sqrt{2} \sqrt{x}+1\right)",1,"(2*x^(3/2))/3 + Sqrt[2]*ArcTan[1 - Sqrt[2]*Sqrt[x]] - Sqrt[2]*ArcTan[1 + Sqrt[2]*Sqrt[x]]","A",8,5,18,0.2778,1,"{1802, 827, 1162, 617, 204}"
710,1,20,0,0.1049245,"\int \frac{1}{2 \sqrt{-1+x} \sqrt{-\sqrt{-1+x}+x}} \, dx","Int[1/(2*Sqrt[-1 + x]*Sqrt[-Sqrt[-1 + x] + x]),x]","-\sinh ^{-1}\left(\frac{1-2 \sqrt{x-1}}{\sqrt{3}}\right)","-\sinh ^{-1}\left(\frac{1-2 \sqrt{x-1}}{\sqrt{3}}\right)",1,"-ArcSinh[(1 - 2*Sqrt[-1 + x])/Sqrt[3]]","A",4,3,26,0.1154,1,"{12, 619, 215}"
711,1,31,0,0.068065,"\int \frac{1+x^{7/2}}{1-x^2} \, dx","Int[(1 + x^(7/2))/(1 - x^2),x]","-\frac{2 x^{5/2}}{5}-2 \sqrt{x}+\tan ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}(x)","-\frac{2 x^{5/2}}{5}-2 \sqrt{x}-\log \left(1-\sqrt{x}\right)+\frac{1}{2} \log (x+1)+\tan ^{-1}\left(\sqrt{x}\right)",1,"-2*Sqrt[x] - (2*x^(5/2))/5 + ArcTan[Sqrt[x]] + ArcTanh[Sqrt[x]] + ArcTanh[x]","A",10,6,17,0.3529,1,"{1833, 275, 206, 302, 212, 203}"
712,1,116,0,0.1381343,"\int \frac{4+2 x}{\sqrt[3]{-1+2 x}+\sqrt{-1+2 x}} \, dx","Int[(4 + 2*x)/((-1 + 2*x)^(1/3) + Sqrt[-1 + 2*x]),x]","\frac{1}{3} (2 x-1)^{3/2}-\frac{3}{8} (2 x-1)^{4/3}+\frac{3}{7} (2 x-1)^{7/6}+\frac{3}{5} (2 x-1)^{5/6}-\frac{3}{4} (2 x-1)^{2/3}+6 \sqrt{2 x-1}-9 \sqrt[3]{2 x-1}+18 \sqrt[6]{2 x-1}-x-18 \log \left(\sqrt[6]{2 x-1}+1\right)","\frac{1}{3} (2 x-1)^{3/2}-\frac{3}{8} (2 x-1)^{4/3}+\frac{3}{7} (2 x-1)^{7/6}+\frac{3}{5} (2 x-1)^{5/6}-\frac{3}{4} (2 x-1)^{2/3}+6 \sqrt{2 x-1}-9 \sqrt[3]{2 x-1}+18 \sqrt[6]{2 x-1}-x-18 \log \left(\sqrt[6]{2 x-1}+1\right)",1,"-x + 18*(-1 + 2*x)^(1/6) - 9*(-1 + 2*x)^(1/3) + 6*Sqrt[-1 + 2*x] - (3*(-1 + 2*x)^(2/3))/4 + (3*(-1 + 2*x)^(5/6))/5 + (3*(-1 + 2*x)^(7/6))/7 - (3*(-1 + 2*x)^(4/3))/8 + (-1 + 2*x)^(3/2)/3 - 18*Log[1 + (-1 + 2*x)^(1/6)]","A",3,1,27,0.03704,1,"{1620}"
713,1,83,0,0.0588152,"\int \frac{1}{\sqrt{2+\sqrt{1+\sqrt{x}}}} \, dx","Int[1/Sqrt[2 + Sqrt[1 + Sqrt[x]]],x]","\frac{8}{7} \left(\sqrt{\sqrt{x}+1}+2\right)^{7/2}-\frac{48}{5} \left(\sqrt{\sqrt{x}+1}+2\right)^{5/2}+\frac{88}{3} \left(\sqrt{\sqrt{x}+1}+2\right)^{3/2}-48 \sqrt{\sqrt{\sqrt{x}+1}+2}","\frac{8}{7} \left(\sqrt{\sqrt{x}+1}+2\right)^{7/2}-\frac{48}{5} \left(\sqrt{\sqrt{x}+1}+2\right)^{5/2}+\frac{88}{3} \left(\sqrt{\sqrt{x}+1}+2\right)^{3/2}-48 \sqrt{\sqrt{\sqrt{x}+1}+2}",1,"-48*Sqrt[2 + Sqrt[1 + Sqrt[x]]] + (88*(2 + Sqrt[1 + Sqrt[x]])^(3/2))/3 - (48*(2 + Sqrt[1 + Sqrt[x]])^(5/2))/5 + (8*(2 + Sqrt[1 + Sqrt[x]])^(7/2))/7","A",5,3,17,0.1765,1,"{371, 1398, 772}"
714,1,64,0,0.0491043,"\int \sqrt{2+\sqrt{4+\sqrt{x}}} \, dx","Int[Sqrt[2 + Sqrt[4 + Sqrt[x]]],x]","\frac{8}{9} \left(\sqrt{\sqrt{x}+4}+2\right)^{9/2}-\frac{48}{7} \left(\sqrt{\sqrt{x}+4}+2\right)^{7/2}+\frac{64}{5} \left(\sqrt{\sqrt{x}+4}+2\right)^{5/2}","\frac{8}{9} \left(\sqrt{\sqrt{x}+4}+2\right)^{9/2}-\frac{48}{7} \left(\sqrt{\sqrt{x}+4}+2\right)^{7/2}+\frac{64}{5} \left(\sqrt{\sqrt{x}+4}+2\right)^{5/2}",1,"(64*(2 + Sqrt[4 + Sqrt[x]])^(5/2))/5 - (48*(2 + Sqrt[4 + Sqrt[x]])^(7/2))/7 + (8*(2 + Sqrt[4 + Sqrt[x]])^(9/2))/9","A",5,3,17,0.1765,1,"{371, 1398, 772}"
715,1,82,0,0.0801328,"\int \sqrt{2-\sqrt{4+\sqrt{-9+5 x}}} \, dx","Int[Sqrt[2 - Sqrt[4 + Sqrt[-9 + 5*x]]],x]","\frac{8}{45} \left(2-\sqrt{\sqrt{5 x-9}+4}\right)^{9/2}-\frac{48}{35} \left(2-\sqrt{\sqrt{5 x-9}+4}\right)^{7/2}+\frac{64}{25} \left(2-\sqrt{\sqrt{5 x-9}+4}\right)^{5/2}","\frac{8}{45} \left(2-\sqrt{\sqrt{5 x-9}+4}\right)^{9/2}-\frac{48}{35} \left(2-\sqrt{\sqrt{5 x-9}+4}\right)^{7/2}+\frac{64}{25} \left(2-\sqrt{\sqrt{5 x-9}+4}\right)^{5/2}",1,"(64*(2 - Sqrt[4 + Sqrt[-9 + 5*x]])^(5/2))/25 - (48*(2 - Sqrt[4 + Sqrt[-9 + 5*x]])^(7/2))/35 + (8*(2 - Sqrt[4 + Sqrt[-9 + 5*x]])^(9/2))/45","A",5,3,23,0.1304,1,"{371, 1398, 772}"
716,1,83,0,0.0465592,"\int \frac{1}{\sqrt{2+\sqrt{1+\sqrt{x}}}} \, dx","Int[1/Sqrt[2 + Sqrt[1 + Sqrt[x]]],x]","\frac{8}{7} \left(\sqrt{\sqrt{x}+1}+2\right)^{7/2}-\frac{48}{5} \left(\sqrt{\sqrt{x}+1}+2\right)^{5/2}+\frac{88}{3} \left(\sqrt{\sqrt{x}+1}+2\right)^{3/2}-48 \sqrt{\sqrt{\sqrt{x}+1}+2}","\frac{8}{7} \left(\sqrt{\sqrt{x}+1}+2\right)^{7/2}-\frac{48}{5} \left(\sqrt{\sqrt{x}+1}+2\right)^{5/2}+\frac{88}{3} \left(\sqrt{\sqrt{x}+1}+2\right)^{3/2}-48 \sqrt{\sqrt{\sqrt{x}+1}+2}",1,"-48*Sqrt[2 + Sqrt[1 + Sqrt[x]]] + (88*(2 + Sqrt[1 + Sqrt[x]])^(3/2))/3 - (48*(2 + Sqrt[1 + Sqrt[x]])^(5/2))/5 + (8*(2 + Sqrt[1 + Sqrt[x]])^(7/2))/7","A",5,3,17,0.1765,1,"{371, 1398, 772}"
717,1,190,0,0.3661675,"\int \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{x}}}} \, dx","Int[Sqrt[1 + Sqrt[1 + Sqrt[1 + Sqrt[x]]]],x]","\frac{16}{17} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{17/2}-\frac{112}{15} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{15/2}+\frac{288}{13} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{13/2}-\frac{320}{11} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{11/2}+\frac{112}{9} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{9/2}+\frac{48}{7} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{7/2}-\frac{32}{5} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{5/2}","\frac{16}{17} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{17/2}-\frac{112}{15} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{15/2}+\frac{288}{13} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{13/2}-\frac{320}{11} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{11/2}+\frac{112}{9} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{9/2}+\frac{48}{7} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{7/2}-\frac{32}{5} \left(\sqrt{\sqrt{\sqrt{x}+1}+1}+1\right)^{5/2}",1,"(-32*(1 + Sqrt[1 + Sqrt[1 + Sqrt[x]]])^(5/2))/5 + (48*(1 + Sqrt[1 + Sqrt[1 + Sqrt[x]]])^(7/2))/7 + (112*(1 + Sqrt[1 + Sqrt[1 + Sqrt[x]]])^(9/2))/9 - (320*(1 + Sqrt[1 + Sqrt[1 + Sqrt[x]]])^(11/2))/11 + (288*(1 + Sqrt[1 + Sqrt[1 + Sqrt[x]]])^(13/2))/13 - (112*(1 + Sqrt[1 + Sqrt[1 + Sqrt[x]]])^(15/2))/15 + (16*(1 + Sqrt[1 + Sqrt[1 + Sqrt[x]]])^(17/2))/17","A",6,2,23,0.08696,1,"{1618, 1620}"
718,1,233,0,0.3813304,"\int \sqrt{2+\sqrt{3+\sqrt{-1+2 \sqrt{x}}}} \, dx","Int[Sqrt[2 + Sqrt[3 + Sqrt[-1 + 2*Sqrt[x]]]],x]","\frac{4}{17} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{17/2}-\frac{56}{15} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{15/2}+\frac{300}{13} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{13/2}-\frac{760}{11} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{11/2}+\frac{304}{3} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{9/2}-\frac{480}{7} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{7/2}+\frac{136}{5} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{5/2}-\frac{16}{3} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{3/2}","\frac{4}{17} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{17/2}-\frac{56}{15} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{15/2}+\frac{300}{13} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{13/2}-\frac{760}{11} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{11/2}+\frac{304}{3} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{9/2}-\frac{480}{7} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{7/2}+\frac{136}{5} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{5/2}-\frac{16}{3} \left(\sqrt{\sqrt{2 \sqrt{x}-1}+3}+2\right)^{3/2}",1,"(-16*(2 + Sqrt[3 + Sqrt[-1 + 2*Sqrt[x]]])^(3/2))/3 + (136*(2 + Sqrt[3 + Sqrt[-1 + 2*Sqrt[x]]])^(5/2))/5 - (480*(2 + Sqrt[3 + Sqrt[-1 + 2*Sqrt[x]]])^(7/2))/7 + (304*(2 + Sqrt[3 + Sqrt[-1 + 2*Sqrt[x]]])^(9/2))/3 - (760*(2 + Sqrt[3 + Sqrt[-1 + 2*Sqrt[x]]])^(11/2))/11 + (300*(2 + Sqrt[3 + Sqrt[-1 + 2*Sqrt[x]]])^(13/2))/13 - (56*(2 + Sqrt[3 + Sqrt[-1 + 2*Sqrt[x]]])^(15/2))/15 + (4*(2 + Sqrt[3 + Sqrt[-1 + 2*Sqrt[x]]])^(17/2))/17","A",5,1,25,0.04000,1,"{1620}"
719,1,160,0,0.2757127,"\int \sqrt{1+\sqrt{1+\sqrt{-1+x}}} x \, dx","Int[Sqrt[1 + Sqrt[1 + Sqrt[-1 + x]]]*x,x]","\frac{8}{17} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{17/2}-\frac{56}{15} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{15/2}+\frac{144}{13} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{13/2}-\frac{160}{11} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{11/2}+8 \left(\sqrt{\sqrt{x-1}+1}+1\right)^{9/2}-\frac{24}{7} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{7/2}+\frac{16}{5} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{5/2}","\frac{8}{17} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{17/2}-\frac{56}{15} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{15/2}+\frac{144}{13} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{13/2}-\frac{160}{11} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{11/2}+8 \left(\sqrt{\sqrt{x-1}+1}+1\right)^{9/2}-\frac{24}{7} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{7/2}+\frac{16}{5} \left(\sqrt{\sqrt{x-1}+1}+1\right)^{5/2}",1,"(16*(1 + Sqrt[1 + Sqrt[-1 + x]])^(5/2))/5 - (24*(1 + Sqrt[1 + Sqrt[-1 + x]])^(7/2))/7 + 8*(1 + Sqrt[1 + Sqrt[-1 + x]])^(9/2) - (160*(1 + Sqrt[1 + Sqrt[-1 + x]])^(11/2))/11 + (144*(1 + Sqrt[1 + Sqrt[-1 + x]])^(13/2))/13 - (56*(1 + Sqrt[1 + Sqrt[-1 + x]])^(15/2))/15 + (8*(1 + Sqrt[1 + Sqrt[-1 + x]])^(17/2))/17","A",5,2,21,0.09524,1,"{1618, 1620}"
720,1,20,0,0.0778544,"\int \frac{1}{\sqrt{-1+x} \sqrt{-\sqrt{-1+x}+x}} \, dx","Int[1/(Sqrt[-1 + x]*Sqrt[-Sqrt[-1 + x] + x]),x]","-2 \sinh ^{-1}\left(\frac{1-2 \sqrt{x-1}}{\sqrt{3}}\right)","-2 \sinh ^{-1}\left(\frac{1-2 \sqrt{x-1}}{\sqrt{3}}\right)",1,"-2*ArcSinh[(1 - 2*Sqrt[-1 + x])/Sqrt[3]]","A",3,2,23,0.08696,1,"{619, 215}"
721,1,52,0,0.0351152,"\int \frac{1}{\sqrt{1+x+\sqrt{-1+2 x}}} \, dx","Int[1/Sqrt[1 + x + Sqrt[-1 + 2*x]],x]","\sqrt{2} \sqrt{2 x+2 \sqrt{2 x-1}+2}-\sqrt{2} \sinh ^{-1}\left(\frac{\sqrt{2 x-1}+1}{\sqrt{2}}\right)","2 \sqrt{x+\sqrt{2 x-1}+1}-\sqrt{2} \sinh ^{-1}\left(\frac{\sqrt{2 x-1}+1}{\sqrt{2}}\right)",1,"Sqrt[2]*Sqrt[2 + 2*x + 2*Sqrt[-1 + 2*x]] - Sqrt[2]*ArcSinh[(1 + Sqrt[-1 + 2*x])/Sqrt[2]]","A",4,3,16,0.1875,1,"{640, 619, 215}"
722,1,54,0,0.3806308,"\int \frac{q+p x}{\sqrt{b+a x} \left(f+\sqrt{b+a x}\right)} \, dx","Int[(q + p*x)/(Sqrt[b + a*x]*(f + Sqrt[b + a*x])),x]","-\frac{2 \left(-a q+b p+f^2 (-p)\right) \log \left(\sqrt{a x+b}+f\right)}{a^2}-\frac{2 f p \sqrt{a x+b}}{a^2}+\frac{p x}{a}","-\frac{2 \left(-a q+b p+f^2 (-p)\right) \log \left(\sqrt{a x+b}+f\right)}{a^2}-\frac{2 f p \sqrt{a x+b}}{a^2}+\frac{p x}{a}",1,"(p*x)/a - (2*f*p*Sqrt[b + a*x])/a^2 - (2*(b*p - f^2*p - a*q)*Log[f + Sqrt[b + a*x]])/a^2","A",3,1,28,0.03571,1,"{697}"
723,1,70,0,0.0347816,"\int \sqrt{1-\sqrt{x}-x} \, dx","Int[Sqrt[1 - Sqrt[x] - x],x]","-\frac{2}{3} \left(-x-\sqrt{x}+1\right)^{3/2}-\frac{1}{4} \left(2 \sqrt{x}+1\right) \sqrt{-x-\sqrt{x}+1}-\frac{5}{8} \sin ^{-1}\left(\frac{2 \sqrt{x}+1}{\sqrt{5}}\right)","-\frac{2}{3} \left(-x-\sqrt{x}+1\right)^{3/2}-\frac{1}{4} \left(2 \sqrt{x}+1\right) \sqrt{-x-\sqrt{x}+1}-\frac{5}{8} \sin ^{-1}\left(\frac{2 \sqrt{x}+1}{\sqrt{5}}\right)",1,"-((1 + 2*Sqrt[x])*Sqrt[1 - Sqrt[x] - x])/4 - (2*(1 - Sqrt[x] - x)^(3/2))/3 - (5*ArcSin[(1 + 2*Sqrt[x])/Sqrt[5]])/8","A",5,5,16,0.3125,1,"{1341, 640, 612, 619, 216}"
724,1,19,0,0.0207082,"\int \frac{9+6 \sqrt{x}+x}{4 \sqrt{x}+x} \, dx","Int[(9 + 6*Sqrt[x] + x)/(4*Sqrt[x] + x),x]","x+4 \sqrt{x}+2 \log \left(\sqrt{x}+4\right)","x+4 \sqrt{x}+2 \log \left(\sqrt{x}+4\right)",1,"4*Sqrt[x] + x + 2*Log[4 + Sqrt[x]]","A",4,3,22,0.1364,1,"{28, 1397, 771}"
725,1,77,0,0.0656674,"\int \frac{6-8 x^{7/2}}{5-9 \sqrt{x}} \, dx","Int[(6 - 8*x^(7/2))/(5 - 9*Sqrt[x]),x]","\frac{2 x^4}{9}+\frac{80 x^{7/2}}{567}+\frac{200 x^3}{2187}+\frac{400 x^{5/2}}{6561}+\frac{2500 x^2}{59049}+\frac{50000 x^{3/2}}{1594323}+\frac{125000 x}{4782969}-\frac{56145628 \sqrt{x}}{43046721}-\frac{280728140 \log \left(5-9 \sqrt{x}\right)}{387420489}","\frac{2 x^4}{9}+\frac{80 x^{7/2}}{567}+\frac{200 x^3}{2187}+\frac{400 x^{5/2}}{6561}+\frac{2500 x^2}{59049}+\frac{50000 x^{3/2}}{1594323}+\frac{125000 x}{4782969}-\frac{56145628 \sqrt{x}}{43046721}-\frac{280728140 \log \left(5-9 \sqrt{x}\right)}{387420489}",1,"(-56145628*Sqrt[x])/43046721 + (125000*x)/4782969 + (50000*x^(3/2))/1594323 + (2500*x^2)/59049 + (400*x^(5/2))/6561 + (200*x^3)/2187 + (80*x^(7/2))/567 + (2*x^4)/9 - (280728140*Log[5 - 9*Sqrt[x]])/387420489","A",8,4,21,0.1905,1,"{1893, 190, 43, 266}"
726,1,224,0,0.2856217,"\int \frac{\sqrt{1+x} \left(1+x^3\right)}{1+x^2} \, dx","Int[(Sqrt[1 + x]*(1 + x^3))/(1 + x^2),x]","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}-2 \sqrt{x+1}-\frac{\log \left(x-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}}}+\frac{\log \left(x+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}}}-\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{x+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)+\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{x+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)","\frac{2}{5} (x+1)^{5/2}-\frac{2}{3} (x+1)^{3/2}-2 \sqrt{x+1}+(1-i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{1-i}}\right)+(1+i)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{x+1}}{\sqrt{1+i}}\right)",1,"-2*Sqrt[1 + x] - (2*(1 + x)^(3/2))/3 + (2*(1 + x)^(5/2))/5 - Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + x])/Sqrt[2*(-1 + Sqrt[2])]] + Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + x])/Sqrt[2*(-1 + Sqrt[2])]] - Log[1 + Sqrt[2] + x - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + x]]/(2*Sqrt[1 + Sqrt[2]]) + Log[1 + Sqrt[2] + x + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + x]]/(2*Sqrt[1 + Sqrt[2]])","B",16,10,20,0.5000,0,"{1625, 1629, 825, 12, 708, 1094, 634, 618, 204, 628}"
727,1,89,0,0.2630233,"\int \frac{\sqrt{-1-\sqrt{x}+x}}{(-1+x) \sqrt{x}} \, dx","Int[Sqrt[-1 - Sqrt[x] + x]/((-1 + x)*Sqrt[x]),x]","\tan ^{-1}\left(\frac{3-\sqrt{x}}{2 \sqrt{x-\sqrt{x}-1}}\right)-2 \tanh ^{-1}\left(\frac{1-2 \sqrt{x}}{2 \sqrt{x-\sqrt{x}-1}}\right)-\tanh ^{-1}\left(\frac{3 \sqrt{x}+1}{2 \sqrt{x-\sqrt{x}-1}}\right)","\tan ^{-1}\left(\frac{3-\sqrt{x}}{2 \sqrt{x-\sqrt{x}-1}}\right)-2 \tanh ^{-1}\left(\frac{1-2 \sqrt{x}}{2 \sqrt{x-\sqrt{x}-1}}\right)-\tanh ^{-1}\left(\frac{3 \sqrt{x}+1}{2 \sqrt{x-\sqrt{x}-1}}\right)",1,"ArcTan[(3 - Sqrt[x])/(2*Sqrt[-1 - Sqrt[x] + x])] - 2*ArcTanh[(1 - 2*Sqrt[x])/(2*Sqrt[-1 - Sqrt[x] + x])] - ArcTanh[(1 + 3*Sqrt[x])/(2*Sqrt[-1 - Sqrt[x] + x])]","A",9,6,25,0.2400,1,"{990, 621, 206, 1033, 724, 204}"
728,1,61,0,0.5127151,"\int \frac{1+2 \sqrt{1+x}}{x \sqrt{1+x} \sqrt{x+\sqrt{1+x}}} \, dx","Int[(1 + 2*Sqrt[1 + x])/(x*Sqrt[1 + x]*Sqrt[x + Sqrt[1 + x]]),x]","3 \tanh ^{-1}\left(\frac{1-3 \sqrt{x+1}}{2 \sqrt{x+\sqrt{x+1}}}\right)-\tan ^{-1}\left(\frac{\sqrt{x+1}+3}{2 \sqrt{x+\sqrt{x+1}}}\right)","3 \tanh ^{-1}\left(\frac{1-3 \sqrt{x+1}}{2 \sqrt{x+\sqrt{x+1}}}\right)-\tan ^{-1}\left(\frac{\sqrt{x+1}+3}{2 \sqrt{x+\sqrt{x+1}}}\right)",1,"-ArcTan[(3 + Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])] + 3*ArcTanh[(1 - 3*Sqrt[1 + x])/(2*Sqrt[x + Sqrt[1 + x]])]","A",6,4,35,0.1143,1,"{1033, 724, 206, 204}"
729,1,8,0,0.0018681,"\int \frac{1}{\sqrt{x} \sqrt{1+x}} \, dx","Int[1/(Sqrt[x]*Sqrt[1 + x]),x]","2 \sinh ^{-1}\left(\sqrt{x}\right)","2 \sinh ^{-1}\left(\sqrt{x}\right)",1,"2*ArcSinh[Sqrt[x]]","A",2,2,13,0.1538,1,"{54, 215}"
730,1,8,0,0.0113483,"\int \frac{\sqrt{\frac{x}{1+x}}}{x} \, dx","Int[Sqrt[x/(1 + x)]/x,x]","2 \sinh ^{-1}\left(\sqrt{x}\right)","2 \sinh ^{-1}\left(\sqrt{x}\right)",1,"2*ArcSinh[Sqrt[x]]","A",3,3,15,0.2000,1,"{1958, 54, 215}"
731,1,22,0,0.0033112,"\int \frac{\sqrt{x}}{\sqrt{1+x}} \, dx","Int[Sqrt[x]/Sqrt[1 + x],x]","\sqrt{x} \sqrt{x+1}-\sinh ^{-1}\left(\sqrt{x}\right)","\sqrt{x} \sqrt{x+1}-\sinh ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[x]*Sqrt[1 + x] - ArcSinh[Sqrt[x]]","A",3,3,13,0.2308,1,"{50, 54, 215}"
732,1,22,0,0.0047217,"\int \sqrt{\frac{x}{1+x}} \, dx","Int[Sqrt[x/(1 + x)],x]","\sqrt{x} \sqrt{x+1}-\sinh ^{-1}\left(\sqrt{x}\right)","\sqrt{x} \sqrt{x+1}-\sinh ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[x]*Sqrt[1 + x] - ArcSinh[Sqrt[x]]","A",4,4,11,0.3636,1,"{1958, 50, 54, 215}"
733,1,36,0,0.0038911,"\int \frac{\sqrt{-1+x}}{x^2 \sqrt{1+x}} \, dx","Int[Sqrt[-1 + x]/(x^2*Sqrt[1 + x]),x]","\tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}","\tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"-((Sqrt[-1 + x]*Sqrt[1 + x])/x) + ArcTan[Sqrt[-1 + x]*Sqrt[1 + x]]","A",3,3,18,0.1667,1,"{94, 92, 203}"
734,1,36,0,0.0144775,"\int \frac{\sqrt{\frac{-1+x}{1+x}}}{x^2} \, dx","Int[Sqrt[(-1 + x)/(1 + x)]/x^2,x]","\tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}","\tan ^{-1}\left(\sqrt{x-1} \sqrt{x+1}\right)-\frac{\sqrt{x-1} \sqrt{x+1}}{x}",1,"-((Sqrt[-1 + x]*Sqrt[1 + x])/x) + ArcTan[Sqrt[-1 + x]*Sqrt[1 + x]]","A",4,4,17,0.2353,1,"{1958, 94, 92, 203}"
735,1,69,0,0.012763,"\int \frac{\sqrt{-1+x} x^3}{\sqrt{1+x}} \, dx","Int[(Sqrt[-1 + x]*x^3)/Sqrt[1 + x],x]","\frac{1}{4} (x-1)^{3/2} \sqrt{x+1} x^2+\frac{1}{24} (7-2 x) (x-1)^{3/2} \sqrt{x+1}-\frac{3}{8} \sqrt{x-1} \sqrt{x+1}+\frac{3}{8} \cosh ^{-1}(x)","\frac{1}{4} (x-1)^{3/2} \sqrt{x+1} x^2+\frac{1}{24} (7-2 x) (x-1)^{3/2} \sqrt{x+1}-\frac{3}{8} \sqrt{x-1} \sqrt{x+1}+\frac{3}{8} \cosh ^{-1}(x)",1,"(-3*Sqrt[-1 + x]*Sqrt[1 + x])/8 + ((7 - 2*x)*(-1 + x)^(3/2)*Sqrt[1 + x])/24 + ((-1 + x)^(3/2)*x^2*Sqrt[1 + x])/4 + (3*ArcCosh[x])/8","A",4,4,18,0.2222,1,"{100, 147, 50, 52}"
736,1,69,0,0.0248089,"\int x^3 \sqrt{\frac{-1+x}{1+x}} \, dx","Int[x^3*Sqrt[(-1 + x)/(1 + x)],x]","\frac{1}{4} (x-1)^{3/2} \sqrt{x+1} x^2+\frac{1}{24} (7-2 x) (x-1)^{3/2} \sqrt{x+1}-\frac{3}{8} \sqrt{x-1} \sqrt{x+1}+\frac{3}{8} \cosh ^{-1}(x)","\frac{1}{4} (x-1)^{3/2} \sqrt{x+1} x^2+\frac{1}{24} (7-2 x) (x-1)^{3/2} \sqrt{x+1}-\frac{3}{8} \sqrt{x-1} \sqrt{x+1}+\frac{3}{8} \cosh ^{-1}(x)",1,"(-3*Sqrt[-1 + x]*Sqrt[1 + x])/8 + ((7 - 2*x)*(-1 + x)^(3/2)*Sqrt[1 + x])/24 + ((-1 + x)^(3/2)*x^2*Sqrt[1 + x])/4 + (3*ArcCosh[x])/8","A",5,5,17,0.2941,1,"{1958, 100, 147, 50, 52}"
737,1,15,0,0.012346,"\int \frac{\sqrt{-\frac{x}{1+x}}}{x} \, dx","Int[Sqrt[-(x/(1 + x))]/x,x]","2 \tan ^{-1}\left(\sqrt{-\frac{x}{x+1}}\right)","2 \tan ^{-1}\left(\sqrt{-\frac{x}{x+1}}\right)",1,"2*ArcTan[Sqrt[-(x/(1 + x))]]","A",2,2,16,0.1250,1,"{1960, 204}"
738,1,18,0,0.0210876,"\int \frac{\sqrt{\frac{1-x}{1+x}}}{-1+x} \, dx","Int[Sqrt[(1 - x)/(1 + x)]/(-1 + x),x]","2 \tan ^{-1}\left(\sqrt{\frac{1-x}{x+1}}\right)","2 \tan ^{-1}\left(\sqrt{\frac{1-x}{x+1}}\right)",1,"2*ArcTan[Sqrt[(1 - x)/(1 + x)]]","A",2,2,21,0.09524,1,"{1961, 204}"
739,1,24,0,0.0600706,"\int \frac{\sqrt{\frac{a+b x}{c-b x}}}{a+b x} \, dx","Int[Sqrt[(a + b*x)/(c - b*x)]/(a + b*x),x]","\frac{2 \tan ^{-1}\left(\sqrt{\frac{a+b x}{c-b x}}\right)}{b}","\frac{2 \tan ^{-1}\left(\sqrt{\frac{a+b x}{c-b x}}\right)}{b}",1,"(2*ArcTan[Sqrt[(a + b*x)/(c - b*x)]])/b","A",3,3,26,0.1154,1,"{1961, 12, 203}"
740,1,41,0,0.066614,"\int \frac{\sqrt{\frac{a+b x}{c+d x}}}{a+b x} \, dx","Int[Sqrt[(a + b*x)/(c + d*x)]/(a + b*x),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{a+b x}{c+d x}}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{d}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{a+b x}{c+d x}}}{\sqrt{b}}\right)}{\sqrt{b} \sqrt{d}}",1,"(2*ArcTanh[(Sqrt[d]*Sqrt[(a + b*x)/(c + d*x)])/Sqrt[b]])/(Sqrt[b]*Sqrt[d])","A",3,3,25,0.1200,1,"{1961, 12, 208}"
741,1,32,0,0.0116393,"\int \sqrt{-\frac{x}{1+x}} \, dx","Int[Sqrt[-(x/(1 + x))],x]","\sqrt{-\frac{x}{x+1}} (x+1)-\tan ^{-1}\left(\sqrt{-\frac{x}{x+1}}\right)","\sqrt{-\frac{x}{x+1}} (x+1)-\tan ^{-1}\left(\sqrt{-\frac{x}{x+1}}\right)",1,"Sqrt[-(x/(1 + x))]*(1 + x) - ArcTan[Sqrt[-(x/(1 + x))]]","A",3,3,12,0.2500,1,"{1959, 288, 204}"
742,1,38,0,0.0136912,"\int \sqrt{\frac{1-x}{1+x}} \, dx","Int[Sqrt[(1 - x)/(1 + x)],x]","\sqrt{\frac{1-x}{x+1}} (x+1)-2 \tan ^{-1}\left(\sqrt{\frac{1-x}{x+1}}\right)","\sqrt{\frac{1-x}{x+1}} (x+1)-2 \tan ^{-1}\left(\sqrt{\frac{1-x}{x+1}}\right)",1,"Sqrt[(1 - x)/(1 + x)]*(1 + x) - 2*ArcTan[Sqrt[(1 - x)/(1 + x)]]","A",3,3,15,0.2000,1,"{1959, 288, 204}"
743,1,42,0,0.0161238,"\int \sqrt{\frac{a+x}{a-x}} \, dx","Int[Sqrt[(a + x)/(a - x)],x]","2 a \tan ^{-1}\left(\sqrt{\frac{a+x}{a-x}}\right)-(a-x) \sqrt{\frac{a+x}{a-x}}","2 a \tan ^{-1}\left(\sqrt{\frac{a+x}{a-x}}\right)-(a-x) \sqrt{\frac{a+x}{a-x}}",1,"-((a - x)*Sqrt[(a + x)/(a - x)]) + 2*a*ArcTan[Sqrt[(a + x)/(a - x)]]","A",3,3,15,0.2000,1,"{1959, 288, 203}"
744,1,41,0,0.0192864,"\int \sqrt{\frac{-a+x}{a+x}} \, dx","Int[Sqrt[(-a + x)/(a + x)],x]","\sqrt{-\frac{a-x}{a+x}} (a+x)-2 a \tanh ^{-1}\left(\sqrt{-\frac{a-x}{a+x}}\right)","\sqrt{-\frac{a-x}{a+x}} (a+x)-2 a \tanh ^{-1}\left(\sqrt{-\frac{a-x}{a+x}}\right)",1,"Sqrt[-((a - x)/(a + x))]*(a + x) - 2*a*ArcTanh[Sqrt[-((a - x)/(a + x))]]","A",3,3,15,0.2000,1,"{1959, 288, 206}"
745,1,76,0,0.039146,"\int \sqrt{\frac{a+b x}{c+d x}} \, dx","Int[Sqrt[(a + b*x)/(c + d*x)],x]","\frac{(c+d x) \sqrt{\frac{a+b x}{c+d x}}}{d}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{a+b x}{c+d x}}}{\sqrt{b}}\right)}{\sqrt{b} d^{3/2}}","\frac{(c+d x) \sqrt{\frac{a+b x}{c+d x}}}{d}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{\frac{a+b x}{c+d x}}}{\sqrt{b}}\right)}{\sqrt{b} d^{3/2}}",1,"(Sqrt[(a + b*x)/(c + d*x)]*(c + d*x))/d - ((b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[(a + b*x)/(c + d*x)])/Sqrt[b]])/(Sqrt[b]*d^(3/2))","A",3,3,17,0.1765,1,"{1959, 288, 208}"
746,1,49,0,0.0123619,"\int \sqrt{\frac{-1+x}{5+3 x}} \, dx","Int[Sqrt[(-1 + x)/(5 + 3*x)],x]","\frac{1}{3} \sqrt{x-1} \sqrt{3 x+5}-\frac{8 \sinh ^{-1}\left(\frac{1}{2} \sqrt{\frac{3}{2}} \sqrt{x-1}\right)}{3 \sqrt{3}}","\frac{1}{3} \sqrt{x-1} \sqrt{3 x+5}-\frac{8 \sinh ^{-1}\left(\frac{1}{2} \sqrt{\frac{3}{2}} \sqrt{x-1}\right)}{3 \sqrt{3}}",1,"(Sqrt[-1 + x]*Sqrt[5 + 3*x])/3 - (8*ArcSinh[(Sqrt[3/2]*Sqrt[-1 + x])/2])/(3*Sqrt[3])","A",4,4,15,0.2667,1,"{1958, 50, 54, 215}"
747,1,46,0,0.0226765,"\int \frac{\sqrt{\frac{-1+5 x}{1+7 x}}}{x^2} \, dx","Int[Sqrt[(-1 + 5*x)/(1 + 7*x)]/x^2,x]","-\frac{\sqrt{5 x-1} \sqrt{7 x+1}}{x}-12 \tan ^{-1}\left(\frac{\sqrt{7 x+1}}{\sqrt{5 x-1}}\right)","-\frac{\sqrt{5 x-1} \sqrt{7 x+1}}{x}-12 \tan ^{-1}\left(\frac{\sqrt{7 x+1}}{\sqrt{5 x-1}}\right)",1,"-((Sqrt[-1 + 5*x]*Sqrt[1 + 7*x])/x) - 12*ArcTan[Sqrt[1 + 7*x]/Sqrt[-1 + 5*x]]","A",4,4,21,0.1905,1,"{1958, 94, 93, 204}"
748,1,20,0,0.055983,"\int \frac{x}{\sqrt{\frac{1-x}{1+x}} (1+x)} \, dx","Int[x/(Sqrt[(1 - x)/(1 + x)]*(1 + x)),x]","-\sqrt{\frac{1-x}{x+1}} (x+1)","-\sqrt{\frac{1-x}{x+1}} (x+1)",1,"-(Sqrt[(1 - x)/(1 + x)]*(1 + x))","A",3,3,22,0.1364,1,"{1962, 12, 383}"
749,1,18,0,0.0306565,"\int \frac{x}{(1+x) \sqrt{-1+\frac{2}{1+x}}} \, dx","Int[x/((1 + x)*Sqrt[-1 + 2/(1 + x)]),x]","-(x+1) \sqrt{\frac{2}{x+1}-1}","-(x+1) \sqrt{\frac{2}{x+1}-1}",1,"-((1 + x)*Sqrt[-1 + 2/(1 + x)])","A",4,4,20,0.2000,1,"{512, 514, 375, 74}"
750,1,54,0,0.0567202,"\int \frac{x}{(1+x) \sqrt{\frac{2+x}{3+x}}} \, dx","Int[x/((1 + x)*Sqrt[(2 + x)/(3 + x)]),x]","\sqrt{x+2} \sqrt{x+3}-\sinh ^{-1}\left(\sqrt{x+2}\right)+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x+2}}{\sqrt{x+3}}\right)","\sqrt{x+2} \sqrt{x+3}-\sinh ^{-1}\left(\sqrt{x+2}\right)+2 \sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{x+2}}{\sqrt{x+3}}\right)",1,"Sqrt[2 + x]*Sqrt[3 + x] - ArcSinh[Sqrt[2 + x]] + 2*Sqrt[2]*ArcTanh[(Sqrt[2]*Sqrt[2 + x])/Sqrt[3 + x]]","A",7,7,20,0.3500,1,"{1958, 154, 157, 54, 215, 93, 207}"
751,1,11,0,0.0034446,"\int \frac{\sqrt{1+\frac{1}{x}}}{(1+x)^2} \, dx","Int[Sqrt[1 + x^(-1)]/(1 + x)^2,x]","\frac{2}{\sqrt{\frac{1}{x}+1}}","\frac{2}{\sqrt{\frac{1}{x}+1}}",1,"2/Sqrt[1 + x^(-1)]","A",2,2,15,0.1333,1,"{25, 261}"
752,1,29,0,0.0122943,"\int \frac{\sqrt{1+\frac{1}{x}}}{\sqrt{1-x^2}} \, dx","Int[Sqrt[1 + x^(-1)]/Sqrt[1 - x^2],x]","-\frac{\sqrt{\frac{1}{x}+1} \sqrt{x} \sin ^{-1}(1-2 x)}{\sqrt{x+1}}","-\frac{\sqrt{\frac{1}{x}+1} \sqrt{x} \sin ^{-1}(1-2 x)}{\sqrt{x+1}}",1,"-((Sqrt[1 + x^(-1)]*Sqrt[x]*ArcSin[1 - 2*x])/Sqrt[1 + x])","A",5,5,21,0.2381,1,"{1448, 26, 53, 619, 216}"
753,1,180,0,0.1950662,"\int \frac{1}{x+\sqrt{3-2 x-x^2}} \, dx","Int[(x + Sqrt[3 - 2*x - x^2])^(-1),x]","-\frac{1}{2} \log \left(-\frac{-\sqrt{3} \sqrt{-x^2-2 x+3}-x+3}{x^2}\right)+\frac{1}{14} \left(7+\sqrt{7}\right) \log \left(-\frac{\sqrt{3} \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-\sqrt{7}+\sqrt{3}+1\right)+\frac{1}{14} \left(7-\sqrt{7}\right) \log \left(-\frac{\sqrt{3} \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}+\sqrt{7}+\sqrt{3}+1\right)+\tan ^{-1}\left(\frac{\sqrt{3}-\sqrt{-x^2-2 x+3}}{x}\right)","-\frac{1}{2} \log \left(-\frac{-\sqrt{3} \sqrt{-x^2-2 x+3}-x+3}{x^2}\right)+\frac{1}{14} \left(7+\sqrt{7}\right) \log \left(-\frac{\sqrt{3} \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-\sqrt{7}+\sqrt{3}+1\right)+\frac{1}{14} \left(7-\sqrt{7}\right) \log \left(-\frac{\sqrt{3} \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}+\sqrt{7}+\sqrt{3}+1\right)+\tan ^{-1}\left(\frac{\sqrt{3}-\sqrt{-x^2-2 x+3}}{x}\right)",1,"ArcTan[(Sqrt[3] - Sqrt[3 - 2*x - x^2])/x] - Log[-((3 - x - Sqrt[3]*Sqrt[3 - 2*x - x^2])/x^2)]/2 + ((7 + Sqrt[7])*Log[1 + Sqrt[3] - Sqrt[7] - (Sqrt[3]*(Sqrt[3] - Sqrt[3 - 2*x - x^2]))/x])/14 + ((7 - Sqrt[7])*Log[1 + Sqrt[3] + Sqrt[7] - (Sqrt[3]*(Sqrt[3] - Sqrt[3 - 2*x - x^2]))/x])/14","A",8,6,18,0.3333,1,"{1074, 632, 31, 635, 203, 260}"
754,1,172,0,0.1436867,"\int \frac{1}{\left(x+\sqrt{3-2 x-x^2}\right)^2} \, dx","Int[(x + Sqrt[3 - 2*x - x^2])^(-2),x]","\frac{2 \left(\frac{3 \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-\sqrt{3}+4\right)}{7 \left(\frac{\sqrt{3} \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)^2}{x^2}-\frac{2 \left(1+\sqrt{3}\right) \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-\sqrt{3}+2\right)}+\frac{8 \tanh ^{-1}\left(\frac{-\sqrt{3} \sqrt{-x^2-2 x+3}-\sqrt{3} x-x+3}{\sqrt{7} x}\right)}{7 \sqrt{7}}","\frac{2 \left(\frac{3 \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-\sqrt{3}+4\right)}{7 \left(\frac{\sqrt{3} \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)^2}{x^2}-\frac{2 \left(1+\sqrt{3}\right) \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-\sqrt{3}+2\right)}+\frac{8 \tanh ^{-1}\left(\frac{-\sqrt{3} \sqrt{-x^2-2 x+3}-\sqrt{3} x-x+3}{\sqrt{7} x}\right)}{7 \sqrt{7}}",1,"(2*(4 - Sqrt[3] + (3*(Sqrt[3] - Sqrt[3 - 2*x - x^2]))/x))/(7*(2 - Sqrt[3] - (2*(1 + Sqrt[3])*(Sqrt[3] - Sqrt[3 - 2*x - x^2]))/x + (Sqrt[3]*(Sqrt[3] - Sqrt[3 - 2*x - x^2])^2)/x^2)) + (8*ArcTanh[(3 - x - Sqrt[3]*x - Sqrt[3]*Sqrt[3 - 2*x - x^2])/(Sqrt[7]*x)])/(7*Sqrt[7])","A",5,4,18,0.2222,1,"{1660, 12, 618, 206}"
755,1,307,0,0.2507186,"\int \frac{1}{\left(x+\sqrt{3-2 x-x^2}\right)^3} \, dx","Int[(x + Sqrt[3 - 2*x - x^2])^(-3),x]","-\frac{4 \left(\frac{\left(21+5 \sqrt{3}\right) \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-5 \sqrt{3}+9\right)}{21 \left(\frac{\sqrt{3} \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)^2}{x^2}-\frac{2 \left(1+\sqrt{3}\right) \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-\sqrt{3}+2\right)^2}+\frac{2 \left(-\frac{\left(18+49 \sqrt{3}\right) \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-43 \sqrt{3}+18\right)}{147 \left(\frac{\sqrt{3} \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)^2}{x^2}-\frac{2 \left(1+\sqrt{3}\right) \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-\sqrt{3}+2\right)}+\frac{12 \tanh ^{-1}\left(\frac{-\sqrt{3} \sqrt{-x^2-2 x+3}-\sqrt{3} x-x+3}{\sqrt{7} x}\right)}{49 \sqrt{7}}","-\frac{4 \left(\frac{\left(21+5 \sqrt{3}\right) \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-5 \sqrt{3}+9\right)}{21 \left(\frac{\sqrt{3} \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)^2}{x^2}-\frac{2 \left(1+\sqrt{3}\right) \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-\sqrt{3}+2\right)^2}+\frac{2 \left(-\frac{\left(18+49 \sqrt{3}\right) \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-43 \sqrt{3}+18\right)}{147 \left(\frac{\sqrt{3} \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)^2}{x^2}-\frac{2 \left(1+\sqrt{3}\right) \left(\sqrt{3}-\sqrt{-x^2-2 x+3}\right)}{x}-\sqrt{3}+2\right)}+\frac{12 \tanh ^{-1}\left(\frac{-\sqrt{3} \sqrt{-x^2-2 x+3}-\sqrt{3} x-x+3}{\sqrt{7} x}\right)}{49 \sqrt{7}}",1,"(-4*(9 - 5*Sqrt[3] + ((21 + 5*Sqrt[3])*(Sqrt[3] - Sqrt[3 - 2*x - x^2]))/x))/(21*(2 - Sqrt[3] - (2*(1 + Sqrt[3])*(Sqrt[3] - Sqrt[3 - 2*x - x^2]))/x + (Sqrt[3]*(Sqrt[3] - Sqrt[3 - 2*x - x^2])^2)/x^2)^2) + (2*(18 - 43*Sqrt[3] - ((18 + 49*Sqrt[3])*(Sqrt[3] - Sqrt[3 - 2*x - x^2]))/x))/(147*(2 - Sqrt[3] - (2*(1 + Sqrt[3])*(Sqrt[3] - Sqrt[3 - 2*x - x^2]))/x + (Sqrt[3]*(Sqrt[3] - Sqrt[3 - 2*x - x^2])^2)/x^2)) + (12*ArcTanh[(3 - x - Sqrt[3]*x - Sqrt[3]*Sqrt[3 - 2*x - x^2])/(Sqrt[7]*x)])/(49*Sqrt[7])","A",6,4,18,0.2222,1,"{1660, 12, 618, 206}"
756,1,65,0,0.0300388,"\int \frac{1}{x+\sqrt{-3-2 x+x^2}} \, dx","Int[(x + Sqrt[-3 - 2*x + x^2])^(-1),x]","-\frac{2}{-\sqrt{x^2-2 x-3}-x+1}+2 \log \left(-\sqrt{x^2-2 x-3}-x+1\right)-\frac{3}{2} \log \left(\sqrt{x^2-2 x-3}+x\right)","-\frac{2}{-\sqrt{x^2-2 x-3}-x+1}+2 \log \left(-\sqrt{x^2-2 x-3}-x+1\right)-\frac{3}{2} \log \left(\sqrt{x^2-2 x-3}+x\right)",1,"-2/(1 - x - Sqrt[-3 - 2*x + x^2]) + 2*Log[1 - x - Sqrt[-3 - 2*x + x^2]] - (3*Log[x + Sqrt[-3 - 2*x + x^2]])/2","A",3,2,16,0.1250,1,"{2116, 893}"
757,1,83,0,0.0330327,"\int \frac{1}{\left(x+\sqrt{-3-2 x+x^2}\right)^2} \, dx","Int[(x + Sqrt[-3 - 2*x + x^2])^(-2),x]","-\frac{2}{-\sqrt{x^2-2 x-3}-x+1}+\frac{3}{2 \left(\sqrt{x^2-2 x-3}+x\right)}+4 \log \left(-\sqrt{x^2-2 x-3}-x+1\right)-4 \log \left(\sqrt{x^2-2 x-3}+x\right)","-\frac{2}{-\sqrt{x^2-2 x-3}-x+1}+\frac{3}{2 \left(\sqrt{x^2-2 x-3}+x\right)}+4 \log \left(-\sqrt{x^2-2 x-3}-x+1\right)-4 \log \left(\sqrt{x^2-2 x-3}+x\right)",1,"-2/(1 - x - Sqrt[-3 - 2*x + x^2]) + 3/(2*(x + Sqrt[-3 - 2*x + x^2])) + 4*Log[1 - x - Sqrt[-3 - 2*x + x^2]] - 4*Log[x + Sqrt[-3 - 2*x + x^2]]","A",3,2,16,0.1250,1,"{2116, 893}"
758,1,101,0,0.037457,"\int \frac{1}{\left(x+\sqrt{-3-2 x+x^2}\right)^3} \, dx","Int[(x + Sqrt[-3 - 2*x + x^2])^(-3),x]","-\frac{2}{-\sqrt{x^2-2 x-3}-x+1}+\frac{4}{\sqrt{x^2-2 x-3}+x}+\frac{3}{4 \left(\sqrt{x^2-2 x-3}+x\right)^2}+6 \log \left(-\sqrt{x^2-2 x-3}-x+1\right)-6 \log \left(\sqrt{x^2-2 x-3}+x\right)","-\frac{2}{-\sqrt{x^2-2 x-3}-x+1}+\frac{4}{\sqrt{x^2-2 x-3}+x}+\frac{3}{4 \left(\sqrt{x^2-2 x-3}+x\right)^2}+6 \log \left(-\sqrt{x^2-2 x-3}-x+1\right)-6 \log \left(\sqrt{x^2-2 x-3}+x\right)",1,"-2/(1 - x - Sqrt[-3 - 2*x + x^2]) + 3/(4*(x + Sqrt[-3 - 2*x + x^2])^2) + 4/(x + Sqrt[-3 - 2*x + x^2]) + 6*Log[1 - x - Sqrt[-3 - 2*x + x^2]] - 6*Log[x + Sqrt[-3 - 2*x + x^2]]","A",3,2,16,0.1250,1,"{2116, 893}"
759,1,108,0,0.1015552,"\int \frac{1}{x+\sqrt{-3-4 x-x^2}} \, dx","Int[(x + Sqrt[-3 - 4*x - x^2])^(-1),x]","\frac{1}{2} \log (x+3)+\frac{1}{2} \log \left(\frac{\sqrt{-x-1} x+\sqrt{x+3} x+3 \sqrt{-x-1}}{(x+3)^{3/2}}\right)-\tan ^{-1}\left(\frac{\sqrt{-x-1}}{\sqrt{x+3}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{1-\frac{3 \sqrt{-x-1}}{\sqrt{x+3}}}{\sqrt{2}}\right)","\frac{1}{2} \log (x+3)+\frac{1}{2} \log \left(\frac{\sqrt{-x-1} x+\sqrt{x+3} x+3 \sqrt{-x-1}}{(x+3)^{3/2}}\right)-\tan ^{-1}\left(\frac{\sqrt{-x-1}}{\sqrt{x+3}}\right)-\sqrt{2} \tan ^{-1}\left(\frac{1-\frac{3 \sqrt{-x-1}}{\sqrt{x+3}}}{\sqrt{2}}\right)",1,"-ArcTan[Sqrt[-1 - x]/Sqrt[3 + x]] - Sqrt[2]*ArcTan[(1 - (3*Sqrt[-1 - x])/Sqrt[3 + x])/Sqrt[2]] + Log[3 + x]/2 + Log[(3*Sqrt[-1 - x] + Sqrt[-1 - x]*x + x*Sqrt[3 + x])/(3 + x)^(3/2)]/2","A",10,9,18,0.5000,1,"{12, 1023, 634, 618, 204, 628, 635, 203, 260}"
760,1,87,0,0.0651296,"\int \frac{1}{\left(x+\sqrt{-3-4 x-x^2}\right)^2} \, dx","Int[(x + Sqrt[-3 - 4*x - x^2])^(-2),x]","\frac{1-\frac{\sqrt{-x-1}}{\sqrt{x+3}}}{-\frac{3 (x+1)}{x+3}-\frac{2 \sqrt{-x-1}}{\sqrt{x+3}}+1}+\frac{\tan ^{-1}\left(\frac{1-\frac{3 \sqrt{-x-1}}{\sqrt{x+3}}}{\sqrt{2}}\right)}{\sqrt{2}}","\frac{1-\frac{\sqrt{-x-1}}{\sqrt{x+3}}}{-\frac{3 (x+1)}{x+3}-\frac{2 \sqrt{-x-1}}{\sqrt{x+3}}+1}+\frac{\tan ^{-1}\left(\frac{1-\frac{3 \sqrt{-x-1}}{\sqrt{x+3}}}{\sqrt{2}}\right)}{\sqrt{2}}",1,"(1 - Sqrt[-1 - x]/Sqrt[3 + x])/(1 - (3*(1 + x))/(3 + x) - (2*Sqrt[-1 - x])/Sqrt[3 + x]) + ArcTan[(1 - (3*Sqrt[-1 - x])/Sqrt[3 + x])/Sqrt[2]]/Sqrt[2]","A",5,4,18,0.2222,1,"{12, 638, 618, 204}"
761,1,149,0,0.09538,"\int \frac{1}{\left(x+\sqrt{-3-4 x-x^2}\right)^3} \, dx","Int[(x + Sqrt[-3 - 4*x - x^2])^(-3),x]","-\frac{13-\frac{27 \sqrt{-x-1}}{\sqrt{x+3}}}{18 \left(-\frac{3 (x+1)}{x+3}-\frac{2 \sqrt{-x-1}}{\sqrt{x+3}}+1\right)}-\frac{2 \left(2-\frac{\sqrt{-x-1}}{\sqrt{x+3}}\right)}{9 \left(-\frac{3 (x+1)}{x+3}-\frac{2 \sqrt{-x-1}}{\sqrt{x+3}}+1\right)^2}-\frac{3 \tan ^{-1}\left(\frac{1-\frac{3 \sqrt{-x-1}}{\sqrt{x+3}}}{\sqrt{2}}\right)}{2 \sqrt{2}}","-\frac{13-\frac{27 \sqrt{-x-1}}{\sqrt{x+3}}}{18 \left(-\frac{3 (x+1)}{x+3}-\frac{2 \sqrt{-x-1}}{\sqrt{x+3}}+1\right)}-\frac{2 \left(2-\frac{\sqrt{-x-1}}{\sqrt{x+3}}\right)}{9 \left(-\frac{3 (x+1)}{x+3}-\frac{2 \sqrt{-x-1}}{\sqrt{x+3}}+1\right)^2}-\frac{3 \tan ^{-1}\left(\frac{1-\frac{3 \sqrt{-x-1}}{\sqrt{x+3}}}{\sqrt{2}}\right)}{2 \sqrt{2}}",1,"-(13 - (27*Sqrt[-1 - x])/Sqrt[3 + x])/(18*(1 - (3*(1 + x))/(3 + x) - (2*Sqrt[-1 - x])/Sqrt[3 + x])) - (2*(2 - Sqrt[-1 - x]/Sqrt[3 + x]))/(9*(1 - (3*(1 + x))/(3 + x) - (2*Sqrt[-1 - x])/Sqrt[3 + x])^2) - (3*ArcTan[(1 - (3*Sqrt[-1 - x])/Sqrt[3 + x])/Sqrt[2]])/(2*Sqrt[2])","A",6,5,18,0.2778,1,"{12, 1660, 638, 618, 204}"
762,1,59,0,0.2151171,"\int x^3 (1+x)^3 (1+2 x) \sqrt{1-x^2-2 x^3-x^4} \, dx","Int[x^3*(1 + x)^3*(1 + 2*x)*Sqrt[1 - x^2 - 2*x^3 - x^4],x]","-\frac{1}{5} x^2 \left(-x^4-2 x^3-x^2+1\right)^{3/2} (x+1)^2-\frac{2}{15} \left(-x^4-2 x^3-x^2+1\right)^{3/2}","-\frac{1}{15} \left(-x^4-2 x^3-x^2+1\right)^{3/2} \left(3 x^4+6 x^3+3 x^2+2\right)",1,"(-2*(1 - x^2 - 2*x^3 - x^4)^(3/2))/15 - (x^2*(1 + x)^2*(1 - x^2 - 2*x^3 - x^4)^(3/2))/5","A",5,5,35,0.1429,1,"{1680, 12, 1247, 692, 629}"
763,1,59,0,0.2389254,"\int (1+2 x) \left(x+x^2\right)^3 \sqrt{1-\left(x+x^2\right)^2} \, dx","Int[(1 + 2*x)*(x + x^2)^3*Sqrt[1 - (x + x^2)^2],x]","-\frac{1}{5} x^2 \left(-x^4-2 x^3-x^2+1\right)^{3/2} (x+1)^2-\frac{2}{15} \left(-x^4-2 x^3-x^2+1\right)^{3/2}","-\frac{1}{15} \left(-x^4-2 x^3-x^2+1\right)^{3/2} \left(3 x^4+6 x^3+3 x^2+2\right)",1,"(-2*(1 - x^2 - 2*x^3 - x^4)^(3/2))/15 - (x^2*(1 + x)^2*(1 - x^2 - 2*x^3 - x^4)^(3/2))/5","A",6,6,28,0.2143,1,"{1593, 1680, 12, 1247, 692, 629}"
764,1,102,0,0.0712901,"\int \left(8 x-8 x^2+4 x^3-x^4\right)^{3/2} \, dx","Int[(8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x]","\frac{1}{7} (x-1) \left(-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{2}{35} \left(13-3 (x-1)^2\right) (x-1) \sqrt{-(x-1)^4-2 (x-1)^2+3}-\frac{176}{35} \sqrt{3} F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)+\frac{16}{5} \sqrt{3} E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)","\frac{1}{7} (x-1) \left(-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{2}{35} \left(13-3 (x-1)^2\right) (x-1) \sqrt{-(x-1)^4-2 (x-1)^2+3}-\frac{176}{35} \sqrt{3} F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)+\frac{16}{5} \sqrt{3} E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)",1,"(2*(13 - 3*(-1 + x)^2)*Sqrt[3 - 2*(-1 + x)^2 - (-1 + x)^4]*(-1 + x))/35 + ((3 - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)*(-1 + x))/7 + (16*Sqrt[3]*EllipticE[ArcSin[1 - x], -1/3])/5 - (176*Sqrt[3]*EllipticF[ArcSin[1 - x], -1/3])/35","A",7,7,23,0.3043,1,"{1106, 1091, 1176, 1180, 524, 424, 419}"
765,1,62,0,0.0490289,"\int \sqrt{8 x-8 x^2+4 x^3-x^4} \, dx","Int[Sqrt[8*x - 8*x^2 + 4*x^3 - x^4],x]","\frac{1}{3} \sqrt{-(x-1)^4-2 (x-1)^2+3} (x-1)-\frac{4 F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}+\frac{2 E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}","\frac{1}{3} \sqrt{-(x-1)^4-2 (x-1)^2+3} (x-1)-\frac{4 F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}+\frac{2 E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}",1,"(Sqrt[3 - 2*(-1 + x)^2 - (-1 + x)^4]*(-1 + x))/3 + (2*EllipticE[ArcSin[1 - x], -1/3])/Sqrt[3] - (4*EllipticF[ArcSin[1 - x], -1/3])/Sqrt[3]","A",6,6,23,0.2609,1,"{1106, 1091, 1180, 524, 424, 419}"
766,1,17,0,0.0135043,"\int \frac{1}{\sqrt{8 x-8 x^2+4 x^3-x^4}} \, dx","Int[1/Sqrt[8*x - 8*x^2 + 4*x^3 - x^4],x]","-\frac{F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}","-\frac{F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}",1,"-(EllipticF[ArcSin[1 - x], -1/3]/Sqrt[3])","A",3,3,23,0.1304,1,"{1106, 1095, 419}"
767,1,73,0,0.0514859,"\int \frac{1}{\left(8 x-8 x^2+4 x^3-x^4\right)^{3/2}} \, dx","Int[(8*x - 8*x^2 + 4*x^3 - x^4)^(-3/2),x]","\frac{\left((x-1)^2+5\right) (x-1)}{24 \sqrt{-(x-1)^4-2 (x-1)^2+3}}-\frac{F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{4 \sqrt{3}}+\frac{E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{8 \sqrt{3}}","\frac{\left((x-1)^2+5\right) (x-1)}{24 \sqrt{-(x-1)^4-2 (x-1)^2+3}}-\frac{F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{4 \sqrt{3}}+\frac{E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{8 \sqrt{3}}",1,"((5 + (-1 + x)^2)*(-1 + x))/(24*Sqrt[3 - 2*(-1 + x)^2 - (-1 + x)^4]) + EllipticE[ArcSin[1 - x], -1/3]/(8*Sqrt[3]) - EllipticF[ArcSin[1 - x], -1/3]/(4*Sqrt[3])","A",6,6,23,0.2609,1,"{1106, 1092, 1180, 524, 424, 419}"
768,1,109,0,0.0732775,"\int \frac{1}{\left(8 x-8 x^2+4 x^3-x^4\right)^{5/2}} \, dx","Int[(8*x - 8*x^2 + 4*x^3 - x^4)^(-5/2),x]","\frac{\left(7 (x-1)^2+26\right) (x-1)}{432 \sqrt{-(x-1)^4-2 (x-1)^2+3}}+\frac{\left((x-1)^2+5\right) (x-1)}{72 \left(-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}-\frac{11 F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{144 \sqrt{3}}+\frac{7 E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{144 \sqrt{3}}","\frac{\left(7 (x-1)^2+26\right) (x-1)}{432 \sqrt{-(x-1)^4-2 (x-1)^2+3}}+\frac{\left((x-1)^2+5\right) (x-1)}{72 \left(-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}-\frac{11 F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{144 \sqrt{3}}+\frac{7 E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{144 \sqrt{3}}",1,"((5 + (-1 + x)^2)*(-1 + x))/(72*(3 - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)) + ((26 + 7*(-1 + x)^2)*(-1 + x))/(432*Sqrt[3 - 2*(-1 + x)^2 - (-1 + x)^4]) + (7*EllipticE[ArcSin[1 - x], -1/3])/(144*Sqrt[3]) - (11*EllipticF[ArcSin[1 - x], -1/3])/(144*Sqrt[3])","A",7,7,23,0.3043,1,"{1106, 1092, 1178, 1180, 524, 424, 419}"
769,1,102,0,0.069017,"\int \left((2-x) x \left(4-2 x+x^2\right)\right)^{3/2} \, dx","Int[((2 - x)*x*(4 - 2*x + x^2))^(3/2),x]","\frac{1}{7} (x-1) \left(-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{2}{35} \left(13-3 (x-1)^2\right) (x-1) \sqrt{-(x-1)^4-2 (x-1)^2+3}-\frac{176}{35} \sqrt{3} F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)+\frac{16}{5} \sqrt{3} E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)","\frac{1}{7} (x-1) \left(-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{2}{35} \left(13-3 (x-1)^2\right) (x-1) \sqrt{-(x-1)^4-2 (x-1)^2+3}-\frac{176}{35} \sqrt{3} F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)+\frac{16}{5} \sqrt{3} E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)",1,"(2*(13 - 3*(-1 + x)^2)*Sqrt[3 - 2*(-1 + x)^2 - (-1 + x)^4]*(-1 + x))/35 + ((3 - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)*(-1 + x))/7 + (16*Sqrt[3]*EllipticE[ArcSin[1 - x], -1/3])/5 - (176*Sqrt[3]*EllipticF[ArcSin[1 - x], -1/3])/35","A",7,7,19,0.3684,1,"{1106, 1091, 1176, 1180, 524, 424, 419}"
770,1,62,0,0.0486551,"\int \sqrt{(2-x) x \left(4-2 x+x^2\right)} \, dx","Int[Sqrt[(2 - x)*x*(4 - 2*x + x^2)],x]","\frac{1}{3} \sqrt{-(x-1)^4-2 (x-1)^2+3} (x-1)-\frac{4 F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}+\frac{2 E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}","\frac{1}{3} \sqrt{-(x-1)^4-2 (x-1)^2+3} (x-1)-\frac{4 F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}+\frac{2 E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}",1,"(Sqrt[3 - 2*(-1 + x)^2 - (-1 + x)^4]*(-1 + x))/3 + (2*EllipticE[ArcSin[1 - x], -1/3])/Sqrt[3] - (4*EllipticF[ArcSin[1 - x], -1/3])/Sqrt[3]","A",6,6,19,0.3158,1,"{1106, 1091, 1180, 524, 424, 419}"
771,1,17,0,0.0118359,"\int \frac{1}{\sqrt{(2-x) x \left(4-2 x+x^2\right)}} \, dx","Int[1/Sqrt[(2 - x)*x*(4 - 2*x + x^2)],x]","-\frac{F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}","-\frac{F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{\sqrt{3}}",1,"-(EllipticF[ArcSin[1 - x], -1/3]/Sqrt[3])","A",3,3,19,0.1579,1,"{1106, 1095, 419}"
772,1,73,0,0.0505107,"\int \frac{1}{\left((2-x) x \left(4-2 x+x^2\right)\right)^{3/2}} \, dx","Int[((2 - x)*x*(4 - 2*x + x^2))^(-3/2),x]","\frac{\left((x-1)^2+5\right) (x-1)}{24 \sqrt{-(x-1)^4-2 (x-1)^2+3}}-\frac{F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{4 \sqrt{3}}+\frac{E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{8 \sqrt{3}}","\frac{\left((x-1)^2+5\right) (x-1)}{24 \sqrt{-(x-1)^4-2 (x-1)^2+3}}-\frac{F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{4 \sqrt{3}}+\frac{E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{8 \sqrt{3}}",1,"((5 + (-1 + x)^2)*(-1 + x))/(24*Sqrt[3 - 2*(-1 + x)^2 - (-1 + x)^4]) + EllipticE[ArcSin[1 - x], -1/3]/(8*Sqrt[3]) - EllipticF[ArcSin[1 - x], -1/3]/(4*Sqrt[3])","A",6,6,19,0.3158,1,"{1106, 1092, 1180, 524, 424, 419}"
773,1,109,0,0.0704578,"\int \frac{1}{\left((2-x) x \left(4-2 x+x^2\right)\right)^{5/2}} \, dx","Int[((2 - x)*x*(4 - 2*x + x^2))^(-5/2),x]","\frac{\left(7 (x-1)^2+26\right) (x-1)}{432 \sqrt{-(x-1)^4-2 (x-1)^2+3}}+\frac{\left((x-1)^2+5\right) (x-1)}{72 \left(-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}-\frac{11 F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{144 \sqrt{3}}+\frac{7 E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{144 \sqrt{3}}","\frac{\left(7 (x-1)^2+26\right) (x-1)}{432 \sqrt{-(x-1)^4-2 (x-1)^2+3}}+\frac{\left((x-1)^2+5\right) (x-1)}{72 \left(-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}-\frac{11 F\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{144 \sqrt{3}}+\frac{7 E\left(\sin ^{-1}(1-x)|-\frac{1}{3}\right)}{144 \sqrt{3}}",1,"((5 + (-1 + x)^2)*(-1 + x))/(72*(3 - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)) + ((26 + 7*(-1 + x)^2)*(-1 + x))/(432*Sqrt[3 - 2*(-1 + x)^2 - (-1 + x)^4]) + (7*EllipticE[ArcSin[1 - x], -1/3])/(144*Sqrt[3]) - (11*EllipticF[ArcSin[1 - x], -1/3])/(144*Sqrt[3])","A",7,7,19,0.3684,1,"{1106, 1092, 1178, 1180, 524, 424, 419}"
774,1,730,0,0.9030184,"\int \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^{3/2} \, dx","Int[(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^(3/2),x]","-\frac{16 c^3 \left(8 a d^2+c^3\right) \left(\frac{c}{d}+x\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}{35 d^2 \sqrt{4 a d^2+c^3} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)}+\frac{2 c \left(\frac{c}{d}+x\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4} \left(20 a d^2+7 c^3-3 c d^2 \left(\frac{c}{d}+x\right)^2\right)}{35 d^2}+\frac{1}{7} \left(\frac{c}{d}+x\right) \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^{3/2}+\frac{8 c^{7/4} \left(4 a d^2+c^3\right)^{3/4} \left(\sqrt{4 a d^2+c^3} \left(5 a d^2+c^3\right)-c^{3/2} \left(8 a d^2+c^3\right)\right) \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{35 d^5 \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}+\frac{16 c^{13/4} \left(4 a d^2+c^3\right)^{3/4} \left(8 a d^2+c^3\right) \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) E\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{35 d^5 \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}","-\frac{16 c^3 \left(8 a d^2+c^3\right) \left(\frac{c}{d}+x\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}{35 d^2 \sqrt{4 a d^2+c^3} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)}+\frac{2 c \left(\frac{c}{d}+x\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4} \left(20 a d^2+7 c^3-3 c d^2 \left(\frac{c}{d}+x\right)^2\right)}{35 d^2}+\frac{1}{7} \left(\frac{c}{d}+x\right) \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^{3/2}+\frac{8 c^{7/4} \left(4 a d^2+c^3\right)^{3/4} \left(\sqrt{4 a d^2+c^3} \left(5 a d^2+c^3\right)-c^{3/2} \left(8 a d^2+c^3\right)\right) \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{35 d^5 \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}+\frac{16 c^{13/4} \left(4 a d^2+c^3\right)^{3/4} \left(8 a d^2+c^3\right) \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) E\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{35 d^5 \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}",1,"((c/d + x)*(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^(3/2))/7 + (2*c*(c/d + x)*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4]*(7*c^3 + 20*a*d^2 - 3*c*d^2*(c/d + x)^2))/(35*d^2) - (16*c^3*(c^3 + 8*a*d^2)*(c/d + x)*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4])/(35*d^2*Sqrt[c^3 + 4*a*d^2]*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])) + (16*c^(13/4)*(c^3 + 4*a*d^2)^(3/4)*(c^3 + 8*a*d^2)*Sqrt[(d^2*(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4))/((c^3 + 4*a*d^2)*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])^2)]*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])*EllipticE[2*ArcTan[(c + d*x)/(c^(1/4)*(c^3 + 4*a*d^2)^(1/4))], (1 + c^(3/2)/Sqrt[c^3 + 4*a*d^2])/2])/(35*d^5*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4]) + (8*c^(7/4)*(c^3 + 4*a*d^2)^(3/4)*(Sqrt[c^3 + 4*a*d^2]*(c^3 + 5*a*d^2) - c^(3/2)*(c^3 + 8*a*d^2))*Sqrt[(d^2*(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4))/((c^3 + 4*a*d^2)*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])^2)]*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])*EllipticF[2*ArcTan[(c + d*x)/(c^(1/4)*(c^3 + 4*a*d^2)^(1/4))], (1 + c^(3/2)/Sqrt[c^3 + 4*a*d^2])/2])/(35*d^5*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4])","A",6,6,31,0.1935,1,"{1106, 1091, 1176, 1197, 1103, 1195}"
775,1,622,0,0.6601938,"\int \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4} \, dx","Int[Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4],x]","-\frac{2 c^2 \left(\frac{c}{d}+x\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}{3 \sqrt{4 a d^2+c^3} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)}+\frac{1}{3} \left(\frac{c}{d}+x\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}+\frac{c^{3/4} \sqrt[4]{4 a d^2+c^3} \left(-c^{3/2} \sqrt{4 a d^2+c^3}+4 a d^2+c^3\right) \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{3 d^3 \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}+\frac{2 c^{9/4} \left(4 a d^2+c^3\right)^{3/4} \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) E\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{3 d^3 \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}","-\frac{2 c^2 \left(\frac{c}{d}+x\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}{3 \sqrt{4 a d^2+c^3} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)}+\frac{1}{3} \left(\frac{c}{d}+x\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}+\frac{c^{3/4} \sqrt[4]{4 a d^2+c^3} \left(-c^{3/2} \sqrt{4 a d^2+c^3}+4 a d^2+c^3\right) \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{3 d^3 \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}+\frac{2 c^{9/4} \left(4 a d^2+c^3\right)^{3/4} \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) E\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{3 d^3 \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}",1,"((c/d + x)*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4])/3 - (2*c^2*(c/d + x)*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4])/(3*Sqrt[c^3 + 4*a*d^2]*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])) + (2*c^(9/4)*(c^3 + 4*a*d^2)^(3/4)*Sqrt[(d^2*(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4))/((c^3 + 4*a*d^2)*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])^2)]*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])*EllipticE[2*ArcTan[(c + d*x)/(c^(1/4)*(c^3 + 4*a*d^2)^(1/4))], (1 + c^(3/2)/Sqrt[c^3 + 4*a*d^2])/2])/(3*d^3*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4]) + (c^(3/4)*(c^3 + 4*a*d^2)^(1/4)*(c^3 + 4*a*d^2 - c^(3/2)*Sqrt[c^3 + 4*a*d^2])*Sqrt[(d^2*(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4))/((c^3 + 4*a*d^2)*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])^2)]*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])*EllipticF[2*ArcTan[(c + d*x)/(c^(1/4)*(c^3 + 4*a*d^2)^(1/4))], (1 + c^(3/2)/Sqrt[c^3 + 4*a*d^2])/2])/(3*d^3*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4])","A",5,5,31,0.1613,1,"{1106, 1091, 1197, 1103, 1195}"
776,1,227,0,0.1730976,"\int \frac{1}{\sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}} \, dx","Int[1/Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4],x]","\frac{\sqrt[4]{4 a d^2+c^3} \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{2 \sqrt[4]{c} d \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}","\frac{\sqrt[4]{4 a d^2+c^3} \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{2 \sqrt[4]{c} d \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}",1,"((c^3 + 4*a*d^2)^(1/4)*Sqrt[(d^2*(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4))/((c^3 + 4*a*d^2)*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])^2)]*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])*EllipticF[2*ArcTan[(c + d*x)/(c^(1/4)*(c^3 + 4*a*d^2)^(1/4))], (1 + c^(3/2)/Sqrt[c^3 + 4*a*d^2])/2])/(2*c^(1/4)*d*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4])","A",2,2,31,0.06452,1,"{1106, 1103}"
777,1,674,0,0.6830765,"\int \frac{1}{\left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)^{3/2}} \, dx","Int[(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4)^(-3/2),x]","-\frac{d^2 \left(\frac{c}{d}+x\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}{8 a \left(4 a d^2+c^3\right)^{3/2} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)}-\frac{\left(\frac{c}{d}+x\right) \left(-4 a d^2+c^3-c d^2 \left(\frac{c}{d}+x\right)^2\right)}{8 a c \left(4 a d^2+c^3\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}+\frac{\left(-c^{3/2} \sqrt{4 a d^2+c^3}+4 a d^2+c^3\right) \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{16 a c^{5/4} d \left(4 a d^2+c^3\right)^{3/4} \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}+\frac{\sqrt[4]{c} \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) E\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{8 a d \sqrt[4]{4 a d^2+c^3} \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}","-\frac{d^2 \left(\frac{c}{d}+x\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}{8 a \left(4 a d^2+c^3\right)^{3/2} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)}-\frac{\left(\frac{c}{d}+x\right) \left(-4 a d^2+c^3-c d^2 \left(\frac{c}{d}+x\right)^2\right)}{8 a c \left(4 a d^2+c^3\right) \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}+\frac{\left(-c^{3/2} \sqrt{4 a d^2+c^3}+4 a d^2+c^3\right) \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{16 a c^{5/4} d \left(4 a d^2+c^3\right)^{3/4} \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}+\frac{\sqrt[4]{c} \sqrt{\frac{d^2 \left(4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4\right)}{\left(4 a d^2+c^3\right) \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right)^2}} \left(\frac{d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{4 a d^2+c^3}}+\sqrt{c}\right) E\left(2 \tan ^{-1}\left(\frac{c+d x}{\sqrt[4]{c} \sqrt[4]{c^3+4 a d^2}}\right)|\frac{1}{2} \left(\frac{c^{3/2}}{\sqrt{c^3+4 a d^2}}+1\right)\right)}{8 a d \sqrt[4]{4 a d^2+c^3} \sqrt{4 a c+4 c^2 x^2+4 c d x^3+d^2 x^4}}",1,"-((c/d + x)*(c^3 - 4*a*d^2 - c*d^2*(c/d + x)^2))/(8*a*c*(c^3 + 4*a*d^2)*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4]) - (d^2*(c/d + x)*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4])/(8*a*(c^3 + 4*a*d^2)^(3/2)*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])) + (c^(1/4)*Sqrt[(d^2*(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4))/((c^3 + 4*a*d^2)*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])^2)]*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])*EllipticE[2*ArcTan[(c + d*x)/(c^(1/4)*(c^3 + 4*a*d^2)^(1/4))], (1 + c^(3/2)/Sqrt[c^3 + 4*a*d^2])/2])/(8*a*d*(c^3 + 4*a*d^2)^(1/4)*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4]) + ((c^3 + 4*a*d^2 - c^(3/2)*Sqrt[c^3 + 4*a*d^2])*Sqrt[(d^2*(4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4))/((c^3 + 4*a*d^2)*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])^2)]*(Sqrt[c] + (d^2*(c/d + x)^2)/Sqrt[c^3 + 4*a*d^2])*EllipticF[2*ArcTan[(c + d*x)/(c^(1/4)*(c^3 + 4*a*d^2)^(1/4))], (1 + c^(3/2)/Sqrt[c^3 + 4*a*d^2])/2])/(16*a*c^(5/4)*d*(c^3 + 4*a*d^2)^(3/4)*Sqrt[4*a*c + 4*c^2*x^2 + 4*c*d*x^3 + d^2*x^4])","A",5,5,31,0.1613,1,"{1106, 1092, 1197, 1103, 1195}"
778,1,663,0,0.8104763,"\int \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4} \, dx","Int[Sqrt[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4],x]","-\frac{2 d^2 \left(\frac{d}{4 e}+x\right) \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}{\sqrt{256 a e^3+5 d^4} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)}+\frac{1}{3} \left(\frac{d}{4 e}+x\right) \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}+\frac{\sqrt[4]{256 a e^3+5 d^4} \left(-3 d^2 \sqrt{256 a e^3+5 d^4}+256 a e^3+5 d^4\right) \sqrt{\frac{e \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}{\left(256 a e^3+5 d^4\right) \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)^2}} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right) F\left(2 \tan ^{-1}\left(\frac{d+4 e x}{\sqrt[4]{5 d^4+256 a e^3}}\right)|\frac{1}{2} \left(\frac{3 d^2}{\sqrt{5 d^4+256 a e^3}}+1\right)\right)}{48 \sqrt{2} e^2 \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}+\frac{d^2 \left(256 a e^3+5 d^4\right)^{3/4} \sqrt{\frac{e \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}{\left(256 a e^3+5 d^4\right) \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)^2}} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right) E\left(2 \tan ^{-1}\left(\frac{d+4 e x}{\sqrt[4]{5 d^4+256 a e^3}}\right)|\frac{1}{2} \left(\frac{3 d^2}{\sqrt{5 d^4+256 a e^3}}+1\right)\right)}{8 \sqrt{2} e^2 \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}","-\frac{2 d^2 \left(\frac{d}{4 e}+x\right) \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}{\sqrt{256 a e^3+5 d^4} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)}+\frac{1}{3} \left(\frac{d}{4 e}+x\right) \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}+\frac{\sqrt[4]{256 a e^3+5 d^4} \left(-3 d^2 \sqrt{256 a e^3+5 d^4}+256 a e^3+5 d^4\right) \sqrt{\frac{e \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}{\left(256 a e^3+5 d^4\right) \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)^2}} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right) F\left(2 \tan ^{-1}\left(\frac{d+4 e x}{\sqrt[4]{5 d^4+256 a e^3}}\right)|\frac{1}{2} \left(\frac{3 d^2}{\sqrt{5 d^4+256 a e^3}}+1\right)\right)}{48 \sqrt{2} e^2 \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}+\frac{d^2 \left(256 a e^3+5 d^4\right)^{3/4} \sqrt{\frac{e \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}{\left(256 a e^3+5 d^4\right) \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)^2}} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right) E\left(2 \tan ^{-1}\left(\frac{d+4 e x}{\sqrt[4]{5 d^4+256 a e^3}}\right)|\frac{1}{2} \left(\frac{3 d^2}{\sqrt{5 d^4+256 a e^3}}+1\right)\right)}{8 \sqrt{2} e^2 \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}",1,"((d/(4*e) + x)*Sqrt[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4])/3 - (2*d^2*(d/(4*e) + x)*Sqrt[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4])/(Sqrt[5*d^4 + 256*a*e^3]*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])) + (d^2*(5*d^4 + 256*a*e^3)^(3/4)*Sqrt[(e*(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4))/((5*d^4 + 256*a*e^3)*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])^2)]*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])*EllipticE[2*ArcTan[(d + 4*e*x)/(5*d^4 + 256*a*e^3)^(1/4)], (1 + (3*d^2)/Sqrt[5*d^4 + 256*a*e^3])/2])/(8*Sqrt[2]*e^2*Sqrt[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4]) + ((5*d^4 + 256*a*e^3)^(1/4)*(5*d^4 + 256*a*e^3 - 3*d^2*Sqrt[5*d^4 + 256*a*e^3])*Sqrt[(e*(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4))/((5*d^4 + 256*a*e^3)*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])^2)]*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])*EllipticF[2*ArcTan[(d + 4*e*x)/(5*d^4 + 256*a*e^3)^(1/4)], (1 + (3*d^2)/Sqrt[5*d^4 + 256*a*e^3])/2])/(48*Sqrt[2]*e^2*Sqrt[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4])","A",5,5,34,0.1471,1,"{1106, 1091, 1197, 1103, 1195}"
779,1,235,0,0.1770374,"\int \frac{1}{\sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}} \, dx","Int[1/Sqrt[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4],x]","\frac{\sqrt[4]{256 a e^3+5 d^4} \sqrt{\frac{e \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}{\left(256 a e^3+5 d^4\right) \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)^2}} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right) F\left(2 \tan ^{-1}\left(\frac{d+4 e x}{\sqrt[4]{5 d^4+256 a e^3}}\right)|\frac{1}{2} \left(\frac{3 d^2}{\sqrt{5 d^4+256 a e^3}}+1\right)\right)}{\sqrt{2} e \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}","\frac{\sqrt[4]{256 a e^3+5 d^4} \sqrt{\frac{e \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}{\left(256 a e^3+5 d^4\right) \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)^2}} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right) F\left(2 \tan ^{-1}\left(\frac{d+4 e x}{\sqrt[4]{5 d^4+256 a e^3}}\right)|\frac{1}{2} \left(\frac{3 d^2}{\sqrt{5 d^4+256 a e^3}}+1\right)\right)}{\sqrt{2} e \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}",1,"((5*d^4 + 256*a*e^3)^(1/4)*Sqrt[(e*(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4))/((5*d^4 + 256*a*e^3)*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])^2)]*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])*EllipticF[2*ArcTan[(d + 4*e*x)/(5*d^4 + 256*a*e^3)^(1/4)], (1 + (3*d^2)/Sqrt[5*d^4 + 256*a*e^3])/2])/(Sqrt[2]*e*Sqrt[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4])","A",2,2,34,0.05882,1,"{1106, 1103}"
780,1,748,0,0.786038,"\int \frac{1}{\left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)^{3/2}} \, dx","Int[(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4)^(-3/2),x]","\frac{4 e \left(\frac{d}{4 e}+x\right) \left(-256 a e^3-48 d^2 e^2 \left(\frac{d}{4 e}+x\right)^2+13 d^4\right)}{\left(-16384 a^2 e^6-64 a d^4 e^3+5 d^8\right) \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}+\frac{384 d^2 e^2 \left(\frac{d}{4 e}+x\right) \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}{\left(d^4-64 a e^3\right) \left(256 a e^3+5 d^4\right)^{3/2} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)}-\frac{2 \sqrt{2} \left(-3 d^2 \sqrt{256 a e^3+5 d^4}+256 a e^3+5 d^4\right) \sqrt{\frac{e \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}{\left(256 a e^3+5 d^4\right) \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)^2}} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right) F\left(2 \tan ^{-1}\left(\frac{d+4 e x}{\sqrt[4]{5 d^4+256 a e^3}}\right)|\frac{1}{2} \left(\frac{3 d^2}{\sqrt{5 d^4+256 a e^3}}+1\right)\right)}{\left(d^4-64 a e^3\right) \left(256 a e^3+5 d^4\right)^{3/4} \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}-\frac{12 \sqrt{2} d^2 \sqrt{\frac{e \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}{\left(256 a e^3+5 d^4\right) \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)^2}} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right) E\left(2 \tan ^{-1}\left(\frac{d+4 e x}{\sqrt[4]{5 d^4+256 a e^3}}\right)|\frac{1}{2} \left(\frac{3 d^2}{\sqrt{5 d^4+256 a e^3}}+1\right)\right)}{\left(d^4-64 a e^3\right) \sqrt[4]{256 a e^3+5 d^4} \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}","\frac{4 e \left(\frac{d}{4 e}+x\right) \left(-256 a e^3-48 d^2 e^2 \left(\frac{d}{4 e}+x\right)^2+13 d^4\right)}{\left(-16384 a^2 e^6-64 a d^4 e^3+5 d^8\right) \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}+\frac{384 d^2 e^2 \left(\frac{d}{4 e}+x\right) \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}{\left(d^4-64 a e^3\right) \left(256 a e^3+5 d^4\right)^{3/2} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)}-\frac{2 \sqrt{2} \left(-3 d^2 \sqrt{256 a e^3+5 d^4}+256 a e^3+5 d^4\right) \sqrt{\frac{e \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}{\left(256 a e^3+5 d^4\right) \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)^2}} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right) F\left(2 \tan ^{-1}\left(\frac{d+4 e x}{\sqrt[4]{5 d^4+256 a e^3}}\right)|\frac{1}{2} \left(\frac{3 d^2}{\sqrt{5 d^4+256 a e^3}}+1\right)\right)}{\left(d^4-64 a e^3\right) \left(256 a e^3+5 d^4\right)^{3/4} \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}-\frac{12 \sqrt{2} d^2 \sqrt{\frac{e \left(8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4\right)}{\left(256 a e^3+5 d^4\right) \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right)^2}} \left(\frac{16 e^2 \left(\frac{d}{4 e}+x\right)^2}{\sqrt{256 a e^3+5 d^4}}+1\right) E\left(2 \tan ^{-1}\left(\frac{d+4 e x}{\sqrt[4]{5 d^4+256 a e^3}}\right)|\frac{1}{2} \left(\frac{3 d^2}{\sqrt{5 d^4+256 a e^3}}+1\right)\right)}{\left(d^4-64 a e^3\right) \sqrt[4]{256 a e^3+5 d^4} \sqrt{8 a e^2-d^3 x+8 d e^2 x^3+8 e^3 x^4}}",1,"(4*e*(d/(4*e) + x)*(13*d^4 - 256*a*e^3 - 48*d^2*e^2*(d/(4*e) + x)^2))/((5*d^8 - 64*a*d^4*e^3 - 16384*a^2*e^6)*Sqrt[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4]) + (384*d^2*e^2*(d/(4*e) + x)*Sqrt[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4])/((d^4 - 64*a*e^3)*(5*d^4 + 256*a*e^3)^(3/2)*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])) - (12*Sqrt[2]*d^2*Sqrt[(e*(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4))/((5*d^4 + 256*a*e^3)*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])^2)]*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])*EllipticE[2*ArcTan[(d + 4*e*x)/(5*d^4 + 256*a*e^3)^(1/4)], (1 + (3*d^2)/Sqrt[5*d^4 + 256*a*e^3])/2])/((d^4 - 64*a*e^3)*(5*d^4 + 256*a*e^3)^(1/4)*Sqrt[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4]) - (2*Sqrt[2]*(5*d^4 + 256*a*e^3 - 3*d^2*Sqrt[5*d^4 + 256*a*e^3])*Sqrt[(e*(8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4))/((5*d^4 + 256*a*e^3)*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])^2)]*(1 + (16*e^2*(d/(4*e) + x)^2)/Sqrt[5*d^4 + 256*a*e^3])*EllipticF[2*ArcTan[(d + 4*e*x)/(5*d^4 + 256*a*e^3)^(1/4)], (1 + (3*d^2)/Sqrt[5*d^4 + 256*a*e^3])/2])/((d^4 - 64*a*e^3)*(5*d^4 + 256*a*e^3)^(3/4)*Sqrt[8*a*e^2 - d^3*x + 8*d*e^2*x^3 + 8*e^3*x^4])","A",5,5,34,0.1471,1,"{1106, 1092, 1197, 1103, 1195}"
781,1,452,0,0.5786404,"\int \left(a+8 x-8 x^2+4 x^3-x^4\right)^{3/2} \, dx","Int[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x]","\frac{1}{7} (x-1) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{2}{35} (x-1) \left(5 a-3 (x-1)^2+13\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}-\frac{16 (2 a+7) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{35 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{4 (a+3) (5 a+16) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{35 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{16 (2 a+7) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{35 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{1}{7} (x-1) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{2}{35} (x-1) \left(5 a-3 (x-1)^2+13\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}-\frac{16 (2 a+7) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{35 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{4 (a+3) (5 a+16) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{35 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{16 (2 a+7) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{35 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"(-16*(7 + 2*a)*(1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(35*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (2*(13 + 5*a - 3*(-1 + x)^2)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]*(-1 + x))/35 + ((3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)*(-1 + x))/7 + (16*(7 + 2*a)*(1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(35*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (4*(3 + a)*(16 + 5*a)*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(35*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",8,8,24,0.3333,1,"{1106, 1091, 1176, 1202, 531, 418, 492, 411}"
782,1,397,0,0.4009121,"\int \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx","Int[Sqrt[a + 8*x - 8*x^2 + 4*x^3 - x^4],x]","\frac{1}{3} (x-1) \sqrt{a-(x-1)^4-2 (x-1)^2+3}-\frac{2 \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{3 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{2 (a+3) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{2 \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{1}{3} (x-1) \sqrt{a-(x-1)^4-2 (x-1)^2+3}-\frac{2 \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{3 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{2 (a+3) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{2 \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"(-2*(1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(3*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]*(-1 + x))/3 + (2*(1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(3*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (2*(3 + a)*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(3*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",7,7,24,0.2917,1,"{1106, 1091, 1202, 531, 418, 492, 411}"
783,1,144,0,0.103659,"\int \frac{1}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx","Int[1/Sqrt[a + 8*x - 8*x^2 + 4*x^3 - x^4],x]","\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{\sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{\sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"(Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",3,3,24,0.1250,1,"{1106, 1104, 418}"
784,1,437,0,0.4159377,"\int \frac{1}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^{3/2}} \, dx","Int[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(-3/2),x]","\frac{(x-1) \left(a+(x-1)^2+5\right)}{2 \left(a^2+7 a+12\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{\left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{2 (a+3) (a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{2 (a+4) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{\left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{2 (a+3) (a+4) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{(x-1) \left(a+(x-1)^2+5\right)}{2 \left(a^2+7 a+12\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{\left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{2 (a+3) (a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{2 (a+4) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{\left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{2 (a+3) (a+4) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"((5 + a + (-1 + x)^2)*(-1 + x))/(2*(12 + 7*a + a^2)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) - ((1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(2*(3 + a)*(4 + a)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(2*(3 + a)*(4 + a)*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(2*(4 + a)*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",7,7,24,0.2917,1,"{1106, 1092, 1202, 531, 418, 492, 411}"
785,1,517,0,0.5598558,"\int \frac{1}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^{5/2}} \, dx","Int[(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(-5/2),x]","\frac{(x-1) \left(5 a^2+4 (2 a+7) (x-1)^2+47 a+104\right)}{12 (a+3)^2 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1) \left(a+(x-1)^2+5\right)}{6 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}-\frac{(2 a+7) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{3 (a+3)^2 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(5 a+16) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{12 (a+3) (a+4)^2 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(2 a+7) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 (a+3)^2 (a+4)^2 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{(x-1) \left(5 a^2+4 (2 a+7) (x-1)^2+47 a+104\right)}{12 (a+3)^2 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1) \left(a+(x-1)^2+5\right)}{6 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}-\frac{(2 a+7) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{3 (a+3)^2 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(5 a+16) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{12 (a+3) (a+4)^2 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(2 a+7) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 (a+3)^2 (a+4)^2 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"((5 + a + (-1 + x)^2)*(-1 + x))/(6*(12 + 7*a + a^2)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)) + ((104 + 47*a + 5*a^2 + 4*(7 + 2*a)*(-1 + x)^2)*(-1 + x))/(12*(3 + a)^2*(4 + a)^2*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) - ((7 + 2*a)*(1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(3*(3 + a)^2*(4 + a)^2*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((7 + 2*a)*(1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(3*(3 + a)^2*(4 + a)^2*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((16 + 5*a)*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(12*(3 + a)*(4 + a)^2*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",8,8,24,0.3333,1,"{1106, 1092, 1178, 1202, 531, 418, 492, 411}"
786,1,558,0,0.5650673,"\int x \left(a+8 x-8 x^2+4 x^3-x^4\right)^{3/2} \, dx","Int[x*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x]","\frac{3}{16} (a+4) \left((x-1)^2+1\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{1}{8} \left((x-1)^2+1\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{1}{7} (x-1) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{2}{35} (x-1) \left(5 a-3 (x-1)^2+13\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}-\frac{16 (2 a+7) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{35 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{3}{16} (a+4)^2 \tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{4 (a+3) (5 a+16) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{35 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{16 (2 a+7) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{35 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{3}{16} (a+4) \left((x-1)^2+1\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{1}{8} \left((x-1)^2+1\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{1}{7} (x-1) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{2}{35} (x-1) \left(5 a-3 (x-1)^2+13\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}-\frac{16 (2 a+7) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{35 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{3}{16} (a+4)^2 \tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{4 (a+3) (5 a+16) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{35 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{16 (2 a+7) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{35 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"(3*(4 + a)*(1 + (-1 + x)^2)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])/16 + ((1 + (-1 + x)^2)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2))/8 - (16*(7 + 2*a)*(1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(35*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (2*(13 + 5*a - 3*(-1 + x)^2)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]*(-1 + x))/35 + ((3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)*(-1 + x))/7 + (3*(4 + a)^2*ArcTan[(1 + (-1 + x)^2)/Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]])/16 + (16*(7 + 2*a)*(1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(35*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (4*(3 + a)*(16 + 5*a)*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(35*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",14,13,26,0.5000,1,"{1680, 1673, 1091, 1176, 1202, 531, 418, 492, 411, 1107, 612, 621, 204}"
787,1,466,0,0.4545771,"\int x \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx","Int[x*Sqrt[a + 8*x - 8*x^2 + 4*x^3 - x^4],x]","\frac{1}{4} \left((x-1)^2+1\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{1}{3} (x-1) \sqrt{a-(x-1)^4-2 (x-1)^2+3}-\frac{2 \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{3 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{1}{4} (a+4) \tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{2 (a+3) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{2 \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{1}{4} \left((x-1)^2+1\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{1}{3} (x-1) \sqrt{a-(x-1)^4-2 (x-1)^2+3}-\frac{2 \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{3 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{1}{4} (a+4) \tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{2 (a+3) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{2 \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"((1 + (-1 + x)^2)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])/4 - (2*(1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(3*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]*(-1 + x))/3 + ((4 + a)*ArcTan[(1 + (-1 + x)^2)/Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]])/4 + (2*(1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(3*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (2*(3 + a)*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(3*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",12,12,26,0.4615,1,"{1680, 1673, 1091, 1202, 531, 418, 492, 411, 1107, 612, 621, 204}"
788,1,179,0,0.1524366,"\int \frac{x}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx","Int[x/Sqrt[a + 8*x - 8*x^2 + 4*x^3 - x^4],x]","\frac{1}{2} \tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{\sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{1}{2} \tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{\sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"ArcTan[(1 + (-1 + x)^2)/Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]]/2 + (Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",7,7,26,0.2692,1,"{1680, 1673, 1104, 418, 1107, 621, 204}"
789,1,474,0,0.4351399,"\int \frac{x}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^{3/2}} \, dx","Int[x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x]","\frac{(x-1) \left(a+(x-1)^2+5\right)}{2 \left(a^2+7 a+12\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1)^2+1}{2 (a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{\left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{2 (a+3) (a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{2 (a+4) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{\left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{2 (a+3) (a+4) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{(x-1) \left(a+(x-1)^2+5\right)}{2 \left(a^2+7 a+12\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1)^2+1}{2 (a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{\left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{2 (a+3) (a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{2 (a+4) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{\left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{2 (a+3) (a+4) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"(1 + (-1 + x)^2)/(2*(4 + a)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((5 + a + (-1 + x)^2)*(-1 + x))/(2*(12 + 7*a + a^2)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) - ((1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(2*(3 + a)*(4 + a)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(2*(3 + a)*(4 + a)*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(2*(4 + a)*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",10,10,26,0.3846,1,"{1680, 1673, 1092, 1202, 531, 418, 492, 411, 1107, 613}"
790,1,591,0,0.5842792,"\int \frac{x}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^{5/2}} \, dx","Int[x/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(5/2),x]","\frac{(x-1) \left(5 a^2+4 (2 a+7) (x-1)^2+47 a+104\right)}{12 (a+3)^2 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1) \left(a+(x-1)^2+5\right)}{6 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}+\frac{(x-1)^2+1}{3 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1)^2+1}{6 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}-\frac{(2 a+7) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{3 (a+3)^2 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(5 a+16) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{12 (a+3) (a+4)^2 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(2 a+7) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 (a+3)^2 (a+4)^2 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{(x-1) \left(5 a^2+4 (2 a+7) (x-1)^2+47 a+104\right)}{12 (a+3)^2 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1) \left(a+(x-1)^2+5\right)}{6 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}+\frac{(x-1)^2+1}{3 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1)^2+1}{6 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}-\frac{(2 a+7) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{3 (a+3)^2 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(5 a+16) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{12 (a+3) (a+4)^2 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(2 a+7) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{3 (a+3)^2 (a+4)^2 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"(1 + (-1 + x)^2)/(6*(4 + a)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)) + (1 + (-1 + x)^2)/(3*(4 + a)^2*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((5 + a + (-1 + x)^2)*(-1 + x))/(6*(12 + 7*a + a^2)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)) + ((104 + 47*a + 5*a^2 + 4*(7 + 2*a)*(-1 + x)^2)*(-1 + x))/(12*(3 + a)^2*(4 + a)^2*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) - ((7 + 2*a)*(1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(3*(3 + a)^2*(4 + a)^2*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((7 + 2*a)*(1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(3*(3 + a)^2*(4 + a)^2*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((16 + 5*a)*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(12*(3 + a)*(4 + a)^2*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",12,12,26,0.4615,1,"{1680, 1673, 1092, 1178, 1202, 531, 418, 492, 411, 1107, 614, 613}"
791,1,585,0,0.6789021,"\int x^2 \left(a+8 x-8 x^2+4 x^3-x^4\right)^{3/2} \, dx","Int[x^2*(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x]","\frac{4 \left(21 a^2+111 a+140\right) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{315 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{4 \left(21 a^2+111 a+140\right) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{315 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{3}{8} (a+4) \left((x-1)^2+1\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{1}{4} \left((x-1)^2+1\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{1}{63} \left(7 (x-1)^2+15\right) (x-1) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{2}{315} (x-1) \left(3 (7 a+20) (x-1)^2+2 (27 a+80)\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{3}{8} (a+4)^2 \tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{4 (a+3) (33 a+100) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{315 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{4 \left(21 a^2+111 a+140\right) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{315 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{4 \left(21 a^2+111 a+140\right) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{315 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{3}{8} (a+4) \left((x-1)^2+1\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{1}{4} \left((x-1)^2+1\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{1}{63} \left(7 (x-1)^2+15\right) (x-1) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}+\frac{2}{315} (x-1) \left(3 (7 a+20) (x-1)^2+2 (27 a+80)\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{3}{8} (a+4)^2 \tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{4 (a+3) (33 a+100) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{315 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"(3*(4 + a)*(1 + (-1 + x)^2)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])/8 + ((1 + (-1 + x)^2)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2))/4 + (4*(140 + 111*a + 21*a^2)*(1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(315*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (2*(2*(80 + 27*a) + 3*(20 + 7*a)*(-1 + x)^2)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]*(-1 + x))/315 + ((15 + 7*(-1 + x)^2)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)*(-1 + x))/63 + (3*(4 + a)^2*ArcTan[(1 + (-1 + x)^2)/Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]])/8 - (4*(140 + 111*a + 21*a^2)*(1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(315*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (4*(3 + a)*(100 + 33*a)*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(315*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",15,13,28,0.4643,1,"{1680, 1673, 1176, 1202, 531, 418, 492, 411, 12, 1107, 612, 621, 204}"
792,1,485,0,0.529802,"\int x^2 \sqrt{a+8 x-8 x^2+4 x^3-x^4} \, dx","Int[x^2*Sqrt[a + 8*x - 8*x^2 + 4*x^3 - x^4],x]","\frac{1}{2} \left((x-1)^2+1\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{1}{15} \left(3 (x-1)^2+7\right) (x-1) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{2 (3 a+8) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{15 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{1}{2} (a+4) \tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{8 (a+3) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{15 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{2 (3 a+8) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{15 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{1}{2} \left((x-1)^2+1\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{1}{15} \left(3 (x-1)^2+7\right) (x-1) \sqrt{a-(x-1)^4-2 (x-1)^2+3}+\frac{2 (3 a+8) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{15 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{1}{2} (a+4) \tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{8 (a+3) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{15 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{2 (3 a+8) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{15 \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"((1 + (-1 + x)^2)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])/2 + (2*(8 + 3*a)*(1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(15*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((7 + 3*(-1 + x)^2)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]*(-1 + x))/15 + ((4 + a)*ArcTan[(1 + (-1 + x)^2)/Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]])/2 - (2*(8 + 3*a)*(1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(15*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (8*(3 + a)*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(15*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",13,13,28,0.4643,1,"{1680, 1673, 1176, 1202, 531, 418, 492, 411, 12, 1107, 612, 621, 204}"
793,1,388,0,0.3871018,"\int \frac{x^2}{\sqrt{a+8 x-8 x^2+4 x^3-x^4}} \, dx","Int[x^2/Sqrt[a + 8*x - 8*x^2 + 4*x^3 - x^4],x]","\frac{\left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{\sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{\left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{\sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{\left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\tan ^{-1}\left(\frac{(x-1)^2+1}{\sqrt{a-(x-1)^4-2 (x-1)^2+3}}\right)+\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{\sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{\left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{\sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"((1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4] + ArcTan[(1 + (-1 + x)^2)/Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]] - ((1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",11,11,28,0.3929,1,"{1680, 1673, 1202, 531, 418, 492, 411, 12, 1107, 621, 204}"
794,1,311,0,0.3271723,"\int \frac{x^2}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^{3/2}} \, dx","Int[x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(3/2),x]","\frac{(a+4) \left((x-1)^2+2\right) (x-1)}{2 \left(a^2+7 a+12\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1)^2+1}{(a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{\left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{2 (a+3) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{\left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{2 (a+3) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{(a+4) \left((x-1)^2+2\right) (x-1)}{2 \left(a^2+7 a+12\right) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1)^2+1}{(a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{\left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{2 (a+3) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{\left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{2 (a+3) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"(1 + (-1 + x)^2)/((4 + a)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((4 + a)*(2 + (-1 + x)^2)*(-1 + x))/(2*(12 + 7*a + a^2)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) - ((1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(2*(3 + a)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(2*(3 + a)*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",10,9,28,0.3214,1,"{1680, 1673, 1178, 12, 1140, 492, 411, 1107, 613}"
795,1,582,0,0.6748277,"\int \frac{x^2}{\left(a+8 x-8 x^2+4 x^3-x^4\right)^{5/2}} \, dx","Int[x^2/(a + 8*x - 8*x^2 + 4*x^3 - x^4)^(5/2),x]","\frac{(a+4) \left((x-1)^2+2\right) (x-1)}{6 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}+\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{12 \left(a^2+7 a+12\right) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{2 \left((x-1)^2+1\right)}{3 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1)^2+1}{3 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}+\frac{(x-1) \left((3 a+13) (x-1)^2+7 a+29\right)}{12 (a+3)^2 (a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{(3 a+13) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{12 (a+3)^2 (a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(3 a+13) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{12 (a+3)^2 (a+4) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}","\frac{(a+4) \left((x-1)^2+2\right) (x-1)}{6 \left(a^2+7 a+12\right) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}+\frac{\sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) F\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{12 \left(a^2+7 a+12\right) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{2 \left((x-1)^2+1\right)}{3 (a+4)^2 \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(x-1)^2+1}{3 (a+4) \left(a-(x-1)^4-2 (x-1)^2+3\right)^{3/2}}+\frac{(x-1) \left((3 a+13) (x-1)^2+7 a+29\right)}{12 (a+3)^2 (a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}-\frac{(3 a+13) \left(1-\sqrt{a+4}\right) (x-1) \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right)}{12 (a+3)^2 (a+4) \sqrt{a-(x-1)^4-2 (x-1)^2+3}}+\frac{(3 a+13) \left(1-\sqrt{a+4}\right) \sqrt{\sqrt{a+4}+1} \left(\frac{(x-1)^2}{1-\sqrt{a+4}}+1\right) E\left(\tan ^{-1}\left(\frac{x-1}{\sqrt{\sqrt{a+4}+1}}\right)|-\frac{2 \sqrt{a+4}}{1-\sqrt{a+4}}\right)}{12 (a+3)^2 (a+4) \sqrt{\frac{\frac{(x-1)^2}{1-\sqrt{a+4}}+1}{\frac{(x-1)^2}{\sqrt{a+4}+1}+1}} \sqrt{a-(x-1)^4-2 (x-1)^2+3}}",1,"(1 + (-1 + x)^2)/(3*(4 + a)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)) + (2*(1 + (-1 + x)^2))/(3*(4 + a)^2*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((4 + a)*(2 + (-1 + x)^2)*(-1 + x))/(6*(12 + 7*a + a^2)*(3 + a - 2*(-1 + x)^2 - (-1 + x)^4)^(3/2)) + ((29 + 7*a + (13 + 3*a)*(-1 + x)^2)*(-1 + x))/(12*(3 + a)^2*(4 + a)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) - ((13 + 3*a)*(1 - Sqrt[4 + a])*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*(-1 + x))/(12*(3 + a)^2*(4 + a)*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + ((13 + 3*a)*(1 - Sqrt[4 + a])*Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticE[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(12*(3 + a)^2*(4 + a)*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4]) + (Sqrt[1 + Sqrt[4 + a]]*(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))*EllipticF[ArcTan[(-1 + x)/Sqrt[1 + Sqrt[4 + a]]], (-2*Sqrt[4 + a])/(1 - Sqrt[4 + a])])/(12*(12 + 7*a + a^2)*Sqrt[(1 + (-1 + x)^2/(1 - Sqrt[4 + a]))/(1 + (-1 + x)^2/(1 + Sqrt[4 + a]))]*Sqrt[3 + a - 2*(-1 + x)^2 - (-1 + x)^4])","A",13,12,28,0.4286,1,"{1680, 1673, 1178, 1202, 531, 418, 492, 411, 12, 1107, 614, 613}"
796,1,129,0,0.3024337,"\int \frac{1}{\sqrt{8+8 x-x^3+8 x^4}} \, dx","Int[1/Sqrt[8 + 8*x - x^3 + 8*x^4],x]","-\frac{x^2 \sqrt{\frac{\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261}{\left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right)^2}} \left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right) F\left(2 \tan ^{-1}\left(\frac{x+4}{\sqrt{3} \sqrt[4]{29} x}\right)|\frac{1}{58} \left(29+\sqrt{29}\right)\right)}{8 \sqrt{3} \sqrt[4]{29} \sqrt{8 x^4-x^3+8 x+8}}","-\frac{x^2 \sqrt{\frac{\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261}{\left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right)^2}} \left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right) F\left(2 \tan ^{-1}\left(\frac{x+4}{\sqrt{3} \sqrt[4]{29} x}\right)|\frac{1}{58} \left(29+\sqrt{29}\right)\right)}{8 \sqrt{3} \sqrt[4]{29} \sqrt{8 x^4-x^3+8 x+8}}",1,"-(x^2*Sqrt[(261 - 6*(1 + 4/x)^2 + (1 + 4/x)^4)/(87 + (Sqrt[29]*(4 + x)^2)/x^2)^2]*(87 + (Sqrt[29]*(4 + x)^2)/x^2)*EllipticF[2*ArcTan[(4 + x)/(Sqrt[3]*29^(1/4)*x)], (29 + Sqrt[29])/58])/(8*Sqrt[3]*29^(1/4)*Sqrt[8 + 8*x - x^3 + 8*x^4])","A",4,4,19,0.2105,1,"{2069, 12, 6719, 1103}"
797,1,431,0,0.5281478,"\int \frac{1}{\left(8+8 x-x^3+8 x^4\right)^{3/2}} \, dx","Int[(8 + 8*x - x^3 + 8*x^4)^(-3/2),x]","-\frac{\left(66-\left(\frac{4}{x}+1\right)^2\right) x^2}{1008 \sqrt{8 x^4-x^3+8 x+8}}+\frac{\left(216-7 \left(\frac{4}{x}+1\right)^2\right) \left(\frac{4}{x}+1\right) x^2}{12528 \sqrt{8 x^4-x^3+8 x+8}}+\frac{7 \left(\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261\right) \left(\frac{4}{x}+1\right) x^2}{432 \sqrt{29} \sqrt{8 x^4-x^3+8 x+8} \left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right)}+\frac{\left(14-5 \sqrt{29}\right) \sqrt{\frac{\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261}{\left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right)^2}} \left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right) x^2 F\left(2 \tan ^{-1}\left(\frac{x+4}{\sqrt{3} \sqrt[4]{29} x}\right)|\frac{1}{58} \left(29+\sqrt{29}\right)\right)}{576 \sqrt{3} 29^{3/4} \sqrt{8 x^4-x^3+8 x+8}}-\frac{7 \sqrt{\frac{\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261}{\left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right)^2}} \left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right) x^2 E\left(2 \tan ^{-1}\left(\frac{x+4}{\sqrt{3} \sqrt[4]{29} x}\right)|\frac{1}{58} \left(29+\sqrt{29}\right)\right)}{144 \sqrt{3} 29^{3/4} \sqrt{8 x^4-x^3+8 x+8}}","-\frac{\left(66-\left(\frac{4}{x}+1\right)^2\right) x^2}{1008 \sqrt{8 x^4-x^3+8 x+8}}+\frac{\left(216-7 \left(\frac{4}{x}+1\right)^2\right) \left(\frac{4}{x}+1\right) x^2}{12528 \sqrt{8 x^4-x^3+8 x+8}}+\frac{7 \left(\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261\right) \left(\frac{4}{x}+1\right) x^2}{432 \sqrt{29} \sqrt{8 x^4-x^3+8 x+8} \left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right)}+\frac{\left(14-5 \sqrt{29}\right) \sqrt{\frac{\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261}{\left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right)^2}} \left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right) x^2 F\left(2 \tan ^{-1}\left(\frac{x+4}{\sqrt{3} \sqrt[4]{29} x}\right)|\frac{1}{58} \left(29+\sqrt{29}\right)\right)}{576 \sqrt{3} 29^{3/4} \sqrt{8 x^4-x^3+8 x+8}}-\frac{7 \sqrt{\frac{\left(\frac{4}{x}+1\right)^4-6 \left(\frac{4}{x}+1\right)^2+261}{\left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right)^2}} \left(\frac{\sqrt{29} (x+4)^2}{x^2}+87\right) x^2 E\left(2 \tan ^{-1}\left(\frac{x+4}{\sqrt{3} \sqrt[4]{29} x}\right)|\frac{1}{58} \left(29+\sqrt{29}\right)\right)}{144 \sqrt{3} 29^{3/4} \sqrt{8 x^4-x^3+8 x+8}}",1,"-((66 - (1 + 4/x)^2)*x^2)/(1008*Sqrt[8 + 8*x - x^3 + 8*x^4]) + ((216 - 7*(1 + 4/x)^2)*(1 + 4/x)*x^2)/(12528*Sqrt[8 + 8*x - x^3 + 8*x^4]) + (7*(261 - 6*(1 + 4/x)^2 + (1 + 4/x)^4)*(1 + 4/x)*x^2)/(432*Sqrt[29]*Sqrt[8 + 8*x - x^3 + 8*x^4]*(87 + (Sqrt[29]*(4 + x)^2)/x^2)) - (7*x^2*Sqrt[(261 - 6*(1 + 4/x)^2 + (1 + 4/x)^4)/(87 + (Sqrt[29]*(4 + x)^2)/x^2)^2]*(87 + (Sqrt[29]*(4 + x)^2)/x^2)*EllipticE[2*ArcTan[(4 + x)/(Sqrt[3]*29^(1/4)*x)], (29 + Sqrt[29])/58])/(144*Sqrt[3]*29^(3/4)*Sqrt[8 + 8*x - x^3 + 8*x^4]) + ((14 - 5*Sqrt[29])*x^2*Sqrt[(261 - 6*(1 + 4/x)^2 + (1 + 4/x)^4)/(87 + (Sqrt[29]*(4 + x)^2)/x^2)^2]*(87 + (Sqrt[29]*(4 + x)^2)/x^2)*EllipticF[2*ArcTan[(4 + x)/(Sqrt[3]*29^(1/4)*x)], (29 + Sqrt[29])/58])/(576*Sqrt[3]*29^(3/4)*Sqrt[8 + 8*x - x^3 + 8*x^4])","A",10,10,19,0.5263,1,"{2069, 12, 6719, 1673, 1678, 1197, 1103, 1195, 1247, 636}"
798,1,108,0,0.2166571,"\int \frac{1}{\sqrt{1+4 x+4 x^2+4 x^4}} \, dx","Int[1/Sqrt[1 + 4*x + 4*x^2 + 4*x^4],x]","-\frac{\left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right) \sqrt{\frac{\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5}{\left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right)^2}} x^2 F\left(2 \tan ^{-1}\left(\frac{1+\frac{1}{x}}{\sqrt[4]{5}}\right)|\frac{1}{10} \left(5+\sqrt{5}\right)\right)}{2 \sqrt[4]{5} \sqrt{4 x^4+4 x^2+4 x+1}}","-\frac{\left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right) \sqrt{\frac{\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5}{\left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right)^2}} x^2 F\left(2 \tan ^{-1}\left(\frac{1+\frac{1}{x}}{\sqrt[4]{5}}\right)|\frac{1}{10} \left(5+\sqrt{5}\right)\right)}{2 \sqrt[4]{5} \sqrt{4 x^4+4 x^2+4 x+1}}",1,"-((Sqrt[5] + (1 + x^(-1))^2)*Sqrt[(5 - 2*(1 + x^(-1))^2 + (1 + x^(-1))^4)/(Sqrt[5] + (1 + x^(-1))^2)^2]*x^2*EllipticF[2*ArcTan[(1 + x^(-1))/5^(1/4)], (5 + Sqrt[5])/10])/(2*5^(1/4)*Sqrt[1 + 4*x + 4*x^2 + 4*x^4])","A",3,3,19,0.1579,1,"{2069, 6719, 1103}"
799,1,367,0,0.376027,"\int \frac{1}{\left(1+4 x+4 x^2+4 x^4\right)^{3/2}} \, dx","Int[(1 + 4*x + 4*x^2 + 4*x^4)^(-3/2),x]","-\frac{\left(3-\left(\frac{1}{x}+1\right)^2\right) x^2}{\sqrt{4 x^4+4 x^2+4 x+1}}+\frac{\left(13-9 \left(\frac{1}{x}+1\right)^2\right) \left(\frac{1}{x}+1\right) x^2}{10 \sqrt{4 x^4+4 x^2+4 x+1}}+\frac{9 \left(\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5\right) \left(\frac{1}{x}+1\right) x^2}{10 \left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right) \sqrt{4 x^4+4 x^2+4 x+1}}+\frac{3 \left(3-\sqrt{5}\right) \left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right) \sqrt{\frac{\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5}{\left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right)^2}} x^2 F\left(2 \tan ^{-1}\left(\frac{1+\frac{1}{x}}{\sqrt[4]{5}}\right)|\frac{1}{10} \left(5+\sqrt{5}\right)\right)}{4\ 5^{3/4} \sqrt{4 x^4+4 x^2+4 x+1}}-\frac{9 \left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right) \sqrt{\frac{\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5}{\left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right)^2}} x^2 E\left(2 \tan ^{-1}\left(\frac{1+\frac{1}{x}}{\sqrt[4]{5}}\right)|\frac{1}{10} \left(5+\sqrt{5}\right)\right)}{2\ 5^{3/4} \sqrt{4 x^4+4 x^2+4 x+1}}","-\frac{\left(3-\left(\frac{1}{x}+1\right)^2\right) x^2}{\sqrt{4 x^4+4 x^2+4 x+1}}+\frac{\left(13-9 \left(\frac{1}{x}+1\right)^2\right) \left(\frac{1}{x}+1\right) x^2}{10 \sqrt{4 x^4+4 x^2+4 x+1}}+\frac{9 \left(\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5\right) \left(\frac{1}{x}+1\right) x^2}{10 \left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right) \sqrt{4 x^4+4 x^2+4 x+1}}+\frac{3 \left(3-\sqrt{5}\right) \left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right) \sqrt{\frac{\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5}{\left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right)^2}} x^2 F\left(2 \tan ^{-1}\left(\frac{1+\frac{1}{x}}{\sqrt[4]{5}}\right)|\frac{1}{10} \left(5+\sqrt{5}\right)\right)}{4\ 5^{3/4} \sqrt{4 x^4+4 x^2+4 x+1}}-\frac{9 \left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right) \sqrt{\frac{\left(\frac{1}{x}+1\right)^4-2 \left(\frac{1}{x}+1\right)^2+5}{\left(\left(\frac{1}{x}+1\right)^2+\sqrt{5}\right)^2}} x^2 E\left(2 \tan ^{-1}\left(\frac{1+\frac{1}{x}}{\sqrt[4]{5}}\right)|\frac{1}{10} \left(5+\sqrt{5}\right)\right)}{2\ 5^{3/4} \sqrt{4 x^4+4 x^2+4 x+1}}",1,"-(((3 - (1 + x^(-1))^2)*x^2)/Sqrt[1 + 4*x + 4*x^2 + 4*x^4]) + ((13 - 9*(1 + x^(-1))^2)*(1 + x^(-1))*x^2)/(10*Sqrt[1 + 4*x + 4*x^2 + 4*x^4]) + (9*(5 - 2*(1 + x^(-1))^2 + (1 + x^(-1))^4)*(1 + x^(-1))*x^2)/(10*(Sqrt[5] + (1 + x^(-1))^2)*Sqrt[1 + 4*x + 4*x^2 + 4*x^4]) - (9*(Sqrt[5] + (1 + x^(-1))^2)*Sqrt[(5 - 2*(1 + x^(-1))^2 + (1 + x^(-1))^4)/(Sqrt[5] + (1 + x^(-1))^2)^2]*x^2*EllipticE[2*ArcTan[(1 + x^(-1))/5^(1/4)], (5 + Sqrt[5])/10])/(2*5^(3/4)*Sqrt[1 + 4*x + 4*x^2 + 4*x^4]) + (3*(3 - Sqrt[5])*(Sqrt[5] + (1 + x^(-1))^2)*Sqrt[(5 - 2*(1 + x^(-1))^2 + (1 + x^(-1))^4)/(Sqrt[5] + (1 + x^(-1))^2)^2]*x^2*EllipticF[2*ArcTan[(1 + x^(-1))/5^(1/4)], (5 + Sqrt[5])/10])/(4*5^(3/4)*Sqrt[1 + 4*x + 4*x^2 + 4*x^4])","A",9,9,19,0.4737,1,"{2069, 6719, 1673, 1678, 1197, 1103, 1195, 1247, 636}"
800,1,126,0,0.3259878,"\int \frac{1}{\sqrt{8+24 x+8 x^2-15 x^3+8 x^4}} \, dx","Int[1/Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4],x]","-\frac{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{\frac{\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517}{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right)^2}} x^2 F\left(2 \tan ^{-1}\left(\frac{3 x+4}{\sqrt[4]{517} x}\right)|\frac{517+19 \sqrt{517}}{1034}\right)}{8 \sqrt[4]{517} \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}","-\frac{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{\frac{\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517}{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right)^2}} x^2 F\left(2 \tan ^{-1}\left(\frac{3 x+4}{\sqrt[4]{517} x}\right)|\frac{517+19 \sqrt{517}}{1034}\right)}{8 \sqrt[4]{517} \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}",1,"-((Sqrt[517] + (3 + 4/x)^2)*Sqrt[(517 - 38*(3 + 4/x)^2 + (3 + 4/x)^4)/(Sqrt[517] + (3 + 4/x)^2)^2]*x^2*EllipticF[2*ArcTan[(4 + 3*x)/(517^(1/4)*x)], (517 + 19*Sqrt[517])/1034])/(8*517^(1/4)*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4])","A",4,4,24,0.1667,1,"{2069, 12, 6719, 1103}"
801,1,434,0,0.5275795,"\int \frac{1}{\left(8+24 x+8 x^2-15 x^3+8 x^4\right)^{3/2}} \, dx","Int[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^(-3/2),x]","-\frac{\left(172-7 \left(\frac{4}{x}+3\right)^2\right) x^2}{208 \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{\left(50896-2455 \left(\frac{4}{x}+3\right)^2\right) \left(\frac{4}{x}+3\right) x^2}{322608 \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{2455 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right) \left(\frac{4}{x}+3\right) x^2}{322608 \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{\left(4910-203 \sqrt{517}\right) \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{\frac{\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517}{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right)^2}} x^2 F\left(2 \tan ^{-1}\left(\frac{3 x+4}{\sqrt[4]{517} x}\right)|\frac{517+19 \sqrt{517}}{1034}\right)}{2496\ 517^{3/4} \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}-\frac{2455 \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{\frac{\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517}{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right)^2}} x^2 E\left(2 \tan ^{-1}\left(\frac{3 x+4}{\sqrt[4]{517} x}\right)|\frac{517+19 \sqrt{517}}{1034}\right)}{624\ 517^{3/4} \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}","-\frac{\left(172-7 \left(\frac{4}{x}+3\right)^2\right) x^2}{208 \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{\left(50896-2455 \left(\frac{4}{x}+3\right)^2\right) \left(\frac{4}{x}+3\right) x^2}{322608 \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{2455 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right) \left(\frac{4}{x}+3\right) x^2}{322608 \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{\left(4910-203 \sqrt{517}\right) \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{\frac{\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517}{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right)^2}} x^2 F\left(2 \tan ^{-1}\left(\frac{3 x+4}{\sqrt[4]{517} x}\right)|\frac{517+19 \sqrt{517}}{1034}\right)}{2496\ 517^{3/4} \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}-\frac{2455 \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{\frac{\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517}{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right)^2}} x^2 E\left(2 \tan ^{-1}\left(\frac{3 x+4}{\sqrt[4]{517} x}\right)|\frac{517+19 \sqrt{517}}{1034}\right)}{624\ 517^{3/4} \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}",1,"-((172 - 7*(3 + 4/x)^2)*x^2)/(208*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4]) + ((50896 - 2455*(3 + 4/x)^2)*(3 + 4/x)*x^2)/(322608*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4]) + (2455*(517 - 38*(3 + 4/x)^2 + (3 + 4/x)^4)*(3 + 4/x)*x^2)/(322608*(Sqrt[517] + (3 + 4/x)^2)*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4]) - (2455*(Sqrt[517] + (3 + 4/x)^2)*Sqrt[(517 - 38*(3 + 4/x)^2 + (3 + 4/x)^4)/(Sqrt[517] + (3 + 4/x)^2)^2]*x^2*EllipticE[2*ArcTan[(4 + 3*x)/(517^(1/4)*x)], (517 + 19*Sqrt[517])/1034])/(624*517^(3/4)*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4]) + ((4910 - 203*Sqrt[517])*(Sqrt[517] + (3 + 4/x)^2)*Sqrt[(517 - 38*(3 + 4/x)^2 + (3 + 4/x)^4)/(Sqrt[517] + (3 + 4/x)^2)^2]*x^2*EllipticF[2*ArcTan[(4 + 3*x)/(517^(1/4)*x)], (517 + 19*Sqrt[517])/1034])/(2496*517^(3/4)*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4])","A",10,10,24,0.4167,1,"{2069, 12, 6719, 1673, 1678, 1197, 1103, 1195, 1247, 636}"
802,1,577,0,0.6881934,"\int \frac{1}{\left(8+24 x+8 x^2-15 x^3+8 x^4\right)^{5/2}} \, dx","Int[(8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4)^(-5/2),x]","-\frac{\left(124415-6308 \left(\frac{4}{x}+3\right)^2\right) x^2}{97344 \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{\left(18932921731-1086525994 \left(\frac{4}{x}+3\right)^2\right) \left(\frac{4}{x}+3\right) x^2}{78056941248 \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{543262997 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right) \left(\frac{4}{x}+3\right) x^2}{39028470624 \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{\left(11921698-359497 \left(\frac{4}{x}+3\right)^2\right) \left(\frac{4}{x}+3\right) x^2}{483912 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right) \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}-\frac{\left(64489-1399 \left(\frac{4}{x}+3\right)^2\right) x^2}{624 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right) \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{\left(4346103976-175318963 \sqrt{517}\right) \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{\frac{\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517}{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right)^2}} x^2 F\left(2 \tan ^{-1}\left(\frac{3 x+4}{\sqrt[4]{517} x}\right)|\frac{517+19 \sqrt{517}}{1034}\right)}{1207844352\ 517^{3/4} \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}-\frac{543262997 \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{\frac{\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517}{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right)^2}} x^2 E\left(2 \tan ^{-1}\left(\frac{3 x+4}{\sqrt[4]{517} x}\right)|\frac{517+19 \sqrt{517}}{1034}\right)}{75490272\ 517^{3/4} \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}","-\frac{\left(124415-6308 \left(\frac{4}{x}+3\right)^2\right) x^2}{97344 \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{\left(18932921731-1086525994 \left(\frac{4}{x}+3\right)^2\right) \left(\frac{4}{x}+3\right) x^2}{78056941248 \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{543262997 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right) \left(\frac{4}{x}+3\right) x^2}{39028470624 \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{\left(11921698-359497 \left(\frac{4}{x}+3\right)^2\right) \left(\frac{4}{x}+3\right) x^2}{483912 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right) \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}-\frac{\left(64489-1399 \left(\frac{4}{x}+3\right)^2\right) x^2}{624 \left(\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517\right) \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}+\frac{\left(4346103976-175318963 \sqrt{517}\right) \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{\frac{\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517}{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right)^2}} x^2 F\left(2 \tan ^{-1}\left(\frac{3 x+4}{\sqrt[4]{517} x}\right)|\frac{517+19 \sqrt{517}}{1034}\right)}{1207844352\ 517^{3/4} \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}-\frac{543262997 \left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right) \sqrt{\frac{\left(\frac{4}{x}+3\right)^4-38 \left(\frac{4}{x}+3\right)^2+517}{\left(\left(\frac{4}{x}+3\right)^2+\sqrt{517}\right)^2}} x^2 E\left(2 \tan ^{-1}\left(\frac{3 x+4}{\sqrt[4]{517} x}\right)|\frac{517+19 \sqrt{517}}{1034}\right)}{75490272\ 517^{3/4} \sqrt{8 x^4-15 x^3+8 x^2+24 x+8}}",1,"-((124415 - 6308*(3 + 4/x)^2)*x^2)/(97344*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4]) - ((64489 - 1399*(3 + 4/x)^2)*x^2)/(624*(517 - 38*(3 + 4/x)^2 + (3 + 4/x)^4)*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4]) + ((18932921731 - 1086525994*(3 + 4/x)^2)*(3 + 4/x)*x^2)/(78056941248*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4]) + ((11921698 - 359497*(3 + 4/x)^2)*(3 + 4/x)*x^2)/(483912*(517 - 38*(3 + 4/x)^2 + (3 + 4/x)^4)*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4]) + (543262997*(517 - 38*(3 + 4/x)^2 + (3 + 4/x)^4)*(3 + 4/x)*x^2)/(39028470624*(Sqrt[517] + (3 + 4/x)^2)*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4]) - (543262997*(Sqrt[517] + (3 + 4/x)^2)*Sqrt[(517 - 38*(3 + 4/x)^2 + (3 + 4/x)^4)/(Sqrt[517] + (3 + 4/x)^2)^2]*x^2*EllipticE[2*ArcTan[(4 + 3*x)/(517^(1/4)*x)], (517 + 19*Sqrt[517])/1034])/(75490272*517^(3/4)*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4]) + ((4346103976 - 175318963*Sqrt[517])*(Sqrt[517] + (3 + 4/x)^2)*Sqrt[(517 - 38*(3 + 4/x)^2 + (3 + 4/x)^4)/(Sqrt[517] + (3 + 4/x)^2)^2]*x^2*EllipticF[2*ArcTan[(4 + 3*x)/(517^(1/4)*x)], (517 + 19*Sqrt[517])/1034])/(1207844352*517^(3/4)*Sqrt[8 + 24*x + 8*x^2 - 15*x^3 + 8*x^4])","A",12,11,24,0.4583,1,"{2069, 12, 6719, 1673, 1678, 1197, 1103, 1195, 1663, 1660, 636}"
803,1,130,0,0.2600628,"\int \frac{1}{\sqrt{9-6 x-44 x^2+15 x^3+3 x^4}} \, dx","Int[1/Sqrt[9 - 6*x - 44*x^2 + 15*x^3 + 3*x^4],x]","-\frac{\sqrt{\frac{\left(\frac{6}{x}-1\right)^4-182 \left(1-\frac{6}{x}\right)^2+613}{\left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right)^2}} \left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right) x^2 F\left(2 \tan ^{-1}\left(\frac{6-x}{\sqrt[4]{613} x}\right)|\frac{613+91 \sqrt{613}}{1226}\right)}{12 \sqrt[4]{613} \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}","-\frac{\sqrt{\frac{\left(\frac{6}{x}-1\right)^4-182 \left(1-\frac{6}{x}\right)^2+613}{\left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right)^2}} \left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right) x^2 F\left(2 \tan ^{-1}\left(\frac{6-x}{\sqrt[4]{613} x}\right)|\frac{613+91 \sqrt{613}}{1226}\right)}{12 \sqrt[4]{613} \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}",1,"-(Sqrt[(613 - 182*(1 - 6/x)^2 + (-1 + 6/x)^4)/(Sqrt[613] + (6 - x)^2/x^2)^2]*(Sqrt[613] + (6 - x)^2/x^2)*x^2*EllipticF[2*ArcTan[(6 - x)/(613^(1/4)*x)], (613 + 91*Sqrt[613])/1226])/(12*613^(1/4)*Sqrt[9 - 6*x - 44*x^2 + 15*x^3 + 3*x^4])","A",4,4,24,0.1667,1,"{2069, 12, 6719, 1096}"
804,1,444,0,0.4680236,"\int \frac{1}{\left(9-6 x-44 x^2+15 x^3+3 x^4\right)^{3/2}} \, dx","Int[(9 - 6*x - 44*x^2 + 15*x^3 + 3*x^4)^(-3/2),x]","-\frac{\left(176-23 \left(1-\frac{6}{x}\right)^2\right) x^2}{51759 \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}+\frac{\left(45401-3722 \left(1-\frac{6}{x}\right)^2\right) \left(1-\frac{6}{x}\right) x^2}{31728267 \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}+\frac{3722 \left(\left(\frac{6}{x}-1\right)^4-182 \left(1-\frac{6}{x}\right)^2+613\right) \left(1-\frac{6}{x}\right) x^2}{31728267 \left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right) \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}-\frac{\left(7444-145 \sqrt{613}\right) \sqrt{\frac{\left(\frac{6}{x}-1\right)^4-182 \left(1-\frac{6}{x}\right)^2+613}{\left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right)^2}} \left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right) x^2 F\left(2 \tan ^{-1}\left(\frac{6-x}{\sqrt[4]{613} x}\right)|\frac{613+91 \sqrt{613}}{1226}\right)}{207036\ 613^{3/4} \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}+\frac{3722 \sqrt{\frac{\left(\frac{6}{x}-1\right)^4-182 \left(1-\frac{6}{x}\right)^2+613}{\left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right)^2}} \left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right) x^2 E\left(2 \tan ^{-1}\left(\frac{6-x}{\sqrt[4]{613} x}\right)|\frac{613+91 \sqrt{613}}{1226}\right)}{51759\ 613^{3/4} \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}","-\frac{\left(176-23 \left(1-\frac{6}{x}\right)^2\right) x^2}{51759 \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}+\frac{\left(45401-3722 \left(1-\frac{6}{x}\right)^2\right) \left(1-\frac{6}{x}\right) x^2}{31728267 \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}+\frac{3722 \left(\left(\frac{6}{x}-1\right)^4-182 \left(1-\frac{6}{x}\right)^2+613\right) \left(1-\frac{6}{x}\right) x^2}{31728267 \left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right) \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}-\frac{\left(7444-145 \sqrt{613}\right) \sqrt{\frac{\left(\frac{6}{x}-1\right)^4-182 \left(1-\frac{6}{x}\right)^2+613}{\left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right)^2}} \left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right) x^2 F\left(2 \tan ^{-1}\left(\frac{6-x}{\sqrt[4]{613} x}\right)|\frac{613+91 \sqrt{613}}{1226}\right)}{207036\ 613^{3/4} \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}+\frac{3722 \sqrt{\frac{\left(\frac{6}{x}-1\right)^4-182 \left(1-\frac{6}{x}\right)^2+613}{\left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right)^2}} \left(\frac{(6-x)^2}{x^2}+\sqrt{613}\right) x^2 E\left(2 \tan ^{-1}\left(\frac{6-x}{\sqrt[4]{613} x}\right)|\frac{613+91 \sqrt{613}}{1226}\right)}{51759\ 613^{3/4} \sqrt{3 x^4+15 x^3-44 x^2-6 x+9}}",1,"-((176 - 23*(1 - 6/x)^2)*x^2)/(51759*Sqrt[9 - 6*x - 44*x^2 + 15*x^3 + 3*x^4]) + ((45401 - 3722*(1 - 6/x)^2)*(1 - 6/x)*x^2)/(31728267*Sqrt[9 - 6*x - 44*x^2 + 15*x^3 + 3*x^4]) + (3722*(613 - 182*(1 - 6/x)^2 + (-1 + 6/x)^4)*(1 - 6/x)*x^2)/(31728267*(Sqrt[613] + (6 - x)^2/x^2)*Sqrt[9 - 6*x - 44*x^2 + 15*x^3 + 3*x^4]) + (3722*Sqrt[(613 - 182*(1 - 6/x)^2 + (-1 + 6/x)^4)/(Sqrt[613] + (6 - x)^2/x^2)^2]*(Sqrt[613] + (6 - x)^2/x^2)*x^2*EllipticE[2*ArcTan[(6 - x)/(613^(1/4)*x)], (613 + 91*Sqrt[613])/1226])/(51759*613^(3/4)*Sqrt[9 - 6*x - 44*x^2 + 15*x^3 + 3*x^4]) - ((7444 - 145*Sqrt[613])*Sqrt[(613 - 182*(1 - 6/x)^2 + (-1 + 6/x)^4)/(Sqrt[613] + (6 - x)^2/x^2)^2]*(Sqrt[613] + (6 - x)^2/x^2)*x^2*EllipticF[2*ArcTan[(6 - x)/(613^(1/4)*x)], (613 + 91*Sqrt[613])/1226])/(207036*613^(3/4)*Sqrt[9 - 6*x - 44*x^2 + 15*x^3 + 3*x^4])","A",10,10,24,0.4167,1,"{2069, 12, 6719, 1673, 1678, 1183, 1096, 1182, 1247, 636}"
805,1,56,0,0.2106058,"\int \frac{\left(2 \sqrt{3-x}+\frac{3}{\sqrt{1+x}}\right)^2}{x} \, dx","Int[(2*Sqrt[3 - x] + 3/Sqrt[1 + x])^2/x,x]","-4 x+21 \log (x)-9 \log (x+1)+12 \sin ^{-1}\left(\frac{1-x}{2}\right)-24 \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x+1}}{\sqrt{3-x}}\right)","-4 x+21 \log (x)-9 \log (x+1)+12 \sin ^{-1}\left(\frac{1-x}{2}\right)-24 \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt{3} \sqrt{x+1}}{\sqrt{3-x}}\right)",1,"-4*x + 12*ArcSin[(1 - x)/2] - 24*Sqrt[3]*ArcTanh[(Sqrt[3]*Sqrt[1 + x])/Sqrt[3 - x]] + 21*Log[x] - 9*Log[1 + x]","A",11,10,27,0.3704,1,"{6742, 36, 29, 31, 105, 53, 619, 216, 93, 207}"
806,1,65,0,0.1589755,"\int \frac{-1+x+x^2}{1+\sqrt{1+x^2}} \, dx","Int[(-1 + x + x^2)/(1 + Sqrt[1 + x^2]),x]","\frac{1}{2} \sqrt{x^2+1} x+\sqrt{x^2+1}+\frac{\sqrt{x^2+1}}{x}-\log \left(\sqrt{x^2+1}+1\right)-x-\frac{1}{x}-\frac{1}{2} \sinh ^{-1}(x)","\frac{1}{2} \sqrt{x^2+1} x+\sqrt{x^2+1}+\frac{\sqrt{x^2+1}}{x}-\log \left(\sqrt{x^2+1}+1\right)-x-\frac{1}{x}-\frac{1}{2} \sinh ^{-1}(x)",1,"-x^(-1) - x + Sqrt[1 + x^2] + Sqrt[1 + x^2]/x + (x*Sqrt[1 + x^2])/2 - ArcSinh[x]/2 - Log[1 + Sqrt[1 + x^2]]","A",14,7,20,0.3500,1,"{6742, 277, 215, 1591, 190, 43, 195}"
807,1,101,0,0.2148805,"\int \frac{-1+x+x^2}{1+x+\sqrt{1+x^2}} \, dx","Int[(-1 + x + x^2)/(1 + x + Sqrt[1 + x^2]),x]","\frac{x^3}{6}+\frac{x^2}{2}-\frac{1}{4} \sqrt{x^2+1} x-\frac{1}{6} \left(x^2+1\right)^{3/2}+\frac{1}{2 \left(\sqrt{x^2+1}+x\right)}+\frac{1}{2} \log \left(\sqrt{x^2+1}+x\right)-\log \left(\sqrt{x^2+1}+x+1\right)+\frac{x}{2}-\frac{1}{4} \sinh ^{-1}(x)","\frac{1}{12} \left(2 x^3+6 x^2+\left(-2 x^2-3 x+4\right) \sqrt{x^2+1}-6 \log \left(\sqrt{x^2+1}+1\right)-3 \sinh ^{-1}(x)\right)",1,"x/2 + x^2/2 + x^3/6 - (x*Sqrt[1 + x^2])/4 - (1 + x^2)^(3/2)/6 + 1/(2*(x + Sqrt[1 + x^2])) - ArcSinh[x]/4 + Log[x + Sqrt[1 + x^2]]/2 - Log[1 + x + Sqrt[1 + x^2]]","A",12,6,21,0.2857,1,"{6742, 2117, 893, 195, 215, 261}"
808,1,14,0,0.1174061,"\int \frac{2 \sqrt{-1+x}+x}{\sqrt{-1+x} x} \, dx","Int[(2*Sqrt[-1 + x] + x)/(Sqrt[-1 + x]*x),x]","2 \sqrt{x-1}+2 \log (x)","2 \sqrt{x-1}+2 \log (x)",1,"2*Sqrt[-1 + x] + 2*Log[x]","A",2,1,22,0.04545,1,"{6688}"
809,1,61,0,0.165853,"\int \left(a+c \sqrt{x}+b x^{2/3}\right)^2 \, dx","Int[(a + c*Sqrt[x] + b*x^(2/3))^2,x]","a^2 x+\frac{6}{5} a b x^{5/3}+\frac{4}{3} a c x^{3/2}+\frac{3}{7} b^2 x^{7/3}+\frac{12}{13} b c x^{13/6}+\frac{c^2 x^2}{2}","a^2 x+\frac{6}{5} a b x^{5/3}+\frac{4}{3} a c x^{3/2}+\frac{3}{7} b^2 x^{7/3}+\frac{12}{13} b c x^{13/6}+\frac{c^2 x^2}{2}",1,"a^2*x + (4*a*c*x^(3/2))/3 + (6*a*b*x^(5/3))/5 + (c^2*x^2)/2 + (12*b*c*x^(13/6))/13 + (3*b^2*x^(7/3))/7","A",4,2,18,0.1111,1,"{6741, 6742}"
810,1,114,0,0.1925075,"\int \left(a+c \sqrt{x}+b x^{2/3}\right)^3 \, dx","Int[(a + c*Sqrt[x] + b*x^(2/3))^3,x]","\frac{9}{5} a^2 b x^{5/3}+2 a^2 c x^{3/2}+a^3 x+\frac{9}{7} a b^2 x^{7/3}+\frac{36}{13} a b c x^{13/6}+\frac{3}{2} a c^2 x^2+\frac{18}{17} b^2 c x^{17/6}+\frac{b^3 x^3}{3}+\frac{9}{8} b c^2 x^{8/3}+\frac{2}{5} c^3 x^{5/2}","\frac{9}{5} a^2 b x^{5/3}+2 a^2 c x^{3/2}+a^3 x+\frac{9}{7} a b^2 x^{7/3}+\frac{36}{13} a b c x^{13/6}+\frac{3}{2} a c^2 x^2+\frac{18}{17} b^2 c x^{17/6}+\frac{b^3 x^3}{3}+\frac{9}{8} b c^2 x^{8/3}+\frac{2}{5} c^3 x^{5/2}",1,"a^3*x + 2*a^2*c*x^(3/2) + (9*a^2*b*x^(5/3))/5 + (3*a*c^2*x^2)/2 + (36*a*b*c*x^(13/6))/13 + (9*a*b^2*x^(7/3))/7 + (2*c^3*x^(5/2))/5 + (9*b*c^2*x^(8/3))/8 + (18*b^2*c*x^(17/6))/17 + (b^3*x^3)/3","A",4,2,18,0.1111,1,"{6741, 6742}"
811,1,58,0,0.0568747,"\int \frac{-1+x^2}{\sqrt{a-b+\frac{b}{x^2}} x^3} \, dx","Int[(-1 + x^2)/(Sqrt[a - b + b/x^2]*x^3),x]","\frac{\sqrt{a-b \left(1-\frac{1}{x^2}\right)}}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b \left(1-\frac{1}{x^2}\right)}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}","\frac{\sqrt{a-b \left(1-\frac{1}{x^2}\right)}}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b \left(1-\frac{1}{x^2}\right)}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}",1,"Sqrt[a - b*(1 - x^(-2))]/b + ArcTanh[Sqrt[a - b*(1 - x^(-2))]/Sqrt[a - b]]/Sqrt[a - b]","A",5,5,23,0.2174,1,"{514, 446, 80, 63, 208}"
812,1,58,0,0.1374055,"\int \frac{-1+x^2}{\sqrt{a+b \left(-1+\frac{1}{x^2}\right)} x^3} \, dx","Int[(-1 + x^2)/(Sqrt[a + b*(-1 + x^(-2))]*x^3),x]","\frac{\sqrt{a-b \left(1-\frac{1}{x^2}\right)}}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b \left(1-\frac{1}{x^2}\right)}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}","\frac{\sqrt{a-b \left(1-\frac{1}{x^2}\right)}}{b}+\frac{\tanh ^{-1}\left(\frac{\sqrt{a-b \left(1-\frac{1}{x^2}\right)}}{\sqrt{a-b}}\right)}{\sqrt{a-b}}",1,"Sqrt[a - b*(1 - x^(-2))]/b + ArcTanh[Sqrt[a - b*(1 - x^(-2))]/Sqrt[a - b]]/Sqrt[a - b]","A",6,6,22,0.2727,1,"{1978, 514, 446, 80, 63, 208}"
813,1,53,0,0.0307952,"\int \frac{1+x}{\left(4+x^2\right) \sqrt{9+x^2}} \, dx","Int[(1 + x)/((4 + x^2)*Sqrt[9 + x^2]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{5} x}{2 \sqrt{x^2+9}}\right)}{2 \sqrt{5}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+9}}{\sqrt{5}}\right)}{\sqrt{5}}","\frac{\tan ^{-1}\left(\frac{\sqrt{5} x}{2 \sqrt{x^2+9}}\right)}{2 \sqrt{5}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{x^2+9}}{\sqrt{5}}\right)}{\sqrt{5}}",1,"ArcTan[(Sqrt[5]*x)/(2*Sqrt[9 + x^2])]/(2*Sqrt[5]) - ArcTanh[Sqrt[9 + x^2]/Sqrt[5]]/Sqrt[5]","A",6,6,20,0.3000,1,"{1010, 377, 203, 444, 63, 207}"
814,1,23,0,0.0071066,"\int x \left(1+\sqrt{1-x^2}\right) \, dx","Int[x*(1 + Sqrt[1 - x^2]),x]","\frac{x^2}{2}-\frac{1}{3} \left(1-x^2\right)^{3/2}","\frac{x^2}{2}-\frac{1}{3} \left(1-x^2\right)^{3/2}",1,"x^2/2 - (1 - x^2)^(3/2)/3","A",3,2,15,0.1333,1,"{14, 261}"
815,1,23,0,0.008017,"\int x \left(1+\sqrt{1-x} \sqrt{1+x}\right) \, dx","Int[x*(1 + Sqrt[1 - x]*Sqrt[1 + x]),x]","\frac{x^2}{2}-\frac{1}{3} \left(1-x^2\right)^{3/2}","\frac{x^2}{2}-\frac{1}{3} \left(1-x^2\right)^{3/2}",1,"x^2/2 - (1 - x^2)^(3/2)/3","A",3,2,21,0.09524,1,"{14, 261}"
816,1,33,0,0.0154203,"\int x \left(1+\frac{1}{\sqrt{2+x} \sqrt{3+x}}\right) \, dx","Int[x*(1 + 1/(Sqrt[2 + x]*Sqrt[3 + x])),x]","\frac{x^2}{2}+\sqrt{x+2} \sqrt{x+3}-5 \sinh ^{-1}\left(\sqrt{x+2}\right)","\frac{x^2}{2}+\sqrt{x+2} \sqrt{x+3}-5 \sinh ^{-1}\left(\sqrt{x+2}\right)",1,"x^2/2 + Sqrt[2 + x]*Sqrt[3 + x] - 5*ArcSinh[Sqrt[2 + x]]","A",5,4,19,0.2105,1,"{14, 80, 54, 215}"
817,1,45,0,0.1580172,"\int \frac{x-\sqrt{x^6}}{x \left(1-x^4\right)} \, dx","Int[(x - Sqrt[x^6])/(x*(1 - x^4)),x]","\frac{\sqrt{x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)","\frac{\sqrt{x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)",1,"ArcTan[x]/2 + (Sqrt[x^6]*ArcTan[x])/(2*x^3) + ArcTanh[x]/2 - (Sqrt[x^6]*ArcTanh[x])/(2*x^3)","A",9,6,24,0.2500,1,"{6725, 212, 206, 203, 15, 298}"
818,1,45,0,0.0552958,"\int \frac{1-\frac{\sqrt{x^6}}{x}}{1-x^4} \, dx","Int[(1 - Sqrt[x^6]/x)/(1 - x^4),x]","\frac{\sqrt{x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)","\frac{\sqrt{x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)",1,"ArcTan[x]/2 + (Sqrt[x^6]*ArcTan[x])/(2*x^3) + ArcTanh[x]/2 - (Sqrt[x^6]*ArcTanh[x])/(2*x^3)","A",9,6,24,0.2500,1,"{6725, 212, 206, 203, 15, 298}"
819,1,45,0,0.0981848,"\int \frac{x-\sqrt{x^6}}{x-x^5} \, dx","Int[(x - Sqrt[x^6])/(x - x^5),x]","\frac{\sqrt{x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)","\frac{\sqrt{x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)",1,"ArcTan[x]/2 + (Sqrt[x^6]*ArcTan[x])/(2*x^3) + ArcTanh[x]/2 - (Sqrt[x^6]*ArcTanh[x])/(2*x^3)","A",10,7,21,0.3333,1,"{1593, 6725, 212, 206, 203, 15, 298}"
820,1,45,0,0.1330115,"\int \frac{x}{x+\sqrt{x^6}} \, dx","Int[x/(x + Sqrt[x^6]),x]","\frac{\sqrt{x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)","\frac{\sqrt{x^6} \tan ^{-1}(x)}{2 x^3}-\frac{\sqrt{x^6} \tanh ^{-1}(x)}{2 x^3}+\frac{1}{2} \tan ^{-1}(x)+\frac{1}{2} \tanh ^{-1}(x)",1,"ArcTan[x]/2 + (Sqrt[x^6]*ArcTan[x])/(2*x^3) + ArcTanh[x]/2 - (Sqrt[x^6]*ArcTanh[x])/(2*x^3)","A",11,8,13,0.6154,1,"{6729, 1584, 6725, 212, 206, 203, 15, 298}"
821,1,52,0,0.183135,"\int \frac{\sqrt{x}-\sqrt{x^3}}{x-x^3} \, dx","Int[(Sqrt[x] - Sqrt[x^3])/(x - x^3),x]","\frac{\sqrt{x^3} \tan ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}-\frac{\sqrt{x^3} \tanh ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}+\tan ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}\left(\sqrt{x}\right)","\frac{\sqrt{x^3} \tan ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}-\frac{\sqrt{x^3} \tanh ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}+\tan ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}\left(\sqrt{x}\right)",1,"ArcTan[Sqrt[x]] + (Sqrt[x^3]*ArcTan[Sqrt[x]])/x^(3/2) + ArcTanh[Sqrt[x]] - (Sqrt[x^3]*ArcTanh[Sqrt[x]])/x^(3/2)","A",12,8,25,0.3200,1,"{1593, 6725, 329, 212, 206, 203, 15, 298}"
822,1,52,0,0.1258484,"\int \frac{1}{\sqrt{x}+\sqrt{x^3}} \, dx","Int[(Sqrt[x] + Sqrt[x^3])^(-1),x]","\frac{\sqrt{x^3} \tan ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}-\frac{\sqrt{x^3} \tanh ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}+\tan ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}\left(\sqrt{x}\right)","\frac{\sqrt{x^3} \tan ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}-\frac{\sqrt{x^3} \tanh ^{-1}\left(\sqrt{x}\right)}{x^{3/2}}+\tan ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}\left(\sqrt{x}\right)",1,"ArcTan[Sqrt[x]] + (Sqrt[x^3]*ArcTan[Sqrt[x]])/x^(3/2) + ArcTanh[Sqrt[x]] - (Sqrt[x^3]*ArcTanh[Sqrt[x]])/x^(3/2)","A",13,9,15,0.6000,1,"{6729, 1593, 6725, 329, 212, 206, 203, 15, 298}"
823,1,68,0,0.1553325,"\int \frac{1}{\sqrt{-1+x}+\sqrt{(-1+x)^3}} \, dx","Int[(Sqrt[-1 + x] + Sqrt[(-1 + x)^3])^(-1),x]","\frac{\sqrt{(x-1)^3} \tan ^{-1}\left(\sqrt{x-1}\right)}{(x-1)^{3/2}}+\tan ^{-1}\left(\sqrt{x-1}\right)-\frac{\sqrt{(x-1)^3} \tanh ^{-1}\left(\sqrt{x-1}\right)}{(x-1)^{3/2}}+\tanh ^{-1}\left(\sqrt{x-1}\right)","\frac{\sqrt{(x-1)^3} \tan ^{-1}\left(\sqrt{x-1}\right)}{(x-1)^{3/2}}+\tan ^{-1}\left(\sqrt{x-1}\right)-\frac{\sqrt{(x-1)^3} \tanh ^{-1}\left(\sqrt{x-1}\right)}{(x-1)^{3/2}}+\tanh ^{-1}\left(\sqrt{x-1}\right)",1,"ArcTan[Sqrt[-1 + x]] + (Sqrt[(-1 + x)^3]*ArcTan[Sqrt[-1 + x]])/(-1 + x)^(3/2) + ArcTanh[Sqrt[-1 + x]] - (Sqrt[(-1 + x)^3]*ArcTanh[Sqrt[-1 + x]])/(-1 + x)^(3/2)","A",14,9,19,0.4737,1,"{6729, 1593, 6725, 329, 212, 206, 203, 15, 298}"
824,1,31,0,0.0152564,"\int \left(-\frac{3}{(4+5 x)^2}-\frac{5+4 x}{(4+5 x)^2 \sqrt{1-x^2}}\right) \, dx","Int[-3/(4 + 5*x)^2 - (5 + 4*x)/((4 + 5*x)^2*Sqrt[1 - x^2]),x]","\frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)}","\frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)}",1,"3/(5*(4 + 5*x)) + Sqrt[1 - x^2]/(4 + 5*x)","A",2,1,35,0.02857,1,"{803}"
825,1,31,0,0.2877472,"\int \frac{-5-4 x-3 \sqrt{1-x^2}}{(4+5 x)^2 \sqrt{1-x^2}} \, dx","Int[(-5 - 4*x - 3*Sqrt[1 - x^2])/((4 + 5*x)^2*Sqrt[1 - x^2]),x]","\frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)}","\frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)}",1,"3/(5*(4 + 5*x)) + Sqrt[1 - x^2]/(4 + 5*x)","A",8,5,37,0.1351,1,"{6742, 731, 725, 206, 807}"
826,1,31,0,0.1403781,"\int \frac{1}{(-5-4 x) \sqrt{1-x^2}+3 \left(1-x^2\right)} \, dx","Int[((-5 - 4*x)*Sqrt[1 - x^2] + 3*(1 - x^2))^(-1),x]","\frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)}","\frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)}",1,"3/(5*(4 + 5*x)) + Sqrt[1 - x^2]/(4 + 5*x)","A",16,8,29,0.2759,1,"{6742, 665, 216, 733, 844, 725, 206, 735}"
827,1,31,0,0.1251234,"\int \frac{1}{3-3 x^2-5 \sqrt{1-x^2}-4 x \sqrt{1-x^2}} \, dx","Int[(3 - 3*x^2 - 5*Sqrt[1 - x^2] - 4*x*Sqrt[1 - x^2])^(-1),x]","\frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)}","\frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)}",1,"3/(5*(4 + 5*x)) + Sqrt[1 - x^2]/(4 + 5*x)","A",16,8,36,0.2222,1,"{6742, 665, 216, 733, 844, 725, 206, 735}"
828,1,31,0,0.6541718,"\int \frac{-1+\sqrt{1-x^2}}{\sqrt{1-x^2} \left(2+x-2 \sqrt{1-x^2}\right)^2} \, dx","Int[(-1 + Sqrt[1 - x^2])/(Sqrt[1 - x^2]*(2 + x - 2*Sqrt[1 - x^2])^2),x]","\frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)}","\frac{\sqrt{1-x^2}}{5 x+4}+\frac{3}{5 (5 x+4)}",1,"3/(5*(4 + 5*x)) + Sqrt[1 - x^2]/(4 + 5*x)","A",31,13,43,0.3023,1,"{6742, 277, 216, 266, 50, 63, 206, 733, 844, 725, 735, 264, 731}"
829,1,43,0,0.0668804,"\int \frac{a+b x^{-1+n}}{c x+d x^n} \, dx","Int[(a + b*x^(-1 + n))/(c*x + d*x^n),x]","\frac{b \log (x)}{d}-\frac{(b c-a d) \log \left(c x^{1-n}+d\right)}{c d (1-n)}","\frac{b \log (x)}{d}-\frac{(b c-a d) \log \left(c x^{1-n}+d\right)}{c d (1-n)}",1,"(b*Log[x])/d - ((b*c - a*d)*Log[d + c*x^(1 - n)])/(c*d*(1 - n))","A",5,4,21,0.1905,1,"{1593, 514, 446, 72}"
830,1,42,0,0.129511,"\int \frac{\sqrt{1+2 x^2}}{1+\sqrt{1+2 x^2}} \, dx","Int[Sqrt[1 + 2*x^2]/(1 + Sqrt[1 + 2*x^2]),x]","\frac{\sqrt{2 x^2+1}}{2 x}+x-\frac{1}{2 x}-\frac{\sinh ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}","\frac{\sqrt{2 x^2+1}}{2 x}+x-\frac{1}{2 x}-\frac{\sinh ^{-1}\left(\sqrt{2} x\right)}{\sqrt{2}}",1,"-1/(2*x) + x + Sqrt[1 + 2*x^2]/(2*x) - ArcSinh[Sqrt[2]*x]/Sqrt[2]","A",6,4,27,0.1481,1,"{6740, 6742, 277, 215}"
831,1,65,0,0.1328596,"\int \frac{\sqrt{-1+4 x^2}}{x+\sqrt{-1+4 x^2}} \, dx","Int[Sqrt[-1 + 4*x^2]/(x + Sqrt[-1 + 4*x^2]),x]","-\frac{1}{3} \sqrt{4 x^2-1}+\frac{\tanh ^{-1}\left(\sqrt{3} \sqrt{4 x^2-1}\right)}{3 \sqrt{3}}+\frac{4 x}{3}-\frac{\tanh ^{-1}\left(\sqrt{3} x\right)}{3 \sqrt{3}}","-\frac{1}{3} \sqrt{4 x^2-1}+\frac{\tanh ^{-1}\left(\sqrt{3} \sqrt{4 x^2-1}\right)}{3 \sqrt{3}}+\frac{4 x}{3}-\frac{\tanh ^{-1}\left(\sqrt{3} x\right)}{3 \sqrt{3}}",1,"(4*x)/3 - Sqrt[-1 + 4*x^2]/3 - ArcTanh[Sqrt[3]*x]/(3*Sqrt[3]) + ArcTanh[Sqrt[3]*Sqrt[-1 + 4*x^2]]/(3*Sqrt[3])","A",8,6,27,0.2222,1,"{6742, 444, 50, 63, 207, 388}"
832,1,195,0,0.2066528,"\int \frac{a+b x+c x^2}{(d+e x)^3 \sqrt{-1+x^2}} \, dx","Int[(a + b*x + c*x^2)/((d + e*x)^3*Sqrt[-1 + x^2]),x]","-\frac{\sqrt{x^2-1} \left(a e^2-b d e+c d^2\right)}{2 e \left(d^2-e^2\right) (d+e x)^2}+\frac{\sqrt{x^2-1} \left(c \left(d^3-4 d e^2\right)-e \left(3 a d e-b \left(d^2+2 e^2\right)\right)\right)}{2 e \left(d^2-e^2\right)^2 (d+e x)}-\frac{\tanh ^{-1}\left(\frac{d x+e}{\sqrt{x^2-1} \sqrt{d^2-e^2}}\right) \left(-a \left(2 d^2+e^2\right)+3 b d e-c \left(d^2+2 e^2\right)\right)}{2 \left(d^2-e^2\right)^{5/2}}","-\frac{\sqrt{x^2-1} \left(a e^2-b d e+c d^2\right)}{2 e \left(d^2-e^2\right) (d+e x)^2}+\frac{\sqrt{x^2-1} \left(c \left(d^3-4 d e^2\right)-e \left(3 a d e-b \left(d^2+2 e^2\right)\right)\right)}{2 e \left(d^2-e^2\right)^2 (d+e x)}-\frac{\tanh ^{-1}\left(\frac{d x+e}{\sqrt{x^2-1} \sqrt{d^2-e^2}}\right) \left(-a \left(2 d^2+e^2\right)+3 b d e-c \left(d^2+2 e^2\right)\right)}{2 \left(d^2-e^2\right)^{5/2}}",1,"-((c*d^2 - b*d*e + a*e^2)*Sqrt[-1 + x^2])/(2*e*(d^2 - e^2)*(d + e*x)^2) + ((c*(d^3 - 4*d*e^2) - e*(3*a*d*e - b*(d^2 + 2*e^2)))*Sqrt[-1 + x^2])/(2*e*(d^2 - e^2)^2*(d + e*x)) - ((3*b*d*e - a*(2*d^2 + e^2) - c*(d^2 + 2*e^2))*ArcTanh[(e + d*x)/(Sqrt[d^2 - e^2]*Sqrt[-1 + x^2])])/(2*(d^2 - e^2)^(5/2))","A",4,4,27,0.1481,1,"{1651, 807, 725, 206}"
833,1,28,0,0.0143167,"\int \frac{1+2 x^8}{x \left(1+x^8\right)^{3/2}} \, dx","Int[(1 + 2*x^8)/(x*(1 + x^8)^(3/2)),x]","-\frac{1}{4 \sqrt{x^8+1}}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)","-\frac{1}{4 \sqrt{x^8+1}}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)",1,"-1/(4*Sqrt[1 + x^8]) - ArcTanh[Sqrt[1 + x^8]]/4","A",4,4,20,0.2000,1,"{446, 78, 63, 207}"
834,1,28,0,0.0583902,"\int \frac{\sqrt{1+x^8} \left(1+2 x^8\right)}{x+2 x^9+x^{17}} \, dx","Int[(Sqrt[1 + x^8]*(1 + 2*x^8))/(x + 2*x^9 + x^17),x]","-\frac{1}{4 \sqrt{x^8+1}}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)","-\frac{1}{4 \sqrt{x^8+1}}-\frac{1}{4} \tanh ^{-1}\left(\sqrt{x^8+1}\right)",1,"-1/(4*Sqrt[1 + x^8]) - ArcTanh[Sqrt[1 + x^8]]/4","A",6,6,29,0.2069,1,"{1586, 1593, 446, 78, 63, 207}"
835,1,22,0,0.0050603,"\int \left(1-9 x^2+\frac{x}{\sqrt{1-9 x^2}}\right) \, dx","Int[1 - 9*x^2 + x/Sqrt[1 - 9*x^2],x]","-3 x^3-\frac{1}{9} \sqrt{1-9 x^2}+x","-3 x^3-\frac{1}{9} \sqrt{1-9 x^2}+x",1,"x - 3*x^3 - Sqrt[1 - 9*x^2]/9","A",2,1,20,0.05000,1,"{261}"
836,1,22,0,0.0820809,"\int \frac{x+\left(1-9 x^2\right)^{3/2}}{\sqrt{1-9 x^2}} \, dx","Int[(x + (1 - 9*x^2)^(3/2))/Sqrt[1 - 9*x^2],x]","-3 x^3-\frac{1}{9} \sqrt{1-9 x^2}+x","-3 x^3-\frac{1}{9} \sqrt{1-9 x^2}+x",1,"x - 3*x^3 - Sqrt[1 - 9*x^2]/9","A",3,2,25,0.08000,1,"{6742, 261}"
837,1,17,0,0.0613476,"\int \frac{\left(-3+2 \sqrt{x}\right) \left(-3 \sqrt{x}+x\right)^{2/3}}{\sqrt{x}} \, dx","Int[((-3 + 2*Sqrt[x])*(-3*Sqrt[x] + x)^(2/3))/Sqrt[x],x]","\frac{6}{5} \left(x-3 \sqrt{x}\right)^{5/3}","\frac{6}{5} \left(x-3 \sqrt{x}\right)^{5/3}",1,"(6*(-3*Sqrt[x] + x)^(5/3))/5","A",2,2,28,0.07143,1,"{2034, 629}"
838,1,17,0,0.0466631,"\int \frac{9-9 \sqrt{x}+2 x}{\sqrt[3]{-3 \sqrt{x}+x}} \, dx","Int[(9 - 9*Sqrt[x] + 2*x)/(-3*Sqrt[x] + x)^(1/3),x]","\frac{6}{5} \left(x-3 \sqrt{x}\right)^{5/3}","\frac{6}{5} \left(x-3 \sqrt{x}\right)^{5/3}",1,"(6*(-3*Sqrt[x] + x)^(5/3))/5","A",3,3,26,0.1154,1,"{2043, 1631, 629}"
839,1,10,0,0.0014107,"\int \frac{1}{\sqrt{4-9 x^2}} \, dx","Int[1/Sqrt[4 - 9*x^2],x]","\frac{1}{3} \sin ^{-1}\left(\frac{3 x}{2}\right)","\frac{1}{3} \sin ^{-1}\left(\frac{3 x}{2}\right)",1,"ArcSin[(3*x)/2]/3","A",1,1,11,0.09091,1,"{216}"
840,1,10,0,0.002131,"\int \frac{1}{\sqrt{2-3 x} \sqrt{2+3 x}} \, dx","Int[1/(Sqrt[2 - 3*x]*Sqrt[2 + 3*x]),x]","\frac{1}{3} \sin ^{-1}\left(\frac{3 x}{2}\right)","\frac{1}{3} \sin ^{-1}\left(\frac{3 x}{2}\right)",1,"ArcSin[(3*x)/2]/3","A",2,2,19,0.1053,1,"{41, 216}"
841,1,10,0,0.0037278,"\int \frac{1}{\sqrt{(2-3 x) (2+3 x)}} \, dx","Int[1/Sqrt[(2 - 3*x)*(2 + 3*x)],x]","\frac{1}{3} \sin ^{-1}\left(\frac{3 x}{2}\right)","\frac{1}{3} \sin ^{-1}\left(\frac{3 x}{2}\right)",1,"ArcSin[(3*x)/2]/3","A",2,2,15,0.1333,1,"{1972, 216}"
842,1,12,0,0.0066258,"\int \frac{1}{\sqrt{15-2 x-x^2}} \, dx","Int[1/Sqrt[15 - 2*x - x^2],x]","-\sin ^{-1}\left(\frac{1}{4} (-x-1)\right)","-\sin ^{-1}\left(\frac{1}{4} (-x-1)\right)",1,"-ArcSin[(-1 - x)/4]","A",2,2,14,0.1429,1,"{619, 216}"
843,1,12,0,0.0074626,"\int \frac{1}{\sqrt{3-x} \sqrt{5+x}} \, dx","Int[1/(Sqrt[3 - x]*Sqrt[5 + x]),x]","-\sin ^{-1}\left(\frac{1}{4} (-x-1)\right)","-\sin ^{-1}\left(\frac{1}{4} (-x-1)\right)",1,"-ArcSin[(-1 - x)/4]","A",3,3,17,0.1765,1,"{53, 619, 216}"
844,1,12,0,0.008832,"\int \frac{1}{\sqrt{(3-x) (5+x)}} \, dx","Int[1/Sqrt[(3 - x)*(5 + x)],x]","-\sin ^{-1}\left(\frac{1}{4} (-x-1)\right)","-\sin ^{-1}\left(\frac{1}{4} (-x-1)\right)",1,"-ArcSin[(-1 - x)/4]","A",3,3,13,0.2308,1,"{1981, 619, 216}"
845,1,4,0,0.0051104,"\int \frac{1}{\sqrt{-15-8 x-x^2}} \, dx","Int[1/Sqrt[-15 - 8*x - x^2],x]","\sin ^{-1}(x+4)","\sin ^{-1}(x+4)",1,"ArcSin[4 + x]","A",2,2,14,0.1429,1,"{619, 216}"
846,1,4,0,0.0059976,"\int \frac{1}{\sqrt{-3-x} \sqrt{5+x}} \, dx","Int[1/(Sqrt[-3 - x]*Sqrt[5 + x]),x]","\sin ^{-1}(x+4)","\sin ^{-1}(x+4)",1,"ArcSin[4 + x]","A",3,3,17,0.1765,1,"{53, 619, 216}"
847,1,4,0,0.0070078,"\int \frac{1}{\sqrt{(-3-x) (5+x)}} \, dx","Int[1/Sqrt[(-3 - x)*(5 + x)],x]","\sin ^{-1}(x+4)","\sin ^{-1}(x+4)",1,"ArcSin[4 + x]","A",3,3,13,0.2308,1,"{1981, 619, 216}"
848,1,11,0,0.0010962,"\int \left(1-\sqrt{x}\right) \, dx","Int[1 - Sqrt[x],x]","x-\frac{2 x^{3/2}}{3}","x-\frac{2 x^{3/2}}{3}",1,"x - (2*x^(3/2))/3","A",1,0,9,0,1,"{}"
849,1,11,0,0.008115,"\int \frac{1-x}{1+\sqrt{x}} \, dx","Int[(1 - x)/(1 + Sqrt[x]),x]","x-\frac{2 x^{3/2}}{3}","x-\frac{2 x^{3/2}}{3}",1,"x - (2*x^(3/2))/3","A",4,3,15,0.2000,1,"{1398, 26, 43}"
850,1,27,0,0.014481,"\int \sqrt{\frac{1}{1-x^2}} \, dx","Int[Sqrt[(1 - x^2)^(-1)],x]","\sqrt{\frac{1}{1-x^2}} \sqrt{1-x^2} \sin ^{-1}(x)","\sqrt{\frac{1}{1-x^2}} \sqrt{1-x^2} \sin ^{-1}(x)",1,"Sqrt[(1 - x^2)^(-1)]*Sqrt[1 - x^2]*ArcSin[x]","A",2,2,13,0.1538,1,"{6720, 216}"
851,1,27,0,0.0206499,"\int \sqrt{\frac{1+x^2}{1-x^4}} \, dx","Int[Sqrt[(1 + x^2)/(1 - x^4)],x]","\sqrt{\frac{1}{1-x^2}} \sqrt{1-x^2} \sin ^{-1}(x)","\sqrt{\frac{1}{1-x^2}} \sqrt{1-x^2} \sin ^{-1}(x)",1,"Sqrt[(1 - x^2)^(-1)]*Sqrt[1 - x^2]*ArcSin[x]","A",3,3,19,0.1579,1,"{6688, 6720, 216}"
852,1,33,0,0.014449,"\int \sqrt{\frac{1}{-1+x^2}} \, dx","Int[Sqrt[(-1 + x^2)^(-1)],x]","\sqrt{\frac{1}{x^2-1}} \sqrt{x^2-1} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)","\sqrt{1-x^2} \sqrt{\frac{1}{x^2-1}} \sin ^{-1}(x)",1,"Sqrt[(-1 + x^2)^(-1)]*Sqrt[-1 + x^2]*ArcTanh[x/Sqrt[-1 + x^2]]","A",3,3,11,0.2727,1,"{6720, 217, 206}"
853,1,33,0,0.0216021,"\int \sqrt{\frac{1+x^2}{-1+x^4}} \, dx","Int[Sqrt[(1 + x^2)/(-1 + x^4)],x]","\sqrt{\frac{1}{x^2-1}} \sqrt{x^2-1} \tanh ^{-1}\left(\frac{x}{\sqrt{x^2-1}}\right)","\sqrt{1-x^2} \sqrt{\frac{1}{x^2-1}} \sin ^{-1}(x)",1,"Sqrt[(-1 + x^2)^(-1)]*Sqrt[-1 + x^2]*ArcTanh[x/Sqrt[-1 + x^2]]","A",4,4,17,0.2353,1,"{6688, 6720, 217, 206}"
854,1,11,0,0.0009113,"\int \frac{1}{\sqrt{1-x}} \, dx","Int[1/Sqrt[1 - x],x]","-2 \sqrt{1-x}","-2 \sqrt{1-x}",1,"-2*Sqrt[1 - x]","A",1,1,9,0.1111,1,"{32}"
855,1,11,0,0.001246,"\int \frac{\sqrt{1+x}}{\sqrt{1-x^2}} \, dx","Int[Sqrt[1 + x]/Sqrt[1 - x^2],x]","-2 \sqrt{1-x}","-2 \sqrt{1-x}",1,"-2*Sqrt[1 - x]","A",2,2,19,0.1053,1,"{26, 32}"
856,1,9,0,0.0007305,"\int \frac{1}{\sqrt{1+x}} \, dx","Int[1/Sqrt[1 + x],x]","2 \sqrt{x+1}","2 \sqrt{x+1}",1,"2*Sqrt[1 + x]","A",1,1,7,0.1429,1,"{32}"
857,1,9,0,0.0011453,"\int \frac{\sqrt{1-x}}{\sqrt{1-x^2}} \, dx","Int[Sqrt[1 - x]/Sqrt[1 - x^2],x]","2 \sqrt{x+1}","2 \sqrt{x+1}",1,"2*Sqrt[1 + x]","A",2,2,21,0.09524,1,"{26, 32}"
858,1,13,0,0.0008786,"\int \sqrt{1-x} \, dx","Int[Sqrt[1 - x],x]","-\frac{2}{3} (1-x)^{3/2}","-\frac{2}{3} (1-x)^{3/2}",1,"(-2*(1 - x)^(3/2))/3","A",1,1,9,0.1111,1,"{32}"
859,1,13,0,0.0013626,"\int \frac{\sqrt{1-x^2}}{\sqrt{1+x}} \, dx","Int[Sqrt[1 - x^2]/Sqrt[1 + x],x]","-\frac{2}{3} (1-x)^{3/2}","-\frac{2}{3} (1-x)^{3/2}",1,"(-2*(1 - x)^(3/2))/3","A",2,2,19,0.1053,1,"{26, 32}"
860,1,11,0,0.0006516,"\int \sqrt{1+x} \, dx","Int[Sqrt[1 + x],x]","\frac{2}{3} (x+1)^{3/2}","\frac{2}{3} (x+1)^{3/2}",1,"(2*(1 + x)^(3/2))/3","A",1,1,7,0.1429,1,"{32}"
861,1,11,0,0.0010932,"\int \frac{\sqrt{1-x^2}}{\sqrt{1-x}} \, dx","Int[Sqrt[1 - x^2]/Sqrt[1 - x],x]","\frac{2}{3} (x+1)^{3/2}","\frac{2}{3} (x+1)^{3/2}",1,"(2*(1 + x)^(3/2))/3","A",2,2,21,0.09524,1,"{26, 32}"
862,1,35,0,0.006951,"\int \frac{\sqrt{2+3 x}}{\sqrt{1+x}} \, dx","Int[Sqrt[2 + 3*x]/Sqrt[1 + x],x]","\sqrt{x+1} \sqrt{3 x+2}-\frac{\sinh ^{-1}\left(\sqrt{3 x+2}\right)}{\sqrt{3}}","\sqrt{x+1} \sqrt{3 x+2}-\frac{\sinh ^{-1}\left(\sqrt{3 x+2}\right)}{\sqrt{3}}",1,"Sqrt[1 + x]*Sqrt[2 + 3*x] - ArcSinh[Sqrt[2 + 3*x]]/Sqrt[3]","A",3,3,17,0.1765,1,"{50, 54, 215}"
863,1,35,0,0.0066087,"\int \frac{\sqrt{1-x} \sqrt{2+3 x}}{\sqrt{1-x^2}} \, dx","Int[(Sqrt[1 - x]*Sqrt[2 + 3*x])/Sqrt[1 - x^2],x]","\sqrt{x+1} \sqrt{3 x+2}-\frac{\sinh ^{-1}\left(\sqrt{3 x+2}\right)}{\sqrt{3}}","\sqrt{x+1} \sqrt{3 x+2}-\frac{\sinh ^{-1}\left(\sqrt{3 x+2}\right)}{\sqrt{3}}",1,"Sqrt[1 + x]*Sqrt[2 + 3*x] - ArcSinh[Sqrt[2 + 3*x]]/Sqrt[3]","A",4,4,30,0.1333,1,"{26, 50, 54, 215}"
864,1,43,0,0.0129731,"\int \frac{(1+x)^{3/2}}{(1-x)^{3/2} x} \, dx","Int[(1 + x)^(3/2)/((1 - x)^(3/2)*x),x]","\frac{4 \sqrt{x+1}}{\sqrt{1-x}}-\sin ^{-1}(x)-\tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)","\frac{4 \sqrt{x+1}}{\sqrt{1-x}}-\sin ^{-1}(x)-\tanh ^{-1}\left(\sqrt{1-x} \sqrt{x+1}\right)",1,"(4*Sqrt[1 + x])/Sqrt[1 - x] - ArcSin[x] - ArcTanh[Sqrt[1 - x]*Sqrt[1 + x]]","A",7,7,20,0.3500,1,"{98, 21, 105, 41, 216, 92, 206}"
865,1,35,0,0.0606364,"\int \frac{(1+x)^3}{x \left(1-x^2\right)^{3/2}} \, dx","Int[(1 + x)^3/(x*(1 - x^2)^(3/2)),x]","\frac{4 (x+1)}{\sqrt{1-x^2}}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)-\sin ^{-1}(x)","\frac{4 (x+1)}{\sqrt{1-x^2}}-\tanh ^{-1}\left(\sqrt{1-x^2}\right)-\sin ^{-1}(x)",1,"(4*(1 + x))/Sqrt[1 - x^2] - ArcSin[x] - ArcTanh[Sqrt[1 - x^2]]","A",6,6,20,0.3000,1,"{1805, 844, 216, 266, 63, 206}"
866,1,51,0,0.0236908,"\int \frac{(1+a x)^{3/2}}{x (1-a x)^{3/2}} \, dx","Int[(1 + a*x)^(3/2)/(x*(1 - a*x)^(3/2)),x]","\frac{4 \sqrt{a x+1}}{\sqrt{1-a x}}-\sin ^{-1}(a x)-\tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)","\frac{4 \sqrt{a x+1}}{\sqrt{1-a x}}-\sin ^{-1}(a x)-\tanh ^{-1}\left(\sqrt{1-a x} \sqrt{a x+1}\right)",1,"(4*Sqrt[1 + a*x])/Sqrt[1 - a*x] - ArcSin[a*x] - ArcTanh[Sqrt[1 - a*x]*Sqrt[1 + a*x]]","A",7,7,23,0.3043,1,"{98, 21, 105, 41, 216, 92, 208}"
867,1,45,0,0.0910878,"\int \frac{(1+a x)^3}{x \left(1-a^2 x^2\right)^{3/2}} \, dx","Int[(1 + a*x)^3/(x*(1 - a^2*x^2)^(3/2)),x]","\frac{4 (a x+1)}{\sqrt{1-a^2 x^2}}-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\sin ^{-1}(a x)","\frac{4 (a x+1)}{\sqrt{1-a^2 x^2}}-\tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)-\sin ^{-1}(a x)",1,"(4*(1 + a*x))/Sqrt[1 - a^2*x^2] - ArcSin[a*x] - ArcTanh[Sqrt[1 - a^2*x^2]]","A",6,6,25,0.2400,1,"{1805, 844, 216, 266, 63, 208}"
868,1,2,0,0.0010183,"\int \frac{1}{\sqrt{1-x^2}} \, dx","Int[1/Sqrt[1 - x^2],x]","\sin ^{-1}(x)","\sin ^{-1}(x)",1,"ArcSin[x]","A",1,1,11,0.09091,1,"{216}"
869,1,2,0,0.0013687,"\int \frac{\sqrt{1+x^2}}{\sqrt{1-x^4}} \, dx","Int[Sqrt[1 + x^2]/Sqrt[1 - x^4],x]","\sin ^{-1}(x)","\sin ^{-1}(x)",1,"ArcSin[x]","A",2,2,21,0.09524,1,"{26, 216}"
870,1,2,0,0.0007175,"\int \frac{1}{\sqrt{1+x^2}} \, dx","Int[1/Sqrt[1 + x^2],x]","\sinh ^{-1}(x)","\sinh ^{-1}(x)",1,"ArcSinh[x]","A",1,1,9,0.1111,1,"{215}"
871,1,2,0,0.0011891,"\int \frac{\sqrt{1-x^2}}{\sqrt{1-x^4}} \, dx","Int[Sqrt[1 - x^2]/Sqrt[1 - x^4],x]","\sinh ^{-1}(x)","\sinh ^{-1}(x)",1,"ArcSinh[x]","A",2,2,23,0.08696,1,"{26, 215}"
872,1,23,0,0.0026651,"\int \sqrt{1-x^2} \, dx","Int[Sqrt[1 - x^2],x]","\frac{1}{2} \sqrt{1-x^2} x+\frac{1}{2} \sin ^{-1}(x)","\frac{1}{2} \sqrt{1-x^2} x+\frac{1}{2} \sin ^{-1}(x)",1,"(x*Sqrt[1 - x^2])/2 + ArcSin[x]/2","A",2,2,11,0.1818,1,"{195, 216}"
873,1,23,0,0.0030979,"\int \frac{\sqrt{1-x^4}}{\sqrt{1+x^2}} \, dx","Int[Sqrt[1 - x^4]/Sqrt[1 + x^2],x]","\frac{1}{2} \sqrt{1-x^2} x+\frac{1}{2} \sin ^{-1}(x)","\frac{1}{2} \sqrt{1-x^2} x+\frac{1}{2} \sin ^{-1}(x)",1,"(x*Sqrt[1 - x^2])/2 + ArcSin[x]/2","A",3,3,21,0.1429,1,"{26, 195, 216}"
874,1,21,0,0.0020896,"\int \sqrt{1+x^2} \, dx","Int[Sqrt[1 + x^2],x]","\frac{1}{2} \sqrt{x^2+1} x+\frac{1}{2} \sinh ^{-1}(x)","\frac{1}{2} \sqrt{x^2+1} x+\frac{1}{2} \sinh ^{-1}(x)",1,"(x*Sqrt[1 + x^2])/2 + ArcSinh[x]/2","A",2,2,9,0.2222,1,"{195, 215}"
875,1,21,0,0.0025367,"\int \frac{\sqrt{1-x^4}}{\sqrt{1-x^2}} \, dx","Int[Sqrt[1 - x^4]/Sqrt[1 - x^2],x]","\frac{1}{2} \sqrt{x^2+1} x+\frac{1}{2} \sinh ^{-1}(x)","\frac{1}{2} \sqrt{x^2+1} x+\frac{1}{2} \sinh ^{-1}(x)",1,"(x*Sqrt[1 + x^2])/2 + ArcSinh[x]/2","A",3,3,23,0.1304,1,"{26, 195, 215}"
876,1,57,0,0.0167575,"\int \left(\frac{a+b+c x^2}{d}\right)^m \, dx","Int[((a + b + c*x^2)/d)^m,x]","x \left(\frac{c x^2}{a+b}+1\right)^{-m} \left(\frac{a+b}{d}+\frac{c x^2}{d}\right)^m \, _2F_1\left(\frac{1}{2},-m;\frac{3}{2};-\frac{c x^2}{a+b}\right)","\frac{d x \left(\frac{a+b}{d}+\frac{c x^2}{d}\right)^{m+1} \, _2F_1\left(1,m+\frac{3}{2};\frac{3}{2};-\frac{c x^2}{a+b}\right)}{a+b}",1,"(x*((a + b)/d + (c*x^2)/d)^m*Hypergeometric2F1[1/2, -m, 3/2, -((c*x^2)/(a + b))])/(1 + (c*x^2)/(a + b))^m","A",3,3,14,0.2143,1,"{1972, 246, 245}"
877,1,28,0,0.0091935,"\int \frac{1}{x-\sqrt{1+x^2}} \, dx","Int[(x - Sqrt[1 + x^2])^(-1),x]","-\frac{x^2}{2}-\frac{1}{2} \sqrt{x^2+1} x-\frac{1}{2} \sinh ^{-1}(x)","-\frac{x^2}{2}-\frac{1}{2} \sqrt{x^2+1} x-\frac{1}{2} \sinh ^{-1}(x)",1,"-x^2/2 - (x*Sqrt[1 + x^2])/2 - ArcSinh[x]/2","A",4,4,15,0.2667,1,"{2106, 30, 195, 215}"
878,1,37,0,0.0418386,"\int \frac{1}{x-\sqrt{1-x^2}} \, dx","Int[(x - Sqrt[1 - x^2])^(-1),x]","\frac{1}{4} \log \left(1-2 x^2\right)-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right)-\frac{1}{2} \sin ^{-1}(x)","\frac{1}{4} \log \left(1-2 x^2\right)-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{1-x^2}}\right)-\frac{1}{2} \sin ^{-1}(x)",1,"-ArcSin[x]/2 - ArcTanh[x/Sqrt[1 - x^2]]/2 + Log[1 - 2*x^2]/4","A",7,6,17,0.3529,1,"{6742, 260, 402, 216, 377, 207}"
879,1,40,0,0.0429,"\int \frac{1}{x-\sqrt{1+2 x^2}} \, dx","Int[(x - Sqrt[1 + 2*x^2])^(-1),x]","-\frac{1}{2} \log \left(x^2+1\right)+\tanh ^{-1}\left(\frac{x}{\sqrt{2 x^2+1}}\right)-\sqrt{2} \sinh ^{-1}\left(\sqrt{2} x\right)","-\frac{1}{2} \log \left(x^2+1\right)+\tanh ^{-1}\left(\frac{x}{\sqrt{2 x^2+1}}\right)-\sqrt{2} \sinh ^{-1}\left(\sqrt{2} x\right)",1,"-(Sqrt[2]*ArcSinh[Sqrt[2]*x]) + ArcTanh[x/Sqrt[1 + 2*x^2]] - Log[1 + x^2]/2","A",7,6,17,0.3529,1,"{6742, 260, 402, 215, 377, 206}"
880,1,54,0,0.1282396,"\int \frac{2 x-x^3+x^2 \sqrt{2-x^2}}{-2+2 x^2} \, dx","Int[(2*x - x^3 + x^2*Sqrt[2 - x^2])/(-2 + 2*x^2),x]","-\frac{x^2}{4}+\frac{1}{4} \sqrt{2-x^2} x+\frac{1}{4} \log \left(1-x^2\right)-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{2-x^2}}\right)","-\frac{x^2}{4}+\frac{1}{4} \sqrt{2-x^2} x+\frac{1}{4} \log \left(1-x^2\right)-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{2-x^2}}\right)",1,"-x^2/4 + (x*Sqrt[2 - x^2])/4 - ArcTanh[x/Sqrt[2 - x^2]]/2 + Log[1 - x^2]/4","A",10,8,34,0.2353,1,"{6725, 260, 266, 43, 478, 12, 377, 207}"
881,1,60,0,0.2995839,"\int \frac{x \sqrt{2-x^2}}{x-\sqrt{2-x^2}} \, dx","Int[(x*Sqrt[2 - x^2])/(x - Sqrt[2 - x^2]),x]","-\frac{x^2}{4}+\frac{1}{4} \sqrt{2-x^2} x-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{2-x^2}}\right)+\frac{1}{4} \log (1-x)+\frac{1}{4} \log (x+1)","-\frac{x^2}{4}+\frac{1}{4} \sqrt{2-x^2} x-\frac{1}{2} \tanh ^{-1}\left(\frac{x}{\sqrt{2-x^2}}\right)+\frac{1}{4} \log (1-x)+\frac{1}{4} \log (x+1)",1,"-x^2/4 + (x*Sqrt[2 - x^2])/4 - ArcTanh[x/Sqrt[2 - x^2]]/2 + Log[1 - x]/4 + Log[1 + x]/4","A",12,7,30,0.2333,1,"{6742, 195, 216, 697, 402, 377, 207}"
882,1,51,0,0.1111843,"\int \frac{x}{-x+\sqrt{2 x-x^2}} \, dx","Int[x/(-x + Sqrt[2*x - x^2]),x]","-\frac{1}{2} \sqrt{2 x-x^2}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)-\frac{x}{2}-\frac{1}{2} \log (1-x)","-\frac{1}{2} \sqrt{2 x-x^2}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)-\frac{x}{2}-\frac{1}{2} \log (1-x)",1,"-x/2 - Sqrt[2*x - x^2]/2 + ArcTanh[Sqrt[2*x - x^2]]/2 - Log[1 - x]/2","A",5,4,21,0.1905,1,"{6742, 685, 688, 207}"
883,1,51,0,0.0967327,"\int \frac{x+\sqrt{2 x-x^2}}{2-2 x} \, dx","Int[(x + Sqrt[2*x - x^2])/(2 - 2*x),x]","-\frac{1}{2} \sqrt{2 x-x^2}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)-\frac{x}{2}-\frac{1}{2} \log (1-x)","-\frac{1}{2} \sqrt{2 x-x^2}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)-\frac{x}{2}-\frac{1}{2} \log (1-x)",1,"-x/2 - Sqrt[2*x - x^2]/2 + ArcTanh[Sqrt[2*x - x^2]]/2 - Log[1 - x]/2","A",7,5,23,0.2174,1,"{6742, 43, 685, 688, 207}"
884,1,51,0,0.1478196,"\int \frac{\sqrt{2-x} \sqrt{x}+x}{2-2 x} \, dx","Int[(Sqrt[2 - x]*Sqrt[x] + x)/(2 - 2*x),x]","-\frac{1}{2} \sqrt{2 x-x^2}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)-\frac{x}{2}-\frac{1}{2} \log (1-x)","-\frac{1}{2} \sqrt{2 x-x^2}+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2 x-x^2}\right)-\frac{x}{2}-\frac{1}{2} \log (1-x)",1,"-x/2 - Sqrt[2*x - x^2]/2 + ArcTanh[Sqrt[2*x - x^2]]/2 - Log[1 - x]/2","A",9,7,25,0.2800,1,"{6688, 2115, 6742, 43, 685, 688, 207}"
885,1,54,0,0.0491659,"\int \frac{\sqrt{x}}{\sqrt{2-x}-\sqrt{x}} \, dx","Int[Sqrt[x]/(Sqrt[2 - x] - Sqrt[x]),x]","-\frac{x}{2}-\frac{1}{2} \sqrt{2-x} \sqrt{x}-\frac{1}{2} \log (1-x)+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2-x} \sqrt{x}\right)","-\frac{x}{2}-\frac{1}{2} \sqrt{2-x} \sqrt{x}-\frac{1}{2} \log (1-x)+\frac{1}{2} \tanh ^{-1}\left(\sqrt{2-x} \sqrt{x}\right)",1,"-(Sqrt[2 - x]*Sqrt[x])/2 - x/2 + ArcTanh[Sqrt[2 - x]*Sqrt[x]]/2 - Log[1 - x]/2","A",7,6,25,0.2400,1,"{2105, 101, 12, 92, 206, 43}"
886,1,27,0,0.0298237,"\int \frac{1}{\left((1+x) \left(-1+x^2\right)\right)^{2/3}} \, dx","Int[((1 + x)*(-1 + x^2))^(-2/3),x]","-\frac{3 (1-x) (x+1)}{2 \left(x^3+x^2-x-1\right)^{2/3}}","-\frac{3 \left(1-x^2\right)}{2 \left(-(x+1) \left(1-x^2\right)\right)^{2/3}}",1,"(-3*(1 - x)*(1 + x))/(2*(-1 - x + x^2 + x^3)^(2/3))","A",3,3,13,0.2308,1,"{2067, 2064, 37}"
887,1,14,0,0.1494412,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x \left(1+x^2\right)}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[x*(1 + x^2)]),x]","-\frac{2 x}{\sqrt{x \left(x^2+1\right)}}","-\frac{2 x}{\sqrt{x \left(x^2+1\right)}}",1,"(-2*x)/Sqrt[x*(1 + x^2)]","A",2,2,24,0.08333,1,"{6719, 449}"
888,1,12,0,0.0701814,"\int \frac{-1+x^2}{\left(1+x^2\right) \sqrt{x+x^3}} \, dx","Int[(-1 + x^2)/((1 + x^2)*Sqrt[x + x^3]),x]","-\frac{2 x}{\sqrt{x^3+x}}","-\frac{2 x}{\sqrt{x^3+x}}",1,"(-2*x)/Sqrt[x + x^3]","A",2,2,22,0.09091,1,"{2056, 449}"
889,1,36,0,0.1399779,"\int \frac{\sqrt{\frac{\left(-1+x^2\right)^2}{x \left(1+x^2\right)}}}{1+x^2} \, dx","Int[Sqrt[(-1 + x^2)^2/(x*(1 + x^2))]/(1 + x^2),x]","\frac{2 x \sqrt{\frac{\left(1-x^2\right)^2}{x \left(x^2+1\right)}}}{1-x^2}","\frac{2 x \sqrt{\frac{\left(1-x^2\right)^2}{x \left(x^2+1\right)}}}{1-x^2}",1,"(2*x*Sqrt[(1 - x^2)^2/(x*(1 + x^2))])/(1 - x^2)","A",2,2,30,0.06667,1,"{6718, 449}"
890,1,33,0,0.1925762,"\int \frac{\sqrt{\frac{\left(-1+x^2\right)^2}{x+x^3}}}{1+x^2} \, dx","Int[Sqrt[(-1 + x^2)^2/(x + x^3)]/(1 + x^2),x]","\frac{2 x \sqrt{\frac{\left(1-x^2\right)^2}{x^3+x}}}{1-x^2}","\frac{2 x \sqrt{\frac{\left(1-x^2\right)^2}{x^3+x}}}{1-x^2}",1,"(2*x*Sqrt[(1 - x^2)^2/(x + x^3)])/(1 - x^2)","A",3,3,27,0.1111,1,"{6719, 2056, 449}"
891,1,70,0,0.0681262,"\int \frac{1}{\sqrt{a+\frac{b}{x^2}} \sqrt{c+d x^2}} \, dx","Int[1/(Sqrt[a + b/x^2]*Sqrt[c + d*x^2]),x]","\frac{\sqrt{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a x^2+b}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} \sqrt{d} x \sqrt{a+\frac{b}{x^2}}}","\frac{\sqrt{a x^2+b} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a x^2+b}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} \sqrt{d} x \sqrt{a+\frac{b}{x^2}}}",1,"(Sqrt[b + a*x^2]*ArcTanh[(Sqrt[d]*Sqrt[b + a*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/(Sqrt[a]*Sqrt[d]*Sqrt[a + b/x^2]*x)","A",5,5,23,0.2174,1,"{435, 444, 63, 217, 206}"
892,1,83,0,0.1540271,"\int \frac{\sqrt{-2 x^2+x^4}}{\left(-1+x^2\right) \left(2+x^2\right)} \, dx","Int[Sqrt[-2*x^2 + x^4]/((-1 + x^2)*(2 + x^2)),x]","\frac{2 \sqrt{x^4-2 x^2} \tan ^{-1}\left(\frac{\sqrt{x^2-2}}{2}\right)}{3 x \sqrt{x^2-2}}-\frac{\sqrt{x^4-2 x^2} \tan ^{-1}\left(\sqrt{x^2-2}\right)}{3 x \sqrt{x^2-2}}","\frac{2 \sqrt{x^4-2 x^2} \tan ^{-1}\left(\frac{\sqrt{x^2-2}}{2}\right)}{3 x \sqrt{x^2-2}}-\frac{\sqrt{x^4-2 x^2} \tan ^{-1}\left(\sqrt{x^2-2}\right)}{3 x \sqrt{x^2-2}}",1,"(2*Sqrt[-2*x^2 + x^4]*ArcTan[Sqrt[-2 + x^2]/2])/(3*x*Sqrt[-2 + x^2]) - (Sqrt[-2*x^2 + x^4]*ArcTan[Sqrt[-2 + x^2]])/(3*x*Sqrt[-2 + x^2])","A",7,5,28,0.1786,1,"{2056, 571, 83, 63, 203}"
893,1,73,0,0.4603364,"\int \frac{\sqrt{1-\frac{1}{\left(-1+x^2\right)^2}}}{2-x^2} \, dx","Int[Sqrt[1 - (-1 + x^2)^(-2)]/(2 - x^2),x]","\frac{\left(1-x^2\right) \sqrt{x^4-2 x^2} \sqrt{1-\frac{1}{\left(1-x^2\right)^2}} \tan ^{-1}\left(\sqrt{x^2-2}\right)}{x \sqrt{x^2-2} \sqrt{\left(x^2-1\right)^2-1}}","\frac{\left(1-x^2\right) \sqrt{1-\frac{1}{\left(1-x^2\right)^2}} \tan ^{-1}\left(\sqrt{x^2-2}\right)}{x \sqrt{x^2-2}}",1,"((1 - x^2)*Sqrt[-2*x^2 + x^4]*Sqrt[1 - (1 - x^2)^(-2)]*ArcTan[Sqrt[-2 + x^2]])/(x*Sqrt[-2 + x^2]*Sqrt[-1 + (-1 + x^2)^2])","A",13,10,25,0.4000,1,"{6722, 6725, 1990, 1146, 21, 261, 444, 50, 63, 203}"
894,1,123,0,0.2856721,"\int \frac{\sqrt{\frac{-2 x^2+x^4}{\left(-1+x^2\right)^2}}}{2+x^2} \, dx","Int[Sqrt[(-2*x^2 + x^4)/(-1 + x^2)^2]/(2 + x^2),x]","\frac{\left(1-x^2\right) \sqrt{-\frac{2 x^2-x^4}{\left(1-x^2\right)^2}} \tan ^{-1}\left(\sqrt{x^2-2}\right)}{3 x \sqrt{x^2-2}}-\frac{2 \left(1-x^2\right) \sqrt{-\frac{2 x^2-x^4}{\left(1-x^2\right)^2}} \tan ^{-1}\left(\frac{\sqrt{x^2-2}}{2}\right)}{3 x \sqrt{x^2-2}}","\frac{\left(1-x^2\right) \sqrt{-\frac{2 x^2-x^4}{\left(1-x^2\right)^2}} \tan ^{-1}\left(\sqrt{x^2-2}\right)}{3 x \sqrt{x^2-2}}-\frac{2 \left(1-x^2\right) \sqrt{-\frac{2 x^2-x^4}{\left(1-x^2\right)^2}} \tan ^{-1}\left(\frac{\sqrt{x^2-2}}{2}\right)}{3 x \sqrt{x^2-2}}",1,"(-2*(1 - x^2)*Sqrt[-((2*x^2 - x^4)/(1 - x^2)^2)]*ArcTan[Sqrt[-2 + x^2]/2])/(3*x*Sqrt[-2 + x^2]) + ((1 - x^2)*Sqrt[-((2*x^2 - x^4)/(1 - x^2)^2)]*ArcTan[Sqrt[-2 + x^2]])/(3*x*Sqrt[-2 + x^2])","A",8,6,29,0.2069,1,"{6719, 2056, 571, 83, 63, 203}"
895,1,133,0,0.0737738,"\int \left(1+\frac{2 x}{1+x^2}\right)^{5/2} \, dx","Int[(1 + (2*x)/(1 + x^2))^(5/2),x]","-\frac{(1-x) \sqrt{\frac{2 x}{x^2+1}+1} (x+1)^3}{3 \left(x^2+1\right)}-\frac{4}{3} (1-2 x) \sqrt{\frac{2 x}{x^2+1}+1} (x+1)-\frac{(3 x+4) \left(x^2+1\right) \sqrt{\frac{2 x}{x^2+1}+1}}{x+1}+\frac{5 \sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1} \sinh ^{-1}(x)}{x+1}","-\frac{(1-x) \sqrt{\frac{2 x}{x^2+1}+1} (x+1)^3}{3 \left(x^2+1\right)}-\frac{4}{3} (1-2 x) \sqrt{\frac{2 x}{x^2+1}+1} (x+1)-\frac{(3 x+4) \left(x^2+1\right) \sqrt{\frac{2 x}{x^2+1}+1}}{x+1}+\frac{5 \sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1} \sinh ^{-1}(x)}{x+1}",1,"(-4*(1 - 2*x)*(1 + x)*Sqrt[1 + (2*x)/(1 + x^2)])/3 - ((1 - x)*(1 + x)^3*Sqrt[1 + (2*x)/(1 + x^2)])/(3*(1 + x^2)) - ((4 + 3*x)*(1 + x^2)*Sqrt[1 + (2*x)/(1 + x^2)])/(1 + x) + (5*Sqrt[1 + x^2]*Sqrt[1 + (2*x)/(1 + x^2)]*ArcSinh[x])/(1 + x)","A",6,6,16,0.3750,1,"{6723, 970, 739, 819, 780, 215}"
896,1,90,0,0.0478881,"\int \left(1+\frac{2 x}{1+x^2}\right)^{3/2} \, dx","Int[(1 + (2*x)/(1 + x^2))^(3/2),x]","-(1-x) \sqrt{\frac{2 x}{x^2+1}+1} (x+1)-\frac{x \left(x^2+1\right) \sqrt{\frac{2 x}{x^2+1}+1}}{x+1}+\frac{3 \sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1} \sinh ^{-1}(x)}{x+1}","-(1-x) \sqrt{\frac{2 x}{x^2+1}+1} (x+1)-\frac{x \left(x^2+1\right) \sqrt{\frac{2 x}{x^2+1}+1}}{x+1}+\frac{3 \sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1} \sinh ^{-1}(x)}{x+1}",1,"-((1 - x)*(1 + x)*Sqrt[1 + (2*x)/(1 + x^2)]) - (x*(1 + x^2)*Sqrt[1 + (2*x)/(1 + x^2)])/(1 + x) + (3*Sqrt[1 + x^2]*Sqrt[1 + (2*x)/(1 + x^2)]*ArcSinh[x])/(1 + x)","A",6,6,16,0.3750,1,"{6723, 970, 739, 517, 388, 215}"
897,1,61,0,0.0302999,"\int \sqrt{1+\frac{2 x}{1+x^2}} \, dx","Int[Sqrt[1 + (2*x)/(1 + x^2)],x]","\frac{\sqrt{\frac{2 x}{x^2+1}+1} \left(x^2+1\right)}{x+1}+\frac{\sqrt{\frac{2 x}{x^2+1}+1} \sqrt{x^2+1} \sinh ^{-1}(x)}{x+1}","\frac{\sqrt{\frac{2 x}{x^2+1}+1} \left(x^2+1\right)}{x+1}+\frac{\sqrt{\frac{2 x}{x^2+1}+1} \sqrt{x^2+1} \sinh ^{-1}(x)}{x+1}",1,"((1 + x^2)*Sqrt[1 + (2*x)/(1 + x^2)])/(1 + x) + (Sqrt[1 + x^2]*Sqrt[1 + (2*x)/(1 + x^2)]*ArcSinh[x])/(1 + x)","A",4,4,16,0.2500,1,"{6723, 970, 641, 215}"
898,1,109,0,0.0648028,"\int \frac{1}{\sqrt{1+\frac{2 x}{1+x^2}}} \, dx","Int[1/Sqrt[1 + (2*x)/(1 + x^2)],x]","\frac{x+1}{\sqrt{\frac{2 x}{x^2+1}+1}}-\frac{(x+1) \sinh ^{-1}(x)}{\sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1}}-\frac{\sqrt{2} (x+1) \tanh ^{-1}\left(\frac{1-x}{\sqrt{2} \sqrt{x^2+1}}\right)}{\sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1}}","\frac{x+1}{\sqrt{\frac{2 x}{x^2+1}+1}}-\frac{(x+1) \sinh ^{-1}(x)}{\sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1}}-\frac{\sqrt{2} (x+1) \tanh ^{-1}\left(\frac{1-x}{\sqrt{2} \sqrt{x^2+1}}\right)}{\sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1}}",1,"(1 + x)/Sqrt[1 + (2*x)/(1 + x^2)] - ((1 + x)*ArcSinh[x])/(Sqrt[1 + x^2]*Sqrt[1 + (2*x)/(1 + x^2)]) - (Sqrt[2]*(1 + x)*ArcTanh[(1 - x)/(Sqrt[2]*Sqrt[1 + x^2])])/(Sqrt[1 + x^2]*Sqrt[1 + (2*x)/(1 + x^2)])","A",7,7,16,0.4375,1,"{6723, 970, 735, 844, 215, 725, 206}"
899,1,144,0,0.0817175,"\int \frac{1}{\left(1+\frac{2 x}{1+x^2}\right)^{3/2}} \, dx","Int[(1 + (2*x)/(1 + x^2))^(-3/2),x]","\frac{3 (x+2)}{2 \sqrt{\frac{2 x}{x^2+1}+1}}-\frac{x^2+1}{2 (x+1) \sqrt{\frac{2 x}{x^2+1}+1}}-\frac{3 (x+1) \sinh ^{-1}(x)}{\sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1}}-\frac{9 (x+1) \tanh ^{-1}\left(\frac{1-x}{\sqrt{2} \sqrt{x^2+1}}\right)}{2 \sqrt{2} \sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1}}","\frac{3 (x+2)}{2 \sqrt{\frac{2 x}{x^2+1}+1}}-\frac{x^2+1}{2 (x+1) \sqrt{\frac{2 x}{x^2+1}+1}}-\frac{3 (x+1) \sinh ^{-1}(x)}{\sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1}}-\frac{9 (x+1) \tanh ^{-1}\left(\frac{1-x}{\sqrt{2} \sqrt{x^2+1}}\right)}{2 \sqrt{2} \sqrt{x^2+1} \sqrt{\frac{2 x}{x^2+1}+1}}",1,"(3*(2 + x))/(2*Sqrt[1 + (2*x)/(1 + x^2)]) - (1 + x^2)/(2*(1 + x)*Sqrt[1 + (2*x)/(1 + x^2)]) - (3*(1 + x)*ArcSinh[x])/(Sqrt[1 + x^2]*Sqrt[1 + (2*x)/(1 + x^2)]) - (9*(1 + x)*ArcTanh[(1 - x)/(Sqrt[2]*Sqrt[1 + x^2])])/(2*Sqrt[2]*Sqrt[1 + x^2]*Sqrt[1 + (2*x)/(1 + x^2)])","A",8,8,16,0.5000,1,"{6723, 970, 733, 813, 844, 215, 725, 206}"
900,1,28,0,0.1160699,"\int \frac{\sqrt{1+\frac{2 x}{1+x^2}}}{1+x^2} \, dx","Int[Sqrt[1 + (2*x)/(1 + x^2)]/(1 + x^2),x]","-\frac{(1-x) \sqrt{\frac{2 x}{x^2+1}+1}}{x+1}","-\frac{(1-x) \sqrt{\frac{2 x}{x^2+1}+1}}{x+1}",1,"-(((1 - x)*Sqrt[1 + (2*x)/(1 + x^2)])/(1 + x))","A",3,3,24,0.1250,1,"{6723, 970, 637}"
901,0,0,0,0.0337432,"\int \sqrt{x-x^2} F(x) \, dx","Int[Sqrt[x - x^2]*F[x],x]","\int \sqrt{x-x^2} F(x) \, dx","\text{Int}\left(\sqrt{x-x^2} F(x),x\right)",0,"Defer[Int][Sqrt[x - x^2]*F[x], x]","A",0,0,0,0,-1,"{}"
902,0,0,0,0.0376719,"\int \frac{F(x)}{\sqrt{x-x^2}} \, dx","Int[F[x]/Sqrt[x - x^2],x]","\int \frac{F(x)}{\sqrt{x-x^2}} \, dx","\text{Int}\left(\frac{F(x)}{\sqrt{x-x^2}},x\right)",0,"Defer[Int][F[x]/Sqrt[x - x^2], x]","A",0,0,0,0,-1,"{}"
903,0,0,0,0.1036571,"\int \sqrt{1-x} \sqrt{x} F(x) \, dx","Int[Sqrt[1 - x]*Sqrt[x]*F[x],x]","\int \sqrt{1-x} \sqrt{x} F(x) \, dx","\text{Int}\left(\sqrt{x-x^2} F(x),x\right)",0,"Defer[Int][Sqrt[x - x^2]*F[x], x]","A",0,0,0,0,-1,"{}"
904,0,0,0,0.1126531,"\int \frac{F(x)}{\sqrt{1-x} \sqrt{x}} \, dx","Int[F[x]/(Sqrt[1 - x]*Sqrt[x]),x]","\int \frac{F(x)}{\sqrt{1-x} \sqrt{x}} \, dx","\text{Int}\left(\frac{F(x)}{\sqrt{x-x^2}},x\right)",0,"Defer[Int][F[x]/Sqrt[x - x^2], x]","A",0,0,0,0,-1,"{}"
905,0,0,0,0.0123544,"\int F\left(\frac{a+b x}{x}\right) \, dx","Int[F[(a + b*x)/x],x]","\int F\left(\frac{a+b x}{x}\right) \, dx","\text{Int}\left(F\left(\frac{a}{x}+b\right),x\right)",0,"Defer[Int][F[b + a/x], x]","A",0,0,0,0,-1,"{}"
906,0,0,0,0.0126367,"\int F\left(\frac{a+b x^2}{x^2}\right) \, dx","Int[F[(a + b*x^2)/x^2],x]","\int F\left(\frac{a+b x^2}{x^2}\right) \, dx","\text{Int}\left(F\left(\frac{a}{x^2}+b\right),x\right)",0,"Defer[Int][F[b + a/x^2], x]","A",0,0,0,0,-1,"{}"
907,0,0,0,0.0078925,"\int F\left(\frac{x}{a+b x}\right) \, dx","Int[F[x/(a + b*x)],x]","\int F\left(\frac{x}{a+b x}\right) \, dx","\text{Int}\left(F\left(\frac{x}{a+b x}\right),x\right)",0,"Defer[Int][F[x/(a + b*x)], x]","A",0,0,0,0,-1,"{}"
908,0,0,0,0.008748,"\int F\left(\frac{x^2}{a+b x^2}\right) \, dx","Int[F[x^2/(a + b*x^2)],x]","\int F\left(\frac{x^2}{a+b x^2}\right) \, dx","\text{Int}\left(F\left(\frac{x^2}{a+b x^2}\right),x\right)",0,"Defer[Int][F[x^2/(a + b*x^2)], x]","A",0,0,0,0,-1,"{}"
909,0,0,0,0.0084059,"\int F\left(\frac{x^2}{(a+b x)^2}\right) \, dx","Int[F[x^2/(a + b*x)^2],x]","\int F\left(\frac{x^2}{(a+b x)^2}\right) \, dx","\text{Int}\left(F\left(\frac{x^2}{(a+b x)^2}\right),x\right)",0,"Defer[Int][F[x^2/(a + b*x)^2], x]","A",0,0,0,0,-1,"{}"
910,0,0,0,0.0089925,"\int F\left(\frac{x^4}{\left(a+b x^2\right)^2}\right) \, dx","Int[F[x^4/(a + b*x^2)^2],x]","\int F\left(\frac{x^4}{\left(a+b x^2\right)^2}\right) \, dx","\text{Int}\left(F\left(\frac{x^4}{\left(a+b x^2\right)^2}\right),x\right)",0,"Defer[Int][F[x^4/(a + b*x^2)^2], x]","A",0,0,0,0,-1,"{}"
911,1,47,0,0.1090798,"\int \frac{\sqrt{b x^2+\sqrt{a+b^2 x^4}}}{\sqrt{a+b^2 x^4}} \, dx","Int[Sqrt[b*x^2 + Sqrt[a + b^2*x^4]]/Sqrt[a + b^2*x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{\sqrt{a+b^2 x^4}+b x^2}}\right)}{\sqrt{2} \sqrt{b}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{\sqrt{a+b^2 x^4}+b x^2}}\right)}{\sqrt{2} \sqrt{b}}",1,"ArcTanh[(Sqrt[2]*Sqrt[b]*x)/Sqrt[b*x^2 + Sqrt[a + b^2*x^4]]]/(Sqrt[2]*Sqrt[b])","A",2,2,37,0.05405,1,"{2132, 206}"
912,1,48,0,0.1080933,"\int \frac{\sqrt{-b x^2+\sqrt{a+b^2 x^4}}}{\sqrt{a+b^2 x^4}} \, dx","Int[Sqrt[-(b*x^2) + Sqrt[a + b^2*x^4]]/Sqrt[a + b^2*x^4],x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{\sqrt{a+b^2 x^4}-b x^2}}\right)}{\sqrt{2} \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2} \sqrt{b} x}{\sqrt{\sqrt{a+b^2 x^4}-b x^2}}\right)}{\sqrt{2} \sqrt{b}}",1,"ArcTan[(Sqrt[2]*Sqrt[b]*x)/Sqrt[-(b*x^2) + Sqrt[a + b^2*x^4]]]/(Sqrt[2]*Sqrt[b])","A",2,2,38,0.05263,1,"{2132, 203}"
913,1,169,0,0.2657676,"\int \frac{\sqrt{2 x^2+\sqrt{3+4 x^4}}}{(c+d x) \sqrt{3+4 x^4}} \, dx","Int[Sqrt[2*x^2 + Sqrt[3 + 4*x^4]]/((c + d*x)*Sqrt[3 + 4*x^4]),x]","\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \tan ^{-1}\left(\frac{\sqrt{3} d+2 i c x}{\sqrt{\sqrt{3}-2 i x^2} \sqrt{-\sqrt{3} d^2+2 i c^2}}\right)}{\sqrt{-\sqrt{3} d^2+2 i c^2}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \tanh ^{-1}\left(\frac{\sqrt{3} d-2 i c x}{\sqrt{\sqrt{3}+2 i x^2} \sqrt{\sqrt{3} d^2+2 i c^2}}\right)}{\sqrt{\sqrt{3} d^2+2 i c^2}}","\frac{\left(\frac{1}{2}-\frac{i}{2}\right) \tan ^{-1}\left(\frac{\sqrt{3} d+2 i c x}{\sqrt{\sqrt{3}-2 i x^2} \sqrt{-\sqrt{3} d^2+2 i c^2}}\right)}{\sqrt{-\sqrt{3} d^2+2 i c^2}}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) \tanh ^{-1}\left(\frac{\sqrt{3} d-2 i c x}{\sqrt{\sqrt{3}+2 i x^2} \sqrt{\sqrt{3} d^2+2 i c^2}}\right)}{\sqrt{\sqrt{3} d^2+2 i c^2}}",1,"((1/2 - I/2)*ArcTan[(Sqrt[3]*d + (2*I)*c*x)/(Sqrt[(2*I)*c^2 - Sqrt[3]*d^2]*Sqrt[Sqrt[3] - (2*I)*x^2])])/Sqrt[(2*I)*c^2 - Sqrt[3]*d^2] - ((1/2 + I/2)*ArcTanh[(Sqrt[3]*d - (2*I)*c*x)/(Sqrt[(2*I)*c^2 + Sqrt[3]*d^2]*Sqrt[Sqrt[3] + (2*I)*x^2])])/Sqrt[(2*I)*c^2 + Sqrt[3]*d^2]","A",5,4,40,0.1000,1,"{2133, 725, 204, 206}"
914,1,268,0,0.3110405,"\int \frac{\sqrt{2 x^2+\sqrt{3+4 x^4}}}{(c+d x)^2 \sqrt{3+4 x^4}} \, dx","Int[Sqrt[2*x^2 + Sqrt[3 + 4*x^4]]/((c + d*x)^2*Sqrt[3 + 4*x^4]),x]","\frac{\left(\frac{1}{2}-\frac{i}{2}\right) d \sqrt{\sqrt{3}-2 i x^2}}{\left(-\sqrt{3} d^2+2 i c^2\right) (c+d x)}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) d \sqrt{\sqrt{3}+2 i x^2}}{\left(\sqrt{3} d^2+2 i c^2\right) (c+d x)}+\frac{(1+i) c \tan ^{-1}\left(\frac{\sqrt{3} d+2 i c x}{\sqrt{\sqrt{3}-2 i x^2} \sqrt{-\sqrt{3} d^2+2 i c^2}}\right)}{\left(-\sqrt{3} d^2+2 i c^2\right)^{3/2}}+\frac{(1-i) c \tanh ^{-1}\left(\frac{\sqrt{3} d-2 i c x}{\sqrt{\sqrt{3}+2 i x^2} \sqrt{\sqrt{3} d^2+2 i c^2}}\right)}{\left(\sqrt{3} d^2+2 i c^2\right)^{3/2}}","\frac{\left(\frac{1}{2}-\frac{i}{2}\right) d \sqrt{\sqrt{3}-2 i x^2}}{\left(-\sqrt{3} d^2+2 i c^2\right) (c+d x)}-\frac{\left(\frac{1}{2}+\frac{i}{2}\right) d \sqrt{\sqrt{3}+2 i x^2}}{\left(\sqrt{3} d^2+2 i c^2\right) (c+d x)}+\frac{(1+i) c \tan ^{-1}\left(\frac{\sqrt{3} d+2 i c x}{\sqrt{\sqrt{3}-2 i x^2} \sqrt{-\sqrt{3} d^2+2 i c^2}}\right)}{\left(-\sqrt{3} d^2+2 i c^2\right)^{3/2}}+\frac{(1-i) c \tanh ^{-1}\left(\frac{\sqrt{3} d-2 i c x}{\sqrt{\sqrt{3}+2 i x^2} \sqrt{\sqrt{3} d^2+2 i c^2}}\right)}{\left(\sqrt{3} d^2+2 i c^2\right)^{3/2}}",1,"((1/2 - I/2)*d*Sqrt[Sqrt[3] - (2*I)*x^2])/(((2*I)*c^2 - Sqrt[3]*d^2)*(c + d*x)) - ((1/2 + I/2)*d*Sqrt[Sqrt[3] + (2*I)*x^2])/(((2*I)*c^2 + Sqrt[3]*d^2)*(c + d*x)) + ((1 + I)*c*ArcTan[(Sqrt[3]*d + (2*I)*c*x)/(Sqrt[(2*I)*c^2 - Sqrt[3]*d^2]*Sqrt[Sqrt[3] - (2*I)*x^2])])/((2*I)*c^2 - Sqrt[3]*d^2)^(3/2) + ((1 - I)*c*ArcTanh[(Sqrt[3]*d - (2*I)*c*x)/(Sqrt[(2*I)*c^2 + Sqrt[3]*d^2]*Sqrt[Sqrt[3] + (2*I)*x^2])])/((2*I)*c^2 + Sqrt[3]*d^2)^(3/2)","A",7,5,40,0.1250,1,"{2133, 731, 725, 204, 206}"
915,1,41,0,0.0451169,"\int \frac{-4+x}{\left(1+\sqrt[3]{x}\right) \sqrt{x}} \, dx","Int[(-4 + x)/((1 + x^(1/3))*Sqrt[x]),x]","\frac{6 x^{7/6}}{7}-\frac{6 x^{5/6}}{5}+2 \sqrt{x}-30 \sqrt[6]{x}+30 \tan ^{-1}\left(\sqrt[6]{x}\right)","\frac{6 x^{7/6}}{7}-\frac{6 x^{5/6}}{5}+2 \sqrt{x}-30 \sqrt[6]{x}+30 \tan ^{-1}\left(\sqrt[6]{x}\right)",1,"-30*x^(1/6) + 2*Sqrt[x] - (6*x^(5/6))/5 + (6*x^(7/6))/7 + 30*ArcTan[x^(1/6)]","A",6,5,18,0.2778,1,"{1840, 1620, 50, 63, 203}"
916,1,26,0,0.0400841,"\int \frac{1+\sqrt{x}}{x^{5/6}+x^{7/6}} \, dx","Int[(1 + Sqrt[x])/(x^(5/6) + x^(7/6)),x]","3 \sqrt[3]{x}-3 \log \left(\sqrt[3]{x}+1\right)+6 \tan ^{-1}\left(\sqrt[6]{x}\right)","3 \sqrt[3]{x}-3 \log \left(\sqrt[3]{x}+1\right)+6 \tan ^{-1}\left(\sqrt[6]{x}\right)",1,"3*x^(1/3) + 6*ArcTan[x^(1/6)] - 3*Log[1 + x^(1/3)]","A",7,6,21,0.2857,1,"{1593, 1819, 1810, 635, 203, 260}"
917,1,42,0,0.1535549,"\int \frac{1+\sqrt{x}}{\left(1+\sqrt[3]{x}\right) \sqrt{x}} \, dx","Int[(1 + Sqrt[x])/((1 + x^(1/3))*Sqrt[x]),x]","\frac{3 x^{2/3}}{2}-3 \sqrt[3]{x}+6 \sqrt[6]{x}+3 \log \left(\sqrt[3]{x}+1\right)-6 \tan ^{-1}\left(\sqrt[6]{x}\right)","\frac{3 x^{2/3}}{2}-3 \sqrt[3]{x}+6 \sqrt[6]{x}+3 \log \left(\sqrt[3]{x}+1\right)-6 \tan ^{-1}\left(\sqrt[6]{x}\right)",1,"6*x^(1/6) - 3*x^(1/3) + (3*x^(2/3))/2 - 6*ArcTan[x^(1/6)] + 3*Log[1 + x^(1/3)]","A",8,6,22,0.2727,1,"{6688, 1593, 1802, 635, 203, 260}"
918,1,20,0,0.0081978,"\int \frac{\sqrt{2+\frac{b}{x^2}}}{b+2 x^2} \, dx","Int[Sqrt[2 + b/x^2]/(b + 2*x^2),x]","-\frac{\text{csch}^{-1}\left(\frac{\sqrt{2} x}{\sqrt{b}}\right)}{\sqrt{b}}","-\frac{\text{csch}^{-1}\left(\frac{\sqrt{2} x}{\sqrt{b}}\right)}{\sqrt{b}}",1,"-(ArcCsch[(Sqrt[2]*x)/Sqrt[b]]/Sqrt[b])","A",3,3,21,0.1429,1,"{25, 335, 215}"
919,1,20,0,0.00904,"\int \frac{\sqrt{2-\frac{b}{x^2}}}{-b+2 x^2} \, dx","Int[Sqrt[2 - b/x^2]/(-b + 2*x^2),x]","-\frac{\csc ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{b}}\right)}{\sqrt{b}}","-\frac{\csc ^{-1}\left(\frac{\sqrt{2} x}{\sqrt{b}}\right)}{\sqrt{b}}",1,"-(ArcCsc[(Sqrt[2]*x)/Sqrt[b]]/Sqrt[b])","A",3,3,24,0.1250,1,"{25, 335, 216}"
920,1,121,0,0.1649573,"\int \frac{\sqrt{a+\frac{c}{x^2}}}{d+e x} \, dx","Int[Sqrt[a + c/x^2]/(d + e*x),x]","-\frac{\sqrt{a d^2+c e^2} \tanh ^{-1}\left(\frac{a d-\frac{c e}{x}}{\sqrt{a+\frac{c}{x^2}} \sqrt{a d^2+c e^2}}\right)}{d e}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c}}{x \sqrt{a+\frac{c}{x^2}}}\right)}{d}+\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{c}{x^2}}}{\sqrt{a}}\right)}{e}","-\frac{\sqrt{a d^2+c e^2} \tanh ^{-1}\left(\frac{a d-\frac{c e}{x}}{\sqrt{a+\frac{c}{x^2}} \sqrt{a d^2+c e^2}}\right)}{d e}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c}}{x \sqrt{a+\frac{c}{x^2}}}\right)}{d}+\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a+\frac{c}{x^2}}}{\sqrt{a}}\right)}{e}",1,"(Sqrt[a]*ArcTanh[Sqrt[a + c/x^2]/Sqrt[a]])/e - (Sqrt[a*d^2 + c*e^2]*ArcTanh[(a*d - (c*e)/x)/(Sqrt[a*d^2 + c*e^2]*Sqrt[a + c/x^2])])/(d*e) - (Sqrt[c]*ArcTanh[Sqrt[c]/(Sqrt[a + c/x^2]*x)])/d","A",11,10,19,0.5263,1,"{1444, 1475, 896, 266, 63, 208, 844, 217, 206, 725}"
921,1,181,0,0.2725935,"\int \frac{\sqrt{a+\frac{c}{x^2}+\frac{b}{x}}}{d+e x} \, dx","Int[Sqrt[a + c/x^2 + b/x]/(d + e*x),x]","-\frac{\sqrt{a d^2-e (b d-c e)} \tanh ^{-1}\left(\frac{2 a d+\frac{b d-2 c e}{x}-b e}{2 \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{a d^2-e (b d-c e)}}\right)}{d e}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+\frac{2 c}{x}}{2 \sqrt{c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{d}+\frac{\sqrt{a} \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{e}","-\frac{\sqrt{a d^2-e (b d-c e)} \tanh ^{-1}\left(\frac{2 a d+\frac{b d-2 c e}{x}-b e}{2 \sqrt{a+\frac{b}{x}+\frac{c}{x^2}} \sqrt{a d^2-e (b d-c e)}}\right)}{d e}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{b+\frac{2 c}{x}}{2 \sqrt{c} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{d}+\frac{\sqrt{a} \tanh ^{-1}\left(\frac{2 a+\frac{b}{x}}{2 \sqrt{a} \sqrt{a+\frac{b}{x}+\frac{c}{x^2}}}\right)}{e}",1,"(Sqrt[a]*ArcTanh[(2*a + b/x)/(2*Sqrt[a]*Sqrt[a + c/x^2 + b/x])])/e - (Sqrt[c]*ArcTanh[(b + (2*c)/x)/(2*Sqrt[c]*Sqrt[a + c/x^2 + b/x])])/d - (Sqrt[a*d^2 - e*(b*d - c*e)]*ArcTanh[(2*a*d - b*e + (b*d - 2*c*e)/x)/(2*Sqrt[a*d^2 - e*(b*d - c*e)]*Sqrt[a + c/x^2 + b/x])])/(d*e)","A",10,7,24,0.2917,1,"{1443, 1474, 895, 724, 206, 843, 621}"
922,1,26,0,0.0063937,"\int \frac{\sqrt[6]{x}+\sqrt[5]{x^3}}{\sqrt{x}} \, dx","Int[(x^(1/6) + (x^3)^(1/5))/Sqrt[x],x]","\frac{3 x^{2/3}}{2}+\frac{10}{11} \sqrt[5]{x^3} \sqrt{x}","\frac{3 x^{2/3}}{2}+\frac{10}{11} \sqrt[5]{x^3} \sqrt{x}",1,"(3*x^(2/3))/2 + (10*Sqrt[x]*(x^3)^(1/5))/11","A",4,3,19,0.1579,1,"{14, 15, 30}"
923,1,26,0,0.0112103,"\int \frac{2+x}{\sqrt{4 x-x^2}} \, dx","Int[(2 + x)/Sqrt[4*x - x^2],x]","-\sqrt{4 x-x^2}-4 \sin ^{-1}\left(1-\frac{x}{2}\right)","-\sqrt{4 x-x^2}-4 \sin ^{-1}\left(1-\frac{x}{2}\right)",1,"-Sqrt[4*x - x^2] - 4*ArcSin[1 - x/2]","A",3,3,17,0.1765,1,"{640, 619, 216}"
924,1,15,0,0.0033134,"\int \frac{3+x}{\sqrt[3]{6 x+x^2}} \, dx","Int[(3 + x)/(6*x + x^2)^(1/3),x]","\frac{3}{4} \left(x^2+6 x\right)^{2/3}","\frac{3}{4} \left(x^2+6 x\right)^{2/3}",1,"(3*(6*x + x^2)^(2/3))/4","A",1,1,15,0.06667,1,"{629}"
925,1,22,0,0.0047028,"\int \frac{4+x}{\left(6 x-x^2\right)^{3/2}} \, dx","Int[(4 + x)/(6*x - x^2)^(3/2),x]","-\frac{12-7 x}{9 \sqrt{6 x-x^2}}","-\frac{12-7 x}{9 \sqrt{6 x-x^2}}",1,"-(12 - 7*x)/(9*Sqrt[6*x - x^2])","A",1,1,17,0.05882,1,"{636}"
926,1,12,0,0.0074974,"\int \frac{1}{(1+x) \sqrt{2 x+x^2}} \, dx","Int[1/((1 + x)*Sqrt[2*x + x^2]),x]","\tan ^{-1}\left(\sqrt{x^2+2 x}\right)","\tan ^{-1}\left(\sqrt{x^2+2 x}\right)",1,"ArcTan[Sqrt[2*x + x^2]]","A",2,2,17,0.1176,1,"{688, 203}"
927,1,12,0,0.0081645,"\int \frac{1}{(1+2 x) \sqrt{x+x^2}} \, dx","Int[1/((1 + 2*x)*Sqrt[x + x^2]),x]","\tan ^{-1}\left(2 \sqrt{x^2+x}\right)","\tan ^{-1}\left(2 \sqrt{x^2+x}\right)",1,"ArcTan[2*Sqrt[x + x^2]]","A",2,2,17,0.1176,1,"{688, 203}"
928,1,15,0,0.0038994,"\int \frac{-1+x}{\sqrt{2 x-x^2}} \, dx","Int[(-1 + x)/Sqrt[2*x - x^2],x]","-\sqrt{2 x-x^2}","-\sqrt{2 x-x^2}",1,"-Sqrt[2*x - x^2]","A",1,1,17,0.05882,1,"{629}"
929,1,54,0,0.039589,"\int \frac{\sqrt{x-x^2}}{1+x} \, dx","Int[Sqrt[x - x^2]/(1 + x),x]","\sqrt{x-x^2}+\sqrt{2} \tan ^{-1}\left(\frac{1-3 x}{2 \sqrt{2} \sqrt{x-x^2}}\right)-\frac{3}{2} \sin ^{-1}(1-2 x)","\sqrt{x-x^2}+\sqrt{2} \tan ^{-1}\left(\frac{1-3 x}{2 \sqrt{2} \sqrt{x-x^2}}\right)-\frac{3}{2} \sin ^{-1}(1-2 x)",1,"Sqrt[x - x^2] - (3*ArcSin[1 - 2*x])/2 + Sqrt[2]*ArcTan[(1 - 3*x)/(2*Sqrt[2]*Sqrt[x - x^2])]","A",6,6,17,0.3529,1,"{734, 843, 619, 216, 724, 204}"
930,1,59,0,0.0685488,"\int \sqrt{\sqrt[4]{x}+x} \, dx","Int[Sqrt[x^(1/4) + x],x]","\frac{2}{3} \sqrt{x+\sqrt[4]{x}} x+\frac{1}{3} \sqrt{x+\sqrt[4]{x}} \sqrt[4]{x}-\frac{1}{3} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x+\sqrt[4]{x}}}\right)","\frac{2}{3} \sqrt{x+\sqrt[4]{x}} x+\frac{1}{3} \sqrt{x+\sqrt[4]{x}} \sqrt[4]{x}-\frac{1}{3} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x+\sqrt[4]{x}}}\right)",1,"(x^(1/4)*Sqrt[x^(1/4) + x])/3 + (2*x*Sqrt[x^(1/4) + x])/3 - ArcTanh[Sqrt[x]/Sqrt[x^(1/4) + x]]/3","A",5,5,11,0.4545,1,"{2004, 2018, 2024, 2029, 206}"
931,1,59,0,0.0515844,"\int \sqrt{x+x^{3/2}} \, dx","Int[Sqrt[x + x^(3/2)],x]","\frac{4 \left(x^{3/2}+x\right)^{3/2}}{7 \sqrt{x}}-\frac{16 \left(x^{3/2}+x\right)^{3/2}}{35 x}+\frac{32 \left(x^{3/2}+x\right)^{3/2}}{105 x^{3/2}}","\frac{4 \left(x^{3/2}+x\right)^{3/2}}{7 \sqrt{x}}-\frac{16 \left(x^{3/2}+x\right)^{3/2}}{35 x}+\frac{32 \left(x^{3/2}+x\right)^{3/2}}{105 x^{3/2}}",1,"(32*(x + x^(3/2))^(3/2))/(105*x^(3/2)) - (16*(x + x^(3/2))^(3/2))/(35*x) + (4*(x + x^(3/2))^(3/2))/(7*Sqrt[x])","A",3,3,11,0.2727,1,"{2002, 2016, 2014}"
932,1,94,0,0.0907418,"\int x \sqrt{x+x^{3/2}} \, dx","Int[x*Sqrt[x + x^(3/2)],x]","\frac{4}{11} \sqrt{x} \left(x^{3/2}+x\right)^{3/2}+\frac{64 \left(x^{3/2}+x\right)^{3/2}}{231 \sqrt{x}}-\frac{256 \left(x^{3/2}+x\right)^{3/2}}{1155 x}+\frac{512 \left(x^{3/2}+x\right)^{3/2}}{3465 x^{3/2}}-\frac{32}{99} \left(x^{3/2}+x\right)^{3/2}","\frac{4}{11} \sqrt{x} \left(x^{3/2}+x\right)^{3/2}+\frac{64 \left(x^{3/2}+x\right)^{3/2}}{231 \sqrt{x}}-\frac{256 \left(x^{3/2}+x\right)^{3/2}}{1155 x}+\frac{512 \left(x^{3/2}+x\right)^{3/2}}{3465 x^{3/2}}-\frac{32}{99} \left(x^{3/2}+x\right)^{3/2}",1,"(-32*(x + x^(3/2))^(3/2))/99 + (512*(x + x^(3/2))^(3/2))/(3465*x^(3/2)) - (256*(x + x^(3/2))^(3/2))/(1155*x) + (64*(x + x^(3/2))^(3/2))/(231*Sqrt[x]) + (4*Sqrt[x]*(x + x^(3/2))^(3/2))/11","A",5,3,13,0.2308,1,"{2016, 2002, 2014}"
933,1,18,0,0.0488586,"\int \left(1-x^2\right) \sqrt{\frac{1}{2-x^2}} \, dx","Int[(1 - x^2)*Sqrt[(2 - x^2)^(-1)],x]","\frac{x}{2 \sqrt{\frac{1}{2-x^2}}}","\frac{x}{2 \sqrt{\frac{1}{2-x^2}}}",1,"x/(2*Sqrt[(2 - x^2)^(-1)])","A",2,2,21,0.09524,1,"{6720, 383}"
934,1,107,0,0.0288431,"\int \sqrt{x^2+x^3-x^4} \, dx","Int[Sqrt[x^2 + x^3 - x^4],x]","-\frac{\sqrt{-x^4+x^3+x^2} (1-2 x)}{8 x}-\frac{\left(-x^2+x+1\right) \sqrt{-x^4+x^3+x^2}}{3 x}-\frac{5 \sqrt{-x^4+x^3+x^2} \sin ^{-1}\left(\frac{1-2 x}{\sqrt{5}}\right)}{16 x \sqrt{-x^2+x+1}}","-\frac{\sqrt{-x^4+x^3+x^2} (1-2 x)}{8 x}-\frac{\left(-x^2+x+1\right) \sqrt{-x^4+x^3+x^2}}{3 x}-\frac{5 \sqrt{-x^4+x^3+x^2} \sin ^{-1}\left(\frac{1-2 x}{\sqrt{5}}\right)}{16 x \sqrt{-x^2+x+1}}",1,"-((1 - 2*x)*Sqrt[x^2 + x^3 - x^4])/(8*x) - ((1 + x - x^2)*Sqrt[x^2 + x^3 - x^4])/(3*x) - (5*Sqrt[x^2 + x^3 - x^4]*ArcSin[(1 - 2*x)/Sqrt[5]])/(16*x*Sqrt[1 + x - x^2])","A",5,5,16,0.3125,1,"{1903, 640, 612, 619, 216}"
935,1,25,0,0.0164506,"\int \frac{1}{\sqrt{\left(a^2+x^2\right)^3}} \, dx","Int[1/Sqrt[(a^2 + x^2)^3],x]","\frac{x \left(a^2+x^2\right)}{a^2 \sqrt{\left(a^2+x^2\right)^3}}","\frac{x \left(a^2+x^2\right)}{a^2 \sqrt{\left(a^2+x^2\right)^3}}",1,"(x*(a^2 + x^2))/(a^2*Sqrt[(a^2 + x^2)^3])","A",2,2,13,0.1538,1,"{6720, 191}"
936,1,42,0,0.0287223,"\int \frac{\sqrt{x}}{1+\sqrt{x}+x} \, dx","Int[Sqrt[x]/(1 + Sqrt[x] + x),x]","2 \sqrt{x}-\log \left(x+\sqrt{x}+1\right)-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt{x}+1}{\sqrt{3}}\right)}{\sqrt{3}}","2 \sqrt{x}-\log \left(x+\sqrt{x}+1\right)-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt{x}+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"2*Sqrt[x] - (2*ArcTan[(1 + 2*Sqrt[x])/Sqrt[3]])/Sqrt[3] - Log[1 + Sqrt[x] + x]","A",6,6,16,0.3750,1,"{1357, 703, 634, 618, 204, 628}"
937,1,32,0,0.023297,"\int \frac{x}{1+\sqrt{x}+x} \, dx","Int[x/(1 + Sqrt[x] + x),x]","x-2 \sqrt{x}+\frac{4 \tan ^{-1}\left(\frac{2 \sqrt{x}+1}{\sqrt{3}}\right)}{\sqrt{3}}","x-2 \sqrt{x}+\frac{4 \tan ^{-1}\left(\frac{2 \sqrt{x}+1}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-2*Sqrt[x] + x + (4*ArcTan[(1 + 2*Sqrt[x])/Sqrt[3]])/Sqrt[3]","A",5,4,12,0.3333,1,"{1357, 701, 618, 204}"
938,1,76,0,0.0225249,"\int \frac{1}{\sqrt{x} \left(1+\sqrt{x}+x\right)^{7/2}} \, dx","Int[1/(Sqrt[x]*(1 + Sqrt[x] + x)^(7/2)),x]","\frac{512 \left(2 \sqrt{x}+1\right)}{405 \sqrt{x+\sqrt{x}+1}}+\frac{64 \left(2 \sqrt{x}+1\right)}{135 \left(x+\sqrt{x}+1\right)^{3/2}}+\frac{4 \left(2 \sqrt{x}+1\right)}{15 \left(x+\sqrt{x}+1\right)^{5/2}}","\frac{512 \left(2 \sqrt{x}+1\right)}{405 \sqrt{x+\sqrt{x}+1}}+\frac{64 \left(2 \sqrt{x}+1\right)}{135 \left(x+\sqrt{x}+1\right)^{3/2}}+\frac{4 \left(2 \sqrt{x}+1\right)}{15 \left(x+\sqrt{x}+1\right)^{5/2}}",1,"(4*(1 + 2*Sqrt[x]))/(15*(1 + Sqrt[x] + x)^(5/2)) + (64*(1 + 2*Sqrt[x]))/(135*(1 + Sqrt[x] + x)^(3/2)) + (512*(1 + 2*Sqrt[x]))/(405*Sqrt[1 + Sqrt[x] + x])","A",4,3,18,0.1667,1,"{1352, 614, 613}"
939,1,46,0,0.0857062,"\int \frac{-1+x}{1+\sqrt{1+x^2}} \, dx","Int[(-1 + x)/(1 + Sqrt[1 + x^2]),x]","\frac{\sqrt{x^2+1}}{x}+\sqrt{x^2+1}-\log \left(\sqrt{x^2+1}+1\right)-\frac{1}{x}-\sinh ^{-1}(x)","\frac{\sqrt{x^2+1}}{x}+\sqrt{x^2+1}-\log \left(\sqrt{x^2+1}+1\right)-\frac{1}{x}-\sinh ^{-1}(x)",1,"-x^(-1) + Sqrt[1 + x^2] + Sqrt[1 + x^2]/x - ArcSinh[x] - Log[1 + Sqrt[1 + x^2]]","A",10,6,17,0.3529,1,"{6742, 277, 215, 1591, 190, 43}"
940,1,20,0,0.0056524,"\int \frac{1}{(1+x)^{2/3} \left(-1+x^2\right)^{2/3}} \, dx","Int[1/((1 + x)^(2/3)*(-1 + x^2)^(2/3)),x]","\frac{3 \sqrt[3]{x^2-1}}{2 (x+1)^{2/3}}","\frac{3 \sqrt[3]{x^2-1}}{2 (x+1)^{2/3}}",1,"(3*(-1 + x^2)^(1/3))/(2*(1 + x)^(2/3))","A",1,1,17,0.05882,1,"{651}"
941,1,36,0,0.0111609,"\int \left(\left(1-x^6\right)^{2/3}+\frac{\left(1-x^6\right)^{2/3}}{x^6}\right) \, dx","Int[(1 - x^6)^(2/3) + (1 - x^6)^(2/3)/x^6,x]","x \, _2F_1\left(-\frac{2}{3},\frac{1}{6};\frac{7}{6};x^6\right)-\frac{\, _2F_1\left(-\frac{5}{6},-\frac{2}{3};\frac{1}{6};x^6\right)}{5 x^5}","\frac{1}{5} x \left(1-x^6\right)^{2/3}-\frac{\left(1-x^6\right)^{2/3}}{5 x^5}",1,"-Hypergeometric2F1[-5/6, -2/3, 1/6, x^6]/(5*x^5) + x*Hypergeometric2F1[-2/3, 1/6, 7/6, x^6]","C",3,2,27,0.07407,1,"{245, 364}"
942,1,15,0,0.0181481,"\int \frac{x^{-1+m} \left(2 a m+b (2 m-n) x^n\right)}{2 \left(a+b x^n\right)^{3/2}} \, dx","Int[(x^(-1 + m)*(2*a*m + b*(2*m - n)*x^n))/(2*(a + b*x^n)^(3/2)),x]","\frac{x^m}{\sqrt{a+b x^n}}","\frac{x^m}{\sqrt{a+b x^n}}",1,"x^m/Sqrt[a + b*x^n]","A",2,2,37,0.05405,1,"{12, 449}"
943,1,53,0,0.0208054,"\int \frac{x-2 x^3}{\sqrt{2+3 x}} \, dx","Int[(x - 2*x^3)/Sqrt[2 + 3*x],x]","-\frac{4}{567} (3 x+2)^{7/2}+\frac{8}{135} (3 x+2)^{5/2}-\frac{10}{81} (3 x+2)^{3/2}-\frac{4}{81} \sqrt{3 x+2}","-\frac{4}{567} (3 x+2)^{7/2}+\frac{8}{135} (3 x+2)^{5/2}-\frac{10}{81} (3 x+2)^{3/2}-\frac{4}{81} \sqrt{3 x+2}",1,"(-4*Sqrt[2 + 3*x])/81 - (10*(2 + 3*x)^(3/2))/81 + (8*(2 + 3*x)^(5/2))/135 - (4*(2 + 3*x)^(7/2))/567","A",3,2,17,0.1176,1,"{1593, 772}"
944,1,31,0,0.0152038,"\int \frac{1}{\sqrt[4]{1+x}+\sqrt{1+x}} \, dx","Int[((1 + x)^(1/4) + Sqrt[1 + x])^(-1),x]","2 \sqrt{x+1}-4 \sqrt[4]{x+1}+4 \log \left(\sqrt[4]{x+1}+1\right)","2 \sqrt{x+1}-4 \sqrt[4]{x+1}+4 \log \left(\sqrt[4]{x+1}+1\right)",1,"-4*(1 + x)^(1/4) + 2*Sqrt[1 + x] + 4*Log[1 + (1 + x)^(1/4)]","A",5,4,17,0.2353,1,"{2012, 1593, 266, 43}"
945,1,11,0,0.0030018,"\int \frac{1+2 x}{\sqrt{x+x^2}} \, dx","Int[(1 + 2*x)/Sqrt[x + x^2],x]","2 \sqrt{x^2+x}","2 \sqrt{x^2+x}",1,"2*Sqrt[x + x^2]","A",1,1,15,0.06667,1,"{629}"
946,1,6,0,0.0024988,"\int \frac{1}{2 \sqrt{x} (1+x)} \, dx","Int[1/(2*Sqrt[x]*(1 + x)),x]","\tan ^{-1}\left(\sqrt{x}\right)","\tan ^{-1}\left(\sqrt{x}\right)",1,"ArcTan[Sqrt[x]]","A",3,3,14,0.2143,1,"{12, 63, 203}"
947,1,20,0,0.0049185,"\int \frac{1}{x \sqrt{6 x-x^2}} \, dx","Int[1/(x*Sqrt[6*x - x^2]),x]","-\frac{\sqrt{6 x-x^2}}{3 x}","-\frac{\sqrt{6 x-x^2}}{3 x}",1,"-Sqrt[6*x - x^2]/(3*x)","A",1,1,17,0.05882,1,"{650}"
948,1,17,0,0.0029993,"\int \left(1+\sqrt{x}\right) \sqrt{x} \, dx","Int[(1 + Sqrt[x])*Sqrt[x],x]","\frac{x^2}{2}+\frac{2 x^{3/2}}{3}","\frac{x^2}{2}+\frac{2 x^{3/2}}{3}",1,"(2*x^(3/2))/3 + x^2/2","A",2,1,13,0.07692,1,"{14}"
949,1,19,0,0.0033615,"\int \frac{1-\sqrt{x}}{\sqrt[3]{x}} \, dx","Int[(1 - Sqrt[x])/x^(1/3),x]","\frac{3 x^{2/3}}{2}-\frac{6 x^{7/6}}{7}","\frac{3 x^{2/3}}{2}-\frac{6 x^{7/6}}{7}",1,"(3*x^(2/3))/2 - (6*x^(7/6))/7","A",2,1,15,0.06667,1,"{14}"
950,1,41,0,0.010337,"\int \frac{\sqrt{x}}{1+\sqrt[3]{x}} \, dx","Int[Sqrt[x]/(1 + x^(1/3)),x]","\frac{6 x^{7/6}}{7}-\frac{6 x^{5/6}}{5}+2 \sqrt{x}-6 \sqrt[6]{x}+6 \tan ^{-1}\left(\sqrt[6]{x}\right)","\frac{6 x^{7/6}}{7}-\frac{6 x^{5/6}}{5}+2 \sqrt{x}-6 \sqrt[6]{x}+6 \tan ^{-1}\left(\sqrt[6]{x}\right)",1,"-6*x^(1/6) + 2*Sqrt[x] - (6*x^(5/6))/5 + (6*x^(7/6))/7 + 6*ArcTan[x^(1/6)]","A",7,4,15,0.2667,1,"{341, 50, 63, 203}"
951,1,67,0,0.0302427,"\int \frac{\sqrt[3]{1+\sqrt{x}}}{x} \, dx","Int[(1 + Sqrt[x])^(1/3)/x,x]","6 \sqrt[3]{\sqrt{x}+1}+3 \log \left(1-\sqrt[3]{\sqrt{x}+1}\right)-\frac{\log (x)}{2}-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\sqrt{x}+1}+1}{\sqrt{3}}\right)","6 \sqrt[3]{\sqrt{x}+1}+3 \log \left(1-\sqrt[3]{\sqrt{x}+1}\right)-\frac{\log (x)}{2}-2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{\sqrt{x}+1}+1}{\sqrt{3}}\right)",1,"6*(1 + Sqrt[x])^(1/3) - 2*Sqrt[3]*ArcTan[(1 + 2*(1 + Sqrt[x])^(1/3))/Sqrt[3]] + 3*Log[1 - (1 + Sqrt[x])^(1/3)] - Log[x]/2","A",6,6,15,0.4000,1,"{266, 50, 57, 618, 204, 31}"
952,1,11,0,0.0011952,"\int \left(1-\sqrt{x}\right) \, dx","Int[1 - Sqrt[x],x]","x-\frac{2 x^{3/2}}{3}","x-\frac{2 x^{3/2}}{3}",1,"x - (2*x^(3/2))/3","A",1,0,9,0,1,"{}"
953,1,11,0,0.0012273,"\int \left(1-\sqrt[4]{x}\right) \, dx","Int[1 - x^(1/4),x]","x-\frac{4 x^{5/4}}{5}","x-\frac{4 x^{5/4}}{5}",1,"x - (4*x^(5/4))/5","A",1,0,9,0,1,"{}"
954,1,11,0,0.0015401,"\int \frac{1-\sqrt{x}}{1+\sqrt[4]{x}} \, dx","Int[(1 - Sqrt[x])/(1 + x^(1/4)),x]","x-\frac{4 x^{5/4}}{5}","x-\frac{4 x^{5/4}}{5}",1,"x - (4*x^(5/4))/5","A",2,1,19,0.05263,1,"{26}"
955,1,61,0,0.0254436,"\int \frac{1}{\sqrt{(a+b x) (c+d x)}} \, dx","Int[1/Sqrt[(a + b*x)*(c + d*x)],x]","\frac{\tanh ^{-1}\left(\frac{a d+b c+2 b d x}{2 \sqrt{b} \sqrt{d} \sqrt{x (a d+b c)+a c+b d x^2}}\right)}{\sqrt{b} \sqrt{d}}","\frac{\tanh ^{-1}\left(\frac{a d+b c+2 b d x}{2 \sqrt{b} \sqrt{d} \sqrt{x (a d+b c)+a c+b d x^2}}\right)}{\sqrt{b} \sqrt{d}}",1,"ArcTanh[(b*c + a*d + 2*b*d*x)/(2*Sqrt[b]*Sqrt[d]*Sqrt[a*c + (b*c + a*d)*x + b*d*x^2])]/(Sqrt[b]*Sqrt[d])","A",3,3,15,0.2000,1,"{1981, 621, 206}"
956,1,65,0,0.0249964,"\int \frac{1}{\sqrt{(a+b x) (c-d x)}} \, dx","Int[1/Sqrt[(a + b*x)*(c - d*x)],x]","-\frac{\tan ^{-1}\left(\frac{-a d+b c-2 b d x}{2 \sqrt{b} \sqrt{d} \sqrt{x (b c-a d)+a c-b d x^2}}\right)}{\sqrt{b} \sqrt{d}}","-\frac{\tan ^{-1}\left(\frac{-a d+b c-2 b d x}{2 \sqrt{b} \sqrt{d} \sqrt{x (b c-a d)+a c-b d x^2}}\right)}{\sqrt{b} \sqrt{d}}",1,"-(ArcTan[(b*c - a*d - 2*b*d*x)/(2*Sqrt[b]*Sqrt[d]*Sqrt[a*c + (b*c - a*d)*x - b*d*x^2])]/(Sqrt[b]*Sqrt[d]))","A",3,3,16,0.1875,1,"{1981, 621, 204}"
957,1,13,0,0.0065155,"\int \frac{1}{\sqrt{x} \left(1-x^2\right)} \, dx","Int[1/(Sqrt[x]*(1 - x^2)),x]","\tan ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}\left(\sqrt{x}\right)","\tan ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}\left(\sqrt{x}\right)",1,"ArcTan[Sqrt[x]] + ArcTanh[Sqrt[x]]","A",4,4,15,0.2667,1,"{329, 212, 206, 203}"
958,1,13,0,0.0106321,"\int \frac{\sqrt{x}}{x-x^3} \, dx","Int[Sqrt[x]/(x - x^3),x]","\tan ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}\left(\sqrt{x}\right)","\tan ^{-1}\left(\sqrt{x}\right)+\tanh ^{-1}\left(\sqrt{x}\right)",1,"ArcTan[Sqrt[x]] + ArcTanh[Sqrt[x]]","A",5,5,15,0.3333,1,"{1584, 329, 212, 206, 203}"
959,1,72,0,0.1037065,"\int \frac{x}{2-\sqrt{3}+\left(1+\sqrt{3}\right) x+x^2} \, dx","Int[x/(2 - Sqrt[3] + (1 + Sqrt[3])*x + x^2),x]","\frac{1}{2} \log \left(x^2+\left(1+\sqrt{3}\right) x-\sqrt{3}+2\right)+\sqrt{\frac{1}{23} \left(13+8 \sqrt{3}\right)} \tanh ^{-1}\left(\frac{2 x+\sqrt{3}+1}{\sqrt{2 \left(3 \sqrt{3}-2\right)}}\right)","\frac{1}{2} \log \left(x^2+\left(1+\sqrt{3}\right) x-\sqrt{3}+2\right)+\sqrt{\frac{1}{23} \left(13+8 \sqrt{3}\right)} \tanh ^{-1}\left(\frac{2 x+\sqrt{3}+1}{\sqrt{2 \left(3 \sqrt{3}-2\right)}}\right)",1,"Sqrt[(13 + 8*Sqrt[3])/23]*ArcTanh[(1 + Sqrt[3] + 2*x)/Sqrt[2*(-2 + 3*Sqrt[3])]] + Log[2 - Sqrt[3] + (1 + Sqrt[3])*x + x^2]/2","A",4,4,25,0.1600,1,"{634, 618, 206, 628}"
960,1,37,0,0.026565,"\int \sqrt{x^2+x^3} \, dx","Int[Sqrt[x^2 + x^3],x]","\frac{2 \left(x^3+x^2\right)^{3/2}}{5 x^2}-\frac{4 \left(x^3+x^2\right)^{3/2}}{15 x^3}","\frac{2 \left(x^3+x^2\right)^{3/2}}{5 x^2}-\frac{4 \left(x^3+x^2\right)^{3/2}}{15 x^3}",1,"(-4*(x^2 + x^3)^(3/2))/(15*x^3) + (2*(x^2 + x^3)^(3/2))/(5*x^2)","A",2,2,11,0.1818,1,"{2002, 2014}"
961,1,12,0,0.0073857,"\int \frac{1}{(1+x) \sqrt{2 x+x^2}} \, dx","Int[1/((1 + x)*Sqrt[2*x + x^2]),x]","\tan ^{-1}\left(\sqrt{x^2+2 x}\right)","\tan ^{-1}\left(\sqrt{x^2+2 x}\right)",1,"ArcTan[Sqrt[2*x + x^2]]","A",2,2,17,0.1176,1,"{688, 203}"
962,1,95,0,0.0541581,"\int \sqrt{1-\sqrt{x}-x} \sqrt{x} \, dx","Int[Sqrt[1 - Sqrt[x] - x]*Sqrt[x],x]","-\frac{1}{2} \sqrt{x} \left(-x-\sqrt{x}+1\right)^{3/2}+\frac{5}{12} \left(-x-\sqrt{x}+1\right)^{3/2}+\frac{9}{32} \left(2 \sqrt{x}+1\right) \sqrt{-x-\sqrt{x}+1}+\frac{45}{64} \sin ^{-1}\left(\frac{2 \sqrt{x}+1}{\sqrt{5}}\right)","-\frac{1}{2} \sqrt{x} \left(-x-\sqrt{x}+1\right)^{3/2}+\frac{5}{12} \left(-x-\sqrt{x}+1\right)^{3/2}+\frac{9}{32} \left(2 \sqrt{x}+1\right) \sqrt{-x-\sqrt{x}+1}+\frac{45}{64} \sin ^{-1}\left(\frac{2 \sqrt{x}+1}{\sqrt{5}}\right)",1,"(9*(1 + 2*Sqrt[x])*Sqrt[1 - Sqrt[x] - x])/32 + (5*(1 - Sqrt[x] - x)^(3/2))/12 - ((1 - Sqrt[x] - x)^(3/2)*Sqrt[x])/2 + (45*ArcSin[(1 + 2*Sqrt[x])/Sqrt[5]])/64","A",6,6,22,0.2727,1,"{1357, 742, 640, 612, 619, 216}"
963,1,35,0,0.0111444,"\int \sqrt[3]{1+\sqrt{-3+x}} \, dx","Int[(1 + Sqrt[-3 + x])^(1/3),x]","\frac{6}{7} \left(\sqrt{x-3}+1\right)^{7/3}-\frac{3}{2} \left(\sqrt{x-3}+1\right)^{4/3}","\frac{6}{7} \left(\sqrt{x-3}+1\right)^{7/3}-\frac{3}{2} \left(\sqrt{x-3}+1\right)^{4/3}",1,"(-3*(1 + Sqrt[-3 + x])^(4/3))/2 + (6*(1 + Sqrt[-3 + x])^(7/3))/7","A",4,3,13,0.2308,1,"{247, 190, 43}"
964,1,37,0,0.0133593,"\int \frac{1}{\sqrt{3+\sqrt{-1+2 x}}} \, dx","Int[1/Sqrt[3 + Sqrt[-1 + 2*x]],x]","\frac{2}{3} \left(\sqrt{2 x-1}+3\right)^{3/2}-6 \sqrt{\sqrt{2 x-1}+3}","\frac{2}{3} \left(\sqrt{2 x-1}+3\right)^{3/2}-6 \sqrt{\sqrt{2 x-1}+3}",1,"-6*Sqrt[3 + Sqrt[-1 + 2*x]] + (2*(3 + Sqrt[-1 + 2*x])^(3/2))/3","A",4,3,15,0.2000,1,"{247, 190, 43}"
965,1,29,0,0.0258106,"\int \frac{\sqrt{1-x}}{1+\sqrt{x}} \, dx","Int[Sqrt[1 - x]/(1 + Sqrt[x]),x]","-\sqrt{1-x} \left(2-\sqrt{x}\right)-\sin ^{-1}\left(\sqrt{x}\right)","-\sqrt{1-x} \left(2-\sqrt{x}\right)-\sin ^{-1}\left(\sqrt{x}\right)",1,"-((2 - Sqrt[x])*Sqrt[1 - x]) - ArcSin[Sqrt[x]]","A",4,4,19,0.2105,1,"{1398, 785, 780, 216}"
966,1,25,0,0.0252974,"\int \frac{\sqrt{1-x}}{1-\sqrt{x}} \, dx","Int[Sqrt[1 - x]/(1 - Sqrt[x]),x]","\sin ^{-1}\left(\sqrt{x}\right)-\left(\sqrt{x}+2\right) \sqrt{1-x}","\sin ^{-1}\left(\sqrt{x}\right)-\left(\sqrt{x}+2\right) \sqrt{1-x}",1,"-((2 + Sqrt[x])*Sqrt[1 - x]) + ArcSin[Sqrt[x]]","A",4,4,21,0.1905,1,"{1398, 785, 780, 216}"
967,1,21,0,0.0230596,"\int \frac{x}{x-\sqrt{1+x^2}} \, dx","Int[x/(x - Sqrt[1 + x^2]),x]","-\frac{x^3}{3}-\frac{1}{3} \left(x^2+1\right)^{3/2}","-\frac{x^3}{3}-\frac{1}{3} \left(x^2+1\right)^{3/2}",1,"-x^3/3 - (1 + x^2)^(3/2)/3","A",3,3,17,0.1765,1,"{2106, 30, 261}"
968,1,65,0,0.0535978,"\int \frac{x}{x-\sqrt{1-x^2}} \, dx","Int[x/(x - Sqrt[1 - x^2]),x]","\frac{\sqrt{1-x^2}}{2}-\frac{\tanh ^{-1}\left(\sqrt{2} \sqrt{1-x^2}\right)}{2 \sqrt{2}}+\frac{x}{2}-\frac{\tanh ^{-1}\left(\sqrt{2} x\right)}{2 \sqrt{2}}","\frac{\sqrt{1-x^2}}{2}-\frac{\tanh ^{-1}\left(\sqrt{2} \sqrt{1-x^2}\right)}{2 \sqrt{2}}+\frac{x}{2}-\frac{\tanh ^{-1}\left(\sqrt{2} x\right)}{2 \sqrt{2}}",1,"x/2 + Sqrt[1 - x^2]/2 - ArcTanh[Sqrt[2]*x]/(2*Sqrt[2]) - ArcTanh[Sqrt[2]*Sqrt[1 - x^2]]/(2*Sqrt[2])","A",7,7,19,0.3684,1,"{2107, 321, 206, 444, 50, 63, 207}"
969,1,31,0,0.0423509,"\int \frac{x}{x-\sqrt{1+2 x^2}} \, dx","Int[x/(x - Sqrt[1 + 2*x^2]),x]","-\sqrt{2 x^2+1}+\tan ^{-1}\left(\sqrt{2 x^2+1}\right)-x+\tan ^{-1}(x)","-\sqrt{2 x^2+1}+\tan ^{-1}\left(\sqrt{2 x^2+1}\right)-x+\tan ^{-1}(x)",1,"-x - Sqrt[1 + 2*x^2] + ArcTan[x] + ArcTan[Sqrt[1 + 2*x^2]]","A",7,6,19,0.3158,1,"{2107, 321, 203, 444, 50, 63}"
970,1,82,0,0.0436464,"\int \sqrt{x} \sqrt{\sqrt{x}+x} \, dx","Int[Sqrt[x]*Sqrt[Sqrt[x] + x],x]","\frac{1}{2} \sqrt{x} \left(x+\sqrt{x}\right)^{3/2}-\frac{5}{12} \left(x+\sqrt{x}\right)^{3/2}+\frac{5}{32} \left(2 \sqrt{x}+1\right) \sqrt{x+\sqrt{x}}-\frac{5}{32} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x+\sqrt{x}}}\right)","\frac{1}{2} \sqrt{x} \left(x+\sqrt{x}\right)^{3/2}-\frac{5}{12} \left(x+\sqrt{x}\right)^{3/2}+\frac{5}{32} \left(2 \sqrt{x}+1\right) \sqrt{x+\sqrt{x}}-\frac{5}{32} \tanh ^{-1}\left(\frac{\sqrt{x}}{\sqrt{x+\sqrt{x}}}\right)",1,"(5*(1 + 2*Sqrt[x])*Sqrt[Sqrt[x] + x])/32 - (5*(Sqrt[x] + x)^(3/2))/12 + (Sqrt[x]*(Sqrt[x] + x)^(3/2))/2 - (5*ArcTanh[Sqrt[x]/Sqrt[Sqrt[x] + x]])/32","A",6,6,17,0.3529,1,"{2018, 670, 640, 612, 620, 206}"
971,1,74,0,0.1112347,"\int \frac{1+\sqrt[3]{x}}{1+\sqrt{x}} \, dx","Int[(1 + x^(1/3))/(1 + Sqrt[x]),x]","\frac{6 x^{5/6}}{5}+2 \sqrt{x}-3 \sqrt[3]{x}-4 \log \left(\sqrt[6]{x}+1\right)-\log \left(\sqrt[3]{x}-\sqrt[6]{x}+1\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[6]{x}}{\sqrt{3}}\right)","\frac{6 x^{5/6}}{5}+2 \sqrt{x}-3 \sqrt[3]{x}-4 \log \left(\sqrt[6]{x}+1\right)-\log \left(\sqrt[3]{x}-\sqrt[6]{x}+1\right)-2 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[6]{x}}{\sqrt{3}}\right)",1,"-3*x^(1/3) + 2*Sqrt[x] + (6*x^(5/6))/5 - 2*Sqrt[3]*ArcTan[(1 - 2*x^(1/6))/Sqrt[3]] - 4*Log[1 + x^(1/6)] - Log[1 - x^(1/6) + x^(1/3)]","A",10,8,17,0.4706,1,"{1593, 1887, 1874, 31, 634, 618, 204, 628}"
972,1,115,0,0.1496869,"\int \frac{1+\sqrt[3]{x}}{1+\sqrt[4]{x}} \, dx","Int[(1 + x^(1/3))/(1 + x^(1/4)),x]","\frac{12 x^{13/12}}{13}-\frac{6 x^{5/6}}{5}+\frac{4 x^{3/4}}{3}+\frac{12 x^{7/12}}{7}-2 \sqrt{x}-3 \sqrt[3]{x}+4 \sqrt[4]{x}+12 \sqrt[12]{x}-8 \log \left(\sqrt[12]{x}+1\right)-2 \log \left(\sqrt[6]{x}-\sqrt[12]{x}+1\right)+4 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[12]{x}}{\sqrt{3}}\right)","\frac{12 x^{13/12}}{13}-\frac{6 x^{5/6}}{5}+\frac{4 x^{3/4}}{3}+\frac{12 x^{7/12}}{7}-2 \sqrt{x}-3 \sqrt[3]{x}+4 \sqrt[4]{x}+12 \sqrt[12]{x}-8 \log \left(\sqrt[12]{x}+1\right)-2 \log \left(\sqrt[6]{x}-\sqrt[12]{x}+1\right)+4 \sqrt{3} \tan ^{-1}\left(\frac{1-2 \sqrt[12]{x}}{\sqrt{3}}\right)",1,"12*x^(1/12) + 4*x^(1/4) - 3*x^(1/3) - 2*Sqrt[x] + (12*x^(7/12))/7 + (4*x^(3/4))/3 - (6*x^(5/6))/5 + (12*x^(13/12))/13 + 4*Sqrt[3]*ArcTan[(1 - 2*x^(1/12))/Sqrt[3]] - 8*Log[1 + x^(1/12)] - 2*Log[1 - x^(1/12) + x^(1/6)]","A",11,9,17,0.5294,1,"{1593, 1836, 1887, 1874, 31, 634, 618, 204, 628}"
973,1,4,0,0.0428694,"\int \frac{x^2}{-1+x^2+\sqrt{1-x^2}} \, dx","Int[x^2/(-1 + x^2 + Sqrt[1 - x^2]),x]","x+\sin ^{-1}(x)","x+\sin ^{-1}(x)",1,"x + ArcSin[x]","A",3,3,22,0.1364,1,"{2156, 8, 216}"
974,1,22,0,0.0095616,"\int \sqrt{\frac{1+x}{x}} \, dx","Int[Sqrt[(1 + x)/x],x]","\sqrt{\frac{1}{x}+1} x+\tanh ^{-1}\left(\sqrt{\frac{1}{x}+1}\right)","\sqrt{\frac{1}{x}+1} x+\tanh ^{-1}\left(\sqrt{\frac{1}{x}+1}\right)",1,"Sqrt[1 + x^(-1)]*x + ArcTanh[Sqrt[1 + x^(-1)]]","A",5,5,11,0.4545,1,"{1972, 242, 47, 63, 207}"
975,1,24,0,0.0089003,"\int \sqrt{\frac{1-x}{x}} \, dx","Int[Sqrt[(1 - x)/x],x]","\sqrt{\frac{1}{x}-1} x-\tan ^{-1}\left(\sqrt{\frac{1}{x}-1}\right)","\sqrt{\frac{1}{x}-1} x-\tan ^{-1}\left(\sqrt{\frac{1}{x}-1}\right)",1,"Sqrt[-1 + x^(-1)]*x - ArcTan[Sqrt[-1 + x^(-1)]]","A",5,5,13,0.3846,1,"{1972, 242, 47, 63, 203}"
976,1,28,0,0.0112379,"\int \sqrt{\frac{-1+x}{x}} \, dx","Int[Sqrt[(-1 + x)/x],x]","\sqrt{\frac{x-1}{x}} x-\tanh ^{-1}\left(\sqrt{\frac{x-1}{x}}\right)","\sqrt{x-1} \sqrt{x}-\sinh ^{-1}\left(\sqrt{x-1}\right)",1,"Sqrt[(-1 + x)/x]*x - ArcTanh[Sqrt[(-1 + x)/x]]","A",5,5,11,0.4545,1,"{1972, 242, 47, 63, 206}"
977,1,24,0,0.0170135,"\int \frac{\sqrt{\frac{1+x}{x}}}{x} \, dx","Int[Sqrt[(1 + x)/x]/x,x]","2 \tanh ^{-1}\left(\sqrt{\frac{1}{x}+1}\right)-2 \sqrt{\frac{1}{x}+1}","2 \tanh ^{-1}\left(\sqrt{\frac{1}{x}+1}\right)-2 \sqrt{\frac{1}{x}+1}",1,"-2*Sqrt[1 + x^(-1)] + 2*ArcTanh[Sqrt[1 + x^(-1)]]","A",5,5,15,0.3333,1,"{1973, 266, 50, 63, 207}"
978,1,22,0,0.004786,"\int \sqrt{\frac{x}{1+x}} \, dx","Int[Sqrt[x/(1 + x)],x]","\sqrt{x} \sqrt{x+1}-\sinh ^{-1}\left(\sqrt{x}\right)","\sqrt{x} \sqrt{x+1}-\sinh ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[x]*Sqrt[1 + x] - ArcSinh[Sqrt[x]]","A",4,4,11,0.3636,1,"{1958, 50, 54, 215}"
979,1,29,0,0.0118638,"\int \frac{1}{\sqrt{\frac{-1-x}{x}}} \, dx","Int[1/Sqrt[(-1 - x)/x],x]","\tan ^{-1}\left(\sqrt{-\frac{x+1}{x}}\right)-x \sqrt{-\frac{x+1}{x}}","\tan ^{-1}\left(\sqrt{-\frac{x+1}{x}}\right)-x \sqrt{-\frac{x+1}{x}}",1,"-(x*Sqrt[-((1 + x)/x)]) + ArcTan[Sqrt[-((1 + x)/x)]]","A",5,5,13,0.3846,1,"{1972, 242, 51, 63, 204}"
980,1,33,0,0.0116904,"\int \sqrt{(4-x) x} \, dx","Int[Sqrt[(4 - x)*x],x]","-\frac{1}{2} \sqrt{4 x-x^2} (2-x)-2 \sin ^{-1}\left(1-\frac{x}{2}\right)","-\frac{1}{2} \sqrt{4 x-x^2} (2-x)-2 \sin ^{-1}\left(1-\frac{x}{2}\right)",1,"-((2 - x)*Sqrt[4*x - x^2])/2 - 2*ArcSin[1 - x/2]","A",4,4,11,0.3636,1,"{1979, 612, 619, 216}"
981,1,8,0,0.0049172,"\int \frac{1}{\sqrt{(1-x) x}} \, dx","Int[1/Sqrt[(1 - x)*x],x]","-\sin ^{-1}(1-2 x)","-\sin ^{-1}(1-2 x)",1,"-ArcSin[1 - 2*x]","A",3,3,11,0.2727,1,"{1979, 619, 216}"
982,1,13,0,0.0126261,"\int \frac{x}{(x (2+x))^{3/2}} \, dx","Int[x/(x*(2 + x))^(3/2),x]","\frac{x}{\sqrt{x^2+2 x}}","\frac{x}{\sqrt{x^2+2 x}}",1,"x/Sqrt[2*x + x^2]","A",2,2,11,0.1818,1,"{1980, 636}"
983,1,22,0,0.0321021,"\int \frac{\sqrt{1+\frac{1}{x}}}{1-x^2} \, dx","Int[Sqrt[1 + x^(-1)]/(1 - x^2),x]","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{x}+1}}{\sqrt{2}}\right)","\sqrt{2} \tanh ^{-1}\left(\frac{\sqrt{\frac{1}{x}+1}}{\sqrt{2}}\right)",1,"Sqrt[2]*ArcTanh[Sqrt[1 + x^(-1)]/Sqrt[2]]","A",5,5,19,0.2632,1,"{1446, 1469, 627, 63, 207}"
984,1,24,0,0.027343,"\int \frac{1}{1+\sqrt{5}-x^2+\sqrt{5} x^2} \, dx","Int[(1 + Sqrt[5] - x^2 + Sqrt[5]*x^2)^(-1),x]","\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3-\sqrt{5}\right)} x\right)","\frac{1}{2} \tan ^{-1}\left(\sqrt{\frac{1}{2} \left(3-\sqrt{5}\right)} x\right)",1,"ArcTan[Sqrt[(3 - Sqrt[5])/2]*x]/2","A",2,2,23,0.08696,1,"{6, 203}"
985,1,28,0,0.0095421,"\int \frac{1}{\sqrt{a x+b x^2}} \, dx","Int[1/Sqrt[a*x + b*x^2],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/Sqrt[b]","A",2,2,13,0.1538,1,"{620, 206}"
986,1,28,0,0.0113654,"\int \frac{1}{\sqrt{x (a+b x)}} \, dx","Int[1/Sqrt[x*(a + b*x)],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/Sqrt[b]","A",3,3,11,0.2727,1,"{1979, 620, 206}"
987,1,28,0,0.0123569,"\int \frac{1}{\sqrt{\left(b+\frac{a}{x}\right) x^2}} \, dx","Int[1/Sqrt[(b + a/x)*x^2],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/Sqrt[b]","A",3,3,15,0.2000,1,"{1979, 620, 206}"
988,1,28,0,0.0128981,"\int \frac{1}{\sqrt{\left(\frac{a}{x^2}+\frac{b}{x}\right) x^3}} \, dx","Int[1/Sqrt[(a/x^2 + b/x)*x^3],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/Sqrt[b]","A",3,3,19,0.1579,1,"{1979, 620, 206}"
989,1,28,0,0.0120017,"\int \frac{1}{\sqrt{\frac{a x^2+b x^3}{x}}} \, dx","Int[1/Sqrt[(a*x^2 + b*x^3)/x],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/Sqrt[b]","A",3,3,19,0.1579,1,"{1979, 620, 206}"
990,1,28,0,0.0129292,"\int \frac{1}{\sqrt{\frac{a x^3+b x^4}{x^2}}} \, dx","Int[1/Sqrt[(a*x^3 + b*x^4)/x^2],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a x+b x^2}}\right)}{\sqrt{b}}",1,"(2*ArcTanh[(Sqrt[b]*x)/Sqrt[a*x + b*x^2]])/Sqrt[b]","A",3,3,19,0.1579,1,"{1979, 620, 206}"
991,1,40,0,0.0169132,"\int \frac{1}{\sqrt{a c x+b c x^2}} \, dx","Int[1/Sqrt[a*c*x + b*c*x^2],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a c x+b c x^2}}\right)}{\sqrt{b} \sqrt{c}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a c x+b c x^2}}\right)}{\sqrt{b} \sqrt{c}}",1,"(2*ArcTanh[(Sqrt[b]*Sqrt[c]*x)/Sqrt[a*c*x + b*c*x^2]])/(Sqrt[b]*Sqrt[c])","A",2,2,15,0.1333,1,"{620, 206}"
992,1,40,0,0.0172882,"\int \frac{1}{\sqrt{c \left(a x+b x^2\right)}} \, dx","Int[1/Sqrt[c*(a*x + b*x^2)],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a c x+b c x^2}}\right)}{\sqrt{b} \sqrt{c}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a c x+b c x^2}}\right)}{\sqrt{b} \sqrt{c}}",1,"(2*ArcTanh[(Sqrt[b]*Sqrt[c]*x)/Sqrt[a*c*x + b*c*x^2]])/(Sqrt[b]*Sqrt[c])","A",3,3,15,0.2000,1,"{1979, 620, 206}"
993,1,40,0,0.0167859,"\int \frac{1}{\sqrt{c x (a+b x)}} \, dx","Int[1/Sqrt[c*x*(a + b*x)],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a c x+b c x^2}}\right)}{\sqrt{b} \sqrt{c}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a c x+b c x^2}}\right)}{\sqrt{b} \sqrt{c}}",1,"(2*ArcTanh[(Sqrt[b]*Sqrt[c]*x)/Sqrt[a*c*x + b*c*x^2]])/(Sqrt[b]*Sqrt[c])","A",3,3,12,0.2500,1,"{1979, 620, 206}"
994,1,40,0,0.0189369,"\int \frac{1}{\sqrt{c \left(b+\frac{a}{x}\right) x^2}} \, dx","Int[1/Sqrt[c*(b + a/x)*x^2],x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a c x+b c x^2}}\right)}{\sqrt{b} \sqrt{c}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c} x}{\sqrt{a c x+b c x^2}}\right)}{\sqrt{b} \sqrt{c}}",1,"(2*ArcTanh[(Sqrt[b]*Sqrt[c]*x)/Sqrt[a*c*x + b*c*x^2]])/(Sqrt[b]*Sqrt[c])","A",3,3,16,0.1875,1,"{1979, 620, 206}"
995,0,0,0,0.0266277,"\int \sqrt{1-x^2+x \sqrt{-1+x^2}} \, dx","Int[Sqrt[1 - x^2 + x*Sqrt[-1 + x^2]],x]","\int \sqrt{1-x^2+x \sqrt{-1+x^2}} \, dx","\frac{1}{4} \sqrt{-x^2+\sqrt{x^2-1} x+1} \left(\sqrt{x^2-1}+3 x\right)+\frac{3 \sin ^{-1}\left(x-\sqrt{x^2-1}\right)}{4 \sqrt{2}}",1,"Defer[Int][Sqrt[1 - x^2 + x*Sqrt[-1 + x^2]], x]","F",0,0,0,0,-1,"{}"
996,0,0,0,0.138587,"\int \frac{\sqrt{-x+\sqrt{x} \sqrt{1+x}}}{\sqrt{1+x}} \, dx","Int[Sqrt[-x + Sqrt[x]*Sqrt[1 + x]]/Sqrt[1 + x],x]","\int \frac{\sqrt{-x+\sqrt{x} \sqrt{1+x}}}{\sqrt{1+x}} \, dx","\frac{1}{2} \left(\sqrt{x}+3 \sqrt{x+1}\right) \sqrt{\sqrt{x} \sqrt{x+1}-x}-\frac{3 \sin ^{-1}\left(\sqrt{x}-\sqrt{x+1}\right)}{2 \sqrt{2}}",1,"2*Defer[Subst][Defer[Int][Sqrt[1 - x^2 + x*Sqrt[-1 + x^2]], x], x, Sqrt[1 + x]]","F",0,0,0,0,-1,"{}"
997,1,319,0,0.5680534,"\int -\frac{x+2 \sqrt{1+x^2}}{x+x^3+\sqrt{1+x^2}} \, dx","Int[-((x + 2*Sqrt[1 + x^2])/(x + x^3 + Sqrt[1 + x^2])),x]","-\sqrt{\frac{2}{5} \left(\sqrt{5}-1\right)} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x^2+1}\right)-\sqrt{\frac{2}{5 \left(\sqrt{5}-1\right)}} \tan ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} \sqrt{x^2+1}\right)+\sqrt{\frac{2}{5} \left(1+\sqrt{5}\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x^2+1}\right)-\sqrt{\frac{2}{5 \left(1+\sqrt{5}\right)}} \tanh ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} \sqrt{x^2+1}\right)-\sqrt{\frac{1}{10} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)-2 \sqrt{\frac{2}{5 \left(1+\sqrt{5}\right)}} \tan ^{-1}\left(\sqrt{\frac{2}{1+\sqrt{5}}} x\right)+\sqrt{\frac{1}{10} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} x\right)-2 \sqrt{\frac{2}{5 \left(\sqrt{5}-1\right)}} \tanh ^{-1}\left(\sqrt{\frac{2}{\sqrt{5}-1}} x\right)","\sqrt{2 \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\sqrt{2+\sqrt{5}} \left(\sqrt{x^2+1}+x\right)\right)-\sqrt{2 \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\sqrt{\sqrt{5}-2} \left(\sqrt{x^2+1}+x\right)\right)",1,"-2*Sqrt[2/(5*(1 + Sqrt[5]))]*ArcTan[Sqrt[2/(1 + Sqrt[5])]*x] - Sqrt[(1 + Sqrt[5])/10]*ArcTan[Sqrt[2/(1 + Sqrt[5])]*x] - Sqrt[2/(5*(-1 + Sqrt[5]))]*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[1 + x^2]] - Sqrt[(2*(-1 + Sqrt[5]))/5]*ArcTan[Sqrt[2/(-1 + Sqrt[5])]*Sqrt[1 + x^2]] - 2*Sqrt[2/(5*(-1 + Sqrt[5]))]*ArcTanh[Sqrt[2/(-1 + Sqrt[5])]*x] + Sqrt[(-1 + Sqrt[5])/10]*ArcTanh[Sqrt[2/(-1 + Sqrt[5])]*x] - Sqrt[2/(5*(1 + Sqrt[5]))]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[1 + x^2]] + Sqrt[(2*(1 + Sqrt[5]))/5]*ArcTanh[Sqrt[2/(1 + Sqrt[5])]*Sqrt[1 + x^2]]","B",25,12,31,0.3871,1,"{6742, 261, 1130, 203, 207, 1251, 824, 707, 1093, 1247, 699, 1279}"
998,1,126,0,0.1567959,"\int \frac{1+2 x}{\left(1+x^2\right) \sqrt{2+2 x+x^2}} \, dx","Int[(1 + 2*x)/((1 + x^2)*Sqrt[2 + 2*x + x^2]),x]","-\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{2 \sqrt{5}-\left(5+\sqrt{5}\right) x}{\sqrt{10 \left(1+\sqrt{5}\right)} \sqrt{x^2+2 x+2}}\right)-\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\left(5-\sqrt{5}\right) x+2 \sqrt{5}}{\sqrt{10 \left(\sqrt{5}-1\right)} \sqrt{x^2+2 x+2}}\right)","-\sqrt{\frac{1}{2} \left(1+\sqrt{5}\right)} \tan ^{-1}\left(\frac{2 \sqrt{5}-\left(5+\sqrt{5}\right) x}{\sqrt{10 \left(1+\sqrt{5}\right)} \sqrt{x^2+2 x+2}}\right)-\sqrt{\frac{1}{2} \left(\sqrt{5}-1\right)} \tanh ^{-1}\left(\frac{\left(5-\sqrt{5}\right) x+2 \sqrt{5}}{\sqrt{10 \left(\sqrt{5}-1\right)} \sqrt{x^2+2 x+2}}\right)",1,"-(Sqrt[(1 + Sqrt[5])/2]*ArcTan[(2*Sqrt[5] - (5 + Sqrt[5])*x)/(Sqrt[10*(1 + Sqrt[5])]*Sqrt[2 + 2*x + x^2])]) - Sqrt[(-1 + Sqrt[5])/2]*ArcTanh[(2*Sqrt[5] + (5 - Sqrt[5])*x)/(Sqrt[10*(-1 + Sqrt[5])]*Sqrt[2 + 2*x + x^2])]","A",5,4,25,0.1600,1,"{1036, 1030, 207, 203}"
999,1,22,0,0.0623883,"\int \frac{1}{\left(1+x^4\right) \sqrt{-x^2+\sqrt{1+x^4}}} \, dx","Int[1/((1 + x^4)*Sqrt[-x^2 + Sqrt[1 + x^4]]),x]","\tan ^{-1}\left(\frac{x}{\sqrt{\sqrt{x^4+1}-x^2}}\right)","\tan ^{-1}\left(\frac{x}{\sqrt{\sqrt{x^4+1}-x^2}}\right)",1,"ArcTan[x/Sqrt[-x^2 + Sqrt[1 + x^4]]]","A",2,2,27,0.07407,1,"{2128, 203}"
1000,1,40,0,0.135462,"\int \frac{1}{\left(a+b x^4\right) \sqrt{c x^2+d \sqrt{a+b x^4}}} \, dx","Int[1/((a + b*x^4)*Sqrt[c*x^2 + d*Sqrt[a + b*x^4]]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d \sqrt{a+b x^4}+c x^2}}\right)}{a \sqrt{c}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d \sqrt{a+b x^4}+c x^2}}\right)}{a \sqrt{c}}",1,"ArcTanh[(Sqrt[c]*x)/Sqrt[c*x^2 + d*Sqrt[a + b*x^4]]]/(a*Sqrt[c])","A",2,2,33,0.06061,1,"{2128, 206}"
1001,1,41,0,0.1415695,"\int \frac{1}{\left(a+b x^4\right) \sqrt{-c x^2+d \sqrt{a+b x^4}}} \, dx","Int[1/((a + b*x^4)*Sqrt[-(c*x^2) + d*Sqrt[a + b*x^4]]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d \sqrt{a+b x^4}-c x^2}}\right)}{a \sqrt{c}}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{d \sqrt{a+b x^4}-c x^2}}\right)}{a \sqrt{c}}",1,"ArcTan[(Sqrt[c]*x)/Sqrt[-(c*x^2) + d*Sqrt[a + b*x^4]]]/(a*Sqrt[c])","A",2,2,34,0.05882,1,"{2128, 203}"
1002,1,184,0,0.232949,"\int \frac{x}{\sqrt{a+b c^4+4 b c^3 d x+6 b c^2 d^2 x^2+4 b c d^3 x^3+b d^4 x^4}} \, dx","Int[x/Sqrt[a + b*c^4 + 4*b*c^3*d*x + 6*b*c^2*d^2*x^2 + 4*b*c*d^3*x^3 + b*d^4*x^4],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{a+b d^4 \left(\frac{c}{d}+x\right)^4}}\right)}{2 \sqrt{b} d^2}-\frac{c \left(\sqrt{a}+\sqrt{b} d^2 \left(\frac{c}{d}+x\right)^2\right) \sqrt{\frac{a+b d^4 \left(\frac{c}{d}+x\right)^4}{\left(\sqrt{a}+\sqrt{b} d^2 \left(\frac{c}{d}+x\right)^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} d^2 \sqrt{a+b d^4 \left(\frac{c}{d}+x\right)^4}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{b} d^2 \left(\frac{c}{d}+x\right)^2}{\sqrt{a+b d^4 \left(\frac{c}{d}+x\right)^4}}\right)}{2 \sqrt{b} d^2}-\frac{c \left(\sqrt{a}+\sqrt{b} d^2 \left(\frac{c}{d}+x\right)^2\right) \sqrt{\frac{a+b d^4 \left(\frac{c}{d}+x\right)^4}{\left(\sqrt{a}+\sqrt{b} d^2 \left(\frac{c}{d}+x\right)^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} d^2 \sqrt{a+b d^4 \left(\frac{c}{d}+x\right)^4}}",1,"ArcTanh[(Sqrt[b]*d^2*(c/d + x)^2)/Sqrt[a + b*d^4*(c/d + x)^4]]/(2*Sqrt[b]*d^2) - (c*(Sqrt[a] + Sqrt[b]*d^2*(c/d + x)^2)*Sqrt[(a + b*d^4*(c/d + x)^4)/(Sqrt[a] + Sqrt[b]*d^2*(c/d + x)^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*(c + d*x))/a^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*d^2*Sqrt[a + b*d^4*(c/d + x)^4])","A",7,6,51,0.1176,1,"{1680, 1885, 220, 275, 217, 206}"
1003,1,131,0,0.1004347,"\int \frac{1}{\sqrt{a+b c^4+4 b c^3 d x+6 b c^2 d^2 x^2+4 b c d^3 x^3+b d^4 x^4}} \, dx","Int[1/Sqrt[a + b*c^4 + 4*b*c^3*d*x + 6*b*c^2*d^2*x^2 + 4*b*c*d^3*x^3 + b*d^4*x^4],x]","\frac{\left(\sqrt{a}+\sqrt{b} d^2 \left(\frac{c}{d}+x\right)^2\right) \sqrt{\frac{a+b d^4 \left(\frac{c}{d}+x\right)^4}{\left(\sqrt{a}+\sqrt{b} d^2 \left(\frac{c}{d}+x\right)^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} d \sqrt{a+b d^4 \left(\frac{c}{d}+x\right)^4}}","\frac{\left(\sqrt{a}+\sqrt{b} d^2 \left(\frac{c}{d}+x\right)^2\right) \sqrt{\frac{a+b d^4 \left(\frac{c}{d}+x\right)^4}{\left(\sqrt{a}+\sqrt{b} d^2 \left(\frac{c}{d}+x\right)^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} (c+d x)}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} \sqrt[4]{b} d \sqrt{a+b d^4 \left(\frac{c}{d}+x\right)^4}}",1,"((Sqrt[a] + Sqrt[b]*d^2*(c/d + x)^2)*Sqrt[(a + b*d^4*(c/d + x)^4)/(Sqrt[a] + Sqrt[b]*d^2*(c/d + x)^2)^2]*EllipticF[2*ArcTan[(b^(1/4)*(c + d*x))/a^(1/4)], 1/2])/(2*a^(1/4)*b^(1/4)*d*Sqrt[a + b*d^4*(c/d + x)^4])","A",2,2,49,0.04082,1,"{1106, 220}"
1004,1,54,0,0.2533167,"\int \frac{a-c x^4}{\sqrt{a+b x^2+c x^4} \left(a d+a e x^2+c d x^4\right)} \, dx","Int[(a - c*x^4)/(Sqrt[a + b*x^2 + c*x^4]*(a*d + a*e*x^2 + c*d*x^4)),x]","\frac{\tanh ^{-1}\left(\frac{x \sqrt{b d-a e}}{\sqrt{d} \sqrt{a+b x^2+c x^4}}\right)}{\sqrt{d} \sqrt{b d-a e}}","\frac{\tanh ^{-1}\left(\frac{x \sqrt{b d-a e}}{\sqrt{d} \sqrt{a+b x^2+c x^4}}\right)}{\sqrt{d} \sqrt{b d-a e}}",1,"ArcTanh[(Sqrt[b*d - a*e]*x)/(Sqrt[d]*Sqrt[a + b*x^2 + c*x^4])]/(Sqrt[d]*Sqrt[b*d - a*e])","A",2,2,43,0.04651,1,"{2112, 208}"
1005,1,53,0,0.2603111,"\int \frac{a-c x^4}{\sqrt{a-b x^2+c x^4} \left(a d+a e x^2+c d x^4\right)} \, dx","Int[(a - c*x^4)/(Sqrt[a - b*x^2 + c*x^4]*(a*d + a*e*x^2 + c*d*x^4)),x]","\frac{\tan ^{-1}\left(\frac{x \sqrt{a e+b d}}{\sqrt{d} \sqrt{a-b x^2+c x^4}}\right)}{\sqrt{d} \sqrt{a e+b d}}","\frac{\tan ^{-1}\left(\frac{x \sqrt{a e+b d}}{\sqrt{d} \sqrt{a-b x^2+c x^4}}\right)}{\sqrt{d} \sqrt{a e+b d}}",1,"ArcTan[(Sqrt[b*d + a*e]*x)/(Sqrt[d]*Sqrt[a - b*x^2 + c*x^4])]/(Sqrt[d]*Sqrt[b*d + a*e])","A",2,2,44,0.04545,1,"{2112, 205}"
1006,1,84,0,0.1221488,"\int \frac{1}{\sqrt{5-2 x+x^2} \left(8+x^3\right)} \, dx","Int[1/(Sqrt[5 - 2*x + x^2]*(8 + x^3)),x]","-\frac{\tan ^{-1}\left(\frac{1-x}{\sqrt{3} \sqrt{x^2-2 x+5}}\right)}{4 \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{7-3 x}{\sqrt{13} \sqrt{x^2-2 x+5}}\right)}{12 \sqrt{13}}+\frac{1}{12} \tanh ^{-1}\left(\sqrt{x^2-2 x+5}\right)","-\frac{\tan ^{-1}\left(\frac{1-x}{\sqrt{3} \sqrt{x^2-2 x+5}}\right)}{4 \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{7-3 x}{\sqrt{13} \sqrt{x^2-2 x+5}}\right)}{12 \sqrt{13}}+\frac{1}{12} \tanh ^{-1}\left(\sqrt{x^2-2 x+5}\right)",1,"-ArcTan[(1 - x)/(Sqrt[3]*Sqrt[5 - 2*x + x^2])]/(4*Sqrt[3]) - ArcTanh[(7 - 3*x)/(Sqrt[13]*Sqrt[5 - 2*x + x^2])]/(12*Sqrt[13]) + ArcTanh[Sqrt[5 - 2*x + x^2]]/12","A",9,8,20,0.4000,1,"{2074, 724, 206, 1025, 982, 203, 1024, 207}"
1007,1,20,0,0.0044744,"\int \sqrt{\frac{x^2}{1+x^2}} \, dx","Int[Sqrt[x^2/(1 + x^2)],x]","\frac{\sqrt{x^2} \sqrt{x^2+1}}{x}","\frac{\sqrt{x^2} \sqrt{x^2+1}}{x}",1,"(Sqrt[x^2]*Sqrt[1 + x^2])/x","A",3,3,15,0.2000,1,"{1958, 15, 261}"
1008,1,46,0,0.0159383,"\int \sqrt{\frac{x^n}{1+x^n}} \, dx","Int[Sqrt[x^n/(1 + x^n)],x]","\frac{2 x \sqrt{x^n} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(1+\frac{2}{n}\right);\frac{1}{2} \left(3+\frac{2}{n}\right);-x^n\right)}{n+2}","\frac{2 x \sqrt{x^n} \, _2F_1\left(\frac{1}{2},\frac{1}{2} \left(1+\frac{2}{n}\right);\frac{1}{2} \left(3+\frac{2}{n}\right);-x^n\right)}{n+2}",1,"(2*x*Sqrt[x^n]*Hypergeometric2F1[1/2, (1 + 2/n)/2, (3 + 2/n)/2, -x^n])/(2 + n)","A",3,3,15,0.2000,1,"{1958, 15, 364}"
1009,1,88,0,0.2491512,"\int \frac{e f-e f x^2}{\left(a d+b d x+a d x^2\right) \sqrt{a+b x+c x^2+b x^3+a x^4}} \, dx","Int[(e*f - e*f*x^2)/((a*d + b*d*x + a*d*x^2)*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4]),x]","\frac{e f \tan ^{-1}\left(\frac{x \left(4 a^2-2 a c+b^2\right)+a b x^2+a b}{2 a \sqrt{2 a-c} \sqrt{a x^4+a+b x^3+b x+c x^2}}\right)}{a d \sqrt{2 a-c}}","\frac{e f \tan ^{-1}\left(\frac{x \left(4 a^2-2 a c+b^2\right)+a b x^2+a b}{2 a \sqrt{2 a-c} \sqrt{a x^4+a+b x^3+b x+c x^2}}\right)}{a d \sqrt{2 a-c}}",1,"(e*f*ArcTan[(a*b + (4*a^2 + b^2 - 2*a*c)*x + a*b*x^2)/(2*a*Sqrt[2*a - c]*Sqrt[a + b*x + c*x^2 + b*x^3 + a*x^4])])/(a*Sqrt[2*a - c]*d)","A",1,1,52,0.01923,1,"{2084}"
1010,1,88,0,0.3294983,"\int \frac{e f-e f x^2}{\left(-a d+b d x-a d x^2\right) \sqrt{-a+b x+c x^2+b x^3-a x^4}} \, dx","Int[(e*f - e*f*x^2)/((-(a*d) + b*d*x - a*d*x^2)*Sqrt[-a + b*x + c*x^2 + b*x^3 - a*x^4]),x]","\frac{e f \tanh ^{-1}\left(\frac{-x \left(4 a^2+2 a c+b^2\right)+a b x^2+a b}{2 a \sqrt{2 a+c} \sqrt{-a x^4-a+b x^3+b x+c x^2}}\right)}{a d \sqrt{2 a+c}}","\frac{e f \tanh ^{-1}\left(\frac{-x \left(4 a^2+2 a c+b^2\right)+a b x^2+a b}{2 a \sqrt{2 a+c} \sqrt{-a x^4-a+b x^3+b x+c x^2}}\right)}{a d \sqrt{2 a+c}}",1,"(e*f*ArcTanh[(a*b - (4*a^2 + b^2 + 2*a*c)*x + a*b*x^2)/(2*a*Sqrt[2*a + c]*Sqrt[-a + b*x + c*x^2 + b*x^3 - a*x^4])])/(a*Sqrt[2*a + c]*d)","A",1,1,57,0.01754,1,"{2085}"
1011,1,46,0,0.6215264,"\int \frac{\sqrt{a x^2+b x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}}{x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx","Int[Sqrt[a*x^2 + b*x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]]/(x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]),x]","\frac{\sqrt{2} b \sinh ^{-1}\left(\frac{b \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\sqrt{2} b \sinh ^{-1}\left(\frac{b \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(Sqrt[2]*b*ArcSinh[(a*x + b*Sqrt[-(a/b^2) + (a^2*x^2)/b^2])/Sqrt[a]])/Sqrt[a]","A",2,2,59,0.03390,1,"{2130, 215}"
1012,1,46,0,0.6235714,"\int \frac{\sqrt{-a x^2+b x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}}}{x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx","Int[Sqrt[-(a*x^2) + b*x*Sqrt[a/b^2 + (a^2*x^2)/b^2]]/(x*Sqrt[a/b^2 + (a^2*x^2)/b^2]),x]","\frac{\sqrt{2} b \sin ^{-1}\left(\frac{a x-b \sqrt{\frac{a^2 x^2}{b^2}+\frac{a}{b^2}}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\sqrt{2} b \sin ^{-1}\left(\frac{a x-b \sqrt{\frac{a^2 x^2}{b^2}+\frac{a}{b^2}}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(Sqrt[2]*b*ArcSin[(a*x - b*Sqrt[a/b^2 + (a^2*x^2)/b^2])/Sqrt[a]])/Sqrt[a]","A",2,2,58,0.03448,1,"{2130, 216}"
1013,1,46,0,1.1712606,"\int \frac{\sqrt{x \left(a x+b \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}\right)}}{x \sqrt{-\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx","Int[Sqrt[x*(a*x + b*Sqrt[-(a/b^2) + (a^2*x^2)/b^2])]/(x*Sqrt[-(a/b^2) + (a^2*x^2)/b^2]),x]","\frac{\sqrt{2} b \sinh ^{-1}\left(\frac{b \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\sqrt{2} b \sinh ^{-1}\left(\frac{b \sqrt{\frac{a^2 x^2}{b^2}-\frac{a}{b^2}}+a x}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(Sqrt[2]*b*ArcSinh[(a*x + b*Sqrt[-(a/b^2) + (a^2*x^2)/b^2])/Sqrt[a]])/Sqrt[a]","A",3,3,58,0.05172,1,"{2131, 2130, 215}"
1014,1,46,0,1.1675558,"\int \frac{\sqrt{x \left(-a x+b \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}\right)}}{x \sqrt{\frac{a}{b^2}+\frac{a^2 x^2}{b^2}}} \, dx","Int[Sqrt[x*(-(a*x) + b*Sqrt[a/b^2 + (a^2*x^2)/b^2])]/(x*Sqrt[a/b^2 + (a^2*x^2)/b^2]),x]","\frac{\sqrt{2} b \sin ^{-1}\left(\frac{a x-b \sqrt{\frac{a^2 x^2}{b^2}+\frac{a}{b^2}}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{\sqrt{2} b \sin ^{-1}\left(\frac{a x-b \sqrt{\frac{a^2 x^2}{b^2}+\frac{a}{b^2}}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(Sqrt[2]*b*ArcSin[(a*x - b*Sqrt[a/b^2 + (a^2*x^2)/b^2])/Sqrt[a]])/Sqrt[a]","A",3,3,57,0.05263,1,"{2131, 2130, 216}"
1015,1,19,0,0.556945,"\int \frac{-\sqrt{-4+x}-4 \sqrt{-1+x}+\sqrt{-4+x} x+\sqrt{-1+x} x}{\left(1+\sqrt{-4+x}+\sqrt{-1+x}\right) \left(4-5 x+x^2\right)} \, dx","Int[(-Sqrt[-4 + x] - 4*Sqrt[-1 + x] + Sqrt[-4 + x]*x + Sqrt[-1 + x]*x)/((1 + Sqrt[-4 + x] + Sqrt[-1 + x])*(4 - 5*x + x^2)),x]","2 \log \left(\sqrt{x-4}+\sqrt{x-1}+1\right)","2 \log \left(\sqrt{x-4}+\sqrt{x-1}+1\right)",1,"2*Log[1 + Sqrt[-4 + x] + Sqrt[-1 + x]]","A",3,3,66,0.04545,1,"{6688, 1586, 6684}"
1016,1,123,0,0.1143917,"\int \frac{1}{x \left(3+3 x+x^2\right) \sqrt[3]{3+3 x+3 x^2+x^3}} \, dx","Int[1/(x*(3 + 3*x + x^2)*(3 + 3*x + 3*x^2 + x^3)^(1/3)),x]","\frac{\log \left(1-\frac{\sqrt[3]{3} (x+1)}{\sqrt[3]{(x+1)^3+2}}\right)}{3 \sqrt[3]{3}}-\frac{\log \left(\frac{3^{2/3} (x+1)^2}{\left((x+1)^3+2\right)^{2/3}}+\frac{\sqrt[3]{3} (x+1)}{\sqrt[3]{(x+1)^3+2}}+1\right)}{6 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{2 (x+1)}{\sqrt[6]{3} \sqrt[3]{(x+1)^3+2}}+\frac{1}{\sqrt{3}}\right)}{3^{5/6}}","-\frac{\log \left(1-(x+1)^3\right)}{6 \sqrt[3]{3}}+\frac{\log \left(\sqrt[3]{3} (x+1)-\sqrt[3]{(x+1)^3+2}\right)}{2 \sqrt[3]{3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{3} (x+1)}{\sqrt[3]{(x+1)^3+2}}+1}{\sqrt{3}}\right)}{3^{5/6}}",1,"-(ArcTan[1/Sqrt[3] + (2*(1 + x))/(3^(1/6)*(2 + (1 + x)^3)^(1/3))]/3^(5/6)) + Log[1 - (3^(1/3)*(1 + x))/(2 + (1 + x)^3)^(1/3)]/(3*3^(1/3)) - Log[1 + (3^(2/3)*(1 + x)^2)/(2 + (1 + x)^3)^(2/3) + (3^(1/3)*(1 + x))/(2 + (1 + x)^3)^(1/3)]/(6*3^(1/3))","A",9,9,31,0.2903,1,"{433, 431, 377, 200, 31, 634, 617, 204, 628}"
1017,0,0,0,0.5340649,"\int \frac{1-x^2}{\left(1-x+x^2\right) \left(1-x^3\right)^{2/3}} \, dx","Int[(1 - x^2)/((1 - x + x^2)*(1 - x^3)^(2/3)),x]","\int \frac{1-x^2}{\left(1-x+x^2\right) \left(1-x^3\right)^{2/3}} \, dx","-\frac{\log \left(-x^3+2 (1-x)^3+1\right)}{2\ 2^{2/3}}+\frac{3 \log \left(\sqrt[3]{1-x^3}+\sqrt[3]{2} (1-x)\right)}{2\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3}}",1,"-(x*Hypergeometric2F1[1/3, 2/3, 4/3, x^3]) - (1 + I*Sqrt[3])*Defer[Int][1/((-1 - I*Sqrt[3] + 2*x)*(1 - x^3)^(2/3)), x] - (1 - I*Sqrt[3])*Defer[Int][1/((-1 + I*Sqrt[3] + 2*x)*(1 - x^3)^(2/3)), x]","F",0,0,0,0,-1,"{}"
1018,1,47,0,0.1196325,"\int \frac{x^2}{\sqrt{-1+x^4} \left(1+x^4\right)} \, dx","Int[x^2/(Sqrt[-1 + x^4]*(1 + x^4)),x]","\left(\frac{1}{8}+\frac{i}{8}\right) \tanh ^{-1}\left(\frac{(1+i) x}{\sqrt{x^4-1}}\right)-\left(\frac{1}{8}+\frac{i}{8}\right) \tan ^{-1}\left(\frac{(1+i) x}{\sqrt{x^4-1}}\right)","-\frac{1}{4} \tan ^{-1}\left(\frac{x^2+1}{x \sqrt{x^4-1}}\right)-\frac{1}{4} \tanh ^{-1}\left(\frac{1-x^2}{x \sqrt{x^4-1}}\right)",1,"(-1/8 - I/8)*ArcTan[((1 + I)*x)/Sqrt[-1 + x^4]] + (1/8 + I/8)*ArcTanh[((1 + I)*x)/Sqrt[-1 + x^4]]","C",9,6,20,0.3000,1,"{490, 1211, 222, 1699, 206, 203}"
1019,1,80,0,0.4490934,"\int \frac{a-c x^4}{\left(a e+c d x^2\right) \left(d+e x^2\right) \sqrt{a+b x^2+c x^4}} \, dx","Int[(a - c*x^4)/((a*e + c*d*x^2)*(d + e*x^2)*Sqrt[a + b*x^2 + c*x^4]),x]","\frac{\tan ^{-1}\left(\frac{x \sqrt{a e^2-b d e+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+b x^2+c x^4}}\right)}{\sqrt{d} \sqrt{e} \sqrt{a e^2-b d e+c d^2}}","\frac{\tan ^{-1}\left(\frac{x \sqrt{a e^2-b d e+c d^2}}{\sqrt{d} \sqrt{e} \sqrt{a+b x^2+c x^4}}\right)}{\sqrt{d} \sqrt{e} \sqrt{a e^2-b d e+c d^2}}",1,"ArcTan[(Sqrt[c*d^2 - b*d*e + a*e^2]*x)/(Sqrt[d]*Sqrt[e]*Sqrt[a + b*x^2 + c*x^4])]/(Sqrt[d]*Sqrt[e]*Sqrt[c*d^2 - b*d*e + a*e^2])","A",2,2,46,0.04348,1,"{2112, 205}"
1020,1,1,0,0.0014713,"\int \left(x+\frac{1-x^2}{1+x}\right) \, dx","Int[x + (1 - x^2)/(1 + x),x]","x","x",1,"x","A",1,0,15,0,1,"{}"
1021,1,122,0,0.1199763,"\int \frac{1}{\frac{1}{x}+\sqrt{1-x^2}} \, dx","Int[(x^(-1) + Sqrt[1 - x^2])^(-1),x]","-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt{1-x^2}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} x}{\sqrt{1-x^2}}\right)}{\sqrt{3}}+\sin ^{-1}(x)","\sin ^{-1}(x)-\frac{\tan ^{-1}\left(\frac{4 \sqrt{1-x^2} x+1}{\sqrt{3} \left(1-2 x^2\right)}\right)}{\sqrt{3}}",1,"ArcSin[x] - ArcTan[(1 - 2*x^2)/Sqrt[3]]/Sqrt[3] - ArcTan[x/(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*Sqrt[1 - x^2])]/Sqrt[3] - ArcTan[(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*x)/Sqrt[1 - x^2]]/Sqrt[3]","C",12,9,17,0.5294,1,"{6742, 1107, 618, 204, 1293, 216, 1174, 377, 205}"
1022,1,149,0,0.2628498,"\int \frac{x \sqrt{1-x^2}}{x-x^3+\sqrt{1-x^2}} \, dx","Int[(x*Sqrt[1 - x^2])/(x - x^3 + Sqrt[1 - x^2]),x]","-\frac{x^2}{2}-\frac{\tan ^{-1}\left(\frac{1-2 x^2}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{x}{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} \sqrt{1-x^2}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\sqrt{-\frac{-\sqrt{3}+i}{\sqrt{3}+i}} x}{\sqrt{1-x^2}}\right)}{\sqrt{3}}+\frac{1}{4} (1-x)^2+\frac{1}{4} (x+1)^2+\sin ^{-1}(x)","\sin ^{-1}(x)-\frac{\tan ^{-1}\left(\frac{4 \sqrt{1-x^2} x+1}{\sqrt{3} \left(1-2 x^2\right)}\right)}{\sqrt{3}}",1,"(1 - x)^2/4 - x^2/2 + (1 + x)^2/4 + ArcSin[x] - ArcTan[(1 - 2*x^2)/Sqrt[3]]/Sqrt[3] - ArcTan[x/(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*Sqrt[1 - x^2])]/Sqrt[3] - ArcTan[(Sqrt[-((I - Sqrt[3])/(I + Sqrt[3]))]*x)/Sqrt[1 - x^2]]/Sqrt[3]","C",13,10,33,0.3030,1,"{6742, 1293, 216, 1174, 377, 205, 1251, 773, 618, 204}"
1023,0,0,0,0.0647157,"\int \left(1+x+x^2+x^3\right)^{-n} \left(1-x^4\right)^n \, dx","Int[(1 - x^4)^n/(1 + x + x^2 + x^3)^n,x]","\int \left(1+x+x^2+x^3\right)^{-n} \left(1-x^4\right)^n \, dx","-\frac{(1-x) \left(x^3+x^2+x+1\right)^{-n} \left(1-x^4\right)^n}{n+1}",1,"Defer[Int][(1 - x^4)^n/(1 + x + x^2 + x^3)^n, x]","F",0,0,0,0,-1,"{}"
1024,1,177,0,0.0888565,"\int \frac{x}{\sqrt{-44375 b^4+576000 b^3 c x+576000 b^2 c^2 x^2+5308416 c^4 x^4}} \, dx","Int[x/Sqrt[-44375*b^4 + 576000*b^3*c*x + 576000*b^2*c^2*x^2 + 5308416*c^4*x^4],x]","\frac{\log \left(32462531054272512000 b^2 c^{10} x^6+21641687369515008000 b^3 c^9 x^5+951050714480640000 b^4 c^8 x^4+2583100705996800000 b^5 c^7 x^3+597005697024000000 b^6 c^6 x^2+5308416 \sqrt{576000 b^2 c^2 x^2+576000 b^3 c x-44375 b^4+5308416 c^4 x^4} \left(1990656000 b^2 c^8 x^4+1105920000 b^3 c^7 x^3+38880000 b^4 c^6 x^2+79200000 b^5 c^5 x+12203125 b^6 c^4+12230590464 c^{10} x^6\right)+20738073600000000 b^8 c^4+149587343098087735296 c^{12} x^8\right)}{18432 c^2}","\frac{\log \left(32462531054272512000 b^2 c^{10} x^6+21641687369515008000 b^3 c^9 x^5+951050714480640000 b^4 c^8 x^4+2583100705996800000 b^5 c^7 x^3+597005697024000000 b^6 c^6 x^2+5308416 \sqrt{576000 b^2 c^2 x^2+576000 b^3 c x-44375 b^4+5308416 c^4 x^4} \left(1990656000 b^2 c^8 x^4+1105920000 b^3 c^7 x^3+38880000 b^4 c^6 x^2+79200000 b^5 c^5 x+12203125 b^6 c^4+12230590464 c^{10} x^6\right)+20738073600000000 b^8 c^4+149587343098087735296 c^{12} x^8\right)}{18432 c^2}",1,"Log[20738073600000000*b^8*c^4 + 597005697024000000*b^6*c^6*x^2 + 2583100705996800000*b^5*c^7*x^3 + 951050714480640000*b^4*c^8*x^4 + 21641687369515008000*b^3*c^9*x^5 + 32462531054272512000*b^2*c^10*x^6 + 149587343098087735296*c^12*x^8 + 5308416*Sqrt[-44375*b^4 + 576000*b^3*c*x + 576000*b^2*c^2*x^2 + 5308416*c^4*x^4]*(12203125*b^6*c^4 + 79200000*b^5*c^5*x + 38880000*b^4*c^6*x^2 + 1105920000*b^3*c^7*x^3 + 1990656000*b^2*c^8*x^4 + 12230590464*c^10*x^6)]/(18432*c^2)","A",1,1,38,0.02632,1,"{2082}"
1025,1,243,0,0.1385494,"\int \frac{1+4 x}{\sqrt{9+120 x+64 x^2+64 x^3+64 x^4}} \, dx","Int[(1 + 4*x)/Sqrt[9 + 120*x + 64*x^2 + 64*x^3 + 64*x^4],x]","\frac{1}{16} \log \left(4096 x^8+8192 x^7+512 \sqrt{64 x^4+64 x^3+64 x^2+120 x+9} x^6+12288 x^6+768 \sqrt{64 x^4+64 x^3+64 x^2+120 x+9} x^5+19456 x^5+960 \sqrt{64 x^4+64 x^3+64 x^2+120 x+9} x^4+17024 x^4+1280 \sqrt{64 x^4+64 x^3+64 x^2+120 x+9} x^3+13440 x^3+744 \sqrt{64 x^4+64 x^3+64 x^2+120 x+9} x^2+9280 x^2+444 \sqrt{64 x^4+64 x^3+64 x^2+120 x+9} x+179 \sqrt{64 x^4+64 x^3+64 x^2+120 x+9}+2864 x+921\right)","\frac{1}{16} \log \left(4096 x^8+8192 x^7+12288 x^6+19456 x^5+17024 x^4+13440 x^3+9280 x^2+\sqrt{64 x^4+64 x^3+64 x^2+120 x+9} \left(512 x^6+768 x^5+960 x^4+1280 x^3+744 x^2+444 x+179\right)+2864 x+921\right)",1,"Log[921 + 2864*x + 9280*x^2 + 13440*x^3 + 17024*x^4 + 19456*x^5 + 12288*x^6 + 8192*x^7 + 4096*x^8 + 179*Sqrt[9 + 120*x + 64*x^2 + 64*x^3 + 64*x^4] + 444*x*Sqrt[9 + 120*x + 64*x^2 + 64*x^3 + 64*x^4] + 744*x^2*Sqrt[9 + 120*x + 64*x^2 + 64*x^3 + 64*x^4] + 1280*x^3*Sqrt[9 + 120*x + 64*x^2 + 64*x^3 + 64*x^4] + 960*x^4*Sqrt[9 + 120*x + 64*x^2 + 64*x^3 + 64*x^4] + 768*x^5*Sqrt[9 + 120*x + 64*x^2 + 64*x^3 + 64*x^4] + 512*x^6*Sqrt[9 + 120*x + 64*x^2 + 64*x^3 + 64*x^4]]/16","B",2,2,30,0.06667,1,"{2083, 2082}"