1,1,74,80,0.0473762,"\int x^4 \log \left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x^4*Log[c*(a + b*x^2)^p],x]","\frac{1}{75} \left(\frac{30 a^{5/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2}}-\frac{30 a^2 p x}{b^2}+15 x^5 \log \left(c \left(a+b x^2\right)^p\right)+\frac{10 a p x^3}{b}-6 p x^5\right)","\frac{2 a^{5/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{5 b^{5/2}}-\frac{2 a^2 p x}{5 b^2}+\frac{1}{5} x^5 \log \left(c \left(a+b x^2\right)^p\right)+\frac{2 a p x^3}{15 b}-\frac{2 p x^5}{25}",1,"((-30*a^2*p*x)/b^2 + (10*a*p*x^3)/b - 6*p*x^5 + (30*a^(5/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(5/2) + 15*x^5*Log[c*(a + b*x^2)^p])/75","A",1
2,1,59,59,0.0147106,"\int x^3 \log \left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x^3*Log[c*(a + b*x^2)^p],x]","-\frac{a^2 p \log \left(a+b x^2\right)}{4 b^2}+\frac{1}{4} x^4 \log \left(c \left(a+b x^2\right)^p\right)+\frac{a p x^2}{4 b}-\frac{p x^4}{8}","-\frac{a^2 p \log \left(a+b x^2\right)}{4 b^2}+\frac{1}{4} x^4 \log \left(c \left(a+b x^2\right)^p\right)+\frac{a p x^2}{4 b}-\frac{p x^4}{8}",1,"(a*p*x^2)/(4*b) - (p*x^4)/8 - (a^2*p*Log[a + b*x^2])/(4*b^2) + (x^4*Log[c*(a + b*x^2)^p])/4","A",1
3,1,62,66,0.0244454,"\int x^2 \log \left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x^2*Log[c*(a + b*x^2)^p],x]","\frac{1}{9} \left(-\frac{6 a^{3/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}+3 x^3 \log \left(c \left(a+b x^2\right)^p\right)+\frac{6 a p x}{b}-2 p x^3\right)","-\frac{2 a^{3/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{3 b^{3/2}}+\frac{1}{3} x^3 \log \left(c \left(a+b x^2\right)^p\right)+\frac{2 a p x}{3 b}-\frac{2 p x^3}{9}",1,"((6*a*p*x)/b - 2*p*x^3 - (6*a^(3/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(3/2) + 3*x^3*Log[c*(a + b*x^2)^p])/9","A",1
4,1,34,35,0.009195,"\int x \log \left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x*Log[c*(a + b*x^2)^p],x]","\frac{1}{2} \left(\frac{\left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b}-p x^2\right)","\frac{\left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 b}-\frac{p x^2}{2}",1,"(-(p*x^2) + ((a + b*x^2)*Log[c*(a + b*x^2)^p])/b)/2","A",1
5,1,45,45,0.0128125,"\int \log \left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[Log[c*(a + b*x^2)^p],x]","x \log \left(c \left(a+b x^2\right)^p\right)+\frac{2 \sqrt{a} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}-2 p x","x \log \left(c \left(a+b x^2\right)^p\right)+\frac{2 \sqrt{a} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}-2 p x",1,"-2*p*x + (2*Sqrt[a]*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[b] + x*Log[c*(a + b*x^2)^p]","A",1
6,1,43,44,0.0071265,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x} \, dx","Integrate[Log[c*(a + b*x^2)^p]/x,x]","\frac{1}{2} \left(\log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)+p \text{Li}_2\left(\frac{b x^2+a}{a}\right)\right)","\frac{1}{2} \log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)+\frac{1}{2} p \text{Li}_2\left(\frac{b x^2}{a}+1\right)",1,"(Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p] + p*PolyLog[2, (a + b*x^2)/a])/2","A",1
7,1,44,44,0.0095754,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^2} \, dx","Integrate[Log[c*(a + b*x^2)^p]/x^2,x]","\frac{2 \sqrt{b} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{x}","\frac{2 \sqrt{b} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a}}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{x}",1,"(2*Sqrt[b]*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[a] - Log[c*(a + b*x^2)^p]/x","A",1
8,1,45,38,0.0031533,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^3} \, dx","Integrate[Log[c*(a + b*x^2)^p]/x^3,x]","-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{2 x^2}-\frac{b p \log \left(a+b x^2\right)}{2 a}+\frac{b p \log (x)}{a}","\frac{b p \log (x)}{a}-\frac{\left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 a x^2}",1,"(b*p*Log[x])/a - (b*p*Log[a + b*x^2])/(2*a) - Log[c*(a + b*x^2)^p]/(2*x^2)","A",1
9,1,49,60,0.0031109,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^4} \, dx","Integrate[Log[c*(a + b*x^2)^p]/x^4,x]","-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{3 x^3}-\frac{2 b p \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x^2}{a}\right)}{3 a x}","-\frac{2 b^{3/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{3 x^3}-\frac{2 b p}{3 a x}",1,"(-2*b*p*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x^2)/a)])/(3*a*x) - Log[c*(a + b*x^2)^p]/(3*x^3)","C",1
10,1,56,64,0.0407495,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^5} \, dx","Integrate[Log[c*(a + b*x^2)^p]/x^5,x]","\frac{1}{4} b p \left(\frac{b \log \left(a+b x^2\right)}{a^2}-\frac{2 b \log (x)}{a^2}-\frac{1}{a x^2}\right)-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{4 x^4}","\frac{b^2 p \log \left(a+b x^2\right)}{4 a^2}-\frac{b^2 p \log (x)}{2 a^2}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{4 x^4}-\frac{b p}{4 a x^2}",1,"(b*p*(-(1/(a*x^2)) - (2*b*Log[x])/a^2 + (b*Log[a + b*x^2])/a^2))/4 - Log[c*(a + b*x^2)^p]/(4*x^4)","A",1
11,1,49,74,0.003026,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^6} \, dx","Integrate[Log[c*(a + b*x^2)^p]/x^6,x]","-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{5 x^5}-\frac{2 b p \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{b x^2}{a}\right)}{15 a x^3}","\frac{2 b^{5/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{5 a^{5/2}}+\frac{2 b^2 p}{5 a^2 x}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{5 x^5}-\frac{2 b p}{15 a x^3}",1,"(-2*b*p*Hypergeometric2F1[-3/2, 1, -1/2, -((b*x^2)/a)])/(15*a*x^3) - Log[c*(a + b*x^2)^p]/(5*x^5)","C",1
12,1,68,78,0.069313,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^7} \, dx","Integrate[Log[c*(a + b*x^2)^p]/x^7,x]","-\frac{\frac{b p x^2 \left(2 b^2 x^4 \log \left(a+b x^2\right)+a \left(a-2 b x^2\right)-4 b^2 x^4 \log (x)\right)}{a^3}+2 \log \left(c \left(a+b x^2\right)^p\right)}{12 x^6}","-\frac{b^3 p \log \left(a+b x^2\right)}{6 a^3}+\frac{b^3 p \log (x)}{3 a^3}+\frac{b^2 p}{6 a^2 x^2}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{6 x^6}-\frac{b p}{12 a x^4}",1,"-1/12*((b*p*x^2*(a*(a - 2*b*x^2) - 4*b^2*x^4*Log[x] + 2*b^2*x^4*Log[a + b*x^2]))/a^3 + 2*Log[c*(a + b*x^2)^p])/x^6","A",1
13,1,59,59,0.0138233,"\int x^5 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Integrate[x^5*Log[c*(a + b*x^3)^p],x]","-\frac{a^2 p \log \left(a+b x^3\right)}{6 b^2}+\frac{1}{6} x^6 \log \left(c \left(a+b x^3\right)^p\right)+\frac{a p x^3}{6 b}-\frac{p x^6}{12}","-\frac{a^2 p \log \left(a+b x^3\right)}{6 b^2}+\frac{1}{6} x^6 \log \left(c \left(a+b x^3\right)^p\right)+\frac{a p x^3}{6 b}-\frac{p x^6}{12}",1,"(a*p*x^3)/(6*b) - (p*x^6)/12 - (a^2*p*Log[a + b*x^3])/(6*b^2) + (x^6*Log[c*(a + b*x^3)^p])/6","A",1
14,1,69,159,0.0035845,"\int x^4 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Integrate[x^4*Log[c*(a + b*x^3)^p],x]","\frac{1}{5} x^5 \log \left(c \left(a+b x^3\right)^p\right)-\frac{3 a p x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)}{10 b}+\frac{3 a p x^2}{10 b}-\frac{3 p x^5}{25}","-\frac{a^{5/3} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{10 b^{5/3}}+\frac{a^{5/3} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{5 b^{5/3}}+\frac{\sqrt{3} a^{5/3} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{5 b^{5/3}}+\frac{1}{5} x^5 \log \left(c \left(a+b x^3\right)^p\right)+\frac{3 a p x^2}{10 b}-\frac{3 p x^5}{25}",1,"(3*a*p*x^2)/(10*b) - (3*p*x^5)/25 - (3*a*p*x^2*Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)])/(10*b) + (x^5*Log[c*(a + b*x^3)^p])/5","C",1
15,1,147,157,0.052887,"\int x^3 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Integrate[x^3*Log[c*(a + b*x^3)^p],x]","\frac{2 a^{4/3} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)-4 a^{4/3} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+4 \sqrt{3} a^{4/3} p \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)+4 b^{4/3} x^4 \log \left(c \left(a+b x^3\right)^p\right)+12 a \sqrt[3]{b} p x-3 b^{4/3} p x^4}{16 b^{4/3}}","\frac{a^{4/3} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{8 b^{4/3}}-\frac{a^{4/3} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{4 b^{4/3}}+\frac{\sqrt{3} a^{4/3} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{4 b^{4/3}}+\frac{1}{4} x^4 \log \left(c \left(a+b x^3\right)^p\right)+\frac{3 a p x}{4 b}-\frac{3 p x^4}{16}",1,"(12*a*b^(1/3)*p*x - 3*b^(4/3)*p*x^4 + 4*Sqrt[3]*a^(4/3)*p*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 4*a^(4/3)*p*Log[a^(1/3) + b^(1/3)*x] + 2*a^(4/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2] + 4*b^(4/3)*x^4*Log[c*(a + b*x^3)^p])/(16*b^(4/3))","A",1
16,1,34,35,0.0103362,"\int x^2 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Integrate[x^2*Log[c*(a + b*x^3)^p],x]","\frac{1}{3} \left(\frac{\left(a+b x^3\right) \log \left(c \left(a+b x^3\right)^p\right)}{b}-p x^3\right)","\frac{\left(a+b x^3\right) \log \left(c \left(a+b x^3\right)^p\right)}{3 b}-\frac{p x^3}{3}",1,"(-(p*x^3) + ((a + b*x^3)*Log[c*(a + b*x^3)^p])/b)/3","A",1
17,1,53,147,0.0028862,"\int x \log \left(c \left(a+b x^3\right)^p\right) \, dx","Integrate[x*Log[c*(a + b*x^3)^p],x]","\frac{1}{2} x^2 \log \left(c \left(a+b x^3\right)^p\right)+\frac{3}{4} p x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)-\frac{3 p x^2}{4}","\frac{a^{2/3} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{4 b^{2/3}}-\frac{a^{2/3} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 b^{2/3}}-\frac{\sqrt{3} a^{2/3} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{2 b^{2/3}}+\frac{1}{2} x^2 \log \left(c \left(a+b x^3\right)^p\right)-\frac{3 p x^2}{4}",1,"(-3*p*x^2)/4 + (3*p*x^2*Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)])/4 + (x^2*Log[c*(a + b*x^3)^p])/2","C",1
18,1,129,133,0.0375437,"\int \log \left(c \left(a+b x^3\right)^p\right) \, dx","Integrate[Log[c*(a + b*x^3)^p],x]","-\frac{\sqrt[3]{a} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \sqrt[3]{b}}+x \log \left(c \left(a+b x^3\right)^p\right)+\frac{\sqrt[3]{a} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{\sqrt{3} \sqrt[3]{a} p \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{\sqrt[3]{b}}-3 p x","-\frac{\sqrt[3]{a} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \sqrt[3]{b}}+x \log \left(c \left(a+b x^3\right)^p\right)+\frac{\sqrt[3]{a} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{\sqrt{3} \sqrt[3]{a} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{b}}-3 p x",1,"-3*p*x - (Sqrt[3]*a^(1/3)*p*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/b^(1/3) + (a^(1/3)*p*Log[a^(1/3) + b^(1/3)*x])/b^(1/3) - (a^(1/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(2*b^(1/3)) + x*Log[c*(a + b*x^3)^p]","A",1
19,1,43,44,0.0084317,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x} \, dx","Integrate[Log[c*(a + b*x^3)^p]/x,x]","\frac{1}{3} \left(\log \left(-\frac{b x^3}{a}\right) \log \left(c \left(a+b x^3\right)^p\right)+p \text{Li}_2\left(\frac{b x^3+a}{a}\right)\right)","\frac{1}{3} \log \left(-\frac{b x^3}{a}\right) \log \left(c \left(a+b x^3\right)^p\right)+\frac{1}{3} p \text{Li}_2\left(\frac{b x^3}{a}+1\right)",1,"(Log[-((b*x^3)/a)]*Log[c*(a + b*x^3)^p] + p*PolyLog[2, (a + b*x^3)/a])/3","A",1
20,1,47,133,0.0028433,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^2} \, dx","Integrate[Log[c*(a + b*x^3)^p]/x^2,x]","\frac{3 b p x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)}{2 a}-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{x}","\frac{\sqrt[3]{b} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \sqrt[3]{a}}-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{x}-\frac{\sqrt[3]{b} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a}}-\frac{\sqrt{3} \sqrt[3]{b} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a}}",1,"(3*b*p*x^2*Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)])/(2*a) - Log[c*(a + b*x^3)^p]/x","C",1
21,1,134,139,0.0352597,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^3} \, dx","Integrate[Log[c*(a + b*x^3)^p]/x^3,x]","-\frac{b^{2/3} p x^2 \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)+2 a^{2/3} \log \left(c \left(a+b x^3\right)^p\right)-2 b^{2/3} p x^2 \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+2 \sqrt{3} b^{2/3} p x^2 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{4 a^{2/3} x^2}","-\frac{b^{2/3} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{4 a^{2/3}}+\frac{b^{2/3} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 a^{2/3}}-\frac{\sqrt{3} b^{2/3} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{2 a^{2/3}}-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{2 x^2}",1,"-1/4*(2*Sqrt[3]*b^(2/3)*p*x^2*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 2*b^(2/3)*p*x^2*Log[a^(1/3) + b^(1/3)*x] + b^(2/3)*p*x^2*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2] + 2*a^(2/3)*Log[c*(a + b*x^3)^p])/(a^(2/3)*x^2)","A",1
22,1,45,45,0.0027931,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^4} \, dx","Integrate[Log[c*(a + b*x^3)^p]/x^4,x]","-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{3 x^3}-\frac{b p \log \left(a+b x^3\right)}{3 a}+\frac{b p \log (x)}{a}","-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{3 x^3}-\frac{b p \log \left(a+b x^3\right)}{3 a}+\frac{b p \log (x)}{a}",1,"(b*p*Log[x])/a - (b*p*Log[a + b*x^3])/(3*a) - Log[c*(a + b*x^3)^p]/(3*x^3)","A",1
23,1,49,151,0.0030344,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^5} \, dx","Integrate[Log[c*(a + b*x^3)^p]/x^5,x]","-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{4 x^4}-\frac{3 b p \, _2F_1\left(-\frac{1}{3},1;\frac{2}{3};-\frac{b x^3}{a}\right)}{4 a x}","-\frac{b^{4/3} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{8 a^{4/3}}+\frac{b^{4/3} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{4 a^{4/3}}+\frac{\sqrt{3} b^{4/3} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{4 a^{4/3}}-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{4 x^4}-\frac{3 b p}{4 a x}",1,"(-3*b*p*Hypergeometric2F1[-1/3, 1, 2/3, -((b*x^3)/a)])/(4*a*x) - Log[c*(a + b*x^3)^p]/(4*x^4)","C",1
24,1,49,151,0.0030712,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^6} \, dx","Integrate[Log[c*(a + b*x^3)^p]/x^6,x]","-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{5 x^5}-\frac{3 b p \, _2F_1\left(-\frac{2}{3},1;\frac{1}{3};-\frac{b x^3}{a}\right)}{10 a x^2}","\frac{b^{5/3} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{10 a^{5/3}}-\frac{b^{5/3} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{5 a^{5/3}}+\frac{\sqrt{3} b^{5/3} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{5 a^{5/3}}-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{5 x^5}-\frac{3 b p}{10 a x^2}",1,"(-3*b*p*Hypergeometric2F1[-2/3, 1, 1/3, -((b*x^3)/a)])/(10*a*x^2) - Log[c*(a + b*x^3)^p]/(5*x^5)","C",1
25,1,56,64,0.0394294,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^7} \, dx","Integrate[Log[c*(a + b*x^3)^p]/x^7,x]","\frac{1}{6} b p \left(\frac{b \log \left(a+b x^3\right)}{a^2}-\frac{3 b \log (x)}{a^2}-\frac{1}{a x^3}\right)-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{6 x^6}","\frac{b^2 p \log \left(a+b x^3\right)}{6 a^2}-\frac{b^2 p \log (x)}{2 a^2}-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{6 x^6}-\frac{b p}{6 a x^3}",1,"(b*p*(-(1/(a*x^3)) - (3*b*Log[x])/a^2 + (b*Log[a + b*x^3])/a^2))/6 - Log[c*(a + b*x^3)^p]/(6*x^6)","A",1
26,1,85,89,0.0491252,"\int x^4 \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Integrate[x^4*Log[c*(a + b/x)^p],x]","\frac{12 a^5 x^5 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+a b p x \left(3 a^3 x^3-4 a^2 b x^2+6 a b^2 x-12 b^3\right)+12 b^5 p \log \left(a+\frac{b}{x}\right)+12 b^5 p \log (x)}{60 a^5}","\frac{b^5 p \log (a x+b)}{5 a^5}-\frac{b^4 p x}{5 a^4}+\frac{b^3 p x^2}{10 a^3}-\frac{b^2 p x^3}{15 a^2}+\frac{1}{5} x^5 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p x^4}{20 a}",1,"(a*b*p*x*(-12*b^3 + 6*a*b^2*x - 4*a^2*b*x^2 + 3*a^3*x^3) + 12*b^5*p*Log[a + b/x] + 12*a^5*x^5*Log[c*(a + b/x)^p] + 12*b^5*p*Log[x])/(60*a^5)","A",1
27,1,74,75,0.0329718,"\int x^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Integrate[x^3*Log[c*(a + b/x)^p],x]","\frac{6 a^4 x^4 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+a b p x \left(2 a^2 x^2-3 a b x+6 b^2\right)-6 b^4 p \log \left(a+\frac{b}{x}\right)-6 b^4 p \log (x)}{24 a^4}","-\frac{b^4 p \log (a x+b)}{4 a^4}+\frac{b^3 p x}{4 a^3}-\frac{b^2 p x^2}{8 a^2}+\frac{1}{4} x^4 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p x^3}{12 a}",1,"(a*b*p*x*(6*b^2 - 3*a*b*x + 2*a^2*x^2) - 6*b^4*p*Log[a + b/x] + 6*a^4*x^4*Log[c*(a + b/x)^p] - 6*b^4*p*Log[x])/(24*a^4)","A",1
28,1,62,61,0.0258235,"\int x^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Integrate[x^2*Log[c*(a + b/x)^p],x]","\frac{2 a^3 x^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+2 b^3 p \log \left(a+\frac{b}{x}\right)+a b p x (a x-2 b)+2 b^3 p \log (x)}{6 a^3}","\frac{b^3 p \log (a x+b)}{3 a^3}-\frac{b^2 p x}{3 a^2}+\frac{1}{3} x^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p x^2}{6 a}",1,"(a*b*p*x*(-2*b + a*x) + 2*b^3*p*Log[a + b/x] + 2*a^3*x^3*Log[c*(a + b/x)^p] + 2*b^3*p*Log[x])/(6*a^3)","A",1
29,1,40,47,0.0183199,"\int x \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Integrate[x*Log[c*(a + b/x)^p],x]","\frac{1}{2} \left(\frac{b p (a x-b \log (a x+b))}{a^2}+x^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right)\right)","-\frac{b^2 p \log (a x+b)}{2 a^2}+\frac{1}{2} x^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p x}{2 a}",1,"(x^2*Log[c*(a + b/x)^p] + (b*p*(a*x - b*Log[b + a*x]))/a^2)/2","A",1
30,1,37,27,0.0022922,"\int \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Integrate[Log[c*(a + b/x)^p],x]","x \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p \log \left(a+\frac{b}{x}\right)}{a}+\frac{b p \log (x)}{a}","x \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p \log (a x+b)}{a}",1,"(b*p*Log[a + b/x])/a + x*Log[c*(a + b/x)^p] + (b*p*Log[x])/a","A",1
31,1,41,40,0.002937,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x} \, dx","Integrate[Log[c*(a + b/x)^p]/x,x]","\log \left(-\frac{b}{a x}\right) \left(-\log \left(c \left(a+\frac{b}{x}\right)^p\right)\right)-p \text{Li}_2\left(\frac{a+\frac{b}{x}}{a}\right)","\log \left(-\frac{b}{a x}\right) \left(-\log \left(c \left(a+\frac{b}{x}\right)^p\right)\right)-p \text{Li}_2\left(\frac{b}{a x}+1\right)",1,"-(Log[c*(a + b/x)^p]*Log[-(b/(a*x))]) - p*PolyLog[2, (a + b/x)/a]","A",1
32,1,30,30,0.0045633,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^2} \, dx","Integrate[Log[c*(a + b/x)^p]/x^2,x]","\frac{p}{x}-\frac{\left(a+\frac{b}{x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{b}","\frac{p}{x}-\frac{\left(a+\frac{b}{x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{b}",1,"p/x - ((a + b/x)*Log[c*(a + b/x)^p])/b","A",1
33,1,59,59,0.0148361,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^3} \, dx","Integrate[Log[c*(a + b/x)^p]/x^3,x]","\frac{a^2 p \log \left(a+\frac{b}{x}\right)}{2 b^2}-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{2 x^2}-\frac{a p}{2 b x}+\frac{p}{4 x^2}","\frac{a^2 p \log \left(a+\frac{b}{x}\right)}{2 b^2}-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{2 x^2}-\frac{a p}{2 b x}+\frac{p}{4 x^2}",1,"p/(4*x^2) - (a*p)/(2*b*x) + (a^2*p*Log[a + b/x])/(2*b^2) - Log[c*(a + b/x)^p]/(2*x^2)","A",1
34,1,73,73,0.0179295,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^4} \, dx","Integrate[Log[c*(a + b/x)^p]/x^4,x]","-\frac{a^3 p \log \left(a+\frac{b}{x}\right)}{3 b^3}+\frac{a^2 p}{3 b^2 x}-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{3 x^3}-\frac{a p}{6 b x^2}+\frac{p}{9 x^3}","-\frac{a^3 p \log \left(a+\frac{b}{x}\right)}{3 b^3}+\frac{a^2 p}{3 b^2 x}-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{3 x^3}-\frac{a p}{6 b x^2}+\frac{p}{9 x^3}",1,"p/(9*x^3) - (a*p)/(6*b*x^2) + (a^2*p)/(3*b^2*x) - (a^3*p*Log[a + b/x])/(3*b^3) - Log[c*(a + b/x)^p]/(3*x^3)","A",1
35,1,87,87,0.0213927,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^5} \, dx","Integrate[Log[c*(a + b/x)^p]/x^5,x]","\frac{a^4 p \log \left(a+\frac{b}{x}\right)}{4 b^4}-\frac{a^3 p}{4 b^3 x}+\frac{a^2 p}{8 b^2 x^2}-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{4 x^4}-\frac{a p}{12 b x^3}+\frac{p}{16 x^4}","\frac{a^4 p \log \left(a+\frac{b}{x}\right)}{4 b^4}-\frac{a^3 p}{4 b^3 x}+\frac{a^2 p}{8 b^2 x^2}-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{4 x^4}-\frac{a p}{12 b x^3}+\frac{p}{16 x^4}",1,"p/(16*x^4) - (a*p)/(12*b*x^3) + (a^2*p)/(8*b^2*x^2) - (a^3*p)/(4*b^3*x) + (a^4*p*Log[a + b/x])/(4*b^4) - Log[c*(a + b/x)^p]/(4*x^4)","A",1
36,1,49,72,0.0071368,"\int x^4 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Integrate[x^4*Log[c*(a + b/x^2)^p],x]","\frac{1}{5} x^5 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+\frac{2 b p x^3 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{b}{a x^2}\right)}{15 a}","\frac{2 b^{5/2} p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{5 a^{5/2}}-\frac{2 b^2 p x}{5 a^2}+\frac{1}{5} x^5 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+\frac{2 b p x^3}{15 a}",1,"(2*b*p*x^3*Hypergeometric2F1[-3/2, 1, -1/2, -(b/(a*x^2))])/(15*a) + (x^5*Log[c*(a + b/x^2)^p])/5","C",1
37,1,56,51,0.0218451,"\int x^3 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Integrate[x^3*Log[c*(a + b/x^2)^p],x]","\frac{1}{4} b p \left(-\frac{b \log \left(a+\frac{b}{x^2}\right)}{a^2}-\frac{2 b \log (x)}{a^2}+\frac{x^2}{a}\right)+\frac{1}{4} x^4 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)","-\frac{b^2 p \log \left(a x^2+b\right)}{4 a^2}+\frac{1}{4} x^4 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+\frac{b p x^2}{4 a}",1,"(x^4*Log[c*(a + b/x^2)^p])/4 + (b*p*(x^2/a - (b*Log[a + b/x^2])/a^2 - (2*b*Log[x])/a^2))/4","A",1
38,1,47,58,0.0029225,"\int x^2 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Integrate[x^2*Log[c*(a + b/x^2)^p],x]","\frac{1}{3} x^3 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+\frac{2 b p x \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b}{a x^2}\right)}{3 a}","-\frac{2 b^{3/2} p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{3 a^{3/2}}+\frac{1}{3} x^3 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+\frac{2 b p x}{3 a}",1,"(2*b*p*x*Hypergeometric2F1[-1/2, 1, 1/2, -(b/(a*x^2))])/(3*a) + (x^3*Log[c*(a + b/x^2)^p])/3","C",1
39,1,45,37,0.0026351,"\int x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Integrate[x*Log[c*(a + b/x^2)^p],x]","\frac{1}{2} x^2 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+\frac{b p \log \left(a+\frac{b}{x^2}\right)}{2 a}+\frac{b p \log (x)}{a}","\frac{1}{2} x^2 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+\frac{b p \log \left(a x^2+b\right)}{2 a}",1,"(b*p*Log[a + b/x^2])/(2*a) + (x^2*Log[c*(a + b/x^2)^p])/2 + (b*p*Log[x])/a","A",1
40,1,43,41,0.0077893,"\int \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Integrate[Log[c*(a + b/x^2)^p],x]","x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)-\frac{2 \sqrt{b} p \tan ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} x}\right)}{\sqrt{a}}","x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+\frac{2 \sqrt{b} p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{\sqrt{a}}",1,"(-2*Sqrt[b]*p*ArcTan[Sqrt[b]/(Sqrt[a]*x)])/Sqrt[a] + x*Log[c*(a + b/x^2)^p]","A",1
41,1,45,44,0.0032098,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x} \, dx","Integrate[Log[c*(a + b/x^2)^p]/x,x]","-\frac{1}{2} \log \left(-\frac{b}{a x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)-\frac{1}{2} p \text{Li}_2\left(\frac{a+\frac{b}{x^2}}{a}\right)","-\frac{1}{2} \log \left(-\frac{b}{a x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)-\frac{1}{2} p \text{Li}_2\left(\frac{b}{a x^2}+1\right)",1,"-1/2*(Log[c*(a + b/x^2)^p]*Log[-(b/(a*x^2))]) - (p*PolyLog[2, (a + b/x^2)/a])/2","A",1
42,1,52,50,0.014421,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x^2} \, dx","Integrate[Log[c*(a + b/x^2)^p]/x^2,x]","-\frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x}-\frac{2 \sqrt{a} p \tan ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} x}\right)}{\sqrt{b}}+\frac{2 p}{x}","-\frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x}+\frac{2 \sqrt{a} p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{\sqrt{b}}+\frac{2 p}{x}",1,"(2*p)/x - (2*Sqrt[a]*p*ArcTan[Sqrt[b]/(Sqrt[a]*x)])/Sqrt[b] - Log[c*(a + b/x^2)^p]/x","A",1
43,1,34,35,0.00872,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x^3} \, dx","Integrate[Log[c*(a + b/x^2)^p]/x^3,x]","\frac{1}{2} \left(\frac{p}{x^2}-\frac{\left(a+\frac{b}{x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{b}\right)","\frac{p}{2 x^2}-\frac{\left(a+\frac{b}{x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{2 b}",1,"(p/x^2 - ((a + b/x^2)*Log[c*(a + b/x^2)^p])/b)/2","A",1
44,1,70,68,0.0224111,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x^4} \, dx","Integrate[Log[c*(a + b/x^2)^p]/x^4,x]","\frac{2 a^{3/2} p \tan ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} x}\right)}{3 b^{3/2}}-\frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{3 x^3}-\frac{2 a p}{3 b x}+\frac{2 p}{9 x^3}","-\frac{2 a^{3/2} p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{3 b^{3/2}}-\frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{3 x^3}-\frac{2 a p}{3 b x}+\frac{2 p}{9 x^3}",1,"(2*p)/(9*x^3) - (2*a*p)/(3*b*x) + (2*a^(3/2)*p*ArcTan[Sqrt[b]/(Sqrt[a]*x)])/(3*b^(3/2)) - Log[c*(a + b/x^2)^p]/(3*x^3)","A",1
45,1,34,8,0.0036406,"\int \frac{\log \left(1+\frac{b}{x}\right)}{x} \, dx","Integrate[Log[1 + b/x]/x,x]","-\text{Li}_2\left(-\frac{-b-x}{x}\right)-\log \left(-\frac{b}{x}\right) \log \left(\frac{b+x}{x}\right)","\text{Li}_2\left(-\frac{b}{x}\right)",1,"-(Log[-(b/x)]*Log[(b + x)/x]) - PolyLog[2, -((-b - x)/x)]","B",1
46,1,134,153,0.1371966,"\int x^3 \log \left(c \left(a+b \sqrt{x}\right)^p\right) \, dx","Integrate[x^3*Log[c*(a + b*Sqrt[x])^p],x]","\frac{1}{4} \left(x^4 \log \left(c \left(a+b \sqrt{x}\right)^p\right)-\frac{p \left(840 a^8 \log \left(a+b \sqrt{x}\right)-840 a^7 b \sqrt{x}+420 a^6 b^2 x-280 a^5 b^3 x^{3/2}+210 a^4 b^4 x^2-168 a^3 b^5 x^{5/2}+140 a^2 b^6 x^3-120 a b^7 x^{7/2}+105 b^8 x^4\right)}{840 b^8}\right)","-\frac{a^8 p \log \left(a+b \sqrt{x}\right)}{4 b^8}+\frac{a^7 p \sqrt{x}}{4 b^7}-\frac{a^6 p x}{8 b^6}+\frac{a^5 p x^{3/2}}{12 b^5}-\frac{a^4 p x^2}{16 b^4}+\frac{a^3 p x^{5/2}}{20 b^3}-\frac{a^2 p x^3}{24 b^2}+\frac{1}{4} x^4 \log \left(c \left(a+b \sqrt{x}\right)^p\right)+\frac{a p x^{7/2}}{28 b}-\frac{p x^4}{32}",1,"(-1/840*(p*(-840*a^7*b*Sqrt[x] + 420*a^6*b^2*x - 280*a^5*b^3*x^(3/2) + 210*a^4*b^4*x^2 - 168*a^3*b^5*x^(5/2) + 140*a^2*b^6*x^3 - 120*a*b^7*x^(7/2) + 105*b^8*x^4 + 840*a^8*Log[a + b*Sqrt[x]]))/b^8 + x^4*Log[c*(a + b*Sqrt[x])^p])/4","A",1
47,1,112,123,0.055183,"\int x^2 \log \left(c \left(a+b \sqrt{x}\right)^p\right) \, dx","Integrate[x^2*Log[c*(a + b*Sqrt[x])^p],x]","\frac{-60 a^6 p \log \left(a+b \sqrt{x}\right)+b p \sqrt{x} \left(60 a^5-30 a^4 b \sqrt{x}+20 a^3 b^2 x-15 a^2 b^3 x^{3/2}+12 a b^4 x^2-10 b^5 x^{5/2}\right)+60 b^6 x^3 \log \left(c \left(a+b \sqrt{x}\right)^p\right)}{180 b^6}","-\frac{a^6 p \log \left(a+b \sqrt{x}\right)}{3 b^6}+\frac{a^5 p \sqrt{x}}{3 b^5}-\frac{a^4 p x}{6 b^4}+\frac{a^3 p x^{3/2}}{9 b^3}-\frac{a^2 p x^2}{12 b^2}+\frac{1}{3} x^3 \log \left(c \left(a+b \sqrt{x}\right)^p\right)+\frac{a p x^{5/2}}{15 b}-\frac{p x^3}{18}",1,"(b*p*Sqrt[x]*(60*a^5 - 30*a^4*b*Sqrt[x] + 20*a^3*b^2*x - 15*a^2*b^3*x^(3/2) + 12*a*b^4*x^2 - 10*b^5*x^(5/2)) - 60*a^6*p*Log[a + b*Sqrt[x]] + 60*b^6*x^3*Log[c*(a + b*Sqrt[x])^p])/(180*b^6)","A",1
48,1,88,93,0.0382671,"\int x \log \left(c \left(a+b \sqrt{x}\right)^p\right) \, dx","Integrate[x*Log[c*(a + b*Sqrt[x])^p],x]","\frac{-12 a^4 p \log \left(a+b \sqrt{x}\right)+b p \sqrt{x} \left(12 a^3-6 a^2 b \sqrt{x}+4 a b^2 x-3 b^3 x^{3/2}\right)+12 b^4 x^2 \log \left(c \left(a+b \sqrt{x}\right)^p\right)}{24 b^4}","-\frac{a^4 p \log \left(a+b \sqrt{x}\right)}{2 b^4}+\frac{a^3 p \sqrt{x}}{2 b^3}-\frac{a^2 p x}{4 b^2}+\frac{1}{2} x^2 \log \left(c \left(a+b \sqrt{x}\right)^p\right)+\frac{a p x^{3/2}}{6 b}-\frac{p x^2}{8}",1,"(b*p*Sqrt[x]*(12*a^3 - 6*a^2*b*Sqrt[x] + 4*a*b^2*x - 3*b^3*x^(3/2)) - 12*a^4*p*Log[a + b*Sqrt[x]] + 12*b^4*x^2*Log[c*(a + b*Sqrt[x])^p])/(24*b^4)","A",1
49,1,53,53,0.0248445,"\int \log \left(c \left(a+b \sqrt{x}\right)^p\right) \, dx","Integrate[Log[c*(a + b*Sqrt[x])^p],x]","-\frac{a^2 p \log \left(a+b \sqrt{x}\right)}{b^2}+x \log \left(c \left(a+b \sqrt{x}\right)^p\right)+\frac{a p \sqrt{x}}{b}-\frac{p x}{2}","-\frac{a^2 p \log \left(a+b \sqrt{x}\right)}{b^2}+x \log \left(c \left(a+b \sqrt{x}\right)^p\right)+\frac{a p \sqrt{x}}{b}-\frac{p x}{2}",1,"(a*p*Sqrt[x])/b - (p*x)/2 - (a^2*p*Log[a + b*Sqrt[x]])/b^2 + x*Log[c*(a + b*Sqrt[x])^p]","A",1
50,1,47,46,0.0030339,"\int \frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{x} \, dx","Integrate[Log[c*(a + b*Sqrt[x])^p]/x,x]","2 \log \left(-\frac{b \sqrt{x}}{a}\right) \log \left(c \left(a+b \sqrt{x}\right)^p\right)+2 p \text{Li}_2\left(\frac{a+b \sqrt{x}}{a}\right)","2 \log \left(-\frac{b \sqrt{x}}{a}\right) \log \left(c \left(a+b \sqrt{x}\right)^p\right)+2 p \text{Li}_2\left(\frac{\sqrt{x} b}{a}+1\right)",1,"2*Log[c*(a + b*Sqrt[x])^p]*Log[-((b*Sqrt[x])/a)] + 2*p*PolyLog[2, (a + b*Sqrt[x])/a]","A",1
51,1,55,63,0.0411751,"\int \frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{x^2} \, dx","Integrate[Log[c*(a + b*Sqrt[x])^p]/x^2,x]","-\frac{b p \left(-2 b \log \left(a+b \sqrt{x}\right)+\frac{2 a}{\sqrt{x}}+b \log (x)\right)}{2 a^2}-\frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{x}","\frac{b^2 p \log \left(a+b \sqrt{x}\right)}{a^2}-\frac{b^2 p \log (x)}{2 a^2}-\frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{x}-\frac{b p}{a \sqrt{x}}",1,"-(Log[c*(a + b*Sqrt[x])^p]/x) - (b*p*((2*a)/Sqrt[x] - 2*b*Log[a + b*Sqrt[x]] + b*Log[x]))/(2*a^2)","A",1
52,1,90,100,0.0481093,"\int \frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{x^3} \, dx","Integrate[Log[c*(a + b*Sqrt[x])^p]/x^3,x]","\frac{-6 a^4 \log \left(c \left(a+b \sqrt{x}\right)^p\right)+a b p \sqrt{x} \left(-2 a^2+3 a b \sqrt{x}-6 b^2 x\right)+6 b^4 p x^2 \log \left(a+b \sqrt{x}\right)-3 b^4 p x^2 \log (x)}{12 a^4 x^2}","\frac{b^4 p \log \left(a+b \sqrt{x}\right)}{2 a^4}-\frac{b^4 p \log (x)}{4 a^4}-\frac{b^3 p}{2 a^3 \sqrt{x}}+\frac{b^2 p}{4 a^2 x}-\frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{2 x^2}-\frac{b p}{6 a x^{3/2}}",1,"(a*b*p*Sqrt[x]*(-2*a^2 + 3*a*b*Sqrt[x] - 6*b^2*x) + 6*b^4*p*x^2*Log[a + b*Sqrt[x]] - 6*a^4*Log[c*(a + b*Sqrt[x])^p] - 3*b^4*p*x^2*Log[x])/(12*a^4*x^2)","A",1
53,1,114,130,0.0668908,"\int \frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{x^4} \, dx","Integrate[Log[c*(a + b*Sqrt[x])^p]/x^4,x]","\frac{-60 a^6 \log \left(c \left(a+b \sqrt{x}\right)^p\right)+a b p \sqrt{x} \left(-12 a^4+15 a^3 b \sqrt{x}-20 a^2 b^2 x+30 a b^3 x^{3/2}-60 b^4 x^2\right)+60 b^6 p x^3 \log \left(a+b \sqrt{x}\right)-30 b^6 p x^3 \log (x)}{180 a^6 x^3}","\frac{b^6 p \log \left(a+b \sqrt{x}\right)}{3 a^6}-\frac{b^6 p \log (x)}{6 a^6}-\frac{b^5 p}{3 a^5 \sqrt{x}}+\frac{b^4 p}{6 a^4 x}-\frac{b^3 p}{9 a^3 x^{3/2}}+\frac{b^2 p}{12 a^2 x^2}-\frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{3 x^3}-\frac{b p}{15 a x^{5/2}}",1,"(a*b*p*Sqrt[x]*(-12*a^4 + 15*a^3*b*Sqrt[x] - 20*a^2*b^2*x + 30*a*b^3*x^(3/2) - 60*b^4*x^2) + 60*b^6*p*x^3*Log[a + b*Sqrt[x]] - 60*a^6*Log[c*(a + b*Sqrt[x])^p] - 30*b^6*p*x^3*Log[x])/(180*a^6*x^3)","A",1
54,1,33,32,0.0101329,"\int \frac{\log \left(a+b \sqrt{x}\right)}{\sqrt{x}} \, dx","Integrate[Log[a + b*Sqrt[x]]/Sqrt[x],x]","2 \left(\frac{\left(a+b \sqrt{x}\right) \log \left(a+b \sqrt{x}\right)}{b}-\sqrt{x}\right)","\frac{2 \left(a+b \sqrt{x}\right) \log \left(a+b \sqrt{x}\right)}{b}-2 \sqrt{x}",1,"2*(-Sqrt[x] + ((a + b*Sqrt[x])*Log[a + b*Sqrt[x]])/b)","A",1
55,1,70,81,0.0286756,"\int (f x)^m \log \left(c \left(d+e x^3\right)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e*x^3)^p],x]","\frac{x (f x)^m \left(d (m+4) \log \left(c \left(d+e x^3\right)^p\right)-3 e p x^3 \, _2F_1\left(1,\frac{m+4}{3};\frac{m+7}{3};-\frac{e x^3}{d}\right)\right)}{d (m+1) (m+4)}","\frac{(f x)^{m+1} \log \left(c \left(d+e x^3\right)^p\right)}{f (m+1)}-\frac{3 e p (f x)^{m+4} \, _2F_1\left(1,\frac{m+4}{3};\frac{m+7}{3};-\frac{e x^3}{d}\right)}{d f^4 (m+1) (m+4)}",1,"(x*(f*x)^m*(-3*e*p*x^3*Hypergeometric2F1[1, (4 + m)/3, (7 + m)/3, -((e*x^3)/d)] + d*(4 + m)*Log[c*(d + e*x^3)^p]))/(d*(1 + m)*(4 + m))","A",1
56,1,70,81,0.028486,"\int (f x)^m \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e*x^2)^p],x]","\frac{x (f x)^m \left(d (m+3) \log \left(c \left(d+e x^2\right)^p\right)-2 e p x^2 \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};-\frac{e x^2}{d}\right)\right)}{d (m+1) (m+3)}","\frac{(f x)^{m+1} \log \left(c \left(d+e x^2\right)^p\right)}{f (m+1)}-\frac{2 e p (f x)^{m+3} \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};-\frac{e x^2}{d}\right)}{d f^3 (m+1) (m+3)}",1,"(x*(f*x)^m*(-2*e*p*x^2*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, -((e*x^2)/d)] + d*(3 + m)*Log[c*(d + e*x^2)^p]))/(d*(1 + m)*(3 + m))","A",1
57,1,56,69,0.0258926,"\int (f x)^m \log \left(c (d+e x)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e*x)^p],x]","\frac{x (f x)^m \left(d (m+2) \log \left(c (d+e x)^p\right)-e p x \, _2F_1\left(1,m+2;m+3;-\frac{e x}{d}\right)\right)}{d (m+1) (m+2)}","\frac{(f x)^{m+1} \log \left(c (d+e x)^p\right)}{f (m+1)}-\frac{e p (f x)^{m+2} \, _2F_1\left(1,m+2;m+3;-\frac{e x}{d}\right)}{d f^2 (m+1) (m+2)}",1,"(x*(f*x)^m*(-(e*p*x*Hypergeometric2F1[1, 2 + m, 3 + m, -((e*x)/d)]) + d*(2 + m)*Log[c*(d + e*x)^p]))/(d*(1 + m)*(2 + m))","A",1
58,1,56,67,0.0167692,"\int (f x)^m \log \left(c \left(d+\frac{e}{x}\right)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e/x)^p],x]","\frac{(f x)^m \left(d m x \log \left(c \left(d+\frac{e}{x}\right)^p\right)+e p \, _2F_1\left(1,-m;1-m;-\frac{e}{d x}\right)\right)}{d m (m+1)}","\frac{(f x)^{m+1} \log \left(c \left(d+\frac{e}{x}\right)^p\right)}{f (m+1)}+\frac{e p (f x)^m \, _2F_1\left(1,-m;1-m;-\frac{e}{d x}\right)}{d m (m+1)}",1,"((f*x)^m*(e*p*Hypergeometric2F1[1, -m, 1 - m, -(e/(d*x))] + d*m*x*Log[c*(d + e/x)^p]))/(d*m*(1 + m))","A",1
59,1,76,82,0.030436,"\int (f x)^m \log \left(c \left(d+\frac{e}{x^2}\right)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e/x^2)^p],x]","\frac{(f x)^m \left(d (m-1) x^2 \log \left(c \left(d+\frac{e}{x^2}\right)^p\right)+2 e p \, _2F_1\left(1,\frac{1}{2}-\frac{m}{2};\frac{3}{2}-\frac{m}{2};-\frac{e}{d x^2}\right)\right)}{d (m-1) (m+1) x}","\frac{(f x)^{m+1} \log \left(c \left(d+\frac{e}{x^2}\right)^p\right)}{f (m+1)}-\frac{2 e f p (f x)^{m-1} \, _2F_1\left(1,\frac{1-m}{2};\frac{3-m}{2};-\frac{e}{d x^2}\right)}{d \left(1-m^2\right)}",1,"((f*x)^m*(2*e*p*Hypergeometric2F1[1, 1/2 - m/2, 3/2 - m/2, -(e/(d*x^2))] + d*(-1 + m)*x^2*Log[c*(d + e/x^2)^p]))/(d*(-1 + m)*(1 + m)*x)","A",1
60,1,76,85,0.0321929,"\int (f x)^m \log \left(c \left(d+\frac{e}{x^3}\right)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e/x^3)^p],x]","\frac{(f x)^m \left(d (m-2) x^3 \log \left(c \left(d+\frac{e}{x^3}\right)^p\right)+3 e p \, _2F_1\left(1,\frac{2}{3}-\frac{m}{3};\frac{5}{3}-\frac{m}{3};-\frac{e}{d x^3}\right)\right)}{d (m-2) (m+1) x^2}","\frac{(f x)^{m+1} \log \left(c \left(d+\frac{e}{x^3}\right)^p\right)}{f (m+1)}-\frac{3 e f^2 p (f x)^{m-2} \, _2F_1\left(1,\frac{2-m}{3};\frac{5-m}{3};-\frac{e}{d x^3}\right)}{d \left(-m^2+m+2\right)}",1,"((f*x)^m*(3*e*p*Hypergeometric2F1[1, 2/3 - m/3, 5/3 - m/3, -(e/(d*x^3))] + d*(-2 + m)*x^3*Log[c*(d + e/x^3)^p]))/(d*(-2 + m)*(1 + m)*x^2)","A",1
61,1,76,83,0.0354874,"\int (f x)^m \log \left(c \left(d+e \sqrt{x}\right)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e*Sqrt[x])^p],x]","\frac{x (f x)^m \left(d (2 m+3) \log \left(c \left(d+e \sqrt{x}\right)^p\right)-e p \sqrt{x} \, _2F_1\left(1,2 m+3;2 m+4;-\frac{e \sqrt{x}}{d}\right)\right)}{d (m+1) (2 m+3)}","\frac{(f x)^{m+1} \log \left(c \left(d+e \sqrt{x}\right)^p\right)}{f (m+1)}-\frac{e p x^{3/2} (f x)^m \, _2F_1\left(1,2 m+3;2 (m+2);-\frac{e \sqrt{x}}{d}\right)}{d \left(2 m^2+5 m+3\right)}",1,"(x*(f*x)^m*(-(e*p*Sqrt[x]*Hypergeometric2F1[1, 3 + 2*m, 4 + 2*m, -((e*Sqrt[x])/d)]) + d*(3 + 2*m)*Log[c*(d + e*Sqrt[x])^p]))/(d*(1 + m)*(3 + 2*m))","A",1
62,1,77,70,0.0388513,"\int (f x)^m \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e/Sqrt[x])^p],x]","\frac{\sqrt{x} (f x)^m \left(d (2 m+1) \sqrt{x} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right)+e p \, _2F_1\left(1,-2 m-1;-2 m;-\frac{e}{d \sqrt{x}}\right)\right)}{d (m+1) (2 m+1)}","\frac{(f x)^{m+1} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right)}{f (m+1)}+\frac{p x (f x)^m \, _2F_1\left(1,2 (m+1);2 m+3;-\frac{d \sqrt{x}}{e}\right)}{2 (m+1)^2}",1,"(Sqrt[x]*(f*x)^m*(e*p*Hypergeometric2F1[1, -1 - 2*m, -2*m, -(e/(d*Sqrt[x]))] + d*(1 + 2*m)*Sqrt[x]*Log[c*(d + e/Sqrt[x])^p]))/(d*(1 + m)*(1 + 2*m))","A",1
63,1,77,87,0.0381699,"\int (f x)^m \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e*x^n)^p],x]","\frac{x (f x)^m \left(d (m+n+1) \log \left(c \left(d+e x^n\right)^p\right)-e n p x^n \, _2F_1\left(1,\frac{m+n+1}{n};\frac{m+2 n+1}{n};-\frac{e x^n}{d}\right)\right)}{d (m+1) (m+n+1)}","\frac{(f x)^{m+1} \log \left(c \left(d+e x^n\right)^p\right)}{f (m+1)}-\frac{e n p x^{n+1} (f x)^m \, _2F_1\left(1,\frac{m+n+1}{n};\frac{m+2 n+1}{n};-\frac{e x^n}{d}\right)}{d (m+1) (m+n+1)}",1,"(x*(f*x)^m*(-(e*n*p*x^n*Hypergeometric2F1[1, (1 + m + n)/n, (1 + m + 2*n)/n, -((e*x^n)/d)]) + d*(1 + m + n)*Log[c*(d + e*x^n)^p]))/(d*(1 + m)*(1 + m + n))","A",1
64,1,92,141,0.0800417,"\int (f x)^{-1+3 n} \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f*x)^(-1 + 3*n)*Log[c*(d + e*x^n)^p],x]","\frac{x^{-3 n} (f x)^{3 n} \left(6 e^3 x^{3 n} \log \left(c \left(d+e x^n\right)^p\right)+6 d^3 p \log \left(d+e x^n\right)-e p x^n \left(6 d^2-3 d e x^n+2 e^2 x^{2 n}\right)\right)}{18 e^3 f n}","\frac{(f x)^{3 n} \log \left(c \left(d+e x^n\right)^p\right)}{3 f n}+\frac{d^3 p x^{-3 n} (f x)^{3 n} \log \left(d+e x^n\right)}{3 e^3 f n}-\frac{d^2 p x^{-2 n} (f x)^{3 n}}{3 e^2 f n}+\frac{d p x^{-n} (f x)^{3 n}}{6 e f n}-\frac{p (f x)^{3 n}}{9 f n}",1,"((f*x)^(3*n)*(-(e*p*x^n*(6*d^2 - 3*d*e*x^n + 2*e^2*x^(2*n))) + 6*d^3*p*Log[d + e*x^n] + 6*e^3*x^(3*n)*Log[c*(d + e*x^n)^p]))/(18*e^3*f*n*x^(3*n))","A",1
65,1,74,112,0.0407066,"\int (f x)^{-1+2 n} \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f*x)^(-1 + 2*n)*Log[c*(d + e*x^n)^p],x]","-\frac{x^{-2 n} (f x)^{2 n} \left(e x^n \left(-2 e x^n \log \left(c \left(d+e x^n\right)^p\right)-2 d p+e p x^n\right)+2 d^2 p \log \left(d+e x^n\right)\right)}{4 e^2 f n}","\frac{(f x)^{2 n} \log \left(c \left(d+e x^n\right)^p\right)}{2 f n}-\frac{d^2 p x^{-2 n} (f x)^{2 n} \log \left(d+e x^n\right)}{2 e^2 f n}+\frac{d p x^{-n} (f x)^{2 n}}{2 e f n}-\frac{p (f x)^{2 n}}{4 f n}",1,"-1/4*((f*x)^(2*n)*(2*d^2*p*Log[d + e*x^n] + e*x^n*(-2*d*p + e*p*x^n - 2*e*x^n*Log[c*(d + e*x^n)^p])))/(e^2*f*n*x^(2*n))","A",1
66,1,48,69,0.0337523,"\int (f x)^{-1+n} \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f*x)^(-1 + n)*Log[c*(d + e*x^n)^p],x]","\frac{x^{1-n} (f x)^{n-1} \left(\frac{\left(d+e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)}{e}-p x^n\right)}{n}","\frac{(f x)^n \log \left(c \left(d+e x^n\right)^p\right)}{f n}+\frac{d p x^{-n} (f x)^n \log \left(d+e x^n\right)}{e f n}-\frac{p (f x)^n}{f n}",1,"(x^(1 - n)*(f*x)^(-1 + n)*(-(p*x^n) + ((d + e*x^n)*Log[c*(d + e*x^n)^p])/e))/n","A",1
67,1,46,50,0.0105488,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{f x} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(f*x),x]","\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)+p \text{Li}_2\left(\frac{e x^n+d}{d}\right)}{f n}","\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{f n}+\frac{p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{f n}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p] + p*PolyLog[2, (d + e*x^n)/d])/(f*n)","A",1
68,1,57,80,0.0181357,"\int (f x)^{-1-n} \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f*x)^(-1 - n)*Log[c*(d + e*x^n)^p],x]","-\frac{(f x)^{-n} \left(d \log \left(c \left(d+e x^n\right)^p\right)+e p x^n \log \left(d+e x^n\right)-e n p x^n \log (x)\right)}{d f n}","-\frac{(f x)^{-n} \log \left(c \left(d+e x^n\right)^p\right)}{f n}+\frac{e p x^n \log (x) (f x)^{-n}}{d f}-\frac{e p x^n (f x)^{-n} \log \left(d+e x^n\right)}{d f n}",1,"-((-(e*n*p*x^n*Log[x]) + e*p*x^n*Log[d + e*x^n] + d*Log[c*(d + e*x^n)^p])/(d*f*n*(f*x)^n))","A",1
69,1,76,120,0.0481217,"\int (f x)^{-1-2 n} \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f*x)^(-1 - 2*n)*Log[c*(d + e*x^n)^p],x]","-\frac{(f x)^{-2 n} \left(d \left(d \log \left(c \left(d+e x^n\right)^p\right)+e p x^n\right)-e^2 p x^{2 n} \log \left(d+e x^n\right)+e^2 n p x^{2 n} \log (x)\right)}{2 d^2 f n}","-\frac{(f x)^{-2 n} \log \left(c \left(d+e x^n\right)^p\right)}{2 f n}-\frac{e^2 p x^{2 n} \log (x) (f x)^{-2 n}}{2 d^2 f}+\frac{e^2 p x^{2 n} (f x)^{-2 n} \log \left(d+e x^n\right)}{2 d^2 f n}-\frac{e p x^n (f x)^{-2 n}}{2 d f n}",1,"-1/2*(e^2*n*p*x^(2*n)*Log[x] - e^2*p*x^(2*n)*Log[d + e*x^n] + d*(e*p*x^n + d*Log[c*(d + e*x^n)^p]))/(d^2*f*n*(f*x)^(2*n))","A",1
70,1,61,65,0.0329444,"\int x^2 \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[x^2*Log[c*(d + e*x^n)^p],x]","\frac{1}{3} x^3 \left(\log \left(c \left(d+e x^n\right)^p\right)-\frac{e n p x^n \, _2F_1\left(1,\frac{n+3}{n};2+\frac{3}{n};-\frac{e x^n}{d}\right)}{d (n+3)}\right)","\frac{1}{3} x^3 \log \left(c \left(d+e x^n\right)^p\right)-\frac{e n p x^{n+3} \, _2F_1\left(1,\frac{n+3}{n};2+\frac{3}{n};-\frac{e x^n}{d}\right)}{3 d (n+3)}",1,"(x^3*(-((e*n*p*x^n*Hypergeometric2F1[1, (3 + n)/n, 2 + 3/n, -((e*x^n)/d)])/(d*(3 + n))) + Log[c*(d + e*x^n)^p]))/3","A",1
71,1,61,65,0.0326618,"\int x \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[x*Log[c*(d + e*x^n)^p],x]","\frac{1}{2} x^2 \left(\log \left(c \left(d+e x^n\right)^p\right)-\frac{e n p x^n \, _2F_1\left(1,\frac{n+2}{n};2+\frac{2}{n};-\frac{e x^n}{d}\right)}{d (n+2)}\right)","\frac{1}{2} x^2 \log \left(c \left(d+e x^n\right)^p\right)-\frac{e n p x^{n+2} \, _2F_1\left(1,\frac{n+2}{n};2 \left(1+\frac{1}{n}\right);-\frac{e x^n}{d}\right)}{2 d (n+2)}",1,"(x^2*(-((e*n*p*x^n*Hypergeometric2F1[1, (2 + n)/n, 2 + 2/n, -((e*x^n)/d)])/(d*(2 + n))) + Log[c*(d + e*x^n)^p]))/2","A",1
72,1,52,54,0.0302555,"\int \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[Log[c*(d + e*x^n)^p],x]","x \left(\log \left(c \left(d+e x^n\right)^p\right)-\frac{e n p x^n \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{e x^n}{d}\right)}{d (n+1)}\right)","x \log \left(c \left(d+e x^n\right)^p\right)-\frac{e n p x^{n+1} \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{e x^n}{d}\right)}{d (n+1)}",1,"x*(-((e*n*p*x^n*Hypergeometric2F1[1, 1 + n^(-1), 2 + n^(-1), -((e*x^n)/d)])/(d*(1 + n))) + Log[c*(d + e*x^n)^p])","A",1
73,1,43,44,0.0030867,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[Log[c*(d + e*x^n)^p]/x,x]","\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)+p \text{Li}_2\left(\frac{e x^n+d}{d}\right)}{n}","\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p] + p*PolyLog[2, (d + e*x^n)/d])/n","A",1
74,1,59,66,0.0338616,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x^2} \, dx","Integrate[Log[c*(d + e*x^n)^p]/x^2,x]","\frac{\frac{e n p x^n \, _2F_1\left(1,\frac{n-1}{n};2-\frac{1}{n};-\frac{e x^n}{d}\right)}{d (n-1)}-\log \left(c \left(d+e x^n\right)^p\right)}{x}","-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{x}-\frac{e n p x^{n-1} \, _2F_1\left(1,-\frac{1-n}{n};2-\frac{1}{n};-\frac{e x^n}{d}\right)}{d (1-n)}",1,"((e*n*p*x^n*Hypergeometric2F1[1, (-1 + n)/n, 2 - n^(-1), -((e*x^n)/d)])/(d*(-1 + n)) - Log[c*(d + e*x^n)^p])/x","A",1
75,1,62,72,0.0271359,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x^3} \, dx","Integrate[Log[c*(d + e*x^n)^p]/x^3,x]","\frac{\frac{e n p x^n \, _2F_1\left(1,\frac{n-2}{n};2-\frac{2}{n};-\frac{e x^n}{d}\right)}{d (n-2)}-\log \left(c \left(d+e x^n\right)^p\right)}{2 x^2}","-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{2 x^2}-\frac{e n p x^{n-2} \, _2F_1\left(1,-\frac{2-n}{n};2 \left(1-\frac{1}{n}\right);-\frac{e x^n}{d}\right)}{2 d (2-n)}",1,"((e*n*p*x^n*Hypergeometric2F1[1, (-2 + n)/n, 2 - 2/n, -((e*x^n)/d)])/(d*(-2 + n)) - Log[c*(d + e*x^n)^p])/(2*x^2)","A",1
76,1,62,70,0.0264465,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x^4} \, dx","Integrate[Log[c*(d + e*x^n)^p]/x^4,x]","\frac{\frac{e n p x^n \, _2F_1\left(1,\frac{n-3}{n};2-\frac{3}{n};-\frac{e x^n}{d}\right)}{d (n-3)}-\log \left(c \left(d+e x^n\right)^p\right)}{3 x^3}","-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{3 x^3}-\frac{e n p x^{n-3} \, _2F_1\left(1,-\frac{3-n}{n};2-\frac{3}{n};-\frac{e x^n}{d}\right)}{3 d (3-n)}",1,"((e*n*p*x^n*Hypergeometric2F1[1, (-3 + n)/n, 2 - 3/n, -((e*x^n)/d)])/(d*(-3 + n)) - Log[c*(d + e*x^n)^p])/(3*x^3)","A",1
77,1,200,215,0.0650277,"\int x^5 \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x^5*Log[c*(a + b*x^2)^p]^2,x]","\frac{a^3 \log ^2\left(c \left(a+b x^2\right)^p\right)}{6 b^3}-\frac{a^3 p \log \left(c \left(a+b x^2\right)^p\right)}{3 b^3}-\frac{5 a^3 p^2 \log \left(a+b x^2\right)}{18 b^3}-\frac{a^2 p x^2 \log \left(c \left(a+b x^2\right)^p\right)}{3 b^2}+\frac{11 a^2 p^2 x^2}{18 b^2}+\frac{1}{6} x^6 \log ^2\left(c \left(a+b x^2\right)^p\right)-\frac{1}{9} p x^6 \log \left(c \left(a+b x^2\right)^p\right)+\frac{a p x^4 \log \left(c \left(a+b x^2\right)^p\right)}{6 b}-\frac{5 a p^2 x^4}{36 b}+\frac{p^2 x^6}{27}","\frac{a^3 p \log \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{3 b^3}-\frac{a^3 p^2 \log ^2\left(a+b x^2\right)}{6 b^3}-\frac{a^2 p \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b^3}+\frac{a^2 p^2 x^2}{b^2}-\frac{p \left(a+b x^2\right)^3 \log \left(c \left(a+b x^2\right)^p\right)}{9 b^3}+\frac{a p \left(a+b x^2\right)^2 \log \left(c \left(a+b x^2\right)^p\right)}{2 b^3}+\frac{p^2 \left(a+b x^2\right)^3}{27 b^3}-\frac{a p^2 \left(a+b x^2\right)^2}{4 b^3}+\frac{1}{6} x^6 \log ^2\left(c \left(a+b x^2\right)^p\right)",1,"(11*a^2*p^2*x^2)/(18*b^2) - (5*a*p^2*x^4)/(36*b) + (p^2*x^6)/27 - (5*a^3*p^2*Log[a + b*x^2])/(18*b^3) - (a^3*p*Log[c*(a + b*x^2)^p])/(3*b^3) - (a^2*p*x^2*Log[c*(a + b*x^2)^p])/(3*b^2) + (a*p*x^4*Log[c*(a + b*x^2)^p])/(6*b) - (p*x^6*Log[c*(a + b*x^2)^p])/9 + (a^3*Log[c*(a + b*x^2)^p]^2)/(6*b^3) + (x^6*Log[c*(a + b*x^2)^p]^2)/6","A",1
78,1,105,145,0.0592573,"\int x^3 \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x^3*Log[c*(a + b*x^2)^p]^2,x]","\frac{-2 \left(a^2-b^2 x^4\right) \log ^2\left(c \left(a+b x^2\right)^p\right)+2 p \left(2 a^2+2 a b x^2-b^2 x^4\right) \log \left(c \left(a+b x^2\right)^p\right)+2 a^2 p^2 \log \left(a+b x^2\right)+b p^2 x^2 \left(b x^2-6 a\right)}{8 b^2}","\frac{\left(a+b x^2\right)^2 \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 b^2}-\frac{a \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 b^2}-\frac{p \left(a+b x^2\right)^2 \log \left(c \left(a+b x^2\right)^p\right)}{4 b^2}+\frac{a p \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b^2}+\frac{p^2 \left(a+b x^2\right)^2}{8 b^2}-\frac{a p^2 x^2}{b}",1,"(b*p^2*x^2*(-6*a + b*x^2) + 2*a^2*p^2*Log[a + b*x^2] + 2*p*(2*a^2 + 2*a*b*x^2 - b^2*x^4)*Log[c*(a + b*x^2)^p] - 2*(a^2 - b^2*x^4)*Log[c*(a + b*x^2)^p]^2)/(8*b^2)","A",1
79,1,63,61,0.0095119,"\int x \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x*Log[c*(a + b*x^2)^p]^2,x]","\frac{1}{2} \left(\frac{\left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{b}-2 p \left(\frac{\left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b}-p x^2\right)\right)","\frac{\left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 b}-\frac{p \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b}+p^2 x^2",1,"(((a + b*x^2)*Log[c*(a + b*x^2)^p]^2)/b - 2*p*(-(p*x^2) + ((a + b*x^2)*Log[c*(a + b*x^2)^p])/b))/2","A",1
80,1,163,72,0.0653556,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x} \, dx","Integrate[Log[c*(a + b*x^2)^p]^2/x,x]","2 p \left(\log (x) \left(\log \left(a+b x^2\right)-\log \left(\frac{b x^2}{a}+1\right)\right)-\frac{1}{2} \text{Li}_2\left(-\frac{b x^2}{a}\right)\right) \left(\log \left(c \left(a+b x^2\right)^p\right)-p \log \left(a+b x^2\right)\right)+\log (x) \left(\log \left(c \left(a+b x^2\right)^p\right)-p \log \left(a+b x^2\right)\right)^2+\frac{1}{2} p^2 \left(-2 \text{Li}_3\left(\frac{b x^2}{a}+1\right)+2 \text{Li}_2\left(\frac{b x^2}{a}+1\right) \log \left(a+b x^2\right)+\log \left(-\frac{b x^2}{a}\right) \log ^2\left(a+b x^2\right)\right)","p \text{Li}_2\left(\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)+\frac{1}{2} \log \left(-\frac{b x^2}{a}\right) \log ^2\left(c \left(a+b x^2\right)^p\right)+p^2 \left(-\text{Li}_3\left(\frac{b x^2}{a}+1\right)\right)",1,"Log[x]*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2 + 2*p*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])*(Log[x]*(Log[a + b*x^2] - Log[1 + (b*x^2)/a]) - PolyLog[2, -((b*x^2)/a)]/2) + (p^2*(Log[-((b*x^2)/a)]*Log[a + b*x^2]^2 + 2*Log[a + b*x^2]*PolyLog[2, 1 + (b*x^2)/a] - 2*PolyLog[3, 1 + (b*x^2)/a]))/2","B",1
81,1,93,80,0.025093,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^3} \, dx","Integrate[Log[c*(a + b*x^2)^p]^2/x^3,x]","-\frac{b \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 a}-\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{2 x^2}+\frac{b p \log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)}{a}+\frac{b p^2 \text{Li}_2\left(\frac{b x^2+a}{a}\right)}{a}","-\frac{\left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 a x^2}+\frac{b p \log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)}{a}+\frac{b p^2 \text{Li}_2\left(\frac{b x^2}{a}+1\right)}{a}",1,"(b*p*Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p])/a - (b*Log[c*(a + b*x^2)^p]^2)/(2*a) - Log[c*(a + b*x^2)^p]^2/(2*x^2) + (b*p^2*PolyLog[2, (a + b*x^2)/a])/a","A",1
82,1,137,129,0.0812232,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^5} \, dx","Integrate[Log[c*(a + b*x^2)^p]^2/x^5,x]","\frac{\frac{b x^2 \left(-2 b p x^2 \left(\log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)+p \text{Li}_2\left(\frac{b x^2}{a}+1\right)\right)+b x^2 \log ^2\left(c \left(a+b x^2\right)^p\right)-2 a p \log \left(c \left(a+b x^2\right)^p\right)+2 b p^2 x^2 \left(2 \log (x)-\log \left(a+b x^2\right)\right)\right)}{a^2}-\log ^2\left(c \left(a+b x^2\right)^p\right)}{4 x^4}","-\frac{b^2 p \log \left(1-\frac{a}{a+b x^2}\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 a^2}+\frac{b^2 p^2 \text{Li}_2\left(\frac{a}{b x^2+a}\right)}{2 a^2}+\frac{b^2 p^2 \log (x)}{a^2}-\frac{b p \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 a^2 x^2}-\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{4 x^4}",1,"(-Log[c*(a + b*x^2)^p]^2 + (b*x^2*(2*b*p^2*x^2*(2*Log[x] - Log[a + b*x^2]) - 2*a*p*Log[c*(a + b*x^2)^p] + b*x^2*Log[c*(a + b*x^2)^p]^2 - 2*b*p*x^2*(Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p] + p*PolyLog[2, 1 + (b*x^2)/a])))/a^2)/(4*x^4)","A",1
83,1,205,193,0.0582743,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^7} \, dx","Integrate[Log[c*(a + b*x^2)^p]^2/x^7,x]","-\frac{b^3 \log ^2\left(c \left(a+b x^2\right)^p\right)}{6 a^3}+\frac{b^3 p \log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)}{3 a^3}+\frac{b^3 p^2 \text{Li}_2\left(\frac{b x^2+a}{a}\right)}{3 a^3}+\frac{b^3 p^2 \log \left(a+b x^2\right)}{2 a^3}-\frac{b^3 p^2 \log (x)}{a^3}+\frac{b^2 p \log \left(c \left(a+b x^2\right)^p\right)}{3 a^2 x^2}-\frac{b^2 p^2}{6 a^2 x^2}-\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{6 x^6}-\frac{b p \log \left(c \left(a+b x^2\right)^p\right)}{6 a x^4}","\frac{b^3 p \log \left(1-\frac{a}{a+b x^2}\right) \log \left(c \left(a+b x^2\right)^p\right)}{3 a^3}-\frac{b^3 p^2 \text{Li}_2\left(\frac{a}{b x^2+a}\right)}{3 a^3}+\frac{b^3 p^2 \log \left(a+b x^2\right)}{6 a^3}-\frac{b^3 p^2 \log (x)}{a^3}+\frac{b^2 p \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{3 a^3 x^2}-\frac{b^2 p^2}{6 a^2 x^2}-\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{6 x^6}-\frac{b p \log \left(c \left(a+b x^2\right)^p\right)}{6 a x^4}",1,"-1/6*(b^2*p^2)/(a^2*x^2) - (b^3*p^2*Log[x])/a^3 + (b^3*p^2*Log[a + b*x^2])/(2*a^3) - (b*p*Log[c*(a + b*x^2)^p])/(6*a*x^4) + (b^2*p*Log[c*(a + b*x^2)^p])/(3*a^2*x^2) + (b^3*p*Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p])/(3*a^3) - (b^3*Log[c*(a + b*x^2)^p]^2)/(6*a^3) - Log[c*(a + b*x^2)^p]^2/(6*x^6) + (b^3*p^2*PolyLog[2, (a + b*x^2)/a])/(3*a^3)","A",1
84,1,248,336,0.2052527,"\int x^4 \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x^4*Log[c*(a + b*x^2)^p]^2,x]","\frac{60 a^{5/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(15 \log \left(c \left(a+b x^2\right)^p\right)+30 p \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)-46 p\right)+900 i a^{5/2} p^2 \text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)+900 i a^{5/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2+\sqrt{b} x \left(-60 p \left(15 a^2-5 a b x^2+3 b^2 x^4\right) \log \left(c \left(a+b x^2\right)^p\right)+8 p^2 \left(345 a^2-40 a b x^2+9 b^2 x^4\right)+225 b^2 x^4 \log ^2\left(c \left(a+b x^2\right)^p\right)\right)}{1125 b^{5/2}}","\frac{4 a^{5/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)}{5 b^{5/2}}+\frac{4 i a^{5/2} p^2 \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)}{5 b^{5/2}}+\frac{4 i a^{5/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{5 b^{5/2}}-\frac{184 a^{5/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{75 b^{5/2}}+\frac{8 a^{5/2} p^2 \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{5 b^{5/2}}-\frac{4 a^2 p x \log \left(c \left(a+b x^2\right)^p\right)}{5 b^2}+\frac{184 a^2 p^2 x}{75 b^2}+\frac{1}{5} x^5 \log ^2\left(c \left(a+b x^2\right)^p\right)-\frac{4}{25} p x^5 \log \left(c \left(a+b x^2\right)^p\right)+\frac{4 a p x^3 \log \left(c \left(a+b x^2\right)^p\right)}{15 b}-\frac{64 a p^2 x^3}{225 b}+\frac{8 p^2 x^5}{125}",1,"((900*I)*a^(5/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2 + 60*a^(5/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(-46*p + 30*p*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)] + 15*Log[c*(a + b*x^2)^p]) + Sqrt[b]*x*(8*p^2*(345*a^2 - 40*a*b*x^2 + 9*b^2*x^4) - 60*p*(15*a^2 - 5*a*b*x^2 + 3*b^2*x^4)*Log[c*(a + b*x^2)^p] + 225*b^2*x^4*Log[c*(a + b*x^2)^p]^2) + (900*I)*a^(5/2)*p^2*PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)])/(1125*b^(5/2))","A",1
85,1,223,294,0.1365944,"\int x^2 \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x^2*Log[c*(a + b*x^2)^p]^2,x]","\frac{-12 a^{3/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(3 \log \left(c \left(a+b x^2\right)^p\right)+6 p \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)-8 p\right)-36 i a^{3/2} p^2 \text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)-36 i a^{3/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2+\sqrt{b} x \left(9 b x^2 \log ^2\left(c \left(a+b x^2\right)^p\right)+12 p \left(3 a-b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)+8 p^2 \left(b x^2-12 a\right)\right)}{27 b^{3/2}}","-\frac{4 a^{3/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)}{3 b^{3/2}}-\frac{4 i a^{3/2} p^2 \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)}{3 b^{3/2}}-\frac{4 i a^{3/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{3 b^{3/2}}+\frac{32 a^{3/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{9 b^{3/2}}-\frac{8 a^{3/2} p^2 \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{3 b^{3/2}}+\frac{4 a p x \log \left(c \left(a+b x^2\right)^p\right)}{3 b}+\frac{1}{3} x^3 \log ^2\left(c \left(a+b x^2\right)^p\right)-\frac{4}{9} p x^3 \log \left(c \left(a+b x^2\right)^p\right)-\frac{32 a p^2 x}{9 b}+\frac{8 p^2 x^3}{27}",1,"((-36*I)*a^(3/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2 - 12*a^(3/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(-8*p + 6*p*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)] + 3*Log[c*(a + b*x^2)^p]) + Sqrt[b]*x*(8*p^2*(-12*a + b*x^2) + 12*p*(3*a - b*x^2)*Log[c*(a + b*x^2)^p] + 9*b*x^2*Log[c*(a + b*x^2)^p]^2) - (36*I)*a^(3/2)*p^2*PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)])/(27*b^(3/2))","A",1
86,1,193,237,0.0828519,"\int \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[Log[c*(a + b*x^2)^p]^2,x]","\frac{\sqrt{b} x \left(\log ^2\left(c \left(a+b x^2\right)^p\right)-4 p \log \left(c \left(a+b x^2\right)^p\right)+8 p^2\right)+4 \sqrt{a} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(\log \left(c \left(a+b x^2\right)^p\right)+2 p \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)-2 p\right)+4 i \sqrt{a} p^2 \text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)+4 i \sqrt{a} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{\sqrt{b}}","x \log ^2\left(c \left(a+b x^2\right)^p\right)-4 p x \log \left(c \left(a+b x^2\right)^p\right)+\frac{4 \sqrt{a} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)}{\sqrt{b}}+\frac{4 i \sqrt{a} p^2 \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)}{\sqrt{b}}+\frac{4 i \sqrt{a} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{\sqrt{b}}-\frac{8 \sqrt{a} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}+\frac{8 \sqrt{a} p^2 \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}+8 p^2 x",1,"((4*I)*Sqrt[a]*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2 + 4*Sqrt[a]*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(-2*p + 2*p*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)] + Log[c*(a + b*x^2)^p]) + Sqrt[b]*x*(8*p^2 - 4*p*Log[c*(a + b*x^2)^p] + Log[c*(a + b*x^2)^p]^2) + (4*I)*Sqrt[a]*p^2*PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)])/Sqrt[b]","A",1
87,1,173,190,0.0539127,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^2} \, dx","Integrate[Log[c*(a + b*x^2)^p]^2/x^2,x]","\frac{-\sqrt{a} \log ^2\left(c \left(a+b x^2\right)^p\right)+4 \sqrt{b} p x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(\log \left(c \left(a+b x^2\right)^p\right)+2 p \log \left(\frac{2 i}{-\frac{\sqrt{b} x}{\sqrt{a}}+i}\right)\right)+4 i \sqrt{b} p^2 x \text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)+4 i \sqrt{b} p^2 x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{\sqrt{a} x}","-\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x}+\frac{4 \sqrt{b} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)}{\sqrt{a}}+\frac{4 i \sqrt{b} p^2 \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)}{\sqrt{a}}+\frac{4 i \sqrt{b} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{\sqrt{a}}+\frac{8 \sqrt{b} p^2 \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a}}",1,"((4*I)*Sqrt[b]*p^2*x*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2 - Sqrt[a]*Log[c*(a + b*x^2)^p]^2 + 4*Sqrt[b]*p*x*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(2*p*Log[(2*I)/(I - (Sqrt[b]*x)/Sqrt[a])] + Log[c*(a + b*x^2)^p]) + (4*I)*Sqrt[b]*p^2*x*PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)])/(Sqrt[a]*x)","A",1
88,1,207,254,0.0954057,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^4} \, dx","Integrate[Log[c*(a + b*x^2)^p]^2/x^4,x]","\frac{-4 b^{3/2} p x^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(\log \left(c \left(a+b x^2\right)^p\right)+2 p \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)-2 p\right)-4 i b^{3/2} p^2 x^3 \text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)-4 i b^{3/2} p^2 x^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2-\sqrt{a} \log \left(c \left(a+b x^2\right)^p\right) \left(a \log \left(c \left(a+b x^2\right)^p\right)+4 b p x^2\right)}{3 a^{3/2} x^3}","-\frac{4 b^{3/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)}{3 a^{3/2}}-\frac{4 i b^{3/2} p^2 \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)}{3 a^{3/2}}-\frac{4 i b^{3/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{3 a^{3/2}}+\frac{8 b^{3/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{8 b^{3/2} p^2 \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{4 b p \log \left(c \left(a+b x^2\right)^p\right)}{3 a x}-\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{3 x^3}",1,"((-4*I)*b^(3/2)*p^2*x^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2 - 4*b^(3/2)*p*x^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(-2*p + 2*p*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)] + Log[c*(a + b*x^2)^p]) - Sqrt[a]*Log[c*(a + b*x^2)^p]*(4*b*p*x^2 + a*Log[c*(a + b*x^2)^p]) - (4*I)*b^(3/2)*p^2*x^3*PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)])/(3*a^(3/2)*x^3)","A",1
89,1,277,296,0.2856521,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^6} \, dx","Integrate[Log[c*(a + b*x^2)^p]^2/x^6,x]","-\frac{3 \log ^2\left(c \left(a+b x^2\right)^p\right)+\frac{4 b p x^2 \left(a^{3/2} \log \left(c \left(a+b x^2\right)^p\right)-3 b^{3/2} x^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)-3 i b^{3/2} p x^3 \left(\text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)+\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)-2 i \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)\right)\right)+6 b^{3/2} p x^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)-3 \sqrt{a} b x^2 \log \left(c \left(a+b x^2\right)^p\right)+2 \sqrt{a} b p x^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x^2}{a}\right)\right)}{a^{5/2}}}{15 x^5}","\frac{4 b^{5/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)}{5 a^{5/2}}+\frac{4 i b^{5/2} p^2 \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)}{5 a^{5/2}}+\frac{4 i b^{5/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{5 a^{5/2}}-\frac{32 b^{5/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{15 a^{5/2}}+\frac{8 b^{5/2} p^2 \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{5 a^{5/2}}+\frac{4 b^2 p \log \left(c \left(a+b x^2\right)^p\right)}{5 a^2 x}-\frac{8 b^2 p^2}{15 a^2 x}-\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{5 x^5}-\frac{4 b p \log \left(c \left(a+b x^2\right)^p\right)}{15 a x^3}",1,"-1/15*(3*Log[c*(a + b*x^2)^p]^2 + (4*b*p*x^2*(6*b^(3/2)*p*x^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]] + 2*Sqrt[a]*b*p*x^2*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x^2)/a)] + a^(3/2)*Log[c*(a + b*x^2)^p] - 3*Sqrt[a]*b*x^2*Log[c*(a + b*x^2)^p] - 3*b^(3/2)*x^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p] - (3*I)*b^(3/2)*p*x^3*(ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(ArcTan[(Sqrt[b]*x)/Sqrt[a]] - (2*I)*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)]) + PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)])))/a^(5/2))/x^5","C",1
90,1,334,338,0.2358129,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^8} \, dx","Integrate[Log[c*(a + b*x^2)^p]^2/x^8,x]","-\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{7 x^7}+\frac{4 b p \left(5 a^{3/2} b x^2 \log \left(c \left(a+b x^2\right)^p\right)-3 a^{5/2} \log \left(c \left(a+b x^2\right)^p\right)-2 a^{3/2} b p x^2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{b x^2}{a}\right)-15 b^{5/2} x^5 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)-15 i b^{5/2} p x^5 \left(\text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)+\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)-2 i \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)\right)\right)+30 b^{5/2} p x^5 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)-15 \sqrt{a} b^2 x^4 \log \left(c \left(a+b x^2\right)^p\right)+10 \sqrt{a} b^2 p x^4 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b x^2}{a}\right)\right)}{105 a^{7/2} x^5}","-\frac{4 b^{7/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)}{7 a^{7/2}}-\frac{4 i b^{7/2} p^2 \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)}{7 a^{7/2}}-\frac{4 i b^{7/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{7 a^{7/2}}+\frac{184 b^{7/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{105 a^{7/2}}-\frac{8 b^{7/2} p^2 \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{7 a^{7/2}}-\frac{4 b^3 p \log \left(c \left(a+b x^2\right)^p\right)}{7 a^3 x}+\frac{64 b^3 p^2}{105 a^3 x}+\frac{4 b^2 p \log \left(c \left(a+b x^2\right)^p\right)}{21 a^2 x^3}-\frac{8 b^2 p^2}{105 a^2 x^3}-\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{7 x^7}-\frac{4 b p \log \left(c \left(a+b x^2\right)^p\right)}{35 a x^5}",1,"-1/7*Log[c*(a + b*x^2)^p]^2/x^7 + (4*b*p*(30*b^(5/2)*p*x^5*ArcTan[(Sqrt[b]*x)/Sqrt[a]] - 2*a^(3/2)*b*p*x^2*Hypergeometric2F1[-3/2, 1, -1/2, -((b*x^2)/a)] + 10*Sqrt[a]*b^2*p*x^4*Hypergeometric2F1[-1/2, 1, 1/2, -((b*x^2)/a)] - 3*a^(5/2)*Log[c*(a + b*x^2)^p] + 5*a^(3/2)*b*x^2*Log[c*(a + b*x^2)^p] - 15*Sqrt[a]*b^2*x^4*Log[c*(a + b*x^2)^p] - 15*b^(5/2)*x^5*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p] - (15*I)*b^(5/2)*p*x^5*(ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(ArcTan[(Sqrt[b]*x)/Sqrt[a]] - (2*I)*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)]) + PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)])))/(105*a^(7/2)*x^5)","C",1
91,1,309,334,0.200188,"\int x^5 \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x^5*Log[c*(a + b*x^2)^p]^3,x]","\frac{11 a^3 p^2 \log \left(c \left(a+b x^2\right)^p\right)}{6 b^3}+\frac{a^3 \log ^3\left(c \left(a+b x^2\right)^p\right)}{6 b^3}-\frac{11 a^3 p \log ^2\left(c \left(a+b x^2\right)^p\right)}{12 b^3}+\frac{19 a^3 p^3 \log \left(a+b x^2\right)}{36 b^3}+\frac{11 a^2 p^2 x^2 \log \left(c \left(a+b x^2\right)^p\right)}{6 b^2}-\frac{a^2 p x^2 \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 b^2}-\frac{85 a^2 p^3 x^2}{36 b^2}+\frac{1}{9} p^2 x^6 \log \left(c \left(a+b x^2\right)^p\right)-\frac{5 a p^2 x^4 \log \left(c \left(a+b x^2\right)^p\right)}{12 b}+\frac{1}{6} x^6 \log ^3\left(c \left(a+b x^2\right)^p\right)-\frac{1}{6} p x^6 \log ^2\left(c \left(a+b x^2\right)^p\right)+\frac{a p x^4 \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 b}+\frac{19 a p^3 x^4}{72 b}-\frac{1}{27} p^3 x^6","\frac{3 a^2 p^2 \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b^3}+\frac{a^2 \left(a+b x^2\right) \log ^3\left(c \left(a+b x^2\right)^p\right)}{2 b^3}-\frac{3 a^2 p \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 b^3}-\frac{3 a^2 p^3 x^2}{b^2}+\frac{p^2 \left(a+b x^2\right)^3 \log \left(c \left(a+b x^2\right)^p\right)}{9 b^3}-\frac{3 a p^2 \left(a+b x^2\right)^2 \log \left(c \left(a+b x^2\right)^p\right)}{4 b^3}+\frac{\left(a+b x^2\right)^3 \log ^3\left(c \left(a+b x^2\right)^p\right)}{6 b^3}-\frac{a \left(a+b x^2\right)^2 \log ^3\left(c \left(a+b x^2\right)^p\right)}{2 b^3}-\frac{p \left(a+b x^2\right)^3 \log ^2\left(c \left(a+b x^2\right)^p\right)}{6 b^3}+\frac{3 a p \left(a+b x^2\right)^2 \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 b^3}-\frac{p^3 \left(a+b x^2\right)^3}{27 b^3}+\frac{3 a p^3 \left(a+b x^2\right)^2}{8 b^3}",1,"(-85*a^2*p^3*x^2)/(36*b^2) + (19*a*p^3*x^4)/(72*b) - (p^3*x^6)/27 + (19*a^3*p^3*Log[a + b*x^2])/(36*b^3) + (11*a^3*p^2*Log[c*(a + b*x^2)^p])/(6*b^3) + (11*a^2*p^2*x^2*Log[c*(a + b*x^2)^p])/(6*b^2) - (5*a*p^2*x^4*Log[c*(a + b*x^2)^p])/(12*b) + (p^2*x^6*Log[c*(a + b*x^2)^p])/9 - (11*a^3*p*Log[c*(a + b*x^2)^p]^2)/(12*b^3) - (a^2*p*x^2*Log[c*(a + b*x^2)^p]^2)/(2*b^2) + (a*p*x^4*Log[c*(a + b*x^2)^p]^2)/(4*b) - (p*x^6*Log[c*(a + b*x^2)^p]^2)/6 + (a^3*Log[c*(a + b*x^2)^p]^3)/(6*b^3) + (x^6*Log[c*(a + b*x^2)^p]^3)/6","A",1
92,1,237,211,0.092113,"\int x^3 \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x^3*Log[c*(a + b*x^2)^p]^3,x]","-\frac{9 a^2 p^2 \log \left(c \left(a+b x^2\right)^p\right)}{4 b^2}-\frac{a^2 \log ^3\left(c \left(a+b x^2\right)^p\right)}{4 b^2}+\frac{9 a^2 p \log ^2\left(c \left(a+b x^2\right)^p\right)}{8 b^2}-\frac{3 a^2 p^3 \log \left(a+b x^2\right)}{8 b^2}-\frac{9 a p^2 x^2 \log \left(c \left(a+b x^2\right)^p\right)}{4 b}+\frac{3}{8} p^2 x^4 \log \left(c \left(a+b x^2\right)^p\right)+\frac{3 a p x^2 \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 b}+\frac{1}{4} x^4 \log ^3\left(c \left(a+b x^2\right)^p\right)-\frac{3}{8} p x^4 \log ^2\left(c \left(a+b x^2\right)^p\right)+\frac{21 a p^3 x^2}{8 b}-\frac{3}{16} p^3 x^4","\frac{3 p^2 \left(a+b x^2\right)^2 \log \left(c \left(a+b x^2\right)^p\right)}{8 b^2}-\frac{3 a p^2 \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b^2}+\frac{\left(a+b x^2\right)^2 \log ^3\left(c \left(a+b x^2\right)^p\right)}{4 b^2}-\frac{a \left(a+b x^2\right) \log ^3\left(c \left(a+b x^2\right)^p\right)}{2 b^2}-\frac{3 p \left(a+b x^2\right)^2 \log ^2\left(c \left(a+b x^2\right)^p\right)}{8 b^2}+\frac{3 a p \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 b^2}-\frac{3 p^3 \left(a+b x^2\right)^2}{16 b^2}+\frac{3 a p^3 x^2}{b}",1,"(21*a*p^3*x^2)/(8*b) - (3*p^3*x^4)/16 - (3*a^2*p^3*Log[a + b*x^2])/(8*b^2) - (9*a^2*p^2*Log[c*(a + b*x^2)^p])/(4*b^2) - (9*a*p^2*x^2*Log[c*(a + b*x^2)^p])/(4*b) + (3*p^2*x^4*Log[c*(a + b*x^2)^p])/8 + (9*a^2*p*Log[c*(a + b*x^2)^p]^2)/(8*b^2) + (3*a*p*x^2*Log[c*(a + b*x^2)^p]^2)/(4*b) - (3*p*x^4*Log[c*(a + b*x^2)^p]^2)/8 - (a^2*Log[c*(a + b*x^2)^p]^3)/(4*b^2) + (x^4*Log[c*(a + b*x^2)^p]^3)/4","A",1
93,1,87,93,0.0127233,"\int x \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x*Log[c*(a + b*x^2)^p]^3,x]","\frac{6 p^2 \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)+\left(a+b x^2\right) \log ^3\left(c \left(a+b x^2\right)^p\right)-3 p \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)-6 b p^3 x^2}{2 b}","\frac{3 p^2 \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b}+\frac{\left(a+b x^2\right) \log ^3\left(c \left(a+b x^2\right)^p\right)}{2 b}-\frac{3 p \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 b}-3 p^3 x^2",1,"(-6*b*p^3*x^2 + 6*p^2*(a + b*x^2)*Log[c*(a + b*x^2)^p] - 3*p*(a + b*x^2)*Log[c*(a + b*x^2)^p]^2 + (a + b*x^2)*Log[c*(a + b*x^2)^p]^3)/(2*b)","A",1
94,1,279,106,0.1049078,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x} \, dx","Integrate[Log[c*(a + b*x^2)^p]^3/x,x]","-\frac{3}{2} p^2 \left(-2 \text{Li}_3\left(\frac{b x^2}{a}+1\right)+2 \text{Li}_2\left(\frac{b x^2}{a}+1\right) \log \left(a+b x^2\right)+\log \left(-\frac{b x^2}{a}\right) \log ^2\left(a+b x^2\right)\right) \left(p \log \left(a+b x^2\right)-\log \left(c \left(a+b x^2\right)^p\right)\right)+3 p \left(\log (x) \left(\log \left(a+b x^2\right)-\log \left(\frac{b x^2}{a}+1\right)\right)-\frac{1}{2} \text{Li}_2\left(-\frac{b x^2}{a}\right)\right) \left(\log \left(c \left(a+b x^2\right)^p\right)-p \log \left(a+b x^2\right)\right)^2+\log (x) \left(\log \left(c \left(a+b x^2\right)^p\right)-p \log \left(a+b x^2\right)\right)^3+\frac{1}{2} p^3 \left(6 \text{Li}_4\left(\frac{b x^2}{a}+1\right)+3 \text{Li}_2\left(\frac{b x^2}{a}+1\right) \log ^2\left(a+b x^2\right)-6 \text{Li}_3\left(\frac{b x^2}{a}+1\right) \log \left(a+b x^2\right)+\log \left(-\frac{b x^2}{a}\right) \log ^3\left(a+b x^2\right)\right)","-3 p^2 \text{Li}_3\left(\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)+\frac{3}{2} p \text{Li}_2\left(\frac{b x^2}{a}+1\right) \log ^2\left(c \left(a+b x^2\right)^p\right)+\frac{1}{2} \log \left(-\frac{b x^2}{a}\right) \log ^3\left(c \left(a+b x^2\right)^p\right)+3 p^3 \text{Li}_4\left(\frac{b x^2}{a}+1\right)",1,"Log[x]*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^3 + 3*p*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2*(Log[x]*(Log[a + b*x^2] - Log[1 + (b*x^2)/a]) - PolyLog[2, -((b*x^2)/a)]/2) - (3*p^2*(p*Log[a + b*x^2] - Log[c*(a + b*x^2)^p])*(Log[-((b*x^2)/a)]*Log[a + b*x^2]^2 + 2*Log[a + b*x^2]*PolyLog[2, 1 + (b*x^2)/a] - 2*PolyLog[3, 1 + (b*x^2)/a]))/2 + (p^3*(Log[-((b*x^2)/a)]*Log[a + b*x^2]^3 + 3*Log[a + b*x^2]^2*PolyLog[2, 1 + (b*x^2)/a] - 6*Log[a + b*x^2]*PolyLog[3, 1 + (b*x^2)/a] + 6*PolyLog[4, 1 + (b*x^2)/a]))/2","B",1
95,1,302,119,0.2975442,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^3} \, dx","Integrate[Log[c*(a + b*x^2)^p]^3/x^3,x]","-\frac{-6 b p^2 x^2 \text{Li}_2\left(\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)-3 b p^2 x^2 \log ^2\left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)+12 b p^2 x^2 \log (x) \log \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)-6 b p^2 x^2 \log \left(-\frac{b x^2}{a}\right) \log \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)+a \log ^3\left(c \left(a+b x^2\right)^p\right)-6 b p x^2 \log (x) \log ^2\left(c \left(a+b x^2\right)^p\right)+3 b p x^2 \log \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)+6 b p^3 x^2 \text{Li}_3\left(\frac{b x^2}{a}+1\right)+b p^3 x^2 \log ^3\left(a+b x^2\right)-6 b p^3 x^2 \log (x) \log ^2\left(a+b x^2\right)+3 b p^3 x^2 \log \left(-\frac{b x^2}{a}\right) \log ^2\left(a+b x^2\right)}{2 a x^2}","\frac{3 b p^2 \text{Li}_2\left(\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)}{a}-\frac{\left(a+b x^2\right) \log ^3\left(c \left(a+b x^2\right)^p\right)}{2 a x^2}+\frac{3 b p \log \left(-\frac{b x^2}{a}\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 a}-\frac{3 b p^3 \text{Li}_3\left(\frac{b x^2}{a}+1\right)}{a}",1,"-1/2*(-6*b*p^3*x^2*Log[x]*Log[a + b*x^2]^2 + 3*b*p^3*x^2*Log[-((b*x^2)/a)]*Log[a + b*x^2]^2 + b*p^3*x^2*Log[a + b*x^2]^3 + 12*b*p^2*x^2*Log[x]*Log[a + b*x^2]*Log[c*(a + b*x^2)^p] - 6*b*p^2*x^2*Log[-((b*x^2)/a)]*Log[a + b*x^2]*Log[c*(a + b*x^2)^p] - 3*b*p^2*x^2*Log[a + b*x^2]^2*Log[c*(a + b*x^2)^p] - 6*b*p*x^2*Log[x]*Log[c*(a + b*x^2)^p]^2 + 3*b*p*x^2*Log[a + b*x^2]*Log[c*(a + b*x^2)^p]^2 + a*Log[c*(a + b*x^2)^p]^3 - 6*b*p^2*x^2*Log[c*(a + b*x^2)^p]*PolyLog[2, 1 + (b*x^2)/a] + 6*b*p^3*x^2*PolyLog[3, 1 + (b*x^2)/a])/(a*x^2)","B",1
96,1,478,219,0.366672,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^5} \, dx","Integrate[Log[c*(a + b*x^2)^p]^3/x^5,x]","\frac{-a^2 \log ^3\left(c \left(a+b x^2\right)^p\right)+6 b^2 p^2 x^4 \text{Li}_2\left(\frac{b x^2}{a}+1\right) \left(p-\log \left(c \left(a+b x^2\right)^p\right)\right)-3 b^2 p^2 x^4 \log ^2\left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)+12 b^2 p^2 x^4 \log (x) \log \left(c \left(a+b x^2\right)^p\right)-6 b^2 p^2 x^4 \log \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)+12 b^2 p^2 x^4 \log (x) \log \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)-6 b^2 p^2 x^4 \log \left(-\frac{b x^2}{a}\right) \log \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)-6 b^2 p x^4 \log (x) \log ^2\left(c \left(a+b x^2\right)^p\right)+3 b^2 p x^4 \log \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)+6 b^2 p^3 x^4 \text{Li}_3\left(\frac{b x^2}{a}+1\right)+b^2 p^3 x^4 \log ^3\left(a+b x^2\right)+3 b^2 p^3 x^4 \log ^2\left(a+b x^2\right)-6 b^2 p^3 x^4 \log (x) \log ^2\left(a+b x^2\right)+3 b^2 p^3 x^4 \log \left(-\frac{b x^2}{a}\right) \log ^2\left(a+b x^2\right)-12 b^2 p^3 x^4 \log (x) \log \left(a+b x^2\right)+6 b^2 p^3 x^4 \log \left(-\frac{b x^2}{a}\right) \log \left(a+b x^2\right)-3 a b p x^2 \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 a^2 x^4}","\frac{3 b^2 p^2 \text{Li}_2\left(\frac{a}{b x^2+a}\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 a^2}+\frac{3 b^2 p^2 \log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 a^2}-\frac{3 b^2 p \log \left(1-\frac{a}{a+b x^2}\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 a^2}+\frac{3 b^2 p^3 \text{Li}_2\left(\frac{b x^2}{a}+1\right)}{2 a^2}+\frac{3 b^2 p^3 \text{Li}_3\left(\frac{a}{b x^2+a}\right)}{2 a^2}-\frac{3 b p \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 a^2 x^2}-\frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{4 x^4}",1,"(-12*b^2*p^3*x^4*Log[x]*Log[a + b*x^2] + 6*b^2*p^3*x^4*Log[-((b*x^2)/a)]*Log[a + b*x^2] + 3*b^2*p^3*x^4*Log[a + b*x^2]^2 - 6*b^2*p^3*x^4*Log[x]*Log[a + b*x^2]^2 + 3*b^2*p^3*x^4*Log[-((b*x^2)/a)]*Log[a + b*x^2]^2 + b^2*p^3*x^4*Log[a + b*x^2]^3 + 12*b^2*p^2*x^4*Log[x]*Log[c*(a + b*x^2)^p] - 6*b^2*p^2*x^4*Log[a + b*x^2]*Log[c*(a + b*x^2)^p] + 12*b^2*p^2*x^4*Log[x]*Log[a + b*x^2]*Log[c*(a + b*x^2)^p] - 6*b^2*p^2*x^4*Log[-((b*x^2)/a)]*Log[a + b*x^2]*Log[c*(a + b*x^2)^p] - 3*b^2*p^2*x^4*Log[a + b*x^2]^2*Log[c*(a + b*x^2)^p] - 3*a*b*p*x^2*Log[c*(a + b*x^2)^p]^2 - 6*b^2*p*x^4*Log[x]*Log[c*(a + b*x^2)^p]^2 + 3*b^2*p*x^4*Log[a + b*x^2]*Log[c*(a + b*x^2)^p]^2 - a^2*Log[c*(a + b*x^2)^p]^3 + 6*b^2*p^2*x^4*(p - Log[c*(a + b*x^2)^p])*PolyLog[2, 1 + (b*x^2)/a] + 6*b^2*p^3*x^4*PolyLog[3, 1 + (b*x^2)/a])/(4*a^2*x^4)","B",1
97,1,571,352,0.4161713,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^7} \, dx","Integrate[Log[c*(a + b*x^2)^p]^3/x^7,x]","-\frac{2 a^3 \log ^3\left(c \left(a+b x^2\right)^p\right)+3 a^2 b p x^2 \log ^2\left(c \left(a+b x^2\right)^p\right)+6 b^3 p^2 x^6 \text{Li}_2\left(\frac{b x^2}{a}+1\right) \left(3 p-2 \log \left(c \left(a+b x^2\right)^p\right)\right)-6 b^3 p^2 x^6 \log ^2\left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)+36 b^3 p^2 x^6 \log (x) \log \left(c \left(a+b x^2\right)^p\right)-18 b^3 p^2 x^6 \log \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)+24 b^3 p^2 x^6 \log (x) \log \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)-12 b^3 p^2 x^6 \log \left(-\frac{b x^2}{a}\right) \log \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)-12 b^3 p x^6 \log (x) \log ^2\left(c \left(a+b x^2\right)^p\right)+6 b^3 p x^6 \log \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)+12 b^3 p^3 x^6 \text{Li}_3\left(\frac{b x^2}{a}+1\right)+2 b^3 p^3 x^6 \log ^3\left(a+b x^2\right)+9 b^3 p^3 x^6 \log ^2\left(a+b x^2\right)-12 b^3 p^3 x^6 \log (x) \log ^2\left(a+b x^2\right)+6 b^3 p^3 x^6 \log \left(-\frac{b x^2}{a}\right) \log ^2\left(a+b x^2\right)-6 b^3 p^3 x^6 \log \left(-\frac{b x^2}{a}\right)+6 b^3 p^3 x^6 \log \left(a+b x^2\right)-36 b^3 p^3 x^6 \log (x) \log \left(a+b x^2\right)+18 b^3 p^3 x^6 \log \left(-\frac{b x^2}{a}\right) \log \left(a+b x^2\right)+6 a b^2 p^2 x^4 \log \left(c \left(a+b x^2\right)^p\right)-6 a b^2 p x^4 \log ^2\left(c \left(a+b x^2\right)^p\right)}{12 a^3 x^6}","-\frac{b^3 p^2 \text{Li}_2\left(\frac{a}{b x^2+a}\right) \log \left(c \left(a+b x^2\right)^p\right)}{a^3}-\frac{b^3 p^2 \log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)}{a^3}-\frac{b^3 p^2 \log \left(1-\frac{a}{a+b x^2}\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 a^3}+\frac{b^3 p \log \left(1-\frac{a}{a+b x^2}\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 a^3}+\frac{b^3 p^3 \text{Li}_2\left(\frac{a}{b x^2+a}\right)}{2 a^3}-\frac{b^3 p^3 \text{Li}_2\left(\frac{b x^2}{a}+1\right)}{a^3}-\frac{b^3 p^3 \text{Li}_3\left(\frac{a}{b x^2+a}\right)}{a^3}+\frac{b^3 p^3 \log (x)}{a^3}-\frac{b^2 p^2 \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 a^3 x^2}+\frac{b^2 p \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 a^3 x^2}-\frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{6 x^6}-\frac{b p \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 a x^4}",1,"-1/12*(-6*b^3*p^3*x^6*Log[-((b*x^2)/a)] + 6*b^3*p^3*x^6*Log[a + b*x^2] - 36*b^3*p^3*x^6*Log[x]*Log[a + b*x^2] + 18*b^3*p^3*x^6*Log[-((b*x^2)/a)]*Log[a + b*x^2] + 9*b^3*p^3*x^6*Log[a + b*x^2]^2 - 12*b^3*p^3*x^6*Log[x]*Log[a + b*x^2]^2 + 6*b^3*p^3*x^6*Log[-((b*x^2)/a)]*Log[a + b*x^2]^2 + 2*b^3*p^3*x^6*Log[a + b*x^2]^3 + 6*a*b^2*p^2*x^4*Log[c*(a + b*x^2)^p] + 36*b^3*p^2*x^6*Log[x]*Log[c*(a + b*x^2)^p] - 18*b^3*p^2*x^6*Log[a + b*x^2]*Log[c*(a + b*x^2)^p] + 24*b^3*p^2*x^6*Log[x]*Log[a + b*x^2]*Log[c*(a + b*x^2)^p] - 12*b^3*p^2*x^6*Log[-((b*x^2)/a)]*Log[a + b*x^2]*Log[c*(a + b*x^2)^p] - 6*b^3*p^2*x^6*Log[a + b*x^2]^2*Log[c*(a + b*x^2)^p] + 3*a^2*b*p*x^2*Log[c*(a + b*x^2)^p]^2 - 6*a*b^2*p*x^4*Log[c*(a + b*x^2)^p]^2 - 12*b^3*p*x^6*Log[x]*Log[c*(a + b*x^2)^p]^2 + 6*b^3*p*x^6*Log[a + b*x^2]*Log[c*(a + b*x^2)^p]^2 + 2*a^3*Log[c*(a + b*x^2)^p]^3 + 6*b^3*p^2*x^6*(3*p - 2*Log[c*(a + b*x^2)^p])*PolyLog[2, 1 + (b*x^2)/a] + 12*b^3*p^3*x^6*PolyLog[3, 1 + (b*x^2)/a])/(a^3*x^6)","A",1
98,1,909,380,3.8949307,"\int x^2 \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[x^2*Log[c*(a + b*x^2)^p]^3,x]","\frac{\left(-48 \left(4 \sqrt{b x^2} \tanh ^{-1}\left(\frac{\sqrt{b x^2}}{\sqrt{-a}}\right) \left(\log \left(b x^2+a\right)-\log \left(\frac{b x^2}{a}+1\right)\right)-\sqrt{-a} \sqrt{-\frac{b x^2}{a}} \left(\log ^2\left(\frac{b x^2}{a}+1\right)-4 \log \left(\frac{1}{2} \left(\sqrt{-\frac{b x^2}{a}}+1\right)\right) \log \left(\frac{b x^2}{a}+1\right)+2 \log ^2\left(\frac{1}{2} \left(\sqrt{-\frac{b x^2}{a}}+1\right)\right)-4 \text{Li}_2\left(\frac{1}{2}-\frac{1}{2} \sqrt{-\frac{b x^2}{a}}\right)\right)\right) a^2+416 \sqrt{-a} \sqrt{\frac{b x^2}{b x^2+a}} \sqrt{b x^2+a} \sin ^{-1}\left(\frac{\sqrt{a}}{\sqrt{b x^2+a}}\right) a^{3/2}+36 \sqrt{-a} \sqrt{\frac{b x^2}{b x^2+a}} \left(8 \sqrt{a} \, _4F_3\left(\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2},\frac{3}{2};\frac{a}{b x^2+a}\right)+\log \left(b x^2+a\right) \left(4 \sqrt{a} \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};\frac{a}{b x^2+a}\right)+\sqrt{b x^2+a} \sin ^{-1}\left(\frac{\sqrt{a}}{\sqrt{b x^2+a}}\right) \log \left(b x^2+a\right)\right)\right) a^{3/2}+\frac{2}{3} \sqrt{-a} b x^2 \left(9 b x^2 \log ^3\left(b x^2+a\right)+18 \left(3 a-b x^2\right) \log ^2\left(b x^2+a\right)+\left(24 b x^2-288 a\right) \log \left(b x^2+a\right)-16 b x^2+624 a\right)\right) p^3}{18 \sqrt{-a} b^2 x}+3 \left(\log \left(c \left(b x^2+a\right)^p\right)-p \log \left(b x^2+a\right)\right) \left(\frac{1}{3} x^3 \log ^2\left(b x^2+a\right)-\frac{4 \left(9 i a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2+3 a^{3/2} \left(6 \log \left(\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)+3 \log \left(b x^2+a\right)-8\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)+\sqrt{b} x \left(-2 b x^2+24 a+\left(3 b x^2-9 a\right) \log \left(b x^2+a\right)\right)+9 i a^{3/2} \text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)\right)}{27 b^{3/2}}\right) p^2+\frac{2 a x \left(\log \left(c \left(b x^2+a\right)^p\right)-p \log \left(b x^2+a\right)\right)^2 p}{b}-\frac{2 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(\log \left(c \left(b x^2+a\right)^p\right)-p \log \left(b x^2+a\right)\right)^2 p}{b^{3/2}}+x^3 \log \left(b x^2+a\right) \left(\log \left(c \left(b x^2+a\right)^p\right)-p \log \left(b x^2+a\right)\right)^2 p+\frac{1}{3} x^3 \left(\log \left(c \left(b x^2+a\right)^p\right)-p \log \left(b x^2+a\right)\right)^2 \left(-\log \left(b x^2+a\right) p-2 p+\log \left(c \left(b x^2+a\right)^p\right)\right)","-\frac{2 a^2 p \text{Int}\left(\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{a+b x^2},x\right)}{b}+\frac{32 a^{3/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)}{3 b^{3/2}}+\frac{32 i a^{3/2} p^3 \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)}{3 b^{3/2}}+\frac{32 i a^{3/2} p^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{3 b^{3/2}}-\frac{208 a^{3/2} p^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{9 b^{3/2}}+\frac{64 a^{3/2} p^3 \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{3 b^{3/2}}-\frac{32 a p^2 x \log \left(c \left(a+b x^2\right)^p\right)}{3 b}+\frac{8}{9} p^2 x^3 \log \left(c \left(a+b x^2\right)^p\right)+\frac{2 a p x \log ^2\left(c \left(a+b x^2\right)^p\right)}{b}+\frac{1}{3} x^3 \log ^3\left(c \left(a+b x^2\right)^p\right)-\frac{2}{3} p x^3 \log ^2\left(c \left(a+b x^2\right)^p\right)+\frac{208 a p^3 x}{9 b}-\frac{16}{27} p^3 x^3",0,"(2*a*p*x*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2)/b - (2*a^(3/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2)/b^(3/2) + p*x^3*Log[a + b*x^2]*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2 + (x^3*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2*(-2*p - p*Log[a + b*x^2] + Log[c*(a + b*x^2)^p]))/3 + 3*p^2*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])*((x^3*Log[a + b*x^2]^2)/3 - (4*((9*I)*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2 + 3*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(-8 + 6*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)] + 3*Log[a + b*x^2]) + Sqrt[b]*x*(24*a - 2*b*x^2 + (-9*a + 3*b*x^2)*Log[a + b*x^2]) + (9*I)*a^(3/2)*PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)]))/(27*b^(3/2))) + (p^3*(416*Sqrt[-a]*a^(3/2)*Sqrt[(b*x^2)/(a + b*x^2)]*Sqrt[a + b*x^2]*ArcSin[Sqrt[a]/Sqrt[a + b*x^2]] + (2*Sqrt[-a]*b*x^2*(624*a - 16*b*x^2 + (-288*a + 24*b*x^2)*Log[a + b*x^2] + 18*(3*a - b*x^2)*Log[a + b*x^2]^2 + 9*b*x^2*Log[a + b*x^2]^3))/3 + 36*Sqrt[-a]*a^(3/2)*Sqrt[(b*x^2)/(a + b*x^2)]*(8*Sqrt[a]*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {3/2, 3/2, 3/2}, a/(a + b*x^2)] + Log[a + b*x^2]*(4*Sqrt[a]*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, a/(a + b*x^2)] + Sqrt[a + b*x^2]*ArcSin[Sqrt[a]/Sqrt[a + b*x^2]]*Log[a + b*x^2])) - 48*a^2*(4*Sqrt[b*x^2]*ArcTanh[Sqrt[b*x^2]/Sqrt[-a]]*(Log[a + b*x^2] - Log[1 + (b*x^2)/a]) - Sqrt[-a]*Sqrt[-((b*x^2)/a)]*(Log[1 + (b*x^2)/a]^2 - 4*Log[1 + (b*x^2)/a]*Log[(1 + Sqrt[-((b*x^2)/a)])/2] + 2*Log[(1 + Sqrt[-((b*x^2)/a)])/2]^2 - 4*PolyLog[2, 1/2 - Sqrt[-((b*x^2)/a)]/2]))))/(18*Sqrt[-a]*b^2*x)","B",1
99,1,789,290,3.5315568,"\int \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[Log[c*(a + b*x^2)^p]^3,x]","\frac{p^3 \left(-6 \sqrt{-a^2} \sqrt{\frac{b x^2}{a+b x^2}} \left(8 \sqrt{a} \, _4F_3\left(\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2},\frac{3}{2};\frac{a}{b x^2+a}\right)+\log \left(a+b x^2\right) \left(4 \sqrt{a} \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};\frac{a}{b x^2+a}\right)+\sqrt{a+b x^2} \log \left(a+b x^2\right) \sin ^{-1}\left(\frac{\sqrt{a}}{\sqrt{a+b x^2}}\right)\right)\right)-48 \sqrt{-a^2} \sqrt{\frac{b x^2}{a+b x^2}} \sqrt{a+b x^2} \sin ^{-1}\left(\frac{\sqrt{a}}{\sqrt{a+b x^2}}\right)+6 (-a)^{3/2} \sqrt{-\frac{b x^2}{a}} \left(-4 \text{Li}_2\left(\frac{1}{2}-\frac{1}{2} \sqrt{-\frac{b x^2}{a}}\right)+\log ^2\left(\frac{b x^2}{a}+1\right)+2 \log ^2\left(\frac{1}{2} \left(\sqrt{-\frac{b x^2}{a}}+1\right)\right)-4 \log \left(\frac{1}{2} \left(\sqrt{-\frac{b x^2}{a}}+1\right)\right) \log \left(\frac{b x^2}{a}+1\right)\right)+\sqrt{-a} b x^2 \left(\log ^3\left(a+b x^2\right)-6 \log ^2\left(a+b x^2\right)+24 \log \left(a+b x^2\right)-48\right)+24 a \sqrt{b x^2} \left(\log \left(a+b x^2\right)-\log \left(\frac{b x^2}{a}+1\right)\right) \tanh ^{-1}\left(\frac{\sqrt{b x^2}}{\sqrt{-a}}\right)\right)}{\sqrt{-a} b x}-\frac{3 p^2 \left(p \log \left(a+b x^2\right)-\log \left(c \left(a+b x^2\right)^p\right)\right) \left(4 i \sqrt{a} \text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)+\sqrt{b} x \left(\log ^2\left(a+b x^2\right)-4 \log \left(a+b x^2\right)+8\right)+4 \sqrt{a} \left(\log \left(a+b x^2\right)+2 \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)-2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)+4 i \sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2\right)}{\sqrt{b}}+3 p x \log \left(a+b x^2\right) \left(\log \left(c \left(a+b x^2\right)^p\right)-p \log \left(a+b x^2\right)\right)^2+x \left(\log \left(c \left(a+b x^2\right)^p\right)-p \log \left(a+b x^2\right)\right)^2 \left(\log \left(c \left(a+b x^2\right)^p\right)+p \left(-\log \left(a+b x^2\right)\right)-6 p\right)+\frac{6 \sqrt{a} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(\log \left(c \left(a+b x^2\right)^p\right)-p \log \left(a+b x^2\right)\right)^2}{\sqrt{b}}","6 a p \text{Int}\left(\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{a+b x^2},x\right)+24 p^2 x \log \left(c \left(a+b x^2\right)^p\right)-\frac{24 \sqrt{a} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)}{\sqrt{b}}+x \log ^3\left(c \left(a+b x^2\right)^p\right)-6 p x \log ^2\left(c \left(a+b x^2\right)^p\right)-\frac{24 i \sqrt{a} p^3 \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)}{\sqrt{b}}-\frac{24 i \sqrt{a} p^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{\sqrt{b}}+\frac{48 \sqrt{a} p^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}-\frac{48 \sqrt{a} p^3 \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}-48 p^3 x",0,"(6*Sqrt[a]*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2)/Sqrt[b] + 3*p*x*Log[a + b*x^2]*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2 + x*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2*(-6*p - p*Log[a + b*x^2] + Log[c*(a + b*x^2)^p]) - (3*p^2*(p*Log[a + b*x^2] - Log[c*(a + b*x^2)^p])*((4*I)*Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2 + 4*Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(-2 + 2*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)] + Log[a + b*x^2]) + Sqrt[b]*x*(8 - 4*Log[a + b*x^2] + Log[a + b*x^2]^2) + (4*I)*Sqrt[a]*PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)]))/Sqrt[b] + (p^3*(-48*Sqrt[-a^2]*Sqrt[(b*x^2)/(a + b*x^2)]*Sqrt[a + b*x^2]*ArcSin[Sqrt[a]/Sqrt[a + b*x^2]] + Sqrt[-a]*b*x^2*(-48 + 24*Log[a + b*x^2] - 6*Log[a + b*x^2]^2 + Log[a + b*x^2]^3) - 6*Sqrt[-a^2]*Sqrt[(b*x^2)/(a + b*x^2)]*(8*Sqrt[a]*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {3/2, 3/2, 3/2}, a/(a + b*x^2)] + Log[a + b*x^2]*(4*Sqrt[a]*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, a/(a + b*x^2)] + Sqrt[a + b*x^2]*ArcSin[Sqrt[a]/Sqrt[a + b*x^2]]*Log[a + b*x^2])) + 24*a*Sqrt[b*x^2]*ArcTanh[Sqrt[b*x^2]/Sqrt[-a]]*(Log[a + b*x^2] - Log[1 + (b*x^2)/a]) + 6*(-a)^(3/2)*Sqrt[-((b*x^2)/a)]*(Log[1 + (b*x^2)/a]^2 - 4*Log[1 + (b*x^2)/a]*Log[(1 + Sqrt[-((b*x^2)/a)])/2] + 2*Log[(1 + Sqrt[-((b*x^2)/a)])/2]^2 - 4*PolyLog[2, 1/2 - Sqrt[-((b*x^2)/a)]/2])))/(Sqrt[-a]*b*x)","B",0
100,1,505,51,0.8272983,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^2} \, dx","Integrate[Log[c*(a + b*x^2)^p]^3/x^2,x]","\frac{p^3 \left(-96 \sqrt{a} \sqrt{1-\frac{a}{a+b x^2}} \, _4F_3\left(\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2},\frac{3}{2};\frac{a}{b x^2+a}\right)-48 \sqrt{a} \sqrt{1-\frac{a}{a+b x^2}} \log \left(a+b x^2\right) \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};\frac{a}{b x^2+a}\right)-2 \log ^2\left(a+b x^2\right) \left(\sqrt{a} \log \left(a+b x^2\right)+6 \sqrt{a+b x^2} \sqrt{1-\frac{a}{a+b x^2}} \sin ^{-1}\left(\frac{\sqrt{a}}{\sqrt{a+b x^2}}\right)\right)\right)}{2 \sqrt{a} x}+3 p^2 \left(\log \left(c \left(a+b x^2\right)^p\right)-p \log \left(a+b x^2\right)\right) \left(-\frac{\log ^2\left(a+b x^2\right)}{x}+\frac{4 \sqrt{b} \left(i \text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)+\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(\log \left(a+b x^2\right)+2 \log \left(\frac{2 i}{-\frac{\sqrt{b} x}{\sqrt{a}}+i}\right)+i \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right)\right)}{\sqrt{a}}\right)-\frac{3 p \log \left(a+b x^2\right) \left(\log \left(c \left(a+b x^2\right)^p\right)-p \log \left(a+b x^2\right)\right)^2}{x}-\frac{\left(\log \left(c \left(a+b x^2\right)^p\right)-p \log \left(a+b x^2\right)\right)^3}{x}+\frac{6 \sqrt{b} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(\log \left(c \left(a+b x^2\right)^p\right)-p \log \left(a+b x^2\right)\right)^2}{\sqrt{a}}","6 b p \text{Int}\left(\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{a+b x^2},x\right)-\frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x}",0,"(p^3*(-96*Sqrt[a]*Sqrt[1 - a/(a + b*x^2)]*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {3/2, 3/2, 3/2}, a/(a + b*x^2)] - 48*Sqrt[a]*Sqrt[1 - a/(a + b*x^2)]*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, a/(a + b*x^2)]*Log[a + b*x^2] - 2*Log[a + b*x^2]^2*(6*Sqrt[a + b*x^2]*Sqrt[1 - a/(a + b*x^2)]*ArcSin[Sqrt[a]/Sqrt[a + b*x^2]] + Sqrt[a]*Log[a + b*x^2])))/(2*Sqrt[a]*x) + (6*Sqrt[b]*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2)/Sqrt[a] - (3*p*Log[a + b*x^2]*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2)/x - (-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^3/x + 3*p^2*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])*(-(Log[a + b*x^2]^2/x) + (4*Sqrt[b]*(ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(I*ArcTan[(Sqrt[b]*x)/Sqrt[a]] + 2*Log[(2*I)/(I - (Sqrt[b]*x)/Sqrt[a])] + Log[a + b*x^2]) + I*PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)]))/Sqrt[a])","C",1
101,1,851,254,2.7102599,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^4} \, dx","Integrate[Log[c*(a + b*x^2)^p]^3/x^4,x]","\frac{\left(-a^2 \log ^3\left(b x^2+a\right)-6 a b x^2 \log ^2\left(b x^2+a\right)+6 \sqrt{a} \left(\frac{b x^2}{b x^2+a}\right)^{3/2} \left(b x^2+a\right)^{3/2} \sin ^{-1}\left(\frac{\sqrt{a}}{\sqrt{b x^2+a}}\right) \log ^2\left(b x^2+a\right)+24 \sqrt{-a} \left(b x^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b x^2}}{\sqrt{-a}}\right) \log \left(b x^2+a\right)+24 a b x^2 \sqrt{\frac{b x^2}{b x^2+a}} \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};\frac{a}{b x^2+a}\right) \log \left(b x^2+a\right)-6 a^2 \left(-\frac{b x^2}{a}\right)^{3/2} \log ^2\left(\frac{b x^2}{a}+1\right)-12 a^2 \left(-\frac{b x^2}{a}\right)^{3/2} \log ^2\left(\frac{1}{2} \left(\sqrt{-\frac{b x^2}{a}}+1\right)\right)+48 a b x^2 \sqrt{\frac{b x^2}{b x^2+a}} \, _4F_3\left(\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2},\frac{3}{2};\frac{a}{b x^2+a}\right)-24 \sqrt{-a} \left(b x^2\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b x^2}}{\sqrt{-a}}\right) \log \left(\frac{b x^2}{a}+1\right)+24 a^2 \left(-\frac{b x^2}{a}\right)^{3/2} \log \left(\frac{b x^2}{a}+1\right) \log \left(\frac{1}{2} \left(\sqrt{-\frac{b x^2}{a}}+1\right)\right)+24 a^2 \left(-\frac{b x^2}{a}\right)^{3/2} \text{Li}_2\left(\frac{1}{2}-\frac{1}{2} \sqrt{-\frac{b x^2}{a}}\right)\right) p^3+3 \sqrt{a} \left(p \log \left(b x^2+a\right)-\log \left(c \left(b x^2+a\right)^p\right)\right) \left(4 b \left(i \sqrt{b} x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2+\sqrt{b} x \left(2 \log \left(\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)+\log \left(b x^2+a\right)-2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)+\sqrt{a} \log \left(b x^2+a\right)+i \sqrt{b} x \text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)\right) x^2+a^{3/2} \log ^2\left(b x^2+a\right)\right) p^2-6 a b x^2 \left(\log \left(c \left(b x^2+a\right)^p\right)-p \log \left(b x^2+a\right)\right)^2 p-6 \sqrt{a} b^{3/2} x^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(\log \left(c \left(b x^2+a\right)^p\right)-p \log \left(b x^2+a\right)\right)^2 p-3 a^2 \log \left(b x^2+a\right) \left(\log \left(c \left(b x^2+a\right)^p\right)-p \log \left(b x^2+a\right)\right)^2 p+a^2 \left(p \log \left(b x^2+a\right)-\log \left(c \left(b x^2+a\right)^p\right)\right)^3}{3 a^2 x^3}","-\frac{2 b^2 p \text{Int}\left(\frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{a+b x^2},x\right)}{a}+\frac{8 b^{3/2} p^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^p\right)}{a^{3/2}}+\frac{8 i b^{3/2} p^3 \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)}{a^{3/2}}+\frac{8 i b^{3/2} p^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{a^{3/2}}+\frac{16 b^{3/2} p^3 \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{2 b p \log ^2\left(c \left(a+b x^2\right)^p\right)}{a x}-\frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{3 x^3}",0,"(a^2*(p*Log[a + b*x^2] - Log[c*(a + b*x^2)^p])^3 - 6*a*b*p*x^2*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2 - 6*Sqrt[a]*b^(3/2)*p*x^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2 - 3*a^2*p*Log[a + b*x^2]*(-(p*Log[a + b*x^2]) + Log[c*(a + b*x^2)^p])^2 + 3*Sqrt[a]*p^2*(p*Log[a + b*x^2] - Log[c*(a + b*x^2)^p])*(a^(3/2)*Log[a + b*x^2]^2 + 4*b*x^2*(I*Sqrt[b]*x*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2 + Sqrt[a]*Log[a + b*x^2] + Sqrt[b]*x*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(-2 + 2*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)] + Log[a + b*x^2]) + I*Sqrt[b]*x*PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)])) + p^3*(48*a*b*x^2*Sqrt[(b*x^2)/(a + b*x^2)]*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {3/2, 3/2, 3/2}, a/(a + b*x^2)] + 24*Sqrt[-a]*(b*x^2)^(3/2)*ArcTanh[Sqrt[b*x^2]/Sqrt[-a]]*Log[a + b*x^2] + 24*a*b*x^2*Sqrt[(b*x^2)/(a + b*x^2)]*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, a/(a + b*x^2)]*Log[a + b*x^2] - 6*a*b*x^2*Log[a + b*x^2]^2 + 6*Sqrt[a]*((b*x^2)/(a + b*x^2))^(3/2)*(a + b*x^2)^(3/2)*ArcSin[Sqrt[a]/Sqrt[a + b*x^2]]*Log[a + b*x^2]^2 - a^2*Log[a + b*x^2]^3 - 24*Sqrt[-a]*(b*x^2)^(3/2)*ArcTanh[Sqrt[b*x^2]/Sqrt[-a]]*Log[1 + (b*x^2)/a] - 6*a^2*(-((b*x^2)/a))^(3/2)*Log[1 + (b*x^2)/a]^2 + 24*a^2*(-((b*x^2)/a))^(3/2)*Log[1 + (b*x^2)/a]*Log[(1 + Sqrt[-((b*x^2)/a)])/2] - 12*a^2*(-((b*x^2)/a))^(3/2)*Log[(1 + Sqrt[-((b*x^2)/a)])/2]^2 + 24*a^2*(-((b*x^2)/a))^(3/2)*PolyLog[2, 1/2 - Sqrt[-((b*x^2)/a)]/2]))/(3*a^2*x^3)","B",1
102,1,96,107,0.1459237,"\int \frac{x^3}{\log \left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[x^3/Log[c*(a + b*x^2)^p],x]","-\frac{\left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-2/p} \left(a \left(c \left(a+b x^2\right)^p\right)^{\frac{1}{p}} \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)-\left(a+b x^2\right) \text{Ei}\left(\frac{2 \log \left(c \left(b x^2+a\right)^p\right)}{p}\right)\right)}{2 b^2 p}","\frac{\left(a+b x^2\right)^2 \left(c \left(a+b x^2\right)^p\right)^{-2/p} \text{Ei}\left(\frac{2 \log \left(c \left(b x^2+a\right)^p\right)}{p}\right)}{2 b^2 p}-\frac{a \left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)}{2 b^2 p}",1,"-1/2*((a + b*x^2)*(a*(c*(a + b*x^2)^p)^p^(-1)*ExpIntegralEi[Log[c*(a + b*x^2)^p]/p] - (a + b*x^2)*ExpIntegralEi[(2*Log[c*(a + b*x^2)^p])/p]))/(b^2*p*(c*(a + b*x^2)^p)^(2/p))","A",1
103,1,51,51,0.0446616,"\int \frac{x}{\log \left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[x/Log[c*(a + b*x^2)^p],x]","\frac{\left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)}{2 b p}","\frac{\left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)}{2 b p}",1,"((a + b*x^2)*ExpIntegralEi[Log[c*(a + b*x^2)^p]/p])/(2*b*p*(c*(a + b*x^2)^p)^p^(-1))","A",1
104,0,0,21,0.1910323,"\int \frac{1}{x \log \left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[1/(x*Log[c*(a + b*x^2)^p]),x]","\int \frac{1}{x \log \left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x \log \left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[1/(x*Log[c*(a + b*x^2)^p]), x]","A",-1
105,0,0,21,0.3508224,"\int \frac{1}{x^3 \log \left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[1/(x^3*Log[c*(a + b*x^2)^p]),x]","\int \frac{1}{x^3 \log \left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^3 \log \left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[1/(x^3*Log[c*(a + b*x^2)^p]), x]","A",-1
106,0,0,21,0.3082741,"\int \frac{x^2}{\log \left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[x^2/Log[c*(a + b*x^2)^p],x]","\int \frac{x^2}{\log \left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{x^2}{\log \left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[x^2/Log[c*(a + b*x^2)^p], x]","A",-1
107,0,0,17,0.0097348,"\int \frac{1}{\log \left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[Log[c*(a + b*x^2)^p]^(-1),x]","\int \frac{1}{\log \left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\log \left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[Log[c*(a + b*x^2)^p]^(-1), x]","A",-1
108,0,0,21,0.4156639,"\int \frac{1}{x^2 \log \left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[1/(x^2*Log[c*(a + b*x^2)^p]),x]","\int \frac{1}{x^2 \log \left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \log \left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[1/(x^2*Log[c*(a + b*x^2)^p]), x]","A",-1
109,1,157,138,0.1595636,"\int \frac{x^3}{\log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[x^3/Log[c*(a + b*x^2)^p]^2,x]","-\frac{\left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-2/p} \left(a \left(c \left(a+b x^2\right)^p\right)^{\frac{1}{p}} \log \left(c \left(a+b x^2\right)^p\right) \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)-2 \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right) \text{Ei}\left(\frac{2 \log \left(c \left(b x^2+a\right)^p\right)}{p}\right)+b p x^2 \left(c \left(a+b x^2\right)^p\right)^{2/p}\right)}{2 b^2 p^2 \log \left(c \left(a+b x^2\right)^p\right)}","\frac{\left(a+b x^2\right)^2 \left(c \left(a+b x^2\right)^p\right)^{-2/p} \text{Ei}\left(\frac{2 \log \left(c \left(b x^2+a\right)^p\right)}{p}\right)}{b^2 p^2}-\frac{a \left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)}{2 b^2 p^2}-\frac{x^2 \left(a+b x^2\right)}{2 b p \log \left(c \left(a+b x^2\right)^p\right)}",1,"-1/2*((a + b*x^2)*(b*p*x^2*(c*(a + b*x^2)^p)^(2/p) + a*(c*(a + b*x^2)^p)^p^(-1)*ExpIntegralEi[Log[c*(a + b*x^2)^p]/p]*Log[c*(a + b*x^2)^p] - 2*(a + b*x^2)*ExpIntegralEi[(2*Log[c*(a + b*x^2)^p])/p]*Log[c*(a + b*x^2)^p]))/(b^2*p^2*(c*(a + b*x^2)^p)^(2/p)*Log[c*(a + b*x^2)^p])","A",1
110,1,97,83,0.0469623,"\int \frac{x}{\log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[x/Log[c*(a + b*x^2)^p]^2,x]","-\frac{\left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-1/p} \left(p \left(c \left(a+b x^2\right)^p\right)^{\frac{1}{p}}-\log \left(c \left(a+b x^2\right)^p\right) \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)\right)}{2 b p^2 \log \left(c \left(a+b x^2\right)^p\right)}","\frac{\left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)}{2 b p^2}-\frac{a+b x^2}{2 b p \log \left(c \left(a+b x^2\right)^p\right)}",1,"-1/2*((a + b*x^2)*(p*(c*(a + b*x^2)^p)^p^(-1) - ExpIntegralEi[Log[c*(a + b*x^2)^p]/p]*Log[c*(a + b*x^2)^p]))/(b*p^2*(c*(a + b*x^2)^p)^p^(-1)*Log[c*(a + b*x^2)^p])","A",1
111,0,0,21,0.3000973,"\int \frac{1}{x \log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[1/(x*Log[c*(a + b*x^2)^p]^2),x]","\int \frac{1}{x \log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x \log ^2\left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[1/(x*Log[c*(a + b*x^2)^p]^2), x]","A",-1
112,0,0,21,1.5507674,"\int \frac{1}{x^3 \log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[1/(x^3*Log[c*(a + b*x^2)^p]^2),x]","\int \frac{1}{x^3 \log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^3 \log ^2\left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[1/(x^3*Log[c*(a + b*x^2)^p]^2), x]","A",-1
113,0,0,21,0.350371,"\int \frac{x^2}{\log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[x^2/Log[c*(a + b*x^2)^p]^2,x]","\int \frac{x^2}{\log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{x^2}{\log ^2\left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[x^2/Log[c*(a + b*x^2)^p]^2, x]","A",-1
114,0,0,17,0.3842056,"\int \frac{1}{\log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[Log[c*(a + b*x^2)^p]^(-2),x]","\int \frac{1}{\log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\log ^2\left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[Log[c*(a + b*x^2)^p]^(-2), x]","A",-1
115,0,0,21,1.2519271,"\int \frac{1}{x^2 \log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[1/(x^2*Log[c*(a + b*x^2)^p]^2),x]","\int \frac{1}{x^2 \log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \log ^2\left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[1/(x^2*Log[c*(a + b*x^2)^p]^2), x]","A",-1
116,1,185,204,0.2131383,"\int \frac{x^3}{\log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[x^3/Log[c*(a + b*x^2)^p]^3,x]","-\frac{\left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-2/p} \left(a \left(c \left(a+b x^2\right)^p\right)^{\frac{1}{p}} \log ^2\left(c \left(a+b x^2\right)^p\right) \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)-4 \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right) \text{Ei}\left(\frac{2 \log \left(c \left(b x^2+a\right)^p\right)}{p}\right)+p \left(c \left(a+b x^2\right)^p\right)^{2/p} \left(\left(a+2 b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)+b p x^2\right)\right)}{4 b^2 p^3 \log ^2\left(c \left(a+b x^2\right)^p\right)}","\frac{\left(a+b x^2\right)^2 \left(c \left(a+b x^2\right)^p\right)^{-2/p} \text{Ei}\left(\frac{2 \log \left(c \left(b x^2+a\right)^p\right)}{p}\right)}{b^2 p^3}-\frac{a \left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)}{4 b^2 p^3}-\frac{a \left(a+b x^2\right)}{4 b^2 p^2 \log \left(c \left(a+b x^2\right)^p\right)}-\frac{x^2 \left(a+b x^2\right)}{2 b p^2 \log \left(c \left(a+b x^2\right)^p\right)}-\frac{x^2 \left(a+b x^2\right)}{4 b p \log ^2\left(c \left(a+b x^2\right)^p\right)}",1,"-1/4*((a + b*x^2)*(a*(c*(a + b*x^2)^p)^p^(-1)*ExpIntegralEi[Log[c*(a + b*x^2)^p]/p]*Log[c*(a + b*x^2)^p]^2 - 4*(a + b*x^2)*ExpIntegralEi[(2*Log[c*(a + b*x^2)^p])/p]*Log[c*(a + b*x^2)^p]^2 + p*(c*(a + b*x^2)^p)^(2/p)*(b*p*x^2 + (a + 2*b*x^2)*Log[c*(a + b*x^2)^p])))/(b^2*p^3*(c*(a + b*x^2)^p)^(2/p)*Log[c*(a + b*x^2)^p]^2)","A",1
117,1,113,114,0.0579371,"\int \frac{x}{\log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[x/Log[c*(a + b*x^2)^p]^3,x]","-\frac{\left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-1/p} \left(p \left(c \left(a+b x^2\right)^p\right)^{\frac{1}{p}} \left(\log \left(c \left(a+b x^2\right)^p\right)+p\right)-\log ^2\left(c \left(a+b x^2\right)^p\right) \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)\right)}{4 b p^3 \log ^2\left(c \left(a+b x^2\right)^p\right)}","\frac{\left(a+b x^2\right) \left(c \left(a+b x^2\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(b x^2+a\right)^p\right)}{p}\right)}{4 b p^3}-\frac{a+b x^2}{4 b p^2 \log \left(c \left(a+b x^2\right)^p\right)}-\frac{a+b x^2}{4 b p \log ^2\left(c \left(a+b x^2\right)^p\right)}",1,"-1/4*((a + b*x^2)*(-(ExpIntegralEi[Log[c*(a + b*x^2)^p]/p]*Log[c*(a + b*x^2)^p]^2) + p*(c*(a + b*x^2)^p)^p^(-1)*(p + Log[c*(a + b*x^2)^p])))/(b*p^3*(c*(a + b*x^2)^p)^p^(-1)*Log[c*(a + b*x^2)^p]^2)","A",1
118,0,0,21,0.5876016,"\int \frac{1}{x \log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[1/(x*Log[c*(a + b*x^2)^p]^3),x]","\int \frac{1}{x \log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x \log ^3\left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[1/(x*Log[c*(a + b*x^2)^p]^3), x]","A",-1
119,0,0,21,3.2029714,"\int \frac{1}{x^3 \log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[1/(x^3*Log[c*(a + b*x^2)^p]^3),x]","\int \frac{1}{x^3 \log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^3 \log ^3\left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[1/(x^3*Log[c*(a + b*x^2)^p]^3), x]","A",-1
120,0,0,21,0.5630516,"\int \frac{x^2}{\log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[x^2/Log[c*(a + b*x^2)^p]^3,x]","\int \frac{x^2}{\log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{x^2}{\log ^3\left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[x^2/Log[c*(a + b*x^2)^p]^3, x]","A",-1
121,0,0,17,0.4884624,"\int \frac{1}{\log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[Log[c*(a + b*x^2)^p]^(-3),x]","\int \frac{1}{\log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\log ^3\left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[Log[c*(a + b*x^2)^p]^(-3), x]","A",-1
122,0,0,21,2.2558645,"\int \frac{1}{x^2 \log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Integrate[1/(x^2*Log[c*(a + b*x^2)^p]^3),x]","\int \frac{1}{x^2 \log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \log ^3\left(c \left(a+b x^2\right)^p\right)},x\right)",0,"Integrate[1/(x^2*Log[c*(a + b*x^2)^p]^3), x]","A",-1
123,1,41,45,0.0901695,"\int \frac{x^3}{\log \left(c \left(a+b x^2\right)\right)} \, dx","Integrate[x^3/Log[c*(a + b*x^2)],x]","\frac{\text{Ei}\left(2 \log \left(b c x^2+a c\right)\right)-a c \text{Ei}\left(\log \left(b c x^2+a c\right)\right)}{2 b^2 c^2}","\frac{\text{Ei}\left(2 \log \left(c \left(b x^2+a\right)\right)\right)}{2 b^2 c^2}-\frac{a \text{li}\left(c \left(b x^2+a\right)\right)}{2 b^2 c}",1,"(-(a*c*ExpIntegralEi[Log[a*c + b*c*x^2]]) + ExpIntegralEi[2*Log[a*c + b*c*x^2]])/(2*b^2*c^2)","A",1
124,1,20,20,0.0151324,"\int \frac{x}{\log \left(c \left(a+b x^2\right)\right)} \, dx","Integrate[x/Log[c*(a + b*x^2)],x]","\frac{\text{li}\left(c \left(b x^2+a\right)\right)}{2 b c}","\frac{\text{li}\left(c \left(b x^2+a\right)\right)}{2 b c}",1,"LogIntegral[c*(a + b*x^2)]/(2*b*c)","A",1
125,1,66,71,0.1169855,"\int \frac{x^3}{\log ^2\left(c \left(a+b x^2\right)\right)} \, dx","Integrate[x^3/Log[c*(a + b*x^2)]^2,x]","-\frac{-\frac{2 \text{Ei}\left(2 \log \left(c \left(b x^2+a\right)\right)\right)}{c^2}+\frac{a \text{Ei}\left(\log \left(c \left(b x^2+a\right)\right)\right)}{c}+\frac{b x^2 \left(a+b x^2\right)}{\log \left(c \left(a+b x^2\right)\right)}}{2 b^2}","\frac{\text{Ei}\left(2 \log \left(c \left(b x^2+a\right)\right)\right)}{b^2 c^2}-\frac{a \text{li}\left(c \left(b x^2+a\right)\right)}{2 b^2 c}-\frac{x^2 \left(a+b x^2\right)}{2 b \log \left(c \left(a+b x^2\right)\right)}",1,"-1/2*((a*ExpIntegralEi[Log[c*(a + b*x^2)]])/c - (2*ExpIntegralEi[2*Log[c*(a + b*x^2)]])/c^2 + (b*x^2*(a + b*x^2))/Log[c*(a + b*x^2)])/b^2","A",1
126,1,43,47,0.0205866,"\int \frac{x}{\log ^2\left(c \left(a+b x^2\right)\right)} \, dx","Integrate[x/Log[c*(a + b*x^2)]^2,x]","\frac{\frac{\text{li}\left(c \left(b x^2+a\right)\right)}{c}-\frac{a+b x^2}{\log \left(c \left(a+b x^2\right)\right)}}{2 b}","\frac{\text{li}\left(c \left(b x^2+a\right)\right)}{2 b c}-\frac{a+b x^2}{2 b \log \left(c \left(a+b x^2\right)\right)}",1,"(-((a + b*x^2)/Log[c*(a + b*x^2)]) + LogIntegral[c*(a + b*x^2)]/c)/(2*b)","A",1
127,1,87,127,0.1314925,"\int \frac{x^3}{\log ^3\left(c \left(a+b x^2\right)\right)} \, dx","Integrate[x^3/Log[c*(a + b*x^2)]^3,x]","-\frac{-\frac{4 \text{Ei}\left(2 \log \left(c \left(b x^2+a\right)\right)\right)}{c^2}+\frac{a \text{Ei}\left(\log \left(c \left(b x^2+a\right)\right)\right)}{c}+\frac{\left(a+b x^2\right) \left(\left(a+2 b x^2\right) \log \left(c \left(a+b x^2\right)\right)+b x^2\right)}{\log ^2\left(c \left(a+b x^2\right)\right)}}{4 b^2}","\frac{\text{Ei}\left(2 \log \left(c \left(b x^2+a\right)\right)\right)}{b^2 c^2}-\frac{a \text{li}\left(c \left(b x^2+a\right)\right)}{4 b^2 c}-\frac{a \left(a+b x^2\right)}{4 b^2 \log \left(c \left(a+b x^2\right)\right)}-\frac{x^2 \left(a+b x^2\right)}{4 b \log ^2\left(c \left(a+b x^2\right)\right)}-\frac{x^2 \left(a+b x^2\right)}{2 b \log \left(c \left(a+b x^2\right)\right)}",1,"-1/4*((a*ExpIntegralEi[Log[c*(a + b*x^2)]])/c - (4*ExpIntegralEi[2*Log[c*(a + b*x^2)]])/c^2 + ((a + b*x^2)*(b*x^2 + (a + 2*b*x^2)*Log[c*(a + b*x^2)]))/Log[c*(a + b*x^2)]^2)/b^2","A",1
128,1,55,73,0.0244492,"\int \frac{x}{\log ^3\left(c \left(a+b x^2\right)\right)} \, dx","Integrate[x/Log[c*(a + b*x^2)]^3,x]","\frac{\frac{\text{li}\left(c \left(b x^2+a\right)\right)}{c}-\frac{\left(a+b x^2\right) \left(\log \left(c \left(a+b x^2\right)\right)+1\right)}{\log ^2\left(c \left(a+b x^2\right)\right)}}{4 b}","\frac{\text{li}\left(c \left(b x^2+a\right)\right)}{4 b c}-\frac{a+b x^2}{4 b \log ^2\left(c \left(a+b x^2\right)\right)}-\frac{a+b x^2}{4 b \log \left(c \left(a+b x^2\right)\right)}",1,"(-(((a + b*x^2)*(1 + Log[c*(a + b*x^2)]))/Log[c*(a + b*x^2)]^2) + LogIntegral[c*(a + b*x^2)]/c)/(4*b)","A",1
129,1,105,150,0.0660743,"\int x^5 \log ^2\left(c \left(d+e x^3\right)^p\right) \, dx","Integrate[x^5*Log[c*(d + e*x^3)^p]^2,x]","\frac{-2 \left(d^2-e^2 x^6\right) \log ^2\left(c \left(d+e x^3\right)^p\right)+2 p \left(2 d^2+2 d e x^3-e^2 x^6\right) \log \left(c \left(d+e x^3\right)^p\right)+2 d^2 p^2 \log \left(d+e x^3\right)+e p^2 x^3 \left(e x^3-6 d\right)}{12 e^2}","\frac{\left(d+e x^3\right)^2 \log ^2\left(c \left(d+e x^3\right)^p\right)}{6 e^2}-\frac{d \left(d+e x^3\right) \log ^2\left(c \left(d+e x^3\right)^p\right)}{3 e^2}-\frac{p \left(d+e x^3\right)^2 \log \left(c \left(d+e x^3\right)^p\right)}{6 e^2}+\frac{2 d p \left(d+e x^3\right) \log \left(c \left(d+e x^3\right)^p\right)}{3 e^2}+\frac{p^2 \left(d+e x^3\right)^2}{12 e^2}-\frac{2 d p^2 x^3}{3 e}",1,"(e*p^2*x^3*(-6*d + e*x^3) + 2*d^2*p^2*Log[d + e*x^3] + 2*p*(2*d^2 + 2*d*e*x^3 - e^2*x^6)*Log[c*(d + e*x^3)^p] - 2*(d^2 - e^2*x^6)*Log[c*(d + e*x^3)^p]^2)/(12*e^2)","A",1
130,1,63,66,0.0100252,"\int x^2 \log ^2\left(c \left(d+e x^3\right)^p\right) \, dx","Integrate[x^2*Log[c*(d + e*x^3)^p]^2,x]","\frac{1}{3} \left(\frac{\left(d+e x^3\right) \log ^2\left(c \left(d+e x^3\right)^p\right)}{e}-2 p \left(\frac{\left(d+e x^3\right) \log \left(c \left(d+e x^3\right)^p\right)}{e}-p x^3\right)\right)","\frac{\left(d+e x^3\right) \log ^2\left(c \left(d+e x^3\right)^p\right)}{3 e}-\frac{2 p \left(d+e x^3\right) \log \left(c \left(d+e x^3\right)^p\right)}{3 e}+\frac{2 p^2 x^3}{3}",1,"(((d + e*x^3)*Log[c*(d + e*x^3)^p]^2)/e - 2*p*(-(p*x^3) + ((d + e*x^3)*Log[c*(d + e*x^3)^p])/e))/3","A",1
131,1,163,77,0.1014648,"\int \frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x} \, dx","Integrate[Log[c*(d + e*x^3)^p]^2/x,x]","2 p \left(\log (x) \left(\log \left(d+e x^3\right)-\log \left(\frac{e x^3}{d}+1\right)\right)-\frac{1}{3} \text{Li}_2\left(-\frac{e x^3}{d}\right)\right) \left(\log \left(c \left(d+e x^3\right)^p\right)-p \log \left(d+e x^3\right)\right)+\log (x) \left(\log \left(c \left(d+e x^3\right)^p\right)-p \log \left(d+e x^3\right)\right)^2+\frac{1}{3} p^2 \left(-2 \text{Li}_3\left(\frac{e x^3}{d}+1\right)+2 \text{Li}_2\left(\frac{e x^3}{d}+1\right) \log \left(d+e x^3\right)+\log \left(-\frac{e x^3}{d}\right) \log ^2\left(d+e x^3\right)\right)","\frac{2}{3} p \text{Li}_2\left(\frac{e x^3}{d}+1\right) \log \left(c \left(d+e x^3\right)^p\right)+\frac{1}{3} \log \left(-\frac{e x^3}{d}\right) \log ^2\left(c \left(d+e x^3\right)^p\right)-\frac{2}{3} p^2 \text{Li}_3\left(\frac{e x^3}{d}+1\right)",1,"Log[x]*(-(p*Log[d + e*x^3]) + Log[c*(d + e*x^3)^p])^2 + 2*p*(-(p*Log[d + e*x^3]) + Log[c*(d + e*x^3)^p])*(Log[x]*(Log[d + e*x^3] - Log[1 + (e*x^3)/d]) - PolyLog[2, -((e*x^3)/d)]/3) + (p^2*(Log[-((e*x^3)/d)]*Log[d + e*x^3]^2 + 2*Log[d + e*x^3]*PolyLog[2, 1 + (e*x^3)/d] - 2*PolyLog[3, 1 + (e*x^3)/d]))/3","B",1
132,1,84,86,0.0388211,"\int \frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x^4} \, dx","Integrate[Log[c*(d + e*x^3)^p]^2/x^4,x]","\frac{-\left(d+e x^3\right) \log ^2\left(c \left(d+e x^3\right)^p\right)+2 e p x^3 \log \left(-\frac{e x^3}{d}\right) \log \left(c \left(d+e x^3\right)^p\right)+2 e p^2 x^3 \text{Li}_2\left(\frac{e x^3}{d}+1\right)}{3 d x^3}","-\frac{\left(d+e x^3\right) \log ^2\left(c \left(d+e x^3\right)^p\right)}{3 d x^3}+\frac{2 e p \log \left(-\frac{e x^3}{d}\right) \log \left(c \left(d+e x^3\right)^p\right)}{3 d}+\frac{2 e p^2 \text{Li}_2\left(\frac{e x^3}{d}+1\right)}{3 d}",1,"(2*e*p*x^3*Log[-((e*x^3)/d)]*Log[c*(d + e*x^3)^p] - (d + e*x^3)*Log[c*(d + e*x^3)^p]^2 + 2*e*p^2*x^3*PolyLog[2, 1 + (e*x^3)/d])/(3*d*x^3)","A",1
133,1,823,1294,1.2349397,"\int x \log ^2\left(c \left(d+e x^3\right)^p\right) \, dx","Integrate[x*Log[c*(d + e*x^3)^p]^2,x]","\frac{1}{4} \left(2 x^2 \log ^2\left(c \left(e x^3+d\right)^p\right)+\frac{p \left(-9 e^{2/3} p \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{e x^3}{d}\right)-1\right) x^2-6 e^{2/3} \log \left(c \left(e x^3+d\right)^p\right) x^2-4 d^{2/3} \log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right)+4 \sqrt[3]{-1} d^{2/3} \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right)-4 (-1)^{2/3} d^{2/3} \log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right)-2 \sqrt[3]{-1} d^{2/3} p \left(\log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \left(2 \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right)+2 \log \left(\frac{(-1)^{2/3} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(-1+(-1)^{2/3}\right) \sqrt[3]{d}}\right)\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}}{\left(-1+(-1)^{2/3}\right) \sqrt[3]{d}}\right)\right)+2 (-1)^{2/3} d^{2/3} p \left(\log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) \left(2 \log \left(\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(-1+(-1)^{2/3}\right) \sqrt[3]{d}}\right)+2 \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right)\right)+2 \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right)\right)+2 d^{2/3} p \left(\log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) \left(\log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right)+2 \left(\log \left(\frac{\sqrt[3]{-1} \sqrt[3]{d}-\sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(\frac{-\frac{2 i \sqrt[3]{e} x}{\sqrt[3]{d}}+\sqrt{3}+i}{3 i+\sqrt{3}}\right)\right)\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{2 i \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)}{3 i+\sqrt{3}}\right)\right)\right)}{e^{2/3}}\right)","\frac{9 x^2 p^2}{4}+\frac{d^{2/3} \log ^2\left(\sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{2 e^{2/3}}-\frac{\sqrt[3]{-1} d^{2/3} \log ^2\left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) p^2}{2 e^{2/3}}+\frac{(-1)^{2/3} d^{2/3} \log ^2\left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{2 e^{2/3}}+\frac{3 \sqrt{3} d^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) p^2}{2 e^{2/3}}+\frac{3 d^{2/3} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{2 e^{2/3}}+\frac{d^{2/3} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(-\frac{\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{e^{2/3}}-\frac{\sqrt[3]{-1} d^{2/3} \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) p^2}{e^{2/3}}+\frac{(-1)^{2/3} d^{2/3} \log \left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{e^{2/3}}+\frac{(-1)^{2/3} d^{2/3} \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{e^{2/3}}+\frac{d^{2/3} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{e^{2/3}}-\frac{(-1)^{2/3} d^{2/3} \log \left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{e^{2/3}}-\frac{\sqrt[3]{-1} d^{2/3} \log \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) \log \left(-\frac{(-1)^{2/3} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{e^{2/3}}-\frac{3 d^{2/3} \log \left(e^{2/3} x^2-\sqrt[3]{d} \sqrt[3]{e} x+d^{2/3}\right) p^2}{4 e^{2/3}}+\frac{d^{2/3} \text{Li}_2\left(\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{e^{2/3}}-\frac{(-1)^{2/3} d^{2/3} \text{Li}_2\left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{e^{2/3}}+\frac{d^{2/3} \text{Li}_2\left(\frac{2 \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(3-i \sqrt{3}\right) \sqrt[3]{d}}\right) p^2}{e^{2/3}}-\frac{\sqrt[3]{-1} d^{2/3} \text{Li}_2\left(-\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{e^{2/3}}-\frac{\sqrt[3]{-1} d^{2/3} \text{Li}_2\left(\frac{\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{e^{2/3}}+\frac{(-1)^{2/3} d^{2/3} \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{e^{2/3}}-\frac{3}{2} x^2 \log \left(c \left(e x^3+d\right)^p\right) p-\frac{d^{2/3} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{e^{2/3}}+\frac{\sqrt[3]{-1} d^{2/3} \log \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) \log \left(c \left(e x^3+d\right)^p\right) p}{e^{2/3}}-\frac{(-1)^{2/3} d^{2/3} \log \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{e^{2/3}}+\frac{1}{2} x^2 \log ^2\left(c \left(e x^3+d\right)^p\right)",1,"(2*x^2*Log[c*(d + e*x^3)^p]^2 + (p*(-9*e^(2/3)*p*x^2*(-1 + Hypergeometric2F1[2/3, 1, 5/3, -((e*x^3)/d)]) - 6*e^(2/3)*x^2*Log[c*(d + e*x^3)^p] - 4*d^(2/3)*Log[-d^(1/3) - e^(1/3)*x]*Log[c*(d + e*x^3)^p] + 4*(-1)^(1/3)*d^(2/3)*Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p] - 4*(-1)^(2/3)*d^(2/3)*Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p] - 2*(-1)^(1/3)*d^(2/3)*p*(Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*(2*Log[((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))] + Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x] + 2*Log[((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((-1 + (-1)^(2/3))*d^(1/3))]) + 2*PolyLog[2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, (-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)/((-1 + (-1)^(2/3))*d^(1/3))]) + 2*(-1)^(2/3)*d^(2/3)*p*(Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]*(2*Log[((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((-1 + (-1)^(2/3))*d^(1/3))] + 2*Log[((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))] + Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]) + 2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))]) + 2*d^(2/3)*p*(Log[-d^(1/3) - e^(1/3)*x]*(Log[-d^(1/3) - e^(1/3)*x] + 2*(Log[((-1)^(1/3)*d^(1/3) - e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + Log[(I + Sqrt[3] - ((2*I)*e^(1/3)*x)/d^(1/3))/(3*I + Sqrt[3])])) + 2*PolyLog[2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, ((2*I)*(1 + (e^(1/3)*x)/d^(1/3)))/(3*I + Sqrt[3])])))/e^(2/3))/4","C",1
134,1,1090,1304,0.7268624,"\int \log ^2\left(c \left(d+e x^3\right)^p\right) \, dx","Integrate[Log[c*(d + e*x^3)^p]^2,x]","x \log ^2\left(c \left(e x^3+d\right)^p\right)-6 e p \left(-\frac{1}{2} p \left(\frac{6 x}{e}-\frac{\frac{2 \sqrt[3]{d} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\sqrt[3]{e}}-\sqrt[3]{d} \left(\frac{2 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt[3]{e}}+\frac{\log \left(e^{2/3} x^2-\sqrt[3]{d} \sqrt[3]{e} x+d^{2/3}\right)}{\sqrt[3]{e}}\right)}{e}\right)+\frac{x \log \left(c \left(e x^3+d\right)^p\right)}{e}-\frac{\sqrt[3]{d} \log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right)}{3 e^{4/3}}-\frac{(-1)^{2/3} \sqrt[3]{d} \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right)}{3 e^{4/3}}+\frac{\sqrt[3]{-1} \sqrt[3]{d} \log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right)}{3 e^{4/3}}+\frac{\sqrt[3]{d} p \left(\frac{\log ^2\left(-\sqrt[3]{e} x-\sqrt[3]{d}\right)}{\sqrt[3]{e}}+\frac{2 \log \left(-\frac{\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right)}{\sqrt[3]{e}}+\frac{2 \log \left(\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right)}{\sqrt[3]{e}}+\frac{2 \text{Li}_2\left(\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)}{\sqrt[3]{e}}+\frac{2 \text{Li}_2\left(\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right)}{\sqrt[3]{e}}\right)}{6 e}+\frac{(-1)^{2/3} \sqrt[3]{d} p \left(\frac{\log ^2\left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right)}{\sqrt[3]{e}}+\frac{2 \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right)}{\sqrt[3]{e}}+\frac{2 \log \left(-\frac{(-1)^{2/3} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right)}{\sqrt[3]{e}}+\frac{2 \text{Li}_2\left(\frac{\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)}{\sqrt[3]{e}}+\frac{2 \text{Li}_2\left(\frac{\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right)}{\sqrt[3]{e}}\right)}{6 e}-\frac{\sqrt[3]{-1} \sqrt[3]{d} p \left(\frac{\log ^2\left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right)}{\sqrt[3]{e}}+\frac{2 \log \left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right)}{\sqrt[3]{e}}+\frac{2 \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right)}{\sqrt[3]{e}}+\frac{2 \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)}{\sqrt[3]{e}}+\frac{2 \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right)}{\sqrt[3]{e}}\right)}{6 e}\right)","-\frac{\sqrt[3]{d} \log ^2\left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{\sqrt[3]{e}}-\frac{(-1)^{2/3} \sqrt[3]{d} \log ^2\left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{\sqrt[3]{e}}+\frac{\sqrt[3]{-1} \sqrt[3]{d} \log ^2\left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{\sqrt[3]{e}}+18 x p^2+\frac{6 \sqrt{3} \sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) p^2}{\sqrt[3]{e}}-\frac{6 \sqrt[3]{d} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{\sqrt[3]{e}}-\frac{2 \sqrt[3]{d} \log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(-\frac{\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{e}}-\frac{2 (-1)^{2/3} \sqrt[3]{d} \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{\sqrt[3]{e}}+\frac{2 \sqrt[3]{-1} \sqrt[3]{d} \log \left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{\sqrt[3]{e}}+\frac{2 \sqrt[3]{-1} \sqrt[3]{d} \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{\sqrt[3]{e}}-\frac{2 \sqrt[3]{d} \log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{e}}-\frac{2 \sqrt[3]{-1} \sqrt[3]{d} \log \left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{e}}-\frac{2 (-1)^{2/3} \sqrt[3]{d} \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(-\frac{(-1)^{2/3} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{e}}+\frac{3 \sqrt[3]{d} \log \left(e^{2/3} x^2-\sqrt[3]{d} \sqrt[3]{e} x+d^{2/3}\right) p^2}{\sqrt[3]{e}}-\frac{2 \sqrt[3]{d} \text{Li}_2\left(\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{e}}-\frac{2 \sqrt[3]{-1} \sqrt[3]{d} \text{Li}_2\left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{e}}-\frac{2 \sqrt[3]{d} \text{Li}_2\left(\frac{2 \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(3-i \sqrt{3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{e}}-\frac{2 (-1)^{2/3} \sqrt[3]{d} \text{Li}_2\left(-\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{e}}-\frac{2 (-1)^{2/3} \sqrt[3]{d} \text{Li}_2\left(\frac{\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{e}}+\frac{2 \sqrt[3]{-1} \sqrt[3]{d} \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{e}}-6 x \log \left(c \left(e x^3+d\right)^p\right) p+\frac{2 \sqrt[3]{d} \log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{\sqrt[3]{e}}+\frac{2 (-1)^{2/3} \sqrt[3]{d} \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{\sqrt[3]{e}}-\frac{2 \sqrt[3]{-1} \sqrt[3]{d} \log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{\sqrt[3]{e}}+x \log ^2\left(c \left(e x^3+d\right)^p\right)",1,"x*Log[c*(d + e*x^3)^p]^2 - 6*e*p*(-1/2*(p*((6*x)/e - ((2*d^(1/3)*Log[d^(1/3) + e^(1/3)*x])/e^(1/3) - d^(1/3)*((2*Sqrt[3]*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/e^(1/3) + Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2]/e^(1/3)))/e)) + (x*Log[c*(d + e*x^3)^p])/e - (d^(1/3)*Log[-d^(1/3) - e^(1/3)*x]*Log[c*(d + e*x^3)^p])/(3*e^(4/3)) - ((-1)^(2/3)*d^(1/3)*Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/(3*e^(4/3)) + ((-1)^(1/3)*d^(1/3)*Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/(3*e^(4/3)) + (d^(1/3)*p*(Log[-d^(1/3) - e^(1/3)*x]^2/e^(1/3) + (2*Log[-d^(1/3) - e^(1/3)*x]*Log[-(((-1)^(2/3)*d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3)))])/e^(1/3) + (2*Log[-d^(1/3) - e^(1/3)*x]*Log[((-1)^(1/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))])/e^(1/3) + (2*PolyLog[2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/e^(1/3) + (2*PolyLog[2, (d^(1/3) + e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))])/e^(1/3)))/(6*e) + ((-1)^(2/3)*d^(1/3)*p*((2*Log[((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))]*Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x])/e^(1/3) + Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]^2/e^(1/3) + (2*Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*Log[-(((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))])/e^(1/3) + (2*PolyLog[2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/e^(1/3) + (2*PolyLog[2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))])/e^(1/3)))/(6*e) - ((-1)^(1/3)*d^(1/3)*p*((2*Log[-(((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))]*Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x])/e^(1/3) + (2*Log[((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))]*Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x])/e^(1/3) + Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]^2/e^(1/3) + (2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/e^(1/3) + (2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))])/e^(1/3)))/(6*e))","A",1
135,1,742,1137,0.868803,"\int \frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x^2} \, dx","Integrate[Log[c*(d + e*x^3)^p]^2/x^2,x]","-\frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x}-\frac{\sqrt[3]{e} p \left(2 \log \left(-\sqrt[3]{d}-\sqrt[3]{e} x\right) \log \left(c \left(d+e x^3\right)^p\right)-2 \sqrt[3]{-1} \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(d+e x^3\right)^p\right)+2 (-1)^{2/3} \log \left(-\sqrt[3]{d}-(-1)^{2/3} \sqrt[3]{e} x\right) \log \left(c \left(d+e x^3\right)^p\right)+\sqrt[3]{-1} p \left(2 \text{Li}_2\left(\frac{\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}}{\left(-1+(-1)^{2/3}\right) \sqrt[3]{d}}\right)+\log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \left(2 \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right)+2 \log \left(\frac{(-1)^{2/3} \left(\sqrt[3]{d}+(-1)^{2/3} \sqrt[3]{e} x\right)}{\left((-1)^{2/3}-1\right) \sqrt[3]{d}}\right)\right)\right)-(-1)^{2/3} p \left(2 \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right)+\log \left(-\sqrt[3]{d}-(-1)^{2/3} \sqrt[3]{e} x\right) \left(2 \log \left(\frac{(-1)^{2/3} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left((-1)^{2/3}-1\right) \sqrt[3]{d}}\right)+2 \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(-\sqrt[3]{d}-(-1)^{2/3} \sqrt[3]{e} x\right)\right)\right)-p \left(2 \text{Li}_2\left(\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{2 i \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)}{3 i+\sqrt{3}}\right)+\log \left(-\sqrt[3]{d}-\sqrt[3]{e} x\right) \left(\log \left(-\sqrt[3]{d}-\sqrt[3]{e} x\right)+2 \left(\log \left(\frac{\sqrt[3]{-1} \sqrt[3]{d}-\sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(\frac{-\frac{2 i \sqrt[3]{e} x}{\sqrt[3]{d}}+\sqrt{3}+i}{\sqrt{3}+3 i}\right)\right)\right)\right)\right)}{\sqrt[3]{d}}","\frac{\sqrt[3]{e} \log ^2\left(\sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{\sqrt[3]{d}}-\frac{\sqrt[3]{-1} \sqrt[3]{e} \log ^2\left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) p^2}{\sqrt[3]{d}}+\frac{(-1)^{2/3} \sqrt[3]{e} \log ^2\left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{\sqrt[3]{d}}+\frac{2 \sqrt[3]{e} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(-\frac{\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{d}}-\frac{2 \sqrt[3]{-1} \sqrt[3]{e} \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) p^2}{\sqrt[3]{d}}+\frac{2 (-1)^{2/3} \sqrt[3]{e} \log \left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{\sqrt[3]{d}}+\frac{2 (-1)^{2/3} \sqrt[3]{e} \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{\sqrt[3]{d}}+\frac{2 \sqrt[3]{e} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{d}}-\frac{2 (-1)^{2/3} \sqrt[3]{e} \log \left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{d}}-\frac{2 \sqrt[3]{-1} \sqrt[3]{e} \log \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) \log \left(-\frac{(-1)^{2/3} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{d}}+\frac{2 \sqrt[3]{e} \text{Li}_2\left(\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{d}}-\frac{2 (-1)^{2/3} \sqrt[3]{e} \text{Li}_2\left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{d}}+\frac{2 \sqrt[3]{e} \text{Li}_2\left(\frac{2 \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(3-i \sqrt{3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{d}}-\frac{2 \sqrt[3]{-1} \sqrt[3]{e} \text{Li}_2\left(-\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{d}}-\frac{2 \sqrt[3]{-1} \sqrt[3]{e} \text{Li}_2\left(\frac{\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{d}}+\frac{2 (-1)^{2/3} \sqrt[3]{e} \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{\sqrt[3]{d}}-\frac{2 \sqrt[3]{e} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{\sqrt[3]{d}}+\frac{2 \sqrt[3]{-1} \sqrt[3]{e} \log \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) \log \left(c \left(e x^3+d\right)^p\right) p}{\sqrt[3]{d}}-\frac{2 (-1)^{2/3} \sqrt[3]{e} \log \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{\sqrt[3]{d}}-\frac{\log ^2\left(c \left(e x^3+d\right)^p\right)}{x}",1,"-(Log[c*(d + e*x^3)^p]^2/x) - (e^(1/3)*p*(2*Log[-d^(1/3) - e^(1/3)*x]*Log[c*(d + e*x^3)^p] - 2*(-1)^(1/3)*Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p] + 2*(-1)^(2/3)*Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p] + (-1)^(1/3)*p*(Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*(2*Log[((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))] + Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x] + 2*Log[((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((-1 + (-1)^(2/3))*d^(1/3))]) + 2*PolyLog[2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, (-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)/((-1 + (-1)^(2/3))*d^(1/3))]) - (-1)^(2/3)*p*(Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]*(2*Log[((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((-1 + (-1)^(2/3))*d^(1/3))] + 2*Log[((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))] + Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]) + 2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))]) - p*(Log[-d^(1/3) - e^(1/3)*x]*(Log[-d^(1/3) - e^(1/3)*x] + 2*(Log[((-1)^(1/3)*d^(1/3) - e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + Log[(I + Sqrt[3] - ((2*I)*e^(1/3)*x)/d^(1/3))/(3*I + Sqrt[3])])) + 2*PolyLog[2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, ((2*I)*(1 + (e^(1/3)*x)/d^(1/3)))/(3*I + Sqrt[3])])))/d^(1/3)","A",1
136,1,745,1170,0.8718546,"\int \frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x^3} \, dx","Integrate[Log[c*(d + e*x^3)^p]^2/x^3,x]","\frac{1}{2} \left(-\frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x^2}+\frac{e^{2/3} p \left(2 \log \left(-\sqrt[3]{d}-\sqrt[3]{e} x\right) \log \left(c \left(d+e x^3\right)^p\right)+2 (-1)^{2/3} \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(d+e x^3\right)^p\right)-2 \sqrt[3]{-1} \log \left(-\sqrt[3]{d}-(-1)^{2/3} \sqrt[3]{e} x\right) \log \left(c \left(d+e x^3\right)^p\right)-(-1)^{2/3} p \left(2 \text{Li}_2\left(\frac{\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}}{\left(-1+(-1)^{2/3}\right) \sqrt[3]{d}}\right)+\log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \left(2 \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right)+2 \log \left(\frac{(-1)^{2/3} \left(\sqrt[3]{d}+(-1)^{2/3} \sqrt[3]{e} x\right)}{\left((-1)^{2/3}-1\right) \sqrt[3]{d}}\right)\right)\right)+\sqrt[3]{-1} p \left(2 \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right)+\log \left(-\sqrt[3]{d}-(-1)^{2/3} \sqrt[3]{e} x\right) \left(2 \log \left(\frac{(-1)^{2/3} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left((-1)^{2/3}-1\right) \sqrt[3]{d}}\right)+2 \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(-\sqrt[3]{d}-(-1)^{2/3} \sqrt[3]{e} x\right)\right)\right)-p \left(2 \text{Li}_2\left(\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{2 i \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)}{3 i+\sqrt{3}}\right)+\log \left(-\sqrt[3]{d}-\sqrt[3]{e} x\right) \left(\log \left(-\sqrt[3]{d}-\sqrt[3]{e} x\right)+2 \left(\log \left(\frac{\sqrt[3]{-1} \sqrt[3]{d}-\sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(\frac{-\frac{2 i \sqrt[3]{e} x}{\sqrt[3]{d}}+\sqrt{3}+i}{\sqrt{3}+3 i}\right)\right)\right)\right)\right)}{d^{2/3}}\right)","-\frac{e^{2/3} \log ^2\left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{2 d^{2/3}}-\frac{(-1)^{2/3} e^{2/3} \log ^2\left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{2 d^{2/3}}+\frac{\sqrt[3]{-1} e^{2/3} \log ^2\left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{2 d^{2/3}}-\frac{e^{2/3} \log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(-\frac{\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{d^{2/3}}-\frac{(-1)^{2/3} e^{2/3} \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{d^{2/3}}+\frac{\sqrt[3]{-1} e^{2/3} \log \left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{d^{2/3}}+\frac{\sqrt[3]{-1} e^{2/3} \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) p^2}{d^{2/3}}-\frac{e^{2/3} \log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{d^{2/3}}-\frac{\sqrt[3]{-1} e^{2/3} \log \left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{d^{2/3}}-\frac{(-1)^{2/3} e^{2/3} \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(-\frac{(-1)^{2/3} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{d^{2/3}}-\frac{e^{2/3} \text{Li}_2\left(\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{d^{2/3}}-\frac{\sqrt[3]{-1} e^{2/3} \text{Li}_2\left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{d^{2/3}}-\frac{e^{2/3} \text{Li}_2\left(\frac{2 \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(3-i \sqrt{3}\right) \sqrt[3]{d}}\right) p^2}{d^{2/3}}-\frac{(-1)^{2/3} e^{2/3} \text{Li}_2\left(-\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{d^{2/3}}-\frac{(-1)^{2/3} e^{2/3} \text{Li}_2\left(\frac{\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{d^{2/3}}+\frac{\sqrt[3]{-1} e^{2/3} \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{d^{2/3}}+\frac{e^{2/3} \log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{d^{2/3}}+\frac{(-1)^{2/3} e^{2/3} \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{d^{2/3}}-\frac{\sqrt[3]{-1} e^{2/3} \log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{d^{2/3}}-\frac{\log ^2\left(c \left(e x^3+d\right)^p\right)}{2 x^2}",1,"(-(Log[c*(d + e*x^3)^p]^2/x^2) + (e^(2/3)*p*(2*Log[-d^(1/3) - e^(1/3)*x]*Log[c*(d + e*x^3)^p] + 2*(-1)^(2/3)*Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p] - 2*(-1)^(1/3)*Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p] - (-1)^(2/3)*p*(Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*(2*Log[((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))] + Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x] + 2*Log[((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((-1 + (-1)^(2/3))*d^(1/3))]) + 2*PolyLog[2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, (-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)/((-1 + (-1)^(2/3))*d^(1/3))]) + (-1)^(1/3)*p*(Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]*(2*Log[((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((-1 + (-1)^(2/3))*d^(1/3))] + 2*Log[((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))] + Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]) + 2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))]) - p*(Log[-d^(1/3) - e^(1/3)*x]*(Log[-d^(1/3) - e^(1/3)*x] + 2*(Log[((-1)^(1/3)*d^(1/3) - e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + Log[(I + Sqrt[3] - ((2*I)*e^(1/3)*x)/d^(1/3))/(3*I + Sqrt[3])])) + 2*PolyLog[2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, ((2*I)*(1 + (e^(1/3)*x)/d^(1/3)))/(3*I + Sqrt[3])])))/d^(2/3))/2","A",1
137,1,847,1328,1.6447592,"\int \frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x^5} \, dx","Integrate[Log[c*(d + e*x^3)^p]^2/x^5,x]","\frac{\frac{e p x^3 \left(9 e p \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{e x^3}{d}\right) x^3+2 d^{2/3} \sqrt[3]{e} \log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) x-2 \sqrt[3]{-1} d^{2/3} \sqrt[3]{e} \log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) x+2 (-1)^{2/3} d^{2/3} \sqrt[3]{e} \log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) x+\sqrt[3]{-1} d^{2/3} \sqrt[3]{e} p \left(\log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right) \left(2 \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}\right)+2 \log \left(\frac{(-1)^{2/3} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(-1+(-1)^{2/3}\right) \sqrt[3]{d}}\right)\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{-1} \sqrt[3]{e} x-\sqrt[3]{d}}{\left(-1+(-1)^{2/3}\right) \sqrt[3]{d}}\right)\right) x-(-1)^{2/3} d^{2/3} \sqrt[3]{e} p \left(\log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right) \left(2 \log \left(\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(-1+(-1)^{2/3}\right) \sqrt[3]{d}}\right)+2 \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(-(-1)^{2/3} \sqrt[3]{e} x-\sqrt[3]{d}\right)\right)+2 \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right)\right) x-d^{2/3} \sqrt[3]{e} p \left(\log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right) \left(\log \left(-\sqrt[3]{e} x-\sqrt[3]{d}\right)+2 \left(\log \left(\frac{\sqrt[3]{-1} \sqrt[3]{d}-\sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+\log \left(\frac{-\frac{2 i \sqrt[3]{e} x}{\sqrt[3]{d}}+\sqrt{3}+i}{3 i+\sqrt{3}}\right)\right)\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right)+2 \text{Li}_2\left(\frac{2 i \left(\frac{\sqrt[3]{e} x}{\sqrt[3]{d}}+1\right)}{3 i+\sqrt{3}}\right)\right) x-6 d \log \left(c \left(e x^3+d\right)^p\right)\right)}{d^2}-\log ^2\left(c \left(e x^3+d\right)^p\right)}{4 x^4}","-\frac{e^{4/3} \log ^2\left(\sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{4 d^{4/3}}+\frac{\sqrt[3]{-1} e^{4/3} \log ^2\left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) p^2}{4 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} \log ^2\left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{4 d^{4/3}}-\frac{3 \sqrt{3} e^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} x}{\sqrt{3} \sqrt[3]{d}}\right) p^2}{2 d^{4/3}}-\frac{3 e^{4/3} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{2 d^{4/3}}-\frac{e^{4/3} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(-\frac{\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{2 d^{4/3}}+\frac{\sqrt[3]{-1} e^{4/3} \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) p^2}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} \log \left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} \log \left(\frac{\sqrt[3]{-1} \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) \log \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) p^2}{2 d^{4/3}}-\frac{e^{4/3} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(\frac{\sqrt[3]{-1} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} \log \left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) \log \left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{2 d^{4/3}}+\frac{\sqrt[3]{-1} e^{4/3} \log \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) \log \left(-\frac{(-1)^{2/3} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{2 d^{4/3}}+\frac{3 e^{4/3} \log \left(e^{2/3} x^2-\sqrt[3]{d} \sqrt[3]{e} x+d^{2/3}\right) p^2}{4 d^{4/3}}-\frac{e^{4/3} \text{Li}_2\left(\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} \text{Li}_2\left(-\frac{(-1)^{2/3} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{2 d^{4/3}}-\frac{e^{4/3} \text{Li}_2\left(\frac{2 \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(3-i \sqrt{3}\right) \sqrt[3]{d}}\right) p^2}{2 d^{4/3}}+\frac{\sqrt[3]{-1} e^{4/3} \text{Li}_2\left(-\frac{\sqrt[3]{-1} \left(\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}\right)}{\left(1-(-1)^{2/3}\right) \sqrt[3]{d}}\right) p^2}{2 d^{4/3}}+\frac{\sqrt[3]{-1} e^{4/3} \text{Li}_2\left(\frac{\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} \text{Li}_2\left(\frac{(-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{2 d^{4/3}}+\frac{e^{4/3} \log \left(\sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{2 d^{4/3}}-\frac{\sqrt[3]{-1} e^{4/3} \log \left(\sqrt[3]{d}-\sqrt[3]{-1} \sqrt[3]{e} x\right) \log \left(c \left(e x^3+d\right)^p\right) p}{2 d^{4/3}}+\frac{(-1)^{2/3} e^{4/3} \log \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right) \log \left(c \left(e x^3+d\right)^p\right) p}{2 d^{4/3}}-\frac{3 e \log \left(c \left(e x^3+d\right)^p\right) p}{2 d x}-\frac{\log ^2\left(c \left(e x^3+d\right)^p\right)}{4 x^4}",1,"(-Log[c*(d + e*x^3)^p]^2 + (e*p*x^3*(9*e*p*x^3*Hypergeometric2F1[2/3, 1, 5/3, -((e*x^3)/d)] - 6*d*Log[c*(d + e*x^3)^p] + 2*d^(2/3)*e^(1/3)*x*Log[-d^(1/3) - e^(1/3)*x]*Log[c*(d + e*x^3)^p] - 2*(-1)^(1/3)*d^(2/3)*e^(1/3)*x*Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p] + 2*(-1)^(2/3)*d^(2/3)*e^(1/3)*x*Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p] + (-1)^(1/3)*d^(2/3)*e^(1/3)*p*x*(Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*(2*Log[((-1)^(1/3)*(d^(1/3) + e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))] + Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x] + 2*Log[((-1)^(2/3)*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((-1 + (-1)^(2/3))*d^(1/3))]) + 2*PolyLog[2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, (-d^(1/3) + (-1)^(1/3)*e^(1/3)*x)/((-1 + (-1)^(2/3))*d^(1/3))]) - (-1)^(2/3)*d^(2/3)*e^(1/3)*p*x*(Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]*(2*Log[((-1)^(2/3)*(d^(1/3) + e^(1/3)*x))/((-1 + (-1)^(2/3))*d^(1/3))] + 2*Log[((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))] + Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]) + 2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))]) - d^(2/3)*e^(1/3)*p*x*(Log[-d^(1/3) - e^(1/3)*x]*(Log[-d^(1/3) - e^(1/3)*x] + 2*(Log[((-1)^(1/3)*d^(1/3) - e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + Log[(I + Sqrt[3] - ((2*I)*e^(1/3)*x)/d^(1/3))/(3*I + Sqrt[3])])) + 2*PolyLog[2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))] + 2*PolyLog[2, ((2*I)*(1 + (e^(1/3)*x)/d^(1/3)))/(3*I + Sqrt[3])])))/d^2)/(4*x^4)","C",1
138,1,146,164,0.2465783,"\int \frac{x^8}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[x^8/Log[c*(d + e*x^3)^p],x]","\frac{\left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-3/p} \left(d^2 \left(c \left(d+e x^3\right)^p\right)^{2/p} \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)-\left(d+e x^3\right) \left(2 d \left(c \left(d+e x^3\right)^p\right)^{\frac{1}{p}} \text{Ei}\left(\frac{2 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)-\left(d+e x^3\right) \text{Ei}\left(\frac{3 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)\right)\right)}{3 e^3 p}","\frac{d^2 \left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e^3 p}+\frac{\left(d+e x^3\right)^3 \left(c \left(d+e x^3\right)^p\right)^{-3/p} \text{Ei}\left(\frac{3 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e^3 p}-\frac{2 d \left(d+e x^3\right)^2 \left(c \left(d+e x^3\right)^p\right)^{-2/p} \text{Ei}\left(\frac{2 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e^3 p}",1,"((d + e*x^3)*(d^2*(c*(d + e*x^3)^p)^(2/p)*ExpIntegralEi[Log[c*(d + e*x^3)^p]/p] - (d + e*x^3)*(2*d*(c*(d + e*x^3)^p)^p^(-1)*ExpIntegralEi[(2*Log[c*(d + e*x^3)^p])/p] - (d + e*x^3)*ExpIntegralEi[(3*Log[c*(d + e*x^3)^p])/p])))/(3*e^3*p*(c*(d + e*x^3)^p)^(3/p))","A",1
139,1,96,107,0.1249151,"\int \frac{x^5}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[x^5/Log[c*(d + e*x^3)^p],x]","-\frac{\left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-2/p} \left(d \left(c \left(d+e x^3\right)^p\right)^{\frac{1}{p}} \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)-\left(d+e x^3\right) \text{Ei}\left(\frac{2 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)\right)}{3 e^2 p}","\frac{\left(d+e x^3\right)^2 \left(c \left(d+e x^3\right)^p\right)^{-2/p} \text{Ei}\left(\frac{2 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e^2 p}-\frac{d \left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e^2 p}",1,"-1/3*((d + e*x^3)*(d*(c*(d + e*x^3)^p)^p^(-1)*ExpIntegralEi[Log[c*(d + e*x^3)^p]/p] - (d + e*x^3)*ExpIntegralEi[(2*Log[c*(d + e*x^3)^p])/p]))/(e^2*p*(c*(d + e*x^3)^p)^(2/p))","A",1
140,1,51,51,0.0434839,"\int \frac{x^2}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[x^2/Log[c*(d + e*x^3)^p],x]","\frac{\left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e p}","\frac{\left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e p}",1,"((d + e*x^3)*ExpIntegralEi[Log[c*(d + e*x^3)^p]/p])/(3*e*p*(c*(d + e*x^3)^p)^p^(-1))","A",1
141,0,0,21,0.1900368,"\int \frac{1}{x \log \left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[1/(x*Log[c*(d + e*x^3)^p]),x]","\int \frac{1}{x \log \left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x \log \left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[1/(x*Log[c*(d + e*x^3)^p]), x]","A",-1
142,0,0,21,0.3458318,"\int \frac{1}{x^4 \log \left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[1/(x^4*Log[c*(d + e*x^3)^p]),x]","\int \frac{1}{x^4 \log \left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^4 \log \left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[1/(x^4*Log[c*(d + e*x^3)^p]), x]","A",-1
143,0,0,21,0.2781537,"\int \frac{x^3}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[x^3/Log[c*(d + e*x^3)^p],x]","\int \frac{x^3}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{x^3}{\log \left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[x^3/Log[c*(d + e*x^3)^p], x]","A",-1
144,0,0,19,0.2410609,"\int \frac{x}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[x/Log[c*(d + e*x^3)^p],x]","\int \frac{x}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{x}{\log \left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[x/Log[c*(d + e*x^3)^p], x]","A",-1
145,0,0,17,0.009768,"\int \frac{1}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[Log[c*(d + e*x^3)^p]^(-1),x]","\int \frac{1}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\log \left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[Log[c*(d + e*x^3)^p]^(-1), x]","A",-1
146,0,0,21,0.3839493,"\int \frac{1}{x^2 \log \left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[1/(x^2*Log[c*(d + e*x^3)^p]),x]","\int \frac{1}{x^2 \log \left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \log \left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[1/(x^2*Log[c*(d + e*x^3)^p]), x]","A",-1
147,0,0,21,0.40218,"\int \frac{1}{x^3 \log \left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[1/(x^3*Log[c*(d + e*x^3)^p]),x]","\int \frac{1}{x^3 \log \left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^3 \log \left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[1/(x^3*Log[c*(d + e*x^3)^p]), x]","A",-1
148,1,290,195,0.28113,"\int \frac{x^8}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[x^8/Log[c*(d + e*x^3)^p]^2,x]","\frac{\left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-3/p} \left(d^2 \left(c \left(d+e x^3\right)^p\right)^{2/p} \log \left(c \left(d+e x^3\right)^p\right) \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)+3 d^2 \log \left(c \left(d+e x^3\right)^p\right) \text{Ei}\left(\frac{3 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)+3 e^2 x^6 \log \left(c \left(d+e x^3\right)^p\right) \text{Ei}\left(\frac{3 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)-e^2 p x^6 \left(c \left(d+e x^3\right)^p\right)^{3/p}-4 d \left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{\frac{1}{p}} \log \left(c \left(d+e x^3\right)^p\right) \text{Ei}\left(\frac{2 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)+6 d e x^3 \log \left(c \left(d+e x^3\right)^p\right) \text{Ei}\left(\frac{3 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)\right)}{3 e^3 p^2 \log \left(c \left(d+e x^3\right)^p\right)}","\frac{d^2 \left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e^3 p^2}+\frac{\left(d+e x^3\right)^3 \left(c \left(d+e x^3\right)^p\right)^{-3/p} \text{Ei}\left(\frac{3 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{e^3 p^2}-\frac{4 d \left(d+e x^3\right)^2 \left(c \left(d+e x^3\right)^p\right)^{-2/p} \text{Ei}\left(\frac{2 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e^3 p^2}-\frac{x^6 \left(d+e x^3\right)}{3 e p \log \left(c \left(d+e x^3\right)^p\right)}",1,"((d + e*x^3)*(-(e^2*p*x^6*(c*(d + e*x^3)^p)^(3/p)) + d^2*(c*(d + e*x^3)^p)^(2/p)*ExpIntegralEi[Log[c*(d + e*x^3)^p]/p]*Log[c*(d + e*x^3)^p] - 4*d*(d + e*x^3)*(c*(d + e*x^3)^p)^p^(-1)*ExpIntegralEi[(2*Log[c*(d + e*x^3)^p])/p]*Log[c*(d + e*x^3)^p] + 3*d^2*ExpIntegralEi[(3*Log[c*(d + e*x^3)^p])/p]*Log[c*(d + e*x^3)^p] + 6*d*e*x^3*ExpIntegralEi[(3*Log[c*(d + e*x^3)^p])/p]*Log[c*(d + e*x^3)^p] + 3*e^2*x^6*ExpIntegralEi[(3*Log[c*(d + e*x^3)^p])/p]*Log[c*(d + e*x^3)^p]))/(3*e^3*p^2*(c*(d + e*x^3)^p)^(3/p)*Log[c*(d + e*x^3)^p])","A",1
149,1,157,141,0.1405259,"\int \frac{x^5}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[x^5/Log[c*(d + e*x^3)^p]^2,x]","-\frac{\left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-2/p} \left(d \left(c \left(d+e x^3\right)^p\right)^{\frac{1}{p}} \log \left(c \left(d+e x^3\right)^p\right) \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)-2 \left(d+e x^3\right) \log \left(c \left(d+e x^3\right)^p\right) \text{Ei}\left(\frac{2 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)+e p x^3 \left(c \left(d+e x^3\right)^p\right)^{2/p}\right)}{3 e^2 p^2 \log \left(c \left(d+e x^3\right)^p\right)}","\frac{2 \left(d+e x^3\right)^2 \left(c \left(d+e x^3\right)^p\right)^{-2/p} \text{Ei}\left(\frac{2 \log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e^2 p^2}-\frac{d \left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e^2 p^2}-\frac{x^3 \left(d+e x^3\right)}{3 e p \log \left(c \left(d+e x^3\right)^p\right)}",1,"-1/3*((d + e*x^3)*(e*p*x^3*(c*(d + e*x^3)^p)^(2/p) + d*(c*(d + e*x^3)^p)^p^(-1)*ExpIntegralEi[Log[c*(d + e*x^3)^p]/p]*Log[c*(d + e*x^3)^p] - 2*(d + e*x^3)*ExpIntegralEi[(2*Log[c*(d + e*x^3)^p])/p]*Log[c*(d + e*x^3)^p]))/(e^2*p^2*(c*(d + e*x^3)^p)^(2/p)*Log[c*(d + e*x^3)^p])","A",1
150,1,97,83,0.0487261,"\int \frac{x^2}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[x^2/Log[c*(d + e*x^3)^p]^2,x]","-\frac{\left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-1/p} \left(p \left(c \left(d+e x^3\right)^p\right)^{\frac{1}{p}}-\log \left(c \left(d+e x^3\right)^p\right) \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)\right)}{3 e p^2 \log \left(c \left(d+e x^3\right)^p\right)}","\frac{\left(d+e x^3\right) \left(c \left(d+e x^3\right)^p\right)^{-1/p} \text{Ei}\left(\frac{\log \left(c \left(e x^3+d\right)^p\right)}{p}\right)}{3 e p^2}-\frac{d+e x^3}{3 e p \log \left(c \left(d+e x^3\right)^p\right)}",1,"-1/3*((d + e*x^3)*(p*(c*(d + e*x^3)^p)^p^(-1) - ExpIntegralEi[Log[c*(d + e*x^3)^p]/p]*Log[c*(d + e*x^3)^p]))/(e*p^2*(c*(d + e*x^3)^p)^p^(-1)*Log[c*(d + e*x^3)^p])","A",1
151,0,0,21,0.3063861,"\int \frac{1}{x \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[1/(x*Log[c*(d + e*x^3)^p]^2),x]","\int \frac{1}{x \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x \log ^2\left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[1/(x*Log[c*(d + e*x^3)^p]^2), x]","A",-1
152,0,0,21,1.5338147,"\int \frac{1}{x^4 \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[1/(x^4*Log[c*(d + e*x^3)^p]^2),x]","\int \frac{1}{x^4 \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^4 \log ^2\left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[1/(x^4*Log[c*(d + e*x^3)^p]^2), x]","A",-1
153,0,0,21,0.3438563,"\int \frac{x^3}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[x^3/Log[c*(d + e*x^3)^p]^2,x]","\int \frac{x^3}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{x^3}{\log ^2\left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[x^3/Log[c*(d + e*x^3)^p]^2, x]","A",-1
154,0,0,19,0.4965774,"\int \frac{x}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[x/Log[c*(d + e*x^3)^p]^2,x]","\int \frac{x}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{x}{\log ^2\left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[x/Log[c*(d + e*x^3)^p]^2, x]","A",-1
155,0,0,17,0.3819714,"\int \frac{1}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[Log[c*(d + e*x^3)^p]^(-2),x]","\int \frac{1}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\log ^2\left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[Log[c*(d + e*x^3)^p]^(-2), x]","A",-1
156,0,0,21,1.3071516,"\int \frac{1}{x^2 \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[1/(x^2*Log[c*(d + e*x^3)^p]^2),x]","\int \frac{1}{x^2 \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^2 \log ^2\left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[1/(x^2*Log[c*(d + e*x^3)^p]^2), x]","A",-1
157,0,0,21,1.2441082,"\int \frac{1}{x^3 \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Integrate[1/(x^3*Log[c*(d + e*x^3)^p]^2),x]","\int \frac{1}{x^3 \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{x^3 \log ^2\left(c \left(d+e x^3\right)^p\right)},x\right)",0,"Integrate[1/(x^3*Log[c*(d + e*x^3)^p]^2), x]","A",-1
158,1,994,77,2.1994666,"\int (f x)^m \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e*x^2)^p]^3,x]","\frac{(f x)^m \left(\frac{6 p^3 \left(d \left(\left(-\frac{e x^2}{d}\right)^{\frac{m+1}{2}}-1\right) \log ^2\left(e x^2+d\right)+(m+1) \left(e x^2+d\right) \, _3F_2\left(1,1,\frac{1}{2}-\frac{m}{2};2,2;\frac{e x^2}{d}+1\right) \log \left(e x^2+d\right)-(m+1) \left(e x^2+d\right) \, _4F_3\left(1,1,1,\frac{1}{2}-\frac{m}{2};2,2,2;\frac{e x^2}{d}+1\right)\right) \left(-\frac{e x^2}{d}\right)^{\frac{1}{2}-\frac{m}{2}}}{e}-\frac{3 m p^2 \left(d \left(\left(-\frac{e x^2}{d}\right)^{\frac{m+1}{2}}-1\right) \log ^2\left(e x^2+d\right)+(m+1) \left(e x^2+d\right) \, _3F_2\left(1,1,\frac{1}{2}-\frac{m}{2};2,2;\frac{e x^2}{d}+1\right) \log \left(e x^2+d\right)-(m+1) \left(e x^2+d\right) \, _4F_3\left(1,1,1,\frac{1}{2}-\frac{m}{2};2,2,2;\frac{e x^2}{d}+1\right)\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right) \left(-\frac{e x^2}{d}\right)^{\frac{1}{2}-\frac{m}{2}}}{e}-\frac{3 p^2 \left(d \left(\left(-\frac{e x^2}{d}\right)^{\frac{m+1}{2}}-1\right) \log ^2\left(e x^2+d\right)+(m+1) \left(e x^2+d\right) \, _3F_2\left(1,1,\frac{1}{2}-\frac{m}{2};2,2;\frac{e x^2}{d}+1\right) \log \left(e x^2+d\right)-(m+1) \left(e x^2+d\right) \, _4F_3\left(1,1,1,\frac{1}{2}-\frac{m}{2};2,2,2;\frac{e x^2}{d}+1\right)\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right) \left(-\frac{e x^2}{d}\right)^{\frac{1}{2}-\frac{m}{2}}}{e}+(m+1) p^3 x^2 \log ^3\left(e x^2+d\right)+m x^2 \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^3+x^2 \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^3+\frac{3 m p x^2 \left(d (m+3) \log \left(e x^2+d\right)-2 e x^2 \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};-\frac{e x^2}{d}\right)\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2}{d (m+3)}+\frac{3 p x^2 \left(d (m+3) \log \left(e x^2+d\right)-2 e x^2 \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};-\frac{e x^2}{d}\right)\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2}{d (m+3)}+\frac{6 d (m+1) p^3 \left(\frac{e x^2}{e x^2+d}\right)^{\frac{1}{2}-\frac{m}{2}} \left(8 \, _4F_3\left(\frac{1}{2}-\frac{m}{2},\frac{1}{2}-\frac{m}{2},\frac{1}{2}-\frac{m}{2},\frac{1}{2}-\frac{m}{2};\frac{3}{2}-\frac{m}{2},\frac{3}{2}-\frac{m}{2},\frac{3}{2}-\frac{m}{2};\frac{d}{e x^2+d}\right)+(m-1) \log \left(e x^2+d\right) \left((m-1) \, _2F_1\left(\frac{1}{2}-\frac{m}{2},\frac{1}{2}-\frac{m}{2};\frac{3}{2}-\frac{m}{2};\frac{d}{e x^2+d}\right) \log \left(e x^2+d\right)-4 \, _3F_2\left(\frac{1}{2}-\frac{m}{2},\frac{1}{2}-\frac{m}{2},\frac{1}{2}-\frac{m}{2};\frac{3}{2}-\frac{m}{2},\frac{3}{2}-\frac{m}{2};\frac{d}{e x^2+d}\right)\right)\right)}{e (m-1)^3}\right)}{(m+1)^2 x}","\frac{(f x)^{m+1} \log ^3\left(c \left(d+e x^2\right)^p\right)}{f (m+1)}-\frac{6 e p \text{Int}\left(\frac{(f x)^{m+2} \log ^2\left(c \left(d+e x^2\right)^p\right)}{d+e x^2},x\right)}{f^2 (m+1)}",0,"((f*x)^m*((1 + m)*p^3*x^2*Log[d + e*x^2]^3 + (6*p^3*(-((e*x^2)/d))^(1/2 - m/2)*(-((1 + m)*(d + e*x^2)*HypergeometricPFQ[{1, 1, 1, 1/2 - m/2}, {2, 2, 2}, 1 + (e*x^2)/d]) + (1 + m)*(d + e*x^2)*HypergeometricPFQ[{1, 1, 1/2 - m/2}, {2, 2}, 1 + (e*x^2)/d]*Log[d + e*x^2] + d*(-1 + (-((e*x^2)/d))^((1 + m)/2))*Log[d + e*x^2]^2))/e + (6*d*(1 + m)*p^3*((e*x^2)/(d + e*x^2))^(1/2 - m/2)*(8*HypergeometricPFQ[{1/2 - m/2, 1/2 - m/2, 1/2 - m/2, 1/2 - m/2}, {3/2 - m/2, 3/2 - m/2, 3/2 - m/2}, d/(d + e*x^2)] + (-1 + m)*Log[d + e*x^2]*(-4*HypergeometricPFQ[{1/2 - m/2, 1/2 - m/2, 1/2 - m/2}, {3/2 - m/2, 3/2 - m/2}, d/(d + e*x^2)] + (-1 + m)*Hypergeometric2F1[1/2 - m/2, 1/2 - m/2, 3/2 - m/2, d/(d + e*x^2)]*Log[d + e*x^2])))/(e*(-1 + m)^3) - (3*p^2*(-((e*x^2)/d))^(1/2 - m/2)*(-((1 + m)*(d + e*x^2)*HypergeometricPFQ[{1, 1, 1, 1/2 - m/2}, {2, 2, 2}, 1 + (e*x^2)/d]) + (1 + m)*(d + e*x^2)*HypergeometricPFQ[{1, 1, 1/2 - m/2}, {2, 2}, 1 + (e*x^2)/d]*Log[d + e*x^2] + d*(-1 + (-((e*x^2)/d))^((1 + m)/2))*Log[d + e*x^2]^2)*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/e - (3*m*p^2*(-((e*x^2)/d))^(1/2 - m/2)*(-((1 + m)*(d + e*x^2)*HypergeometricPFQ[{1, 1, 1, 1/2 - m/2}, {2, 2, 2}, 1 + (e*x^2)/d]) + (1 + m)*(d + e*x^2)*HypergeometricPFQ[{1, 1, 1/2 - m/2}, {2, 2}, 1 + (e*x^2)/d]*Log[d + e*x^2] + d*(-1 + (-((e*x^2)/d))^((1 + m)/2))*Log[d + e*x^2]^2)*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/e + (3*p*x^2*(-2*e*x^2*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, -((e*x^2)/d)] + d*(3 + m)*Log[d + e*x^2])*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/(d*(3 + m)) + (3*m*p*x^2*(-2*e*x^2*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, -((e*x^2)/d)] + d*(3 + m)*Log[d + e*x^2])*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/(d*(3 + m)) + x^2*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^3 + m*x^2*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^3))/((1 + m)^2*x)","B",0
159,1,466,75,1.0797706,"\int (f x)^m \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e*x^2)^p]^2,x]","\frac{(f x)^m \left(\frac{4 d (m+1) p^2 \left(\frac{e x^2}{d+e x^2}\right)^{\frac{1}{2}-\frac{m}{2}} \left((m-1) \log \left(d+e x^2\right) \, _2F_1\left(\frac{1}{2}-\frac{m}{2},\frac{1}{2}-\frac{m}{2};\frac{3}{2}-\frac{m}{2};\frac{d}{e x^2+d}\right)-2 \, _3F_2\left(\frac{1}{2}-\frac{m}{2},\frac{1}{2}-\frac{m}{2},\frac{1}{2}-\frac{m}{2};\frac{3}{2}-\frac{m}{2},\frac{3}{2}-\frac{m}{2};\frac{d}{e x^2+d}\right)\right)}{e (m-1)^2 x}+\frac{2 p \left(p \log \left(d+e x^2\right)-\log \left(c \left(d+e x^2\right)^p\right)\right) \left(2 e x^3 \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};-\frac{e x^2}{d}\right)-d (m+3) x \log \left(d+e x^2\right)\right)}{d (m+3)}-\frac{2 m p \left(p \log \left(d+e x^2\right)-\log \left(c \left(d+e x^2\right)^p\right)\right) \left(d (m+3) x \log \left(d+e x^2\right)-2 e x^3 \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};-\frac{e x^2}{d}\right)\right)}{d (m+3)}+m x \left(\log \left(c \left(d+e x^2\right)^p\right)-p \log \left(d+e x^2\right)\right)^2+x \left(\log \left(c \left(d+e x^2\right)^p\right)-p \log \left(d+e x^2\right)\right)^2+4 p^2 x \left(\frac{2 e x^2 \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};-\frac{e x^2}{d}\right)}{d (m+3)}-\log \left(d+e x^2\right)\right)+(m+1) p^2 x \log ^2\left(d+e x^2\right)\right)}{(m+1)^2}","\frac{(f x)^{m+1} \log ^2\left(c \left(d+e x^2\right)^p\right)}{f (m+1)}-\frac{4 e p \text{Int}\left(\frac{(f x)^{m+2} \log \left(c \left(d+e x^2\right)^p\right)}{d+e x^2},x\right)}{f^2 (m+1)}",0,"((f*x)^m*(4*p^2*x*((2*e*x^2*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, -((e*x^2)/d)])/(d*(3 + m)) - Log[d + e*x^2]) + (1 + m)*p^2*x*Log[d + e*x^2]^2 + (4*d*(1 + m)*p^2*((e*x^2)/(d + e*x^2))^(1/2 - m/2)*(-2*HypergeometricPFQ[{1/2 - m/2, 1/2 - m/2, 1/2 - m/2}, {3/2 - m/2, 3/2 - m/2}, d/(d + e*x^2)] + (-1 + m)*Hypergeometric2F1[1/2 - m/2, 1/2 - m/2, 3/2 - m/2, d/(d + e*x^2)]*Log[d + e*x^2]))/(e*(-1 + m)^2*x) + (2*p*(2*e*x^3*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, -((e*x^2)/d)] - d*(3 + m)*x*Log[d + e*x^2])*(p*Log[d + e*x^2] - Log[c*(d + e*x^2)^p]))/(d*(3 + m)) - (2*m*p*(-2*e*x^3*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, -((e*x^2)/d)] + d*(3 + m)*x*Log[d + e*x^2])*(p*Log[d + e*x^2] - Log[c*(d + e*x^2)^p]))/(d*(3 + m)) + x*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2 + m*x*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2))/(1 + m)^2","B",0
160,1,70,81,0.0245691,"\int (f x)^m \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f*x)^m*Log[c*(d + e*x^2)^p],x]","\frac{x (f x)^m \left(d (m+3) \log \left(c \left(d+e x^2\right)^p\right)-2 e p x^2 \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};-\frac{e x^2}{d}\right)\right)}{d (m+1) (m+3)}","\frac{(f x)^{m+1} \log \left(c \left(d+e x^2\right)^p\right)}{f (m+1)}-\frac{2 e p (f x)^{m+3} \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};-\frac{e x^2}{d}\right)}{d f^3 (m+1) (m+3)}",1,"(x*(f*x)^m*(-2*e*p*x^2*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, -((e*x^2)/d)] + d*(3 + m)*Log[c*(d + e*x^2)^p]))/(d*(1 + m)*(3 + m))","A",1
161,0,0,23,0.3360211,"\int \frac{(f x)^m}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[(f*x)^m/Log[c*(d + e*x^2)^p],x]","\int \frac{(f x)^m}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{(f x)^m}{\log \left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[(f*x)^m/Log[c*(d + e*x^2)^p], x]","A",-1
162,0,0,23,0.5686182,"\int \frac{(f x)^m}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[(f*x)^m/Log[c*(d + e*x^2)^p]^2,x]","\int \frac{(f x)^m}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{(f x)^m}{\log ^2\left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[(f*x)^m/Log[c*(d + e*x^2)^p]^2, x]","A",-1
163,1,171,372,0.1725815,"\int (f x)^{-1+3 n} \log ^2\left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f*x)^(-1 + 3*n)*Log[c*(d + e*x^n)^p]^2,x]","\frac{x^{-3 n} (f x)^{3 n} \left(6 d^3 p \log \left(d+e x^n\right) \left(6 \log \left(c \left(d+e x^n\right)^p\right)-11 p\right)+e x^n \left(-6 p \left(6 d^2-3 d e x^n+2 e^2 x^{2 n}\right) \log \left(c \left(d+e x^n\right)^p\right)+18 e^2 x^{2 n} \log ^2\left(c \left(d+e x^n\right)^p\right)+p^2 \left(66 d^2-15 d e x^n+4 e^2 x^{2 n}\right)\right)-18 d^3 p^2 \log ^2\left(d+e x^n\right)\right)}{54 e^3 f n}","\frac{2 d^3 p x^{1-3 n} (f x)^{3 n-1} \log \left(d+e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)}{3 e^3 n}-\frac{2 d^2 p x^{1-3 n} (f x)^{3 n-1} \left(d+e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)}{e^3 n}-\frac{2 p x^{1-3 n} (f x)^{3 n-1} \left(d+e x^n\right)^3 \log \left(c \left(d+e x^n\right)^p\right)}{9 e^3 n}+\frac{d p x^{1-3 n} (f x)^{3 n-1} \left(d+e x^n\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{e^3 n}+\frac{x (f x)^{3 n-1} \log ^2\left(c \left(d+e x^n\right)^p\right)}{3 n}-\frac{d^3 p^2 x^{1-3 n} (f x)^{3 n-1} \log ^2\left(d+e x^n\right)}{3 e^3 n}+\frac{2 d^2 p^2 x^{1-2 n} (f x)^{3 n-1}}{e^2 n}+\frac{2 p^2 x^{1-3 n} (f x)^{3 n-1} \left(d+e x^n\right)^3}{27 e^3 n}-\frac{d p^2 x^{1-3 n} (f x)^{3 n-1} \left(d+e x^n\right)^2}{2 e^3 n}",1,"((f*x)^(3*n)*(-18*d^3*p^2*Log[d + e*x^n]^2 + 6*d^3*p*Log[d + e*x^n]*(-11*p + 6*Log[c*(d + e*x^n)^p]) + e*x^n*(p^2*(66*d^2 - 15*d*e*x^n + 4*e^2*x^(2*n)) - 6*p*(6*d^2 - 3*d*e*x^n + 2*e^2*x^(2*n))*Log[c*(d + e*x^n)^p] + 18*e^2*x^(2*n)*Log[c*(d + e*x^n)^p]^2)))/(54*e^3*f*n*x^(3*n))","A",1
164,1,140,255,0.1260413,"\int (f x)^{-1+2 n} \log ^2\left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f*x)^(-1 + 2*n)*Log[c*(d + e*x^n)^p]^2,x]","\frac{x^{-2 n} (f x)^{2 n} \left(2 d^2 p \log \left(d+e x^n\right) \left(3 p-2 \log \left(c \left(d+e x^n\right)^p\right)\right)+e x^n \left(2 e x^n \log ^2\left(c \left(d+e x^n\right)^p\right)+2 p \left(2 d-e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)+p^2 \left(e x^n-6 d\right)\right)+2 d^2 p^2 \log ^2\left(d+e x^n\right)\right)}{4 e^2 f n}","\frac{x^{1-2 n} (f x)^{2 n-1} \left(d+e x^n\right)^2 \log ^2\left(c \left(d+e x^n\right)^p\right)}{2 e^2 n}-\frac{d x^{1-2 n} (f x)^{2 n-1} \left(d+e x^n\right) \log ^2\left(c \left(d+e x^n\right)^p\right)}{e^2 n}-\frac{p x^{1-2 n} (f x)^{2 n-1} \left(d+e x^n\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{2 e^2 n}+\frac{2 d p x^{1-2 n} (f x)^{2 n-1} \left(d+e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)}{e^2 n}+\frac{p^2 x^{1-2 n} (f x)^{2 n-1} \left(d+e x^n\right)^2}{4 e^2 n}-\frac{2 d p^2 x^{1-n} (f x)^{2 n-1}}{e n}",1,"((f*x)^(2*n)*(2*d^2*p^2*Log[d + e*x^n]^2 + 2*d^2*p*Log[d + e*x^n]*(3*p - 2*Log[c*(d + e*x^n)^p]) + e*x^n*(p^2*(-6*d + e*x^n) + 2*p*(2*d - e*x^n)*Log[c*(d + e*x^n)^p] + 2*e*x^n*Log[c*(d + e*x^n)^p]^2)))/(4*e^2*f*n*x^(2*n))","A",1
165,1,74,101,0.0257067,"\int (f x)^{-1+n} \log ^2\left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f*x)^(-1 + n)*Log[c*(d + e*x^n)^p]^2,x]","\frac{x^{-n} (f x)^n \left(\left(d+e x^n\right) \log ^2\left(c \left(d+e x^n\right)^p\right)-2 p \left(d+e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)+2 e p^2 x^n\right)}{e f n}","\frac{x^{1-n} (f x)^{n-1} \left(d+e x^n\right) \log ^2\left(c \left(d+e x^n\right)^p\right)}{e n}-\frac{2 p x^{1-n} (f x)^{n-1} \left(d+e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)}{e n}+\frac{2 p^2 x (f x)^{n-1}}{n}",1,"((f*x)^n*(2*e*p^2*x^n - 2*p*(d + e*x^n)*Log[c*(d + e*x^n)^p] + (d + e*x^n)*Log[c*(d + e*x^n)^p]^2))/(e*f*n*x^n)","A",1
166,1,168,88,0.1074444,"\int \frac{\log ^2\left(c \left(d+e x^n\right)^p\right)}{f x} \, dx","Integrate[Log[c*(d + e*x^n)^p]^2/(f*x),x]","\frac{2 p \left(\log (x) \left(\log \left(d+e x^n\right)-\log \left(\frac{e x^n}{d}+1\right)\right)-\frac{\text{Li}_2\left(-\frac{e x^n}{d}\right)}{n}\right) \left(\log \left(c \left(d+e x^n\right)^p\right)-p \log \left(d+e x^n\right)\right)+\log (x) \left(\log \left(c \left(d+e x^n\right)^p\right)-p \log \left(d+e x^n\right)\right)^2+\frac{p^2 \left(-2 \text{Li}_3\left(\frac{e x^n}{d}+1\right)+2 \text{Li}_2\left(\frac{e x^n}{d}+1\right) \log \left(d+e x^n\right)+\log \left(-\frac{e x^n}{d}\right) \log ^2\left(d+e x^n\right)\right)}{n}}{f}","\frac{2 p \text{Li}_2\left(\frac{e x^n}{d}+1\right) \log \left(c \left(d+e x^n\right)^p\right)}{f n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log ^2\left(c \left(d+e x^n\right)^p\right)}{f n}-\frac{2 p^2 \text{Li}_3\left(\frac{e x^n}{d}+1\right)}{f n}",1,"(Log[x]*(-(p*Log[d + e*x^n]) + Log[c*(d + e*x^n)^p])^2 + 2*p*(-(p*Log[d + e*x^n]) + Log[c*(d + e*x^n)^p])*(Log[x]*(Log[d + e*x^n] - Log[1 + (e*x^n)/d]) - PolyLog[2, -((e*x^n)/d)]/n) + (p^2*(Log[-((e*x^n)/d)]*Log[d + e*x^n]^2 + 2*Log[d + e*x^n]*PolyLog[2, 1 + (e*x^n)/d] - 2*PolyLog[3, 1 + (e*x^n)/d]))/n)/f","A",1
167,1,148,124,0.0940963,"\int (f x)^{-1-n} \log ^2\left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f*x)^(-1 - n)*Log[c*(d + e*x^n)^p]^2,x]","-\frac{(f x)^{-n} \left(d \log ^2\left(c \left(d+e x^n\right)^p\right)+2 e p x^n \log \left(-d x^{-n}-e\right) \log \left(c \left(d+e x^n\right)^p\right)+2 e p^2 x^n \text{Li}_2\left(\frac{d x^{-n}}{e}+1\right)-e p^2 x^n \log ^2\left(-d x^{-n}-e\right)+2 e p^2 x^n \log \left(-\frac{d x^{-n}}{e}\right) \log \left(-d x^{-n}-e\right)\right)}{d f n}","-\frac{x (f x)^{-n-1} \left(d+e x^n\right) \log ^2\left(c \left(d+e x^n\right)^p\right)}{d n}+\frac{2 e p x^{n+1} (f x)^{-n-1} \log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{d n}+\frac{2 e p^2 x^{n+1} (f x)^{-n-1} \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{d n}",1,"-((2*e*p^2*x^n*Log[-(d/(e*x^n))]*Log[-e - d/x^n] - e*p^2*x^n*Log[-e - d/x^n]^2 + 2*e*p*x^n*Log[-e - d/x^n]*Log[c*(d + e*x^n)^p] + d*Log[c*(d + e*x^n)^p]^2 + 2*e*p^2*x^n*PolyLog[2, 1 + d/(e*x^n)])/(d*f*n*(f*x)^n))","A",1
168,1,288,200,0.3172377,"\int (f x)^{-1-2 n} \log ^2\left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f*x)^(-1 - 2*n)*Log[c*(d + e*x^n)^p]^2,x]","\frac{(f x)^{-2 n} \left(-d^2 \log ^2\left(c \left(d+e x^n\right)^p\right)+2 e^2 p x^{2 n} \log \left(e-e x^{-n}\right) \log \left(c \left(d+e x^n\right)^p\right)+2 e^2 n p x^{2 n} \log (x) \left(-\log \left(c \left(d+e x^n\right)^p\right)+p \log \left(d x^{-n}+e\right)+p \log \left(\frac{e x^n}{d}+1\right)-p \log \left(e-e x^{-n}\right)+p\right)-2 d e p x^n \log \left(c \left(d+e x^n\right)^p\right)+2 e^2 p^2 x^{2 n} \text{Li}_2\left(-\frac{e x^n}{d}\right)+e^2 p^2 x^{2 n} \log ^2\left(d x^{-n}+e\right)-2 e^2 p^2 x^{2 n} \log \left(e-e x^{-n}\right) \log \left(d x^{-n}+e\right)+e^2 n^2 p^2 x^{2 n} \log ^2(x)-2 e^2 p^2 x^{2 n} \log \left(e-e x^{-n}\right)\right)}{2 d^2 f n}","-\frac{e^2 p x^{2 n+1} (f x)^{-2 n-1} \log \left(1-\frac{d}{d+e x^n}\right) \log \left(c \left(d+e x^n\right)^p\right)}{d^2 n}-\frac{e p x^{n+1} (f x)^{-2 n-1} \left(d+e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)}{d^2 n}-\frac{x (f x)^{-2 n-1} \log ^2\left(c \left(d+e x^n\right)^p\right)}{2 n}+\frac{e^2 p^2 x^{2 n+1} (f x)^{-2 n-1} \text{Li}_2\left(\frac{d}{e x^n+d}\right)}{d^2 n}+\frac{e^2 p^2 x^{2 n+1} \log (x) (f x)^{-2 n-1}}{d^2}",1,"(e^2*n^2*p^2*x^(2*n)*Log[x]^2 + e^2*p^2*x^(2*n)*Log[e + d/x^n]^2 - 2*e^2*p^2*x^(2*n)*Log[e - e/x^n] - 2*e^2*p^2*x^(2*n)*Log[e + d/x^n]*Log[e - e/x^n] - 2*d*e*p*x^n*Log[c*(d + e*x^n)^p] + 2*e^2*p*x^(2*n)*Log[e - e/x^n]*Log[c*(d + e*x^n)^p] - d^2*Log[c*(d + e*x^n)^p]^2 + 2*e^2*n*p*x^(2*n)*Log[x]*(p + p*Log[e + d/x^n] - p*Log[e - e/x^n] - Log[c*(d + e*x^n)^p] + p*Log[1 + (e*x^n)/d]) + 2*e^2*p^2*x^(2*n)*PolyLog[2, -((e*x^n)/d)])/(2*d^2*f*n*(f*x)^(2*n))","A",0
169,1,13,13,0.0026083,"\int \frac{\log \left(1+e x^n\right)}{x} \, dx","Integrate[Log[1 + e*x^n]/x,x]","-\frac{\text{Li}_2\left(-e x^n\right)}{n}","-\frac{\text{Li}_2\left(-e x^n\right)}{n}",1,"-(PolyLog[2, -(e*x^n)]/n)","A",1
170,1,21,21,0.0028336,"\int \frac{\log \left(2+e x^n\right)}{x} \, dx","Integrate[Log[2 + e*x^n]/x,x]","\log (2) \log (x)-\frac{\text{Li}_2\left(-\frac{e x^n}{2}\right)}{n}","\log (2) \log (x)-\frac{\text{Li}_2\left(-\frac{e x^n}{2}\right)}{n}",1,"Log[2]*Log[x] - PolyLog[2, -1/2*(e*x^n)]/n","A",1
171,1,21,21,0.0041022,"\int \frac{\log \left(2 \left(3+e x^n\right)\right)}{x} \, dx","Integrate[Log[2*(3 + e*x^n)]/x,x]","\log (6) \log (x)-\frac{\text{Li}_2\left(-\frac{e x^n}{3}\right)}{n}","\log (6) \log (x)-\frac{\text{Li}_2\left(-\frac{e x^n}{3}\right)}{n}",1,"Log[6]*Log[x] - PolyLog[2, -1/3*(e*x^n)]/n","A",1
172,1,39,41,0.0079788,"\int \frac{\log \left(c \left(d+e x^n\right)\right)}{x} \, dx","Integrate[Log[c*(d + e*x^n)]/x,x]","\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)\right)+\text{Li}_2\left(\frac{e x^n+d}{d}\right)}{n}","\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)\right)}{n}+\frac{\text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)] + PolyLog[2, (d + e*x^n)/d])/n","A",1
173,1,43,44,0.005406,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[Log[c*(d + e*x^n)^p]/x,x]","\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)+p \text{Li}_2\left(\frac{e x^n+d}{d}\right)}{n}","\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p] + p*PolyLog[2, (d + e*x^n)/d])/n","A",1
174,1,164,79,0.0672892,"\int \frac{\log ^2\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[Log[c*(d + e*x^n)^p]^2/x,x]","2 p \left(\log (x) \left(\log \left(d+e x^n\right)-\log \left(\frac{e x^n}{d}+1\right)\right)-\frac{\text{Li}_2\left(-\frac{e x^n}{d}\right)}{n}\right) \left(\log \left(c \left(d+e x^n\right)^p\right)-p \log \left(d+e x^n\right)\right)+\log (x) \left(\log \left(c \left(d+e x^n\right)^p\right)-p \log \left(d+e x^n\right)\right)^2+\frac{p^2 \left(-2 \text{Li}_3\left(\frac{e x^n}{d}+1\right)+2 \text{Li}_2\left(\frac{e x^n}{d}+1\right) \log \left(d+e x^n\right)+\log \left(-\frac{e x^n}{d}\right) \log ^2\left(d+e x^n\right)\right)}{n}","\frac{2 p \text{Li}_2\left(\frac{e x^n}{d}+1\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log ^2\left(c \left(d+e x^n\right)^p\right)}{n}-\frac{2 p^2 \text{Li}_3\left(\frac{e x^n}{d}+1\right)}{n}",1,"Log[x]*(-(p*Log[d + e*x^n]) + Log[c*(d + e*x^n)^p])^2 + 2*p*(-(p*Log[d + e*x^n]) + Log[c*(d + e*x^n)^p])*(Log[x]*(Log[d + e*x^n] - Log[1 + (e*x^n)/d]) - PolyLog[2, -((e*x^n)/d)]/n) + (p^2*(Log[-((e*x^n)/d)]*Log[d + e*x^n]^2 + 2*Log[d + e*x^n]*PolyLog[2, 1 + (e*x^n)/d] - 2*PolyLog[3, 1 + (e*x^n)/d]))/n","B",1
175,1,270,113,0.1076767,"\int \frac{\log ^3\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[Log[c*(d + e*x^n)^p]^3/x,x]","\frac{-6 p^2 \text{Li}_3\left(\frac{e x^n}{d}+1\right) \log \left(c \left(d+e x^n\right)^p\right)+3 n p^2 \log (x) \log ^2\left(d+e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)-3 p^2 \log \left(-\frac{e x^n}{d}\right) \log ^2\left(d+e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)+3 p \text{Li}_2\left(\frac{e x^n}{d}+1\right) \log ^2\left(c \left(d+e x^n\right)^p\right)+n \log (x) \log ^3\left(c \left(d+e x^n\right)^p\right)-3 n p \log (x) \log \left(d+e x^n\right) \log ^2\left(c \left(d+e x^n\right)^p\right)+3 p \log \left(-\frac{e x^n}{d}\right) \log \left(d+e x^n\right) \log ^2\left(c \left(d+e x^n\right)^p\right)+6 p^3 \text{Li}_4\left(\frac{e x^n}{d}+1\right)-n p^3 \log (x) \log ^3\left(d+e x^n\right)+p^3 \log \left(-\frac{e x^n}{d}\right) \log ^3\left(d+e x^n\right)}{n}","-\frac{6 p^2 \text{Li}_3\left(\frac{e x^n}{d}+1\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{3 p \text{Li}_2\left(\frac{e x^n}{d}+1\right) \log ^2\left(c \left(d+e x^n\right)^p\right)}{n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log ^3\left(c \left(d+e x^n\right)^p\right)}{n}+\frac{6 p^3 \text{Li}_4\left(\frac{e x^n}{d}+1\right)}{n}",1,"(-(n*p^3*Log[x]*Log[d + e*x^n]^3) + p^3*Log[-((e*x^n)/d)]*Log[d + e*x^n]^3 + 3*n*p^2*Log[x]*Log[d + e*x^n]^2*Log[c*(d + e*x^n)^p] - 3*p^2*Log[-((e*x^n)/d)]*Log[d + e*x^n]^2*Log[c*(d + e*x^n)^p] - 3*n*p*Log[x]*Log[d + e*x^n]*Log[c*(d + e*x^n)^p]^2 + 3*p*Log[-((e*x^n)/d)]*Log[d + e*x^n]*Log[c*(d + e*x^n)^p]^2 + n*Log[x]*Log[c*(d + e*x^n)^p]^3 + 3*p*Log[c*(d + e*x^n)^p]^2*PolyLog[2, 1 + (e*x^n)/d] - 6*p^2*Log[c*(d + e*x^n)^p]*PolyLog[3, 1 + (e*x^n)/d] + 6*p^3*PolyLog[4, 1 + (e*x^n)/d])/n","B",1
176,1,185,140,0.2133166,"\int (d+e x)^3 \log \left(c (a+b x)^p\right) \, dx","Integrate[(d + e*x)^3*Log[c*(a + b*x)^p],x]","-\frac{12 a^2 e p \left(a^2 e^2-4 a b d e+6 b^2 d^2\right) \log (a+b x)+b p x \left(-12 a^3 e^3+6 a^2 b e^2 (8 d+e x)-4 a b^2 e \left(18 d^2+6 d e x+e^2 x^2\right)+b^3 \left(48 d^3+36 d^2 e x+16 d e^2 x^2+3 e^3 x^3\right)\right)-12 b^3 \left(4 a d^3+b x \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)\right) \log \left(c (a+b x)^p\right)}{48 b^4}","-\frac{p (b d-a e)^4 \log (a+b x)}{4 b^4 e}-\frac{p x (b d-a e)^3}{4 b^3}-\frac{p (d+e x)^2 (b d-a e)^2}{8 b^2 e}+\frac{(d+e x)^4 \log \left(c (a+b x)^p\right)}{4 e}-\frac{p (d+e x)^3 (b d-a e)}{12 b e}-\frac{p (d+e x)^4}{16 e}",1,"-1/48*(b*p*x*(-12*a^3*e^3 + 6*a^2*b*e^2*(8*d + e*x) - 4*a*b^2*e*(18*d^2 + 6*d*e*x + e^2*x^2) + b^3*(48*d^3 + 36*d^2*e*x + 16*d*e^2*x^2 + 3*e^3*x^3)) + 12*a^2*e*(6*b^2*d^2 - 4*a*b*d*e + a^2*e^2)*p*Log[a + b*x] - 12*b^3*(4*a*d^3 + b*x*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3))*Log[c*(a + b*x)^p])/b^4","A",1
177,1,121,112,0.1135111,"\int (d+e x)^2 \log \left(c (a+b x)^p\right) \, dx","Integrate[(d + e*x)^2*Log[c*(a + b*x)^p],x]","\frac{b \left(6 b \left(3 a d^2+b x \left(3 d^2+3 d e x+e^2 x^2\right)\right) \log \left(c (a+b x)^p\right)-p x \left(6 a^2 e^2-3 a b e (6 d+e x)+b^2 \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)\right)+6 a^2 e p (a e-3 b d) \log (a+b x)}{18 b^3}","-\frac{p (b d-a e)^3 \log (a+b x)}{3 b^3 e}-\frac{p x (b d-a e)^2}{3 b^2}+\frac{(d+e x)^3 \log \left(c (a+b x)^p\right)}{3 e}-\frac{p (d+e x)^2 (b d-a e)}{6 b e}-\frac{p (d+e x)^3}{9 e}",1,"(6*a^2*e*(-3*b*d + a*e)*p*Log[a + b*x] + b*(-(p*x*(6*a^2*e^2 - 3*a*b*e*(6*d + e*x) + b^2*(18*d^2 + 9*d*e*x + 2*e^2*x^2))) + 6*b*(3*a*d^2 + b*x*(3*d^2 + 3*d*e*x + e^2*x^2))*Log[c*(a + b*x)^p]))/(18*b^3)","A",1
178,1,82,84,0.0478295,"\int (d+e x) \log \left(c (a+b x)^p\right) \, dx","Integrate[(d + e*x)*Log[c*(a + b*x)^p],x]","-\frac{a^2 e p \log (a+b x)}{2 b^2}+\frac{d (a+b x) \log \left(c (a+b x)^p\right)}{b}+\frac{1}{2} e x^2 \log \left(c (a+b x)^p\right)+\frac{a e p x}{2 b}-d p x-\frac{1}{4} e p x^2","-\frac{p (b d-a e)^2 \log (a+b x)}{2 b^2 e}+\frac{(d+e x)^2 \log \left(c (a+b x)^p\right)}{2 e}-\frac{p x (b d-a e)}{2 b}-\frac{p (d+e x)^2}{4 e}",1,"-(d*p*x) + (a*e*p*x)/(2*b) - (e*p*x^2)/4 - (a^2*e*p*Log[a + b*x])/(2*b^2) + (e*x^2*Log[c*(a + b*x)^p])/2 + (d*(a + b*x)*Log[c*(a + b*x)^p])/b","A",1
179,1,24,24,0.0065673,"\int \log \left(c (a+b x)^p\right) \, dx","Integrate[Log[c*(a + b*x)^p],x]","\frac{(a+b x) \log \left(c (a+b x)^p\right)}{b}-p x","\frac{(a+b x) \log \left(c (a+b x)^p\right)}{b}-p x",1,"-(p*x) + ((a + b*x)*Log[c*(a + b*x)^p])/b","A",1
180,1,57,58,0.0040513,"\int \frac{\log \left(c (a+b x)^p\right)}{d+e x} \, dx","Integrate[Log[c*(a + b*x)^p]/(d + e*x),x]","\frac{\log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{e}+\frac{p \text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)}{e}","\frac{\log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{e}+\frac{p \text{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\right)}{e}",1,"(Log[c*(a + b*x)^p]*Log[(b*(d + e*x))/(b*d - a*e)])/e + (p*PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)])/e","A",1
181,1,52,68,0.0485573,"\int \frac{\log \left(c (a+b x)^p\right)}{(d+e x)^2} \, dx","Integrate[Log[c*(a + b*x)^p]/(d + e*x)^2,x]","\frac{\frac{b p (\log (a+b x)-\log (d+e x))}{b d-a e}-\frac{\log \left(c (a+b x)^p\right)}{d+e x}}{e}","-\frac{\log \left(c (a+b x)^p\right)}{e (d+e x)}+\frac{b p \log (a+b x)}{e (b d-a e)}-\frac{b p \log (d+e x)}{e (b d-a e)}",1,"(-(Log[c*(a + b*x)^p]/(d + e*x)) + (b*p*(Log[a + b*x] - Log[d + e*x]))/(b*d - a*e))/e","A",1
182,1,80,105,0.1002855,"\int \frac{\log \left(c (a+b x)^p\right)}{(d+e x)^3} \, dx","Integrate[Log[c*(a + b*x)^p]/(d + e*x)^3,x]","\frac{\frac{b p (d+e x) (b (d+e x) \log (a+b x)-a e-b (d+e x) \log (d+e x)+b d)}{(b d-a e)^2}-\log \left(c (a+b x)^p\right)}{2 e (d+e x)^2}","\frac{b^2 p \log (a+b x)}{2 e (b d-a e)^2}-\frac{b^2 p \log (d+e x)}{2 e (b d-a e)^2}-\frac{\log \left(c (a+b x)^p\right)}{2 e (d+e x)^2}+\frac{b p}{2 e (d+e x) (b d-a e)}",1,"(-Log[c*(a + b*x)^p] + (b*p*(d + e*x)*(b*d - a*e + b*(d + e*x)*Log[a + b*x] - b*(d + e*x)*Log[d + e*x]))/(b*d - a*e)^2)/(2*e*(d + e*x)^2)","A",1
183,1,105,133,0.1498026,"\int \frac{\log \left(c (a+b x)^p\right)}{(d+e x)^4} \, dx","Integrate[Log[c*(a + b*x)^p]/(d + e*x)^4,x]","\frac{\frac{b p (d+e x) \left(2 b^2 (d+e x)^2 \log (a+b x)+(b d-a e) (-a e+3 b d+2 b e x)-2 b^2 (d+e x)^2 \log (d+e x)\right)}{(b d-a e)^3}-2 \log \left(c (a+b x)^p\right)}{6 e (d+e x)^3}","\frac{b^3 p \log (a+b x)}{3 e (b d-a e)^3}-\frac{b^3 p \log (d+e x)}{3 e (b d-a e)^3}+\frac{b^2 p}{3 e (d+e x) (b d-a e)^2}-\frac{\log \left(c (a+b x)^p\right)}{3 e (d+e x)^3}+\frac{b p}{6 e (d+e x)^2 (b d-a e)}",1,"(-2*Log[c*(a + b*x)^p] + (b*p*(d + e*x)*((b*d - a*e)*(3*b*d - a*e + 2*b*e*x) + 2*b^2*(d + e*x)^2*Log[a + b*x] - 2*b^2*(d + e*x)^2*Log[d + e*x]))/(b*d - a*e)^3)/(6*e*(d + e*x)^3)","A",1
184,1,249,178,0.7752026,"\int (d+e x)^3 \log \left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[(d + e*x)^3*Log[c*(a + b*x^2)^p],x]","\frac{-6 p \left(a^2 e^4+4 \sqrt{-a} b^{3/2} d^3 e-6 a b d^2 e^2+4 (-a)^{3/2} \sqrt{b} d e^3+b^2 d^4\right) \log \left(\sqrt{-a}-\sqrt{b} x\right)-6 p \left(a^2 e^4-4 \sqrt{-a} b^{3/2} d^3 e-6 a b d^2 e^2+4 \sqrt{-a} a \sqrt{b} d e^3+b^2 d^4\right) \log \left(\sqrt{-a}+\sqrt{b} x\right)+b \left(6 b (d+e x)^4 \log \left(c \left(a+b x^2\right)^p\right)+6 a e^3 p x (8 d+e x)-b e p x \left(48 d^3+36 d^2 e x+16 d e^2 x^2+3 e^3 x^3\right)\right)}{24 b^2 e}","-\frac{p \left(a^2 e^4-6 a b d^2 e^2+b^2 d^4\right) \log \left(a+b x^2\right)}{4 b^2 e}+\frac{2 \sqrt{a} d p \left(b d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}+\frac{(d+e x)^4 \log \left(c \left(a+b x^2\right)^p\right)}{4 e}-\frac{e p x^2 \left(6 b d^2-a e^2\right)}{4 b}-\frac{2 d p x \left(b d^2-a e^2\right)}{b}-\frac{2}{3} d e^2 p x^3-\frac{1}{8} e^3 p x^4",1,"(-6*(b^2*d^4 + 4*Sqrt[-a]*b^(3/2)*d^3*e - 6*a*b*d^2*e^2 + 4*(-a)^(3/2)*Sqrt[b]*d*e^3 + a^2*e^4)*p*Log[Sqrt[-a] - Sqrt[b]*x] - 6*(b^2*d^4 - 4*Sqrt[-a]*b^(3/2)*d^3*e - 6*a*b*d^2*e^2 + 4*Sqrt[-a]*a*Sqrt[b]*d*e^3 + a^2*e^4)*p*Log[Sqrt[-a] + Sqrt[b]*x] + b*(6*a*e^3*p*x*(8*d + e*x) - b*e*p*x*(48*d^3 + 36*d^2*e*x + 16*d*e^2*x^2 + 3*e^3*x^3) + 6*b*(d + e*x)^4*Log[c*(a + b*x^2)^p]))/(24*b^2*e)","A",1
185,1,211,141,0.4796797,"\int (d+e x)^2 \log \left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[(d + e*x)^2*Log[c*(a + b*x^2)^p],x]","\frac{3 p \left(-3 \sqrt{-a} b d^2 e+3 a \sqrt{b} d e^2+\sqrt{-a} a e^3-b^{3/2} d^3\right) \log \left(\sqrt{-a}-\sqrt{b} x\right)-3 p \left(-3 \sqrt{-a} b d^2 e-3 a \sqrt{b} d e^2+\sqrt{-a} a e^3+b^{3/2} d^3\right) \log \left(\sqrt{-a}+\sqrt{b} x\right)+\sqrt{b} \left(3 b (d+e x)^3 \log \left(c \left(a+b x^2\right)^p\right)+6 a e^3 p x-b e p x \left(18 d^2+9 d e x+2 e^2 x^2\right)\right)}{9 b^{3/2} e}","\frac{2 \sqrt{a} p \left(3 b d^2-a e^2\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{3 b^{3/2}}+\frac{(d+e x)^3 \log \left(c \left(a+b x^2\right)^p\right)}{3 e}-\frac{d p \left(b d^2-3 a e^2\right) \log \left(a+b x^2\right)}{3 b e}-\frac{2 p x \left(3 b d^2-a e^2\right)}{3 b}-d e p x^2-\frac{2}{9} e^2 p x^3",1,"(3*(-(b^(3/2)*d^3) - 3*Sqrt[-a]*b*d^2*e + 3*a*Sqrt[b]*d*e^2 + Sqrt[-a]*a*e^3)*p*Log[Sqrt[-a] - Sqrt[b]*x] - 3*(b^(3/2)*d^3 - 3*Sqrt[-a]*b*d^2*e - 3*a*Sqrt[b]*d*e^2 + Sqrt[-a]*a*e^3)*p*Log[Sqrt[-a] + Sqrt[b]*x] + Sqrt[b]*(6*a*e^3*p*x - b*e*p*x*(18*d^2 + 9*d*e*x + 2*e^2*x^2) + 3*b*(d + e*x)^3*Log[c*(a + b*x^2)^p]))/(9*b^(3/2)*e)","A",1
186,1,83,99,0.0273978,"\int (d+e x) \log \left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[(d + e*x)*Log[c*(a + b*x^2)^p],x]","d x \log \left(c \left(a+b x^2\right)^p\right)+\frac{1}{2} e \left(\frac{\left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b}-p x^2\right)+\frac{2 \sqrt{a} d p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}-2 d p x","\frac{(d+e x)^2 \log \left(c \left(a+b x^2\right)^p\right)}{2 e}-\frac{p \left(b d^2-a e^2\right) \log \left(a+b x^2\right)}{2 b e}+\frac{2 \sqrt{a} d p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}-2 d p x-\frac{1}{2} e p x^2",1,"-2*d*p*x + (2*Sqrt[a]*d*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[b] + d*x*Log[c*(a + b*x^2)^p] + (e*(-(p*x^2) + ((a + b*x^2)*Log[c*(a + b*x^2)^p])/b))/2","A",1
187,1,45,45,0.0140994,"\int \log \left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[Log[c*(a + b*x^2)^p],x]","x \log \left(c \left(a+b x^2\right)^p\right)+\frac{2 \sqrt{a} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}-2 p x","x \log \left(c \left(a+b x^2\right)^p\right)+\frac{2 \sqrt{a} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}-2 p x",1,"-2*p*x + (2*Sqrt[a]*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[b] + x*Log[c*(a + b*x^2)^p]","A",1
188,1,201,201,0.0831052,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{d+e x} \, dx","Integrate[Log[c*(a + b*x^2)^p]/(d + e*x),x]","\frac{\log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}","\frac{\log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}",1,"-((p*Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)]*Log[d + e*x])/e) - (p*Log[-((e*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*d - Sqrt[-a]*e))]*Log[d + e*x])/e + (Log[d + e*x]*Log[c*(a + b*x^2)^p])/e - (p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)])/e - (p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)])/e","A",1
189,1,137,119,0.0776322,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{(d+e x)^2} \, dx","Integrate[Log[c*(a + b*x^2)^p]/(d + e*x)^2,x]","\frac{-b d^2 \log \left(c \left(a+b x^2\right)^p\right)-a e^2 \log \left(c \left(a+b x^2\right)^p\right)+b d^2 p \log \left(a+b x^2\right)+b d e p x \log \left(a+b x^2\right)+2 \sqrt{a} \sqrt{b} e p (d+e x) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)-2 b d p (d+e x) \log (d+e x)}{e (d+e x) \left(a e^2+b d^2\right)}","-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{e (d+e x)}+\frac{b d p \log \left(a+b x^2\right)}{e \left(a e^2+b d^2\right)}-\frac{2 b d p \log (d+e x)}{e \left(a e^2+b d^2\right)}+\frac{2 \sqrt{a} \sqrt{b} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a e^2+b d^2}",1,"(2*Sqrt[a]*Sqrt[b]*e*p*(d + e*x)*ArcTan[(Sqrt[b]*x)/Sqrt[a]] - 2*b*d*p*(d + e*x)*Log[d + e*x] + b*d^2*p*Log[a + b*x^2] + b*d*e*p*x*Log[a + b*x^2] - b*d^2*Log[c*(a + b*x^2)^p] - a*e^2*Log[c*(a + b*x^2)^p])/(e*(b*d^2 + a*e^2)*(d + e*x))","A",1
190,1,217,174,0.5706028,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{(d+e x)^3} \, dx","Integrate[Log[c*(a + b*x^2)^p]/(d + e*x)^3,x]","\frac{\frac{b p (d+e x) \left((d+e x) \left(\sqrt{-a} b d^2+2 a \sqrt{b} d e+(-a)^{3/2} e^2\right) \log \left(\sqrt{-a}-\sqrt{b} x\right)+(d+e x) \left(\sqrt{-a} b d^2-2 a \sqrt{b} d e+(-a)^{3/2} e^2\right) \log \left(\sqrt{-a}+\sqrt{b} x\right)+2 \sqrt{-a} \left(-(d+e x) \left(b d^2-a e^2\right) \log (d+e x)+a d e^2+b d^3\right)\right)}{\sqrt{-a} \left(a e^2+b d^2\right)^2}-\log \left(c \left(a+b x^2\right)^p\right)}{2 e (d+e x)^2}","\frac{2 \sqrt{a} b^{3/2} d p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\left(a e^2+b d^2\right)^2}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{2 e (d+e x)^2}+\frac{b p \left(b d^2-a e^2\right) \log \left(a+b x^2\right)}{2 e \left(a e^2+b d^2\right)^2}+\frac{b d p}{e (d+e x) \left(a e^2+b d^2\right)}-\frac{b p \left(b d^2-a e^2\right) \log (d+e x)}{e \left(a e^2+b d^2\right)^2}",1,"((b*p*(d + e*x)*((Sqrt[-a]*b*d^2 + 2*a*Sqrt[b]*d*e + (-a)^(3/2)*e^2)*(d + e*x)*Log[Sqrt[-a] - Sqrt[b]*x] + (Sqrt[-a]*b*d^2 - 2*a*Sqrt[b]*d*e + (-a)^(3/2)*e^2)*(d + e*x)*Log[Sqrt[-a] + Sqrt[b]*x] + 2*Sqrt[-a]*(b*d^3 + a*d*e^2 - (b*d^2 - a*e^2)*(d + e*x)*Log[d + e*x])))/(Sqrt[-a]*(b*d^2 + a*e^2)^2) - Log[c*(a + b*x^2)^p])/(2*e*(d + e*x)^2)","A",1
191,1,264,320,0.5116714,"\int (d+e x)^3 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Integrate[(d + e*x)^3*Log[c*(a + b*x^3)^p],x]","\frac{\frac{\sqrt[3]{a} e p \left(a e^3-4 b d^3\right) \left(\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)\right)}{2 b^{4/3}}+\frac{\sqrt[3]{a} e p \left(4 b d^3-a e^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{b^{4/3}}+(d+e x)^4 \log \left(c \left(a+b x^3\right)^p\right)-\frac{d p \left(b d^3-4 a e^3\right) \log \left(a+b x^3\right)}{b}+\frac{3 e p x \left(a e^3-4 b d^3\right)}{b}+9 d^2 e^2 p x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)-9 d^2 e^2 p x^2-4 d e^3 p x^3-\frac{3}{4} e^4 p x^4}{4 e}","-\frac{\sqrt[3]{a} p \left(-6 \sqrt[3]{a} b^{2/3} d^2 e-a e^3+4 b d^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{8 b^{4/3}}+\frac{\sqrt[3]{a} p \left(-6 \sqrt[3]{a} b^{2/3} d^2 e-a e^3+4 b d^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{4 b^{4/3}}-\frac{\sqrt{3} \sqrt[3]{a} p \left(6 \sqrt[3]{a} b^{2/3} d^2 e-a e^3+4 b d^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{4 b^{4/3}}+\frac{(d+e x)^4 \log \left(c \left(a+b x^3\right)^p\right)}{4 e}-\frac{d p \left(b d^3-4 a e^3\right) \log \left(a+b x^3\right)}{4 b e}-\frac{3 p x \left(4 b d^3-a e^3\right)}{4 b}-\frac{9}{4} d^2 e p x^2-d e^2 p x^3-\frac{3}{16} e^3 p x^4",1,"((3*e*(-4*b*d^3 + a*e^3)*p*x)/b - 9*d^2*e^2*p*x^2 - 4*d*e^3*p*x^3 - (3*e^4*p*x^4)/4 + 9*d^2*e^2*p*x^2*Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)] + (a^(1/3)*e*(4*b*d^3 - a*e^3)*p*Log[a^(1/3) + b^(1/3)*x])/b^(4/3) + (a^(1/3)*e*(-4*b*d^3 + a*e^3)*p*(2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]))/(2*b^(4/3)) - (d*(b*d^3 - 4*a*e^3)*p*Log[a + b*x^3])/b + (d + e*x)^4*Log[c*(a + b*x^3)^p])/(4*e)","C",1
192,1,218,250,0.3296052,"\int (d+e x)^2 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Integrate[(d + e*x)^2*Log[c*(a + b*x^3)^p],x]","\frac{(d+e x)^3 \log \left(c \left(a+b x^3\right)^p\right)-\frac{p \left(3 \sqrt[3]{a} b^{2/3} d^2 e \left(\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)\right)-6 \sqrt[3]{a} b^{2/3} d^2 e \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+2 \left(b d^3-a e^3\right) \log \left(a+b x^3\right)-9 b d e^2 x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)+18 b d^2 e x+9 b d e^2 x^2+2 b e^3 x^3\right)}{2 b}}{3 e}","-\frac{\sqrt[3]{a} d p \left(\sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 b^{2/3}}+\frac{\sqrt[3]{a} d p \left(\sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{b^{2/3}}-\frac{\sqrt{3} \sqrt[3]{a} d p \left(\sqrt[3]{a} e+\sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{b^{2/3}}+\frac{(d+e x)^3 \log \left(c \left(a+b x^3\right)^p\right)}{3 e}-\frac{p \left(b d^3-a e^3\right) \log \left(a+b x^3\right)}{3 b e}-3 d^2 p x-\frac{3}{2} d e p x^2-\frac{1}{3} e^2 p x^3",1,"(-1/2*(p*(18*b*d^2*e*x + 9*b*d*e^2*x^2 + 2*b*e^3*x^3 - 9*b*d*e^2*x^2*Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)] - 6*a^(1/3)*b^(2/3)*d^2*e*Log[a^(1/3) + b^(1/3)*x] + 3*a^(1/3)*b^(2/3)*d^2*e*(2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]) + 2*(b*d^3 - a*e^3)*Log[a + b*x^3]))/b + (d + e*x)^3*Log[c*(a + b*x^3)^p])/(3*e)","C",1
193,1,204,229,0.0703567,"\int (d+e x) \log \left(c \left(a+b x^3\right)^p\right) \, dx","Integrate[(d + e*x)*Log[c*(a + b*x^3)^p],x]","-\frac{\sqrt[3]{a} d p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \sqrt[3]{b}}+\frac{\sqrt{3} \sqrt[3]{a} d p \tan ^{-1}\left(\frac{2 b^{2/3} x-\sqrt[3]{a} \sqrt[3]{b}}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{b}}\right)}{\sqrt[3]{b}}+d x \log \left(c \left(a+b x^3\right)^p\right)+\frac{1}{2} e x^2 \log \left(c \left(a+b x^3\right)^p\right)+\frac{\sqrt[3]{a} d p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}+\frac{3}{4} e p x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)-3 d p x-\frac{3}{4} e p x^2","-\frac{\sqrt[3]{a} p \left(2 \sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{4 b^{2/3}}+\frac{\sqrt[3]{a} p \left(2 \sqrt[3]{b} d-\sqrt[3]{a} e\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 b^{2/3}}-\frac{\sqrt{3} \sqrt[3]{a} p \left(\sqrt[3]{a} e+2 \sqrt[3]{b} d\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{2 b^{2/3}}+\frac{(d+e x)^2 \log \left(c \left(a+b x^3\right)^p\right)}{2 e}-\frac{d^2 p \log \left(a+b x^3\right)}{2 e}-3 d p x-\frac{3}{4} e p x^2",1,"-3*d*p*x - (3*e*p*x^2)/4 + (Sqrt[3]*a^(1/3)*d*p*ArcTan[(-(a^(1/3)*b^(1/3)) + 2*b^(2/3)*x)/(Sqrt[3]*a^(1/3)*b^(1/3))])/b^(1/3) + (3*e*p*x^2*Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)])/4 + (a^(1/3)*d*p*Log[a^(1/3) + b^(1/3)*x])/b^(1/3) - (a^(1/3)*d*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(2*b^(1/3)) + d*x*Log[c*(a + b*x^3)^p] + (e*x^2*Log[c*(a + b*x^3)^p])/2","C",1
194,1,129,133,0.0419279,"\int \log \left(c \left(a+b x^3\right)^p\right) \, dx","Integrate[Log[c*(a + b*x^3)^p],x]","-\frac{\sqrt[3]{a} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \sqrt[3]{b}}+x \log \left(c \left(a+b x^3\right)^p\right)+\frac{\sqrt[3]{a} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{\sqrt{3} \sqrt[3]{a} p \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{\sqrt[3]{b}}-3 p x","-\frac{\sqrt[3]{a} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \sqrt[3]{b}}+x \log \left(c \left(a+b x^3\right)^p\right)+\frac{\sqrt[3]{a} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{\sqrt{3} \sqrt[3]{a} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{b}}-3 p x",1,"-3*p*x - (Sqrt[3]*a^(1/3)*p*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/b^(1/3) + (a^(1/3)*p*Log[a^(1/3) + b^(1/3)*x])/b^(1/3) - (a^(1/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(2*b^(1/3)) + x*Log[c*(a + b*x^3)^p]","A",1
195,1,313,308,0.1622517,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{d+e x} \, dx","Integrate[Log[c*(a + b*x^3)^p]/(d + e*x),x]","\frac{\log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{(-1)^{2/3} e \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e}","\frac{\log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e}",1,"-((p*Log[-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e))]*Log[d + e*x])/e) - (p*Log[-(((-1)^(2/3)*e*(a^(1/3) - (-1)^(1/3)*b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e))]*Log[d + e*x])/e - (p*Log[((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)]*Log[d + e*x])/e + (Log[d + e*x]*Log[c*(a + b*x^3)^p])/e - (p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)])/e - (p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)])/e - (p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)])/e","A",1
196,1,202,292,0.6392779,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{(d+e x)^2} \, dx","Integrate[Log[c*(a + b*x^3)^p]/(d + e*x)^2,x]","-\frac{\frac{b^{2/3} d p \left(\sqrt[3]{a} e \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)-2 \sqrt[3]{b} d \log \left(a+b x^3\right)-2 \sqrt[3]{a} e \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+2 \sqrt{3} \sqrt[3]{a} e \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)+6 \sqrt[3]{b} d \log (d+e x)\right)+3 b e^2 p x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)}{2 b d^3-2 a e^3}+\frac{\log \left(c \left(a+b x^3\right)^p\right)}{d+e x}}{e}","-\frac{\sqrt[3]{a} \sqrt[3]{b} p \left(\sqrt[3]{a} e+\sqrt[3]{b} d\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \left(b d^3-a e^3\right)}-\frac{\sqrt{3} \sqrt[3]{a} \sqrt[3]{b} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{a^{2/3} e^2+\sqrt[3]{a} \sqrt[3]{b} d e+b^{2/3} d^2}-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{e (d+e x)}+\frac{\sqrt[3]{a} \sqrt[3]{b} p \left(\sqrt[3]{a} e+\sqrt[3]{b} d\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{b d^3-a e^3}+\frac{b d^2 p \log \left(a+b x^3\right)}{e \left(b d^3-a e^3\right)}-\frac{3 b d^2 p \log (d+e x)}{e \left(b d^3-a e^3\right)}",1,"-(((3*b*e^2*p*x^2*Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)] + b^(2/3)*d*p*(2*Sqrt[3]*a^(1/3)*e*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] - 2*a^(1/3)*e*Log[a^(1/3) + b^(1/3)*x] + 6*b^(1/3)*d*Log[d + e*x] + a^(1/3)*e*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2] - 2*b^(1/3)*d*Log[a + b*x^3]))/(2*b*d^3 - 2*a*e^3) + Log[c*(a + b*x^3)^p]/(d + e*x))/e)","C",1
197,1,303,391,0.6907633,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{(d+e x)^3} \, dx","Integrate[Log[c*(a + b*x^3)^p]/(d + e*x)^3,x]","\frac{\frac{b^{2/3} p (d+e x) \left(-\sqrt[3]{a} e (d+e x) \left(a e^3+2 b d^3\right) \left(\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)\right)-9 b^{4/3} d^2 e^2 x^2 (d+e x) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)+2 \sqrt[3]{b} d (d+e x) \left(2 a e^3+b d^3\right) \log \left(a+b x^3\right)-6 \sqrt[3]{b} d (d+e x) \left(2 a e^3+b d^3\right) \log (d+e x)+2 \sqrt[3]{a} e (d+e x) \left(a e^3+2 b d^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+6 \sqrt[3]{b} d^2 \left(b d^3-a e^3\right)\right)}{\left(b d^3-a e^3\right)^2}-2 \log \left(c \left(a+b x^3\right)^p\right)}{4 e (d+e x)^2}","-\frac{\sqrt[3]{a} b^{2/3} p \left(3 \sqrt[3]{a} b^{2/3} d^2 e+a e^3+2 b d^3\right) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{4 \left(b d^3-a e^3\right)^2}+\frac{\sqrt[3]{a} b^{2/3} p \left(3 \sqrt[3]{a} b^{2/3} d^2 e+a e^3+2 b d^3\right) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \left(b d^3-a e^3\right)^2}-\frac{\sqrt{3} \sqrt[3]{a} b^{2/3} p \left(-3 \sqrt[3]{a} b^{2/3} d^2 e+a e^3+2 b d^3\right) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{2 \left(b d^3-a e^3\right)^2}-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{2 e (d+e x)^2}+\frac{b d p \left(2 a e^3+b d^3\right) \log \left(a+b x^3\right)}{2 e \left(b d^3-a e^3\right)^2}-\frac{3 b d p \left(2 a e^3+b d^3\right) \log (d+e x)}{2 e \left(b d^3-a e^3\right)^2}+\frac{3 b d^2 p}{2 e (d+e x) \left(b d^3-a e^3\right)}",1,"((b^(2/3)*p*(d + e*x)*(6*b^(1/3)*d^2*(b*d^3 - a*e^3) - 9*b^(4/3)*d^2*e^2*x^2*(d + e*x)*Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)] + 2*a^(1/3)*e*(2*b*d^3 + a*e^3)*(d + e*x)*Log[a^(1/3) + b^(1/3)*x] - 6*b^(1/3)*d*(b*d^3 + 2*a*e^3)*(d + e*x)*Log[d + e*x] - a^(1/3)*e*(2*b*d^3 + a*e^3)*(d + e*x)*(2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2]) + 2*b^(1/3)*d*(b*d^3 + 2*a*e^3)*(d + e*x)*Log[a + b*x^3]))/(b*d^3 - a*e^3)^2 - 2*Log[c*(a + b*x^3)^p])/(4*e*(d + e*x)^2)","C",1
198,1,114,139,0.1491282,"\int (d+e x)^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Integrate[(d + e*x)^3*Log[c*(a + b/x)^p],x]","\frac{-\frac{p (a d-b e)^4 \log (a x+b)}{a^4}+\frac{b e^2 p x \left(2 a^2 \left(18 d^2+6 d e x+e^2 x^2\right)-3 a b e (8 d+e x)+6 b^2 e^2\right)}{6 a^3}+(d+e x)^4 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+d^4 p \log (x)}{4 e}","-\frac{p (a d-b e)^4 \log (a x+b)}{4 a^4 e}+\frac{b e^2 p x^2 (4 a d-b e)}{8 a^2}+\frac{b e p x \left(6 a^2 d^2-4 a b d e+b^2 e^2\right)}{4 a^3}+\frac{(d+e x)^4 \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{4 e}+\frac{b e^3 p x^3}{12 a}+\frac{d^4 p \log (x)}{4 e}",1,"((b*e^2*p*x*(6*b^2*e^2 - 3*a*b*e*(8*d + e*x) + 2*a^2*(18*d^2 + 6*d*e*x + e^2*x^2)))/(6*a^3) + (d + e*x)^4*Log[c*(a + b/x)^p] + d^4*p*Log[x] - ((a*d - b*e)^4*p*Log[b + a*x])/a^4)/(4*e)","A",1
199,1,86,102,0.0849637,"\int (d+e x)^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Integrate[(d + e*x)^2*Log[c*(a + b/x)^p],x]","\frac{2 a^3 (d+e x)^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+p \left(2 a^3 d^3 \log (x)+a b e^2 x (6 a d+a e x-2 b e)-2 (a d-b e)^3 \log (a x+b)\right)}{6 a^3 e}","-\frac{p (a d-b e)^3 \log (a x+b)}{3 a^3 e}+\frac{b e p x (3 a d-b e)}{3 a^2}+\frac{(d+e x)^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{3 e}+\frac{b e^2 p x^2}{6 a}+\frac{d^3 p \log (x)}{3 e}",1,"(2*a^3*(d + e*x)^3*Log[c*(a + b/x)^p] + p*(a*b*e^2*x*(6*a*d - 2*b*e + a*e*x) + 2*a^3*d^3*Log[x] - 2*(a*d - b*e)^3*Log[b + a*x]))/(6*a^3*e)","A",1
200,1,85,78,0.029027,"\int (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Integrate[(d + e*x)*Log[c*(a + b/x)^p],x]","\frac{1}{2} b e p \left(\frac{x}{a}-\frac{b \log (a x+b)}{a^2}\right)+d x \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{1}{2} e x^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b d p \log \left(a+\frac{b}{x}\right)}{a}+\frac{b d p \log (x)}{a}","-\frac{p (a d-b e)^2 \log (a x+b)}{2 a^2 e}+\frac{(d+e x)^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{2 e}+\frac{b e p x}{2 a}+\frac{d^2 p \log (x)}{2 e}",1,"(b*d*p*Log[a + b/x])/a + d*x*Log[c*(a + b/x)^p] + (e*x^2*Log[c*(a + b/x)^p])/2 + (b*d*p*Log[x])/a + (b*e*p*(x/a - (b*Log[b + a*x])/a^2))/2","A",1
201,1,114,113,0.0269312,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d+e x} \, dx","Integrate[Log[c*(a + b/x)^p]/(d + e*x),x]","\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{e}+\frac{p \text{Li}_2\left(\frac{d+e x}{d}\right)}{e}+\frac{p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}","\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{e}+\frac{p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e}+\frac{p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}",1,"(Log[c*(a + b/x)^p]*Log[d + e*x])/e + (p*Log[-((e*x)/d)]*Log[d + e*x])/e - (p*Log[-((e*(b + a*x))/(a*d - b*e))]*Log[d + e*x])/e + (p*PolyLog[2, (d + e*x)/d])/e - (p*PolyLog[2, (a*(d + e*x))/(a*d - b*e)])/e","A",1
202,1,81,81,0.0678708,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{(d+e x)^2} \, dx","Integrate[Log[c*(a + b/x)^p]/(d + e*x)^2,x]","-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e (d+e x)}+\frac{a p \log (a x+b)}{e (a d-b e)}-\frac{b p \log (d+e x)}{d (a d-b e)}-\frac{p \log (x)}{d e}","-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e (d+e x)}+\frac{a p \log (a x+b)}{e (a d-b e)}-\frac{b p \log (d+e x)}{d (a d-b e)}-\frac{p \log (x)}{d e}",1,"-(Log[c*(a + b/x)^p]/(e*(d + e*x))) - (p*Log[x])/(d*e) + (a*p*Log[b + a*x])/(e*(a*d - b*e)) - (b*p*Log[d + e*x])/(d*(a*d - b*e))","A",1
203,1,113,127,0.1953471,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{(d+e x)^3} \, dx","Integrate[Log[c*(a + b/x)^p]/(d + e*x)^3,x]","\frac{\frac{a^2 p \log (a x+b)}{(a d-b e)^2}-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{(d+e x)^2}+\frac{b e p (b e-2 a d) \log (d+e x)}{d^2 (a d-b e)^2}+\frac{b e p}{d (d+e x) (a d-b e)}-\frac{p \log (x)}{d^2}}{2 e}","\frac{a^2 p \log (a x+b)}{2 e (a d-b e)^2}-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{2 e (d+e x)^2}-\frac{b p (2 a d-b e) \log (d+e x)}{2 d^2 (a d-b e)^2}+\frac{b p}{2 d (d+e x) (a d-b e)}-\frac{p \log (x)}{2 d^2 e}",1,"((b*e*p)/(d*(a*d - b*e)*(d + e*x)) - Log[c*(a + b/x)^p]/(d + e*x)^2 - (p*Log[x])/d^2 + (a^2*p*Log[b + a*x])/(a*d - b*e)^2 + (b*e*(-2*a*d + b*e)*p*Log[d + e*x])/(d^2*(a*d - b*e)^2))/(2*e)","A",1
204,1,164,175,0.2774566,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{(d+e x)^4} \, dx","Integrate[Log[c*(a + b/x)^p]/(d + e*x)^4,x]","\frac{\frac{a^3 p \log (a x+b)}{(a d-b e)^3}-\frac{b e p \left(3 a^2 d^2-3 a b d e+b^2 e^2\right) \log (d+e x)}{d^3 (a d-b e)^3}-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{(d+e x)^3}+\frac{b e p (2 a d-b e)}{d^2 (d+e x) (a d-b e)^2}+\frac{b e p}{2 d (d+e x)^2 (a d-b e)}-\frac{p \log (x)}{d^3}}{3 e}","\frac{a^3 p \log (a x+b)}{3 e (a d-b e)^3}-\frac{b p \left(3 a^2 d^2-3 a b d e+b^2 e^2\right) \log (d+e x)}{3 d^3 (a d-b e)^3}-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{3 e (d+e x)^3}+\frac{b p (2 a d-b e)}{3 d^2 (d+e x) (a d-b e)^2}+\frac{b p}{6 d (d+e x)^2 (a d-b e)}-\frac{p \log (x)}{3 d^3 e}",1,"((b*e*p)/(2*d*(a*d - b*e)*(d + e*x)^2) + (b*e*(2*a*d - b*e)*p)/(d^2*(a*d - b*e)^2*(d + e*x)) - Log[c*(a + b/x)^p]/(d + e*x)^3 - (p*Log[x])/d^3 + (a^3*p*Log[b + a*x])/(a*d - b*e)^3 - (b*e*(3*a^2*d^2 - 3*a*b*d*e + b^2*e^2)*p*Log[d + e*x])/(d^3*(a*d - b*e)^3))/(3*e)","A",1
205,1,80,105,0.0396205,"\int \frac{\log \left(a+\frac{b}{x}\right)}{c+d x} \, dx","Integrate[Log[a + b/x]/(c + d*x),x]","\frac{-\text{Li}_2\left(\frac{a (c+d x)}{a c-b d}\right)+\log (c+d x) \left(-\log \left(\frac{d (a x+b)}{b d-a c}\right)+\log \left(a+\frac{b}{x}\right)+\log \left(-\frac{d x}{c}\right)\right)+\text{Li}_2\left(\frac{d x}{c}+1\right)}{d}","-\frac{\text{Li}_2\left(\frac{a (c+d x)}{a c-b d}\right)}{d}+\frac{\log \left(a+\frac{b}{x}\right) \log (c+d x)}{d}-\frac{\log (c+d x) \log \left(-\frac{d (a x+b)}{a c-b d}\right)}{d}+\frac{\text{Li}_2\left(\frac{d x}{c}+1\right)}{d}+\frac{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{d}",1,"((Log[a + b/x] + Log[-((d*x)/c)] - Log[(d*(b + a*x))/(-(a*c) + b*d)])*Log[c + d*x] - PolyLog[2, (a*(c + d*x))/(a*c - b*d)] + PolyLog[2, 1 + (d*x)/c])/d","A",1
206,1,239,301,0.6764771,"\int (d+e x)^m \log \left(c \left(a+b x^3\right)^p\right) \, dx","Integrate[(d + e*x)^m*Log[c*(a + b*x^3)^p],x]","\frac{(d+e x)^{m+1} \left(\log \left(c \left(a+b x^3\right)^p\right)-\frac{\sqrt[3]{b} p (d+e x) \left(-\frac{\, _2F_1\left(1,m+2;m+3;\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}-\frac{\, _2F_1\left(1,m+2;m+3;\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}-\frac{\, _2F_1\left(1,m+2;m+3;\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{m+2}\right)}{e (m+1)}","\frac{(d+e x)^{m+1} \log \left(c \left(a+b x^3\right)^p\right)}{e (m+1)}+\frac{\sqrt[3]{b} p (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e (m+1) (m+2) \left(\sqrt[3]{b} d-\sqrt[3]{a} e\right)}+\frac{\sqrt[3]{b} p (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{e (m+1) (m+2) \left(\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d\right)}+\frac{\sqrt[3]{b} p (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e (m+1) (m+2) \left(\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e\right)}",1,"((d + e*x)^(1 + m)*(-((b^(1/3)*p*(d + e*x)*(-(Hypergeometric2F1[1, 2 + m, 3 + m, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)]/(b^(1/3)*d - a^(1/3)*e)) - Hypergeometric2F1[1, 2 + m, 3 + m, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)]/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e) - Hypergeometric2F1[1, 2 + m, 3 + m, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)]/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)))/(2 + m)) + Log[c*(a + b*x^3)^p]))/(e*(1 + m))","A",1
207,1,176,205,0.2455135,"\int (d+e x)^m \log \left(c \left(a+b x^2\right)^p\right) \, dx","Integrate[(d + e*x)^m*Log[c*(a + b*x^2)^p],x]","\frac{(d+e x)^{m+1} \left(\log \left(c \left(a+b x^2\right)^p\right)+\frac{\sqrt{b} p (d+e x) \left(\left(\sqrt{-a} e+\sqrt{b} d\right) \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)+\left(\sqrt{b} d-\sqrt{-a} e\right) \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)\right)}{(m+2) \left(a e^2+b d^2\right)}\right)}{e (m+1)}","\frac{(d+e x)^{m+1} \log \left(c \left(a+b x^2\right)^p\right)}{e (m+1)}+\frac{\sqrt{b} p (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e (m+1) (m+2) \left(\sqrt{b} d-\sqrt{-a} e\right)}+\frac{\sqrt{b} p (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)}{e (m+1) (m+2) \left(\sqrt{-a} e+\sqrt{b} d\right)}",1,"((d + e*x)^(1 + m)*((Sqrt[b]*p*(d + e*x)*((Sqrt[b]*d + Sqrt[-a]*e)*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)] + (Sqrt[b]*d - Sqrt[-a]*e)*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)]))/((b*d^2 + a*e^2)*(2 + m)) + Log[c*(a + b*x^2)^p]))/(e*(1 + m))","A",1
208,1,77,89,0.0595377,"\int (d+e x)^m \log \left(c (a+b x)^p\right) \, dx","Integrate[(d + e*x)^m*Log[c*(a + b*x)^p],x]","\frac{(d+e x)^{m+1} \left(\log \left(c (a+b x)^p\right)+\frac{b p (d+e x) \, _2F_1\left(1,m+2;m+3;\frac{b (d+e x)}{b d-a e}\right)}{(m+2) (b d-a e)}\right)}{e (m+1)}","\frac{(d+e x)^{m+1} \log \left(c (a+b x)^p\right)}{e (m+1)}+\frac{b p (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{b (d+e x)}{b d-a e}\right)}{e (m+1) (m+2) (b d-a e)}",1,"((d + e*x)^(1 + m)*((b*p*(d + e*x)*Hypergeometric2F1[1, 2 + m, 3 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)*(2 + m)) + Log[c*(a + b*x)^p]))/(e*(1 + m))","A",1
209,1,123,135,0.0826915,"\int (d+e x)^m \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Integrate[(d + e*x)^m*Log[c*(a + b/x)^p],x]","\frac{(d+e x)^{m+1} \left((a d-b e) \left(p (d+e x) \, _2F_1\left(1,m+2;m+3;\frac{e x}{d}+1\right)-d (m+2) \log \left(c \left(a+\frac{b}{x}\right)^p\right)\right)-a d p (d+e x) \, _2F_1\left(1,m+2;m+3;\frac{a (d+e x)}{a d-b e}\right)\right)}{d e (m+1) (m+2) (b e-a d)}","\frac{(d+e x)^{m+1} \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e (m+1)}+\frac{a p (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{a (d+e x)}{a d-b e}\right)}{e (m+1) (m+2) (a d-b e)}-\frac{p (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{e x}{d}+1\right)}{d e \left(m^2+3 m+2\right)}",1,"((d + e*x)^(1 + m)*(-(a*d*p*(d + e*x)*Hypergeometric2F1[1, 2 + m, 3 + m, (a*(d + e*x))/(a*d - b*e)]) + (a*d - b*e)*(p*(d + e*x)*Hypergeometric2F1[1, 2 + m, 3 + m, 1 + (e*x)/d] - d*(2 + m)*Log[c*(a + b/x)^p])))/(d*e*(-(a*d) + b*e)*(1 + m)*(2 + m))","A",1
210,1,211,257,0.4714852,"\int (d+e x)^m \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Integrate[(d + e*x)^m*Log[c*(a + b/x^2)^p],x]","\frac{(d+e x)^{m+1} \left(\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+\frac{p (d+e x) \left(-2 \left(a d^2+b e^2\right) \, _2F_1\left(1,m+2;m+3;\frac{e x}{d}+1\right)+d \left(a d-\sqrt{-a} \sqrt{b} e\right) \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)+d \left(\sqrt{-a} \sqrt{b} e+a d\right) \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)\right)}{d (m+2) \left(a d^2+b e^2\right)}\right)}{e (m+1)}","\frac{(d+e x)^{m+1} \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{e (m+1)}+\frac{\sqrt{-a} p (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e (m+1) (m+2) \left(\sqrt{-a} d-\sqrt{b} e\right)}+\frac{\sqrt{-a} p (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e (m+1) (m+2) \left(\sqrt{-a} d+\sqrt{b} e\right)}-\frac{2 p (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{e x}{d}+1\right)}{d e \left(m^2+3 m+2\right)}",1,"((d + e*x)^(1 + m)*((p*(d + e*x)*(d*(a*d - Sqrt[-a]*Sqrt[b]*e)*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)] + d*(a*d + Sqrt[-a]*Sqrt[b]*e)*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)] - 2*(a*d^2 + b*e^2)*Hypergeometric2F1[1, 2 + m, 3 + m, 1 + (e*x)/d]))/(d*(a*d^2 + b*e^2)*(2 + m)) + Log[c*(a + b/x^2)^p]))/(e*(1 + m))","A",1
211,0,0,23,0.561057,"\int (f+g x)^m \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f + g*x)^m*Log[c*(d + e*x^n)^p],x]","\int (f+g x)^m \log \left(c \left(d+e x^n\right)^p\right) \, dx","\text{Int}\left((f+g x)^m \log \left(c \left(d+e x^n\right)^p\right),x\right)",0,"Integrate[(f + g*x)^m*Log[c*(d + e*x^n)^p], x]","A",-1
212,1,224,234,0.4901736,"\int (f+g x)^3 \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f + g*x)^3*Log[c*(d + e*x^n)^p],x]","\frac{(f+g x)^4 \log \left(c \left(d+e x^n\right)^p\right)-e n p \left(\frac{f^4 \log \left(d+e x^n\right)}{e n}+\frac{4 f^3 g x^{n+1} \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{e x^n}{d}\right)}{d (n+1)}+\frac{6 f^2 g^2 x^{n+2} \, _2F_1\left(1,\frac{n+2}{n};2 \left(1+\frac{1}{n}\right);-\frac{e x^n}{d}\right)}{d (n+2)}+\frac{4 f g^3 x^{n+3} \, _2F_1\left(1,\frac{n+3}{n};2+\frac{3}{n};-\frac{e x^n}{d}\right)}{d (n+3)}+\frac{g^4 x^{n+4} \, _2F_1\left(1,\frac{n+4}{n};2+\frac{4}{n};-\frac{e x^n}{d}\right)}{d (n+4)}\right)}{4 g}","\frac{(f+g x)^4 \log \left(c \left(d+e x^n\right)^p\right)}{4 g}-\frac{f^4 p \log \left(d+e x^n\right)}{4 g}-\frac{e f^3 n p x^{n+1} \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{e x^n}{d}\right)}{d (n+1)}-\frac{3 e f^2 g n p x^{n+2} \, _2F_1\left(1,\frac{n+2}{n};2 \left(1+\frac{1}{n}\right);-\frac{e x^n}{d}\right)}{2 d (n+2)}-\frac{e f g^2 n p x^{n+3} \, _2F_1\left(1,\frac{n+3}{n};2+\frac{3}{n};-\frac{e x^n}{d}\right)}{d (n+3)}-\frac{e g^3 n p x^{n+4} \, _2F_1\left(1,\frac{n+4}{n};2 \left(1+\frac{2}{n}\right);-\frac{e x^n}{d}\right)}{4 d (n+4)}",1,"(-(e*n*p*((4*f^3*g*x^(1 + n)*Hypergeometric2F1[1, 1 + n^(-1), 2 + n^(-1), -((e*x^n)/d)])/(d*(1 + n)) + (6*f^2*g^2*x^(2 + n)*Hypergeometric2F1[1, (2 + n)/n, 2*(1 + n^(-1)), -((e*x^n)/d)])/(d*(2 + n)) + (4*f*g^3*x^(3 + n)*Hypergeometric2F1[1, (3 + n)/n, 2 + 3/n, -((e*x^n)/d)])/(d*(3 + n)) + (g^4*x^(4 + n)*Hypergeometric2F1[1, (4 + n)/n, 2 + 4/n, -((e*x^n)/d)])/(d*(4 + n)) + (f^4*Log[d + e*x^n])/(e*n))) + (f + g*x)^4*Log[c*(d + e*x^n)^p])/(4*g)","A",1
213,1,178,181,0.2510021,"\int (f+g x)^2 \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f + g*x)^2*Log[c*(d + e*x^n)^p],x]","\frac{(f+g x)^3 \log \left(c \left(d+e x^n\right)^p\right)-e n p \left(\frac{f^3 \log \left(d+e x^n\right)}{e n}+\frac{3 f^2 g x^{n+1} \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{e x^n}{d}\right)}{d (n+1)}+\frac{3 f g^2 x^{n+2} \, _2F_1\left(1,\frac{n+2}{n};2 \left(1+\frac{1}{n}\right);-\frac{e x^n}{d}\right)}{d (n+2)}+\frac{g^3 x^{n+3} \, _2F_1\left(1,\frac{n+3}{n};2+\frac{3}{n};-\frac{e x^n}{d}\right)}{d (n+3)}\right)}{3 g}","\frac{(f+g x)^3 \log \left(c \left(d+e x^n\right)^p\right)}{3 g}-\frac{f^3 p \log \left(d+e x^n\right)}{3 g}-\frac{e f^2 n p x^{n+1} \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{e x^n}{d}\right)}{d (n+1)}-\frac{e f g n p x^{n+2} \, _2F_1\left(1,\frac{n+2}{n};2 \left(1+\frac{1}{n}\right);-\frac{e x^n}{d}\right)}{d (n+2)}-\frac{e g^2 n p x^{n+3} \, _2F_1\left(1,\frac{n+3}{n};2+\frac{3}{n};-\frac{e x^n}{d}\right)}{3 d (n+3)}",1,"(-(e*n*p*((3*f^2*g*x^(1 + n)*Hypergeometric2F1[1, 1 + n^(-1), 2 + n^(-1), -((e*x^n)/d)])/(d*(1 + n)) + (3*f*g^2*x^(2 + n)*Hypergeometric2F1[1, (2 + n)/n, 2*(1 + n^(-1)), -((e*x^n)/d)])/(d*(2 + n)) + (g^3*x^(3 + n)*Hypergeometric2F1[1, (3 + n)/n, 2 + 3/n, -((e*x^n)/d)])/(d*(3 + n)) + (f^3*Log[d + e*x^n])/(e*n))) + (f + g*x)^3*Log[c*(d + e*x^n)^p])/(3*g)","A",1
214,1,130,132,0.1265159,"\int (f+g x) \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[(f + g*x)*Log[c*(d + e*x^n)^p],x]","f x \log \left(c \left(d+e x^n\right)^p\right)+\frac{1}{2} g x^2 \log \left(c \left(d+e x^n\right)^p\right)-\frac{e f n p x^{n+1} \, _2F_1\left(1,\frac{n+1}{n};\frac{n+1}{n}+1;-\frac{e x^n}{d}\right)}{d (n+1)}-\frac{e g n p x^{n+2} \, _2F_1\left(1,\frac{n+2}{n};\frac{n+2}{n}+1;-\frac{e x^n}{d}\right)}{2 d (n+2)}","\frac{(f+g x)^2 \log \left(c \left(d+e x^n\right)^p\right)}{2 g}-\frac{f^2 p \log \left(d+e x^n\right)}{2 g}-\frac{e f n p x^{n+1} \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{e x^n}{d}\right)}{d (n+1)}-\frac{e g n p x^{n+2} \, _2F_1\left(1,\frac{n+2}{n};2 \left(1+\frac{1}{n}\right);-\frac{e x^n}{d}\right)}{2 d (n+2)}",1,"-((e*f*n*p*x^(1 + n)*Hypergeometric2F1[1, (1 + n)/n, 1 + (1 + n)/n, -((e*x^n)/d)])/(d*(1 + n))) - (e*g*n*p*x^(2 + n)*Hypergeometric2F1[1, (2 + n)/n, 1 + (2 + n)/n, -((e*x^n)/d)])/(2*d*(2 + n)) + f*x*Log[c*(d + e*x^n)^p] + (g*x^2*Log[c*(d + e*x^n)^p])/2","A",1
215,1,52,54,0.0305115,"\int \log \left(c \left(d+e x^n\right)^p\right) \, dx","Integrate[Log[c*(d + e*x^n)^p],x]","x \left(\log \left(c \left(d+e x^n\right)^p\right)-\frac{e n p x^n \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{e x^n}{d}\right)}{d (n+1)}\right)","x \log \left(c \left(d+e x^n\right)^p\right)-\frac{e n p x^{n+1} \, _2F_1\left(1,1+\frac{1}{n};2+\frac{1}{n};-\frac{e x^n}{d}\right)}{d (n+1)}",1,"x*(-((e*n*p*x^n*Hypergeometric2F1[1, 1 + n^(-1), 2 + n^(-1), -((e*x^n)/d)])/(d*(1 + n))) + Log[c*(d + e*x^n)^p])","A",1
216,0,0,23,1.7140914,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{f+g x} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(f + g*x),x]","\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{f+g x} \, dx","\text{Int}\left(\frac{\log \left(c \left(d+e x^n\right)^p\right)}{f+g x},x\right)",0,"Integrate[Log[c*(d + e*x^n)^p]/(f + g*x), x]","A",-1
217,0,0,23,0.1938474,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{(f+g x)^2} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(f + g*x)^2,x]","\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{(f+g x)^2} \, dx","\text{Int}\left(\frac{\log \left(c \left(d+e x^n\right)^p\right)}{(f+g x)^2},x\right)",0,"Integrate[Log[c*(d + e*x^n)^p]/(f + g*x)^2, x]","A",-1
218,0,0,23,0.2150647,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{(f+g x)^3} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(f + g*x)^3,x]","\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{(f+g x)^3} \, dx","\text{Int}\left(\frac{\log \left(c \left(d+e x^n\right)^p\right)}{(f+g x)^3},x\right)",0,"Integrate[Log[c*(d + e*x^n)^p]/(f + g*x)^3, x]","A",-1
219,1,183,250,0.1973016,"\int \frac{x^3 \log \left(c (a+b x)^p\right)}{d+e x} \, dx","Integrate[(x^3*Log[c*(a + b*x)^p])/(d + e*x),x]","\frac{b \left(6 b \log \left(c (a+b x)^p\right) \left(-6 b d^3 \log \left(\frac{b (d+e x)}{b d-a e}\right)+6 a d^2 e+b e x \left(6 d^2-3 d e x+2 e^2 x^2\right)\right)-e p x \left(12 a^2 e^2-6 a b e (e x-3 d)+b^2 \left(36 d^2-9 d e x+4 e^2 x^2\right)\right)\right)+6 a^2 e^2 p (2 a e+3 b d) \log (a+b x)-36 b^3 d^3 p \text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)}{36 b^3 e^4}","\frac{a^3 p \log (a+b x)}{3 b^3 e}+\frac{a^2 d p \log (a+b x)}{2 b^2 e^2}-\frac{a^2 p x}{3 b^2 e}-\frac{d^3 \log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{e^4}+\frac{d^2 (a+b x) \log \left(c (a+b x)^p\right)}{b e^3}-\frac{d x^2 \log \left(c (a+b x)^p\right)}{2 e^2}+\frac{x^3 \log \left(c (a+b x)^p\right)}{3 e}-\frac{d^3 p \text{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\right)}{e^4}-\frac{a d p x}{2 b e^2}+\frac{a p x^2}{6 b e}-\frac{d^2 p x}{e^3}+\frac{d p x^2}{4 e^2}-\frac{p x^3}{9 e}",1,"(6*a^2*e^2*(3*b*d + 2*a*e)*p*Log[a + b*x] + b*(-(e*p*x*(12*a^2*e^2 - 6*a*b*e*(-3*d + e*x) + b^2*(36*d^2 - 9*d*e*x + 4*e^2*x^2))) + 6*b*Log[c*(a + b*x)^p]*(6*a*d^2*e + b*e*x*(6*d^2 - 3*d*e*x + 2*e^2*x^2) - 6*b*d^3*Log[(b*(d + e*x))/(b*d - a*e)])) - 36*b^3*d^3*p*PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)])/(36*b^3*e^4)","A",1
220,1,127,159,0.0951999,"\int \frac{x^2 \log \left(c (a+b x)^p\right)}{d+e x} \, dx","Integrate[(x^2*Log[c*(a + b*x)^p])/(d + e*x),x]","\frac{-2 a^2 e^2 p \log (a+b x)+4 b^2 d^2 p \text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)+b \log \left(c (a+b x)^p\right) \left(4 b d^2 \log \left(\frac{b (d+e x)}{b d-a e}\right)-4 a d e+2 b e x (e x-2 d)\right)+b e p x (2 a e+4 b d-b e x)}{4 b^2 e^3}","-\frac{a^2 p \log (a+b x)}{2 b^2 e}+\frac{d^2 \log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{e^3}-\frac{d (a+b x) \log \left(c (a+b x)^p\right)}{b e^2}+\frac{x^2 \log \left(c (a+b x)^p\right)}{2 e}+\frac{d^2 p \text{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\right)}{e^3}+\frac{a p x}{2 b e}+\frac{d p x}{e^2}-\frac{p x^2}{4 e}",1,"(b*e*p*x*(4*b*d + 2*a*e - b*e*x) - 2*a^2*e^2*p*Log[a + b*x] + b*Log[c*(a + b*x)^p]*(-4*a*d*e + 2*b*e*x*(-2*d + e*x) + 4*b*d^2*Log[(b*(d + e*x))/(b*d - a*e)]) + 4*b^2*d^2*p*PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)])/(4*b^2*e^3)","A",1
221,1,79,91,0.0337917,"\int \frac{x \log \left(c (a+b x)^p\right)}{d+e x} \, dx","Integrate[(x*Log[c*(a + b*x)^p])/(d + e*x),x]","\frac{\log \left(c (a+b x)^p\right) \left(-b d \log \left(\frac{b (d+e x)}{b d-a e}\right)+a e+b e x\right)-b d p \text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)-b e p x}{b e^2}","-\frac{d \log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{e^2}+\frac{(a+b x) \log \left(c (a+b x)^p\right)}{b e}-\frac{d p \text{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\right)}{e^2}-\frac{p x}{e}",1,"(-(b*e*p*x) + Log[c*(a + b*x)^p]*(a*e + b*e*x - b*d*Log[(b*(d + e*x))/(b*d - a*e)]) - b*d*p*PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)])/(b*e^2)","A",1
222,1,57,58,0.0044668,"\int \frac{\log \left(c (a+b x)^p\right)}{d+e x} \, dx","Integrate[Log[c*(a + b*x)^p]/(d + e*x),x]","\frac{\log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{e}+\frac{p \text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)}{e}","\frac{\log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{e}+\frac{p \text{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\right)}{e}",1,"(Log[c*(a + b*x)^p]*Log[(b*(d + e*x))/(b*d - a*e)])/e + (p*PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)])/e","A",1
223,1,98,97,0.0224364,"\int \frac{\log \left(c (a+b x)^p\right)}{x (d+e x)} \, dx","Integrate[Log[c*(a + b*x)^p]/(x*(d + e*x)),x]","-\frac{\log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{d}+\frac{\log \left(-\frac{b x}{a}\right) \log \left(c (a+b x)^p\right)}{d}-\frac{p \text{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{a+b x}{a}\right)}{d}","-\frac{\log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{d}+\frac{\log \left(-\frac{b x}{a}\right) \log \left(c (a+b x)^p\right)}{d}-\frac{p \text{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{b x}{a}+1\right)}{d}",1,"(Log[-((b*x)/a)]*Log[c*(a + b*x)^p])/d - (Log[c*(a + b*x)^p]*Log[(b*(d + e*x))/(b*d - a*e)])/d + (p*PolyLog[2, (a + b*x)/a])/d - (p*PolyLog[2, -((e*(a + b*x))/(b*d - a*e))])/d","A",1
224,1,139,146,0.0516667,"\int \frac{\log \left(c (a+b x)^p\right)}{x^2 (d+e x)} \, dx","Integrate[Log[c*(a + b*x)^p]/(x^2*(d + e*x)),x]","\frac{a e x \log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)-a d \log \left(c (a+b x)^p\right)-a e x \log \left(-\frac{b x}{a}\right) \log \left(c (a+b x)^p\right)+a e p x \text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)-b d p x \log (a+b x)-a e p x \text{Li}_2\left(\frac{b x}{a}+1\right)+b d p x \log (x)}{a d^2 x}","-\frac{e \log \left(-\frac{b x}{a}\right) \log \left(c (a+b x)^p\right)}{d^2}+\frac{e \log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{d^2}-\frac{\log \left(c (a+b x)^p\right)}{d x}+\frac{e p \text{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\right)}{d^2}-\frac{e p \text{Li}_2\left(\frac{b x}{a}+1\right)}{d^2}+\frac{b p \log (x)}{a d}-\frac{b p \log (a+b x)}{a d}",1,"(b*d*p*x*Log[x] - b*d*p*x*Log[a + b*x] - a*d*Log[c*(a + b*x)^p] - a*e*x*Log[-((b*x)/a)]*Log[c*(a + b*x)^p] + a*e*x*Log[c*(a + b*x)^p]*Log[(b*(d + e*x))/(b*d - a*e)] + a*e*p*x*PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)] - a*e*p*x*PolyLog[2, 1 + (b*x)/a])/(a*d^2*x)","A",1
225,1,188,227,0.1797366,"\int \frac{\log \left(c (a+b x)^p\right)}{x^3 (d+e x)} \, dx","Integrate[Log[c*(a + b*x)^p]/(x^3*(d + e*x)),x]","-\frac{\frac{b d^2 p (-b x \log (a+b x)+a+b x \log (x))}{a^2 x}+\frac{d^2 \log \left(c (a+b x)^p\right)}{x^2}+2 e^2 \log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)-\frac{2 d e \log \left(c (a+b x)^p\right)}{x}-2 e^2 \log \left(-\frac{b x}{a}\right) \log \left(c (a+b x)^p\right)+2 e^2 p \text{Li}_2\left(\frac{e (a+b x)}{a e-b d}\right)+\frac{2 b d e p (\log (x)-\log (a+b x))}{a}-2 e^2 p \text{Li}_2\left(\frac{b x}{a}+1\right)}{2 d^3}","-\frac{b^2 p \log (x)}{2 a^2 d}+\frac{b^2 p \log (a+b x)}{2 a^2 d}+\frac{e^2 \log \left(-\frac{b x}{a}\right) \log \left(c (a+b x)^p\right)}{d^3}-\frac{e^2 \log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e x)}{b d-a e}\right)}{d^3}+\frac{e \log \left(c (a+b x)^p\right)}{d^2 x}-\frac{\log \left(c (a+b x)^p\right)}{2 d x^2}-\frac{e^2 p \text{Li}_2\left(-\frac{e (a+b x)}{b d-a e}\right)}{d^3}+\frac{e^2 p \text{Li}_2\left(\frac{b x}{a}+1\right)}{d^3}-\frac{b e p \log (x)}{a d^2}+\frac{b e p \log (a+b x)}{a d^2}-\frac{b p}{2 a d x}",1,"-1/2*((2*b*d*e*p*(Log[x] - Log[a + b*x]))/a + (b*d^2*p*(a + b*x*Log[x] - b*x*Log[a + b*x]))/(a^2*x) + (d^2*Log[c*(a + b*x)^p])/x^2 - (2*d*e*Log[c*(a + b*x)^p])/x - 2*e^2*Log[-((b*x)/a)]*Log[c*(a + b*x)^p] + 2*e^2*Log[c*(a + b*x)^p]*Log[(b*(d + e*x))/(b*d - a*e)] + 2*e^2*p*PolyLog[2, (e*(a + b*x))/(-(b*d) + a*e)] - 2*e^2*p*PolyLog[2, 1 + (b*x)/a])/d^3","A",1
226,1,338,394,0.3499376,"\int \frac{x^3 \log \left(c \left(a+b x^2\right)^p\right)}{d+e x} \, dx","Integrate[(x^3*Log[c*(a + b*x^2)^p])/(d + e*x),x]","\frac{-4 e^3 p \left(\frac{3 a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}-\frac{3 a x}{b}+x^3\right)-18 d^3 \log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)+18 d^2 e x \log \left(c \left(a+b x^2\right)^p\right)+9 d e^2 \left(p x^2-\frac{\left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b}\right)+6 e^3 x^3 \log \left(c \left(a+b x^2\right)^p\right)+18 d^3 p \left(\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)+\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)+\log (d+e x) \left(\log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)+\log \left(\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{-a} e-\sqrt{b} d}\right)\right)\right)-36 d^2 e p \left(x-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}\right)}{18 e^4}","-\frac{2 a^{3/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{3 b^{3/2} e}-\frac{d^3 \log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)}{e^4}+\frac{d^2 x \log \left(c \left(a+b x^2\right)^p\right)}{e^3}-\frac{d \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 b e^2}+\frac{x^3 \log \left(c \left(a+b x^2\right)^p\right)}{3 e}+\frac{d^3 p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^4}+\frac{d^3 p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)}{e^4}+\frac{d^3 p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)}{e^4}+\frac{d^3 p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^4}+\frac{2 \sqrt{a} d^2 p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b} e^3}+\frac{2 a p x}{3 b e}-\frac{2 d^2 p x}{e^3}+\frac{d p x^2}{2 e^2}-\frac{2 p x^3}{9 e}",1,"(-4*e^3*p*((-3*a*x)/b + x^3 + (3*a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(3/2)) - 36*d^2*e*p*(x - (Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[b]) + 18*d^2*e*x*Log[c*(a + b*x^2)^p] + 6*e^3*x^3*Log[c*(a + b*x^2)^p] - 18*d^3*Log[d + e*x]*Log[c*(a + b*x^2)^p] + 9*d*e^2*(p*x^2 - ((a + b*x^2)*Log[c*(a + b*x^2)^p])/b) + 18*d^3*p*((Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)] + Log[(e*(Sqrt[-a] + Sqrt[b]*x))/(-(Sqrt[b]*d) + Sqrt[-a]*e)])*Log[d + e*x] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)]))/(18*e^4)","A",1
227,1,271,313,0.1697157,"\int \frac{x^2 \log \left(c \left(a+b x^2\right)^p\right)}{d+e x} \, dx","Integrate[(x^2*Log[c*(a + b*x^2)^p])/(d + e*x),x]","\frac{2 d^2 \log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)-2 d e x \log \left(c \left(a+b x^2\right)^p\right)+\frac{e^2 \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b}-2 d^2 p \left(\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)+\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)+\log (d+e x) \left(\log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)+\log \left(\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{-a} e-\sqrt{b} d}\right)\right)\right)+4 d e p \left(x-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}\right)-e^2 p x^2}{2 e^3}","\frac{d^2 \log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)}{e^3}-\frac{d x \log \left(c \left(a+b x^2\right)^p\right)}{e^2}+\frac{\left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 b e}-\frac{d^2 p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^3}-\frac{d^2 p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)}{e^3}-\frac{d^2 p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)}{e^3}-\frac{d^2 p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^3}-\frac{2 \sqrt{a} d p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b} e^2}+\frac{2 d p x}{e^2}-\frac{p x^2}{2 e}",1,"(-(e^2*p*x^2) + 4*d*e*p*(x - (Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[b]) - 2*d*e*x*Log[c*(a + b*x^2)^p] + (e^2*(a + b*x^2)*Log[c*(a + b*x^2)^p])/b + 2*d^2*Log[d + e*x]*Log[c*(a + b*x^2)^p] - 2*d^2*p*((Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)] + Log[(e*(Sqrt[-a] + Sqrt[b]*x))/(-(Sqrt[b]*d) + Sqrt[-a]*e)])*Log[d + e*x] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)]))/(2*e^3)","A",1
228,1,225,256,0.1229061,"\int \frac{x \log \left(c \left(a+b x^2\right)^p\right)}{d+e x} \, dx","Integrate[(x*Log[c*(a + b*x^2)^p])/(d + e*x),x]","\frac{-d \log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)+e x \log \left(c \left(a+b x^2\right)^p\right)+d p \left(\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)+\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)+\log (d+e x) \left(\log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)+\log \left(\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{-a} e-\sqrt{b} d}\right)\right)\right)-2 e p \left(x-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b}}\right)}{e^2}","-\frac{d \log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)}{e^2}+\frac{x \log \left(c \left(a+b x^2\right)^p\right)}{e}+\frac{d p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^2}+\frac{d p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^2}+\frac{2 \sqrt{a} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b} e}-\frac{2 p x}{e}",1,"(-2*e*p*(x - (Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[b]) + e*x*Log[c*(a + b*x^2)^p] - d*Log[d + e*x]*Log[c*(a + b*x^2)^p] + d*p*((Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)] + Log[(e*(Sqrt[-a] + Sqrt[b]*x))/(-(Sqrt[b]*d) + Sqrt[-a]*e)])*Log[d + e*x] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)]))/e^2","A",1
229,1,201,201,0.0255418,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{d+e x} \, dx","Integrate[Log[c*(a + b*x^2)^p]/(d + e*x),x]","\frac{\log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}","\frac{\log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}",1,"-((p*Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)]*Log[d + e*x])/e) - (p*Log[-((e*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*d - Sqrt[-a]*e))]*Log[d + e*x])/e + (Log[d + e*x]*Log[c*(a + b*x^2)^p])/e - (p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)])/e - (p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)])/e","A",1
230,1,232,247,0.0733514,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x (d+e x)} \, dx","Integrate[Log[c*(a + b*x^2)^p]/(x*(d + e*x)),x]","-\frac{\log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)}{d}+\frac{\log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)+p \text{Li}_2\left(\frac{b x^2+a}{a}\right)}{2 d}+\frac{p \left(\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)+\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)+\log (d+e x) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} d-\sqrt{-a} e}\right)\right)}{d}","-\frac{\log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)}{d}+\frac{\log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 d}+\frac{p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)}{d}+\frac{p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)}{d}+\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{b x^2}{a}+1\right)}{2 d}",1,"-((Log[d + e*x]*Log[c*(a + b*x^2)^p])/d) + (p*(Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)]*Log[d + e*x] + Log[-((e*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*d - Sqrt[-a]*e))]*Log[d + e*x] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)]))/d + (Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p] + p*PolyLog[2, (a + b*x^2)/a])/(2*d)","A",1
231,1,268,306,0.2069401,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^2 (d+e x)} \, dx","Integrate[Log[c*(a + b*x^2)^p]/(x^2*(d + e*x)),x]","-\frac{-2 e \log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)+\frac{2 d \log \left(c \left(a+b x^2\right)^p\right)}{x}+e \left(\log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)+p \text{Li}_2\left(\frac{b x^2}{a}+1\right)\right)+2 e p \left(\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)+\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)+\log (d+e x) \left(\log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)+\log \left(\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{-a} e-\sqrt{b} d}\right)\right)\right)-\frac{4 \sqrt{b} d p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a}}}{2 d^2}","-\frac{e \log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 d^2}+\frac{e \log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)}{d^2}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{d x}-\frac{e p \text{Li}_2\left(\frac{b x^2}{a}+1\right)}{2 d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d^2}+\frac{2 \sqrt{b} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} d}",1,"-1/2*((-4*Sqrt[b]*d*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[a] + (2*d*Log[c*(a + b*x^2)^p])/x - 2*e*Log[d + e*x]*Log[c*(a + b*x^2)^p] + 2*e*p*((Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)] + Log[(e*(Sqrt[-a] + Sqrt[b]*x))/(-(Sqrt[b]*d) + Sqrt[-a]*e)])*Log[d + e*x] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)]) + e*(Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p] + p*PolyLog[2, 1 + (b*x^2)/a]))/d^2","A",1
232,1,320,371,0.2226602,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^3 (d+e x)} \, dx","Integrate[Log[c*(a + b*x^2)^p]/(x^3*(d + e*x)),x]","\frac{-\frac{d^2 \log \left(c \left(a+b x^2\right)^p\right)}{x^2}-2 e^2 \log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)+\frac{2 d e \log \left(c \left(a+b x^2\right)^p\right)}{x}+e^2 \left(\log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)+p \text{Li}_2\left(\frac{b x^2}{a}+1\right)\right)+\frac{b d^2 p \left(2 \log (x)-\log \left(a+b x^2\right)\right)}{a}+2 e^2 p \left(\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)+\text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)+\log (d+e x) \left(\log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)+\log \left(\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{-a} e-\sqrt{b} d}\right)\right)\right)-\frac{4 \sqrt{b} d e p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a}}}{2 d^3}","\frac{e^2 \log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 d^3}-\frac{e^2 \log (d+e x) \log \left(c \left(a+b x^2\right)^p\right)}{d^3}+\frac{e \log \left(c \left(a+b x^2\right)^p\right)}{d^2 x}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{2 d x^2}+\frac{e^2 p \text{Li}_2\left(\frac{b x^2}{a}+1\right)}{2 d^3}+\frac{e^2 p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d^3}+\frac{e^2 p \text{Li}_2\left(\frac{\sqrt{b} (d+e x)}{\sqrt{b} d+\sqrt{-a} e}\right)}{d^3}+\frac{e^2 p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} e+\sqrt{b} d}\right)}{d^3}+\frac{e^2 p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d^3}-\frac{2 \sqrt{b} e p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} d^2}-\frac{b p \log \left(a+b x^2\right)}{2 a d}+\frac{b p \log (x)}{a d}",1,"((-4*Sqrt[b]*d*e*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[a] + (b*d^2*p*(2*Log[x] - Log[a + b*x^2]))/a - (d^2*Log[c*(a + b*x^2)^p])/x^2 + (2*d*e*Log[c*(a + b*x^2)^p])/x - 2*e^2*Log[d + e*x]*Log[c*(a + b*x^2)^p] + 2*e^2*p*((Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)] + Log[(e*(Sqrt[-a] + Sqrt[b]*x))/(-(Sqrt[b]*d) + Sqrt[-a]*e)])*Log[d + e*x] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)] + PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)]) + e^2*(Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p] + p*PolyLog[2, 1 + (b*x^2)/a]))/(2*d^3)","A",1
233,1,497,692,0.6498872,"\int \frac{x^3 \log \left(c \left(a+b x^3\right)^p\right)}{d+e x} \, dx","Integrate[(x^3*Log[c*(a + b*x^3)^p])/(d + e*x),x]","-\frac{\frac{6 d^2 e p \left(\sqrt[3]{a} \left(\log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)\right)-2 \sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)+6 \sqrt[3]{b} x\right)}{\sqrt[3]{b}}+12 d^3 \log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)-12 d^2 e x \log \left(c \left(a+b x^3\right)^p\right)+6 d e^2 x^2 \log \left(c \left(a+b x^3\right)^p\right)+\frac{4 e^3 \left(b p x^3-\left(a+b x^3\right) \log \left(c \left(a+b x^3\right)^p\right)\right)}{b}-12 d^3 p \left(\text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)+\text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)+\text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt[3]{-1} \sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)+\log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} e-\sqrt[3]{b} d}\right)+\log (d+e x) \log \left(\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{a} e-\sqrt[3]{b} d}\right)\right)+9 d e^2 p x^2 \left(\, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)-1\right)}{12 e^4}","-\frac{\sqrt[3]{a} d^2 p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \sqrt[3]{b} e^3}-\frac{a^{2/3} d p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{4 b^{2/3} e^2}+\frac{a^{2/3} d p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 b^{2/3} e^2}+\frac{\sqrt{3} a^{2/3} d p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{2 b^{2/3} e^2}-\frac{d^3 \log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{e^4}+\frac{d^2 x \log \left(c \left(a+b x^3\right)^p\right)}{e^3}-\frac{d x^2 \log \left(c \left(a+b x^3\right)^p\right)}{2 e^2}+\frac{\left(a+b x^3\right) \log \left(c \left(a+b x^3\right)^p\right)}{3 b e}+\frac{d^3 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^4}+\frac{d^3 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{e^4}+\frac{d^3 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e^4}+\frac{d^3 p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^4}+\frac{d^3 p \log (d+e x) \log \left(-\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e^4}+\frac{d^3 p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e^4}+\frac{\sqrt[3]{a} d^2 p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} e^3}-\frac{\sqrt{3} \sqrt[3]{a} d^2 p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{b} e^3}-\frac{3 d^2 p x}{e^3}+\frac{3 d p x^2}{4 e^2}-\frac{p x^3}{3 e}",1,"-1/12*(9*d*e^2*p*x^2*(-1 + Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)]) + (6*d^2*e*p*(6*b^(1/3)*x - 2*a^(1/3)*Log[a^(1/3) + b^(1/3)*x] + a^(1/3)*(2*Sqrt[3]*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]] + Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])))/b^(1/3) - 12*d^2*e*x*Log[c*(a + b*x^3)^p] + 6*d*e^2*x^2*Log[c*(a + b*x^3)^p] + 12*d^3*Log[d + e*x]*Log[c*(a + b*x^3)^p] + (4*e^3*(b*p*x^3 - (a + b*x^3)*Log[c*(a + b*x^3)^p]))/b - 12*d^3*p*(Log[(e*((-1)^(1/3)*a^(1/3) - b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)]*Log[d + e*x] + Log[(e*(a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*d) + a^(1/3)*e)]*Log[d + e*x] + Log[(e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*d) + (-1)^(2/3)*a^(1/3)*e)]*Log[d + e*x] + PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)] + PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)] + PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)]))/e^4","C",1
234,1,504,643,0.4126387,"\int \frac{x^2 \log \left(c \left(a+b x^3\right)^p\right)}{d+e x} \, dx","Integrate[(x^2*Log[c*(a + b*x^3)^p])/(d + e*x),x]","-\frac{-\frac{2 \sqrt[3]{a} d e p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{\sqrt[3]{b}}-4 d^2 \log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)+4 d e x \log \left(c \left(a+b x^3\right)^p\right)-2 e^2 x^2 \log \left(c \left(a+b x^3\right)^p\right)+4 d^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)+4 d^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)+4 d^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)+4 d^2 p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{-1} \sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)+4 d^2 p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} e-\sqrt[3]{b} d}\right)+4 d^2 p \log (d+e x) \log \left(\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{a} e-\sqrt[3]{b} d}\right)+\frac{4 \sqrt[3]{a} d e p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{4 \sqrt{3} \sqrt[3]{a} d e p \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{\sqrt[3]{b}}-3 e^2 p x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)-12 d e p x+3 e^2 p x^2}{4 e^3}","\frac{\sqrt[3]{a} d p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \sqrt[3]{b} e^2}+\frac{a^{2/3} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{4 b^{2/3} e}-\frac{a^{2/3} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 b^{2/3} e}-\frac{\sqrt{3} a^{2/3} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{2 b^{2/3} e}+\frac{d^2 \log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{e^3}-\frac{d x \log \left(c \left(a+b x^3\right)^p\right)}{e^2}+\frac{x^2 \log \left(c \left(a+b x^3\right)^p\right)}{2 e}-\frac{d^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^3}-\frac{d^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{e^3}-\frac{d^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e^3}-\frac{d^2 p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^3}-\frac{d^2 p \log (d+e x) \log \left(-\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e^3}-\frac{d^2 p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e^3}-\frac{\sqrt[3]{a} d p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} e^2}+\frac{\sqrt{3} \sqrt[3]{a} d p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{b} e^2}+\frac{3 d p x}{e^2}-\frac{3 p x^2}{4 e}",1,"-1/4*(-12*d*e*p*x + 3*e^2*p*x^2 - (4*Sqrt[3]*a^(1/3)*d*e*p*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/b^(1/3) - 3*e^2*p*x^2*Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)] + (4*a^(1/3)*d*e*p*Log[a^(1/3) + b^(1/3)*x])/b^(1/3) + 4*d^2*p*Log[(e*((-1)^(1/3)*a^(1/3) - b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)]*Log[d + e*x] + 4*d^2*p*Log[(e*(a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*d) + a^(1/3)*e)]*Log[d + e*x] + 4*d^2*p*Log[(e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*d) + (-1)^(2/3)*a^(1/3)*e)]*Log[d + e*x] - (2*a^(1/3)*d*e*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/b^(1/3) + 4*d*e*x*Log[c*(a + b*x^3)^p] - 2*e^2*x^2*Log[c*(a + b*x^3)^p] - 4*d^2*Log[d + e*x]*Log[c*(a + b*x^3)^p] + 4*d^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)] + 4*d^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)] + 4*d^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)])/e^3","C",1
235,1,430,457,0.2147039,"\int \frac{x \log \left(c \left(a+b x^3\right)^p\right)}{d+e x} \, dx","Integrate[(x*Log[c*(a + b*x^3)^p])/(d + e*x),x]","\frac{-\frac{\sqrt[3]{a} e p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{\sqrt[3]{b}}-2 d \log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)+2 e x \log \left(c \left(a+b x^3\right)^p\right)+2 d p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)+2 d p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)+2 d p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)+2 d p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{-1} \sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)+2 d p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} e-\sqrt[3]{b} d}\right)+2 d p \log (d+e x) \log \left(\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{a} e-\sqrt[3]{b} d}\right)+\frac{2 \sqrt[3]{a} e p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b}}-\frac{2 \sqrt{3} \sqrt[3]{a} e p \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{\sqrt[3]{b}}-6 e p x}{2 e^2}","-\frac{\sqrt[3]{a} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \sqrt[3]{b} e}-\frac{d \log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{e^2}+\frac{x \log \left(c \left(a+b x^3\right)^p\right)}{e}+\frac{d p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^2}+\frac{d p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{e^2}+\frac{d p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(-\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e^2}+\frac{\sqrt[3]{a} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} e}-\frac{\sqrt{3} \sqrt[3]{a} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{b} e}-\frac{3 p x}{e}",1,"(-6*e*p*x - (2*Sqrt[3]*a^(1/3)*e*p*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/b^(1/3) + (2*a^(1/3)*e*p*Log[a^(1/3) + b^(1/3)*x])/b^(1/3) + 2*d*p*Log[(e*((-1)^(1/3)*a^(1/3) - b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)]*Log[d + e*x] + 2*d*p*Log[(e*(a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*d) + a^(1/3)*e)]*Log[d + e*x] + 2*d*p*Log[(e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*d) + (-1)^(2/3)*a^(1/3)*e)]*Log[d + e*x] - (a^(1/3)*e*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/b^(1/3) + 2*e*x*Log[c*(a + b*x^3)^p] - 2*d*Log[d + e*x]*Log[c*(a + b*x^3)^p] + 2*d*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)] + 2*d*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)] + 2*d*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)])/(2*e^2)","A",1
236,1,313,308,0.0565762,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{d+e x} \, dx","Integrate[Log[c*(a + b*x^3)^p]/(d + e*x),x]","\frac{\log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{(-1)^{2/3} e \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e}","\frac{\log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e}",1,"-((p*Log[-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e))]*Log[d + e*x])/e) - (p*Log[-(((-1)^(2/3)*e*(a^(1/3) - (-1)^(1/3)*b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e))]*Log[d + e*x])/e - (p*Log[((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)]*Log[d + e*x])/e + (Log[d + e*x]*Log[c*(a + b*x^3)^p])/e - (p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)])/e - (p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)])/e - (p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)])/e","A",1
237,1,358,352,0.0558191,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x (d+e x)} \, dx","Integrate[Log[c*(a + b*x^3)^p]/(x*(d + e*x)),x]","-\frac{\log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{d}+\frac{\log \left(-\frac{b x^3}{a}\right) \log \left(c \left(a+b x^3\right)^p\right)}{3 d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d}+\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d}+\frac{p \log (d+e x) \log \left(-\frac{(-1)^{2/3} e \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d}+\frac{p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{d}+\frac{p \text{Li}_2\left(\frac{b x^3+a}{a}\right)}{3 d}","-\frac{\log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{d}+\frac{\log \left(-\frac{b x^3}{a}\right) \log \left(c \left(a+b x^3\right)^p\right)}{3 d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d}+\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d}+\frac{p \log (d+e x) \log \left(-\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d}+\frac{p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{d}+\frac{p \text{Li}_2\left(\frac{b x^3}{a}+1\right)}{3 d}",1,"(p*Log[-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e))]*Log[d + e*x])/d + (p*Log[-(((-1)^(2/3)*e*(a^(1/3) - (-1)^(1/3)*b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e))]*Log[d + e*x])/d + (p*Log[((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)]*Log[d + e*x])/d + (Log[-((b*x^3)/a)]*Log[c*(a + b*x^3)^p])/(3*d) - (Log[d + e*x]*Log[c*(a + b*x^3)^p])/d + (p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)])/d + (p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)])/d + (p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)])/d + (p*PolyLog[2, (a + b*x^3)/a])/(3*d)","A",1
238,1,424,510,0.0682012,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^2 (d+e x)} \, dx","Integrate[Log[c*(a + b*x^3)^p]/(x^2*(d + e*x)),x]","-\frac{e \log \left(-\frac{b x^3}{a}\right) \log \left(c \left(a+b x^3\right)^p\right)}{3 d^2}+\frac{e \log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{d^2}-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{d x}-\frac{e p \text{Li}_2\left(\frac{b x^3+a}{a}\right)}{3 d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(-\frac{(-1)^{2/3} e \left(\sqrt[3]{a}-\sqrt[3]{-1} \sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{d^2}+\frac{3 b p x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)}{2 a d}","\frac{\sqrt[3]{b} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \sqrt[3]{a} d}-\frac{e \log \left(-\frac{b x^3}{a}\right) \log \left(c \left(a+b x^3\right)^p\right)}{3 d^2}+\frac{e \log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{d^2}-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{d x}-\frac{e p \text{Li}_2\left(\frac{b x^3}{a}+1\right)}{3 d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(-\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{d^2}-\frac{\sqrt[3]{b} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} d}-\frac{\sqrt{3} \sqrt[3]{b} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a} d}",1,"(3*b*p*x^2*Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)])/(2*a*d) - (e*p*Log[-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e))]*Log[d + e*x])/d^2 - (e*p*Log[-(((-1)^(2/3)*e*(a^(1/3) - (-1)^(1/3)*b^(1/3)*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e))]*Log[d + e*x])/d^2 - (e*p*Log[((-1)^(1/3)*e*(a^(1/3) + (-1)^(2/3)*b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)]*Log[d + e*x])/d^2 - Log[c*(a + b*x^3)^p]/(d*x) - (e*Log[-((b*x^3)/a)]*Log[c*(a + b*x^3)^p])/(3*d^2) + (e*Log[d + e*x]*Log[c*(a + b*x^3)^p])/d^2 - (e*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)])/d^2 - (e*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)])/d^2 - (e*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)])/d^2 - (e*p*PolyLog[2, (a + b*x^3)/a])/(3*d^2)","C",1
239,1,542,674,0.3925213,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^3 (d+e x)} \, dx","Integrate[Log[c*(a + b*x^3)^p]/(x^3*(d + e*x)),x]","\frac{-\frac{3 b^{2/3} d^2 p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{a^{2/3}}+\frac{6 b^{2/3} d^2 p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{a^{2/3}}-\frac{6 \sqrt{3} b^{2/3} d^2 p \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a}}}{\sqrt{3}}\right)}{a^{2/3}}-\frac{6 d^2 \log \left(c \left(a+b x^3\right)^p\right)}{x^2}-12 e^2 \log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)+\frac{12 d e \log \left(c \left(a+b x^3\right)^p\right)}{x}+4 e^2 \log \left(-\frac{b x^3}{a}\right) \log \left(c \left(a+b x^3\right)^p\right)+12 e^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)+12 e^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)+12 e^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)+12 e^2 p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{-1} \sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)+12 e^2 p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} e-\sqrt[3]{b} d}\right)+12 e^2 p \log (d+e x) \log \left(\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{(-1)^{2/3} \sqrt[3]{a} e-\sqrt[3]{b} d}\right)-\frac{18 b d e p x^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a}\right)}{a}+4 e^2 p \text{Li}_2\left(\frac{b x^3}{a}+1\right)}{12 d^3}","-\frac{\sqrt[3]{b} e p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{2 \sqrt[3]{a} d^2}-\frac{b^{2/3} p \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{4 a^{2/3} d}+\frac{b^{2/3} p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 a^{2/3} d}-\frac{\sqrt{3} b^{2/3} p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{2 a^{2/3} d}+\frac{e^2 \log \left(-\frac{b x^3}{a}\right) \log \left(c \left(a+b x^3\right)^p\right)}{3 d^3}-\frac{e^2 \log (d+e x) \log \left(c \left(a+b x^3\right)^p\right)}{d^3}+\frac{e \log \left(c \left(a+b x^3\right)^p\right)}{d^2 x}-\frac{\log \left(c \left(a+b x^3\right)^p\right)}{2 d x^2}+\frac{e^2 p \text{Li}_2\left(\frac{b x^3}{a}+1\right)}{3 d^3}+\frac{e^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d^3}+\frac{e^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d+\sqrt[3]{-1} \sqrt[3]{a} e}\right)}{d^3}+\frac{e^2 p \text{Li}_2\left(\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d^3}+\frac{e^2 p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d^3}+\frac{e^2 p \log (d+e x) \log \left(-\frac{e \left((-1)^{2/3} \sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d^3}+\frac{e^2 p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left(\sqrt[3]{a}+(-1)^{2/3} \sqrt[3]{b} x\right)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{d^3}+\frac{\sqrt[3]{b} e p \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a} d^2}+\frac{\sqrt{3} \sqrt[3]{b} e p \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt[3]{a} d^2}",1,"((-6*Sqrt[3]*b^(2/3)*d^2*p*ArcTan[(1 - (2*b^(1/3)*x)/a^(1/3))/Sqrt[3]])/a^(2/3) - (18*b*d*e*p*x^2*Hypergeometric2F1[2/3, 1, 5/3, -((b*x^3)/a)])/a + (6*b^(2/3)*d^2*p*Log[a^(1/3) + b^(1/3)*x])/a^(2/3) + 12*e^2*p*Log[(e*((-1)^(1/3)*a^(1/3) - b^(1/3)*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)]*Log[d + e*x] + 12*e^2*p*Log[(e*(a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*d) + a^(1/3)*e)]*Log[d + e*x] + 12*e^2*p*Log[(e*((-1)^(2/3)*a^(1/3) + b^(1/3)*x))/(-(b^(1/3)*d) + (-1)^(2/3)*a^(1/3)*e)]*Log[d + e*x] - (3*b^(2/3)*d^2*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/a^(2/3) - (6*d^2*Log[c*(a + b*x^3)^p])/x^2 + (12*d*e*Log[c*(a + b*x^3)^p])/x + 4*e^2*Log[-((b*x^3)/a)]*Log[c*(a + b*x^3)^p] - 12*e^2*Log[d + e*x]*Log[c*(a + b*x^3)^p] + 12*e^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)] + 12*e^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)] + 12*e^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)] + 4*e^2*p*PolyLog[2, 1 + (b*x^3)/a])/(12*d^3)","C",1
240,1,251,297,0.228171,"\int \frac{x^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d+e x} \, dx","Integrate[(x^3*Log[c*(a + b/x)^p])/(d + e*x),x]","\frac{\frac{b e^3 p \left(2 b^2 \log \left(a+\frac{b}{x}\right)+a x (a x-2 b)+2 b^2 \log (x)\right)}{a^3}+\frac{3 b d e^2 p (b \log (a x+b)-a x)}{a^2}-6 d^3 \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)+6 d^2 e x \log \left(c \left(a+\frac{b}{x}\right)^p\right)-3 d e^2 x^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+2 e^3 x^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right)-6 d^3 p \left(-\text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)+\log (d+e x) \left(\log \left(-\frac{e x}{d}\right)-\log \left(\frac{e (a x+b)}{b e-a d}\right)\right)+\text{Li}_2\left(\frac{e x}{d}+1\right)\right)+\frac{6 b d^2 e p \left(\log \left(a+\frac{b}{x}\right)+\log (x)\right)}{a}}{6 e^4}","\frac{b^3 p \log (a x+b)}{3 a^3 e}+\frac{b^2 d p \log (a x+b)}{2 a^2 e^2}-\frac{b^2 p x}{3 a^2 e}-\frac{d^3 \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e^4}+\frac{d^2 x \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e^3}-\frac{d x^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{2 e^2}+\frac{x^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{3 e}+\frac{d^3 p \text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)}{e^4}+\frac{d^3 p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{e^4}+\frac{b d^2 p \log (a x+b)}{a e^3}-\frac{b d p x}{2 a e^2}+\frac{b p x^2}{6 a e}-\frac{d^3 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e^4}-\frac{d^3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^4}",1,"(6*d^2*e*x*Log[c*(a + b/x)^p] - 3*d*e^2*x^2*Log[c*(a + b/x)^p] + 2*e^3*x^3*Log[c*(a + b/x)^p] + (6*b*d^2*e*p*(Log[a + b/x] + Log[x]))/a + (b*e^3*p*(a*x*(-2*b + a*x) + 2*b^2*Log[a + b/x] + 2*b^2*Log[x]))/a^3 + (3*b*d*e^2*p*(-(a*x) + b*Log[b + a*x]))/a^2 - 6*d^3*Log[c*(a + b/x)^p]*Log[d + e*x] - 6*d^3*p*((Log[-((e*x)/d)] - Log[(e*(b + a*x))/(-(a*d) + b*e)])*Log[d + e*x] - PolyLog[2, (a*(d + e*x))/(a*d - b*e)] + PolyLog[2, 1 + (e*x)/d]))/(6*e^4)","A",1
241,1,183,219,0.1341377,"\int \frac{x^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d+e x} \, dx","Integrate[(x^2*Log[c*(a + b/x)^p])/(d + e*x),x]","\frac{\frac{b e^2 p (a x-b \log (a x+b))}{a^2}+2 d^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)-2 d e x \log \left(c \left(a+\frac{b}{x}\right)^p\right)+e^2 x^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+2 d^2 p \left(-\text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)+\log (d+e x) \left(\log \left(-\frac{e x}{d}\right)-\log \left(\frac{e (a x+b)}{b e-a d}\right)\right)+\text{Li}_2\left(\frac{e x}{d}+1\right)\right)-\frac{2 b d e p \left(\log \left(a+\frac{b}{x}\right)+\log (x)\right)}{a}}{2 e^3}","-\frac{b^2 p \log (a x+b)}{2 a^2 e}+\frac{d^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e^3}-\frac{d x \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e^2}+\frac{x^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{2 e}-\frac{d^2 p \text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)}{e^3}-\frac{d^2 p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{e^3}-\frac{b d p \log (a x+b)}{a e^2}+\frac{b p x}{2 a e}+\frac{d^2 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e^3}+\frac{d^2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^3}",1,"(-2*d*e*x*Log[c*(a + b/x)^p] + e^2*x^2*Log[c*(a + b/x)^p] - (2*b*d*e*p*(Log[a + b/x] + Log[x]))/a + (b*e^2*p*(a*x - b*Log[b + a*x]))/a^2 + 2*d^2*Log[c*(a + b/x)^p]*Log[d + e*x] + 2*d^2*p*((Log[-((e*x)/d)] - Log[(e*(b + a*x))/(-(a*d) + b*e)])*Log[d + e*x] - PolyLog[2, (a*(d + e*x))/(a*d - b*e)] + PolyLog[2, 1 + (e*x)/d]))/(2*e^3)","A",1
242,1,149,151,0.0593063,"\int \frac{x \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d+e x} \, dx","Integrate[(x*Log[c*(a + b/x)^p])/(d + e*x),x]","-\frac{d \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e^2}+\frac{x \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e}-\frac{d p \left(-\text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)-\log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)+\text{Li}_2\left(\frac{d+e x}{d}\right)+\log \left(-\frac{e x}{d}\right) \log (d+e x)\right)}{e^2}+\frac{b p \left(\frac{\log \left(a+\frac{b}{x}\right)}{a}+\frac{\log (x)}{a}\right)}{e}","-\frac{d \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e^2}+\frac{x \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e}+\frac{d p \text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{e^2}+\frac{b p \log (a x+b)}{a e}-\frac{d p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e^2}-\frac{d p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^2}",1,"(x*Log[c*(a + b/x)^p])/e + (b*p*(Log[a + b/x]/a + Log[x]/a))/e - (d*Log[c*(a + b/x)^p]*Log[d + e*x])/e^2 - (d*p*(Log[-((e*x)/d)]*Log[d + e*x] - Log[-((e*(b + a*x))/(a*d - b*e))]*Log[d + e*x] + PolyLog[2, (d + e*x)/d] - PolyLog[2, (a*(d + e*x))/(a*d - b*e)]))/e^2","A",1
243,1,114,113,0.0185708,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d+e x} \, dx","Integrate[Log[c*(a + b/x)^p]/(d + e*x),x]","\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{e}+\frac{p \text{Li}_2\left(\frac{d+e x}{d}\right)}{e}+\frac{p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}","\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{e}+\frac{p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e}+\frac{p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}",1,"(Log[c*(a + b/x)^p]*Log[d + e*x])/e + (p*Log[-((e*x)/d)]*Log[d + e*x])/e - (p*Log[-((e*(b + a*x))/(a*d - b*e))]*Log[d + e*x])/e + (p*PolyLog[2, (d + e*x)/d])/e - (p*PolyLog[2, (a*(d + e*x))/(a*d - b*e)])/e","A",1
244,1,139,159,0.061366,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x (d+e x)} \, dx","Integrate[Log[c*(a + b/x)^p]/(x*(d + e*x)),x]","-\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\log \left(-\frac{b}{a x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)-p \text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)-p \log (d+e x) \log \left(\frac{e (a x+b)}{b e-a d}\right)+p \text{Li}_2\left(\frac{b}{a x}+1\right)+p \text{Li}_2\left(\frac{e x}{d}+1\right)+p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d}","-\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d}-\frac{\log \left(-\frac{b}{a x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d}+\frac{p \text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)}{d}+\frac{p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{d}-\frac{p \text{Li}_2\left(\frac{b}{a x}+1\right)}{d}-\frac{p \text{Li}_2\left(\frac{e x}{d}+1\right)}{d}-\frac{p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d}",1,"-((Log[c*(a + b/x)^p]*Log[-(b/(a*x))] + Log[c*(a + b/x)^p]*Log[d + e*x] + p*Log[-((e*x)/d)]*Log[d + e*x] - p*Log[(e*(b + a*x))/(-(a*d) + b*e)]*Log[d + e*x] + p*PolyLog[2, 1 + b/(a*x)] - p*PolyLog[2, (a*(d + e*x))/(a*d - b*e)] + p*PolyLog[2, 1 + (e*x)/d])/d)","A",1
245,1,166,198,0.096926,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^2 (d+e x)} \, dx","Integrate[Log[c*(a + b/x)^p]/(x^2*(d + e*x)),x]","\frac{e \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)-\frac{d \left(a+\frac{b}{x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{b}+e \log \left(-\frac{b}{a x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)+e p \left(-\text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)+\log (d+e x) \left(\log \left(-\frac{e x}{d}\right)-\log \left(\frac{e (a x+b)}{b e-a d}\right)\right)+\text{Li}_2\left(\frac{e x}{d}+1\right)\right)+e p \text{Li}_2\left(\frac{b}{a x}+1\right)+\frac{d p}{x}}{d^2}","\frac{e \log \left(-\frac{b}{a x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d^2}+\frac{e \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d^2}-\frac{\left(a+\frac{b}{x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{b d}+\frac{e p \text{Li}_2\left(\frac{b}{a x}+1\right)}{d^2}-\frac{e p \text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{d^2}+\frac{e p \text{Li}_2\left(\frac{e x}{d}+1\right)}{d^2}+\frac{e p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^2}+\frac{p}{d x}",1,"((d*p)/x - (d*(a + b/x)*Log[c*(a + b/x)^p])/b + e*Log[c*(a + b/x)^p]*Log[-(b/(a*x))] + e*Log[c*(a + b/x)^p]*Log[d + e*x] + e*p*PolyLog[2, 1 + b/(a*x)] + e*p*((Log[-((e*x)/d)] - Log[(e*(b + a*x))/(-(a*d) + b*e)])*Log[d + e*x] - PolyLog[2, (a*(d + e*x))/(a*d - b*e)] + PolyLog[2, 1 + (e*x)/d]))/d^2","A",1
246,1,241,287,0.2372405,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^3 (d+e x)} \, dx","Integrate[Log[c*(a + b/x)^p]/(x^3*(d + e*x)),x]","-\frac{-\frac{d^2 p \left(2 a^2 x^2 \log \left(a+\frac{b}{x}\right)+b (b-2 a x)\right)}{b^2 x^2}+\frac{2 d^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^2}+4 e^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)-\frac{4 d e \left(a+\frac{b}{x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{b}+4 e^2 \log \left(-\frac{b}{a x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)+4 e^2 p \left(-\text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)+\log (d+e x) \left(\log \left(-\frac{e x}{d}\right)-\log \left(\frac{e (a x+b)}{b e-a d}\right)\right)+\text{Li}_2\left(\frac{e x}{d}+1\right)\right)+4 e^2 p \text{Li}_2\left(\frac{b}{a x}+1\right)+\frac{4 d e p}{x}}{4 d^3}","\frac{a^2 p \log \left(a+\frac{b}{x}\right)}{2 b^2 d}-\frac{e^2 \log \left(-\frac{b}{a x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d^3}-\frac{e^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d^3}+\frac{e \left(a+\frac{b}{x}\right) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{b d^2}-\frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{2 d x^2}-\frac{e^2 p \text{Li}_2\left(\frac{b}{a x}+1\right)}{d^3}+\frac{e^2 p \text{Li}_2\left(\frac{a (d+e x)}{a d-b e}\right)}{d^3}+\frac{e^2 p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{d^3}-\frac{a p}{2 b d x}-\frac{e^2 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{d^3}-\frac{e^2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^3}-\frac{e p}{d^2 x}+\frac{p}{4 d x^2}",1,"-1/4*((4*d*e*p)/x - (d^2*p*(b*(b - 2*a*x) + 2*a^2*x^2*Log[a + b/x]))/(b^2*x^2) - (4*d*e*(a + b/x)*Log[c*(a + b/x)^p])/b + (2*d^2*Log[c*(a + b/x)^p])/x^2 + 4*e^2*Log[c*(a + b/x)^p]*Log[-(b/(a*x))] + 4*e^2*Log[c*(a + b/x)^p]*Log[d + e*x] + 4*e^2*p*PolyLog[2, 1 + b/(a*x)] + 4*e^2*p*((Log[-((e*x)/d)] - Log[(e*(b + a*x))/(-(a*d) + b*e)])*Log[d + e*x] - PolyLog[2, (a*(d + e*x))/(a*d - b*e)] + PolyLog[2, 1 + (e*x)/d]))/d^3","A",1
247,1,375,421,0.4400305,"\int \frac{x^3 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d+e x} \, dx","Integrate[(x^3*Log[c*(a + b/x^2)^p])/(d + e*x),x]","-\frac{6 d^3 \log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)-6 d^2 e x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+3 d e^2 x^2 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)-2 e^3 x^3 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+6 d^3 p \left(-\text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)-\text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)-\log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)-\log (d+e x) \log \left(\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{b} e-\sqrt{-a} d}\right)+2 \text{Li}_2\left(\frac{e x}{d}+1\right)+2 \log \left(-\frac{e x}{d}\right) \log (d+e x)\right)+\frac{12 \sqrt{b} d^2 e p \tan ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} x}\right)}{\sqrt{a}}+\frac{3 b d e^2 p \left(\log \left(a+\frac{b}{x^2}\right)+2 \log (x)\right)}{a}-\frac{4 b e^3 p x \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{b}{a x^2}\right)}{a}}{6 e^4}","-\frac{2 b^{3/2} p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{3 a^{3/2} e}-\frac{d^3 \log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{e^4}+\frac{d^2 x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{e^3}-\frac{d x^2 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{2 e^2}+\frac{x^3 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{3 e}+\frac{d^3 p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^4}+\frac{d^3 p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^4}+\frac{d^3 p \log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^4}+\frac{d^3 p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^4}+\frac{2 \sqrt{b} d^2 p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{\sqrt{a} e^3}-\frac{b d p \log \left(a x^2+b\right)}{2 a e^2}+\frac{2 b p x}{3 a e}-\frac{2 d^3 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e^4}-\frac{2 d^3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^4}",1,"-1/6*((12*Sqrt[b]*d^2*e*p*ArcTan[Sqrt[b]/(Sqrt[a]*x)])/Sqrt[a] - (4*b*e^3*p*x*Hypergeometric2F1[-1/2, 1, 1/2, -(b/(a*x^2))])/a - 6*d^2*e*x*Log[c*(a + b/x^2)^p] + 3*d*e^2*x^2*Log[c*(a + b/x^2)^p] - 2*e^3*x^3*Log[c*(a + b/x^2)^p] + (3*b*d*e^2*p*(Log[a + b/x^2] + 2*Log[x]))/a + 6*d^3*Log[c*(a + b/x^2)^p]*Log[d + e*x] + 6*d^3*p*(2*Log[-((e*x)/d)]*Log[d + e*x] - Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x] - Log[(e*(Sqrt[b] + Sqrt[-a]*x))/(-(Sqrt[-a]*d) + Sqrt[b]*e)]*Log[d + e*x] - PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)] - PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)] + 2*PolyLog[2, 1 + (e*x)/d]))/e^4","C",1
248,1,319,353,0.2323017,"\int \frac{x^2 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d+e x} \, dx","Integrate[(x^2*Log[c*(a + b/x^2)^p])/(d + e*x),x]","\frac{2 d^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)-2 d e x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+e^2 x^2 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+2 d^2 p \left(-\text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)-\text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)-\log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)-\log (d+e x) \log \left(\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{b} e-\sqrt{-a} d}\right)+2 \text{Li}_2\left(\frac{e x}{d}+1\right)+2 \log \left(-\frac{e x}{d}\right) \log (d+e x)\right)+\frac{4 \sqrt{b} d e p \tan ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} x}\right)}{\sqrt{a}}+\frac{b e^2 p \left(\log \left(a+\frac{b}{x^2}\right)+2 \log (x)\right)}{a}}{2 e^3}","\frac{d^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{e^3}-\frac{d x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{e^2}+\frac{x^2 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{2 e}-\frac{d^2 p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^3}-\frac{d^2 p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^3}-\frac{d^2 p \log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^3}-\frac{d^2 p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^3}-\frac{2 \sqrt{b} d p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{\sqrt{a} e^2}+\frac{b p \log \left(a x^2+b\right)}{2 a e}+\frac{2 d^2 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e^3}+\frac{2 d^2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^3}",1,"((4*Sqrt[b]*d*e*p*ArcTan[Sqrt[b]/(Sqrt[a]*x)])/Sqrt[a] - 2*d*e*x*Log[c*(a + b/x^2)^p] + e^2*x^2*Log[c*(a + b/x^2)^p] + (b*e^2*p*(Log[a + b/x^2] + 2*Log[x]))/a + 2*d^2*Log[c*(a + b/x^2)^p]*Log[d + e*x] + 2*d^2*p*(2*Log[-((e*x)/d)]*Log[d + e*x] - Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x] - Log[(e*(Sqrt[b] + Sqrt[-a]*x))/(-(Sqrt[-a]*d) + Sqrt[b]*e)]*Log[d + e*x] - PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)] - PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)] + 2*PolyLog[2, 1 + (e*x)/d]))/(2*e^3)","A",1
249,1,271,291,0.1670557,"\int \frac{x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d+e x} \, dx","Integrate[(x*Log[c*(a + b/x^2)^p])/(d + e*x),x]","\frac{-d \log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+e x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+d p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)+d p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)+d p \log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)+d p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{b} e-\sqrt{-a} d}\right)-\frac{2 \sqrt{b} e p \tan ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} x}\right)}{\sqrt{a}}-2 d p \text{Li}_2\left(\frac{e x}{d}+1\right)-2 d p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^2}","-\frac{d \log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{e^2}+\frac{x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{e}+\frac{d p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^2}+\frac{d p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^2}+\frac{2 \sqrt{b} p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{\sqrt{a} e}-\frac{2 d p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e^2}-\frac{2 d p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^2}",1,"((-2*Sqrt[b]*e*p*ArcTan[Sqrt[b]/(Sqrt[a]*x)])/Sqrt[a] + e*x*Log[c*(a + b/x^2)^p] - d*Log[c*(a + b/x^2)^p]*Log[d + e*x] - 2*d*p*Log[-((e*x)/d)]*Log[d + e*x] + d*p*Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x] + d*p*Log[(e*(Sqrt[b] + Sqrt[-a]*x))/(-(Sqrt[-a]*d) + Sqrt[b]*e)]*Log[d + e*x] + d*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)] + d*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)] - 2*d*p*PolyLog[2, 1 + (e*x)/d])/e^2","A",1
250,1,242,241,0.060803,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d+e x} \, dx","Integrate[Log[c*(a + b/x^2)^p]/(d + e*x),x]","\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e}+\frac{2 p \text{Li}_2\left(\frac{d+e x}{d}\right)}{e}+\frac{2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}","\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e}+\frac{2 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e}+\frac{2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}",1,"(Log[c*(a + b/x^2)^p]*Log[d + e*x])/e + (2*p*Log[-((e*x)/d)]*Log[d + e*x])/e - (p*Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x])/e - (p*Log[-((e*(Sqrt[b] + Sqrt[-a]*x))/(Sqrt[-a]*d - Sqrt[b]*e))]*Log[d + e*x])/e + (2*p*PolyLog[2, (d + e*x)/d])/e - (p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)])/e - (p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)])/e","A",1
251,1,264,287,0.1221774,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x (d+e x)} \, dx","Integrate[Log[c*(a + b/x^2)^p]/(x*(d + e*x)),x]","-\frac{2 \log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+\log \left(-\frac{b}{a x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)-2 p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)-2 p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)-2 p \log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)-2 p \log (d+e x) \log \left(\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{b} e-\sqrt{-a} d}\right)+p \text{Li}_2\left(\frac{b}{a x^2}+1\right)+4 p \text{Li}_2\left(\frac{e x}{d}+1\right)+4 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{2 d}","-\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d}-\frac{\log \left(-\frac{b}{a x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{2 d}+\frac{p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d}+\frac{p \log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d}+\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d}-\frac{p \text{Li}_2\left(\frac{b}{a x^2}+1\right)}{2 d}-\frac{2 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{d}-\frac{2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d}",1,"-1/2*(Log[c*(a + b/x^2)^p]*Log[-(b/(a*x^2))] + 2*Log[c*(a + b/x^2)^p]*Log[d + e*x] + 4*p*Log[-((e*x)/d)]*Log[d + e*x] - 2*p*Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x] - 2*p*Log[(e*(Sqrt[b] + Sqrt[-a]*x))/(-(Sqrt[-a]*d) + Sqrt[b]*e)]*Log[d + e*x] + p*PolyLog[2, 1 + b/(a*x^2)] - 2*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)] - 2*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)] + 4*p*PolyLog[2, 1 + (e*x)/d])/d","A",1
252,1,320,357,0.2079536,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x^2 (d+e x)} \, dx","Integrate[Log[c*(a + b/x^2)^p]/(x^2*(d + e*x)),x]","\frac{2 e \log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)-\frac{2 d \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x}+e \left(\log \left(-\frac{b}{a x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+p \text{Li}_2\left(\frac{b}{a x^2}+1\right)\right)+2 e p \left(-\text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)-\text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)-\log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)-\log (d+e x) \log \left(\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{b} e-\sqrt{-a} d}\right)+2 \text{Li}_2\left(\frac{e x}{d}+1\right)+2 \log \left(-\frac{e x}{d}\right) \log (d+e x)\right)+4 d p \left(\frac{1}{x}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} x}\right)}{\sqrt{b}}\right)}{2 d^2}","\frac{e \log \left(-\frac{b}{a x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{2 d^2}+\frac{e \log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d^2}-\frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d x}+\frac{e p \text{Li}_2\left(\frac{b}{a x^2}+1\right)}{2 d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d^2}+\frac{2 \sqrt{a} p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{\sqrt{b} d}+\frac{2 e p \text{Li}_2\left(\frac{e x}{d}+1\right)}{d^2}+\frac{2 e p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^2}+\frac{2 p}{d x}",1,"(4*d*p*(x^(-1) - (Sqrt[a]*ArcTan[Sqrt[b]/(Sqrt[a]*x)])/Sqrt[b]) - (2*d*Log[c*(a + b/x^2)^p])/x + 2*e*Log[c*(a + b/x^2)^p]*Log[d + e*x] + e*(Log[c*(a + b/x^2)^p]*Log[-(b/(a*x^2))] + p*PolyLog[2, 1 + b/(a*x^2)]) + 2*e*p*(2*Log[-((e*x)/d)]*Log[d + e*x] - Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x] - Log[(e*(Sqrt[b] + Sqrt[-a]*x))/(-(Sqrt[-a]*d) + Sqrt[b]*e)]*Log[d + e*x] - PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)] - PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)] + 2*PolyLog[2, 1 + (e*x)/d]))/(2*d^2)","A",1
253,1,364,414,0.2974607,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x^3 (d+e x)} \, dx","Integrate[Log[c*(a + b/x^2)^p]/(x^3*(d + e*x)),x]","\frac{d^2 \left(\frac{p}{x^2}-\frac{\left(a+\frac{b}{x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{b}\right)-2 e^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+\frac{2 d e \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x}-e^2 \left(\log \left(-\frac{b}{a x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)+p \text{Li}_2\left(\frac{b}{a x^2}+1\right)\right)-2 e^2 p \left(-\text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)-\text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)-\log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)-\log (d+e x) \log \left(\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{b} e-\sqrt{-a} d}\right)+2 \text{Li}_2\left(\frac{e x}{d}+1\right)+2 \log \left(-\frac{e x}{d}\right) \log (d+e x)\right)+4 d e p \left(\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b}}{\sqrt{a} x}\right)}{\sqrt{b}}-\frac{1}{x}\right)}{2 d^3}","-\frac{e^2 \log \left(-\frac{b}{a x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{2 d^3}-\frac{e^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d^3}+\frac{e \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d^2 x}-\frac{\left(a+\frac{b}{x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{2 b d}-\frac{e^2 p \text{Li}_2\left(\frac{b}{a x^2}+1\right)}{2 d^3}+\frac{e^2 p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d^3}+\frac{e^2 p \text{Li}_2\left(\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d^3}+\frac{e^2 p \log (d+e x) \log \left(\frac{e \left(\sqrt{b}-\sqrt{-a} x\right)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d^3}+\frac{e^2 p \log (d+e x) \log \left(-\frac{e \left(\sqrt{-a} x+\sqrt{b}\right)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d^3}-\frac{2 \sqrt{a} e p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{\sqrt{b} d^2}-\frac{2 e^2 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{d^3}-\frac{2 e^2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^3}-\frac{2 e p}{d^2 x}+\frac{p}{2 d x^2}",1,"(4*d*e*p*(-x^(-1) + (Sqrt[a]*ArcTan[Sqrt[b]/(Sqrt[a]*x)])/Sqrt[b]) + (2*d*e*Log[c*(a + b/x^2)^p])/x + d^2*(p/x^2 - ((a + b/x^2)*Log[c*(a + b/x^2)^p])/b) - 2*e^2*Log[c*(a + b/x^2)^p]*Log[d + e*x] - e^2*(Log[c*(a + b/x^2)^p]*Log[-(b/(a*x^2))] + p*PolyLog[2, 1 + b/(a*x^2)]) - 2*e^2*p*(2*Log[-((e*x)/d)]*Log[d + e*x] - Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x] - Log[(e*(Sqrt[b] + Sqrt[-a]*x))/(-(Sqrt[-a]*d) + Sqrt[b]*e)]*Log[d + e*x] - PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)] - PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)] + 2*PolyLog[2, 1 + (e*x)/d]))/(2*d^3)","A",1
254,1,505,714,0.4209991,"\int \frac{x^3 \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d+e x} \, dx","Integrate[(x^3*Log[c*(a + b/x^3)^p])/(d + e*x),x]","\frac{x^2 \left(-6 a d^3 \log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)+6 a d^2 e x \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)-3 a d e^2 x^2 \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)+2 a e^3 x^3 \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)+6 a d^3 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)+6 a d^3 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)+6 a d^3 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)+6 a d^3 p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{-1} \sqrt[3]{b}-\sqrt[3]{a} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)+6 a d^3 p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{b} e-\sqrt[3]{a} d}\right)+6 a d^3 p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a} x+(-1)^{2/3} \sqrt[3]{b}\right)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} d}\right)+2 b e^3 p \log \left(a+\frac{b}{x^3}\right)-18 a d^3 p \text{Li}_2\left(\frac{e x}{d}+1\right)-18 a d^3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)+6 b e^3 p \log (x)\right)-9 b d^2 e p \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b}{a x^3}\right)+9 b d e^2 p x \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{b}{a x^3}\right)}{6 a e^4 x^2}","-\frac{\sqrt[3]{b} d^2 p \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{2 \sqrt[3]{a} e^3}-\frac{b^{2/3} d p \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{4 a^{2/3} e^2}+\frac{b^{2/3} d p \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{2 a^{2/3} e^2}+\frac{\sqrt{3} b^{2/3} d p \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{2 a^{2/3} e^2}-\frac{d^3 \log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{e^4}+\frac{d^2 x \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{e^3}-\frac{d x^2 \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{2 e^2}+\frac{x^3 \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{3 e}+\frac{d^3 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^4}+\frac{d^3 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e^4}+\frac{d^3 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^4}+\frac{d^3 p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^4}+\frac{d^3 p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+(-1)^{2/3} \sqrt[3]{b}\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^4}+\frac{d^3 p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e^4}+\frac{\sqrt[3]{b} d^2 p \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} e^3}-\frac{\sqrt{3} \sqrt[3]{b} d^2 p \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt[3]{a} e^3}+\frac{b p \log \left(a x^3+b\right)}{3 a e}-\frac{3 d^3 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e^4}-\frac{3 d^3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^4}",1,"(9*b*d*e^2*p*x*Hypergeometric2F1[1/3, 1, 4/3, -(b/(a*x^3))] - 9*b*d^2*e*p*Hypergeometric2F1[2/3, 1, 5/3, -(b/(a*x^3))] + x^2*(2*b*e^3*p*Log[a + b/x^3] + 6*a*d^2*e*x*Log[c*(a + b/x^3)^p] - 3*a*d*e^2*x^2*Log[c*(a + b/x^3)^p] + 2*a*e^3*x^3*Log[c*(a + b/x^3)^p] + 6*b*e^3*p*Log[x] - 6*a*d^3*Log[c*(a + b/x^3)^p]*Log[d + e*x] - 18*a*d^3*p*Log[-((e*x)/d)]*Log[d + e*x] + 6*a*d^3*p*Log[(e*((-1)^(1/3)*b^(1/3) - a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)]*Log[d + e*x] + 6*a*d^3*p*Log[(e*(b^(1/3) + a^(1/3)*x))/(-(a^(1/3)*d) + b^(1/3)*e)]*Log[d + e*x] + 6*a*d^3*p*Log[(e*((-1)^(2/3)*b^(1/3) + a^(1/3)*x))/(-(a^(1/3)*d) + (-1)^(2/3)*b^(1/3)*e)]*Log[d + e*x] + 6*a*d^3*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)] + 6*a*d^3*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)] + 6*a*d^3*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)] - 18*a*d^3*p*PolyLog[2, 1 + (e*x)/d]))/(6*a*e^4*x^2)","C",1
255,1,443,666,0.2344102,"\int \frac{x^2 \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d+e x} \, dx","Integrate[(x^2*Log[c*(a + b/x^3)^p])/(d + e*x),x]","\frac{a x^2 \left(2 d^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)-2 d e x \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)+e^2 x^2 \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)-2 d^2 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)-2 d^2 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)-2 d^2 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)-2 d^2 p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{-1} \sqrt[3]{b}-\sqrt[3]{a} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)-2 d^2 p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{b} e-\sqrt[3]{a} d}\right)-2 d^2 p \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a} x+(-1)^{2/3} \sqrt[3]{b}\right)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} d}\right)+6 d^2 p \text{Li}_2\left(\frac{e x}{d}+1\right)+6 d^2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)\right)+3 b d e p \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b}{a x^3}\right)-3 b e^2 p x \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{b}{a x^3}\right)}{2 a e^3 x^2}","\frac{\sqrt[3]{b} d p \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{2 \sqrt[3]{a} e^2}+\frac{b^{2/3} p \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{4 a^{2/3} e}-\frac{b^{2/3} p \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{2 a^{2/3} e}-\frac{\sqrt{3} b^{2/3} p \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{2 a^{2/3} e}+\frac{d^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{e^3}-\frac{d x \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{e^2}+\frac{x^2 \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{2 e}-\frac{d^2 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^3}-\frac{d^2 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e^3}-\frac{d^2 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^3}-\frac{d^2 p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^3}-\frac{d^2 p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+(-1)^{2/3} \sqrt[3]{b}\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^3}-\frac{d^2 p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e^3}-\frac{\sqrt[3]{b} d p \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} e^2}+\frac{\sqrt{3} \sqrt[3]{b} d p \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt[3]{a} e^2}+\frac{3 d^2 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e^3}+\frac{3 d^2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^3}",1,"(-3*b*e^2*p*x*Hypergeometric2F1[1/3, 1, 4/3, -(b/(a*x^3))] + 3*b*d*e*p*Hypergeometric2F1[2/3, 1, 5/3, -(b/(a*x^3))] + a*x^2*(-2*d*e*x*Log[c*(a + b/x^3)^p] + e^2*x^2*Log[c*(a + b/x^3)^p] + 2*d^2*Log[c*(a + b/x^3)^p]*Log[d + e*x] + 6*d^2*p*Log[-((e*x)/d)]*Log[d + e*x] - 2*d^2*p*Log[(e*((-1)^(1/3)*b^(1/3) - a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)]*Log[d + e*x] - 2*d^2*p*Log[(e*(b^(1/3) + a^(1/3)*x))/(-(a^(1/3)*d) + b^(1/3)*e)]*Log[d + e*x] - 2*d^2*p*Log[(e*((-1)^(2/3)*b^(1/3) + a^(1/3)*x))/(-(a^(1/3)*d) + (-1)^(2/3)*b^(1/3)*e)]*Log[d + e*x] - 2*d^2*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)] - 2*d^2*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)] - 2*d^2*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)] + 6*d^2*p*PolyLog[2, 1 + (e*x)/d]))/(2*a*e^3*x^2)","C",1
256,1,403,488,0.1245359,"\int \frac{x \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d+e x} \, dx","Integrate[(x*Log[c*(a + b/x^3)^p])/(d + e*x),x]","-\frac{d \log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{e^2}+\frac{x \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{e}+\frac{d p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^2}+\frac{d p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e^2}+\frac{d p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(-\frac{(-1)^{2/3} e \left(\sqrt[3]{b}-\sqrt[3]{-1} \sqrt[3]{a} x\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e^2}-\frac{3 b p \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{b}{a x^3}\right)}{2 a e x^2}-\frac{3 d p \text{Li}_2\left(\frac{d+e x}{d}\right)}{e^2}-\frac{3 d p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^2}","-\frac{\sqrt[3]{b} p \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{2 \sqrt[3]{a} e}-\frac{d \log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{e^2}+\frac{x \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{e}+\frac{d p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^2}+\frac{d p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e^2}+\frac{d p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+(-1)^{2/3} \sqrt[3]{b}\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^2}+\frac{d p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e^2}+\frac{\sqrt[3]{b} p \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} e}-\frac{\sqrt{3} \sqrt[3]{b} p \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt[3]{a} e}-\frac{3 d p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e^2}-\frac{3 d p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^2}",1,"(-3*b*p*Hypergeometric2F1[2/3, 1, 5/3, -(b/(a*x^3))])/(2*a*e*x^2) + (x*Log[c*(a + b/x^3)^p])/e - (d*Log[c*(a + b/x^3)^p]*Log[d + e*x])/e^2 - (3*d*p*Log[-((e*x)/d)]*Log[d + e*x])/e^2 + (d*p*Log[-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e))]*Log[d + e*x])/e^2 + (d*p*Log[-(((-1)^(2/3)*e*(b^(1/3) - (-1)^(1/3)*a^(1/3)*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e))]*Log[d + e*x])/e^2 + (d*p*Log[((-1)^(1/3)*e*(b^(1/3) + (-1)^(2/3)*a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)]*Log[d + e*x])/e^2 - (3*d*p*PolyLog[2, (d + e*x)/d])/e^2 + (d*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)])/e^2 + (d*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)])/e^2 + (d*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)])/e^2","C",1
257,1,350,344,0.0922774,"\int \frac{\log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d+e x} \, dx","Integrate[Log[c*(a + b/x^3)^p]/(d + e*x),x]","\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{(-1)^{2/3} e \left(\sqrt[3]{b}-\sqrt[3]{-1} \sqrt[3]{a} x\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e}+\frac{3 p \text{Li}_2\left(\frac{d+e x}{d}\right)}{e}+\frac{3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}","\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e}-\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+(-1)^{2/3} \sqrt[3]{b}\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e}-\frac{p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e}+\frac{3 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{e}+\frac{3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}",1,"(Log[c*(a + b/x^3)^p]*Log[d + e*x])/e + (3*p*Log[-((e*x)/d)]*Log[d + e*x])/e - (p*Log[-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e))]*Log[d + e*x])/e - (p*Log[-(((-1)^(2/3)*e*(b^(1/3) - (-1)^(1/3)*a^(1/3)*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e))]*Log[d + e*x])/e - (p*Log[((-1)^(1/3)*e*(b^(1/3) + (-1)^(2/3)*a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)]*Log[d + e*x])/e + (3*p*PolyLog[2, (d + e*x)/d])/e - (p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)])/e - (p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)])/e - (p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)])/e","A",1
258,1,395,388,0.0992715,"\int \frac{\log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{x (d+e x)} \, dx","Integrate[Log[c*(a + b/x^3)^p]/(x*(d + e*x)),x]","-\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d}-\frac{\log \left(-\frac{b}{a x^3}\right) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{3 d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d}+\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d}+\frac{p \log (d+e x) \log \left(-\frac{(-1)^{2/3} e \left(\sqrt[3]{b}-\sqrt[3]{-1} \sqrt[3]{a} x\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d}+\frac{p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{d}-\frac{p \text{Li}_2\left(\frac{a+\frac{b}{x^3}}{a}\right)}{3 d}-\frac{3 p \text{Li}_2\left(\frac{d+e x}{d}\right)}{d}-\frac{3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d}","-\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d}-\frac{\log \left(-\frac{b}{a x^3}\right) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{3 d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{d}+\frac{p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d}+\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d}+\frac{p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+(-1)^{2/3} \sqrt[3]{b}\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d}+\frac{p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{d}-\frac{p \text{Li}_2\left(\frac{b}{a x^3}+1\right)}{3 d}-\frac{3 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{d}-\frac{3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d}",1,"-1/3*(Log[c*(a + b/x^3)^p]*Log[-(b/(a*x^3))])/d - (Log[c*(a + b/x^3)^p]*Log[d + e*x])/d - (3*p*Log[-((e*x)/d)]*Log[d + e*x])/d + (p*Log[-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e))]*Log[d + e*x])/d + (p*Log[-(((-1)^(2/3)*e*(b^(1/3) - (-1)^(1/3)*a^(1/3)*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e))]*Log[d + e*x])/d + (p*Log[((-1)^(1/3)*e*(b^(1/3) + (-1)^(2/3)*a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)]*Log[d + e*x])/d - (p*PolyLog[2, (a + b/x^3)/a])/(3*d) - (3*p*PolyLog[2, (d + e*x)/d])/d + (p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)])/d + (p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)])/d + (p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)])/d","A",1
259,1,429,557,0.2163035,"\int \frac{\log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{x^2 (d+e x)} \, dx","Integrate[Log[c*(a + b/x^3)^p]/(x^2*(d + e*x)),x]","\frac{4 a x^3 \left(3 e x \log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)-3 d \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)+e x \log \left(-\frac{b}{a x^3}\right) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)-3 e p x \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)-3 e p x \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)-3 e p x \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)-3 e p x \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{-1} \sqrt[3]{b}-\sqrt[3]{a} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)-3 e p x \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{b} e-\sqrt[3]{a} d}\right)-3 e p x \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a} x+(-1)^{2/3} \sqrt[3]{b}\right)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} d}\right)+e p x \text{Li}_2\left(\frac{b}{a x^3}+1\right)+9 e p x \text{Li}_2\left(\frac{e x}{d}+1\right)+9 e p x \log \left(-\frac{e x}{d}\right) \log (d+e x)\right)+9 b d p \, _2F_1\left(1,\frac{4}{3};\frac{7}{3};-\frac{b}{a x^3}\right)}{12 a d^2 x^4}","\frac{\sqrt[3]{a} p \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{2 \sqrt[3]{b} d}+\frac{e \log \left(-\frac{b}{a x^3}\right) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{3 d^2}+\frac{e \log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d^2}-\frac{\log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d x}+\frac{e p \text{Li}_2\left(\frac{b}{a x^3}+1\right)}{3 d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{d^2}-\frac{e p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+(-1)^{2/3} \sqrt[3]{b}\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d^2}-\frac{e p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{d^2}-\frac{\sqrt[3]{a} p \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{b} d}-\frac{\sqrt{3} \sqrt[3]{a} p \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt[3]{b} d}+\frac{3 e p \text{Li}_2\left(\frac{e x}{d}+1\right)}{d^2}+\frac{3 e p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^2}+\frac{3 p}{d x}",1,"(9*b*d*p*Hypergeometric2F1[1, 4/3, 7/3, -(b/(a*x^3))] + 4*a*x^3*(-3*d*Log[c*(a + b/x^3)^p] + e*x*Log[c*(a + b/x^3)^p]*Log[-(b/(a*x^3))] + 3*e*x*Log[c*(a + b/x^3)^p]*Log[d + e*x] + 9*e*p*x*Log[-((e*x)/d)]*Log[d + e*x] - 3*e*p*x*Log[(e*((-1)^(1/3)*b^(1/3) - a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)]*Log[d + e*x] - 3*e*p*x*Log[(e*(b^(1/3) + a^(1/3)*x))/(-(a^(1/3)*d) + b^(1/3)*e)]*Log[d + e*x] - 3*e*p*x*Log[(e*((-1)^(2/3)*b^(1/3) + a^(1/3)*x))/(-(a^(1/3)*d) + (-1)^(2/3)*b^(1/3)*e)]*Log[d + e*x] + e*p*x*PolyLog[2, 1 + b/(a*x^3)] - 3*e*p*x*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)] - 3*e*p*x*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)] - 3*e*p*x*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)] + 9*e*p*x*PolyLog[2, 1 + (e*x)/d]))/(12*a*d^2*x^4)","C",1
260,1,520,737,0.302488,"\int \frac{\log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{x^3 (d+e x)} \, dx","Integrate[Log[c*(a + b/x^3)^p]/(x^3*(d + e*x)),x]","\frac{-10 a x^3 \left(3 d^2 \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)+6 e^2 x^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)-6 d e x \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)+2 e^2 x^2 \log \left(-\frac{b}{a x^3}\right) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)-6 e^2 p x^2 \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)-6 e^2 p x^2 \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)-6 e^2 p x^2 \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)-6 e^2 p x^2 \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{-1} \sqrt[3]{b}-\sqrt[3]{a} x\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)-6 e^2 p x^2 \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{b} e-\sqrt[3]{a} d}\right)-6 e^2 p x^2 \log (d+e x) \log \left(\frac{e \left(\sqrt[3]{a} x+(-1)^{2/3} \sqrt[3]{b}\right)}{(-1)^{2/3} \sqrt[3]{b} e-\sqrt[3]{a} d}\right)+2 e^2 p x^2 \text{Li}_2\left(\frac{b}{a x^3}+1\right)+18 e^2 p x^2 \text{Li}_2\left(\frac{e x}{d}+1\right)+18 e^2 p x^2 \log \left(-\frac{e x}{d}\right) \log (d+e x)\right)+18 b d^2 p \, _2F_1\left(1,\frac{5}{3};\frac{8}{3};-\frac{b}{a x^3}\right)-45 b d e p x \, _2F_1\left(1,\frac{4}{3};\frac{7}{3};-\frac{b}{a x^3}\right)}{60 a d^3 x^5}","-\frac{\sqrt[3]{a} e p \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{2 \sqrt[3]{b} d^2}-\frac{a^{2/3} p \log \left(a^{2/3} x^2-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3}\right)}{4 b^{2/3} d}+\frac{a^{2/3} p \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{2 b^{2/3} d}-\frac{\sqrt{3} a^{2/3} p \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{2 b^{2/3} d}-\frac{e^2 \log \left(-\frac{b}{a x^3}\right) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{3 d^3}-\frac{e^2 \log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d^3}+\frac{e \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d^2 x}-\frac{\log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{2 d x^2}-\frac{e^2 p \text{Li}_2\left(\frac{b}{a x^3}+1\right)}{3 d^3}+\frac{e^2 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d^3}+\frac{e^2 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{d^3}+\frac{e^2 p \text{Li}_2\left(\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d^3}+\frac{e^2 p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d^3}+\frac{e^2 p \log (d+e x) \log \left(-\frac{e \left(\sqrt[3]{a} x+(-1)^{2/3} \sqrt[3]{b}\right)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d^3}+\frac{e^2 p \log (d+e x) \log \left(\frac{\sqrt[3]{-1} e \left((-1)^{2/3} \sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{d^3}+\frac{\sqrt[3]{a} e p \log \left(\sqrt[3]{a} x+\sqrt[3]{b}\right)}{\sqrt[3]{b} d^2}+\frac{\sqrt{3} \sqrt[3]{a} e p \tan ^{-1}\left(\frac{\sqrt[3]{b}-2 \sqrt[3]{a} x}{\sqrt{3} \sqrt[3]{b}}\right)}{\sqrt[3]{b} d^2}-\frac{3 e^2 p \text{Li}_2\left(\frac{e x}{d}+1\right)}{d^3}-\frac{3 e^2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^3}-\frac{3 e p}{d^2 x}+\frac{3 p}{4 d x^2}",1,"(-45*b*d*e*p*x*Hypergeometric2F1[1, 4/3, 7/3, -(b/(a*x^3))] + 18*b*d^2*p*Hypergeometric2F1[1, 5/3, 8/3, -(b/(a*x^3))] - 10*a*x^3*(3*d^2*Log[c*(a + b/x^3)^p] - 6*d*e*x*Log[c*(a + b/x^3)^p] + 2*e^2*x^2*Log[c*(a + b/x^3)^p]*Log[-(b/(a*x^3))] + 6*e^2*x^2*Log[c*(a + b/x^3)^p]*Log[d + e*x] + 18*e^2*p*x^2*Log[-((e*x)/d)]*Log[d + e*x] - 6*e^2*p*x^2*Log[(e*((-1)^(1/3)*b^(1/3) - a^(1/3)*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)]*Log[d + e*x] - 6*e^2*p*x^2*Log[(e*(b^(1/3) + a^(1/3)*x))/(-(a^(1/3)*d) + b^(1/3)*e)]*Log[d + e*x] - 6*e^2*p*x^2*Log[(e*((-1)^(2/3)*b^(1/3) + a^(1/3)*x))/(-(a^(1/3)*d) + (-1)^(2/3)*b^(1/3)*e)]*Log[d + e*x] + 2*e^2*p*x^2*PolyLog[2, 1 + b/(a*x^3)] - 6*e^2*p*x^2*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)] - 6*e^2*p*x^2*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)] - 6*e^2*p*x^2*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)] + 18*e^2*p*x^2*PolyLog[2, 1 + (e*x)/d]))/(60*a*d^3*x^5)","C",1
261,1,867,749,0.6161085,"\int \frac{\log \left(c \left(d+e x^3\right)^p\right)}{f+g x^2} \, dx","Integrate[Log[c*(d + e*x^3)^p]/(f + g*x^2),x]","\frac{-p \log \left(\frac{\sqrt{g} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\sqrt[3]{e} \sqrt{-f}+\sqrt[3]{d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} x\right)-p \log \left(\frac{\sqrt{g} \left(\sqrt[3]{e} x-\sqrt[3]{-1} \sqrt[3]{d}\right)}{\sqrt[3]{e} \sqrt{-f}-\sqrt[3]{-1} \sqrt[3]{d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} x\right)-p \log \left(\frac{\sqrt{g} \left(\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}\right)}{\sqrt[3]{e} \sqrt{-f}+(-1)^{2/3} \sqrt[3]{d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} x\right)+\log \left(c \left(e x^3+d\right)^p\right) \log \left(\sqrt{-f}-\sqrt{g} x\right)+p \log \left(-\frac{\sqrt{g} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\sqrt[3]{e} \sqrt{-f}-\sqrt[3]{d} \sqrt{g}}\right) \log \left(\sqrt{g} x+\sqrt{-f}\right)+p \log \left(\frac{\sqrt{g} \left(\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}\right)}{(-1)^{2/3} \sqrt[3]{d} \sqrt{g}-\sqrt[3]{e} \sqrt{-f}}\right) \log \left(\sqrt{g} x+\sqrt{-f}\right)+p \log \left(\frac{\sqrt[3]{-1} \sqrt{g} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\sqrt[3]{e} \sqrt{-f}+\sqrt[3]{-1} \sqrt[3]{d} \sqrt{g}}\right) \log \left(\sqrt{g} x+\sqrt{-f}\right)-\log \left(\sqrt{g} x+\sqrt{-f}\right) \log \left(c \left(e x^3+d\right)^p\right)-p \text{Li}_2\left(\frac{\sqrt[3]{e} \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt[3]{e} \sqrt{-f}+\sqrt[3]{d} \sqrt{g}}\right)-p \text{Li}_2\left(\frac{\sqrt[3]{e} \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt[3]{e} \sqrt{-f}-\sqrt[3]{-1} \sqrt[3]{d} \sqrt{g}}\right)-p \text{Li}_2\left(\frac{\sqrt[3]{e} \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt[3]{e} \sqrt{-f}+(-1)^{2/3} \sqrt[3]{d} \sqrt{g}}\right)+p \text{Li}_2\left(\frac{\sqrt[3]{e} \left(\sqrt{g} x+\sqrt{-f}\right)}{\sqrt[3]{e} \sqrt{-f}-\sqrt[3]{d} \sqrt{g}}\right)+p \text{Li}_2\left(\frac{\sqrt[3]{e} \left(\sqrt{g} x+\sqrt{-f}\right)}{\sqrt[3]{e} \sqrt{-f}+\sqrt[3]{-1} \sqrt[3]{d} \sqrt{g}}\right)+p \text{Li}_2\left(\frac{\sqrt[3]{e} \left(\sqrt{g} x+\sqrt{-f}\right)}{\sqrt[3]{e} \sqrt{-f}-(-1)^{2/3} \sqrt[3]{d} \sqrt{g}}\right)}{2 \sqrt{-f} \sqrt{g}}","\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^3\right)^p\right)}{\sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(i \sqrt[3]{e} \sqrt{f}+\sqrt[3]{d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(\frac{2 i \sqrt{f} \sqrt{g} \left(\sqrt[3]{e} x+(-1)^{2/3} \sqrt[3]{d}\right)}{\left(\sqrt[3]{e} \sqrt{f}+\sqrt[6]{-1} \sqrt[3]{d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(1-\frac{2 (-1)^{5/6} \sqrt{f} \sqrt{g} \left((-1)^{2/3} \sqrt[3]{e} x+\sqrt[3]{d}\right)}{\left(\sqrt[3]{e} \sqrt{f}+(-1)^{5/6} \sqrt[3]{d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt[3]{d} \sqrt{g}+i \sqrt[3]{e} \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 i \sqrt{f} \sqrt{g} \left((-1)^{2/3} \sqrt[3]{d}+\sqrt[3]{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt[6]{-1} \sqrt[3]{d} \sqrt{g}+\sqrt[3]{e} \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 (-1)^{5/6} \sqrt{f} \sqrt{g} \left(\sqrt[3]{d}+(-1)^{2/3} \sqrt[3]{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left((-1)^{5/6} \sqrt[3]{d} \sqrt{g}+\sqrt[3]{e} \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}-\frac{3 i p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 \sqrt{f} \sqrt{g}}+\frac{3 p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}",1,"(-(p*Log[(Sqrt[g]*(d^(1/3) + e^(1/3)*x))/(e^(1/3)*Sqrt[-f] + d^(1/3)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*x]) - p*Log[(Sqrt[g]*(-((-1)^(1/3)*d^(1/3)) + e^(1/3)*x))/(e^(1/3)*Sqrt[-f] - (-1)^(1/3)*d^(1/3)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*x] - p*Log[(Sqrt[g]*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/(e^(1/3)*Sqrt[-f] + (-1)^(2/3)*d^(1/3)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*x] + p*Log[-((Sqrt[g]*(d^(1/3) + e^(1/3)*x))/(e^(1/3)*Sqrt[-f] - d^(1/3)*Sqrt[g]))]*Log[Sqrt[-f] + Sqrt[g]*x] + p*Log[(Sqrt[g]*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/(-(e^(1/3)*Sqrt[-f]) + (-1)^(2/3)*d^(1/3)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*x] + p*Log[((-1)^(1/3)*Sqrt[g]*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/(e^(1/3)*Sqrt[-f] + (-1)^(1/3)*d^(1/3)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*x] + Log[Sqrt[-f] - Sqrt[g]*x]*Log[c*(d + e*x^3)^p] - Log[Sqrt[-f] + Sqrt[g]*x]*Log[c*(d + e*x^3)^p] - p*PolyLog[2, (e^(1/3)*(Sqrt[-f] - Sqrt[g]*x))/(e^(1/3)*Sqrt[-f] + d^(1/3)*Sqrt[g])] - p*PolyLog[2, (e^(1/3)*(Sqrt[-f] - Sqrt[g]*x))/(e^(1/3)*Sqrt[-f] - (-1)^(1/3)*d^(1/3)*Sqrt[g])] - p*PolyLog[2, (e^(1/3)*(Sqrt[-f] - Sqrt[g]*x))/(e^(1/3)*Sqrt[-f] + (-1)^(2/3)*d^(1/3)*Sqrt[g])] + p*PolyLog[2, (e^(1/3)*(Sqrt[-f] + Sqrt[g]*x))/(e^(1/3)*Sqrt[-f] - d^(1/3)*Sqrt[g])] + p*PolyLog[2, (e^(1/3)*(Sqrt[-f] + Sqrt[g]*x))/(e^(1/3)*Sqrt[-f] + (-1)^(1/3)*d^(1/3)*Sqrt[g])] + p*PolyLog[2, (e^(1/3)*(Sqrt[-f] + Sqrt[g]*x))/(e^(1/3)*Sqrt[-f] - (-1)^(2/3)*d^(1/3)*Sqrt[g])])/(2*Sqrt[-f]*Sqrt[g])","A",1
262,1,564,533,0.3739383,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(f + g*x^2),x]","-\frac{i \left(2 i \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)+p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)+p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)-p \text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)-p \text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)+p \log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)+p \log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-p \log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-p \log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)\right)}{2 \sqrt{f} \sqrt{g}}","\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{\sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}-\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\sqrt{f} \sqrt{g}}+\frac{2 p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}",1,"((-1/2*I)*(p*Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] + p*Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] - p*Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] - p*Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] + (2*I)*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p] + p*PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] + p*PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])] - p*PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] - p*PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])]))/(Sqrt[f]*Sqrt[g])","A",0
263,1,178,229,0.1282055,"\int \frac{\log \left(c (d+e x)^p\right)}{f+g x^2} \, dx","Integrate[Log[c*(d + e*x)^p]/(f + g*x^2),x]","\frac{\log \left(c (d+e x)^p\right) \left(\log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right)-\log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right)\right)-p \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)+p \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 \sqrt{-f} \sqrt{g}}","\frac{\log \left(c (d+e x)^p\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x\right)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 \sqrt{-f} \sqrt{g}}-\frac{\log \left(c (d+e x)^p\right) \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 \sqrt{-f} \sqrt{g}}-\frac{p \text{Li}_2\left(-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{p \text{Li}_2\left(\frac{\sqrt{g} (d+e x)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 \sqrt{-f} \sqrt{g}}",1,"(Log[c*(d + e*x)^p]*(Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])] - Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])]) - p*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))] + p*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*Sqrt[-f]*Sqrt[g])","A",1
264,1,373,360,0.2568054,"\int \frac{\log \left(c \left(d+\frac{e}{x}\right)^p\right)}{f+g x^2} \, dx","Integrate[Log[c*(d + e/x)^p]/(f + g*x^2),x]","\frac{\log \left(\sqrt{-f}-\sqrt{g} x\right) \log \left(c \left(d+\frac{e}{x}\right)^p\right)-\log \left(\sqrt{-f}+\sqrt{g} x\right) \log \left(c \left(d+\frac{e}{x}\right)^p\right)-p \text{Li}_2\left(\frac{d \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{-f} d+e \sqrt{g}}\right)+p \text{Li}_2\left(\frac{d \left(\sqrt{g} x+\sqrt{-f}\right)}{d \sqrt{-f}-e \sqrt{g}}\right)-p \log \left(\sqrt{-f}-\sqrt{g} x\right) \log \left(\frac{\sqrt{g} (d x+e)}{d \sqrt{-f}+e \sqrt{g}}\right)+p \log \left(\sqrt{-f}+\sqrt{g} x\right) \log \left(-\frac{\sqrt{g} (d x+e)}{d \sqrt{-f}-e \sqrt{g}}\right)-p \text{Li}_2\left(\frac{\sqrt{g} x}{\sqrt{-f}}+1\right)+p \text{Li}_2\left(\frac{f \sqrt{g} x}{(-f)^{3/2}}+1\right)+p \log \left(\frac{\sqrt{g} x}{\sqrt{-f}}\right) \log \left(\sqrt{-f}-\sqrt{g} x\right)-p \log \left(\frac{f \sqrt{g} x}{(-f)^{3/2}}\right) \log \left(\sqrt{-f}+\sqrt{g} x\right)}{2 \sqrt{-f} \sqrt{g}}","\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+\frac{e}{x}\right)^p\right)}{\sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} (e+d x)}{\left(i \sqrt{f} d+e \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} (d x+e)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(e \sqrt{g}+i d \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(-\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{i p \text{Li}_2\left(\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 \sqrt{f} \sqrt{g}}+\frac{p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}",1,"(Log[c*(d + e/x)^p]*Log[Sqrt[-f] - Sqrt[g]*x] + p*Log[(Sqrt[g]*x)/Sqrt[-f]]*Log[Sqrt[-f] - Sqrt[g]*x] - p*Log[(Sqrt[g]*(e + d*x))/(d*Sqrt[-f] + e*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*x] - Log[c*(d + e/x)^p]*Log[Sqrt[-f] + Sqrt[g]*x] - p*Log[(f*Sqrt[g]*x)/(-f)^(3/2)]*Log[Sqrt[-f] + Sqrt[g]*x] + p*Log[-((Sqrt[g]*(e + d*x))/(d*Sqrt[-f] - e*Sqrt[g]))]*Log[Sqrt[-f] + Sqrt[g]*x] - p*PolyLog[2, (d*(Sqrt[-f] - Sqrt[g]*x))/(d*Sqrt[-f] + e*Sqrt[g])] + p*PolyLog[2, (d*(Sqrt[-f] + Sqrt[g]*x))/(d*Sqrt[-f] - e*Sqrt[g])] - p*PolyLog[2, 1 + (Sqrt[g]*x)/Sqrt[-f]] + p*PolyLog[2, 1 + (f*Sqrt[g]*x)/(-f)^(3/2)])/(2*Sqrt[-f]*Sqrt[g])","A",1
265,1,706,597,0.3923353,"\int \frac{\log \left(c \left(d+\frac{e}{x^2}\right)^p\right)}{f+g x^2} \, dx","Integrate[Log[c*(d + e/x^2)^p]/(f + g*x^2),x]","\frac{\log \left(\sqrt{-f}-\sqrt{g} x\right) \log \left(c \left(d+\frac{e}{x^2}\right)^p\right)-\log \left(\sqrt{-f}+\sqrt{g} x\right) \log \left(c \left(d+\frac{e}{x^2}\right)^p\right)-p \text{Li}_2\left(\frac{\sqrt{-d} \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{-d} \sqrt{-f}-\sqrt{e} \sqrt{g}}\right)-p \text{Li}_2\left(\frac{\sqrt{-d} \left(\sqrt{-f}-\sqrt{g} x\right)}{\sqrt{-d} \sqrt{-f}+\sqrt{e} \sqrt{g}}\right)+p \text{Li}_2\left(\frac{\sqrt{-d} \left(\sqrt{g} x+\sqrt{-f}\right)}{\sqrt{-d} \sqrt{-f}-\sqrt{e} \sqrt{g}}\right)+p \text{Li}_2\left(\frac{\sqrt{-d} \left(\sqrt{g} x+\sqrt{-f}\right)}{\sqrt{-d} \sqrt{-f}+\sqrt{e} \sqrt{g}}\right)-p \log \left(\sqrt{-f}-\sqrt{g} x\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d} x-\sqrt{e}\right)}{\sqrt{-d} \sqrt{-f}-\sqrt{e} \sqrt{g}}\right)-p \log \left(\sqrt{-f}-\sqrt{g} x\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d} x+\sqrt{e}\right)}{\sqrt{-d} \sqrt{-f}+\sqrt{e} \sqrt{g}}\right)+p \log \left(\sqrt{-f}+\sqrt{g} x\right) \log \left(\frac{\sqrt{g} \left(\sqrt{e}-\sqrt{-d} x\right)}{\sqrt{-d} \sqrt{-f}+\sqrt{e} \sqrt{g}}\right)+p \log \left(\sqrt{-f}+\sqrt{g} x\right) \log \left(-\frac{\sqrt{g} \left(\sqrt{-d} x+\sqrt{e}\right)}{\sqrt{-d} \sqrt{-f}-\sqrt{e} \sqrt{g}}\right)-2 p \text{Li}_2\left(\frac{\sqrt{g} x}{\sqrt{-f}}+1\right)+2 p \text{Li}_2\left(\frac{f \sqrt{g} x}{(-f)^{3/2}}+1\right)+2 p \log \left(\frac{\sqrt{g} x}{\sqrt{-f}}\right) \log \left(\sqrt{-f}-\sqrt{g} x\right)-2 p \log \left(\frac{f \sqrt{g} x}{(-f)^{3/2}}\right) \log \left(\sqrt{-f}+\sqrt{g} x\right)}{2 \sqrt{-f} \sqrt{g}}","\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+\frac{e}{x^2}\right)^p\right)}{\sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e}-\sqrt{-d} x\right)}{\left(i \sqrt{-d} \sqrt{f}-\sqrt{e} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d} x+\sqrt{e}\right)}{\left(i \sqrt{-d} \sqrt{f}+\sqrt{e} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e}-\sqrt{-d} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(-\sqrt{e} \sqrt{g}+i \sqrt{-d} \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d} x+\sqrt{e}\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt{e} \sqrt{g}+i \sqrt{-d} \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(-\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}-\frac{i p \text{Li}_2\left(\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}-\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\sqrt{f} \sqrt{g}}+\frac{2 p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}",1,"(Log[c*(d + e/x^2)^p]*Log[Sqrt[-f] - Sqrt[g]*x] + 2*p*Log[(Sqrt[g]*x)/Sqrt[-f]]*Log[Sqrt[-f] - Sqrt[g]*x] - p*Log[(Sqrt[g]*(-Sqrt[e] + Sqrt[-d]*x))/(Sqrt[-d]*Sqrt[-f] - Sqrt[e]*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*x] - p*Log[(Sqrt[g]*(Sqrt[e] + Sqrt[-d]*x))/(Sqrt[-d]*Sqrt[-f] + Sqrt[e]*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*x] - Log[c*(d + e/x^2)^p]*Log[Sqrt[-f] + Sqrt[g]*x] - 2*p*Log[(f*Sqrt[g]*x)/(-f)^(3/2)]*Log[Sqrt[-f] + Sqrt[g]*x] + p*Log[(Sqrt[g]*(Sqrt[e] - Sqrt[-d]*x))/(Sqrt[-d]*Sqrt[-f] + Sqrt[e]*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*x] + p*Log[-((Sqrt[g]*(Sqrt[e] + Sqrt[-d]*x))/(Sqrt[-d]*Sqrt[-f] - Sqrt[e]*Sqrt[g]))]*Log[Sqrt[-f] + Sqrt[g]*x] - p*PolyLog[2, (Sqrt[-d]*(Sqrt[-f] - Sqrt[g]*x))/(Sqrt[-d]*Sqrt[-f] - Sqrt[e]*Sqrt[g])] - p*PolyLog[2, (Sqrt[-d]*(Sqrt[-f] - Sqrt[g]*x))/(Sqrt[-d]*Sqrt[-f] + Sqrt[e]*Sqrt[g])] + p*PolyLog[2, (Sqrt[-d]*(Sqrt[-f] + Sqrt[g]*x))/(Sqrt[-d]*Sqrt[-f] - Sqrt[e]*Sqrt[g])] + p*PolyLog[2, (Sqrt[-d]*(Sqrt[-f] + Sqrt[g]*x))/(Sqrt[-d]*Sqrt[-f] + Sqrt[e]*Sqrt[g])] - 2*p*PolyLog[2, 1 + (Sqrt[g]*x)/Sqrt[-f]] + 2*p*PolyLog[2, 1 + (f*Sqrt[g]*x)/(-f)^(3/2)])/(2*Sqrt[-f]*Sqrt[g])","A",1
266,1,422,541,0.3009171,"\int \frac{\log \left(c \left(d+e \sqrt{x}\right)^p\right)}{f+g x^2} \, dx","Integrate[Log[c*(d + e*Sqrt[x])^p]/(f + g*x^2),x]","\frac{\log \left(c \left(d+e \sqrt{x}\right)^p\right) \log \left(\frac{e \left(\sqrt[4]{-f}-\sqrt[4]{g} \sqrt{x}\right)}{d \sqrt[4]{g}+e \sqrt[4]{-f}}\right)-\log \left(c \left(d+e \sqrt{x}\right)^p\right) \log \left(\frac{e \left(\sqrt[4]{-f}-i \sqrt[4]{g} \sqrt{x}\right)}{e \sqrt[4]{-f}+i d \sqrt[4]{g}}\right)-\log \left(c \left(d+e \sqrt{x}\right)^p\right) \log \left(\frac{e \left(\sqrt[4]{-f}+i \sqrt[4]{g} \sqrt{x}\right)}{e \sqrt[4]{-f}-i d \sqrt[4]{g}}\right)+\log \left(c \left(d+e \sqrt{x}\right)^p\right) \log \left(\frac{e \left(\sqrt[4]{-f}+\sqrt[4]{g} \sqrt{x}\right)}{e \sqrt[4]{-f}-d \sqrt[4]{g}}\right)+p \text{Li}_2\left(-\frac{\sqrt[4]{g} \left(d+e \sqrt{x}\right)}{e \sqrt[4]{-f}-d \sqrt[4]{g}}\right)-p \text{Li}_2\left(\frac{i \sqrt[4]{g} \left(d+e \sqrt{x}\right)}{i \sqrt[4]{g} d+e \sqrt[4]{-f}}\right)-p \text{Li}_2\left(\frac{\sqrt[4]{g} \left(d+e \sqrt{x}\right)}{\sqrt[4]{g} d+i e \sqrt[4]{-f}}\right)+p \text{Li}_2\left(\frac{\sqrt[4]{g} \left(d+e \sqrt{x}\right)}{\sqrt[4]{g} d+e \sqrt[4]{-f}}\right)}{2 \sqrt{-f} \sqrt{g}}","-\frac{\log \left(c \left(d+e \sqrt{x}\right)^p\right) \log \left(\frac{e \left(\sqrt{-\sqrt{-f}}-\sqrt[4]{g} \sqrt{x}\right)}{d \sqrt[4]{g}+e \sqrt{-\sqrt{-f}}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{\log \left(c \left(d+e \sqrt{x}\right)^p\right) \log \left(\frac{e \left(\sqrt[4]{-f}-\sqrt[4]{g} \sqrt{x}\right)}{d \sqrt[4]{g}+e \sqrt[4]{-f}}\right)}{2 \sqrt{-f} \sqrt{g}}-\frac{\log \left(c \left(d+e \sqrt{x}\right)^p\right) \log \left(\frac{e \left(\sqrt{-\sqrt{-f}}+\sqrt[4]{g} \sqrt{x}\right)}{e \sqrt{-\sqrt{-f}}-d \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{\log \left(c \left(d+e \sqrt{x}\right)^p\right) \log \left(\frac{e \left(\sqrt[4]{-f}+\sqrt[4]{g} \sqrt{x}\right)}{e \sqrt[4]{-f}-d \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}-\frac{p \text{Li}_2\left(-\frac{\sqrt[4]{g} \left(d+e \sqrt{x}\right)}{e \sqrt{-\sqrt{-f}}-d \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{p \text{Li}_2\left(-\frac{\sqrt[4]{g} \left(d+e \sqrt{x}\right)}{e \sqrt[4]{-f}-d \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}-\frac{p \text{Li}_2\left(\frac{\sqrt[4]{g} \left(d+e \sqrt{x}\right)}{\sqrt[4]{g} d+e \sqrt{-\sqrt{-f}}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{p \text{Li}_2\left(\frac{\sqrt[4]{g} \left(d+e \sqrt{x}\right)}{\sqrt[4]{g} d+e \sqrt[4]{-f}}\right)}{2 \sqrt{-f} \sqrt{g}}",1,"(Log[c*(d + e*Sqrt[x])^p]*Log[(e*((-f)^(1/4) - g^(1/4)*Sqrt[x]))/(e*(-f)^(1/4) + d*g^(1/4))] - Log[c*(d + e*Sqrt[x])^p]*Log[(e*((-f)^(1/4) - I*g^(1/4)*Sqrt[x]))/(e*(-f)^(1/4) + I*d*g^(1/4))] - Log[c*(d + e*Sqrt[x])^p]*Log[(e*((-f)^(1/4) + I*g^(1/4)*Sqrt[x]))/(e*(-f)^(1/4) - I*d*g^(1/4))] + Log[c*(d + e*Sqrt[x])^p]*Log[(e*((-f)^(1/4) + g^(1/4)*Sqrt[x]))/(e*(-f)^(1/4) - d*g^(1/4))] + p*PolyLog[2, -((g^(1/4)*(d + e*Sqrt[x]))/(e*(-f)^(1/4) - d*g^(1/4)))] - p*PolyLog[2, (I*g^(1/4)*(d + e*Sqrt[x]))/(e*(-f)^(1/4) + I*d*g^(1/4))] - p*PolyLog[2, (g^(1/4)*(d + e*Sqrt[x]))/(I*e*(-f)^(1/4) + d*g^(1/4))] + p*PolyLog[2, (g^(1/4)*(d + e*Sqrt[x]))/(e*(-f)^(1/4) + d*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g])","C",1
267,1,912,561,0.5807026,"\int \frac{\log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right)}{f+g x^2} \, dx","Integrate[Log[c*(d + e/Sqrt[x])^p]/(f + g*x^2),x]","\frac{\log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right) \log \left(-\sqrt[4]{g} \sqrt{x}-\sqrt[4]{-f}\right)-p \log \left(-\frac{\sqrt[4]{g} \left(\sqrt{x} d+e\right)}{d \sqrt[4]{-f}-e \sqrt[4]{g}}\right) \log \left(-\sqrt[4]{g} \sqrt{x}-\sqrt[4]{-f}\right)+p \log \left(\frac{f \sqrt[4]{g} \sqrt{x}}{(-f)^{5/4}}\right) \log \left(-\sqrt[4]{g} \sqrt{x}-\sqrt[4]{-f}\right)-\log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right) \log \left(-\sqrt[4]{g} \sqrt{x}-i \sqrt[4]{-f}\right)+p \log \left(\frac{i \sqrt[4]{g} \left(\sqrt{x} d+e\right)}{\sqrt[4]{-f} d+i e \sqrt[4]{g}}\right) \log \left(-\sqrt[4]{g} \sqrt{x}-i \sqrt[4]{-f}\right)-\log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right) \log \left(i \sqrt[4]{-f}-\sqrt[4]{g} \sqrt{x}\right)+p \log \left(\frac{\sqrt[4]{g} \left(\sqrt{x} d+e\right)}{i \sqrt[4]{-f} d+e \sqrt[4]{g}}\right) \log \left(i \sqrt[4]{-f}-\sqrt[4]{g} \sqrt{x}\right)+\log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right) \log \left(\sqrt[4]{-f}-\sqrt[4]{g} \sqrt{x}\right)-p \log \left(\frac{\sqrt[4]{g} \left(\sqrt{x} d+e\right)}{\sqrt[4]{-f} d+e \sqrt[4]{g}}\right) \log \left(\sqrt[4]{-f}-\sqrt[4]{g} \sqrt{x}\right)-p \log \left(i \sqrt[4]{-f}-\sqrt[4]{g} \sqrt{x}\right) \log \left(-\frac{i \sqrt[4]{g} \sqrt{x}}{\sqrt[4]{-f}}\right)-p \log \left(-\sqrt[4]{g} \sqrt{x}-i \sqrt[4]{-f}\right) \log \left(\frac{i \sqrt[4]{g} \sqrt{x}}{\sqrt[4]{-f}}\right)+p \log \left(\sqrt[4]{-f}-\sqrt[4]{g} \sqrt{x}\right) \log \left(\frac{\sqrt[4]{g} \sqrt{x}}{\sqrt[4]{-f}}\right)-p \text{Li}_2\left(\frac{d \left(\sqrt[4]{-f}-\sqrt[4]{g} \sqrt{x}\right)}{\sqrt[4]{-f} d+e \sqrt[4]{g}}\right)+p \text{Li}_2\left(\frac{d \left(\sqrt[4]{-f}-i \sqrt[4]{g} \sqrt{x}\right)}{\sqrt[4]{-f} d+i e \sqrt[4]{g}}\right)+p \text{Li}_2\left(\frac{d \left(i \sqrt[4]{g} \sqrt{x}+\sqrt[4]{-f}\right)}{d \sqrt[4]{-f}-i e \sqrt[4]{g}}\right)-p \text{Li}_2\left(\frac{d \left(\sqrt[4]{g} \sqrt{x}+\sqrt[4]{-f}\right)}{d \sqrt[4]{-f}-e \sqrt[4]{g}}\right)-p \text{Li}_2\left(1-\frac{i \sqrt[4]{g} \sqrt{x}}{\sqrt[4]{-f}}\right)-p \text{Li}_2\left(\frac{i \sqrt[4]{g} \sqrt{x}}{\sqrt[4]{-f}}+1\right)+p \text{Li}_2\left(\frac{\sqrt[4]{g} \sqrt{x}}{\sqrt[4]{-f}}+1\right)+p \text{Li}_2\left(\frac{\sqrt[4]{g} \sqrt{x} f}{(-f)^{5/4}}+1\right)}{2 \sqrt{-f} \sqrt{g}}","-\frac{\log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right) \log \left(\frac{e \left(\sqrt[4]{g}-\frac{\sqrt{-\sqrt{-f}}}{\sqrt{x}}\right)}{d \sqrt{-\sqrt{-f}}+e \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}-\frac{\log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right) \log \left(-\frac{e \left(\frac{\sqrt{-\sqrt{-f}}}{\sqrt{x}}+\sqrt[4]{g}\right)}{d \sqrt{-\sqrt{-f}}-e \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{\log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right) \log \left(\frac{e \left(\sqrt[4]{g}-\frac{\sqrt[4]{-f}}{\sqrt{x}}\right)}{d \sqrt[4]{-f}+e \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{\log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right) \log \left(-\frac{e \left(\frac{\sqrt[4]{-f}}{\sqrt{x}}+\sqrt[4]{g}\right)}{d \sqrt[4]{-f}-e \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}-\frac{p \text{Li}_2\left(\frac{\sqrt{-\sqrt{-f}} \left(d+\frac{e}{\sqrt{x}}\right)}{d \sqrt{-\sqrt{-f}}-e \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{p \text{Li}_2\left(\frac{\sqrt[4]{-f} \left(d+\frac{e}{\sqrt{x}}\right)}{d \sqrt[4]{-f}-e \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}-\frac{p \text{Li}_2\left(\frac{\sqrt{-\sqrt{-f}} \left(d+\frac{e}{\sqrt{x}}\right)}{\sqrt{-\sqrt{-f}} d+e \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{p \text{Li}_2\left(\frac{\sqrt[4]{-f} \left(d+\frac{e}{\sqrt{x}}\right)}{\sqrt[4]{-f} d+e \sqrt[4]{g}}\right)}{2 \sqrt{-f} \sqrt{g}}",1,"(Log[c*(d + e/Sqrt[x])^p]*Log[-(-f)^(1/4) - g^(1/4)*Sqrt[x]] - p*Log[-((g^(1/4)*(e + d*Sqrt[x]))/(d*(-f)^(1/4) - e*g^(1/4)))]*Log[-(-f)^(1/4) - g^(1/4)*Sqrt[x]] - Log[c*(d + e/Sqrt[x])^p]*Log[(-I)*(-f)^(1/4) - g^(1/4)*Sqrt[x]] + p*Log[(I*g^(1/4)*(e + d*Sqrt[x]))/(d*(-f)^(1/4) + I*e*g^(1/4))]*Log[(-I)*(-f)^(1/4) - g^(1/4)*Sqrt[x]] - Log[c*(d + e/Sqrt[x])^p]*Log[I*(-f)^(1/4) - g^(1/4)*Sqrt[x]] + p*Log[(g^(1/4)*(e + d*Sqrt[x]))/(I*d*(-f)^(1/4) + e*g^(1/4))]*Log[I*(-f)^(1/4) - g^(1/4)*Sqrt[x]] + Log[c*(d + e/Sqrt[x])^p]*Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]] - p*Log[(g^(1/4)*(e + d*Sqrt[x]))/(d*(-f)^(1/4) + e*g^(1/4))]*Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]] - p*Log[I*(-f)^(1/4) - g^(1/4)*Sqrt[x]]*Log[((-I)*g^(1/4)*Sqrt[x])/(-f)^(1/4)] - p*Log[(-I)*(-f)^(1/4) - g^(1/4)*Sqrt[x]]*Log[(I*g^(1/4)*Sqrt[x])/(-f)^(1/4)] + p*Log[(-f)^(1/4) - g^(1/4)*Sqrt[x]]*Log[(g^(1/4)*Sqrt[x])/(-f)^(1/4)] + p*Log[-(-f)^(1/4) - g^(1/4)*Sqrt[x]]*Log[(f*g^(1/4)*Sqrt[x])/(-f)^(5/4)] - p*PolyLog[2, (d*((-f)^(1/4) - g^(1/4)*Sqrt[x]))/(d*(-f)^(1/4) + e*g^(1/4))] + p*PolyLog[2, (d*((-f)^(1/4) - I*g^(1/4)*Sqrt[x]))/(d*(-f)^(1/4) + I*e*g^(1/4))] + p*PolyLog[2, (d*((-f)^(1/4) + I*g^(1/4)*Sqrt[x]))/(d*(-f)^(1/4) - I*e*g^(1/4))] - p*PolyLog[2, (d*((-f)^(1/4) + g^(1/4)*Sqrt[x]))/(d*(-f)^(1/4) - e*g^(1/4))] - p*PolyLog[2, 1 - (I*g^(1/4)*Sqrt[x])/(-f)^(1/4)] - p*PolyLog[2, 1 + (I*g^(1/4)*Sqrt[x])/(-f)^(1/4)] + p*PolyLog[2, 1 + (g^(1/4)*Sqrt[x])/(-f)^(1/4)] + p*PolyLog[2, 1 + (f*g^(1/4)*Sqrt[x])/(-f)^(5/4)])/(2*Sqrt[-f]*Sqrt[g])","C",1
268,1,215,338,0.2800932,"\int \left(f+g x^2\right)^3 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^2)^3*Log[c*(d + e*x^2)^p],x]","\frac{1}{35} x \left(35 f^3+35 f^2 g x^2+21 f g^2 x^4+5 g^3 x^6\right) \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 p x \left(-525 d^3 g^3+35 d^2 e g^2 \left(63 f+5 g x^2\right)-105 d e^2 g \left(35 f^2+7 f g x^2+g^2 x^4\right)+e^3 \left(3675 f^3+1225 f^2 g x^2+441 f g^2 x^4+75 g^3 x^6\right)\right)}{3675 e^3}-\frac{2 \sqrt{d} p \left(5 d^3 g^3-21 d^2 e f g^2+35 d e^2 f^2 g-35 e^3 f^3\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{35 e^{7/2}}","f^3 x \log \left(c \left(d+e x^2\right)^p\right)+f^2 g x^3 \log \left(c \left(d+e x^2\right)^p\right)+\frac{3}{5} f g^2 x^5 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{7} g^3 x^7 \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 d^{3/2} f^2 g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{e^{3/2}}+\frac{6 d^{5/2} f g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{5 e^{5/2}}-\frac{2 d^{7/2} g^3 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{7 e^{7/2}}+\frac{2 d^3 g^3 p x}{7 e^3}-\frac{6 d^2 f g^2 p x}{5 e^2}-\frac{2 d^2 g^3 p x^3}{21 e^2}+\frac{2 \sqrt{d} f^3 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{2 d f^2 g p x}{e}+\frac{2 d f g^2 p x^3}{5 e}+\frac{2 d g^3 p x^5}{35 e}-2 f^3 p x-\frac{2}{3} f^2 g p x^3-\frac{6}{25} f g^2 p x^5-\frac{2}{49} g^3 p x^7",1,"(-2*p*x*(-525*d^3*g^3 + 35*d^2*e*g^2*(63*f + 5*g*x^2) - 105*d*e^2*g*(35*f^2 + 7*f*g*x^2 + g^2*x^4) + e^3*(3675*f^3 + 1225*f^2*g*x^2 + 441*f*g^2*x^4 + 75*g^3*x^6)))/(3675*e^3) - (2*Sqrt[d]*(-35*e^3*f^3 + 35*d*e^2*f^2*g - 21*d^2*e*f*g^2 + 5*d^3*g^3)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(35*e^(7/2)) + (x*(35*f^3 + 35*f^2*g*x^2 + 21*f*g^2*x^4 + 5*g^3*x^6)*Log[c*(d + e*x^2)^p])/35","A",1
269,1,151,221,0.1265133,"\int \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","\frac{\sqrt{e} x \left(15 e^2 \left(15 f^2+10 f g x^2+3 g^2 x^4\right) \log \left(c \left(d+e x^2\right)^p\right)-2 p \left(45 d^2 g^2-15 d e g \left(10 f+g x^2\right)+e^2 \left(225 f^2+50 f g x^2+9 g^2 x^4\right)\right)\right)+30 \sqrt{d} p \left(3 d^2 g^2-10 d e f g+15 e^2 f^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{225 e^{5/2}}","f^2 x \log \left(c \left(d+e x^2\right)^p\right)+\frac{2}{3} f g x^3 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{5} g^2 x^5 \log \left(c \left(d+e x^2\right)^p\right)-\frac{4 d^{3/2} f g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2}}+\frac{2 d^{5/2} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{5 e^{5/2}}-\frac{2 d^2 g^2 p x}{5 e^2}+\frac{2 \sqrt{d} f^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{4 d f g p x}{3 e}+\frac{2 d g^2 p x^3}{15 e}-2 f^2 p x-\frac{4}{9} f g p x^3-\frac{2}{25} g^2 p x^5",1,"(30*Sqrt[d]*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]] + Sqrt[e]*x*(-2*p*(45*d^2*g^2 - 15*d*e*g*(10*f + g*x^2) + e^2*(225*f^2 + 50*f*g*x^2 + 9*g^2*x^4)) + 15*e^2*(15*f^2 + 10*f*g*x^2 + 3*g^2*x^4)*Log[c*(d + e*x^2)^p]))/(225*e^(5/2))","A",1
270,1,117,117,0.0382476,"\int \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^2)*Log[c*(d + e*x^2)^p],x]","f x \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{3} g x^3 \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 d^{3/2} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2}}+\frac{2 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{2 d g p x}{3 e}-2 f p x-\frac{2}{9} g p x^3","f x \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{3} g x^3 \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 d^{3/2} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2}}+\frac{2 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{2 d g p x}{3 e}-2 f p x-\frac{2}{9} g p x^3",1,"-2*f*p*x + (2*d*g*p*x)/(3*e) - (2*g*p*x^3)/9 + (2*Sqrt[d]*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (2*d^(3/2)*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*e^(3/2)) + f*x*Log[c*(d + e*x^2)^p] + (g*x^3*Log[c*(d + e*x^2)^p])/3","A",1
271,1,564,533,0.2690886,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(f + g*x^2),x]","-\frac{i \left(2 i \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)+p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)+p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)-p \text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)-p \text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)+p \log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)+p \log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-p \log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-p \log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)\right)}{2 \sqrt{f} \sqrt{g}}","\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{\sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}-\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\sqrt{f} \sqrt{g}}+\frac{2 p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}",1,"((-1/2*I)*(p*Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] + p*Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] - p*Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] - p*Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] + (2*I)*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p] + p*PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] + p*PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])] - p*PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] - p*PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])]))/(Sqrt[f]*Sqrt[g])","A",0
272,1,1236,751,3.8796192,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(f + g*x^2)^2,x]","\frac{1}{2} \left(\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)}{f^{3/2} \sqrt{g}}+\frac{x \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)}{f \left(g x^2+f\right)}+\frac{1}{2} p \left(\frac{i \left(\frac{\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)}{i \sqrt{g} x+\sqrt{f}}+\frac{\sqrt{e} \left(\log \left(i \sqrt{f}-\sqrt{g} x\right)-\log \left(i \sqrt{d}-\sqrt{e} x\right)\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)}{f \sqrt{g}}+\frac{i \left(\frac{\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)}{i \sqrt{g} x+\sqrt{f}}+\frac{\sqrt{e} \left(\log \left(i \sqrt{f}-\sqrt{g} x\right)-\log \left(\sqrt{e} x+i \sqrt{d}\right)\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)}{f \sqrt{g}}+\frac{\sqrt{e} \left(\sqrt{g} x+i \sqrt{f}\right) \left(\log \left(i \sqrt{d}-\sqrt{e} x\right)-\log \left(\sqrt{g} x+i \sqrt{f}\right)\right)-i \left(\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}\right) \log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)}{f \left(\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}\right) \sqrt{g} \left(\sqrt{f}-i \sqrt{g} x\right)}-\frac{-\frac{\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)}{\sqrt{g} x+i \sqrt{f}}-\frac{i \sqrt{e} \left(\log \left(\sqrt{e} x+i \sqrt{d}\right)-\log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}}{f \sqrt{g}}+2 \left(\frac{x}{f^2+g x^2 f}+\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{f^{3/2} \sqrt{g}}\right) \left(-\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)-\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)+\log \left(e x^2+d\right)\right)+\frac{i \left(\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(-\frac{\sqrt{g} \left(\sqrt{d}-i \sqrt{e} x\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)\right)}{f^{3/2} \sqrt{g}}-\frac{i \left(\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt{g} \left(\sqrt{d}-i \sqrt{e} x\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)\right)}{f^{3/2} \sqrt{g}}-\frac{i \left(\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(-\frac{\sqrt{g} \left(i \sqrt{e} x+\sqrt{d}\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)\right)}{f^{3/2} \sqrt{g}}+\frac{i \left(\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt{g} \left(i \sqrt{e} x+\sqrt{d}\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)\right)}{f^{3/2} \sqrt{g}}\right)\right)","\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{2 f^{3/2} \sqrt{g}}-\frac{\log \left(c \left(d+e x^2\right)^p\right)}{4 f \sqrt{g} \left(\sqrt{-f}-\sqrt{g} x\right)}+\frac{\log \left(c \left(d+e x^2\right)^p\right)}{4 f \sqrt{g} \left(\sqrt{-f}+\sqrt{g} x\right)}+\frac{i p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{4 f^{3/2} \sqrt{g}}+\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{4 f^{3/2} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{2 f^{3/2} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{2 f^{3/2} \sqrt{g}}-\frac{e p \log \left(\sqrt{-f}-\sqrt{g} x\right)}{2 \sqrt{-f} \sqrt{g} (e f-d g)}+\frac{e p \log \left(\sqrt{-f}+\sqrt{g} x\right)}{2 \sqrt{-f} \sqrt{g} (e f-d g)}+\frac{\sqrt{d} \sqrt{e} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{f (e f-d g)}-\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 f^{3/2} \sqrt{g}}+\frac{p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{f^{3/2} \sqrt{g}}",1,"((x*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/(f*(f + g*x^2)) + (ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/(f^(3/2)*Sqrt[g]) + (p*((I*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]/(Sqrt[f] + I*Sqrt[g]*x) + (Sqrt[e]*(-Log[I*Sqrt[d] - Sqrt[e]*x] + Log[I*Sqrt[f] - Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])))/(f*Sqrt[g]) + (I*(Log[(I*Sqrt[d])/Sqrt[e] + x]/(Sqrt[f] + I*Sqrt[g]*x) + (Sqrt[e]*(-Log[I*Sqrt[d] + Sqrt[e]*x] + Log[I*Sqrt[f] - Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])))/(f*Sqrt[g]) + ((-I)*(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])*Log[((-I)*Sqrt[d])/Sqrt[e] + x] + Sqrt[e]*(I*Sqrt[f] + Sqrt[g]*x)*(Log[I*Sqrt[d] - Sqrt[e]*x] - Log[I*Sqrt[f] + Sqrt[g]*x]))/(f*(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])*Sqrt[g]*(Sqrt[f] - I*Sqrt[g]*x)) - (-(Log[(I*Sqrt[d])/Sqrt[e] + x]/(I*Sqrt[f] + Sqrt[g]*x)) - (I*Sqrt[e]*(Log[I*Sqrt[d] + Sqrt[e]*x] - Log[I*Sqrt[f] + Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))/(f*Sqrt[g]) + 2*(x/(f^2 + f*g*x^2) + ArcTan[(Sqrt[g]*x)/Sqrt[f]]/(f^(3/2)*Sqrt[g]))*(-Log[((-I)*Sqrt[d])/Sqrt[e] + x] - Log[(I*Sqrt[d])/Sqrt[e] + x] + Log[d + e*x^2]) + (I*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])] + PolyLog[2, -((Sqrt[g]*(Sqrt[d] - I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))]))/(f^(3/2)*Sqrt[g]) - (I*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(Sqrt[d] - I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])]))/(f^(3/2)*Sqrt[g]) - (I*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])] + PolyLog[2, -((Sqrt[g]*(Sqrt[d] + I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))]))/(f^(3/2)*Sqrt[g]) + (I*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(Sqrt[d] + I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])]))/(f^(3/2)*Sqrt[g])))/2)/2","A",1
273,1,435,945,0.5252405,"\int \left(f+g x^2\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^2)^2*Log[c*(d + e*x^2)^p]^2,x]","\frac{\sqrt{e} x \left(-60 p \left(45 d^2 g^2-15 d e g \left(10 f+g x^2\right)+e^2 \left(225 f^2+50 f g x^2+9 g^2 x^4\right)\right) \log \left(c \left(d+e x^2\right)^p\right)+225 e^2 \left(15 f^2+10 f g x^2+3 g^2 x^4\right) \log ^2\left(c \left(d+e x^2\right)^p\right)+8 p^2 \left(1035 d^2 g^2-120 d e g \left(25 f+g x^2\right)+e^2 \left(3375 f^2+250 f g x^2+27 g^2 x^4\right)\right)\right)+60 \sqrt{d} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(15 \left(3 d^2 g^2-10 d e f g+15 e^2 f^2\right) \log \left(c \left(d+e x^2\right)^p\right)+30 p \left(3 d^2 g^2-10 d e f g+15 e^2 f^2\right) \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right)-2 p \left(69 d^2 g^2-200 d e f g+225 e^2 f^2\right)\right)+900 i \sqrt{d} p^2 \left(3 d^2 g^2-10 d e f g+15 e^2 f^2\right) \text{Li}_2\left(\frac{\sqrt{e} x+i \sqrt{d}}{\sqrt{e} x-i \sqrt{d}}\right)+900 i \sqrt{d} p^2 \left(3 d^2 g^2-10 d e f g+15 e^2 f^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{3375 e^{5/2}}","\frac{8}{125} g^2 p^2 x^5+\frac{1}{5} g^2 \log ^2\left(c \left(e x^2+d\right)^p\right) x^5-\frac{4}{25} g^2 p \log \left(c \left(e x^2+d\right)^p\right) x^5-\frac{64 d g^2 p^2 x^3}{225 e}+\frac{16}{27} f g p^2 x^3+\frac{2}{3} f g \log ^2\left(c \left(e x^2+d\right)^p\right) x^3+\frac{4 d g^2 p \log \left(c \left(e x^2+d\right)^p\right) x^3}{15 e}-\frac{8}{9} f g p \log \left(c \left(e x^2+d\right)^p\right) x^3+8 f^2 p^2 x+\frac{184 d^2 g^2 p^2 x}{75 e^2}-\frac{64 d f g p^2 x}{9 e}+f^2 \log ^2\left(c \left(e x^2+d\right)^p\right) x-4 f^2 p \log \left(c \left(e x^2+d\right)^p\right) x-\frac{4 d^2 g^2 p \log \left(c \left(e x^2+d\right)^p\right) x}{5 e^2}+\frac{8 d f g p \log \left(c \left(e x^2+d\right)^p\right) x}{3 e}+\frac{4 i \sqrt{d} f^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{\sqrt{e}}+\frac{4 i d^{5/2} g^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{5 e^{5/2}}-\frac{8 i d^{3/2} f g p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{3 e^{3/2}}-\frac{8 \sqrt{d} f^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-\frac{184 d^{5/2} g^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{75 e^{5/2}}+\frac{64 d^{3/2} f g p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{9 e^{3/2}}+\frac{8 \sqrt{d} f^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}+\frac{8 d^{5/2} g^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{5 e^{5/2}}-\frac{16 d^{3/2} f g p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{3 e^{3/2}}+\frac{4 \sqrt{d} f^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(e x^2+d\right)^p\right)}{\sqrt{e}}+\frac{4 d^{5/2} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(e x^2+d\right)^p\right)}{5 e^{5/2}}-\frac{8 d^{3/2} f g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(e x^2+d\right)^p\right)}{3 e^{3/2}}+\frac{4 i \sqrt{d} f^2 p^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}+\frac{4 i d^{5/2} g^2 p^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{5 e^{5/2}}-\frac{8 i d^{3/2} f g p^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{3 e^{3/2}}",1,"((900*I)*Sqrt[d]*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2 + 60*Sqrt[d]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(-2*(225*e^2*f^2 - 200*d*e*f*g + 69*d^2*g^2)*p + 30*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)] + 15*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*Log[c*(d + e*x^2)^p]) + Sqrt[e]*x*(8*p^2*(1035*d^2*g^2 - 120*d*e*g*(25*f + g*x^2) + e^2*(3375*f^2 + 250*f*g*x^2 + 27*g^2*x^4)) - 60*p*(45*d^2*g^2 - 15*d*e*g*(10*f + g*x^2) + e^2*(225*f^2 + 50*f*g*x^2 + 9*g^2*x^4))*Log[c*(d + e*x^2)^p] + 225*e^2*(15*f^2 + 10*f*g*x^2 + 3*g^2*x^4)*Log[c*(d + e*x^2)^p]^2) + (900*I)*Sqrt[d]*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p^2*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x)/((-I)*Sqrt[d] + Sqrt[e]*x)])/(3375*e^(5/2))","A",1
274,1,281,548,0.2813101,"\int \left(f+g x^2\right) \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^2)*Log[c*(d + e*x^2)^p]^2,x]","\frac{\sqrt{e} x \left(9 e \left(3 f+g x^2\right) \log ^2\left(c \left(d+e x^2\right)^p\right)-12 p \left(-3 d g+9 e f+e g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)+8 p^2 \left(-12 d g+27 e f+e g x^2\right)\right)-12 \sqrt{d} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left((3 d g-9 e f) \log \left(c \left(d+e x^2\right)^p\right)+6 p (d g-3 e f) \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right)+2 p (9 e f-4 d g)\right)-36 i \sqrt{d} p^2 (d g-3 e f) \text{Li}_2\left(\frac{\sqrt{e} x+i \sqrt{d}}{\sqrt{e} x-i \sqrt{d}}\right)-36 i \sqrt{d} p^2 (d g-3 e f) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{27 e^{3/2}}","-\frac{4 d^{3/2} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{3 e^{3/2}}+f x \log ^2\left(c \left(d+e x^2\right)^p\right)-4 f p x \log \left(c \left(d+e x^2\right)^p\right)+\frac{4 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{\sqrt{e}}+\frac{4 d g p x \log \left(c \left(d+e x^2\right)^p\right)}{3 e}+\frac{1}{3} g x^3 \log ^2\left(c \left(d+e x^2\right)^p\right)-\frac{4}{9} g p x^3 \log \left(c \left(d+e x^2\right)^p\right)-\frac{4 i d^{3/2} g p^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{3 e^{3/2}}-\frac{4 i d^{3/2} g p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{3 e^{3/2}}+\frac{32 d^{3/2} g p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{9 e^{3/2}}-\frac{8 d^{3/2} g p^2 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2}}+\frac{4 i \sqrt{d} f p^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}+\frac{4 i \sqrt{d} f p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{\sqrt{e}}-\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{8 \sqrt{d} f p^2 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-\frac{32 d g p^2 x}{9 e}+8 f p^2 x+\frac{8}{27} g p^2 x^3",1,"((-36*I)*Sqrt[d]*(-3*e*f + d*g)*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2 - 12*Sqrt[d]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(2*(9*e*f - 4*d*g)*p + 6*(-3*e*f + d*g)*p*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)] + (-9*e*f + 3*d*g)*Log[c*(d + e*x^2)^p]) + Sqrt[e]*x*(8*p^2*(27*e*f - 12*d*g + e*g*x^2) - 12*p*(9*e*f - 3*d*g + e*g*x^2)*Log[c*(d + e*x^2)^p] + 9*e*(3*f + g*x^2)*Log[c*(d + e*x^2)^p]^2) - (36*I)*Sqrt[d]*(-3*e*f + d*g)*p^2*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x)/((-I)*Sqrt[d] + Sqrt[e]*x)])/(27*e^(3/2))","A",1
275,0,0,27,2.8413022,"\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^2),x]","\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","\text{Int}\left(\frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{f+g x^2},x\right)",0,"Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^2), x]","A",-1
276,0,0,27,8.9541964,"\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^2)^2,x]","\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","\text{Int}\left(\frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2},x\right)",0,"Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^2)^2, x]","A",-1
277,1,1460,683,4.5689387,"\int \left(f+g x^2\right) \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^2)*Log[c*(d + e*x^2)^p]^3,x]","\frac{g x \left(2 d \log ^3\left(e x^2+d\right)-2 d \sqrt{1-\frac{e x^2+d}{d}} \log ^3\left(e x^2+d\right)+2 \left(e x^2+d\right) \sqrt{1-\frac{e x^2+d}{d}} \log ^3\left(e x^2+d\right)-9 \left(e x^2+d\right) \, _3F_2\left(-\frac{1}{2},1,1;2,2;\frac{e x^2+d}{d}\right) \log ^2\left(e x^2+d\right)+18 \left(e x^2+d\right) \, _4F_3\left(-\frac{1}{2},1,1,1;2,2,2;\frac{e x^2+d}{d}\right) \log \left(e x^2+d\right)-18 \left(e x^2+d\right) \, _5F_4\left(-\frac{1}{2},1,1,1,1;2,2,2,2;\frac{e x^2+d}{d}\right)\right) p^3}{6 e \sqrt{1-\frac{e x^2+d}{d}}}+\frac{f \left(\sqrt{-d} e \left(\log ^3\left(e x^2+d\right)-6 \log ^2\left(e x^2+d\right)+24 \log \left(e x^2+d\right)-48\right) x^2-48 \sqrt{-d^2} \sqrt{e x^2+d} \sqrt{1-\frac{d}{e x^2+d}} \sin ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e x^2+d}}\right)-6 \sqrt{-d^2} \sqrt{1-\frac{d}{e x^2+d}} \left(\sqrt{e x^2+d} \sin ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e x^2+d}}\right) \log ^2\left(e x^2+d\right)+4 \sqrt{d} \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};\frac{d}{e x^2+d}\right) \log \left(e x^2+d\right)+8 \sqrt{d} \, _4F_3\left(\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2},\frac{3}{2};\frac{d}{e x^2+d}\right)\right)+24 d \sqrt{e x^2} \tanh ^{-1}\left(\frac{\sqrt{e x^2}}{\sqrt{-d}}\right) \left(\log \left(e x^2+d\right)-\log \left(\frac{e x^2+d}{d}\right)\right)+6 (-d)^{3/2} \sqrt{1-\frac{e x^2+d}{d}} \left(\log ^2\left(\frac{e x^2+d}{d}\right)-4 \log \left(\frac{1}{2} \left(\sqrt{1-\frac{e x^2+d}{d}}+1\right)\right) \log \left(\frac{e x^2+d}{d}\right)+2 \log ^2\left(\frac{1}{2} \left(\sqrt{1-\frac{e x^2+d}{d}}+1\right)\right)-4 \text{Li}_2\left(\frac{1}{2}-\frac{1}{2} \sqrt{1-\frac{e x^2+d}{d}}\right)\right)\right) p^3}{\sqrt{-d} e x}+3 f \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right) \left(x \log ^2\left(e x^2+d\right)-\frac{4 \left(-i \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2-\sqrt{d} \left(2 \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)+\log \left(e x^2+d\right)-2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)+\sqrt{e} x \left(\log \left(e x^2+d\right)-2\right)-i \sqrt{d} \text{Li}_2\left(\frac{\sqrt{e} x+i \sqrt{d}}{\sqrt{e} x-i \sqrt{d}}\right)\right)}{\sqrt{e}}\right) p^2+3 g \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right) \left(\frac{1}{3} x^3 \log ^2\left(e x^2+d\right)-\frac{4 \left(9 i d^{3/2} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2+3 d^{3/2} \left(6 \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)+3 \log \left(e x^2+d\right)-8\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)+\sqrt{e} x \left(-2 e x^2+24 d+\left(3 e x^2-9 d\right) \log \left(e x^2+d\right)\right)+9 i d^{3/2} \text{Li}_2\left(\frac{\sqrt{e} x+i \sqrt{d}}{\sqrt{e} x-i \sqrt{d}}\right)\right)}{27 e^{3/2}}\right) p^2+\frac{2 d g x \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2 p}{e}+\frac{6 \sqrt{d} f \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2 p}{\sqrt{e}}-\frac{2 d^{3/2} g \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2 p}{e^{3/2}}+g x^3 \log \left(e x^2+d\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2 p+3 f x \log \left(e x^2+d\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2 p+f x \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2 \left(-\log \left(e x^2+d\right) p-6 p+\log \left(c \left(e x^2+d\right)^p\right)\right)+\frac{1}{3} g x^3 \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2 \left(-\log \left(e x^2+d\right) p-2 p+\log \left(c \left(e x^2+d\right)^p\right)\right)","-\frac{2 d p (d g-3 e f) \text{Int}\left(\frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{d+e x^2},x\right)}{e}+\frac{32 d^{3/2} g p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{3 e^{3/2}}+24 f p^2 x \log \left(c \left(d+e x^2\right)^p\right)-\frac{24 \sqrt{d} f p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{\sqrt{e}}+f x \log ^3\left(c \left(d+e x^2\right)^p\right)-6 f p x \log ^2\left(c \left(d+e x^2\right)^p\right)-\frac{32 d g p^2 x \log \left(c \left(d+e x^2\right)^p\right)}{3 e}+\frac{8}{9} g p^2 x^3 \log \left(c \left(d+e x^2\right)^p\right)+\frac{2 d g p x \log ^2\left(c \left(d+e x^2\right)^p\right)}{e}+\frac{1}{3} g x^3 \log ^3\left(c \left(d+e x^2\right)^p\right)-\frac{2}{3} g p x^3 \log ^2\left(c \left(d+e x^2\right)^p\right)+\frac{32 i d^{3/2} g p^3 \text{Li}_2\left(-\frac{\sqrt{d}-i \sqrt{e} x}{i \sqrt{e} x+\sqrt{d}}\right)}{3 e^{3/2}}+\frac{32 i d^{3/2} g p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{3 e^{3/2}}-\frac{208 d^{3/2} g p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{9 e^{3/2}}+\frac{64 d^{3/2} g p^3 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2}}-\frac{24 i \sqrt{d} f p^3 \text{Li}_2\left(-\frac{\sqrt{d}-i \sqrt{e} x}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}-\frac{24 i \sqrt{d} f p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{\sqrt{e}}+\frac{48 \sqrt{d} f p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-\frac{48 \sqrt{d} f p^3 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{208 d g p^3 x}{9 e}-48 f p^3 x-\frac{16}{27} g p^3 x^3",0,"(g*p^3*x*(-18*(d + e*x^2)*HypergeometricPFQ[{-1/2, 1, 1, 1, 1}, {2, 2, 2, 2}, (d + e*x^2)/d] + 18*(d + e*x^2)*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^2)/d]*Log[d + e*x^2] - 9*(d + e*x^2)*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, (d + e*x^2)/d]*Log[d + e*x^2]^2 + 2*d*Log[d + e*x^2]^3 - 2*d*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2]^3 + 2*(d + e*x^2)*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2]^3))/(6*e*Sqrt[1 - (d + e*x^2)/d]) + (2*d*g*p*x*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/e + (6*Sqrt[d]*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/Sqrt[e] - (2*d^(3/2)*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/e^(3/2) + 3*f*p*x*Log[d + e*x^2]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2 + g*p*x^3*Log[d + e*x^2]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2 + f*x*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2*(-6*p - p*Log[d + e*x^2] + Log[c*(d + e*x^2)^p]) + (g*x^3*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2*(-2*p - p*Log[d + e*x^2] + Log[c*(d + e*x^2)^p]))/3 + 3*f*p^2*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])*(x*Log[d + e*x^2]^2 - (4*((-I)*Sqrt[d]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2 + Sqrt[e]*x*(-2 + Log[d + e*x^2]) - Sqrt[d]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(-2 + 2*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)] + Log[d + e*x^2]) - I*Sqrt[d]*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x)/((-I)*Sqrt[d] + Sqrt[e]*x)]))/Sqrt[e]) + 3*g*p^2*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])*((x^3*Log[d + e*x^2]^2)/3 - (4*((9*I)*d^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2 + 3*d^(3/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(-8 + 6*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)] + 3*Log[d + e*x^2]) + Sqrt[e]*x*(24*d - 2*e*x^2 + (-9*d + 3*e*x^2)*Log[d + e*x^2]) + (9*I)*d^(3/2)*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x)/((-I)*Sqrt[d] + Sqrt[e]*x)]))/(27*e^(3/2))) + (f*p^3*(-48*Sqrt[-d^2]*Sqrt[d + e*x^2]*Sqrt[1 - d/(d + e*x^2)]*ArcSin[Sqrt[d]/Sqrt[d + e*x^2]] - 6*Sqrt[-d^2]*Sqrt[1 - d/(d + e*x^2)]*(8*Sqrt[d]*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {3/2, 3/2, 3/2}, d/(d + e*x^2)] + 4*Sqrt[d]*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, d/(d + e*x^2)]*Log[d + e*x^2] + Sqrt[d + e*x^2]*ArcSin[Sqrt[d]/Sqrt[d + e*x^2]]*Log[d + e*x^2]^2) + Sqrt[-d]*e*x^2*(-48 + 24*Log[d + e*x^2] - 6*Log[d + e*x^2]^2 + Log[d + e*x^2]^3) + 24*d*Sqrt[e*x^2]*ArcTanh[Sqrt[e*x^2]/Sqrt[-d]]*(Log[d + e*x^2] - Log[(d + e*x^2)/d]) + 6*(-d)^(3/2)*Sqrt[1 - (d + e*x^2)/d]*(Log[(d + e*x^2)/d]^2 - 4*Log[(d + e*x^2)/d]*Log[(1 + Sqrt[1 - (d + e*x^2)/d])/2] + 2*Log[(1 + Sqrt[1 - (d + e*x^2)/d])/2]^2 - 4*PolyLog[2, 1/2 - Sqrt[1 - (d + e*x^2)/d]/2])))/(Sqrt[-d]*e*x)","B",0
278,0,0,27,4.1228508,"\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]^3/(f + g*x^2),x]","\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","\text{Int}\left(\frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{f+g x^2},x\right)",0,"Integrate[Log[c*(d + e*x^2)^p]^3/(f + g*x^2), x]","A",-1
279,0,0,27,18.3214972,"\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]^3/(f + g*x^2)^2,x]","\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","\text{Int}\left(\frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2},x\right)",0,"Integrate[Log[c*(d + e*x^2)^p]^3/(f + g*x^2)^2, x]","A",-1
280,0,0,27,0.4920656,"\int \frac{\left(f+g x^2\right)^2}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[(f + g*x^2)^2/Log[c*(d + e*x^2)^p],x]","\int \frac{\left(f+g x^2\right)^2}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{\left(f+g x^2\right)^2}{\log \left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[(f + g*x^2)^2/Log[c*(d + e*x^2)^p], x]","A",-1
281,0,0,25,0.3130049,"\int \frac{f+g x^2}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[(f + g*x^2)/Log[c*(d + e*x^2)^p],x]","\int \frac{f+g x^2}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{f+g x^2}{\log \left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[(f + g*x^2)/Log[c*(d + e*x^2)^p], x]","A",-1
282,0,0,27,0.5664229,"\int \frac{1}{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[1/((f + g*x^2)*Log[c*(d + e*x^2)^p]),x]","\int \frac{1}{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[1/((f + g*x^2)*Log[c*(d + e*x^2)^p]), x]","A",-1
283,0,0,27,2.6301369,"\int \frac{1}{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[1/((f + g*x^2)^2*Log[c*(d + e*x^2)^p]),x]","\int \frac{1}{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[1/((f + g*x^2)^2*Log[c*(d + e*x^2)^p]), x]","A",-1
284,0,0,27,0.8992468,"\int \frac{\left(f+g x^2\right)^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[(f + g*x^2)^2/Log[c*(d + e*x^2)^p]^2,x]","\int \frac{\left(f+g x^2\right)^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{\left(f+g x^2\right)^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[(f + g*x^2)^2/Log[c*(d + e*x^2)^p]^2, x]","A",-1
285,0,0,25,0.6502998,"\int \frac{f+g x^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[(f + g*x^2)/Log[c*(d + e*x^2)^p]^2,x]","\int \frac{f+g x^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{f+g x^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[(f + g*x^2)/Log[c*(d + e*x^2)^p]^2, x]","A",-1
286,0,0,27,4.604364,"\int \frac{1}{\left(f+g x^2\right) \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[1/((f + g*x^2)*Log[c*(d + e*x^2)^p]^2),x]","\int \frac{1}{\left(f+g x^2\right) \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\left(f+g x^2\right) \log ^2\left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[1/((f + g*x^2)*Log[c*(d + e*x^2)^p]^2), x]","A",-1
287,0,0,27,7.7280014,"\int \frac{1}{\left(f+g x^2\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[1/((f + g*x^2)^2*Log[c*(d + e*x^2)^p]^2),x]","\int \frac{1}{\left(f+g x^2\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\left(f+g x^2\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[1/((f + g*x^2)^2*Log[c*(d + e*x^2)^p]^2), x]","A",-1
288,1,258,366,0.2539812,"\int \left(f+g x^3\right)^3 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^3)^3*Log[c*(d + e*x^2)^p],x]","\frac{210 e^5 x \left(140 f^3+105 f^2 g x^3+60 f g^2 x^6+14 g^3 x^9\right) \log \left(c \left(d+e x^2\right)^p\right)-8400 \sqrt{d} e^{3/2} f p \left(3 d^3 g^2-7 e^3 f^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)+1470 d^2 g p \left(2 d^3 g^2-15 e^3 f^2\right) \log \left(d+e x^2\right)-e p x \left(2940 d^4 g^3 x-210 d^3 e g^2 \left(120 f+7 g x^3\right)+140 d^2 e^2 g^2 x^2 \left(60 f+7 g x^3\right)-105 d e^3 g x \left(210 f^2+48 f g x^3+7 g^2 x^6\right)+3 e^4 \left(19600 f^3+3675 f^2 g x^3+1200 f g^2 x^6+196 g^3 x^9\right)\right)}{29400 e^5}","f^3 x \log \left(c \left(d+e x^2\right)^p\right)+\frac{3}{4} f^2 g x^4 \log \left(c \left(d+e x^2\right)^p\right)+\frac{3}{7} f g^2 x^7 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{10} g^3 x^{10} \log \left(c \left(d+e x^2\right)^p\right)-\frac{6 d^{7/2} f g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{7 e^{7/2}}+\frac{d^5 g^3 p \log \left(d+e x^2\right)}{10 e^5}-\frac{d^4 g^3 p x^2}{10 e^4}+\frac{6 d^3 f g^2 p x}{7 e^3}+\frac{d^3 g^3 p x^4}{20 e^3}-\frac{3 d^2 f^2 g p \log \left(d+e x^2\right)}{4 e^2}-\frac{2 d^2 f g^2 p x^3}{7 e^2}-\frac{d^2 g^3 p x^6}{30 e^2}+\frac{2 \sqrt{d} f^3 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{3 d f^2 g p x^2}{4 e}+\frac{6 d f g^2 p x^5}{35 e}+\frac{d g^3 p x^8}{40 e}-2 f^3 p x-\frac{3}{8} f^2 g p x^4-\frac{6}{49} f g^2 p x^7-\frac{1}{50} g^3 p x^{10}",1,"(-(e*p*x*(2940*d^4*g^3*x + 140*d^2*e^2*g^2*x^2*(60*f + 7*g*x^3) - 210*d^3*e*g^2*(120*f + 7*g*x^3) - 105*d*e^3*g*x*(210*f^2 + 48*f*g*x^3 + 7*g^2*x^6) + 3*e^4*(19600*f^3 + 3675*f^2*g*x^3 + 1200*f*g^2*x^6 + 196*g^3*x^9))) - 8400*Sqrt[d]*e^(3/2)*f*(-7*e^3*f^2 + 3*d^3*g^2)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]] + 1470*d^2*g*(-15*e^3*f^2 + 2*d^3*g^2)*p*Log[d + e*x^2] + 210*e^5*x*(140*f^3 + 105*f^2*g*x^3 + 60*f*g^2*x^6 + 14*g^3*x^9)*Log[c*(d + e*x^2)^p])/(29400*e^5)","A",1
289,1,178,231,0.2143848,"\int \left(f+g x^3\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^3)^2*Log[c*(d + e*x^2)^p],x]","\frac{1}{14} x \left(14 f^2+7 f g x^3+2 g^2 x^6\right) \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 \sqrt{d} p \left(d^3 g^2-7 e^3 f^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{7 e^{7/2}}-\frac{d^2 f g p \log \left(d+e x^2\right)}{2 e^2}+\frac{p x \left(840 d^3 g^2-280 d^2 e g^2 x^2+42 d e^2 g x \left(35 f+4 g x^3\right)-15 e^3 \left(392 f^2+49 f g x^3+8 g^2 x^6\right)\right)}{2940 e^3}","f^2 x \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{2} f g x^4 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{7} g^2 x^7 \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 d^{7/2} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{7 e^{7/2}}+\frac{2 d^3 g^2 p x}{7 e^3}-\frac{d^2 f g p \log \left(d+e x^2\right)}{2 e^2}-\frac{2 d^2 g^2 p x^3}{21 e^2}+\frac{2 \sqrt{d} f^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{d f g p x^2}{2 e}+\frac{2 d g^2 p x^5}{35 e}-2 f^2 p x-\frac{1}{4} f g p x^4-\frac{2}{49} g^2 p x^7",1,"(p*x*(840*d^3*g^2 - 280*d^2*e*g^2*x^2 + 42*d*e^2*g*x*(35*f + 4*g*x^3) - 15*e^3*(392*f^2 + 49*f*g*x^3 + 8*g^2*x^6)))/(2940*e^3) - (2*Sqrt[d]*(-7*e^3*f^2 + d^3*g^2)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(7*e^(7/2)) - (d^2*f*g*p*Log[d + e*x^2])/(2*e^2) + (x*(14*f^2 + 7*f*g*x^3 + 2*g^2*x^6)*Log[c*(d + e*x^2)^p])/14","A",1
290,1,110,110,0.0490906,"\int \left(f+g x^3\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^3)*Log[c*(d + e*x^2)^p],x]","f x \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{4} g x^4 \log \left(c \left(d+e x^2\right)^p\right)-\frac{d^2 g p \log \left(d+e x^2\right)}{4 e^2}+\frac{2 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{d g p x^2}{4 e}-2 f p x-\frac{1}{8} g p x^4","f x \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{4} g x^4 \log \left(c \left(d+e x^2\right)^p\right)-\frac{d^2 g p \log \left(d+e x^2\right)}{4 e^2}+\frac{2 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{d g p x^2}{4 e}-2 f p x-\frac{1}{8} g p x^4",1,"-2*f*p*x + (d*g*p*x^2)/(4*e) - (g*p*x^4)/8 + (2*Sqrt[d]*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (d^2*g*p*Log[d + e*x^2])/(4*e^2) + f*x*Log[c*(d + e*x^2)^p] + (g*x^4*Log[c*(d + e*x^2)^p])/4","A",1
291,1,990,1165,0.8347525,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{f+g x^3} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(f + g*x^3),x]","\frac{-p \log \left(\frac{\sqrt[3]{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right) \log \left(-\sqrt[3]{g} x-\sqrt[3]{f}\right)-p \log \left(\frac{\sqrt[3]{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\sqrt{-d} \sqrt[3]{g}-\sqrt{e} \sqrt[3]{f}}\right) \log \left(-\sqrt[3]{g} x-\sqrt[3]{f}\right)+\log \left(c \left(e x^2+d\right)^p\right) \log \left(-\sqrt[3]{g} x-\sqrt[3]{f}\right)-(-1)^{2/3} p \log \left(\frac{\sqrt[3]{-1} \sqrt[3]{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt[3]{-1} \sqrt{-d} \sqrt[3]{g}-\sqrt{e} \sqrt[3]{f}}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{g} x-\sqrt[3]{f}\right)-(-1)^{2/3} p \log \left(\frac{\sqrt[3]{-1} \sqrt[3]{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\sqrt[3]{-1} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{g} x-\sqrt[3]{f}\right)+\sqrt[3]{-1} p \log \left(\frac{(-1)^{2/3} \sqrt[3]{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{(-1)^{2/3} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right) \log \left(-(-1)^{2/3} \sqrt[3]{g} x-\sqrt[3]{f}\right)+\sqrt[3]{-1} p \log \left(\frac{(-1)^{2/3} \sqrt[3]{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{(-1)^{2/3} \sqrt{-d} \sqrt[3]{g}-\sqrt{e} \sqrt[3]{f}}\right) \log \left(-(-1)^{2/3} \sqrt[3]{g} x-\sqrt[3]{f}\right)+(-1)^{2/3} \log \left(\sqrt[3]{-1} \sqrt[3]{g} x-\sqrt[3]{f}\right) \log \left(c \left(e x^2+d\right)^p\right)-\sqrt[3]{-1} \log \left(-(-1)^{2/3} \sqrt[3]{g} x-\sqrt[3]{f}\right) \log \left(c \left(e x^2+d\right)^p\right)-p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{g} x+\sqrt[3]{f}\right)}{\sqrt{e} \sqrt[3]{f}-\sqrt{-d} \sqrt[3]{g}}\right)-p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{g} x+\sqrt[3]{f}\right)}{\sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right)-(-1)^{2/3} p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{f}-\sqrt[3]{-1} \sqrt[3]{g} x\right)}{\sqrt{e} \sqrt[3]{f}-\sqrt[3]{-1} \sqrt{-d} \sqrt[3]{g}}\right)-(-1)^{2/3} p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{f}-\sqrt[3]{-1} \sqrt[3]{g} x\right)}{\sqrt[3]{-1} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right)+\sqrt[3]{-1} p \text{Li}_2\left(\frac{\sqrt{e} \left((-1)^{2/3} \sqrt[3]{g} x+\sqrt[3]{f}\right)}{\sqrt{e} \sqrt[3]{f}-(-1)^{2/3} \sqrt{-d} \sqrt[3]{g}}\right)+\sqrt[3]{-1} p \text{Li}_2\left(\frac{\sqrt{e} \left((-1)^{2/3} \sqrt[3]{g} x+\sqrt[3]{f}\right)}{(-1)^{2/3} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right)}{3 f^{2/3} \sqrt[3]{g}}","-\frac{p \log \left(\frac{\sqrt[3]{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right) \log \left(-\sqrt[3]{g} x-\sqrt[3]{f}\right)}{3 f^{2/3} \sqrt[3]{g}}-\frac{p \log \left(-\frac{\sqrt[3]{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\sqrt{e} \sqrt[3]{f}-\sqrt{-d} \sqrt[3]{g}}\right) \log \left(-\sqrt[3]{g} x-\sqrt[3]{f}\right)}{3 f^{2/3} \sqrt[3]{g}}+\frac{\log \left(c \left(e x^2+d\right)^p\right) \log \left(-\sqrt[3]{g} x-\sqrt[3]{f}\right)}{3 f^{2/3} \sqrt[3]{g}}-\frac{(-1)^{2/3} p \log \left(-\frac{\sqrt[3]{-1} \sqrt[3]{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{e} \sqrt[3]{f}-\sqrt[3]{-1} \sqrt{-d} \sqrt[3]{g}}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{g} x-\sqrt[3]{f}\right)}{3 f^{2/3} \sqrt[3]{g}}-\frac{(-1)^{2/3} p \log \left(\frac{\sqrt[3]{-1} \sqrt[3]{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\sqrt[3]{-1} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{g} x-\sqrt[3]{f}\right)}{3 f^{2/3} \sqrt[3]{g}}+\frac{\sqrt[3]{-1} p \log \left(\frac{(-1)^{2/3} \sqrt[3]{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{(-1)^{2/3} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right) \log \left(-(-1)^{2/3} \sqrt[3]{g} x-\sqrt[3]{f}\right)}{3 f^{2/3} \sqrt[3]{g}}+\frac{\sqrt[3]{-1} p \log \left(-\frac{(-1)^{2/3} \sqrt[3]{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\sqrt{e} \sqrt[3]{f}-(-1)^{2/3} \sqrt{-d} \sqrt[3]{g}}\right) \log \left(-(-1)^{2/3} \sqrt[3]{g} x-\sqrt[3]{f}\right)}{3 f^{2/3} \sqrt[3]{g}}+\frac{(-1)^{2/3} \log \left(\sqrt[3]{-1} \sqrt[3]{g} x-\sqrt[3]{f}\right) \log \left(c \left(e x^2+d\right)^p\right)}{3 f^{2/3} \sqrt[3]{g}}-\frac{\sqrt[3]{-1} \log \left(-(-1)^{2/3} \sqrt[3]{g} x-\sqrt[3]{f}\right) \log \left(c \left(e x^2+d\right)^p\right)}{3 f^{2/3} \sqrt[3]{g}}-\frac{p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{g} x+\sqrt[3]{f}\right)}{\sqrt{e} \sqrt[3]{f}-\sqrt{-d} \sqrt[3]{g}}\right)}{3 f^{2/3} \sqrt[3]{g}}-\frac{p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{g} x+\sqrt[3]{f}\right)}{\sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right)}{3 f^{2/3} \sqrt[3]{g}}-\frac{(-1)^{2/3} p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{f}-\sqrt[3]{-1} \sqrt[3]{g} x\right)}{\sqrt{e} \sqrt[3]{f}-\sqrt[3]{-1} \sqrt{-d} \sqrt[3]{g}}\right)}{3 f^{2/3} \sqrt[3]{g}}-\frac{(-1)^{2/3} p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{f}-\sqrt[3]{-1} \sqrt[3]{g} x\right)}{\sqrt[3]{-1} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right)}{3 f^{2/3} \sqrt[3]{g}}+\frac{\sqrt[3]{-1} p \text{Li}_2\left(\frac{\sqrt{e} \left((-1)^{2/3} \sqrt[3]{g} x+\sqrt[3]{f}\right)}{\sqrt{e} \sqrt[3]{f}-(-1)^{2/3} \sqrt{-d} \sqrt[3]{g}}\right)}{3 f^{2/3} \sqrt[3]{g}}+\frac{\sqrt[3]{-1} p \text{Li}_2\left(\frac{\sqrt{e} \left((-1)^{2/3} \sqrt[3]{g} x+\sqrt[3]{f}\right)}{(-1)^{2/3} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right)}{3 f^{2/3} \sqrt[3]{g}}",1,"(-(p*Log[(g^(1/3)*(Sqrt[-d] - Sqrt[e]*x))/(Sqrt[e]*f^(1/3) + Sqrt[-d]*g^(1/3))]*Log[-f^(1/3) - g^(1/3)*x]) - p*Log[(g^(1/3)*(Sqrt[-d] + Sqrt[e]*x))/(-(Sqrt[e]*f^(1/3)) + Sqrt[-d]*g^(1/3))]*Log[-f^(1/3) - g^(1/3)*x] - (-1)^(2/3)*p*Log[((-1)^(1/3)*g^(1/3)*(Sqrt[-d] - Sqrt[e]*x))/(-(Sqrt[e]*f^(1/3)) + (-1)^(1/3)*Sqrt[-d]*g^(1/3))]*Log[-f^(1/3) + (-1)^(1/3)*g^(1/3)*x] - (-1)^(2/3)*p*Log[((-1)^(1/3)*g^(1/3)*(Sqrt[-d] + Sqrt[e]*x))/(Sqrt[e]*f^(1/3) + (-1)^(1/3)*Sqrt[-d]*g^(1/3))]*Log[-f^(1/3) + (-1)^(1/3)*g^(1/3)*x] + (-1)^(1/3)*p*Log[((-1)^(2/3)*g^(1/3)*(Sqrt[-d] - Sqrt[e]*x))/(Sqrt[e]*f^(1/3) + (-1)^(2/3)*Sqrt[-d]*g^(1/3))]*Log[-f^(1/3) - (-1)^(2/3)*g^(1/3)*x] + (-1)^(1/3)*p*Log[((-1)^(2/3)*g^(1/3)*(Sqrt[-d] + Sqrt[e]*x))/(-(Sqrt[e]*f^(1/3)) + (-1)^(2/3)*Sqrt[-d]*g^(1/3))]*Log[-f^(1/3) - (-1)^(2/3)*g^(1/3)*x] + Log[-f^(1/3) - g^(1/3)*x]*Log[c*(d + e*x^2)^p] + (-1)^(2/3)*Log[-f^(1/3) + (-1)^(1/3)*g^(1/3)*x]*Log[c*(d + e*x^2)^p] - (-1)^(1/3)*Log[-f^(1/3) - (-1)^(2/3)*g^(1/3)*x]*Log[c*(d + e*x^2)^p] - p*PolyLog[2, (Sqrt[e]*(f^(1/3) + g^(1/3)*x))/(Sqrt[e]*f^(1/3) - Sqrt[-d]*g^(1/3))] - p*PolyLog[2, (Sqrt[e]*(f^(1/3) + g^(1/3)*x))/(Sqrt[e]*f^(1/3) + Sqrt[-d]*g^(1/3))] - (-1)^(2/3)*p*PolyLog[2, (Sqrt[e]*(f^(1/3) - (-1)^(1/3)*g^(1/3)*x))/(Sqrt[e]*f^(1/3) - (-1)^(1/3)*Sqrt[-d]*g^(1/3))] - (-1)^(2/3)*p*PolyLog[2, (Sqrt[e]*(f^(1/3) - (-1)^(1/3)*g^(1/3)*x))/(Sqrt[e]*f^(1/3) + (-1)^(1/3)*Sqrt[-d]*g^(1/3))] + (-1)^(1/3)*p*PolyLog[2, (Sqrt[e]*(f^(1/3) + (-1)^(2/3)*g^(1/3)*x))/(Sqrt[e]*f^(1/3) - (-1)^(2/3)*Sqrt[-d]*g^(1/3))] + (-1)^(1/3)*p*PolyLog[2, (Sqrt[e]*(f^(1/3) + (-1)^(2/3)*g^(1/3)*x))/(Sqrt[e]*f^(1/3) + (-1)^(2/3)*Sqrt[-d]*g^(1/3))])/(3*f^(2/3)*g^(1/3))","A",1
292,1,2168,1861,7.1423319,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^3\right)^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(f + g*x^3)^2,x]","\text{Result too large to show}","\frac{2 \sqrt{d} \sqrt{e} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{9 f^{4/3} \left(g^{2/3} d+e f^{2/3}\right)}+\frac{2 (-1)^{2/3} \sqrt{d} \sqrt{e} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\left(1+\sqrt[3]{-1}\right)^4 f^{4/3} \left((-1)^{2/3} g^{2/3} d+e f^{2/3}\right)}+\frac{4 \sqrt{d} \sqrt{e} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{9 f^{4/3} \left(2 e f^{2/3}-\left(1+i \sqrt{3}\right) d g^{2/3}\right)}-\frac{2 e p \log \left(\sqrt[3]{g} x+\sqrt[3]{f}\right)}{9 f \left(g^{2/3} d+e f^{2/3}\right) \sqrt[3]{g}}-\frac{2 p \log \left(\frac{\sqrt[3]{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right) \log \left(\sqrt[3]{g} x+\sqrt[3]{f}\right)}{9 f^{5/3} \sqrt[3]{g}}-\frac{2 p \log \left(-\frac{\sqrt[3]{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\sqrt{e} \sqrt[3]{f}-\sqrt{-d} \sqrt[3]{g}}\right) \log \left(\sqrt[3]{g} x+\sqrt[3]{f}\right)}{9 f^{5/3} \sqrt[3]{g}}+\frac{2 \sqrt[3]{-1} e p \log \left(\sqrt[3]{f}-\sqrt[3]{-1} \sqrt[3]{g} x\right)}{\left(1+\sqrt[3]{-1}\right)^4 f \left((-1)^{2/3} g^{2/3} d+e f^{2/3}\right) \sqrt[3]{g}}+\frac{2 i \sqrt{3} p \log \left(-\frac{\sqrt[3]{-1} \sqrt[3]{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{e} \sqrt[3]{f}-\sqrt[3]{-1} \sqrt{-d} \sqrt[3]{g}}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{g} x-\sqrt[3]{f}\right)}{\left(1+\sqrt[3]{-1}\right)^5 f^{5/3} \sqrt[3]{g}}+\frac{2 i \sqrt{3} p \log \left(\frac{\sqrt[3]{-1} \sqrt[3]{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\sqrt[3]{-1} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right) \log \left(\sqrt[3]{-1} \sqrt[3]{g} x-\sqrt[3]{f}\right)}{\left(1+\sqrt[3]{-1}\right)^5 f^{5/3} \sqrt[3]{g}}+\frac{4 \sqrt[3]{-1} e p \log \left((-1)^{2/3} \sqrt[3]{g} x+\sqrt[3]{f}\right)}{9 f \left(2 e f^{2/3}-\left(1+i \sqrt{3}\right) d g^{2/3}\right) \sqrt[3]{g}}-\frac{2 p \log \left(\frac{(-1)^{2/3} \sqrt[3]{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{(-1)^{2/3} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right) \log \left((-1)^{2/3} \sqrt[3]{g} x+\sqrt[3]{f}\right)}{\left(1+\sqrt[3]{-1}\right)^4 f^{5/3} \sqrt[3]{g}}-\frac{2 p \log \left(-\frac{(-1)^{2/3} \sqrt[3]{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\sqrt{e} \sqrt[3]{f}-(-1)^{2/3} \sqrt{-d} \sqrt[3]{g}}\right) \log \left((-1)^{2/3} \sqrt[3]{g} x+\sqrt[3]{f}\right)}{\left(1+\sqrt[3]{-1}\right)^4 f^{5/3} \sqrt[3]{g}}+\frac{e p \log \left(e x^2+d\right)}{9 f \left(g^{2/3} d+e f^{2/3}\right) \sqrt[3]{g}}-\frac{\sqrt[3]{-1} e p \log \left(e x^2+d\right)}{\left(1+\sqrt[3]{-1}\right)^4 f \left((-1)^{2/3} g^{2/3} d+e f^{2/3}\right) \sqrt[3]{g}}-\frac{2 \sqrt[3]{-1} e p \log \left(e x^2+d\right)}{9 f \left(2 e f^{2/3}-\left(1+i \sqrt{3}\right) d g^{2/3}\right) \sqrt[3]{g}}+\frac{2 \log \left(\sqrt[3]{g} x+\sqrt[3]{f}\right) \log \left(c \left(e x^2+d\right)^p\right)}{9 f^{5/3} \sqrt[3]{g}}-\frac{2 i \sqrt{3} \log \left(\sqrt[3]{-1} \sqrt[3]{g} x-\sqrt[3]{f}\right) \log \left(c \left(e x^2+d\right)^p\right)}{\left(1+\sqrt[3]{-1}\right)^5 f^{5/3} \sqrt[3]{g}}+\frac{2 \log \left((-1)^{2/3} \sqrt[3]{g} x+\sqrt[3]{f}\right) \log \left(c \left(e x^2+d\right)^p\right)}{\left(1+\sqrt[3]{-1}\right)^4 f^{5/3} \sqrt[3]{g}}-\frac{\log \left(c \left(e x^2+d\right)^p\right)}{9 f^{4/3} \sqrt[3]{g} \left(\sqrt[3]{g} x+\sqrt[3]{f}\right)}-\frac{\log \left(c \left(e x^2+d\right)^p\right)}{\left(1+\sqrt[3]{-1}\right)^4 f^{4/3} \sqrt[3]{g} \left(\sqrt[3]{g} x+(-1)^{2/3} \sqrt[3]{f}\right)}+\frac{\sqrt[3]{-1} \log \left(c \left(e x^2+d\right)^p\right)}{9 f^{4/3} \sqrt[3]{g} \left((-1)^{2/3} \sqrt[3]{g} x+\sqrt[3]{f}\right)}-\frac{2 p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{g} x+\sqrt[3]{f}\right)}{\sqrt{e} \sqrt[3]{f}-\sqrt{-d} \sqrt[3]{g}}\right)}{9 f^{5/3} \sqrt[3]{g}}-\frac{2 p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{g} x+\sqrt[3]{f}\right)}{\sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right)}{9 f^{5/3} \sqrt[3]{g}}+\frac{2 i \sqrt{3} p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{f}-\sqrt[3]{-1} \sqrt[3]{g} x\right)}{\sqrt{e} \sqrt[3]{f}-\sqrt[3]{-1} \sqrt{-d} \sqrt[3]{g}}\right)}{\left(1+\sqrt[3]{-1}\right)^5 f^{5/3} \sqrt[3]{g}}+\frac{2 i \sqrt{3} p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt[3]{f}-\sqrt[3]{-1} \sqrt[3]{g} x\right)}{\sqrt[3]{-1} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right)}{\left(1+\sqrt[3]{-1}\right)^5 f^{5/3} \sqrt[3]{g}}-\frac{2 p \text{Li}_2\left(\frac{\sqrt{e} \left((-1)^{2/3} \sqrt[3]{g} x+\sqrt[3]{f}\right)}{\sqrt{e} \sqrt[3]{f}-(-1)^{2/3} \sqrt{-d} \sqrt[3]{g}}\right)}{\left(1+\sqrt[3]{-1}\right)^4 f^{5/3} \sqrt[3]{g}}-\frac{2 p \text{Li}_2\left(\frac{\sqrt{e} \left((-1)^{2/3} \sqrt[3]{g} x+\sqrt[3]{f}\right)}{(-1)^{2/3} \sqrt[3]{g} \sqrt{-d}+\sqrt{e} \sqrt[3]{f}}\right)}{\left(1+\sqrt[3]{-1}\right)^4 f^{5/3} \sqrt[3]{g}}",1,"(x*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/(3*f*(f + g*x^3)) + (2*ArcTan[(-f^(1/3) + 2*g^(1/3)*x)/(Sqrt[3]*f^(1/3))]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/(3*Sqrt[3]*f^(5/3)*g^(1/3)) + (2*Log[f^(1/3) + g^(1/3)*x]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/(9*f^(5/3)*g^(1/3)) - ((-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])*Log[f^(2/3) - f^(1/3)*g^(1/3)*x + g^(2/3)*x^2])/(9*f^(5/3)*g^(1/3)) + p*(-1/3*((-1 + (-1)^(1/3))*(-(Log[((-I)*Sqrt[d])/Sqrt[e] + x]/((-1)^(2/3)*f^(1/3) + g^(1/3)*x)) + (Sqrt[e]*(Log[I*Sqrt[d] - Sqrt[e]*x] - Log[-((-1)^(2/3)*f^(1/3)) - g^(1/3)*x]))/((-1)^(2/3)*Sqrt[e]*f^(1/3) + I*Sqrt[d]*g^(1/3))))/((1 + (-1)^(1/3))^2*f^(4/3)*g^(1/3)) - ((-1 + (-1)^(1/3))*(-(Log[(I*Sqrt[d])/Sqrt[e] + x]/((-1)^(2/3)*f^(1/3) + g^(1/3)*x)) + (Sqrt[e]*(Log[I*Sqrt[d] + Sqrt[e]*x] - Log[-((-1)^(2/3)*f^(1/3)) - g^(1/3)*x]))/((-1)^(2/3)*Sqrt[e]*f^(1/3) - I*Sqrt[d]*g^(1/3))))/(3*(1 + (-1)^(1/3))^2*f^(4/3)*g^(1/3)) + ((-1)^(1/3)*(-(Log[((-I)*Sqrt[d])/Sqrt[e] + x]/(f^(1/3) + g^(1/3)*x)) + (Sqrt[e]*(Log[I*Sqrt[d] - Sqrt[e]*x] - Log[f^(1/3) + g^(1/3)*x]))/(Sqrt[e]*f^(1/3) + I*Sqrt[d]*g^(1/3))))/(3*(1 + (-1)^(1/3))^2*f^(4/3)*g^(1/3)) + ((-1)^(1/3)*(-(Log[(I*Sqrt[d])/Sqrt[e] + x]/(f^(1/3) + g^(1/3)*x)) + (Sqrt[e]*(Log[I*Sqrt[d] + Sqrt[e]*x] - Log[f^(1/3) + g^(1/3)*x]))/(Sqrt[e]*f^(1/3) - I*Sqrt[d]*g^(1/3))))/(3*(1 + (-1)^(1/3))^2*f^(4/3)*g^(1/3)) - (Log[((-I)*Sqrt[d])/Sqrt[e] + x]/((-1)^(1/3)*f^(1/3) - g^(1/3)*x) + (Sqrt[e]*(-Log[I*Sqrt[d] - Sqrt[e]*x] + Log[f^(1/3) + (-1)^(2/3)*g^(1/3)*x]))/((-1)^(1/3)*Sqrt[e]*f^(1/3) - I*Sqrt[d]*g^(1/3)))/(3*(1 + (-1)^(1/3))^2*f^(4/3)*g^(1/3)) - (Log[(I*Sqrt[d])/Sqrt[e] + x]/((-1)^(1/3)*f^(1/3) - g^(1/3)*x) + (Sqrt[e]*(-Log[I*Sqrt[d] + Sqrt[e]*x] + Log[f^(1/3) + (-1)^(2/3)*g^(1/3)*x]))/((-1)^(1/3)*Sqrt[e]*f^(1/3) + I*Sqrt[d]*g^(1/3)))/(3*(1 + (-1)^(1/3))^2*f^(4/3)*g^(1/3)) + ((-Log[((-I)*Sqrt[d])/Sqrt[e] + x] - Log[(I*Sqrt[d])/Sqrt[e] + x] + Log[d + e*x^2])*((3*f^(2/3)*x)/(f + g*x^3) - (2*Sqrt[3]*ArcTan[(1 - (2*g^(1/3)*x)/f^(1/3))/Sqrt[3]])/g^(1/3) + (2*Log[f^(1/3) + g^(1/3)*x])/g^(1/3) - Log[f^(2/3) - f^(1/3)*g^(1/3)*x + g^(2/3)*x^2]/g^(1/3)))/(9*f^(5/3)) - (2*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[((-1)^(2/3)*f^(1/3) + g^(1/3)*x)/((-1)^(2/3)*f^(1/3) - (I*Sqrt[d]*g^(1/3))/Sqrt[e])] + PolyLog[2, -((g^(1/3)*(Sqrt[d] - I*Sqrt[e]*x))/((-1)^(1/6)*Sqrt[e]*f^(1/3) - Sqrt[d]*g^(1/3)))]))/(3*(1 + (-1)^(1/3))^2*f^(5/3)*g^(1/3)) - (2*(-1 + (-1)^(1/3))*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[-((-((-1)^(1/3)*f^(1/3)) + g^(1/3)*x)/((-1)^(1/3)*f^(1/3) + (I*Sqrt[d]*g^(1/3))/Sqrt[e]))] + PolyLog[2, -((g^(1/3)*(Sqrt[d] - I*Sqrt[e]*x))/((-1)^(5/6)*Sqrt[e]*f^(1/3) - Sqrt[d]*g^(1/3)))]))/(3*(1 + (-1)^(1/3))^2*f^(5/3)*g^(1/3)) + (2*(-1)^(1/3)*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(f^(1/3) + g^(1/3)*x)/(f^(1/3) + (I*Sqrt[d]*g^(1/3))/Sqrt[e])] + PolyLog[2, (I*g^(1/3)*(Sqrt[d] + I*Sqrt[e]*x))/(Sqrt[e]*f^(1/3) + I*Sqrt[d]*g^(1/3))]))/(3*(1 + (-1)^(1/3))^2*f^(5/3)*g^(1/3)) - (2*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[((-1)^(2/3)*f^(1/3) + g^(1/3)*x)/((-1)^(2/3)*f^(1/3) + (I*Sqrt[d]*g^(1/3))/Sqrt[e])] + PolyLog[2, (g^(1/3)*(Sqrt[d] + I*Sqrt[e]*x))/((-1)^(1/6)*Sqrt[e]*f^(1/3) + Sqrt[d]*g^(1/3))]))/(3*(1 + (-1)^(1/3))^2*f^(5/3)*g^(1/3)) - (2*(-1 + (-1)^(1/3))*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(-((-1)^(1/3)*f^(1/3)) + g^(1/3)*x)/(-((-1)^(1/3)*f^(1/3)) + (I*Sqrt[d]*g^(1/3))/Sqrt[e])] + PolyLog[2, (g^(1/3)*(Sqrt[d] + I*Sqrt[e]*x))/((-1)^(5/6)*Sqrt[e]*f^(1/3) + Sqrt[d]*g^(1/3))]))/(3*(1 + (-1)^(1/3))^2*f^(5/3)*g^(1/3)) + (2*(-1)^(1/3)*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[(f^(1/3) + g^(1/3)*x)/(f^(1/3) - (I*Sqrt[d]*g^(1/3))/Sqrt[e])] + PolyLog[2, -((g^(1/3)*(I*Sqrt[d] + Sqrt[e]*x))/(Sqrt[e]*f^(1/3) - I*Sqrt[d]*g^(1/3)))]))/(3*(1 + (-1)^(1/3))^2*f^(5/3)*g^(1/3)))","A",0
293,1,1020,1221,0.9929361,"\int \left(f+g x^3\right)^3 \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^3)^3*Log[c*(d + e*x^2)^p]^2,x]","\frac{1}{125} g^3 p^2 x^{10}+\frac{1}{10} g^3 \log ^2\left(c \left(e x^2+d\right)^p\right) x^{10}-\frac{1}{25} g^3 p \log \left(c \left(e x^2+d\right)^p\right) x^{10}-\frac{9 d g^3 p^2 x^8}{400 e}+\frac{d g^3 p \log \left(c \left(e x^2+d\right)^p\right) x^8}{20 e}+\frac{24}{343} f g^2 p^2 x^7+\frac{3}{7} f g^2 \log ^2\left(c \left(e x^2+d\right)^p\right) x^7-\frac{12}{49} f g^2 p \log \left(c \left(e x^2+d\right)^p\right) x^7+\frac{47 d^2 g^3 p^2 x^6}{900 e^2}-\frac{d^2 g^3 p \log \left(c \left(e x^2+d\right)^p\right) x^6}{15 e^2}-\frac{288 d f g^2 p^2 x^5}{1225 e}+\frac{12 d f g^2 p \log \left(c \left(e x^2+d\right)^p\right) x^5}{35 e}-\frac{77 d^3 g^3 p^2 x^4}{600 e^3}+\frac{3}{8} f^2 g p^2 x^4+\frac{3}{4} f^2 g \log ^2\left(c \left(e x^2+d\right)^p\right) x^4+\frac{d^3 g^3 p \log \left(c \left(e x^2+d\right)^p\right) x^4}{10 e^3}-\frac{3}{4} f^2 g p \log \left(c \left(e x^2+d\right)^p\right) x^4+\frac{568 d^2 f g^2 p^2 x^3}{735 e^2}-\frac{4 d^2 f g^2 p \log \left(c \left(e x^2+d\right)^p\right) x^3}{7 e^2}+\frac{137 d^4 g^3 p^2 x^2}{300 e^4}-\frac{9 d f^2 g p^2 x^2}{4 e}-\frac{d^4 g^3 p \log \left(c \left(e x^2+d\right)^p\right) x^2}{5 e^4}+\frac{3 d f^2 g p \log \left(c \left(e x^2+d\right)^p\right) x^2}{2 e}+8 f^3 p^2 x-\frac{1408 d^3 f g^2 p^2 x}{245 e^3}+f^3 \log ^2\left(c \left(e x^2+d\right)^p\right) x-4 f^3 p \log \left(c \left(e x^2+d\right)^p\right) x+\frac{12 d^3 f g^2 p \log \left(c \left(e x^2+d\right)^p\right) x}{7 e^3}-\frac{4 i \sqrt{d} f \left(3 d^3 g^2-7 e^3 f^2\right) p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{7 e^{7/2}}+\frac{d^5 g^3 \log ^2\left(c \left(e x^2+d\right)^p\right)}{10 e^5}-\frac{3 d^2 f^2 g \log ^2\left(c \left(e x^2+d\right)^p\right)}{4 e^2}-\frac{77 d^5 g^3 p^2 \log \left(e x^2+d\right)}{300 e^5}+\frac{3 d^2 f^2 g p^2 \log \left(e x^2+d\right)}{4 e^2}-\frac{d^5 g^3 p \log \left(c \left(e x^2+d\right)^p\right)}{5 e^5}+\frac{3 d^2 f^2 g p \log \left(c \left(e x^2+d\right)^p\right)}{2 e^2}-\frac{4 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(-352 g^2 p d^3+490 e^3 f^2 p-70 \left(7 e^3 f^2-3 d^3 g^2\right) p \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)-35 \left(7 e^3 f^2-3 d^3 g^2\right) \log \left(c \left(e x^2+d\right)^p\right)\right)}{245 e^{7/2}}-\frac{4 i \sqrt{d} f \left(3 d^3 g^2-7 e^3 f^2\right) p^2 \text{Li}_2\left(\frac{\sqrt{e} x+i \sqrt{d}}{\sqrt{e} x-i \sqrt{d}}\right)}{7 e^{7/2}}","\frac{1}{10} g^3 \log ^2\left(c \left(e x^2+d\right)^p\right) x^{10}+\frac{24}{343} f g^2 p^2 x^7+\frac{3}{7} f g^2 \log ^2\left(c \left(e x^2+d\right)^p\right) x^7-\frac{12}{49} f g^2 p \log \left(c \left(e x^2+d\right)^p\right) x^7-\frac{288 d f g^2 p^2 x^5}{1225 e}+\frac{12 d f g^2 p \log \left(c \left(e x^2+d\right)^p\right) x^5}{35 e}+\frac{568 d^2 f g^2 p^2 x^3}{735 e^2}-\frac{4 d^2 f g^2 p \log \left(c \left(e x^2+d\right)^p\right) x^3}{7 e^2}+\frac{d^4 g^3 p^2 x^2}{e^4}-\frac{3 d f^2 g p^2 x^2}{e}+8 f^3 p^2 x-\frac{1408 d^3 f g^2 p^2 x}{245 e^3}+f^3 \log ^2\left(c \left(e x^2+d\right)^p\right) x-4 f^3 p \log \left(c \left(e x^2+d\right)^p\right) x+\frac{12 d^3 f g^2 p \log \left(c \left(e x^2+d\right)^p\right) x}{7 e^3}+\frac{g^3 p^2 \left(e x^2+d\right)^5}{125 e^5}-\frac{d g^3 p^2 \left(e x^2+d\right)^4}{16 e^5}+\frac{2 d^2 g^3 p^2 \left(e x^2+d\right)^3}{9 e^5}-\frac{d^3 g^3 p^2 \left(e x^2+d\right)^2}{2 e^5}+\frac{3 f^2 g p^2 \left(e x^2+d\right)^2}{8 e^2}+\frac{4 i \sqrt{d} f^3 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{\sqrt{e}}-\frac{12 i d^{7/2} f g^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{7 e^{7/2}}-\frac{d^5 g^3 p^2 \log ^2\left(e x^2+d\right)}{10 e^5}+\frac{3 f^2 g \left(e x^2+d\right)^2 \log ^2\left(c \left(e x^2+d\right)^p\right)}{4 e^2}-\frac{3 d f^2 g \left(e x^2+d\right) \log ^2\left(c \left(e x^2+d\right)^p\right)}{2 e^2}-\frac{8 \sqrt{d} f^3 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{1408 d^{7/2} f g^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{245 e^{7/2}}+\frac{8 \sqrt{d} f^3 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}-\frac{24 d^{7/2} f g^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{7 e^{7/2}}-\frac{g^3 p \left(e x^2+d\right)^5 \log \left(c \left(e x^2+d\right)^p\right)}{25 e^5}+\frac{d g^3 p \left(e x^2+d\right)^4 \log \left(c \left(e x^2+d\right)^p\right)}{4 e^5}-\frac{2 d^2 g^3 p \left(e x^2+d\right)^3 \log \left(c \left(e x^2+d\right)^p\right)}{3 e^5}+\frac{d^3 g^3 p \left(e x^2+d\right)^2 \log \left(c \left(e x^2+d\right)^p\right)}{e^5}-\frac{3 f^2 g p \left(e x^2+d\right)^2 \log \left(c \left(e x^2+d\right)^p\right)}{4 e^2}-\frac{d^4 g^3 p \left(e x^2+d\right) \log \left(c \left(e x^2+d\right)^p\right)}{e^5}+\frac{3 d f^2 g p \left(e x^2+d\right) \log \left(c \left(e x^2+d\right)^p\right)}{e^2}+\frac{4 \sqrt{d} f^3 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(e x^2+d\right)^p\right)}{\sqrt{e}}-\frac{12 d^{7/2} f g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(e x^2+d\right)^p\right)}{7 e^{7/2}}+\frac{d^5 g^3 p \log \left(e x^2+d\right) \log \left(c \left(e x^2+d\right)^p\right)}{5 e^5}+\frac{4 i \sqrt{d} f^3 p^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}-\frac{12 i d^{7/2} f g^2 p^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{7 e^{7/2}}",1,"8*f^3*p^2*x - (1408*d^3*f*g^2*p^2*x)/(245*e^3) - (9*d*f^2*g*p^2*x^2)/(4*e) + (137*d^4*g^3*p^2*x^2)/(300*e^4) + (568*d^2*f*g^2*p^2*x^3)/(735*e^2) + (3*f^2*g*p^2*x^4)/8 - (77*d^3*g^3*p^2*x^4)/(600*e^3) - (288*d*f*g^2*p^2*x^5)/(1225*e) + (47*d^2*g^3*p^2*x^6)/(900*e^2) + (24*f*g^2*p^2*x^7)/343 - (9*d*g^3*p^2*x^8)/(400*e) + (g^3*p^2*x^10)/125 - (((4*I)/7)*Sqrt[d]*f*(-7*e^3*f^2 + 3*d^3*g^2)*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/e^(7/2) + (3*d^2*f^2*g*p^2*Log[d + e*x^2])/(4*e^2) - (77*d^5*g^3*p^2*Log[d + e*x^2])/(300*e^5) + (3*d^2*f^2*g*p*Log[c*(d + e*x^2)^p])/(2*e^2) - (d^5*g^3*p*Log[c*(d + e*x^2)^p])/(5*e^5) - 4*f^3*p*x*Log[c*(d + e*x^2)^p] + (12*d^3*f*g^2*p*x*Log[c*(d + e*x^2)^p])/(7*e^3) + (3*d*f^2*g*p*x^2*Log[c*(d + e*x^2)^p])/(2*e) - (d^4*g^3*p*x^2*Log[c*(d + e*x^2)^p])/(5*e^4) - (4*d^2*f*g^2*p*x^3*Log[c*(d + e*x^2)^p])/(7*e^2) - (3*f^2*g*p*x^4*Log[c*(d + e*x^2)^p])/4 + (d^3*g^3*p*x^4*Log[c*(d + e*x^2)^p])/(10*e^3) + (12*d*f*g^2*p*x^5*Log[c*(d + e*x^2)^p])/(35*e) - (d^2*g^3*p*x^6*Log[c*(d + e*x^2)^p])/(15*e^2) - (12*f*g^2*p*x^7*Log[c*(d + e*x^2)^p])/49 + (d*g^3*p*x^8*Log[c*(d + e*x^2)^p])/(20*e) - (g^3*p*x^10*Log[c*(d + e*x^2)^p])/25 - (3*d^2*f^2*g*Log[c*(d + e*x^2)^p]^2)/(4*e^2) + (d^5*g^3*Log[c*(d + e*x^2)^p]^2)/(10*e^5) + f^3*x*Log[c*(d + e*x^2)^p]^2 + (3*f^2*g*x^4*Log[c*(d + e*x^2)^p]^2)/4 + (3*f*g^2*x^7*Log[c*(d + e*x^2)^p]^2)/7 + (g^3*x^10*Log[c*(d + e*x^2)^p]^2)/10 - (4*Sqrt[d]*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(490*e^3*f^2*p - 352*d^3*g^2*p - 70*(7*e^3*f^2 - 3*d^3*g^2)*p*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)] - 35*(7*e^3*f^2 - 3*d^3*g^2)*Log[c*(d + e*x^2)^p]))/(245*e^(7/2)) - (((4*I)/7)*Sqrt[d]*f*(-7*e^3*f^2 + 3*d^3*g^2)*p^2*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x)/((-I)*Sqrt[d] + Sqrt[e]*x)])/e^(7/2)","A",1
294,1,475,835,0.568294,"\int \left(f+g x^3\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^3)^2*Log[c*(d + e*x^2)^p]^2,x]","\frac{-1680 \sqrt{d} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(-105 \left(7 e^3 f^2-d^3 g^2\right) \log \left(c \left(d+e x^2\right)^p\right)-210 p \left(7 e^3 f^2-d^3 g^2\right) \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right)+2 p \left(735 e^3 f^2-176 d^3 g^2\right)\right)+\sqrt{e} \left(22050 \left(e^3 x \left(14 f^2+7 f g x^3+2 g^2 x^6\right)-7 d^2 e f g\right) \log ^2\left(c \left(d+e x^2\right)^p\right)-210 p \left(-840 d^3 g^2 x+70 d^2 e g \left(4 g x^3-21 f\right)-42 d e^2 g x^2 \left(35 f+4 g x^3\right)+15 e^3 x \left(392 f^2+49 f g x^3+8 g^2 x^6\right)\right) \log \left(c \left(d+e x^2\right)^p\right)+154350 d^2 e f g p^2 \log \left(d+e x^2\right)+p^2 x \left(-591360 d^3 g^2+79520 d^2 e g^2 x^2-378 d e^2 g x \left(1225 f+64 g x^3\right)+225 e^3 \left(10976 f^2+343 f g x^3+32 g^2 x^6\right)\right)\right)-176400 i \sqrt{d} p^2 \left(d^3 g^2-7 e^3 f^2\right) \text{Li}_2\left(\frac{\sqrt{e} x+i \sqrt{d}}{\sqrt{e} x-i \sqrt{d}}\right)-176400 i \sqrt{d} p^2 \left(d^3 g^2-7 e^3 f^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{308700 e^{7/2}}","\frac{8}{343} g^2 p^2 x^7+\frac{1}{7} g^2 \log ^2\left(c \left(e x^2+d\right)^p\right) x^7-\frac{4}{49} g^2 p \log \left(c \left(e x^2+d\right)^p\right) x^7-\frac{96 d g^2 p^2 x^5}{1225 e}+\frac{4 d g^2 p \log \left(c \left(e x^2+d\right)^p\right) x^5}{35 e}+\frac{568 d^2 g^2 p^2 x^3}{2205 e^2}-\frac{4 d^2 g^2 p \log \left(c \left(e x^2+d\right)^p\right) x^3}{21 e^2}-\frac{2 d f g p^2 x^2}{e}+8 f^2 p^2 x-\frac{1408 d^3 g^2 p^2 x}{735 e^3}+f^2 \log ^2\left(c \left(e x^2+d\right)^p\right) x-4 f^2 p \log \left(c \left(e x^2+d\right)^p\right) x+\frac{4 d^3 g^2 p \log \left(c \left(e x^2+d\right)^p\right) x}{7 e^3}+\frac{f g p^2 \left(e x^2+d\right)^2}{4 e^2}+\frac{4 i \sqrt{d} f^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{\sqrt{e}}-\frac{4 i d^{7/2} g^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{7 e^{7/2}}+\frac{f g \left(e x^2+d\right)^2 \log ^2\left(c \left(e x^2+d\right)^p\right)}{2 e^2}-\frac{d f g \left(e x^2+d\right) \log ^2\left(c \left(e x^2+d\right)^p\right)}{e^2}-\frac{8 \sqrt{d} f^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{1408 d^{7/2} g^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{735 e^{7/2}}+\frac{8 \sqrt{d} f^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}-\frac{8 d^{7/2} g^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{7 e^{7/2}}-\frac{f g p \left(e x^2+d\right)^2 \log \left(c \left(e x^2+d\right)^p\right)}{2 e^2}+\frac{2 d f g p \left(e x^2+d\right) \log \left(c \left(e x^2+d\right)^p\right)}{e^2}+\frac{4 \sqrt{d} f^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(e x^2+d\right)^p\right)}{\sqrt{e}}-\frac{4 d^{7/2} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(e x^2+d\right)^p\right)}{7 e^{7/2}}+\frac{4 i \sqrt{d} f^2 p^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}-\frac{4 i d^{7/2} g^2 p^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{7 e^{7/2}}",1,"((-176400*I)*Sqrt[d]*(-7*e^3*f^2 + d^3*g^2)*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2 - 1680*Sqrt[d]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(2*(735*e^3*f^2 - 176*d^3*g^2)*p - 210*(7*e^3*f^2 - d^3*g^2)*p*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)] - 105*(7*e^3*f^2 - d^3*g^2)*Log[c*(d + e*x^2)^p]) + Sqrt[e]*(p^2*x*(-591360*d^3*g^2 + 79520*d^2*e*g^2*x^2 - 378*d*e^2*g*x*(1225*f + 64*g*x^3) + 225*e^3*(10976*f^2 + 343*f*g*x^3 + 32*g^2*x^6)) + 154350*d^2*e*f*g*p^2*Log[d + e*x^2] - 210*p*(-840*d^3*g^2*x + 70*d^2*e*g*(-21*f + 4*g*x^3) - 42*d*e^2*g*x^2*(35*f + 4*g*x^3) + 15*e^3*x*(392*f^2 + 49*f*g*x^3 + 8*g^2*x^6))*Log[c*(d + e*x^2)^p] + 22050*(-7*d^2*e*f*g + e^3*x*(14*f^2 + 7*f*g*x^3 + 2*g^2*x^6))*Log[c*(d + e*x^2)^p]^2) - (176400*I)*Sqrt[d]*(-7*e^3*f^2 + d^3*g^2)*p^2*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x)/((-I)*Sqrt[d] + Sqrt[e]*x)])/(308700*e^(7/2))","A",1
295,1,415,395,0.1652074,"\int \left(f+g x^3\right) \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^3)*Log[c*(d + e*x^2)^p]^2,x]","-e g p \left(\frac{d^2 \log ^2\left(c \left(d+e x^2\right)^p\right)}{4 e^3 p}+\frac{d \left(p x^2-\frac{\left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{e}\right)}{2 e^2}+\frac{x^4 \log \left(c \left(d+e x^2\right)^p\right)}{4 e}+\frac{1}{8} p \left(-\frac{2 d^2 \log \left(d+e x^2\right)}{e^3}+\frac{2 d x^2}{e^2}-\frac{x^4}{e}\right)\right)+f x \log ^2\left(c \left(d+e x^2\right)^p\right)-4 f p x \log \left(c \left(d+e x^2\right)^p\right)+\frac{4 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{\sqrt{e}}+\frac{1}{4} g x^4 \log ^2\left(c \left(d+e x^2\right)^p\right)+\frac{4 i \sqrt{d} f p^2 \text{Li}_2\left(-\frac{\sqrt{e} x+i \sqrt{d}}{i \sqrt{d}-\sqrt{e} x}\right)}{\sqrt{e}}+\frac{4 i \sqrt{d} f p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{\sqrt{e}}-\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{8 \sqrt{d} f p^2 \log \left(\frac{2 i \sqrt{d}}{-\sqrt{e} x+i \sqrt{d}}\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+8 f p^2 x","\frac{g \left(d+e x^2\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right)}{4 e^2}-\frac{d g \left(d+e x^2\right) \log ^2\left(c \left(d+e x^2\right)^p\right)}{2 e^2}-\frac{g p \left(d+e x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{4 e^2}+\frac{d g p \left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{e^2}+f x \log ^2\left(c \left(d+e x^2\right)^p\right)-4 f p x \log \left(c \left(d+e x^2\right)^p\right)+\frac{4 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{\sqrt{e}}+\frac{g p^2 \left(d+e x^2\right)^2}{8 e^2}+\frac{4 i \sqrt{d} f p^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}+\frac{4 i \sqrt{d} f p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{\sqrt{e}}-\frac{8 \sqrt{d} f p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{8 \sqrt{d} f p^2 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-\frac{d g p^2 x^2}{e}+8 f p^2 x",1,"8*f*p^2*x - (8*Sqrt[d]*f*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] + ((4*I)*Sqrt[d]*f*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/Sqrt[e] + (8*Sqrt[d]*f*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[((2*I)*Sqrt[d])/(I*Sqrt[d] - Sqrt[e]*x)])/Sqrt[e] - 4*f*p*x*Log[c*(d + e*x^2)^p] + (4*Sqrt[d]*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/Sqrt[e] + f*x*Log[c*(d + e*x^2)^p]^2 + (g*x^4*Log[c*(d + e*x^2)^p]^2)/4 - e*g*p*((p*((2*d*x^2)/e^2 - x^4/e - (2*d^2*Log[d + e*x^2])/e^3))/8 + (x^4*Log[c*(d + e*x^2)^p])/(4*e) + (d^2*Log[c*(d + e*x^2)^p]^2)/(4*e^3*p) + (d*(p*x^2 - ((d + e*x^2)*Log[c*(d + e*x^2)^p])/e))/(2*e^2)) + ((4*I)*Sqrt[d]*f*p^2*PolyLog[2, -((I*Sqrt[d] + Sqrt[e]*x)/(I*Sqrt[d] - Sqrt[e]*x))])/Sqrt[e]","A",1
296,0,0,27,13.8321041,"\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{f+g x^3} \, dx","Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^3),x]","\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{f+g x^3} \, dx","\text{Int}\left(\frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{f+g x^3},x\right)",0,"Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^3), x]","A",-1
297,0,0,27,22.9377576,"\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^3\right)^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^3)^2,x]","\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^3\right)^2} \, dx","\text{Int}\left(\frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^3\right)^2},x\right)",0,"Integrate[Log[c*(d + e*x^2)^p]^2/(f + g*x^3)^2, x]","A",-1
298,1,2727,1126,9.3233256,"\int \left(f+g x^3\right)^2 \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^3)^2*Log[c*(d + e*x^2)^p]^3,x]","\text{Result too large to show}","-\frac{48 g^2 p^3 x^7}{2401}+\frac{1}{7} g^2 \log ^3\left(c \left(e x^2+d\right)^p\right) x^7-\frac{6}{49} g^2 p \log ^2\left(c \left(e x^2+d\right)^p\right) x^7+\frac{24}{343} g^2 p^2 \log \left(c \left(e x^2+d\right)^p\right) x^7+\frac{5232 d g^2 p^3 x^5}{42875 e}+\frac{6 d g^2 p \log ^2\left(c \left(e x^2+d\right)^p\right) x^5}{35 e}-\frac{288 d g^2 p^2 \log \left(c \left(e x^2+d\right)^p\right) x^5}{1225 e}-\frac{55456 d^2 g^2 p^3 x^3}{77175 e^2}-\frac{2 d^2 g^2 p \log ^2\left(c \left(e x^2+d\right)^p\right) x^3}{7 e^2}+\frac{568 d^2 g^2 p^2 \log \left(c \left(e x^2+d\right)^p\right) x^3}{735 e^2}+\frac{6 d f g p^3 x^2}{e}-48 f^2 p^3 x+\frac{351136 d^3 g^2 p^3 x}{25725 e^3}+f^2 \log ^3\left(c \left(e x^2+d\right)^p\right) x-6 f^2 p \log ^2\left(c \left(e x^2+d\right)^p\right) x+\frac{6 d^3 g^2 p \log ^2\left(c \left(e x^2+d\right)^p\right) x}{7 e^3}+24 f^2 p^2 \log \left(c \left(e x^2+d\right)^p\right) x-\frac{1408 d^3 g^2 p^2 \log \left(c \left(e x^2+d\right)^p\right) x}{245 e^3}+\frac{f g \left(e x^2+d\right)^2 \log ^3\left(c \left(e x^2+d\right)^p\right)}{2 e^2}-\frac{d f g \left(e x^2+d\right) \log ^3\left(c \left(e x^2+d\right)^p\right)}{e^2}-\frac{3 f g p^3 \left(e x^2+d\right)^2}{8 e^2}-\frac{24 i \sqrt{d} f^2 p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{\sqrt{e}}+\frac{1408 i d^{7/2} g^2 p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{245 e^{7/2}}-\frac{3 f g p \left(e x^2+d\right)^2 \log ^2\left(c \left(e x^2+d\right)^p\right)}{4 e^2}+\frac{3 d f g p \left(e x^2+d\right) \log ^2\left(c \left(e x^2+d\right)^p\right)}{e^2}+\frac{48 \sqrt{d} f^2 p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-\frac{351136 d^{7/2} g^2 p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{25725 e^{7/2}}-\frac{48 \sqrt{d} f^2 p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}+\frac{2816 d^{7/2} g^2 p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{245 e^{7/2}}+\frac{3 f g p^2 \left(e x^2+d\right)^2 \log \left(c \left(e x^2+d\right)^p\right)}{4 e^2}-\frac{6 d f g p^2 \left(e x^2+d\right) \log \left(c \left(e x^2+d\right)^p\right)}{e^2}-\frac{24 \sqrt{d} f^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(e x^2+d\right)^p\right)}{\sqrt{e}}+\frac{1408 d^{7/2} g^2 p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(e x^2+d\right)^p\right)}{245 e^{7/2}}-\frac{24 i \sqrt{d} f^2 p^3 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}+\frac{1408 i d^{7/2} g^2 p^3 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{245 e^{7/2}}+6 d f^2 p \text{Int}\left(\frac{\log ^2\left(c \left(e x^2+d\right)^p\right)}{e x^2+d},x\right)-\frac{6 d^4 g^2 p \text{Int}\left(\frac{\log ^2\left(c \left(e x^2+d\right)^p\right)}{e x^2+d},x\right)}{7 e^3}",0,"(g^2*p^3*x*(168*d^2*(d + e*x^2)*HypergeometricPFQ[{-5/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^2)/d] - 280*d^2*(d + e*x^2)*HypergeometricPFQ[{-3/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^2)/d] - 112*d^2*(d + e*x^2)*HypergeometricPFQ[{-5/2, 1, 1, 1, 1}, {2, 2, 2, 2}, (d + e*x^2)/d] + 280*d^2*(d + e*x^2)*HypergeometricPFQ[{-3/2, 1, 1, 1, 1}, {2, 2, 2, 2}, (d + e*x^2)/d] - 210*d^2*(d + e*x^2)*HypergeometricPFQ[{-1/2, 1, 1, 1, 1}, {2, 2, 2, 2}, (d + e*x^2)/d] + 16*d^3*Log[d + e*x^2] - 16*d^3*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2] + 48*d^2*(d + e*x^2)*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2] - 48*d*(d + e*x^2)^2*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2] + 16*(d + e*x^2)^3*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2] + 112*d^2*(d + e*x^2)*HypergeometricPFQ[{-5/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^2)/d]*Log[d + e*x^2] - 280*d^2*(d + e*x^2)*HypergeometricPFQ[{-3/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^2)/d]*Log[d + e*x^2] + 210*d^2*(d + e*x^2)*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^2)/d]*Log[d + e*x^2] - 32*d^3*Log[d + e*x^2]^2 + 32*d^3*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2]^2 - 68*d^2*(d + e*x^2)*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2]^2 + 40*d*(d + e*x^2)^2*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2]^2 - 4*(d + e*x^2)^3*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2]^2 - 105*d^2*(d + e*x^2)*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, (d + e*x^2)/d]*Log[d + e*x^2]^2 + 10*d^3*Log[d + e*x^2]^3 - 10*d^3*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2]^3 + 30*d^2*(d + e*x^2)*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2]^3 - 30*d*(d + e*x^2)^2*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2]^3 + 10*(d + e*x^2)^3*Sqrt[1 - (d + e*x^2)/d]*Log[d + e*x^2]^3 + 140*d^2*(d + e*x^2)*HypergeometricPFQ[{-3/2, 1, 1}, {2, 2}, (d + e*x^2)/d]*Log[d + e*x^2]*(2 + Log[d + e*x^2]) - 56*d^2*(d + e*x^2)*HypergeometricPFQ[{-5/2, 1, 1}, {2, 2}, (d + e*x^2)/d]*(1 + 3*Log[d + e*x^2] + Log[d + e*x^2]^2)))/(70*e^3*Sqrt[1 - (d + e*x^2)/d]) + (f*g*p^3*(d + e*x^2)*(-8*d*(-6 + 6*Log[d + e*x^2] - 3*Log[d + e*x^2]^2 + Log[d + e*x^2]^3) + (d + e*x^2)*(-3 + 6*Log[d + e*x^2] - 6*Log[d + e*x^2]^2 + 4*Log[d + e*x^2]^3)))/(8*e^2) + 6*f*g*p^2*((x^4*Log[d + e*x^2]^2)/4 - e*((3*d*x^2)/(4*e^2) - x^4/(8*e) - (3*d^2*Log[d + e*x^2])/(4*e^3) - (d*x^2*Log[d + e*x^2])/(2*e^2) + (x^4*Log[d + e*x^2])/(4*e) + (d^2*Log[d + e*x^2]^2)/(4*e^3)))*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]) + (3*d*f*g*p*x^2*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/(2*e) - (2*d^2*g^2*p*x^3*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/(7*e^2) + (6*d*g^2*p*x^5*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/(35*e) - (3*d^2*f*g*p*Log[d + e*x^2]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/(2*e^2) + (3*p*x*(14*f^2 + 7*f*g*x^3 + 2*g^2*x^6)*Log[d + e*x^2]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/14 + (f*g*x^4*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2*(-3*p + 2*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])))/4 + (g^2*x^7*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2*(-6*p + 7*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])))/49 + (x*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2*(-42*e^3*f^2*p + 6*d^3*g^2*p + 7*e^3*f^2*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])))/(7*e^3) - (6*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(-7*d*e^3*f^2*p*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2 + d^4*g^2*p*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2))/(7*Sqrt[d]*e^(7/2)) + 3*f^2*p^2*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])*(x*Log[d + e*x^2]^2 - (4*((-I)*Sqrt[d]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2 + Sqrt[e]*x*(-2 + Log[d + e*x^2]) - Sqrt[d]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(-2 + 2*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)] + Log[d + e*x^2]) - I*Sqrt[d]*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x)/((-I)*Sqrt[d] + Sqrt[e]*x)]))/Sqrt[e]) + 3*g^2*p^2*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])*((x^7*Log[d + e*x^2]^2)/7 - (4*((11025*I)*d^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2 + 105*d^(7/2)*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(-352 + 210*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)] + 105*Log[d + e*x^2]) + Sqrt[e]*x*(36960*d^3 - 4970*d^2*e*x^2 + 1512*d*e^2*x^4 - 450*e^3*x^6 - 105*(105*d^3 - 35*d^2*e*x^2 + 21*d*e^2*x^4 - 15*e^3*x^6)*Log[d + e*x^2]) + (11025*I)*d^(7/2)*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x)/((-I)*Sqrt[d] + Sqrt[e]*x)]))/(77175*e^(7/2))) + (f^2*p^3*(-48*Sqrt[-d^2]*Sqrt[d + e*x^2]*Sqrt[1 - d/(d + e*x^2)]*ArcSin[Sqrt[d]/Sqrt[d + e*x^2]] - 6*Sqrt[-d^2]*Sqrt[1 - d/(d + e*x^2)]*(8*Sqrt[d]*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {3/2, 3/2, 3/2}, d/(d + e*x^2)] + 4*Sqrt[d]*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, d/(d + e*x^2)]*Log[d + e*x^2] + Sqrt[d + e*x^2]*ArcSin[Sqrt[d]/Sqrt[d + e*x^2]]*Log[d + e*x^2]^2) + Sqrt[-d]*e*x^2*(-48 + 24*Log[d + e*x^2] - 6*Log[d + e*x^2]^2 + Log[d + e*x^2]^3) + 24*d*Sqrt[e*x^2]*ArcTanh[Sqrt[e*x^2]/Sqrt[-d]]*(Log[d + e*x^2] - Log[(d + e*x^2)/d]) + 6*(-d)^(3/2)*Sqrt[1 - (d + e*x^2)/d]*(Log[(d + e*x^2)/d]^2 - 4*Log[(d + e*x^2)/d]*Log[(1 + Sqrt[1 - (d + e*x^2)/d])/2] + 2*Log[(1 + Sqrt[1 - (d + e*x^2)/d])/2]^2 - 4*PolyLog[2, 1/2 - Sqrt[1 - (d + e*x^2)/d]/2])))/(Sqrt[-d]*e*x)","B",0
299,1,1146,518,4.5396189,"\int \left(f+g x^3\right) \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^3)*Log[c*(d + e*x^2)^p]^3,x]","-\frac{1}{8} g \left(2 \log \left(e x^2+d\right) p+3 p-2 \log \left(c \left(e x^2+d\right)^p\right)\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2 x^4+\frac{3 d g p \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2 x^2}{4 e}+\frac{3}{4} p \left(g x^3+4 f\right) \log \left(e x^2+d\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2 x+f \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2 \left(-\log \left(e x^2+d\right) p-6 p+\log \left(c \left(e x^2+d\right)^p\right)\right) x+\frac{6 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2}{\sqrt{e}}-\frac{3 d^2 g p \log \left(e x^2+d\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)^2}{4 e^2}+\frac{g p^3 \left(e x^2+d\right) \left(-4 \left(d-e x^2\right) \log ^3\left(e x^2+d\right)+6 \left(3 d-e x^2\right) \log ^2\left(e x^2+d\right)+\left(6 e x^2-42 d\right) \log \left(e x^2+d\right)-3 e x^2+45 d\right)}{16 e^2}-\frac{3 g p^2 \left(e \left(e x^2-6 d\right) x^2-2 \left(d^2-e^2 x^4\right) \log ^2\left(e x^2+d\right)+\left(-2 e^2 x^4+4 d e x^2+6 d^2\right) \log \left(e x^2+d\right)\right) \left(p \log \left(e x^2+d\right)-\log \left(c \left(e x^2+d\right)^p\right)\right)}{8 e^2}-\frac{3 f p^2 \left(p \log \left(e x^2+d\right)-\log \left(c \left(e x^2+d\right)^p\right)\right) \left(4 i \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2+4 \sqrt{d} \left(2 \log \left(\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)+\log \left(e x^2+d\right)-2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)+\sqrt{e} x \left(\log ^2\left(e x^2+d\right)-4 \log \left(e x^2+d\right)+8\right)+4 i \sqrt{d} \text{Li}_2\left(\frac{\sqrt{e} x+i \sqrt{d}}{\sqrt{e} x-i \sqrt{d}}\right)\right)}{\sqrt{e}}+\frac{f p^3 \left(\sqrt{-d} e \left(\log ^3\left(e x^2+d\right)-6 \log ^2\left(e x^2+d\right)+24 \log \left(e x^2+d\right)-48\right) x^2-48 \sqrt{-d^2} \sqrt{\frac{e x^2}{e x^2+d}} \sqrt{e x^2+d} \sin ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e x^2+d}}\right)-6 \sqrt{-d^2} \sqrt{\frac{e x^2}{e x^2+d}} \left(8 \sqrt{d} \, _4F_3\left(\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2},\frac{3}{2};\frac{d}{e x^2+d}\right)+\log \left(e x^2+d\right) \left(4 \sqrt{d} \, _3F_2\left(\frac{1}{2},\frac{1}{2},\frac{1}{2};\frac{3}{2},\frac{3}{2};\frac{d}{e x^2+d}\right)+\sqrt{e x^2+d} \sin ^{-1}\left(\frac{\sqrt{d}}{\sqrt{e x^2+d}}\right) \log \left(e x^2+d\right)\right)\right)+24 d \sqrt{e x^2} \tanh ^{-1}\left(\frac{\sqrt{e x^2}}{\sqrt{-d}}\right) \left(\log \left(e x^2+d\right)-\log \left(\frac{e x^2}{d}+1\right)\right)+6 (-d)^{3/2} \sqrt{-\frac{e x^2}{d}} \left(\log ^2\left(\frac{e x^2}{d}+1\right)-4 \log \left(\frac{1}{2} \left(\sqrt{-\frac{e x^2}{d}}+1\right)\right) \log \left(\frac{e x^2}{d}+1\right)+2 \log ^2\left(\frac{1}{2} \left(\sqrt{-\frac{e x^2}{d}}+1\right)\right)-4 \text{Li}_2\left(\frac{1}{2}-\frac{1}{2} \sqrt{-\frac{e x^2}{d}}\right)\right)\right)}{\sqrt{-d} e x}","6 d f p \text{Int}\left(\frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{d+e x^2},x\right)+\frac{3 g p^2 \left(d+e x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{8 e^2}-\frac{3 d g p^2 \left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{e^2}+\frac{g \left(d+e x^2\right)^2 \log ^3\left(c \left(d+e x^2\right)^p\right)}{4 e^2}-\frac{d g \left(d+e x^2\right) \log ^3\left(c \left(d+e x^2\right)^p\right)}{2 e^2}-\frac{3 g p \left(d+e x^2\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right)}{8 e^2}+\frac{3 d g p \left(d+e x^2\right) \log ^2\left(c \left(d+e x^2\right)^p\right)}{2 e^2}+24 f p^2 x \log \left(c \left(d+e x^2\right)^p\right)-\frac{24 \sqrt{d} f p^2 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{\sqrt{e}}+f x \log ^3\left(c \left(d+e x^2\right)^p\right)-6 f p x \log ^2\left(c \left(d+e x^2\right)^p\right)-\frac{3 g p^3 \left(d+e x^2\right)^2}{16 e^2}-\frac{24 i \sqrt{d} f p^3 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}-\frac{24 i \sqrt{d} f p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)^2}{\sqrt{e}}+\frac{48 \sqrt{d} f p^3 \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-\frac{48 \sqrt{d} f p^3 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{3 d g p^3 x^2}{e}-48 f p^3 x",0,"(g*p^3*(d + e*x^2)*(45*d - 3*e*x^2 + (-42*d + 6*e*x^2)*Log[d + e*x^2] + 6*(3*d - e*x^2)*Log[d + e*x^2]^2 - 4*(d - e*x^2)*Log[d + e*x^2]^3))/(16*e^2) - (3*g*p^2*(e*x^2*(-6*d + e*x^2) + (6*d^2 + 4*d*e*x^2 - 2*e^2*x^4)*Log[d + e*x^2] - 2*(d^2 - e^2*x^4)*Log[d + e*x^2]^2)*(p*Log[d + e*x^2] - Log[c*(d + e*x^2)^p]))/(8*e^2) + (3*d*g*p*x^2*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/(4*e) + (6*Sqrt[d]*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/Sqrt[e] - (3*d^2*g*p*Log[d + e*x^2]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/(4*e^2) + (3*p*x*(4*f + g*x^3)*Log[d + e*x^2]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/4 - (g*x^4*(3*p + 2*p*Log[d + e*x^2] - 2*Log[c*(d + e*x^2)^p])*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2)/8 + f*x*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p])^2*(-6*p - p*Log[d + e*x^2] + Log[c*(d + e*x^2)^p]) - (3*f*p^2*(p*Log[d + e*x^2] - Log[c*(d + e*x^2)^p])*((4*I)*Sqrt[d]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2 + 4*Sqrt[d]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*(-2 + 2*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)] + Log[d + e*x^2]) + Sqrt[e]*x*(8 - 4*Log[d + e*x^2] + Log[d + e*x^2]^2) + (4*I)*Sqrt[d]*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x)/((-I)*Sqrt[d] + Sqrt[e]*x)]))/Sqrt[e] + (f*p^3*(-48*Sqrt[-d^2]*Sqrt[(e*x^2)/(d + e*x^2)]*Sqrt[d + e*x^2]*ArcSin[Sqrt[d]/Sqrt[d + e*x^2]] + Sqrt[-d]*e*x^2*(-48 + 24*Log[d + e*x^2] - 6*Log[d + e*x^2]^2 + Log[d + e*x^2]^3) - 6*Sqrt[-d^2]*Sqrt[(e*x^2)/(d + e*x^2)]*(8*Sqrt[d]*HypergeometricPFQ[{1/2, 1/2, 1/2, 1/2}, {3/2, 3/2, 3/2}, d/(d + e*x^2)] + Log[d + e*x^2]*(4*Sqrt[d]*HypergeometricPFQ[{1/2, 1/2, 1/2}, {3/2, 3/2}, d/(d + e*x^2)] + Sqrt[d + e*x^2]*ArcSin[Sqrt[d]/Sqrt[d + e*x^2]]*Log[d + e*x^2])) + 24*d*Sqrt[e*x^2]*ArcTanh[Sqrt[e*x^2]/Sqrt[-d]]*(Log[d + e*x^2] - Log[1 + (e*x^2)/d]) + 6*(-d)^(3/2)*Sqrt[-((e*x^2)/d)]*(Log[1 + (e*x^2)/d]^2 - 4*Log[1 + (e*x^2)/d]*Log[(1 + Sqrt[-((e*x^2)/d)])/2] + 2*Log[(1 + Sqrt[-((e*x^2)/d)])/2]^2 - 4*PolyLog[2, 1/2 - Sqrt[-((e*x^2)/d)]/2])))/(Sqrt[-d]*e*x)","B",0
300,0,0,27,17.4021116,"\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{f+g x^3} \, dx","Integrate[Log[c*(d + e*x^2)^p]^3/(f + g*x^3),x]","\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{f+g x^3} \, dx","\text{Int}\left(\frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{f+g x^3},x\right)",0,"Integrate[Log[c*(d + e*x^2)^p]^3/(f + g*x^3), x]","A",-1
301,0,0,27,39.1287899,"\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^3\right)^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]^3/(f + g*x^3)^2,x]","\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^3\right)^2} \, dx","\text{Int}\left(\frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^3\right)^2},x\right)",0,"Integrate[Log[c*(d + e*x^2)^p]^3/(f + g*x^3)^2, x]","A",-1
302,0,0,27,0.3822332,"\int \frac{\left(f+g x^3\right)^2}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[(f + g*x^3)^2/Log[c*(d + e*x^2)^p],x]","\int \frac{\left(f+g x^3\right)^2}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{\left(f+g x^3\right)^2}{\log \left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[(f + g*x^3)^2/Log[c*(d + e*x^2)^p], x]","A",-1
303,0,0,25,0.3382801,"\int \frac{f+g x^3}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[(f + g*x^3)/Log[c*(d + e*x^2)^p],x]","\int \frac{f+g x^3}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{f+g x^3}{\log \left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[(f + g*x^3)/Log[c*(d + e*x^2)^p], x]","A",-1
304,0,0,27,2.9123466,"\int \frac{1}{\left(f+g x^3\right) \log \left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[1/((f + g*x^3)*Log[c*(d + e*x^2)^p]),x]","\int \frac{1}{\left(f+g x^3\right) \log \left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\left(f+g x^3\right) \log \left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[1/((f + g*x^3)*Log[c*(d + e*x^2)^p]), x]","A",-1
305,0,0,27,8.7667742,"\int \frac{1}{\left(f+g x^3\right)^2 \log \left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[1/((f + g*x^3)^2*Log[c*(d + e*x^2)^p]),x]","\int \frac{1}{\left(f+g x^3\right)^2 \log \left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\left(f+g x^3\right)^2 \log \left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[1/((f + g*x^3)^2*Log[c*(d + e*x^2)^p]), x]","A",-1
306,0,0,27,0.7157349,"\int \frac{\left(f+g x^3\right)^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[(f + g*x^3)^2/Log[c*(d + e*x^2)^p]^2,x]","\int \frac{\left(f+g x^3\right)^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{\left(f+g x^3\right)^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[(f + g*x^3)^2/Log[c*(d + e*x^2)^p]^2, x]","A",-1
307,0,0,25,0.562405,"\int \frac{f+g x^3}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[(f + g*x^3)/Log[c*(d + e*x^2)^p]^2,x]","\int \frac{f+g x^3}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{f+g x^3}{\log ^2\left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[(f + g*x^3)/Log[c*(d + e*x^2)^p]^2, x]","A",-1
308,0,0,27,8.1471884,"\int \frac{1}{\left(f+g x^3\right) \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[1/((f + g*x^3)*Log[c*(d + e*x^2)^p]^2),x]","\int \frac{1}{\left(f+g x^3\right) \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\left(f+g x^3\right) \log ^2\left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[1/((f + g*x^3)*Log[c*(d + e*x^2)^p]^2), x]","A",-1
309,0,0,27,14.4787963,"\int \frac{1}{\left(f+g x^3\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Integrate[1/((f + g*x^3)^2*Log[c*(d + e*x^2)^p]^2),x]","\int \frac{1}{\left(f+g x^3\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{\left(f+g x^3\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right)},x\right)",0,"Integrate[1/((f + g*x^3)^2*Log[c*(d + e*x^2)^p]^2), x]","A",-1
310,1,170,142,0.0439864,"\int x^5 \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[x^5*(f + g*x^2)*Log[c*(d + e*x^2)^p],x]","\frac{1}{6} f x^6 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{8} g x^8 \log \left(c \left(d+e x^2\right)^p\right)-\frac{d^4 g p \log \left(d+e x^2\right)}{8 e^4}+\frac{d^3 f p \log \left(d+e x^2\right)}{6 e^3}+\frac{d^3 g p x^2}{8 e^3}-\frac{d^2 f p x^2}{6 e^2}-\frac{d^2 g p x^4}{16 e^2}+\frac{d f p x^4}{12 e}+\frac{d g p x^6}{24 e}-\frac{1}{18} f p x^6-\frac{1}{32} g p x^8","\frac{1}{6} f x^6 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{8} g x^8 \log \left(c \left(d+e x^2\right)^p\right)+\frac{d^3 p (4 e f-3 d g) \log \left(d+e x^2\right)}{24 e^4}-\frac{d^2 p x^2 (4 e f-3 d g)}{24 e^3}+\frac{d p x^4 (4 e f-3 d g)}{48 e^2}-\frac{p x^6 (4 e f-3 d g)}{72 e}-\frac{1}{32} g p x^8",1,"-1/6*(d^2*f*p*x^2)/e^2 + (d^3*g*p*x^2)/(8*e^3) + (d*f*p*x^4)/(12*e) - (d^2*g*p*x^4)/(16*e^2) - (f*p*x^6)/18 + (d*g*p*x^6)/(24*e) - (g*p*x^8)/32 + (d^3*f*p*Log[d + e*x^2])/(6*e^3) - (d^4*g*p*Log[d + e*x^2])/(8*e^4) + (f*x^6*Log[c*(d + e*x^2)^p])/6 + (g*x^8*Log[c*(d + e*x^2)^p])/8","A",1
311,1,140,119,0.0271107,"\int x^3 \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[x^3*(f + g*x^2)*Log[c*(d + e*x^2)^p],x]","\frac{1}{4} f x^4 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{6} g x^6 \log \left(c \left(d+e x^2\right)^p\right)+\frac{d^3 g p \log \left(d+e x^2\right)}{6 e^3}-\frac{d^2 f p \log \left(d+e x^2\right)}{4 e^2}-\frac{d^2 g p x^2}{6 e^2}+\frac{d f p x^2}{4 e}+\frac{d g p x^4}{12 e}-\frac{1}{8} f p x^4-\frac{1}{18} g p x^6","\frac{1}{4} f x^4 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{6} g x^6 \log \left(c \left(d+e x^2\right)^p\right)-\frac{d^2 p (3 e f-2 d g) \log \left(d+e x^2\right)}{12 e^3}+\frac{d p x^2 (3 e f-2 d g)}{12 e^2}-\frac{p x^4 (3 e f-2 d g)}{24 e}-\frac{1}{18} g p x^6",1,"(d*f*p*x^2)/(4*e) - (d^2*g*p*x^2)/(6*e^2) - (f*p*x^4)/8 + (d*g*p*x^4)/(12*e) - (g*p*x^6)/18 - (d^2*f*p*Log[d + e*x^2])/(4*e^2) + (d^3*g*p*Log[d + e*x^2])/(6*e^3) + (f*x^4*Log[c*(d + e*x^2)^p])/4 + (g*x^6*Log[c*(d + e*x^2)^p])/6","A",1
312,1,98,94,0.0460479,"\int x \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[x*(f + g*x^2)*Log[c*(d + e*x^2)^p],x]","\frac{1}{2} f \left(\frac{\left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{e}-p x^2\right)+\frac{1}{4} g x^4 \log \left(c \left(d+e x^2\right)^p\right)-\frac{d^2 g p \log \left(d+e x^2\right)}{4 e^2}+\frac{d g p x^2}{4 e}-\frac{1}{8} g p x^4","\frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{4 g}-\frac{p (e f-d g)^2 \log \left(d+e x^2\right)}{4 e^2 g}-\frac{p x^2 (e f-d g)}{4 e}-\frac{p \left(f+g x^2\right)^2}{8 g}",1,"(d*g*p*x^2)/(4*e) - (g*p*x^4)/8 - (d^2*g*p*Log[d + e*x^2])/(4*e^2) + (g*x^4*Log[c*(d + e*x^2)^p])/4 + (f*(-(p*x^2) + ((d + e*x^2)*Log[c*(d + e*x^2)^p])/e))/2","A",1
313,1,80,82,0.0220958,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x} \, dx","Integrate[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x,x]","\frac{1}{2} f \left(\log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)+p \text{Li}_2\left(\frac{e x^2+d}{d}\right)\right)+\frac{1}{2} g \left(\frac{\left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{e}-p x^2\right)","\frac{1}{2} f \log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)+\frac{g \left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{2 e}+\frac{1}{2} f p \text{Li}_2\left(\frac{e x^2}{d}+1\right)-\frac{1}{2} g p x^2",1,"(g*(-(p*x^2) + ((d + e*x^2)*Log[c*(d + e*x^2)^p])/e))/2 + (f*(Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p] + p*PolyLog[2, (d + e*x^2)/d]))/2","A",1
314,1,92,93,0.032378,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^3} \, dx","Integrate[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x^3,x]","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{2 x^2}+\frac{1}{2} g \left(\log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)+p \text{Li}_2\left(\frac{e x^2+d}{d}\right)\right)-\frac{e f p \log \left(d+e x^2\right)}{2 d}+\frac{e f p \log (x)}{d}","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{2 x^2}+\frac{1}{2} g \log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)-\frac{e f p \log \left(d+e x^2\right)}{2 d}+\frac{e f p \log (x)}{d}+\frac{1}{2} g p \text{Li}_2\left(\frac{e x^2}{d}+1\right)",1,"(e*f*p*Log[x])/d - (e*f*p*Log[d + e*x^2])/(2*d) - (f*Log[c*(d + e*x^2)^p])/(2*x^2) + (g*(Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p] + p*PolyLog[2, (d + e*x^2)/d]))/2","A",1
315,1,105,93,0.0409115,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^5} \, dx","Integrate[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x^5,x]","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{4 x^4}-\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{2 x^2}+\frac{1}{4} e f p \left(\frac{e \log \left(d+e x^2\right)}{d^2}-\frac{2 e \log (x)}{d^2}-\frac{1}{d x^2}\right)-\frac{e g p \log \left(d+e x^2\right)}{2 d}+\frac{e g p \log (x)}{d}","-\frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{4 f x^4}+\frac{p (e f-d g)^2 \log \left(d+e x^2\right)}{4 d^2 f}-\frac{e p \log (x) (e f-2 d g)}{2 d^2}-\frac{e f p}{4 d x^2}",1,"(e*g*p*Log[x])/d - (e*g*p*Log[d + e*x^2])/(2*d) + (e*f*p*(-(1/(d*x^2)) - (2*e*Log[x])/d^2 + (e*Log[d + e*x^2])/d^2))/4 - (f*Log[c*(d + e*x^2)^p])/(4*x^4) - (g*Log[c*(d + e*x^2)^p])/(2*x^2)","A",1
316,1,130,125,0.0700609,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^7} \, dx","Integrate[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x^7,x]","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{6 x^6}-\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{4 x^4}+\frac{1}{4} e g p \left(\frac{e \log \left(d+e x^2\right)}{d^2}-\frac{2 e \log (x)}{d^2}-\frac{1}{d x^2}\right)+\frac{1}{6} e f p \left(-\frac{e^2 \log \left(d+e x^2\right)}{d^3}+\frac{2 e^2 \log (x)}{d^3}+\frac{e}{d^2 x^2}-\frac{1}{2 d x^4}\right)","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{6 x^6}-\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{4 x^4}-\frac{e^2 p (2 e f-3 d g) \log \left(d+e x^2\right)}{12 d^3}+\frac{e^2 p \log (x) (2 e f-3 d g)}{6 d^3}+\frac{e p (2 e f-3 d g)}{12 d^2 x^2}-\frac{e f p}{12 d x^4}",1,"(e*g*p*(-(1/(d*x^2)) - (2*e*Log[x])/d^2 + (e*Log[d + e*x^2])/d^2))/4 + (e*f*p*(-1/2*1/(d*x^4) + e/(d^2*x^2) + (2*e^2*Log[x])/d^3 - (e^2*Log[d + e*x^2])/d^3))/6 - (f*Log[c*(d + e*x^2)^p])/(6*x^6) - (g*Log[c*(d + e*x^2)^p])/(4*x^4)","A",1
317,1,158,148,0.1184028,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^9} \, dx","Integrate[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x^9,x]","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{8 x^8}-\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{6 x^6}+\frac{1}{6} e g p \left(-\frac{e^2 \log \left(d+e x^2\right)}{d^3}+\frac{2 e^2 \log (x)}{d^3}+\frac{e}{d^2 x^2}-\frac{1}{2 d x^4}\right)+\frac{1}{8} e f p \left(\frac{e^3 \log \left(d+e x^2\right)}{d^4}-\frac{2 e^3 \log (x)}{d^4}-\frac{e^2}{d^3 x^2}+\frac{e}{2 d^2 x^4}-\frac{1}{3 d x^6}\right)","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{8 x^8}-\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{6 x^6}+\frac{e^3 p (3 e f-4 d g) \log \left(d+e x^2\right)}{24 d^4}-\frac{e^3 p \log (x) (3 e f-4 d g)}{12 d^4}-\frac{e^2 p (3 e f-4 d g)}{24 d^3 x^2}+\frac{e p (3 e f-4 d g)}{48 d^2 x^4}-\frac{e f p}{24 d x^6}",1,"(e*g*p*(-1/2*1/(d*x^4) + e/(d^2*x^2) + (2*e^2*Log[x])/d^3 - (e^2*Log[d + e*x^2])/d^3))/6 + (e*f*p*(-1/3*1/(d*x^6) + e/(2*d^2*x^4) - e^2/(d^3*x^2) - (2*e^3*Log[x])/d^4 + (e^3*Log[d + e*x^2])/d^4))/8 - (f*Log[c*(d + e*x^2)^p])/(8*x^8) - (g*Log[c*(d + e*x^2)^p])/(6*x^6)","A",1
318,1,118,154,0.0645948,"\int x^2 \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[x^2*(f + g*x^2)*Log[c*(d + e*x^2)^p],x]","\frac{\sqrt{e} x \left(15 e^2 x^2 \left(5 f+3 g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)-2 p \left(45 d^2 g-15 d e \left(5 f+g x^2\right)+e^2 x^2 \left(25 f+9 g x^2\right)\right)\right)+30 d^{3/2} p (3 d g-5 e f) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{225 e^{5/2}}","\frac{1}{3} f x^3 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{5} g x^5 \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 d^{3/2} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2}}+\frac{2 d^{5/2} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{5 e^{5/2}}-\frac{2 d^2 g p x}{5 e^2}+\frac{2 d f p x}{3 e}+\frac{2 d g p x^3}{15 e}-\frac{2}{9} f p x^3-\frac{2}{25} g p x^5",1,"(30*d^(3/2)*(-5*e*f + 3*d*g)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]] + Sqrt[e]*x*(-2*p*(45*d^2*g - 15*d*e*(5*f + g*x^2) + e^2*x^2*(25*f + 9*g*x^2)) + 15*e^2*x^2*(5*f + 3*g*x^2)*Log[c*(d + e*x^2)^p]))/(225*e^(5/2))","A",1
319,1,117,117,0.03949,"\int \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^2)*Log[c*(d + e*x^2)^p],x]","f x \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{3} g x^3 \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 d^{3/2} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2}}+\frac{2 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{2 d g p x}{3 e}-2 f p x-\frac{2}{9} g p x^3","f x \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{3} g x^3 \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 d^{3/2} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2}}+\frac{2 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{2 d g p x}{3 e}-2 f p x-\frac{2}{9} g p x^3",1,"-2*f*p*x + (2*d*g*p*x)/(3*e) - (2*g*p*x^3)/9 + (2*Sqrt[d]*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (2*d^(3/2)*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*e^(3/2)) + f*x*Log[c*(d + e*x^2)^p] + (g*x^3*Log[c*(d + e*x^2)^p])/3","A",1
320,1,62,72,0.0491383,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^2} \, dx","Integrate[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x^2,x]","\left(g x-\frac{f}{x}\right) \log \left(c \left(d+e x^2\right)^p\right)+\frac{2 p (d g+e f) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \sqrt{e}}-2 g p x","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{x}+g x \log \left(c \left(d+e x^2\right)^p\right)+\frac{2 p (d g+e f) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \sqrt{e}}-2 g p x",1,"-2*g*p*x + (2*(e*f + d*g)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*Sqrt[e]) + (-(f/x) + g*x)*Log[c*(d + e*x^2)^p]","A",1
321,1,96,108,0.0428648,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^4} \, dx","Integrate[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x^4,x]","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{3 x^3}-\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{x}-\frac{2 e f p \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{e x^2}{d}\right)}{3 d x}+\frac{2 \sqrt{e} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d}}","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{3 x^3}-\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{x}-\frac{2 e^{3/2} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 d^{3/2}}-\frac{2 e f p}{3 d x}+\frac{2 \sqrt{e} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d}}",1,"(2*Sqrt[e]*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[d] - (2*e*f*p*Hypergeometric2F1[-1/2, 1, 1/2, -((e*x^2)/d)])/(3*d*x) - (f*Log[c*(d + e*x^2)^p])/(3*x^3) - (g*Log[c*(d + e*x^2)^p])/x","C",1
322,1,101,140,0.0069194,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^6} \, dx","Integrate[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x^6,x]","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{5 x^5}-\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{3 x^3}-\frac{2 e f p \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{e x^2}{d}\right)}{15 d x^3}-\frac{2 e g p \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{e x^2}{d}\right)}{3 d x}","-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{5 x^5}-\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{3 x^3}+\frac{2 e^{5/2} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{5 d^{5/2}}-\frac{2 e^{3/2} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 d^{3/2}}+\frac{2 e^2 f p}{5 d^2 x}-\frac{2 e f p}{15 d x^3}-\frac{2 e g p}{3 d x}",1,"(-2*e*f*p*Hypergeometric2F1[-3/2, 1, -1/2, -((e*x^2)/d)])/(15*d*x^3) - (2*e*g*p*Hypergeometric2F1[-1/2, 1, 1/2, -((e*x^2)/d)])/(3*d*x) - (f*Log[c*(d + e*x^2)^p])/(5*x^5) - (g*Log[c*(d + e*x^2)^p])/(3*x^3)","C",1
323,1,205,251,0.1864705,"\int x^5 \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[x^5*(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","\frac{60 e^5 x^6 \left(10 f^2+15 f g x^2+6 g^2 x^4\right) \log \left(c \left(d+e x^2\right)^p\right)+60 d^3 p \left(6 d^2 g^2-15 d e f g+10 e^2 f^2\right) \log \left(d+e x^2\right)-e p x^2 \left(360 d^4 g^2-180 d^3 e g \left(5 f+g x^2\right)+30 d^2 e^2 \left(20 f^2+15 f g x^2+4 g^2 x^4\right)-30 d e^3 x^2 \left(10 f^2+10 f g x^2+3 g^2 x^4\right)+e^4 x^4 \left(200 f^2+225 f g x^2+72 g^2 x^4\right)\right)}{3600 e^5}","\frac{1}{6} f^2 x^6 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{4} f g x^8 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{10} g^2 x^{10} \log \left(c \left(d+e x^2\right)^p\right)-\frac{d^2 p x^2 (e f-d g)^2}{2 e^4}-\frac{p \left(d+e x^2\right)^3 \left(6 d^2 g^2-6 d e f g+e^2 f^2\right)}{18 e^5}+\frac{d^3 p \left(6 d^2 g^2-15 d e f g+10 e^2 f^2\right) \log \left(d+e x^2\right)}{60 e^5}-\frac{g p \left(d+e x^2\right)^4 (e f-2 d g)}{16 e^5}+\frac{d p \left(d+e x^2\right)^2 (e f-2 d g) (e f-d g)}{4 e^5}-\frac{g^2 p \left(d+e x^2\right)^5}{50 e^5}",1,"(-(e*p*x^2*(360*d^4*g^2 - 180*d^3*e*g*(5*f + g*x^2) - 30*d*e^3*x^2*(10*f^2 + 10*f*g*x^2 + 3*g^2*x^4) + 30*d^2*e^2*(20*f^2 + 15*f*g*x^2 + 4*g^2*x^4) + e^4*x^4*(200*f^2 + 225*f*g*x^2 + 72*g^2*x^4))) + 60*d^3*(10*e^2*f^2 - 15*d*e*f*g + 6*d^2*g^2)*p*Log[d + e*x^2] + 60*e^5*x^6*(10*f^2 + 15*f*g*x^2 + 6*g^2*x^4)*Log[c*(d + e*x^2)^p])/(3600*e^5)","A",1
324,1,173,210,0.1429971,"\int x^3 \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[x^3*(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","\frac{12 e^4 x^4 \left(6 f^2+8 f g x^2+3 g^2 x^4\right) \log \left(c \left(d+e x^2\right)^p\right)-12 d^2 p \left(3 d^2 g^2-8 d e f g+6 e^2 f^2\right) \log \left(d+e x^2\right)+e p x^2 \left(36 d^3 g^2-6 d^2 e g \left(16 f+3 g x^2\right)+12 d e^2 \left(6 f^2+4 f g x^2+g^2 x^4\right)-e^3 x^2 \left(36 f^2+32 f g x^2+9 g^2 x^4\right)\right)}{288 e^4}","\frac{1}{4} f^2 x^4 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{3} f g x^6 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{8} g^2 x^8 \log \left(c \left(d+e x^2\right)^p\right)-\frac{d^2 p \left(3 d^2 g^2-8 d e f g+6 e^2 f^2\right) \log \left(d+e x^2\right)}{24 e^4}-\frac{g p \left(d+e x^2\right)^3 (2 e f-3 d g)}{18 e^4}-\frac{p \left(d+e x^2\right)^2 (e f-3 d g) (e f-d g)}{8 e^4}-\frac{g^2 p \left(d+e x^2\right)^4}{32 e^4}+\frac{d p x^2 (e f-d g)^2}{2 e^3}",1,"(e*p*x^2*(36*d^3*g^2 - 6*d^2*e*g*(16*f + 3*g*x^2) + 12*d*e^2*(6*f^2 + 4*f*g*x^2 + g^2*x^4) - e^3*x^2*(36*f^2 + 32*f*g*x^2 + 9*g^2*x^4)) - 12*d^2*(6*e^2*f^2 - 8*d*e*f*g + 3*d^2*g^2)*p*Log[d + e*x^2] + 12*e^4*x^4*(6*f^2 + 8*f*g*x^2 + 3*g^2*x^4)*Log[c*(d + e*x^2)^p])/(288*e^4)","A",1
325,1,135,124,0.1135133,"\int x \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[x*(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","\frac{e \left(6 e \left(3 d f^2+e x^2 \left(3 f^2+3 f g x^2+g^2 x^4\right)\right) \log \left(c \left(d+e x^2\right)^p\right)-p x^2 \left(6 d^2 g^2-3 d e g \left(6 f+g x^2\right)+e^2 \left(18 f^2+9 f g x^2+2 g^2 x^4\right)\right)\right)+6 d^2 g p (d g-3 e f) \log \left(d+e x^2\right)}{36 e^3}","\frac{\left(f+g x^2\right)^3 \log \left(c \left(d+e x^2\right)^p\right)}{6 g}-\frac{p (e f-d g)^3 \log \left(d+e x^2\right)}{6 e^3 g}-\frac{p x^2 (e f-d g)^2}{6 e^2}-\frac{p \left(f+g x^2\right)^2 (e f-d g)}{12 e g}-\frac{p \left(f+g x^2\right)^3}{18 g}",1,"(6*d^2*g*(-3*e*f + d*g)*p*Log[d + e*x^2] + e*(-(p*x^2*(6*d^2*g^2 - 3*d*e*g*(6*f + g*x^2) + e^2*(18*f^2 + 9*f*g*x^2 + 2*g^2*x^4))) + 6*e*(3*d*f^2 + e*x^2*(3*f^2 + 3*f*g*x^2 + g^2*x^4))*Log[c*(d + e*x^2)^p]))/(36*e^3)","A",1
326,1,121,153,0.0906209,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x} \, dx","Integrate[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x,x]","\frac{2 e \log \left(c \left(d+e x^2\right)^p\right) \left(2 e f^2 \log \left(-\frac{e x^2}{d}\right)+g \left(4 d f+4 e f x^2+e g x^4\right)\right)-2 d^2 g^2 p \log \left(d+e x^2\right)+4 e^2 f^2 p \text{Li}_2\left(\frac{e x^2}{d}+1\right)-e g p x^2 \left(-2 d g+8 e f+e g x^2\right)}{8 e^2}","\frac{1}{2} f^2 \log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)+\frac{f g \left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{e}+\frac{1}{4} g^2 x^4 \log \left(c \left(d+e x^2\right)^p\right)-\frac{d^2 g^2 p \log \left(d+e x^2\right)}{4 e^2}+\frac{1}{2} f^2 p \text{Li}_2\left(\frac{e x^2}{d}+1\right)+\frac{d g^2 p x^2}{4 e}-f g p x^2-\frac{1}{8} g^2 p x^4",1,"(-(e*g*p*x^2*(8*e*f - 2*d*g + e*g*x^2)) - 2*d^2*g^2*p*Log[d + e*x^2] + 2*e*(g*(4*d*f + 4*e*f*x^2 + e*g*x^4) + 2*e*f^2*Log[-((e*x^2)/d)])*Log[c*(d + e*x^2)^p] + 4*e^2*f^2*p*PolyLog[2, 1 + (e*x^2)/d])/(8*e^2)","A",1
327,1,126,135,0.0854275,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^3} \, dx","Integrate[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^3,x]","\frac{1}{2} \left(-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^2}+2 f g \left(\log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)+p \text{Li}_2\left(\frac{e x^2}{d}+1\right)\right)+\frac{g^2 \left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{e}+\frac{e f^2 p \left(2 \log (x)-\log \left(d+e x^2\right)\right)}{d}-g^2 p x^2\right)","-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{2 x^2}+f g \log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)+\frac{g^2 \left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{2 e}-\frac{e f^2 p \log \left(d+e x^2\right)}{2 d}+\frac{e f^2 p \log (x)}{d}+f g p \text{Li}_2\left(\frac{e x^2}{d}+1\right)-\frac{1}{2} g^2 p x^2",1,"(-(g^2*p*x^2) + (e*f^2*p*(2*Log[x] - Log[d + e*x^2]))/d - (f^2*Log[c*(d + e*x^2)^p])/x^2 + (g^2*(d + e*x^2)*Log[c*(d + e*x^2)^p])/e + 2*f*g*(Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p] + p*PolyLog[2, 1 + (e*x^2)/d]))/2","A",1
328,1,148,172,0.1209517,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^5} \, dx","Integrate[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^5,x]","\frac{1}{4} \left(-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^4}-\frac{4 f g \log \left(c \left(d+e x^2\right)^p\right)}{x^2}+2 g^2 \left(\log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)+p \text{Li}_2\left(\frac{e x^2}{d}+1\right)\right)-\frac{e f^2 p \left(-e x^2 \log \left(d+e x^2\right)+d+2 e x^2 \log (x)\right)}{d^2 x^2}+\frac{4 e f g p \left(2 \log (x)-\log \left(d+e x^2\right)\right)}{d}\right)","-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{4 x^4}-\frac{f g \log \left(c \left(d+e x^2\right)^p\right)}{x^2}+\frac{1}{2} g^2 \log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)+\frac{e^2 f^2 p \log \left(d+e x^2\right)}{4 d^2}-\frac{e^2 f^2 p \log (x)}{2 d^2}-\frac{e f^2 p}{4 d x^2}-\frac{e f g p \log \left(d+e x^2\right)}{d}+\frac{2 e f g p \log (x)}{d}+\frac{1}{2} g^2 p \text{Li}_2\left(\frac{e x^2}{d}+1\right)",1,"((4*e*f*g*p*(2*Log[x] - Log[d + e*x^2]))/d - (e*f^2*p*(d + 2*e*x^2*Log[x] - e*x^2*Log[d + e*x^2]))/(d^2*x^2) - (f^2*Log[c*(d + e*x^2)^p])/x^4 - (4*f*g*Log[c*(d + e*x^2)^p])/x^2 + 2*g^2*(Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p] + p*PolyLog[2, 1 + (e*x^2)/d]))/4","A",1
329,1,141,130,0.1325594,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^7} \, dx","Integrate[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^7,x]","-\frac{2 d^3 \left(f^2+3 f g x^2+3 g^2 x^4\right) \log \left(c \left(d+e x^2\right)^p\right)-4 e p x^6 \log (x) \left(3 d^2 g^2-3 d e f g+e^2 f^2\right)+2 e p x^6 \left(3 d^2 g^2-3 d e f g+e^2 f^2\right) \log \left(d+e x^2\right)+d e f p x^2 \left(d \left(f+6 g x^2\right)-2 e f x^2\right)}{12 d^3 x^6}","-\frac{\left(f+g x^2\right)^3 \log \left(c \left(d+e x^2\right)^p\right)}{6 f x^6}-\frac{p (e f-d g)^3 \log \left(d+e x^2\right)}{6 d^3 f}+\frac{e f p (e f-3 d g)}{6 d^2 x^2}+\frac{e p \log (x) \left(3 d^2 g^2-3 d e f g+e^2 f^2\right)}{3 d^3}-\frac{e f^2 p}{12 d x^4}",1,"-1/12*(d*e*f*p*x^2*(-2*e*f*x^2 + d*(f + 6*g*x^2)) - 4*e*(e^2*f^2 - 3*d*e*f*g + 3*d^2*g^2)*p*x^6*Log[x] + 2*e*(e^2*f^2 - 3*d*e*f*g + 3*d^2*g^2)*p*x^6*Log[d + e*x^2] + 2*d^3*(f^2 + 3*f*g*x^2 + 3*g^2*x^4)*Log[c*(d + e*x^2)^p])/(d^3*x^6)","A",1
330,1,184,216,0.1776533,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^9} \, dx","Integrate[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^9,x]","-\frac{2 d^4 \left(3 f^2+8 f g x^2+6 g^2 x^4\right) \log \left(c \left(d+e x^2\right)^p\right)+4 e^2 p x^8 \log (x) \left(6 d^2 g^2-8 d e f g+3 e^2 f^2\right)-2 e^2 p x^8 \left(6 d^2 g^2-8 d e f g+3 e^2 f^2\right) \log \left(d+e x^2\right)+d e p x^2 \left(2 d^2 \left(f^2+4 f g x^2+6 g^2 x^4\right)-d e f x^2 \left(3 f+16 g x^2\right)+6 e^2 f^2 x^4\right)}{48 d^4 x^8}","-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{8 x^8}-\frac{f g \log \left(c \left(d+e x^2\right)^p\right)}{3 x^6}-\frac{g^2 \log \left(c \left(d+e x^2\right)^p\right)}{4 x^4}+\frac{e f p (3 e f-8 d g)}{48 d^2 x^4}+\frac{e^2 p \left(6 d^2 g^2-8 d e f g+3 e^2 f^2\right) \log \left(d+e x^2\right)}{24 d^4}-\frac{e^2 p \log (x) \left(6 d^2 g^2-8 d e f g+3 e^2 f^2\right)}{12 d^4}-\frac{e p \left(6 d^2 g^2-8 d e f g+3 e^2 f^2\right)}{24 d^3 x^2}-\frac{e f^2 p}{24 d x^6}",1,"-1/48*(d*e*p*x^2*(6*e^2*f^2*x^4 - d*e*f*x^2*(3*f + 16*g*x^2) + 2*d^2*(f^2 + 4*f*g*x^2 + 6*g^2*x^4)) + 4*e^2*(3*e^2*f^2 - 8*d*e*f*g + 6*d^2*g^2)*p*x^8*Log[x] - 2*e^2*(3*e^2*f^2 - 8*d*e*f*g + 6*d^2*g^2)*p*x^8*Log[d + e*x^2] + 2*d^4*(3*f^2 + 8*f*g*x^2 + 6*g^2*x^4)*Log[c*(d + e*x^2)^p])/(d^4*x^8)","A",1
331,1,215,253,0.239151,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^{11}} \, dx","Integrate[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^11,x]","-\frac{2 d^5 \left(6 f^2+15 f g x^2+10 g^2 x^4\right) \log \left(c \left(d+e x^2\right)^p\right)-4 e^3 p x^{10} \log (x) \left(10 d^2 g^2-15 d e f g+6 e^2 f^2\right)+2 e^3 p x^{10} \left(10 d^2 g^2-15 d e f g+6 e^2 f^2\right) \log \left(d+e x^2\right)+d e p x^2 \left(d^3 \left(3 f^2+10 f g x^2+10 g^2 x^4\right)-d^2 e x^2 \left(4 f^2+15 f g x^2+20 g^2 x^4\right)+6 d e^2 f x^4 \left(f+5 g x^2\right)-12 e^3 f^2 x^6\right)}{120 d^5 x^{10}}","-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{10 x^{10}}-\frac{f g \log \left(c \left(d+e x^2\right)^p\right)}{4 x^8}-\frac{g^2 \log \left(c \left(d+e x^2\right)^p\right)}{6 x^6}+\frac{e f p (2 e f-5 d g)}{60 d^2 x^6}-\frac{e^3 p \left(10 d^2 g^2-15 d e f g+6 e^2 f^2\right) \log \left(d+e x^2\right)}{60 d^5}+\frac{e^3 p \log (x) \left(10 d^2 g^2-15 d e f g+6 e^2 f^2\right)}{30 d^5}+\frac{e^2 p \left(10 d^2 g^2-15 d e f g+6 e^2 f^2\right)}{60 d^4 x^2}-\frac{e p \left(10 d^2 g^2-15 d e f g+6 e^2 f^2\right)}{120 d^3 x^4}-\frac{e f^2 p}{40 d x^8}",1,"-1/120*(d*e*p*x^2*(-12*e^3*f^2*x^6 + 6*d*e^2*f*x^4*(f + 5*g*x^2) + d^3*(3*f^2 + 10*f*g*x^2 + 10*g^2*x^4) - d^2*e*x^2*(4*f^2 + 15*f*g*x^2 + 20*g^2*x^4)) - 4*e^3*(6*e^2*f^2 - 15*d*e*f*g + 10*d^2*g^2)*p*x^10*Log[x] + 2*e^3*(6*e^2*f^2 - 15*d*e*f*g + 10*d^2*g^2)*p*x^10*Log[d + e*x^2] + 2*d^5*(6*f^2 + 15*f*g*x^2 + 10*g^2*x^4)*Log[c*(d + e*x^2)^p])/(d^5*x^10)","A",1
332,1,188,278,0.1818035,"\int x^2 \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[x^2*(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","\frac{\sqrt{e} x \left(105 e^3 x^2 \left(35 f^2+42 f g x^2+15 g^2 x^4\right) \log \left(c \left(d+e x^2\right)^p\right)+2 p \left(1575 d^3 g^2-105 d^2 e g \left(42 f+5 g x^2\right)+105 d e^2 \left(35 f^2+14 f g x^2+3 g^2 x^4\right)-e^3 x^2 \left(1225 f^2+882 f g x^2+225 g^2 x^4\right)\right)\right)-210 d^{3/2} p \left(15 d^2 g^2-42 d e f g+35 e^2 f^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{11025 e^{7/2}}","\frac{1}{3} f^2 x^3 \log \left(c \left(d+e x^2\right)^p\right)+\frac{2}{5} f g x^5 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{7} g^2 x^7 \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 d^{3/2} f^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2}}+\frac{4 d^{5/2} f g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{5 e^{5/2}}-\frac{2 d^{7/2} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{7 e^{7/2}}+\frac{2 d^3 g^2 p x}{7 e^3}-\frac{4 d^2 f g p x}{5 e^2}-\frac{2 d^2 g^2 p x^3}{21 e^2}+\frac{2 d f^2 p x}{3 e}+\frac{4 d f g p x^3}{15 e}+\frac{2 d g^2 p x^5}{35 e}-\frac{2}{9} f^2 p x^3-\frac{4}{25} f g p x^5-\frac{2}{49} g^2 p x^7",1,"(-210*d^(3/2)*(35*e^2*f^2 - 42*d*e*f*g + 15*d^2*g^2)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]] + Sqrt[e]*x*(2*p*(1575*d^3*g^2 - 105*d^2*e*g*(42*f + 5*g*x^2) + 105*d*e^2*(35*f^2 + 14*f*g*x^2 + 3*g^2*x^4) - e^3*x^2*(1225*f^2 + 882*f*g*x^2 + 225*g^2*x^4)) + 105*e^3*x^2*(35*f^2 + 42*f*g*x^2 + 15*g^2*x^4)*Log[c*(d + e*x^2)^p]))/(11025*e^(7/2))","A",1
333,1,151,221,0.1369889,"\int \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Integrate[(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","\frac{\sqrt{e} x \left(15 e^2 \left(15 f^2+10 f g x^2+3 g^2 x^4\right) \log \left(c \left(d+e x^2\right)^p\right)-2 p \left(45 d^2 g^2-15 d e g \left(10 f+g x^2\right)+e^2 \left(225 f^2+50 f g x^2+9 g^2 x^4\right)\right)\right)+30 \sqrt{d} p \left(3 d^2 g^2-10 d e f g+15 e^2 f^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{225 e^{5/2}}","f^2 x \log \left(c \left(d+e x^2\right)^p\right)+\frac{2}{3} f g x^3 \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{5} g^2 x^5 \log \left(c \left(d+e x^2\right)^p\right)-\frac{4 d^{3/2} f g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2}}+\frac{2 d^{5/2} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{5 e^{5/2}}-\frac{2 d^2 g^2 p x}{5 e^2}+\frac{2 \sqrt{d} f^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{4 d f g p x}{3 e}+\frac{2 d g^2 p x^3}{15 e}-2 f^2 p x-\frac{4}{9} f g p x^3-\frac{2}{25} g^2 p x^5",1,"(30*Sqrt[d]*(15*e^2*f^2 - 10*d*e*f*g + 3*d^2*g^2)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]] + Sqrt[e]*x*(-2*p*(45*d^2*g^2 - 15*d*e*g*(10*f + g*x^2) + e^2*(225*f^2 + 50*f*g*x^2 + 9*g^2*x^4)) + 15*e^2*(15*f^2 + 10*f*g*x^2 + 3*g^2*x^4)*Log[c*(d + e*x^2)^p]))/(225*e^(5/2))","A",1
334,1,112,178,0.1467013,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^2} \, dx","Integrate[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^2,x]","\frac{1}{9} \left(\left(-\frac{9 f^2}{x}+18 f g x+3 g^2 x^3\right) \log \left(c \left(d+e x^2\right)^p\right)+\frac{6 p \left(-d^2 g^2+6 d e f g+3 e^2 f^2\right) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} e^{3/2}}-\frac{2 g p x \left(-3 d g+18 e f+e g x^2\right)}{e}\right)","-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{x}+2 f g x \log \left(c \left(d+e x^2\right)^p\right)+\frac{1}{3} g^2 x^3 \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 d^{3/2} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2}}+\frac{2 \sqrt{e} f^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d}}+\frac{4 \sqrt{d} f g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{2 d g^2 p x}{3 e}-4 f g p x-\frac{2}{9} g^2 p x^3",1,"((-2*g*p*x*(18*e*f - 3*d*g + e*g*x^2))/e + (6*(3*e^2*f^2 + 6*d*e*f*g - d^2*g^2)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*e^(3/2)) + ((-9*f^2)/x + 18*f*g*x + 3*g^2*x^3)*Log[c*(d + e*x^2)^p])/9","A",1
335,1,113,169,0.1352216,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^4} \, dx","Integrate[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^4,x]","-\frac{\left(f^2+6 f g x^2-3 g^2 x^4\right) \log \left(c \left(d+e x^2\right)^p\right)}{3 x^3}-\frac{2 e f^2 p \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{e x^2}{d}\right)}{3 d x}+\frac{2 g p (d g+2 e f) \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} \sqrt{e}}-2 g^2 p x","-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{3 x^3}-\frac{2 f g \log \left(c \left(d+e x^2\right)^p\right)}{x}+g^2 x \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 e^{3/2} f^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 d^{3/2}}-\frac{2 e f^2 p}{3 d x}+\frac{4 \sqrt{e} f g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d}}+\frac{2 \sqrt{d} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-2 g^2 p x",1,"-2*g^2*p*x + (2*g*(2*e*f + d*g)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*Sqrt[e]) - (2*e*f^2*p*Hypergeometric2F1[-1/2, 1, 1/2, -((e*x^2)/d)])/(3*d*x) - ((f^2 + 6*f*g*x^2 - 3*g^2*x^4)*Log[c*(d + e*x^2)^p])/(3*x^3)","C",1
336,1,156,200,0.0678574,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^6} \, dx","Integrate[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^6,x]","-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{5 x^5}-\frac{2 f g \log \left(c \left(d+e x^2\right)^p\right)}{3 x^3}-\frac{g^2 \log \left(c \left(d+e x^2\right)^p\right)}{x}-\frac{2 e f^2 p \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{e x^2}{d}\right)}{15 d x^3}-\frac{4 e f g p \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{e x^2}{d}\right)}{3 d x}+\frac{2 \sqrt{e} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d}}","-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{5 x^5}-\frac{2 f g \log \left(c \left(d+e x^2\right)^p\right)}{3 x^3}-\frac{g^2 \log \left(c \left(d+e x^2\right)^p\right)}{x}+\frac{2 e^{5/2} f^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{5 d^{5/2}}-\frac{4 e^{3/2} f g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 d^{3/2}}+\frac{2 e^2 f^2 p}{5 d^2 x}-\frac{2 e f^2 p}{15 d x^3}-\frac{4 e f g p}{3 d x}+\frac{2 \sqrt{e} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d}}",1,"(2*Sqrt[e]*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[d] - (2*e*f^2*p*Hypergeometric2F1[-3/2, 1, -1/2, -((e*x^2)/d)])/(15*d*x^3) - (4*e*f*g*p*Hypergeometric2F1[-1/2, 1, 1/2, -((e*x^2)/d)])/(3*d*x) - (f^2*Log[c*(d + e*x^2)^p])/(5*x^5) - (2*f*g*Log[c*(d + e*x^2)^p])/(3*x^3) - (g^2*Log[c*(d + e*x^2)^p])/x","C",1
337,1,161,252,0.0302066,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^8} \, dx","Integrate[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^8,x]","-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{7 x^7}-\frac{2 f g \log \left(c \left(d+e x^2\right)^p\right)}{5 x^5}-\frac{g^2 \log \left(c \left(d+e x^2\right)^p\right)}{3 x^3}-\frac{2 e f^2 p \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{e x^2}{d}\right)}{35 d x^5}-\frac{4 e f g p \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{e x^2}{d}\right)}{15 d x^3}-\frac{2 e g^2 p \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{e x^2}{d}\right)}{3 d x}","-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{7 x^7}-\frac{2 f g \log \left(c \left(d+e x^2\right)^p\right)}{5 x^5}-\frac{g^2 \log \left(c \left(d+e x^2\right)^p\right)}{3 x^3}-\frac{2 e^{7/2} f^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{7 d^{7/2}}+\frac{4 e^{5/2} f g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{5 d^{5/2}}-\frac{2 e^{3/2} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 d^{3/2}}-\frac{2 e^3 f^2 p}{7 d^3 x}+\frac{2 e^2 f^2 p}{21 d^2 x^3}+\frac{4 e^2 f g p}{5 d^2 x}-\frac{2 e f^2 p}{35 d x^5}-\frac{4 e f g p}{15 d x^3}-\frac{2 e g^2 p}{3 d x}",1,"(-2*e*f^2*p*Hypergeometric2F1[-5/2, 1, -3/2, -((e*x^2)/d)])/(35*d*x^5) - (4*e*f*g*p*Hypergeometric2F1[-3/2, 1, -1/2, -((e*x^2)/d)])/(15*d*x^3) - (2*e*g^2*p*Hypergeometric2F1[-1/2, 1, 1/2, -((e*x^2)/d)])/(3*d*x) - (f^2*Log[c*(d + e*x^2)^p])/(7*x^7) - (2*f*g*Log[c*(d + e*x^2)^p])/(5*x^5) - (g^2*Log[c*(d + e*x^2)^p])/(3*x^3)","C",1
338,1,143,188,0.1264597,"\int \frac{x^5 \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Integrate[(x^5*Log[c*(d + e*x^2)^p])/(f + g*x^2),x]","\frac{e \log \left(c \left(d+e x^2\right)^p\right) \left(4 e f^2 \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)+2 g \left(-2 d f-2 e f x^2+e g x^4\right)\right)-2 d^2 g^2 p \log \left(d+e x^2\right)+4 e^2 f^2 p \text{Li}_2\left(\frac{g \left(e x^2+d\right)}{d g-e f}\right)+e g p x^2 \left(2 d g+4 e f-e g x^2\right)}{8 e^2 g^3}","\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)}{2 g^3}-\frac{f \left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{2 e g^2}+\frac{x^4 \log \left(c \left(d+e x^2\right)^p\right)}{4 g}-\frac{d^2 p \log \left(d+e x^2\right)}{4 e^2 g}+\frac{f^2 p \text{Li}_2\left(-\frac{g \left(e x^2+d\right)}{e f-d g}\right)}{2 g^3}+\frac{d p x^2}{4 e g}+\frac{f p x^2}{2 g^2}-\frac{p x^4}{8 g}",1,"(e*g*p*x^2*(4*e*f + 2*d*g - e*g*x^2) - 2*d^2*g^2*p*Log[d + e*x^2] + e*Log[c*(d + e*x^2)^p]*(2*g*(-2*d*f - 2*e*f*x^2 + e*g*x^4) + 4*e*f^2*Log[(e*(f + g*x^2))/(e*f - d*g)]) + 4*e^2*f^2*p*PolyLog[2, (g*(d + e*x^2))/(-(e*f) + d*g)])/(8*e^2*g^3)","A",1
339,1,91,112,0.0428338,"\int \frac{x^3 \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Integrate[(x^3*Log[c*(d + e*x^2)^p])/(f + g*x^2),x]","-\frac{-\log \left(c \left(d+e x^2\right)^p\right) \left(-e f \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)+d g+e g x^2\right)+e f p \text{Li}_2\left(\frac{g \left(e x^2+d\right)}{d g-e f}\right)+e g p x^2}{2 e g^2}","-\frac{f \log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)}{2 g^2}+\frac{\left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{2 e g}-\frac{f p \text{Li}_2\left(-\frac{g \left(e x^2+d\right)}{e f-d g}\right)}{2 g^2}-\frac{p x^2}{2 g}",1,"-1/2*(e*g*p*x^2 - Log[c*(d + e*x^2)^p]*(d*g + e*g*x^2 - e*f*Log[(e*(f + g*x^2))/(e*f - d*g)]) + e*f*p*PolyLog[2, (g*(d + e*x^2))/(-(e*f) + d*g)])/(e*g^2)","A",1
340,1,64,70,0.007863,"\int \frac{x \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Integrate[(x*Log[c*(d + e*x^2)^p])/(f + g*x^2),x]","\frac{\log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)+p \text{Li}_2\left(\frac{g \left(e x^2+d\right)}{d g-e f}\right)}{2 g}","\frac{\log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)}{2 g}+\frac{p \text{Li}_2\left(-\frac{g \left(e x^2+d\right)}{e f-d g}\right)}{2 g}",1,"(Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)] + p*PolyLog[2, (g*(d + e*x^2))/(-(e*f) + d*g)])/(2*g)","A",1
341,1,92,119,0.0386038,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x \left(f+g x^2\right)} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(x*(f + g*x^2)),x]","\frac{\log \left(c \left(d+e x^2\right)^p\right) \left(\log \left(-\frac{e x^2}{d}\right)-\log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)\right)-p \text{Li}_2\left(\frac{g \left(e x^2+d\right)}{d g-e f}\right)+p \text{Li}_2\left(\frac{e x^2}{d}+1\right)}{2 f}","-\frac{\log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)}{2 f}+\frac{\log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)}{2 f}-\frac{p \text{Li}_2\left(-\frac{g \left(e x^2+d\right)}{e f-d g}\right)}{2 f}+\frac{p \text{Li}_2\left(\frac{e x^2}{d}+1\right)}{2 f}",1,"(Log[c*(d + e*x^2)^p]*(Log[-((e*x^2)/d)] - Log[(e*(f + g*x^2))/(e*f - d*g)]) - p*PolyLog[2, (g*(d + e*x^2))/(-(e*f) + d*g)] + p*PolyLog[2, 1 + (e*x^2)/d])/(2*f)","A",1
342,1,147,176,0.0738339,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x^3 \left(f+g x^2\right)} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(x^3*(f + g*x^2)),x]","\frac{g \log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{x^2}-g \left(\log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)+p \text{Li}_2\left(\frac{e x^2}{d}+1\right)\right)+g p \text{Li}_2\left(\frac{g \left(e x^2+d\right)}{d g-e f}\right)+\frac{e f p \left(2 \log (x)-\log \left(d+e x^2\right)\right)}{d}}{2 f^2}","-\frac{g \log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)}{2 f^2}+\frac{g \log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)}{2 f^2}-\frac{\log \left(c \left(d+e x^2\right)^p\right)}{2 f x^2}+\frac{g p \text{Li}_2\left(-\frac{g \left(e x^2+d\right)}{e f-d g}\right)}{2 f^2}-\frac{g p \text{Li}_2\left(\frac{e x^2}{d}+1\right)}{2 f^2}-\frac{e p \log \left(d+e x^2\right)}{2 d f}+\frac{e p \log (x)}{d f}",1,"((e*f*p*(2*Log[x] - Log[d + e*x^2]))/d - (f*Log[c*(d + e*x^2)^p])/x^2 + g*Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)] + g*p*PolyLog[2, (g*(d + e*x^2))/(-(e*f) + d*g)] - g*(Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p] + p*PolyLog[2, 1 + (e*x^2)/d]))/(2*f^2)","A",1
343,1,691,667,0.5885237,"\int \frac{x^4 \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Integrate[(x^4*Log[c*(d + e*x^2)^p])/(f + g*x^2),x]","\frac{f^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{g^{5/2}}-\frac{f x \log \left(c \left(d+e x^2\right)^p\right)}{g^2}+\frac{x^3 \log \left(c \left(d+e x^2\right)^p\right)}{3 g}+\frac{2 d p \left(\sqrt{e} x-\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)\right)}{3 e^{3/2} g}-\frac{i f^{3/2} p \left(\text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)-\text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)-\text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)+\log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)+\log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-\log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-\log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)\right)}{2 g^{5/2}}+\frac{2 f p \left(x-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}\right)}{g^2}-\frac{2 p x^3}{9 g}","\frac{f^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{g^{5/2}}-\frac{f x \log \left(c \left(d+e x^2\right)^p\right)}{g^2}+\frac{x^3 \log \left(c \left(d+e x^2\right)^p\right)}{3 g}-\frac{2 d^{3/2} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 e^{3/2} g}+\frac{i f^{3/2} p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{2 g^{5/2}}+\frac{i f^{3/2} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 g^{5/2}}-\frac{f^{3/2} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{g^{5/2}}-\frac{f^{3/2} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{g^{5/2}}-\frac{2 \sqrt{d} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e} g^2}+\frac{2 d p x}{3 e g}-\frac{i f^{3/2} p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{g^{5/2}}+\frac{2 f^{3/2} p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{g^{5/2}}+\frac{2 f p x}{g^2}-\frac{2 p x^3}{9 g}",1,"(-2*p*x^3)/(9*g) + (2*d*p*(Sqrt[e]*x - Sqrt[d]*ArcTan[(Sqrt[e]*x)/Sqrt[d]]))/(3*e^(3/2)*g) + (2*f*p*(x - (Sqrt[d]*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e]))/g^2 - (f*x*Log[c*(d + e*x^2)^p])/g^2 + (x^3*Log[c*(d + e*x^2)^p])/(3*g) + (f^(3/2)*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/g^(5/2) - ((I/2)*f^(3/2)*p*(Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] + Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] - Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] - Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] + PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] + PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])] - PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] - PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])]))/g^(5/2)","A",0
344,1,680,585,0.2931509,"\int \frac{x^2 \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Integrate[(x^2*Log[c*(d + e*x^2)^p])/(f + g*x^2),x]","\frac{-2 \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)+2 \sqrt{g} x \log \left(c \left(d+e x^2\right)^p\right)+i \sqrt{f} p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)+i \sqrt{f} p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)-i \sqrt{f} p \text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)-i \sqrt{f} p \text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)+i \sqrt{f} p \log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)+i \sqrt{f} p \log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-i \sqrt{f} p \log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-i \sqrt{f} p \log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)+\frac{4 \sqrt{d} \sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}-4 \sqrt{g} p x}{2 g^{3/2}}","-\frac{\sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{g^{3/2}}+\frac{x \log \left(c \left(d+e x^2\right)^p\right)}{g}-\frac{i \sqrt{f} p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{2 g^{3/2}}-\frac{i \sqrt{f} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 g^{3/2}}+\frac{\sqrt{f} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{g^{3/2}}+\frac{\sqrt{f} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{g^{3/2}}+\frac{2 \sqrt{d} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e} g}+\frac{i \sqrt{f} p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{g^{3/2}}-\frac{2 \sqrt{f} p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{g^{3/2}}-\frac{2 p x}{g}",1,"(-4*Sqrt[g]*p*x + (4*Sqrt[d]*Sqrt[g]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] + I*Sqrt[f]*p*Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] + I*Sqrt[f]*p*Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] - I*Sqrt[f]*p*Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] - I*Sqrt[f]*p*Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] + 2*Sqrt[g]*x*Log[c*(d + e*x^2)^p] - 2*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p] + I*Sqrt[f]*p*PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] + I*Sqrt[f]*p*PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])] - I*Sqrt[f]*p*PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] - I*Sqrt[f]*p*PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])])/(2*g^(3/2))","A",0
345,1,564,533,0.1512773,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(f + g*x^2),x]","-\frac{i \left(2 i \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)+p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)+p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)-p \text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)-p \text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)+p \log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)+p \log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-p \log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-p \log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)\right)}{2 \sqrt{f} \sqrt{g}}","\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{\sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{\sqrt{f} \sqrt{g}}-\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\sqrt{f} \sqrt{g}}+\frac{2 p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}",1,"((-1/2*I)*(p*Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] + p*Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] - p*Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] - p*Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] + (2*I)*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p] + p*PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] + p*PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])] - p*PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] - p*PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])]))/(Sqrt[f]*Sqrt[g])","A",0
346,1,673,581,0.288763,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x^2 \left(f+g x^2\right)} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(x^2*(f + g*x^2)),x]","\frac{-2 \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 \sqrt{f} \log \left(c \left(d+e x^2\right)^p\right)}{x}+i \sqrt{g} p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)+i \sqrt{g} p \text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)-i \sqrt{g} p \text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)-i \sqrt{g} p \text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)+i \sqrt{g} p \log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)+i \sqrt{g} p \log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-i \sqrt{g} p \log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}-i \sqrt{e} \sqrt{f}}\right)-i \sqrt{g} p \log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)+\frac{4 \sqrt{e} \sqrt{f} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d}}}{2 f^{3/2}}","-\frac{\sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{f^{3/2}}-\frac{\log \left(c \left(d+e x^2\right)^p\right)}{f x}-\frac{i \sqrt{g} p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{2 f^{3/2}}-\frac{i \sqrt{g} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 f^{3/2}}+\frac{\sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{f^{3/2}}+\frac{\sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{f^{3/2}}+\frac{2 \sqrt{e} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} f}+\frac{i \sqrt{g} p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{f^{3/2}}-\frac{2 \sqrt{g} p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{f^{3/2}}",1,"((4*Sqrt[e]*Sqrt[f]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[d] + I*Sqrt[g]*p*Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] + I*Sqrt[g]*p*Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]] - I*Sqrt[g]*p*Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((-I)*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] - I*Sqrt[g]*p*Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]] - (2*Sqrt[f]*Log[c*(d + e*x^2)^p])/x - 2*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p] + I*Sqrt[g]*p*PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] + I*Sqrt[g]*p*PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])] - I*Sqrt[g]*p*PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])] - I*Sqrt[g]*p*PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])])/(2*f^(3/2))","A",0
347,1,754,651,0.256932,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x^4 \left(f+g x^2\right)} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(x^4*(f + g*x^2)),x]","\frac{g^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{f^{5/2}}+\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{f^2 x}-\frac{\log \left(c \left(d+e x^2\right)^p\right)}{3 f x^3}-\frac{2 e g^{3/2} p \left(\frac{i \left(\frac{\text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)}{\sqrt{e}}+\frac{\log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)}{\sqrt{e}}\right)}{4 \sqrt{e}}+\frac{i \left(\frac{\text{Li}_2\left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)}{\sqrt{e}}+\frac{\log \left(1-\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)}{\sqrt{e}}\right)}{4 \sqrt{e}}-\frac{i \left(\frac{\text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-i \sqrt{-d} \sqrt{g}}\right)}{\sqrt{e}}+\frac{\log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{\sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)}{\sqrt{e}}\right)}{4 \sqrt{e}}-\frac{i \left(\frac{\text{Li}_2\left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+i \sqrt{-d} \sqrt{g}}\right)}{\sqrt{e}}+\frac{\log \left(1+\frac{i \sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{\sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}}\right)}{\sqrt{e}}\right)}{4 \sqrt{e}}\right)}{f^{5/2}}-\frac{2 \sqrt{e} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} f^2}-\frac{2 e p \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{e x^2}{d}\right)}{3 d f x}","\frac{g^{3/2} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{f^{5/2}}+\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{f^2 x}-\frac{\log \left(c \left(d+e x^2\right)^p\right)}{3 f x^3}-\frac{2 e^{3/2} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{3 d^{3/2} f}+\frac{i g^{3/2} p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{2 f^{5/2}}+\frac{i g^{3/2} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 f^{5/2}}-\frac{g^{3/2} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{f^{5/2}}-\frac{g^{3/2} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{f^{5/2}}-\frac{2 \sqrt{e} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} f^2}-\frac{2 e p}{3 d f x}-\frac{i g^{3/2} p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{f^{5/2}}+\frac{2 g^{3/2} p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{f^{5/2}}",1,"(-2*Sqrt[e]*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*f^2) - (2*e*p*Hypergeometric2F1[-1/2, 1, 1/2, -((e*x^2)/d)])/(3*d*f*x) - Log[c*(d + e*x^2)^p]/(3*f*x^3) + (g*Log[c*(d + e*x^2)^p])/(f^2*x) + (g^(3/2)*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/f^(5/2) - (2*e*g^(3/2)*p*(((I/4)*((Log[(Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]])/Sqrt[e] + PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])]/Sqrt[e]))/Sqrt[e] + ((I/4)*((Log[-((Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g]))]*Log[1 - (I*Sqrt[g]*x)/Sqrt[f]])/Sqrt[e] + PolyLog[2, (Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])]/Sqrt[e]))/Sqrt[e] - ((I/4)*((Log[(Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]])/Sqrt[e] + PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - I*Sqrt[-d]*Sqrt[g])]/Sqrt[e]))/Sqrt[e] - ((I/4)*((Log[-((Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/(I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g]))]*Log[1 + (I*Sqrt[g]*x)/Sqrt[f]])/Sqrt[e] + PolyLog[2, (Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + I*Sqrt[-d]*Sqrt[g])]/Sqrt[e]))/Sqrt[e]))/f^(5/2)","C",0
348,1,166,199,0.2211768,"\int \frac{x^5 \log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[(x^5*Log[c*(d + e*x^2)^p])/(f + g*x^2)^2,x]","-\frac{\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{g \left(f+g x^2\right)}+\frac{2 f \left(\log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)+p \text{Li}_2\left(\frac{g \left(e x^2+d\right)}{d g-e f}\right)\right)}{g}-\frac{\left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{e}+\frac{e f^2 p \left(\log \left(d+e x^2\right)-\log \left(f+g x^2\right)\right)}{g (d g-e f)}+p x^2}{2 g^2}","-\frac{f^2 \log \left(c \left(d+e x^2\right)^p\right)}{2 g^3 \left(f+g x^2\right)}-\frac{f \log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)}{g^3}+\frac{\left(d+e x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{2 e g^2}+\frac{e f^2 p \log \left(d+e x^2\right)}{2 g^3 (e f-d g)}-\frac{e f^2 p \log \left(f+g x^2\right)}{2 g^3 (e f-d g)}-\frac{f p \text{Li}_2\left(-\frac{g \left(e x^2+d\right)}{e f-d g}\right)}{g^3}-\frac{p x^2}{2 g^2}",1,"-1/2*(p*x^2 - ((d + e*x^2)*Log[c*(d + e*x^2)^p])/e + (f^2*Log[c*(d + e*x^2)^p])/(g*(f + g*x^2)) + (e*f^2*p*(Log[d + e*x^2] - Log[f + g*x^2]))/(g*(-(e*f) + d*g)) + (2*f*(Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)] + p*PolyLog[2, (g*(d + e*x^2))/(-(e*f) + d*g)]))/g)/g^2","A",1
349,1,131,155,0.0949798,"\int \frac{x^3 \log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[(x^3*Log[c*(d + e*x^2)^p])/(f + g*x^2)^2,x]","\frac{\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2}+\log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)+p \text{Li}_2\left(\frac{g \left(e x^2+d\right)}{d g-e f}\right)+\frac{e f p \log \left(d+e x^2\right)}{d g-e f}+\frac{e f p \log \left(f+g x^2\right)}{e f-d g}}{2 g^2}","\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{2 g^2 \left(f+g x^2\right)}+\frac{\log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)}{2 g^2}+\frac{p \text{Li}_2\left(-\frac{g \left(e x^2+d\right)}{e f-d g}\right)}{2 g^2}-\frac{e f p \log \left(d+e x^2\right)}{2 g^2 (e f-d g)}+\frac{e f p \log \left(f+g x^2\right)}{2 g^2 (e f-d g)}",1,"((e*f*p*Log[d + e*x^2])/(-(e*f) + d*g) + (f*Log[c*(d + e*x^2)^p])/(f + g*x^2) + (e*f*p*Log[f + g*x^2])/(e*f - d*g) + Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)] + p*PolyLog[2, (g*(d + e*x^2))/(-(e*f) + d*g)])/(2*g^2)","A",1
350,1,63,83,0.0498648,"\int \frac{x \log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[(x*Log[c*(d + e*x^2)^p])/(f + g*x^2)^2,x]","\frac{\frac{e p \left(\log \left(d+e x^2\right)-\log \left(f+g x^2\right)\right)}{e f-d g}-\frac{\log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2}}{2 g}","-\frac{\log \left(c \left(d+e x^2\right)^p\right)}{2 g \left(f+g x^2\right)}+\frac{e p \log \left(d+e x^2\right)}{2 g (e f-d g)}-\frac{e p \log \left(f+g x^2\right)}{2 g (e f-d g)}",1,"(-(Log[c*(d + e*x^2)^p]/(f + g*x^2)) + (e*p*(Log[d + e*x^2] - Log[f + g*x^2]))/(e*f - d*g))/(2*g)","A",1
351,1,170,201,0.1075753,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x \left(f+g x^2\right)^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(x*(f + g*x^2)^2),x]","\frac{\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2}-\log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)+\log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)-p \text{Li}_2\left(\frac{g \left(e x^2+d\right)}{d g-e f}\right)+\frac{e f p \log \left(d+e x^2\right)}{d g-e f}+\frac{e f p \log \left(f+g x^2\right)}{e f-d g}+p \text{Li}_2\left(\frac{e x^2}{d}+1\right)}{2 f^2}","-\frac{\log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)}{2 f^2}+\frac{\log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)}{2 f^2}+\frac{\log \left(c \left(d+e x^2\right)^p\right)}{2 f \left(f+g x^2\right)}-\frac{p \text{Li}_2\left(-\frac{g \left(e x^2+d\right)}{e f-d g}\right)}{2 f^2}+\frac{p \text{Li}_2\left(\frac{e x^2}{d}+1\right)}{2 f^2}-\frac{e p \log \left(d+e x^2\right)}{2 f (e f-d g)}+\frac{e p \log \left(f+g x^2\right)}{2 f (e f-d g)}",1,"((e*f*p*Log[d + e*x^2])/(-(e*f) + d*g) + (f*Log[c*(d + e*x^2)^p])/(f + g*x^2) + Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p] + (e*f*p*Log[f + g*x^2])/(e*f - d*g) - Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)] - p*PolyLog[2, (g*(d + e*x^2))/(-(e*f) + d*g)] + p*PolyLog[2, 1 + (e*x^2)/d])/(2*f^2)","A",1
352,1,208,251,0.1732259,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x^3 \left(f+g x^2\right)^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(x^3*(f + g*x^2)^2),x]","\frac{2 g \left(\log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)+p \text{Li}_2\left(\frac{g \left(e x^2+d\right)}{d g-e f}\right)\right)-\frac{f g \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2}-\frac{f \log \left(c \left(d+e x^2\right)^p\right)}{x^2}-2 g \left(\log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)+p \text{Li}_2\left(\frac{e x^2}{d}+1\right)\right)+\frac{e f g p \left(\log \left(d+e x^2\right)-\log \left(f+g x^2\right)\right)}{e f-d g}+\frac{e f p \left(2 \log (x)-\log \left(d+e x^2\right)\right)}{d}}{2 f^3}","-\frac{g \log \left(-\frac{e x^2}{d}\right) \log \left(c \left(d+e x^2\right)^p\right)}{f^3}+\frac{g \log \left(c \left(d+e x^2\right)^p\right) \log \left(\frac{e \left(f+g x^2\right)}{e f-d g}\right)}{f^3}-\frac{g \log \left(c \left(d+e x^2\right)^p\right)}{2 f^2 \left(f+g x^2\right)}-\frac{\log \left(c \left(d+e x^2\right)^p\right)}{2 f^2 x^2}+\frac{g p \text{Li}_2\left(-\frac{g \left(e x^2+d\right)}{e f-d g}\right)}{f^3}-\frac{g p \text{Li}_2\left(\frac{e x^2}{d}+1\right)}{f^3}+\frac{e g p \log \left(d+e x^2\right)}{2 f^2 (e f-d g)}-\frac{e g p \log \left(f+g x^2\right)}{2 f^2 (e f-d g)}-\frac{e p \log \left(d+e x^2\right)}{2 d f^2}+\frac{e p \log (x)}{d f^2}",1,"((e*f*p*(2*Log[x] - Log[d + e*x^2]))/d - (f*Log[c*(d + e*x^2)^p])/x^2 - (f*g*Log[c*(d + e*x^2)^p])/(f + g*x^2) + (e*f*g*p*(Log[d + e*x^2] - Log[f + g*x^2]))/(e*f - d*g) + 2*g*(Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)] + p*PolyLog[2, (g*(d + e*x^2))/(-(e*f) + d*g)]) - 2*g*(Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p] + p*PolyLog[2, 1 + (e*x^2)/d]))/(2*f^3)","A",1
353,1,1349,802,4.5440898,"\int \frac{x^4 \log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[(x^4*Log[c*(d + e*x^2)^p])/(f + g*x^2)^2,x]","\frac{1}{4} \left(\frac{6 \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(p \log \left(e x^2+d\right)-\log \left(c \left(e x^2+d\right)^p\right)\right)}{g^{5/2}}+\frac{4 x \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)}{g^2}+\frac{2 f x \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)}{g^2 \left(g x^2+f\right)}+p \left(\frac{4 \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right) \left(\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)-1\right)}{g^2}+\frac{4 \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right) \left(\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)-1\right)}{g^2}+\frac{i f \left(\frac{\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)}{i \sqrt{g} x+\sqrt{f}}+\frac{\sqrt{e} \left(\log \left(i \sqrt{f}-\sqrt{g} x\right)-\log \left(i \sqrt{d}-\sqrt{e} x\right)\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)}{g^{5/2}}+\frac{i f \left(\frac{\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)}{i \sqrt{g} x+\sqrt{f}}+\frac{\sqrt{e} \left(\log \left(i \sqrt{f}-\sqrt{g} x\right)-\log \left(\sqrt{e} x+i \sqrt{d}\right)\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)}{g^{5/2}}+\frac{f \left(\sqrt{e} \left(\sqrt{g} x+i \sqrt{f}\right) \left(\log \left(i \sqrt{d}-\sqrt{e} x\right)-\log \left(\sqrt{g} x+i \sqrt{f}\right)\right)-i \left(\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}\right) \log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)\right)}{\left(\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}\right) g^{5/2} \left(\sqrt{f}-i \sqrt{g} x\right)}-\frac{f \left(-\frac{\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)}{\sqrt{g} x+i \sqrt{f}}-\frac{i \sqrt{e} \left(\log \left(\sqrt{e} x+i \sqrt{d}\right)-\log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)}{g^{5/2}}+4 \left(\frac{x \left(\frac{f}{g x^2+f}+2\right)}{2 g^2}-\frac{3 \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 g^{5/2}}\right) \left(-\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)-\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)+\log \left(e x^2+d\right)\right)-\frac{3 i \sqrt{f} \left(\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(-\frac{\sqrt{g} \left(\sqrt{d}-i \sqrt{e} x\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)\right)}{g^{5/2}}+\frac{3 i \sqrt{f} \left(\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt{g} \left(\sqrt{d}-i \sqrt{e} x\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)\right)}{g^{5/2}}+\frac{3 i \sqrt{f} \left(\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(-\frac{\sqrt{g} \left(i \sqrt{e} x+\sqrt{d}\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)\right)}{g^{5/2}}-\frac{3 i \sqrt{f} \left(\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt{g} \left(i \sqrt{e} x+\sqrt{d}\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)\right)}{g^{5/2}}\right)\right)","-\frac{e p \log \left(\sqrt{-f}-\sqrt{g} x\right) (-f)^{3/2}}{2 g^{5/2} (e f-d g)}+\frac{e p \log \left(\sqrt{g} x+\sqrt{-f}\right) (-f)^{3/2}}{2 g^{5/2} (e f-d g)}-\frac{2 p x}{g^2}+\frac{\sqrt{d} \sqrt{e} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{g^2 (e f-d g)}+\frac{2 \sqrt{d} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e} g^2}-\frac{3 \sqrt{f} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{g^{5/2}}+\frac{3 \sqrt{f} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 g^{5/2}}+\frac{3 \sqrt{f} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 g^{5/2}}+\frac{x \log \left(c \left(e x^2+d\right)^p\right)}{g^2}-\frac{3 \sqrt{f} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(e x^2+d\right)^p\right)}{2 g^{5/2}}-\frac{f \log \left(c \left(e x^2+d\right)^p\right)}{4 g^{5/2} \left(\sqrt{-f}-\sqrt{g} x\right)}+\frac{f \log \left(c \left(e x^2+d\right)^p\right)}{4 g^{5/2} \left(\sqrt{g} x+\sqrt{-f}\right)}+\frac{3 i \sqrt{f} p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 g^{5/2}}-\frac{3 i \sqrt{f} p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{4 g^{5/2}}-\frac{3 i \sqrt{f} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{4 g^{5/2}}",1,"((6*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(p*Log[d + e*x^2] - Log[c*(d + e*x^2)^p]))/g^(5/2) + (4*x*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/g^2 + (2*f*x*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/(g^2*(f + g*x^2)) + p*((4*(((-I)*Sqrt[d])/Sqrt[e] + x)*(-1 + Log[((-I)*Sqrt[d])/Sqrt[e] + x]))/g^2 + (4*((I*Sqrt[d])/Sqrt[e] + x)*(-1 + Log[(I*Sqrt[d])/Sqrt[e] + x]))/g^2 + (I*f*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]/(Sqrt[f] + I*Sqrt[g]*x) + (Sqrt[e]*(-Log[I*Sqrt[d] - Sqrt[e]*x] + Log[I*Sqrt[f] - Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])))/g^(5/2) + (I*f*(Log[(I*Sqrt[d])/Sqrt[e] + x]/(Sqrt[f] + I*Sqrt[g]*x) + (Sqrt[e]*(-Log[I*Sqrt[d] + Sqrt[e]*x] + Log[I*Sqrt[f] - Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])))/g^(5/2) + (f*((-I)*(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])*Log[((-I)*Sqrt[d])/Sqrt[e] + x] + Sqrt[e]*(I*Sqrt[f] + Sqrt[g]*x)*(Log[I*Sqrt[d] - Sqrt[e]*x] - Log[I*Sqrt[f] + Sqrt[g]*x])))/((Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])*g^(5/2)*(Sqrt[f] - I*Sqrt[g]*x)) - (f*(-(Log[(I*Sqrt[d])/Sqrt[e] + x]/(I*Sqrt[f] + Sqrt[g]*x)) - (I*Sqrt[e]*(Log[I*Sqrt[d] + Sqrt[e]*x] - Log[I*Sqrt[f] + Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])))/g^(5/2) + 4*((x*(2 + f/(f + g*x^2)))/(2*g^2) - (3*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/(2*g^(5/2)))*(-Log[((-I)*Sqrt[d])/Sqrt[e] + x] - Log[(I*Sqrt[d])/Sqrt[e] + x] + Log[d + e*x^2]) - ((3*I)*Sqrt[f]*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])] + PolyLog[2, -((Sqrt[g]*(Sqrt[d] - I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))]))/g^(5/2) + ((3*I)*Sqrt[f]*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(Sqrt[d] - I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])]))/g^(5/2) + ((3*I)*Sqrt[f]*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])] + PolyLog[2, -((Sqrt[g]*(Sqrt[d] + I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))]))/g^(5/2) - ((3*I)*Sqrt[f]*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(Sqrt[d] + I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])]))/g^(5/2)))/4","A",1
354,1,1231,746,3.5168171,"\int \frac{x^2 \log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[(x^2*Log[c*(d + e*x^2)^p])/(f + g*x^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)}{2 \sqrt{f} g^{3/2}}+\frac{p x \log \left(e x^2+d\right)-x \log \left(c \left(e x^2+d\right)^p\right)}{2 g^2 x^2+2 f g}+\frac{1}{4} p \left(-\frac{i \left(\frac{\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)}{i \sqrt{g} x+\sqrt{f}}+\frac{\sqrt{e} \left(\log \left(i \sqrt{f}-\sqrt{g} x\right)-\log \left(i \sqrt{d}-\sqrt{e} x\right)\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)}{g^{3/2}}-\frac{i \left(\frac{\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)}{i \sqrt{g} x+\sqrt{f}}+\frac{\sqrt{e} \left(\log \left(i \sqrt{f}-\sqrt{g} x\right)-\log \left(\sqrt{e} x+i \sqrt{d}\right)\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)}{g^{3/2}}+\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right) \left(\log \left(i \sqrt{d}-\sqrt{e} x\right)-\log \left(\sqrt{g} x+i \sqrt{f}\right)\right)-\left(\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}\right) \log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)}{\left(\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}\right) g^{3/2} \left(\sqrt{g} x+i \sqrt{f}\right)}+\frac{-\frac{\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)}{\sqrt{g} x+i \sqrt{f}}-\frac{i \sqrt{e} \left(\log \left(\sqrt{e} x+i \sqrt{d}\right)-\log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}}{g^{3/2}}+4 \left(\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 \sqrt{f} g^{3/2}}-\frac{x}{2 g \left(g x^2+f\right)}\right) \left(-\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)-\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)+\log \left(e x^2+d\right)\right)+\frac{i \left(\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(-\frac{\sqrt{g} \left(\sqrt{d}-i \sqrt{e} x\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)\right)}{\sqrt{f} g^{3/2}}-\frac{i \left(\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt{g} \left(\sqrt{d}-i \sqrt{e} x\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)\right)}{\sqrt{f} g^{3/2}}-\frac{i \left(\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(-\frac{\sqrt{g} \left(i \sqrt{e} x+\sqrt{d}\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)\right)}{\sqrt{f} g^{3/2}}+\frac{i \left(\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt{g} \left(i \sqrt{e} x+\sqrt{d}\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)\right)}{\sqrt{f} g^{3/2}}\right)","\frac{\log \left(c \left(d+e x^2\right)^p\right)}{4 g^{3/2} \left(\sqrt{-f}-\sqrt{g} x\right)}-\frac{\log \left(c \left(d+e x^2\right)^p\right)}{4 g^{3/2} \left(\sqrt{-f}+\sqrt{g} x\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{2 \sqrt{f} g^{3/2}}+\frac{i p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{4 \sqrt{f} g^{3/2}}+\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{4 \sqrt{f} g^{3/2}}-\frac{e \sqrt{-f} p \log \left(\sqrt{-f}-\sqrt{g} x\right)}{2 g^{3/2} (e f-d g)}+\frac{e \sqrt{-f} p \log \left(\sqrt{-f}+\sqrt{g} x\right)}{2 g^{3/2} (e f-d g)}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{2 \sqrt{f} g^{3/2}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{2 \sqrt{f} g^{3/2}}-\frac{\sqrt{d} \sqrt{e} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{g (e f-d g)}-\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 \sqrt{f} g^{3/2}}+\frac{p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} g^{3/2}}",1,"(ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/(2*Sqrt[f]*g^(3/2)) + (p*x*Log[d + e*x^2] - x*Log[c*(d + e*x^2)^p])/(2*f*g + 2*g^2*x^2) + (p*(((-I)*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]/(Sqrt[f] + I*Sqrt[g]*x) + (Sqrt[e]*(-Log[I*Sqrt[d] - Sqrt[e]*x] + Log[I*Sqrt[f] - Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])))/g^(3/2) - (I*(Log[(I*Sqrt[d])/Sqrt[e] + x]/(Sqrt[f] + I*Sqrt[g]*x) + (Sqrt[e]*(-Log[I*Sqrt[d] + Sqrt[e]*x] + Log[I*Sqrt[f] - Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])))/g^(3/2) + (-((Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])*Log[((-I)*Sqrt[d])/Sqrt[e] + x]) + Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x)*(Log[I*Sqrt[d] - Sqrt[e]*x] - Log[I*Sqrt[f] + Sqrt[g]*x]))/((Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])*g^(3/2)*(I*Sqrt[f] + Sqrt[g]*x)) + (-(Log[(I*Sqrt[d])/Sqrt[e] + x]/(I*Sqrt[f] + Sqrt[g]*x)) - (I*Sqrt[e]*(Log[I*Sqrt[d] + Sqrt[e]*x] - Log[I*Sqrt[f] + Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))/g^(3/2) + 4*(-1/2*x/(g*(f + g*x^2)) + ArcTan[(Sqrt[g]*x)/Sqrt[f]]/(2*Sqrt[f]*g^(3/2)))*(-Log[((-I)*Sqrt[d])/Sqrt[e] + x] - Log[(I*Sqrt[d])/Sqrt[e] + x] + Log[d + e*x^2]) + (I*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])] + PolyLog[2, -((Sqrt[g]*(Sqrt[d] - I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))]))/(Sqrt[f]*g^(3/2)) - (I*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(Sqrt[d] - I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])]))/(Sqrt[f]*g^(3/2)) - (I*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])] + PolyLog[2, -((Sqrt[g]*(Sqrt[d] + I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))]))/(Sqrt[f]*g^(3/2)) + (I*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(Sqrt[d] + I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])]))/(Sqrt[f]*g^(3/2))))/4","A",1
355,1,1236,751,3.1874645,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(f + g*x^2)^2,x]","\frac{1}{2} \left(\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)}{f^{3/2} \sqrt{g}}+\frac{x \left(\log \left(c \left(e x^2+d\right)^p\right)-p \log \left(e x^2+d\right)\right)}{f \left(g x^2+f\right)}+\frac{1}{2} p \left(\frac{i \left(\frac{\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)}{i \sqrt{g} x+\sqrt{f}}+\frac{\sqrt{e} \left(\log \left(i \sqrt{f}-\sqrt{g} x\right)-\log \left(i \sqrt{d}-\sqrt{e} x\right)\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)}{f \sqrt{g}}+\frac{i \left(\frac{\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)}{i \sqrt{g} x+\sqrt{f}}+\frac{\sqrt{e} \left(\log \left(i \sqrt{f}-\sqrt{g} x\right)-\log \left(\sqrt{e} x+i \sqrt{d}\right)\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)}{f \sqrt{g}}+\frac{\sqrt{e} \left(\sqrt{g} x+i \sqrt{f}\right) \left(\log \left(i \sqrt{d}-\sqrt{e} x\right)-\log \left(\sqrt{g} x+i \sqrt{f}\right)\right)-i \left(\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}\right) \log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)}{f \left(\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}\right) \sqrt{g} \left(\sqrt{f}-i \sqrt{g} x\right)}-\frac{-\frac{\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)}{\sqrt{g} x+i \sqrt{f}}-\frac{i \sqrt{e} \left(\log \left(\sqrt{e} x+i \sqrt{d}\right)-\log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}}{f \sqrt{g}}+2 \left(\frac{x}{f^2+g x^2 f}+\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{f^{3/2} \sqrt{g}}\right) \left(-\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)-\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)+\log \left(e x^2+d\right)\right)+\frac{i \left(\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(-\frac{\sqrt{g} \left(\sqrt{d}-i \sqrt{e} x\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)\right)}{f^{3/2} \sqrt{g}}-\frac{i \left(\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt{g} \left(\sqrt{d}-i \sqrt{e} x\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)\right)}{f^{3/2} \sqrt{g}}-\frac{i \left(\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(-\frac{\sqrt{g} \left(i \sqrt{e} x+\sqrt{d}\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)\right)}{f^{3/2} \sqrt{g}}+\frac{i \left(\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt{g} \left(i \sqrt{e} x+\sqrt{d}\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)\right)}{f^{3/2} \sqrt{g}}\right)\right)","\frac{\tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(d+e x^2\right)^p\right)}{2 f^{3/2} \sqrt{g}}-\frac{\log \left(c \left(d+e x^2\right)^p\right)}{4 f \sqrt{g} \left(\sqrt{-f}-\sqrt{g} x\right)}+\frac{\log \left(c \left(d+e x^2\right)^p\right)}{4 f \sqrt{g} \left(\sqrt{-f}+\sqrt{g} x\right)}+\frac{i p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{4 f^{3/2} \sqrt{g}}+\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{4 f^{3/2} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(-\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{2 f^{3/2} \sqrt{g}}-\frac{p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}+\sqrt{e} x\right)}{\left(\sqrt{f}-i \sqrt{g} x\right) \left(\sqrt{-d} \sqrt{g}+i \sqrt{e} \sqrt{f}\right)}\right)}{2 f^{3/2} \sqrt{g}}-\frac{e p \log \left(\sqrt{-f}-\sqrt{g} x\right)}{2 \sqrt{-f} \sqrt{g} (e f-d g)}+\frac{e p \log \left(\sqrt{-f}+\sqrt{g} x\right)}{2 \sqrt{-f} \sqrt{g} (e f-d g)}+\frac{\sqrt{d} \sqrt{e} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{f (e f-d g)}-\frac{i p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 f^{3/2} \sqrt{g}}+\frac{p \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right) \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{f^{3/2} \sqrt{g}}",1,"((x*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/(f*(f + g*x^2)) + (ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(-(p*Log[d + e*x^2]) + Log[c*(d + e*x^2)^p]))/(f^(3/2)*Sqrt[g]) + (p*((I*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]/(Sqrt[f] + I*Sqrt[g]*x) + (Sqrt[e]*(-Log[I*Sqrt[d] - Sqrt[e]*x] + Log[I*Sqrt[f] - Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])))/(f*Sqrt[g]) + (I*(Log[(I*Sqrt[d])/Sqrt[e] + x]/(Sqrt[f] + I*Sqrt[g]*x) + (Sqrt[e]*(-Log[I*Sqrt[d] + Sqrt[e]*x] + Log[I*Sqrt[f] - Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])))/(f*Sqrt[g]) + ((-I)*(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])*Log[((-I)*Sqrt[d])/Sqrt[e] + x] + Sqrt[e]*(I*Sqrt[f] + Sqrt[g]*x)*(Log[I*Sqrt[d] - Sqrt[e]*x] - Log[I*Sqrt[f] + Sqrt[g]*x]))/(f*(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])*Sqrt[g]*(Sqrt[f] - I*Sqrt[g]*x)) - (-(Log[(I*Sqrt[d])/Sqrt[e] + x]/(I*Sqrt[f] + Sqrt[g]*x)) - (I*Sqrt[e]*(Log[I*Sqrt[d] + Sqrt[e]*x] - Log[I*Sqrt[f] + Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))/(f*Sqrt[g]) + 2*(x/(f^2 + f*g*x^2) + ArcTan[(Sqrt[g]*x)/Sqrt[f]]/(f^(3/2)*Sqrt[g]))*(-Log[((-I)*Sqrt[d])/Sqrt[e] + x] - Log[(I*Sqrt[d])/Sqrt[e] + x] + Log[d + e*x^2]) + (I*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])] + PolyLog[2, -((Sqrt[g]*(Sqrt[d] - I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))]))/(f^(3/2)*Sqrt[g]) - (I*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(Sqrt[d] - I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])]))/(f^(3/2)*Sqrt[g]) - (I*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])] + PolyLog[2, -((Sqrt[g]*(Sqrt[d] + I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))]))/(f^(3/2)*Sqrt[g]) + (I*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(Sqrt[d] + I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])]))/(f^(3/2)*Sqrt[g])))/2)/2","A",1
356,1,1438,803,4.8241333,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x^2 \left(f+g x^2\right)^2} \, dx","Integrate[Log[c*(d + e*x^2)^p]/(x^2*(f + g*x^2)^2),x]","\frac{1}{4} \left(\frac{4 p \log \left(e x^2+d\right)-4 \log \left(c \left(e x^2+d\right)^p\right)}{f^2 x}+\frac{6 \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \left(p \log \left(e x^2+d\right)-\log \left(c \left(e x^2+d\right)^p\right)\right)}{f^{5/2}}+\frac{2 g x \left(p \log \left(e x^2+d\right)-\log \left(c \left(e x^2+d\right)^p\right)\right)}{f^2 \left(g x^2+f\right)}+p \left(\frac{4 i \left(\sqrt{e} x \log (x)+i \sqrt{d} \log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)-\sqrt{e} x \log \left(i \sqrt{d}-\sqrt{e} x\right)\right)}{\sqrt{d} f^2 x}-\frac{4 \left(i \sqrt{e} x \log (x)+\sqrt{d} \log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)-i \sqrt{e} x \log \left(\sqrt{e} x+i \sqrt{d}\right)\right)}{\sqrt{d} f^2 x}-\frac{i \sqrt{g} \left(\frac{\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)}{i \sqrt{g} x+\sqrt{f}}+\frac{\sqrt{e} \left(\log \left(i \sqrt{f}-\sqrt{g} x\right)-\log \left(i \sqrt{d}-\sqrt{e} x\right)\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)}{f^2}-\frac{i \sqrt{g} \left(\frac{\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)}{i \sqrt{g} x+\sqrt{f}}+\frac{\sqrt{e} \left(\log \left(i \sqrt{f}-\sqrt{g} x\right)-\log \left(\sqrt{e} x+i \sqrt{d}\right)\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)}{f^2}+\frac{\sqrt{g} \left(\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right) \left(\log \left(i \sqrt{d}-\sqrt{e} x\right)-\log \left(\sqrt{g} x+i \sqrt{f}\right)\right)-\left(\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}\right) \log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)\right)}{f^2 \left(\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}\right) \left(\sqrt{g} x+i \sqrt{f}\right)}+\frac{\sqrt{g} \left(-\frac{\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)}{\sqrt{g} x+i \sqrt{f}}-\frac{i \sqrt{e} \left(\log \left(\sqrt{e} x+i \sqrt{d}\right)-\log \left(\sqrt{g} x+i \sqrt{f}\right)\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)}{f^2}+4 \left(-\frac{\frac{g x^2}{g x^2+f}+2}{2 f^2 x}-\frac{3 \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right)}{2 f^{5/2}}\right) \left(-\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)-\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)+\log \left(e x^2+d\right)\right)-\frac{3 i \sqrt{g} \left(\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(-\frac{\sqrt{g} \left(\sqrt{d}-i \sqrt{e} x\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)\right)}{f^{5/2}}+\frac{3 i \sqrt{g} \left(\log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt{g} \left(\sqrt{d}-i \sqrt{e} x\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)\right)}{f^{5/2}}+\frac{3 i \sqrt{g} \left(\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(i \sqrt{g} x+\sqrt{f}\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(-\frac{\sqrt{g} \left(i \sqrt{e} x+\sqrt{d}\right)}{\sqrt{e} \sqrt{f}-\sqrt{d} \sqrt{g}}\right)\right)}{f^{5/2}}-\frac{3 i \sqrt{g} \left(\log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right) \log \left(\frac{\sqrt{e} \left(\sqrt{f}-i \sqrt{g} x\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt{g} \left(i \sqrt{e} x+\sqrt{d}\right)}{\sqrt{e} \sqrt{f}+\sqrt{d} \sqrt{g}}\right)\right)}{f^{5/2}}\right)\right)","-\frac{\sqrt{d} \sqrt{e} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{f^2 (e f-d g)}+\frac{2 \sqrt{e} p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d} f^2}-\frac{e \sqrt{g} p \log \left(\sqrt{-f}-\sqrt{g} x\right)}{2 (-f)^{3/2} (e f-d g)}-\frac{3 \sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{f^{5/2}}+\frac{3 \sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 f^{5/2}}+\frac{3 \sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{2 f^{5/2}}+\frac{e \sqrt{g} p \log \left(\sqrt{g} x+\sqrt{-f}\right)}{2 (-f)^{3/2} (e f-d g)}-\frac{3 \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} x}{\sqrt{f}}\right) \log \left(c \left(e x^2+d\right)^p\right)}{2 f^{5/2}}-\frac{\log \left(c \left(e x^2+d\right)^p\right)}{f^2 x}+\frac{\sqrt{g} \log \left(c \left(e x^2+d\right)^p\right)}{4 f^2 \left(\sqrt{-f}-\sqrt{g} x\right)}-\frac{\sqrt{g} \log \left(c \left(e x^2+d\right)^p\right)}{4 f^2 \left(\sqrt{g} x+\sqrt{-f}\right)}+\frac{3 i \sqrt{g} p \text{Li}_2\left(1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 f^{5/2}}-\frac{3 i \sqrt{g} p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(i \sqrt{e} \sqrt{f}-\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}+1\right)}{4 f^{5/2}}-\frac{3 i \sqrt{g} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(i \sqrt{e} \sqrt{f}+\sqrt{-d} \sqrt{g}\right) \left(\sqrt{f}-i \sqrt{g} x\right)}\right)}{4 f^{5/2}}",1,"((4*p*Log[d + e*x^2] - 4*Log[c*(d + e*x^2)^p])/(f^2*x) + (2*g*x*(p*Log[d + e*x^2] - Log[c*(d + e*x^2)^p]))/(f^2*(f + g*x^2)) + (6*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*(p*Log[d + e*x^2] - Log[c*(d + e*x^2)^p]))/f^(5/2) + p*(((4*I)*(Sqrt[e]*x*Log[x] + I*Sqrt[d]*Log[((-I)*Sqrt[d])/Sqrt[e] + x] - Sqrt[e]*x*Log[I*Sqrt[d] - Sqrt[e]*x]))/(Sqrt[d]*f^2*x) - (4*(I*Sqrt[e]*x*Log[x] + Sqrt[d]*Log[(I*Sqrt[d])/Sqrt[e] + x] - I*Sqrt[e]*x*Log[I*Sqrt[d] + Sqrt[e]*x]))/(Sqrt[d]*f^2*x) - (I*Sqrt[g]*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]/(Sqrt[f] + I*Sqrt[g]*x) + (Sqrt[e]*(-Log[I*Sqrt[d] - Sqrt[e]*x] + Log[I*Sqrt[f] - Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])))/f^2 - (I*Sqrt[g]*(Log[(I*Sqrt[d])/Sqrt[e] + x]/(Sqrt[f] + I*Sqrt[g]*x) + (Sqrt[e]*(-Log[I*Sqrt[d] + Sqrt[e]*x] + Log[I*Sqrt[f] - Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])))/f^2 + (Sqrt[g]*(-((Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])*Log[((-I)*Sqrt[d])/Sqrt[e] + x]) + Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x)*(Log[I*Sqrt[d] - Sqrt[e]*x] - Log[I*Sqrt[f] + Sqrt[g]*x])))/(f^2*(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])*(I*Sqrt[f] + Sqrt[g]*x)) + (Sqrt[g]*(-(Log[(I*Sqrt[d])/Sqrt[e] + x]/(I*Sqrt[f] + Sqrt[g]*x)) - (I*Sqrt[e]*(Log[I*Sqrt[d] + Sqrt[e]*x] - Log[I*Sqrt[f] + Sqrt[g]*x]))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])))/f^2 + 4*(-1/2*(2 + (g*x^2)/(f + g*x^2))/(f^2*x) - (3*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]])/(2*f^(5/2)))*(-Log[((-I)*Sqrt[d])/Sqrt[e] + x] - Log[(I*Sqrt[d])/Sqrt[e] + x] + Log[d + e*x^2]) - ((3*I)*Sqrt[g]*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])] + PolyLog[2, -((Sqrt[g]*(Sqrt[d] - I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))]))/f^(5/2) + ((3*I)*Sqrt[g]*(Log[(I*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(Sqrt[d] - I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])]))/f^(5/2) + ((3*I)*Sqrt[g]*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] + I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g])] + PolyLog[2, -((Sqrt[g]*(Sqrt[d] + I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] - Sqrt[d]*Sqrt[g]))]))/f^(5/2) - ((3*I)*Sqrt[g]*(Log[((-I)*Sqrt[d])/Sqrt[e] + x]*Log[(Sqrt[e]*(Sqrt[f] - I*Sqrt[g]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])] + PolyLog[2, (Sqrt[g]*(Sqrt[d] + I*Sqrt[e]*x))/(Sqrt[e]*Sqrt[f] + Sqrt[d]*Sqrt[g])]))/f^(5/2)))/4","A",1
357,1,128,163,0.0488916,"\int \frac{\log \left(c \left(a+b x^2\right)^n\right)}{a+b x^2} \, dx","Integrate[Log[c*(a + b*x^2)^n]/(a + b*x^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \left(\log \left(c \left(a+b x^2\right)^n\right)+2 n \log \left(\frac{2 i}{-\frac{\sqrt{b} x}{\sqrt{a}}+i}\right)+i n \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right)+i n \text{Li}_2\left(\frac{\sqrt{b} x+i \sqrt{a}}{\sqrt{b} x-i \sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right) \log \left(c \left(a+b x^2\right)^n\right)}{\sqrt{a} \sqrt{b}}+\frac{i n \text{Li}_2\left(1-\frac{2 \sqrt{a}}{i \sqrt{b} x+\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}+\frac{i n \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)^2}{\sqrt{a} \sqrt{b}}+\frac{2 n \log \left(\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"(ArcTan[(Sqrt[b]*x)/Sqrt[a]]*(I*n*ArcTan[(Sqrt[b]*x)/Sqrt[a]] + 2*n*Log[(2*I)/(I - (Sqrt[b]*x)/Sqrt[a])] + Log[c*(a + b*x^2)^n]) + I*n*PolyLog[2, (I*Sqrt[a] + Sqrt[b]*x)/((-I)*Sqrt[a] + Sqrt[b]*x)])/(Sqrt[a]*Sqrt[b])","A",1
358,1,248,239,0.1284769,"\int \frac{\log \left(1-x^2\right)}{2-x^2} \, dx","Integrate[Log[1 - x^2]/(2 - x^2),x]","\frac{\text{Li}_2\left(\frac{x-1}{-1-\sqrt{2}}\right)+\log \left(1-\frac{x-1}{-1-\sqrt{2}}\right) \log (x-1)}{2 \sqrt{2}}-\frac{\text{Li}_2\left(\frac{x-1}{-1+\sqrt{2}}\right)+\log \left(1-\frac{x-1}{\sqrt{2}-1}\right) \log (x-1)}{2 \sqrt{2}}+\frac{\text{Li}_2\left(\frac{x+1}{1-\sqrt{2}}\right)+\log (x+1) \log \left(1-\frac{x+1}{1-\sqrt{2}}\right)}{2 \sqrt{2}}-\frac{\text{Li}_2\left(\frac{x+1}{1+\sqrt{2}}\right)+\log (x+1) \log \left(1-\frac{x+1}{1+\sqrt{2}}\right)}{2 \sqrt{2}}-\frac{\left(\log \left(\sqrt{2}-x\right)-\log \left(x+\sqrt{2}\right)\right) \left(\log \left(1-x^2\right)-\log (x-1)-\log (x+1)\right)}{2 \sqrt{2}}","-\frac{\text{Li}_2\left(1-\frac{2 \sqrt{2}}{x+\sqrt{2}}\right)}{\sqrt{2}}+\frac{\text{Li}_2\left(\frac{4 (1-x)}{\left(2-\sqrt{2}\right) \left(x+\sqrt{2}\right)}+1\right)}{2 \sqrt{2}}+\frac{\text{Li}_2\left(1-\frac{4 (x+1)}{\left(2+\sqrt{2}\right) \left(x+\sqrt{2}\right)}\right)}{2 \sqrt{2}}+\frac{\log \left(1-x^2\right) \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}+\sqrt{2} \log \left(\frac{2 \sqrt{2}}{x+\sqrt{2}}\right) \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)-\frac{\log \left(-\frac{4 (1-x)}{\left(2-\sqrt{2}\right) \left(x+\sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}-\frac{\log \left(\frac{4 (x+1)}{\left(2+\sqrt{2}\right) \left(x+\sqrt{2}\right)}\right) \tanh ^{-1}\left(\frac{x}{\sqrt{2}}\right)}{\sqrt{2}}",1,"-1/2*((Log[Sqrt[2] - x] - Log[Sqrt[2] + x])*(-Log[-1 + x] - Log[1 + x] + Log[1 - x^2]))/Sqrt[2] + (Log[1 - (-1 + x)/(-1 - Sqrt[2])]*Log[-1 + x] + PolyLog[2, (-1 + x)/(-1 - Sqrt[2])])/(2*Sqrt[2]) - (Log[1 - (-1 + x)/(-1 + Sqrt[2])]*Log[-1 + x] + PolyLog[2, (-1 + x)/(-1 + Sqrt[2])])/(2*Sqrt[2]) + (Log[1 + x]*Log[1 - (1 + x)/(1 - Sqrt[2])] + PolyLog[2, (1 + x)/(1 - Sqrt[2])])/(2*Sqrt[2]) - (Log[1 + x]*Log[1 - (1 + x)/(1 + Sqrt[2])] + PolyLog[2, (1 + x)/(1 + Sqrt[2])])/(2*Sqrt[2])","A",1
359,1,468,217,0.1331472,"\int \frac{\log \left(d+e x^2\right)}{1-x^2} \, dx","Integrate[Log[d + e*x^2]/(1 - x^2),x]","\frac{1}{2} \left(-\text{Li}_2\left(\frac{\sqrt{d}-i \sqrt{e} x}{\sqrt{d}-i \sqrt{e}}\right)+\text{Li}_2\left(\frac{\sqrt{d}-i \sqrt{e} x}{\sqrt{d}+i \sqrt{e}}\right)+\text{Li}_2\left(\frac{i \sqrt{e} x+\sqrt{d}}{\sqrt{d}-i \sqrt{e}}\right)-\text{Li}_2\left(\frac{i \sqrt{e} x+\sqrt{d}}{\sqrt{d}+i \sqrt{e}}\right)-\log (1-x) \log \left(d+e x^2\right)+\log (x+1) \log \left(d+e x^2\right)+\log (1-x) \log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)-\log \left(\frac{\sqrt{e} (x-1)}{-\sqrt{e}+i \sqrt{d}}\right) \log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)-\log (x+1) \log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)+\log \left(-\frac{i \sqrt{e} (x+1)}{\sqrt{d}-i \sqrt{e}}\right) \log \left(x-\frac{i \sqrt{d}}{\sqrt{e}}\right)+\log (1-x) \log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)-\log \left(\frac{\sqrt{e} (x-1)}{-\sqrt{e}-i \sqrt{d}}\right) \log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)-\log (x+1) \log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)+\log \left(\frac{i \sqrt{e} (x+1)}{\sqrt{d}+i \sqrt{e}}\right) \log \left(x+\frac{i \sqrt{d}}{\sqrt{e}}\right)\right)","\frac{1}{2} \text{Li}_2\left(1-\frac{2 \left(\sqrt{-d}-\sqrt{e} x\right)}{\left(\sqrt{-d}-\sqrt{e}\right) (x+1)}\right)+\frac{1}{2} \text{Li}_2\left(1-\frac{2 \left(\sqrt{e} x+\sqrt{-d}\right)}{\left(\sqrt{-d}+\sqrt{e}\right) (x+1)}\right)+\tanh ^{-1}(x) \log \left(d+e x^2\right)-\tanh ^{-1}(x) \log \left(\frac{2 \left(\sqrt{-d}-\sqrt{e} x\right)}{(x+1) \left(\sqrt{-d}-\sqrt{e}\right)}\right)-\tanh ^{-1}(x) \log \left(\frac{2 \left(\sqrt{-d}+\sqrt{e} x\right)}{(x+1) \left(\sqrt{-d}+\sqrt{e}\right)}\right)-\text{Li}_2\left(1-\frac{2}{x+1}\right)+2 \log \left(\frac{2}{x+1}\right) \tanh ^{-1}(x)",1,"(Log[1 - x]*Log[((-I)*Sqrt[d])/Sqrt[e] + x] - Log[(Sqrt[e]*(-1 + x))/(I*Sqrt[d] - Sqrt[e])]*Log[((-I)*Sqrt[d])/Sqrt[e] + x] - Log[1 + x]*Log[((-I)*Sqrt[d])/Sqrt[e] + x] + Log[((-I)*Sqrt[e]*(1 + x))/(Sqrt[d] - I*Sqrt[e])]*Log[((-I)*Sqrt[d])/Sqrt[e] + x] + Log[1 - x]*Log[(I*Sqrt[d])/Sqrt[e] + x] - Log[(Sqrt[e]*(-1 + x))/((-I)*Sqrt[d] - Sqrt[e])]*Log[(I*Sqrt[d])/Sqrt[e] + x] - Log[1 + x]*Log[(I*Sqrt[d])/Sqrt[e] + x] + Log[(I*Sqrt[e]*(1 + x))/(Sqrt[d] + I*Sqrt[e])]*Log[(I*Sqrt[d])/Sqrt[e] + x] - Log[1 - x]*Log[d + e*x^2] + Log[1 + x]*Log[d + e*x^2] - PolyLog[2, (Sqrt[d] - I*Sqrt[e]*x)/(Sqrt[d] - I*Sqrt[e])] + PolyLog[2, (Sqrt[d] - I*Sqrt[e]*x)/(Sqrt[d] + I*Sqrt[e])] + PolyLog[2, (Sqrt[d] + I*Sqrt[e]*x)/(Sqrt[d] - I*Sqrt[e])] - PolyLog[2, (Sqrt[d] + I*Sqrt[e]*x)/(Sqrt[d] + I*Sqrt[e])])/2","C",1
360,1,118,144,0.1728044,"\int \frac{\left(f+g x^{3 n}\right) \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g*x^(3*n))*Log[c*(d + e*x^n)^p])/x,x]","\frac{18 f \left(\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)+p \text{Li}_2\left(\frac{e x^n}{d}+1\right)\right)+6 g x^{3 n} \log \left(c \left(d+e x^n\right)^p\right)-\frac{g p \left(e x^n \left(6 d^2-3 d e x^n+2 e^2 x^{2 n}\right)-6 d^3 \log \left(d+e x^n\right)\right)}{e^3}}{18 n}","\frac{f \log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{g x^{3 n} \log \left(c \left(d+e x^n\right)^p\right)}{3 n}+\frac{d^3 g p \log \left(d+e x^n\right)}{3 e^3 n}-\frac{d^2 g p x^n}{3 e^2 n}+\frac{f p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}+\frac{d g p x^{2 n}}{6 e n}-\frac{g p x^{3 n}}{9 n}",1,"(-((g*p*(e*x^n*(6*d^2 - 3*d*e*x^n + 2*e^2*x^(2*n)) - 6*d^3*Log[d + e*x^n]))/e^3) + 6*g*x^(3*n)*Log[c*(d + e*x^n)^p] + 18*f*(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p] + p*PolyLog[2, 1 + (e*x^n)/d]))/(18*n)","A",1
361,1,100,124,0.1155695,"\int \frac{\left(f+g x^{2 n}\right) \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g*x^(2*n))*Log[c*(d + e*x^n)^p])/x,x]","\frac{2 e^2 \log \left(c \left(d+e x^n\right)^p\right) \left(2 f \log \left(-\frac{e x^n}{d}\right)+g x^{2 n}\right)-2 d^2 g p \log \left(d+e x^n\right)+4 e^2 f p \text{Li}_2\left(\frac{e x^n}{d}+1\right)-e g p x^n \left(e x^n-2 d\right)}{4 e^2 n}","\frac{f \log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{g x^{2 n} \log \left(c \left(d+e x^n\right)^p\right)}{2 n}-\frac{d^2 g p \log \left(d+e x^n\right)}{2 e^2 n}+\frac{f p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}+\frac{d g p x^n}{2 e n}-\frac{g p x^{2 n}}{4 n}",1,"(-(e*g*p*x^n*(-2*d + e*x^n)) - 2*d^2*g*p*Log[d + e*x^n] + 2*e^2*(g*x^(2*n) + 2*f*Log[-((e*x^n)/d)])*Log[c*(d + e*x^n)^p] + 4*e^2*f*p*PolyLog[2, 1 + (e*x^n)/d])/(4*e^2*n)","A",1
362,1,68,83,0.0593872,"\int \frac{\left(f+g x^n\right) \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g*x^n)*Log[c*(d + e*x^n)^p])/x,x]","\frac{\log \left(c \left(d+e x^n\right)^p\right) \left(e f \log \left(-\frac{e x^n}{d}\right)+d g+e g x^n\right)+e f p \text{Li}_2\left(\frac{e x^n}{d}+1\right)-e g p x^n}{e n}","\frac{f \log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{g \left(d+e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)}{e n}+\frac{f p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}-\frac{g p x^n}{n}",1,"(-(e*g*p*x^n) + (d*g + e*g*x^n + e*f*Log[-((e*x^n)/d)])*Log[c*(d + e*x^n)^p] + e*f*p*PolyLog[2, 1 + (e*x^n)/d])/(e*n)","A",1
363,1,87,97,0.099546,"\int \frac{\left(f+g x^{-n}\right) \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g/x^n)*Log[c*(d + e*x^n)^p])/x,x]","\frac{f \left(\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)+p \text{Li}_2\left(\frac{e x^n}{d}+1\right)\right)-g x^{-n} \log \left(c \left(d+e x^n\right)^p\right)+\frac{e g p \left(n \log (x)-\log \left(d+e x^n\right)\right)}{d}}{n}","\frac{f \log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}-\frac{g x^{-n} \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{f p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}-\frac{e g p \log \left(d+e x^n\right)}{d n}+\frac{e g p \log (x)}{d}",1,"((e*g*p*(n*Log[x] - Log[d + e*x^n]))/d - (g*Log[c*(d + e*x^n)^p])/x^n + f*(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p] + p*PolyLog[2, 1 + (e*x^n)/d]))/n","A",1
364,1,104,126,0.1999494,"\int \frac{\left(f+g x^{-2 n}\right) \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g/x^(2*n))*Log[c*(d + e*x^n)^p])/x,x]","-\frac{-2 f \left(\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)+p \text{Li}_2\left(\frac{e x^n}{d}+1\right)\right)+g x^{-2 n} \log \left(c \left(d+e x^n\right)^p\right)+\frac{e g p x^{-n} \left(-e x^n \log \left(d+e x^n\right)+d+e n x^n \log (x)\right)}{d^2}}{2 n}","\frac{f \log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}-\frac{g x^{-2 n} \log \left(c \left(d+e x^n\right)^p\right)}{2 n}+\frac{e^2 g p \log \left(d+e x^n\right)}{2 d^2 n}-\frac{e^2 g p \log (x)}{2 d^2}+\frac{f p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}-\frac{e g p x^{-n}}{2 d n}",1,"-1/2*((e*g*p*(d + e*n*x^n*Log[x] - e*x^n*Log[d + e*x^n]))/(d^2*x^n) + (g*Log[c*(d + e*x^n)^p])/x^(2*n) - 2*f*(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p] + p*PolyLog[2, 1 + (e*x^n)/d]))/n","A",1
365,1,209,327,0.3063154,"\int \frac{\left(f+g x^{3 n}\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g*x^(3*n))^2*Log[c*(d + e*x^n)^p])/x,x]","\frac{60 e^6 \log \left(c \left(d+e x^n\right)^p\right) \left(6 f^2 \log \left(-\frac{e x^n}{d}\right)+g x^{3 n} \left(4 f+g x^{3 n}\right)\right)-60 d^3 g p \left(d^3 g-4 e^3 f\right) \log \left(d+e x^n\right)-e g p x^n \left(-60 d^5 g+30 d^4 e g x^n-20 d^3 e^2 g x^{2 n}+15 d^2 e^3 \left(16 f+g x^{3 n}\right)-12 d e^4 x^n \left(10 f+g x^{3 n}\right)+10 e^5 x^{2 n} \left(8 f+g x^{3 n}\right)\right)+360 e^6 f^2 p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{360 e^6 n}","\frac{f^2 \log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{2 f g x^{3 n} \log \left(c \left(d+e x^n\right)^p\right)}{3 n}+\frac{g^2 x^{6 n} \log \left(c \left(d+e x^n\right)^p\right)}{6 n}-\frac{d^6 g^2 p \log \left(d+e x^n\right)}{6 e^6 n}+\frac{d^5 g^2 p x^n}{6 e^5 n}-\frac{d^4 g^2 p x^{2 n}}{12 e^4 n}+\frac{2 d^3 f g p \log \left(d+e x^n\right)}{3 e^3 n}+\frac{d^3 g^2 p x^{3 n}}{18 e^3 n}-\frac{2 d^2 f g p x^n}{3 e^2 n}-\frac{d^2 g^2 p x^{4 n}}{24 e^2 n}+\frac{f^2 p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}+\frac{d f g p x^{2 n}}{3 e n}+\frac{d g^2 p x^{5 n}}{30 e n}-\frac{2 f g p x^{3 n}}{9 n}-\frac{g^2 p x^{6 n}}{36 n}",1,"(-(e*g*p*x^n*(-60*d^5*g + 30*d^4*e*g*x^n - 20*d^3*e^2*g*x^(2*n) + 10*e^5*x^(2*n)*(8*f + g*x^(3*n)) - 12*d*e^4*x^n*(10*f + g*x^(3*n)) + 15*d^2*e^3*(16*f + g*x^(3*n)))) - 60*d^3*g*(-4*e^3*f + d^3*g)*p*Log[d + e*x^n] + 60*e^6*(g*x^(3*n)*(4*f + g*x^(3*n)) + 6*f^2*Log[-((e*x^n)/d)])*Log[c*(d + e*x^n)^p] + 360*e^6*f^2*p*PolyLog[2, 1 + (e*x^n)/d])/(360*e^6*n)","A",1
366,1,171,254,0.2678048,"\int \frac{\left(f+g x^{2 n}\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g*x^(2*n))^2*Log[c*(d + e*x^n)^p])/x,x]","\frac{12 e^4 \log \left(c \left(d+e x^n\right)^p\right) \left(4 f^2 \log \left(-\frac{e x^n}{d}\right)+g x^{2 n} \left(4 f+g x^{2 n}\right)\right)-12 d^2 g p \left(d^2 g+4 e^2 f\right) \log \left(d+e x^n\right)-e g p x^n \left(-12 d^3 g+6 d^2 e g x^n-4 d e^2 \left(12 f+g x^{2 n}\right)+3 e^3 x^n \left(8 f+g x^{2 n}\right)\right)+48 e^4 f^2 p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{48 e^4 n}","\frac{f^2 \log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{f g x^{2 n} \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{g^2 x^{4 n} \log \left(c \left(d+e x^n\right)^p\right)}{4 n}-\frac{d^4 g^2 p \log \left(d+e x^n\right)}{4 e^4 n}+\frac{d^3 g^2 p x^n}{4 e^3 n}-\frac{d^2 f g p \log \left(d+e x^n\right)}{e^2 n}-\frac{d^2 g^2 p x^{2 n}}{8 e^2 n}+\frac{f^2 p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}+\frac{d f g p x^n}{e n}+\frac{d g^2 p x^{3 n}}{12 e n}-\frac{f g p x^{2 n}}{2 n}-\frac{g^2 p x^{4 n}}{16 n}",1,"(-(e*g*p*x^n*(-12*d^3*g + 6*d^2*e*g*x^n + 3*e^3*x^n*(8*f + g*x^(2*n)) - 4*d*e^2*(12*f + g*x^(2*n)))) - 12*d^2*g*(4*e^2*f + d^2*g)*p*Log[d + e*x^n] + 12*e^4*(g*x^(2*n)*(4*f + g*x^(2*n)) + 4*f^2*Log[-((e*x^n)/d)])*Log[c*(d + e*x^n)^p] + 48*e^4*f^2*p*PolyLog[2, 1 + (e*x^n)/d])/(48*e^4*n)","A",1
367,1,124,176,0.1922195,"\int \frac{\left(f+g x^n\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g*x^n)^2*Log[c*(d + e*x^n)^p])/x,x]","\frac{2 e \log \left(c \left(d+e x^n\right)^p\right) \left(2 e f^2 \log \left(-\frac{e x^n}{d}\right)+4 d f g+e g x^n \left(4 f+g x^n\right)\right)-2 d^2 g^2 p \log \left(d+e x^n\right)+4 e^2 f^2 p \text{Li}_2\left(\frac{e x^n}{d}+1\right)-e g p x^n \left(-2 d g+8 e f+e g x^n\right)}{4 e^2 n}","\frac{f^2 \log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{2 f g \left(d+e x^n\right) \log \left(c \left(d+e x^n\right)^p\right)}{e n}+\frac{g^2 x^{2 n} \log \left(c \left(d+e x^n\right)^p\right)}{2 n}-\frac{d^2 g^2 p \log \left(d+e x^n\right)}{2 e^2 n}+\frac{f^2 p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}+\frac{d g^2 p x^n}{2 e n}-\frac{2 f g p x^n}{n}-\frac{g^2 p x^{2 n}}{4 n}",1,"(-(e*g*p*x^n*(8*e*f - 2*d*g + e*g*x^n)) - 2*d^2*g^2*p*Log[d + e*x^n] + 2*e*(4*d*f*g + e*g*x^n*(4*f + g*x^n) + 2*e*f^2*Log[-((e*x^n)/d)])*Log[c*(d + e*x^n)^p] + 4*e^2*f^2*p*PolyLog[2, 1 + (e*x^n)/d])/(4*e^2*n)","A",1
368,1,150,193,0.393299,"\int \frac{\left(f+g x^{-n}\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g/x^n)^2*Log[c*(d + e*x^n)^p])/x,x]","-\frac{-2 f^2 \left(\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)+p \text{Li}_2\left(\frac{e x^n}{d}+1\right)\right)+4 f g x^{-n} \log \left(c \left(d+e x^n\right)^p\right)+g^2 x^{-2 n} \log \left(c \left(d+e x^n\right)^p\right)+\frac{e g^2 p \left(-e \log \left(d+e x^n\right)+d x^{-n}+e n \log (x)\right)}{d^2}-\frac{4 e f g p \left(n \log (x)-\log \left(d+e x^n\right)\right)}{d}}{2 n}","\frac{f^2 \log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}-\frac{2 f g x^{-n} \log \left(c \left(d+e x^n\right)^p\right)}{n}-\frac{g^2 x^{-2 n} \log \left(c \left(d+e x^n\right)^p\right)}{2 n}+\frac{e^2 g^2 p \log \left(d+e x^n\right)}{2 d^2 n}-\frac{e^2 g^2 p \log (x)}{2 d^2}+\frac{f^2 p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}-\frac{2 e f g p \log \left(d+e x^n\right)}{d n}+\frac{2 e f g p \log (x)}{d}-\frac{e g^2 p x^{-n}}{2 d n}",1,"-1/2*((-4*e*f*g*p*(n*Log[x] - Log[d + e*x^n]))/d + (e*g^2*p*(d/x^n + e*n*Log[x] - e*Log[d + e*x^n]))/d^2 + (g^2*Log[c*(d + e*x^n)^p])/x^(2*n) + (4*f*g*Log[c*(d + e*x^n)^p])/x^n - 2*f^2*(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p] + p*PolyLog[2, 1 + (e*x^n)/d]))/n","A",1
369,1,188,257,0.584083,"\int \frac{\left(f+g x^{-2 n}\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g/x^(2*n))^2*Log[c*(d + e*x^n)^p])/x,x]","-\frac{-24 f^2 \left(\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)+p \text{Li}_2\left(\frac{e x^n}{d}+1\right)\right)+24 f g x^{-2 n} \log \left(c \left(d+e x^n\right)^p\right)+6 g^2 x^{-4 n} \log \left(c \left(d+e x^n\right)^p\right)+\frac{24 e f g p \left(-e \log \left(d+e x^n\right)+d x^{-n}+e n \log (x)\right)}{d^2}+\frac{e g^2 p \left(d x^{-3 n} \left(2 d^2-3 d e x^n+6 e^2 x^{2 n}\right)-6 e^3 \log \left(d+e x^n\right)+6 e^3 n \log (x)\right)}{d^4}}{24 n}","\frac{f^2 \log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}-\frac{f g x^{-2 n} \log \left(c \left(d+e x^n\right)^p\right)}{n}-\frac{g^2 x^{-4 n} \log \left(c \left(d+e x^n\right)^p\right)}{4 n}+\frac{e^4 g^2 p \log \left(d+e x^n\right)}{4 d^4 n}-\frac{e^4 g^2 p \log (x)}{4 d^4}-\frac{e^3 g^2 p x^{-n}}{4 d^3 n}+\frac{e^2 f g p \log \left(d+e x^n\right)}{d^2 n}-\frac{e^2 f g p \log (x)}{d^2}+\frac{e^2 g^2 p x^{-2 n}}{8 d^2 n}+\frac{f^2 p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{n}-\frac{e f g p x^{-n}}{d n}-\frac{e g^2 p x^{-3 n}}{12 d n}",1,"-1/24*((24*e*f*g*p*(d/x^n + e*n*Log[x] - e*Log[d + e*x^n]))/d^2 + (e*g^2*p*((d*(2*d^2 - 3*d*e*x^n + 6*e^2*x^(2*n)))/x^(3*n) + 6*e^3*n*Log[x] - 6*e^3*Log[d + e*x^n]))/d^4 + (6*g^2*Log[c*(d + e*x^n)^p])/x^(4*n) + (24*f*g*Log[c*(d + e*x^n)^p])/x^(2*n) - 24*f^2*(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p] + p*PolyLog[2, 1 + (e*x^n)/d]))/n","A",1
370,0,0,266,5.1319523,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{2 n}\right)} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g*x^(2*n))),x]","\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{2 n}\right)} \, dx","-\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x^n\right)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f n}-\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x^n\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{f n}-\frac{p \text{Li}_2\left(-\frac{\sqrt{g} \left(e x^n+d\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f n}-\frac{p \text{Li}_2\left(\frac{\sqrt{g} \left(e x^n+d\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 f n}+\frac{p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{f n}",1,"Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g*x^(2*n))), x]","F",-1
371,1,92,121,0.0764022,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^n\right)} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g*x^n)),x]","\frac{\log \left(c \left(d+e x^n\right)^p\right) \left(\log \left(-\frac{e x^n}{d}\right)-\log \left(\frac{e \left(f+g x^n\right)}{e f-d g}\right)\right)-p \text{Li}_2\left(\frac{g \left(e x^n+d\right)}{d g-e f}\right)+p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{f n}","-\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(\frac{e \left(f+g x^n\right)}{e f-d g}\right)}{f n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{f n}-\frac{p \text{Li}_2\left(-\frac{g \left(e x^n+d\right)}{e f-d g}\right)}{f n}+\frac{p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{f n}",1,"(Log[c*(d + e*x^n)^p]*(Log[-((e*x^n)/d)] - Log[(e*(f + g*x^n))/(e*f - d*g)]) - p*PolyLog[2, (g*(d + e*x^n))/(-(e*f) + d*g)] + p*PolyLog[2, 1 + (e*x^n)/d])/(f*n)","A",1
372,1,64,70,0.0241846,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-n}\right)} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g/x^n)),x]","\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(\frac{e \left(f x^n+g\right)}{e g-d f}\right)+p \text{Li}_2\left(\frac{f \left(e x^n+d\right)}{d f-e g}\right)}{f n}","\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(-\frac{e \left(f x^n+g\right)}{d f-e g}\right)}{f n}+\frac{p \text{Li}_2\left(\frac{f \left(e x^n+d\right)}{d f-e g}\right)}{f n}",1,"(Log[c*(d + e*x^n)^p]*Log[(e*(g + f*x^n))/(-(d*f) + e*g)] + p*PolyLog[2, (f*(d + e*x^n))/(d*f - e*g)])/(f*n)","A",1
373,0,0,221,1.4464128,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-2 n}\right)} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g/x^(2*n))),x]","\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-2 n}\right)} \, dx","\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(\frac{e \left(\sqrt{g}-\sqrt{-f} x^n\right)}{d \sqrt{-f}+e \sqrt{g}}\right)}{2 f n}+\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(-\frac{e \left(\sqrt{-f} x^n+\sqrt{g}\right)}{d \sqrt{-f}-e \sqrt{g}}\right)}{2 f n}+\frac{p \text{Li}_2\left(\frac{\sqrt{-f} \left(e x^n+d\right)}{d \sqrt{-f}-e \sqrt{g}}\right)}{2 f n}+\frac{p \text{Li}_2\left(\frac{\sqrt{-f} \left(e x^n+d\right)}{\sqrt{-f} d+e \sqrt{g}}\right)}{2 f n}",1,"Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g/x^(2*n))), x]","F",-1
374,0,0,419,8.1147098,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{2 n}\right)^2} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g*x^(2*n))^2),x]","\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{2 n}\right)^2} \, dx","-\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(\frac{e \left(\sqrt{-f}-\sqrt{g} x^n\right)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f^2 n}-\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(\frac{e \left(\sqrt{-f}+\sqrt{g} x^n\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2 n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{f^2 n}+\frac{\log \left(c \left(d+e x^n\right)^p\right)}{2 f n \left(f+g x^{2 n}\right)}-\frac{d e \sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{g} x^n}{\sqrt{f}}\right)}{2 f^{3/2} n \left(d^2 g+e^2 f\right)}+\frac{e^2 p \log \left(f+g x^{2 n}\right)}{4 f n \left(d^2 g+e^2 f\right)}-\frac{e^2 p \log \left(d+e x^n\right)}{2 f n \left(d^2 g+e^2 f\right)}-\frac{p \text{Li}_2\left(-\frac{\sqrt{g} \left(e x^n+d\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2 n}-\frac{p \text{Li}_2\left(\frac{\sqrt{g} \left(e x^n+d\right)}{\sqrt{g} d+e \sqrt{-f}}\right)}{2 f^2 n}+\frac{p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{f^2 n}",1,"Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g*x^(2*n))^2), x]","F",-1
375,1,171,204,0.1648396,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^n\right)^2} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g*x^n)^2),x]","\frac{\frac{f \log \left(c \left(d+e x^n\right)^p\right)}{f+g x^n}-\log \left(c \left(d+e x^n\right)^p\right) \log \left(\frac{e \left(f+g x^n\right)}{e f-d g}\right)+\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)-p \text{Li}_2\left(\frac{g \left(e x^n+d\right)}{d g-e f}\right)-\frac{e f p \log \left(d+e x^n\right)}{e f-d g}+\frac{e f p \log \left(f+g x^n\right)}{e f-d g}+p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{f^2 n}","-\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(\frac{e \left(f+g x^n\right)}{e f-d g}\right)}{f^2 n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{f^2 n}+\frac{\log \left(c \left(d+e x^n\right)^p\right)}{f n \left(f+g x^n\right)}-\frac{p \text{Li}_2\left(-\frac{g \left(e x^n+d\right)}{e f-d g}\right)}{f^2 n}+\frac{p \text{Li}_2\left(\frac{e x^n}{d}+1\right)}{f^2 n}-\frac{e p \log \left(d+e x^n\right)}{f n (e f-d g)}+\frac{e p \log \left(f+g x^n\right)}{f n (e f-d g)}",1,"(-((e*f*p*Log[d + e*x^n])/(e*f - d*g)) + (f*Log[c*(d + e*x^n)^p])/(f + g*x^n) + Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p] + (e*f*p*Log[f + g*x^n])/(e*f - d*g) - Log[c*(d + e*x^n)^p]*Log[(e*(f + g*x^n))/(e*f - d*g)] - p*PolyLog[2, (g*(d + e*x^n))/(-(e*f) + d*g)] + p*PolyLog[2, 1 + (e*x^n)/d])/(f^2*n)","A",1
376,1,433,156,1.5072745,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-n}\right)^2} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g/x^n)^2),x]","\frac{g \log \left(f-f x^{-n}\right) \log \left(c \left(d+e x^n\right)^p\right)-f x^n \log \left(c \left(d+e x^n\right)^p\right)+f x^n \log \left(f-f x^{-n}\right) \log \left(c \left(d+e x^n\right)^p\right)-p \log \left(d x^{-n}+e\right) \left(\left(f x^n+g\right) \log \left(f-f x^{-n}\right)-f x^n\right)+p \left(f x^n+g\right) \text{Li}_2\left(-\frac{f x^n}{g}\right)+g p \log \left(f-f x^{-n}\right)-g n p \log (x) \log \left(f-f x^{-n}\right)+f n p x^n \log (x) \log \left(\frac{f x^n}{g}+1\right)+g n p \log (x) \log \left(\frac{f x^n}{g}+1\right)+f p x^n \log \left(f-f x^{-n}\right)-f n p x^n \log (x) \log \left(f-f x^{-n}\right)}{f^2 n \left(f x^n+g\right)}-\frac{p \left(-\text{Li}_2\left(-\frac{g \left(d x^{-n}+e\right)}{d f-e g}\right)-\frac{d f \log \left(d x^{-n}+e\right)}{d f-e g}+\frac{d f \log \left(f+g x^{-n}\right)}{d f-e g}-\log \left(d x^{-n}+e\right) \log \left(\frac{d \left(f+g x^{-n}\right)}{d f-e g}\right)+\frac{f x^n \log \left(d x^{-n}+e\right)}{f x^n+g}+\text{Li}_2\left(\frac{d x^{-n}}{e}+1\right)+\log \left(-\frac{d x^{-n}}{e}\right) \log \left(d x^{-n}+e\right)\right)}{f^2 n}","\frac{g \log \left(c \left(d+e x^n\right)^p\right)}{f^2 n \left(f x^n+g\right)}+\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(-\frac{e \left(f x^n+g\right)}{d f-e g}\right)}{f^2 n}+\frac{p \text{Li}_2\left(\frac{f \left(e x^n+d\right)}{d f-e g}\right)}{f^2 n}+\frac{e g p \log \left(d+e x^n\right)}{f^2 n (d f-e g)}-\frac{e g p \log \left(f x^n+g\right)}{f^2 n (d f-e g)}",1,"(g*p*Log[f - f/x^n] + f*p*x^n*Log[f - f/x^n] - g*n*p*Log[x]*Log[f - f/x^n] - f*n*p*x^n*Log[x]*Log[f - f/x^n] - p*Log[e + d/x^n]*(-(f*x^n) + (g + f*x^n)*Log[f - f/x^n]) - f*x^n*Log[c*(d + e*x^n)^p] + g*Log[f - f/x^n]*Log[c*(d + e*x^n)^p] + f*x^n*Log[f - f/x^n]*Log[c*(d + e*x^n)^p] + g*n*p*Log[x]*Log[1 + (f*x^n)/g] + f*n*p*x^n*Log[x]*Log[1 + (f*x^n)/g] + p*(g + f*x^n)*PolyLog[2, -((f*x^n)/g)])/(f^2*n*(g + f*x^n)) - (p*(-((d*f*Log[e + d/x^n])/(d*f - e*g)) + (f*x^n*Log[e + d/x^n])/(g + f*x^n) + Log[-(d/(e*x^n))]*Log[e + d/x^n] + (d*f*Log[f + g/x^n])/(d*f - e*g) - Log[e + d/x^n]*Log[(d*(f + g/x^n))/(d*f - e*g)] - PolyLog[2, -((g*(e + d/x^n))/(d*f - e*g))] + PolyLog[2, 1 + d/(e*x^n)]))/(f^2*n)","B",0
377,0,0,377,1.2577003,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-2 n}\right)^2} \, dx","Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g/x^(2*n))^2),x]","\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-2 n}\right)^2} \, dx","\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(\frac{e \left(\sqrt{g}-\sqrt{-f} x^n\right)}{d \sqrt{-f}+e \sqrt{g}}\right)}{2 f^2 n}+\frac{\log \left(c \left(d+e x^n\right)^p\right) \log \left(-\frac{e \left(\sqrt{-f} x^n+\sqrt{g}\right)}{d \sqrt{-f}-e \sqrt{g}}\right)}{2 f^2 n}+\frac{g \log \left(c \left(d+e x^n\right)^p\right)}{2 f^2 n \left(f x^{2 n}+g\right)}-\frac{d e \sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{f} x^n}{\sqrt{g}}\right)}{2 f^{3/2} n \left(d^2 f+e^2 g\right)}+\frac{e^2 g p \log \left(f x^{2 n}+g\right)}{4 f^2 n \left(d^2 f+e^2 g\right)}-\frac{e^2 g p \log \left(d+e x^n\right)}{2 f^2 n \left(d^2 f+e^2 g\right)}+\frac{p \text{Li}_2\left(\frac{\sqrt{-f} \left(e x^n+d\right)}{d \sqrt{-f}-e \sqrt{g}}\right)}{2 f^2 n}+\frac{p \text{Li}_2\left(\frac{\sqrt{-f} \left(e x^n+d\right)}{\sqrt{-f} d+e \sqrt{g}}\right)}{2 f^2 n}",1,"Integrate[Log[c*(d + e*x^n)^p]/(x*(f + g/x^(2*n))^2), x]","F",-1
378,1,26,25,0.0719578,"\int \frac{\log \left(c \left(d+e x^n\right)\right)}{x \left(c e-(1-c d) x^{-n}\right)} \, dx","Integrate[Log[c*(d + e*x^n)]/(x*(c*e - (1 - c*d)/x^n)),x]","-\frac{\text{Li}_2\left(-c e x^n-c d+1\right)}{c e n}","-\frac{\text{Li}_2\left(1-c \left(e x^n+d\right)\right)}{c e n}",1,"-(PolyLog[2, 1 - c*d - c*e*x^n]/(c*e*n))","A",1
379,1,26,25,0.0216997,"\int \frac{x^{-1+n} \log \left(c \left(d+e x^n\right)\right)}{-1+c d+c e x^n} \, dx","Integrate[(x^(-1 + n)*Log[c*(d + e*x^n)])/(-1 + c*d + c*e*x^n),x]","-\frac{\text{Li}_2\left(-c e x^n-c d+1\right)}{c e n}","-\frac{\text{Li}_2\left(1-c \left(e x^n+d\right)\right)}{c e n}",1,"-(PolyLog[2, 1 - c*d - c*e*x^n]/(c*e*n))","A",1
380,1,34,26,0.073193,"\int \frac{\log \left(c \left(d+e x^{-n}\right)\right)}{x \left(c e-(1-c d) x^n\right)} \, dx","Integrate[Log[c*(d + e/x^n)]/(x*(c*e - (1 - c*d)*x^n)),x]","\frac{\text{Li}_2\left(-x^{-n} \left(c d x^n-x^n+c e\right)\right)}{c e n}","\frac{\text{Li}_2\left(1-c \left(e x^{-n}+d\right)\right)}{c e n}",1,"PolyLog[2, -((c*e - x^n + c*d*x^n)/x^n)]/(c*e*n)","A",1
381,0,0,608,0.4311852,"\int \frac{\left(f+g x^{2 n}\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g*x^(2*n))^2*Log[c*(d + e*x^n)^p]^q)/x,x]","\int \frac{\left(f+g x^{2 n}\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","f^2 \text{Int}\left(\frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x},x\right)-\frac{d^3 g^2 \left(d+e x^n\right) \left(c \left(d+e x^n\right)^p\right)^{-1/p} \log ^q\left(c \left(d+e x^n\right)^p\right) \left(-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)^{-q} \Gamma \left(q+1,-\frac{\log \left(c \left(e x^n+d\right)^p\right)}{p}\right)}{e^4 n}+\frac{3 d^2 g^2 2^{-q-1} \left(d+e x^n\right)^2 \left(c \left(d+e x^n\right)^p\right)^{-2/p} \log ^q\left(c \left(d+e x^n\right)^p\right) \left(-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)^{-q} \Gamma \left(q+1,-\frac{2 \log \left(c \left(e x^n+d\right)^p\right)}{p}\right)}{e^4 n}+\frac{g^2 4^{-q-1} \left(d+e x^n\right)^4 \left(c \left(d+e x^n\right)^p\right)^{-4/p} \log ^q\left(c \left(d+e x^n\right)^p\right) \left(-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)^{-q} \Gamma \left(q+1,-\frac{4 \log \left(c \left(e x^n+d\right)^p\right)}{p}\right)}{e^4 n}-\frac{d g^2 3^{-q} \left(d+e x^n\right)^3 \left(c \left(d+e x^n\right)^p\right)^{-3/p} \log ^q\left(c \left(d+e x^n\right)^p\right) \left(-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)^{-q} \Gamma \left(q+1,-\frac{3 \log \left(c \left(e x^n+d\right)^p\right)}{p}\right)}{e^4 n}+\frac{f g 2^{-q} \left(d+e x^n\right)^2 \left(c \left(d+e x^n\right)^p\right)^{-2/p} \log ^q\left(c \left(d+e x^n\right)^p\right) \left(-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)^{-q} \Gamma \left(q+1,-\frac{2 \log \left(c \left(e x^n+d\right)^p\right)}{p}\right)}{e^2 n}-\frac{2 d f g \left(d+e x^n\right) \left(c \left(d+e x^n\right)^p\right)^{-1/p} \log ^q\left(c \left(d+e x^n\right)^p\right) \left(-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)^{-q} \Gamma \left(q+1,-\frac{\log \left(c \left(e x^n+d\right)^p\right)}{p}\right)}{e^2 n}",0,"Integrate[((f + g*x^(2*n))^2*Log[c*(d + e*x^n)^p]^q)/x, x]","A",-1
382,0,0,307,0.3056994,"\int \frac{\left(f+g x^n\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g*x^n)^2*Log[c*(d + e*x^n)^p]^q)/x,x]","\int \frac{\left(f+g x^n\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","f^2 \text{Int}\left(\frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x},x\right)+\frac{g^2 2^{-q-1} \left(d+e x^n\right)^2 \left(c \left(d+e x^n\right)^p\right)^{-2/p} \log ^q\left(c \left(d+e x^n\right)^p\right) \left(-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)^{-q} \Gamma \left(q+1,-\frac{2 \log \left(c \left(e x^n+d\right)^p\right)}{p}\right)}{e^2 n}-\frac{d g^2 \left(d+e x^n\right) \left(c \left(d+e x^n\right)^p\right)^{-1/p} \log ^q\left(c \left(d+e x^n\right)^p\right) \left(-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)^{-q} \Gamma \left(q+1,-\frac{\log \left(c \left(e x^n+d\right)^p\right)}{p}\right)}{e^2 n}+\frac{2 f g \left(d+e x^n\right) \left(c \left(d+e x^n\right)^p\right)^{-1/p} \log ^q\left(c \left(d+e x^n\right)^p\right) \left(-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)^{-q} \Gamma \left(q+1,-\frac{\log \left(c \left(e x^n+d\right)^p\right)}{p}\right)}{e n}",0,"Integrate[((f + g*x^n)^2*Log[c*(d + e*x^n)^p]^q)/x, x]","A",-1
383,0,0,32,0.4490913,"\int \frac{\left(f+g x^{-n}\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g/x^n)^2*Log[c*(d + e*x^n)^p]^q)/x,x]","\int \frac{\left(f+g x^{-n}\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","\text{Int}\left(\frac{\left(f+g x^{-n}\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x},x\right)",0,"Integrate[((f + g/x^n)^2*Log[c*(d + e*x^n)^p]^q)/x, x]","A",-1
384,0,0,32,0.3816858,"\int \frac{\left(f+g x^{-2 n}\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Integrate[((f + g/x^(2*n))^2*Log[c*(d + e*x^n)^p]^q)/x,x]","\int \frac{\left(f+g x^{-2 n}\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","\text{Int}\left(\frac{\left(f+g x^{-2 n}\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x},x\right)",0,"Integrate[((f + g/x^(2*n))^2*Log[c*(d + e*x^n)^p]^q)/x, x]","A",-1
385,0,0,32,2.4400008,"\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{2 n}\right)} \, dx","Integrate[Log[c*(d + e*x^n)^p]^q/(x*(f + g*x^(2*n))),x]","\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{2 n}\right)} \, dx","\text{Int}\left(\frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{2 n}\right)},x\right)",0,"Integrate[Log[c*(d + e*x^n)^p]^q/(x*(f + g*x^(2*n))), x]","A",-1
386,0,0,30,1.9600448,"\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^n\right)} \, dx","Integrate[Log[c*(d + e*x^n)^p]^q/(x*(f + g*x^n)),x]","\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^n\right)} \, dx","\text{Int}\left(\frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^n\right)},x\right)",0,"Integrate[Log[c*(d + e*x^n)^p]^q/(x*(f + g*x^n)), x]","A",-1
387,0,0,32,1.9597851,"\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-n}\right)} \, dx","Integrate[Log[c*(d + e*x^n)^p]^q/(x*(f + g/x^n)),x]","\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-n}\right)} \, dx","\text{Int}\left(\frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-n}\right)},x\right)",0,"Integrate[Log[c*(d + e*x^n)^p]^q/(x*(f + g/x^n)), x]","A",-1
388,0,0,32,0.2512194,"\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-2 n}\right)} \, dx","Integrate[Log[c*(d + e*x^n)^p]^q/(x*(f + g/x^(2*n))),x]","\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-2 n}\right)} \, dx","\text{Int}\left(\frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-2 n}\right)},x\right)",0,"Integrate[Log[c*(d + e*x^n)^p]^q/(x*(f + g/x^(2*n))), x]","A",-1
389,1,75,69,0.0599427,"\int \frac{\log (x) \log \left(d+e x^m\right)}{x} \, dx","Integrate[(Log[x]*Log[d + e*x^m])/x,x]","\frac{\text{Li}_3\left(-\frac{d x^{-m}}{e}\right)}{m^2}+\frac{\log (x) \text{Li}_2\left(-\frac{d x^{-m}}{e}\right)}{m}-\frac{1}{6} \log ^2(x) \left(3 \log \left(\frac{d x^{-m}}{e}+1\right)-3 \log \left(d+e x^m\right)+m \log (x)\right)","\frac{\text{Li}_3\left(-\frac{e x^m}{d}\right)}{m^2}-\frac{\log (x) \text{Li}_2\left(-\frac{e x^m}{d}\right)}{m}+\frac{1}{2} \log ^2(x) \log \left(d+e x^m\right)-\frac{1}{2} \log ^2(x) \log \left(\frac{e x^m}{d}+1\right)",1,"-1/6*(Log[x]^2*(m*Log[x] + 3*Log[1 + d/(e*x^m)] - 3*Log[d + e*x^m])) + (Log[x]*PolyLog[2, -(d/(e*x^m))])/m + PolyLog[3, -(d/(e*x^m))]/m^2","A",1
390,1,34,8,0.0034049,"\int \frac{\log \left(\frac{a+x}{x}\right)}{x} \, dx","Integrate[Log[(a + x)/x]/x,x]","-\text{Li}_2\left(-\frac{-a-x}{x}\right)-\log \left(-\frac{a}{x}\right) \log \left(\frac{a+x}{x}\right)","\text{Li}_2\left(-\frac{a}{x}\right)",1,"-(Log[-(a/x)]*Log[(a + x)/x]) - PolyLog[2, -((-a - x)/x)]","B",1
391,1,12,12,0.0030038,"\int \frac{\log \left(\frac{a+x^2}{x^2}\right)}{x} \, dx","Integrate[Log[(a + x^2)/x^2]/x,x]","\frac{1}{2} \text{Li}_2\left(-\frac{a}{x^2}\right)","\frac{1}{2} \text{Li}_2\left(-\frac{a}{x^2}\right)",1,"PolyLog[2, -(a/x^2)]/2","A",1
392,1,14,14,0.0045533,"\int \frac{\log \left(x^{-n} \left(a+x^n\right)\right)}{x} \, dx","Integrate[Log[(a + x^n)/x^n]/x,x]","\frac{\text{Li}_2\left(-a x^{-n}\right)}{n}","\frac{\text{Li}_2\left(-a x^{-n}\right)}{n}",1,"PolyLog[2, -(a/x^n)]/n","A",1
393,1,36,35,0.0045999,"\int \frac{\log \left(\frac{a+b x}{x}\right)}{x} \, dx","Integrate[Log[(a + b*x)/x]/x,x]","-\text{Li}_2\left(\frac{\frac{a}{x}+b}{b}\right)-\log \left(\frac{a}{x}+b\right) \log \left(-\frac{a}{b x}\right)","-\text{Li}_2\left(\frac{a}{b x}+1\right)-\log \left(\frac{a}{x}+b\right) \log \left(-\frac{a}{b x}\right)",1,"-(Log[b + a/x]*Log[-(a/(b*x))]) - PolyLog[2, (b + a/x)/b]","A",1
394,1,40,39,0.0041083,"\int \frac{\log \left(\frac{a+b x^2}{x^2}\right)}{x} \, dx","Integrate[Log[(a + b*x^2)/x^2]/x,x]","-\frac{1}{2} \text{Li}_2\left(\frac{\frac{a}{x^2}+b}{b}\right)-\frac{1}{2} \log \left(\frac{a}{x^2}+b\right) \log \left(-\frac{a}{b x^2}\right)","-\frac{1}{2} \text{Li}_2\left(\frac{a}{b x^2}+1\right)-\frac{1}{2} \log \left(\frac{a}{x^2}+b\right) \log \left(-\frac{a}{b x^2}\right)",1,"-1/2*(Log[b + a/x^2]*Log[-(a/(b*x^2))]) - PolyLog[2, (b + a/x^2)/b]/2","A",1
395,1,44,47,0.0173487,"\int \frac{\log \left(x^{-n} \left(a+b x^n\right)\right)}{x} \, dx","Integrate[Log[(a + b*x^n)/x^n]/x,x]","-\frac{\text{Li}_2\left(\frac{a x^{-n}+b}{b}\right)+\log \left(-\frac{a x^{-n}}{b}\right) \log \left(a x^{-n}+b\right)}{n}","-\frac{\text{Li}_2\left(\frac{a x^{-n}}{b}+1\right)}{n}-\frac{\log \left(-\frac{a x^{-n}}{b}\right) \log \left(a x^{-n}+b\right)}{n}",1,"-((Log[-(a/(b*x^n))]*Log[b + a/x^n] + PolyLog[2, (b + a/x^n)/b])/n)","A",1
396,1,80,105,0.0305558,"\int \frac{\log \left(\frac{a+b x}{x}\right)}{c+d x} \, dx","Integrate[Log[(a + b*x)/x]/(c + d*x),x]","\frac{-\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)+\log (c+d x) \left(-\log \left(\frac{d (a+b x)}{a d-b c}\right)+\log \left(\frac{a}{x}+b\right)+\log \left(-\frac{d x}{c}\right)\right)+\text{Li}_2\left(\frac{d x}{c}+1\right)}{d}","-\frac{\text{Li}_2\left(\frac{b (c+d x)}{b c-a d}\right)}{d}+\frac{\log \left(\frac{a}{x}+b\right) \log (c+d x)}{d}-\frac{\log (c+d x) \log \left(-\frac{d (a+b x)}{b c-a d}\right)}{d}+\frac{\text{Li}_2\left(\frac{d x}{c}+1\right)}{d}+\frac{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{d}",1,"((Log[b + a/x] + Log[-((d*x)/c)] - Log[(d*(a + b*x))/(-(b*c) + a*d)])*Log[c + d*x] - PolyLog[2, (b*(c + d*x))/(b*c - a*d)] + PolyLog[2, 1 + (d*x)/c])/d","A",1
397,1,228,227,0.110521,"\int \frac{\log \left(\frac{a+b x^2}{x^2}\right)}{c+d x} \, dx","Integrate[Log[(a + b*x^2)/x^2]/(c + d*x),x]","-\frac{\text{Li}_2\left(\frac{\sqrt{b} (c+d x)}{\sqrt{b} c-\sqrt{-a} d}\right)}{d}-\frac{\text{Li}_2\left(\frac{\sqrt{b} (c+d x)}{\sqrt{b} c+\sqrt{-a} d}\right)}{d}+\frac{\log \left(\frac{a}{x^2}+b\right) \log (c+d x)}{d}-\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} d+\sqrt{b} c}\right)}{d}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} c-\sqrt{-a} d}\right)}{d}+\frac{2 \text{Li}_2\left(\frac{c+d x}{c}\right)}{d}+\frac{2 \log \left(-\frac{d x}{c}\right) \log (c+d x)}{d}","-\frac{\text{Li}_2\left(\frac{\sqrt{b} (c+d x)}{\sqrt{b} c-\sqrt{-a} d}\right)}{d}-\frac{\text{Li}_2\left(\frac{\sqrt{b} (c+d x)}{\sqrt{b} c+\sqrt{-a} d}\right)}{d}+\frac{\log \left(\frac{a}{x^2}+b\right) \log (c+d x)}{d}-\frac{\log (c+d x) \log \left(\frac{d \left(\sqrt{-a}-\sqrt{b} x\right)}{\sqrt{-a} d+\sqrt{b} c}\right)}{d}-\frac{\log (c+d x) \log \left(-\frac{d \left(\sqrt{-a}+\sqrt{b} x\right)}{\sqrt{b} c-\sqrt{-a} d}\right)}{d}+\frac{2 \text{Li}_2\left(\frac{d x}{c}+1\right)}{d}+\frac{2 \log \left(-\frac{d x}{c}\right) \log (c+d x)}{d}",1,"(Log[b + a/x^2]*Log[c + d*x])/d + (2*Log[-((d*x)/c)]*Log[c + d*x])/d - (Log[(d*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*c + Sqrt[-a]*d)]*Log[c + d*x])/d - (Log[-((d*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*c - Sqrt[-a]*d))]*Log[c + d*x])/d + (2*PolyLog[2, (c + d*x)/c])/d - PolyLog[2, (Sqrt[b]*(c + d*x))/(Sqrt[b]*c - Sqrt[-a]*d)]/d - PolyLog[2, (Sqrt[b]*(c + d*x))/(Sqrt[b]*c + Sqrt[-a]*d)]/d","A",1
398,0,0,21,0.501822,"\int \frac{\log \left(x^{-n} \left(a+b x^n\right)\right)}{c+d x} \, dx","Integrate[Log[(a + b*x^n)/x^n]/(c + d*x),x]","\int \frac{\log \left(x^{-n} \left(a+b x^n\right)\right)}{c+d x} \, dx","\text{Int}\left(\frac{\log \left(a x^{-n}+b\right)}{c+d x},x\right)",0,"Integrate[Log[(a + b*x^n)/x^n]/(c + d*x), x]","A",-1
399,1,82,92,0.0551274,"\int (f x)^q \left(a+b \log \left(c \left(d+e x^m\right)^n\right)\right) \, dx","Integrate[(f*x)^q*(a + b*Log[c*(d + e*x^m)^n]),x]","\frac{x (f x)^q \left(d (m+q+1) \left(a+b \log \left(c \left(d+e x^m\right)^n\right)\right)-b e m n x^m \, _2F_1\left(1,\frac{m+q+1}{m};\frac{2 m+q+1}{m};-\frac{e x^m}{d}\right)\right)}{d (q+1) (m+q+1)}","\frac{(f x)^{q+1} \left(a+b \log \left(c \left(d+e x^m\right)^n\right)\right)}{f (q+1)}-\frac{b e m n x^{m+1} (f x)^q \, _2F_1\left(1,\frac{m+q+1}{m};\frac{2 m+q+1}{m};-\frac{e x^m}{d}\right)}{d (q+1) (m+q+1)}",1,"(x*(f*x)^q*(-(b*e*m*n*x^m*Hypergeometric2F1[1, (1 + m + q)/m, (1 + 2*m + q)/m, -((e*x^m)/d)]) + d*(1 + m + q)*(a + b*Log[c*(d + e*x^m)^n])))/(d*(1 + q)*(1 + m + q))","A",1
400,1,159,166,0.1370872,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \, dx","Integrate[x^3*(a + b*Log[c*(d + e*Sqrt[x])^n]),x]","\frac{a x^4}{4}+\frac{1}{4} b x^4 \log \left(c \left(d+e \sqrt{x}\right)^n\right)-\frac{1}{4} b e n \left(\frac{d^8 \log \left(d+e \sqrt{x}\right)}{e^9}-\frac{d^7 \sqrt{x}}{e^8}+\frac{d^6 x}{2 e^7}-\frac{d^5 x^{3/2}}{3 e^6}+\frac{d^4 x^2}{4 e^5}-\frac{d^3 x^{5/2}}{5 e^4}+\frac{d^2 x^3}{6 e^3}-\frac{d x^{7/2}}{7 e^2}+\frac{x^4}{8 e}\right)","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)-\frac{b d^8 n \log \left(d+e \sqrt{x}\right)}{4 e^8}+\frac{b d^7 n \sqrt{x}}{4 e^7}-\frac{b d^6 n x}{8 e^6}+\frac{b d^5 n x^{3/2}}{12 e^5}-\frac{b d^4 n x^2}{16 e^4}+\frac{b d^3 n x^{5/2}}{20 e^3}-\frac{b d^2 n x^3}{24 e^2}+\frac{b d n x^{7/2}}{28 e}-\frac{1}{32} b n x^4",1,"(a*x^4)/4 - (b*e*n*(-((d^7*Sqrt[x])/e^8) + (d^6*x)/(2*e^7) - (d^5*x^(3/2))/(3*e^6) + (d^4*x^2)/(4*e^5) - (d^3*x^(5/2))/(5*e^4) + (d^2*x^3)/(6*e^3) - (d*x^(7/2))/(7*e^2) + x^4/(8*e) + (d^8*Log[d + e*Sqrt[x]])/e^9))/4 + (b*x^4*Log[c*(d + e*Sqrt[x])^n])/4","A",1
401,1,131,134,0.093807,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*(d + e*Sqrt[x])^n]),x]","\frac{a x^3}{3}+\frac{1}{3} b x^3 \log \left(c \left(d+e \sqrt{x}\right)^n\right)-\frac{1}{3} b e n \left(\frac{d^6 \log \left(d+e \sqrt{x}\right)}{e^7}-\frac{d^5 \sqrt{x}}{e^6}+\frac{d^4 x}{2 e^5}-\frac{d^3 x^{3/2}}{3 e^4}+\frac{d^2 x^2}{4 e^3}-\frac{d x^{5/2}}{5 e^2}+\frac{x^3}{6 e}\right)","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)-\frac{b d^6 n \log \left(d+e \sqrt{x}\right)}{3 e^6}+\frac{b d^5 n \sqrt{x}}{3 e^5}-\frac{b d^4 n x}{6 e^4}+\frac{b d^3 n x^{3/2}}{9 e^3}-\frac{b d^2 n x^2}{12 e^2}+\frac{b d n x^{5/2}}{15 e}-\frac{1}{18} b n x^3",1,"(a*x^3)/3 - (b*e*n*(-((d^5*Sqrt[x])/e^6) + (d^4*x)/(2*e^5) - (d^3*x^(3/2))/(3*e^4) + (d^2*x^2)/(4*e^3) - (d*x^(5/2))/(5*e^2) + x^3/(6*e) + (d^6*Log[d + e*Sqrt[x]])/e^7))/3 + (b*x^3*Log[c*(d + e*Sqrt[x])^n])/3","A",1
402,1,107,102,0.0337383,"\int x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \, dx","Integrate[x*(a + b*Log[c*(d + e*Sqrt[x])^n]),x]","\frac{a x^2}{2}+\frac{1}{2} b x^2 \log \left(c \left(d+e \sqrt{x}\right)^n\right)-\frac{b d^4 n \log \left(d+e \sqrt{x}\right)}{2 e^4}+\frac{b d^3 n \sqrt{x}}{2 e^3}-\frac{b d^2 n x}{4 e^2}+\frac{b d n x^{3/2}}{6 e}-\frac{1}{8} b n x^2","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)-\frac{b d^4 n \log \left(d+e \sqrt{x}\right)}{2 e^4}+\frac{b d^3 n \sqrt{x}}{2 e^3}-\frac{b d^2 n x}{4 e^2}+\frac{b d n x^{3/2}}{6 e}-\frac{1}{8} b n x^2",1,"(b*d^3*n*Sqrt[x])/(2*e^3) - (b*d^2*n*x)/(4*e^2) + (b*d*n*x^(3/2))/(6*e) + (a*x^2)/2 - (b*n*x^2)/8 - (b*d^4*n*Log[d + e*Sqrt[x]])/(2*e^4) + (b*x^2*Log[c*(d + e*Sqrt[x])^n])/2","A",1
403,1,60,60,0.0304376,"\int \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \, dx","Integrate[a + b*Log[c*(d + e*Sqrt[x])^n],x]","a x+b x \log \left(c \left(d+e \sqrt{x}\right)^n\right)-\frac{b d^2 n \log \left(d+e \sqrt{x}\right)}{e^2}+\frac{b d n \sqrt{x}}{e}-\frac{b n x}{2}","a x+b x \log \left(c \left(d+e \sqrt{x}\right)^n\right)-\frac{b d^2 n \log \left(d+e \sqrt{x}\right)}{e^2}+\frac{b d n \sqrt{x}}{e}-\frac{b n x}{2}",1,"(b*d*n*Sqrt[x])/e + a*x - (b*n*x)/2 - (b*d^2*n*Log[d + e*Sqrt[x]])/e^2 + b*x*Log[c*(d + e*Sqrt[x])^n]","A",1
404,1,53,51,0.00308,"\int \frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{x} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])/x,x]","a \log (x)+2 b \log \left(-\frac{e \sqrt{x}}{d}\right) \log \left(c \left(d+e \sqrt{x}\right)^n\right)+2 b n \text{Li}_2\left(\frac{d+e \sqrt{x}}{d}\right)","2 \log \left(-\frac{e \sqrt{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+2 b n \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right)",1,"2*b*Log[c*(d + e*Sqrt[x])^n]*Log[-((e*Sqrt[x])/d)] + a*Log[x] + 2*b*n*PolyLog[2, (d + e*Sqrt[x])/d]","A",1
405,1,67,70,0.0464597,"\int \frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])/x^2,x]","-\frac{a}{x}-\frac{b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{x}+b e n \left(\frac{e \log \left(d+e \sqrt{x}\right)}{d^2}-\frac{e \log (x)}{2 d^2}-\frac{1}{d \sqrt{x}}\right)","-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{x}+\frac{b e^2 n \log \left(d+e \sqrt{x}\right)}{d^2}-\frac{b e^2 n \log (x)}{2 d^2}-\frac{b e n}{d \sqrt{x}}",1,"-(a/x) - (b*Log[c*(d + e*Sqrt[x])^n])/x + b*e*n*(-(1/(d*Sqrt[x])) + (e*Log[d + e*Sqrt[x]])/d^2 - (e*Log[x])/(2*d^2))","A",1
406,1,104,109,0.0398886,"\int \frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])/x^3,x]","-\frac{a}{2 x^2}-\frac{b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{2 x^2}+\frac{1}{2} b e n \left(\frac{e^3 \log \left(d+e \sqrt{x}\right)}{d^4}-\frac{e^3 \log (x)}{2 d^4}-\frac{e^2}{d^3 \sqrt{x}}+\frac{e}{2 d^2 x}-\frac{1}{3 d x^{3/2}}\right)","-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{2 x^2}+\frac{b e^4 n \log \left(d+e \sqrt{x}\right)}{2 d^4}-\frac{b e^4 n \log (x)}{4 d^4}-\frac{b e^3 n}{2 d^3 \sqrt{x}}+\frac{b e^2 n}{4 d^2 x}-\frac{b e n}{6 d x^{3/2}}",1,"-1/2*a/x^2 - (b*Log[c*(d + e*Sqrt[x])^n])/(2*x^2) + (b*e*n*(-1/3*1/(d*x^(3/2)) + e/(2*d^2*x) - e^2/(d^3*Sqrt[x]) + (e^3*Log[d + e*Sqrt[x]])/d^4 - (e^3*Log[x])/(2*d^4)))/2","A",1
407,1,132,141,0.1386473,"\int \frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])/x^4,x]","-\frac{a}{3 x^3}-\frac{b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{3 x^3}+\frac{1}{3} b e n \left(\frac{e^5 \log \left(d+e \sqrt{x}\right)}{d^6}-\frac{e^5 \log (x)}{2 d^6}-\frac{e^4}{d^5 \sqrt{x}}+\frac{e^3}{2 d^4 x}-\frac{e^2}{3 d^3 x^{3/2}}+\frac{e}{4 d^2 x^2}-\frac{1}{5 d x^{5/2}}\right)","-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{3 x^3}+\frac{b e^6 n \log \left(d+e \sqrt{x}\right)}{3 d^6}-\frac{b e^6 n \log (x)}{6 d^6}-\frac{b e^5 n}{3 d^5 \sqrt{x}}+\frac{b e^4 n}{6 d^4 x}-\frac{b e^3 n}{9 d^3 x^{3/2}}+\frac{b e^2 n}{12 d^2 x^2}-\frac{b e n}{15 d x^{5/2}}",1,"-1/3*a/x^3 - (b*Log[c*(d + e*Sqrt[x])^n])/(3*x^3) + (b*e*n*(-1/5*1/(d*x^(5/2)) + e/(4*d^2*x^2) - e^2/(3*d^3*x^(3/2)) + e^3/(2*d^4*x) - e^4/(d^5*Sqrt[x]) + (e^5*Log[d + e*Sqrt[x]])/d^6 - (e^5*Log[x])/(2*d^6)))/3","A",1
408,1,295,480,0.3323597,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \, dx","Integrate[x^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^2,x]","\frac{e \sqrt{x} \left(1800 a^2 e^5 x^{5/2}+60 a b n \left(60 d^5-30 d^4 e \sqrt{x}+20 d^3 e^2 x-15 d^2 e^3 x^{3/2}+12 d e^4 x^2-10 e^5 x^{5/2}\right)+b^2 n^2 \left(-8820 d^5+2610 d^4 e \sqrt{x}-1140 d^3 e^2 x+555 d^2 e^3 x^{3/2}-264 d e^4 x^2+100 e^5 x^{5/2}\right)\right)-60 b \left(60 a \left(d^6-e^6 x^3\right)+b n \left(-147 d^6-60 d^5 e \sqrt{x}+30 d^4 e^2 x-20 d^3 e^3 x^{3/2}+15 d^2 e^4 x^2-12 d e^5 x^{5/2}+10 e^6 x^3\right)\right) \log \left(c \left(d+e \sqrt{x}\right)^n\right)-1800 b^2 \left(d^6-e^6 x^3\right) \log ^2\left(c \left(d+e \sqrt{x}\right)^n\right)}{5400 e^6}","-\frac{2 b d^6 n \log \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{3 e^6}+\frac{4 b d^5 n \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{e^6}-\frac{5 b d^4 n \left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{e^6}+\frac{40 b d^3 n \left(d+e \sqrt{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{9 e^6}-\frac{5 b d^2 n \left(d+e \sqrt{x}\right)^4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{2 e^6}+\frac{4 b d n \left(d+e \sqrt{x}\right)^5 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{5 e^6}-\frac{b n \left(d+e \sqrt{x}\right)^6 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{9 e^6}+\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2+\frac{b^2 d^6 n^2 \log ^2\left(d+e \sqrt{x}\right)}{3 e^6}-\frac{4 b^2 d^5 n^2 \sqrt{x}}{e^5}+\frac{5 b^2 d^4 n^2 \left(d+e \sqrt{x}\right)^2}{2 e^6}-\frac{40 b^2 d^3 n^2 \left(d+e \sqrt{x}\right)^3}{27 e^6}+\frac{5 b^2 d^2 n^2 \left(d+e \sqrt{x}\right)^4}{8 e^6}-\frac{4 b^2 d n^2 \left(d+e \sqrt{x}\right)^5}{25 e^6}+\frac{b^2 n^2 \left(d+e \sqrt{x}\right)^6}{54 e^6}",1,"(e*Sqrt[x]*(1800*a^2*e^5*x^(5/2) + 60*a*b*n*(60*d^5 - 30*d^4*e*Sqrt[x] + 20*d^3*e^2*x - 15*d^2*e^3*x^(3/2) + 12*d*e^4*x^2 - 10*e^5*x^(5/2)) + b^2*n^2*(-8820*d^5 + 2610*d^4*e*Sqrt[x] - 1140*d^3*e^2*x + 555*d^2*e^3*x^(3/2) - 264*d*e^4*x^2 + 100*e^5*x^(5/2))) - 60*b*(60*a*(d^6 - e^6*x^3) + b*n*(-147*d^6 - 60*d^5*e*Sqrt[x] + 30*d^4*e^2*x - 20*d^3*e^3*x^(3/2) + 15*d^2*e^4*x^2 - 12*d*e^5*x^(5/2) + 10*e^6*x^3))*Log[c*(d + e*Sqrt[x])^n] - 1800*b^2*(d^6 - e^6*x^3)*Log[c*(d + e*Sqrt[x])^n]^2)/(5400*e^6)","A",1
409,1,223,342,0.2114683,"\int x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \, dx","Integrate[x*(a + b*Log[c*(d + e*Sqrt[x])^n])^2,x]","\frac{e \sqrt{x} \left(72 a^2 e^3 x^{3/2}+12 a b n \left(12 d^3-6 d^2 e \sqrt{x}+4 d e^2 x-3 e^3 x^{3/2}\right)+b^2 n^2 \left(-300 d^3+78 d^2 e \sqrt{x}-28 d e^2 x+9 e^3 x^{3/2}\right)\right)-12 b \left(12 a \left(d^4-e^4 x^2\right)+b n \left(-25 d^4-12 d^3 e \sqrt{x}+6 d^2 e^2 x-4 d e^3 x^{3/2}+3 e^4 x^2\right)\right) \log \left(c \left(d+e \sqrt{x}\right)^n\right)-72 b^2 \left(d^4-e^4 x^2\right) \log ^2\left(c \left(d+e \sqrt{x}\right)^n\right)}{144 e^4}","-\frac{b d^4 n \log \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{e^4}+\frac{4 b d^3 n \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{e^4}-\frac{3 b d^2 n \left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{e^4}+\frac{4 b d n \left(d+e \sqrt{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{3 e^4}-\frac{b n \left(d+e \sqrt{x}\right)^4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{4 e^4}+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2+\frac{b^2 d^4 n^2 \log ^2\left(d+e \sqrt{x}\right)}{2 e^4}-\frac{4 b^2 d^3 n^2 \sqrt{x}}{e^3}+\frac{3 b^2 d^2 n^2 \left(d+e \sqrt{x}\right)^2}{2 e^4}-\frac{4 b^2 d n^2 \left(d+e \sqrt{x}\right)^3}{9 e^4}+\frac{b^2 n^2 \left(d+e \sqrt{x}\right)^4}{16 e^4}",1,"(e*Sqrt[x]*(72*a^2*e^3*x^(3/2) + 12*a*b*n*(12*d^3 - 6*d^2*e*Sqrt[x] + 4*d*e^2*x - 3*e^3*x^(3/2)) + b^2*n^2*(-300*d^3 + 78*d^2*e*Sqrt[x] - 28*d*e^2*x + 9*e^3*x^(3/2))) - 12*b*(12*a*(d^4 - e^4*x^2) + b*n*(-25*d^4 - 12*d^3*e*Sqrt[x] + 6*d^2*e^2*x - 4*d*e^3*x^(3/2) + 3*e^4*x^2))*Log[c*(d + e*Sqrt[x])^n] - 72*b^2*(d^4 - e^4*x^2)*Log[c*(d + e*Sqrt[x])^n]^2)/(144*e^4)","A",1
410,1,150,195,0.0845919,"\int \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])^2,x]","\frac{-2 a^2 \left(d^2-e^2 x\right)+2 b \left(d+e \sqrt{x}\right) \left(-2 a d+2 a e \sqrt{x}+3 b d n-b e n \sqrt{x}\right) \log \left(c \left(d+e \sqrt{x}\right)^n\right)-2 a b n \left(d-e \sqrt{x}\right)^2-2 b^2 \left(d^2-e^2 x\right) \log ^2\left(c \left(d+e \sqrt{x}\right)^n\right)+b^2 e n^2 \sqrt{x} \left(e \sqrt{x}-6 d\right)}{2 e^2}","-\frac{b n \left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{e^2}+\frac{\left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{e^2}-\frac{2 d \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{e^2}+\frac{4 a b d n \sqrt{x}}{e}+\frac{4 b^2 d n \left(d+e \sqrt{x}\right) \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{e^2}+\frac{b^2 n^2 \left(d+e \sqrt{x}\right)^2}{2 e^2}-\frac{4 b^2 d n^2 \sqrt{x}}{e}",1,"(-2*a*b*n*(d - e*Sqrt[x])^2 + b^2*e*n^2*(-6*d + e*Sqrt[x])*Sqrt[x] - 2*a^2*(d^2 - e^2*x) + 2*b*(d + e*Sqrt[x])*(-2*a*d + 3*b*d*n + 2*a*e*Sqrt[x] - b*e*n*Sqrt[x])*Log[c*(d + e*Sqrt[x])^n] - 2*b^2*(d^2 - e^2*x)*Log[c*(d + e*Sqrt[x])^n]^2)/(2*e^2)","A",1
411,1,195,93,0.1418663,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{x} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])^2/x,x]","2 b n \left(\log (x) \left(\log \left(d+e \sqrt{x}\right)-\log \left(\frac{e \sqrt{x}}{d}+1\right)\right)-2 \text{Li}_2\left(-\frac{e \sqrt{x}}{d}\right)\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)-b n \log \left(d+e \sqrt{x}\right)\right)+\log (x) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)-b n \log \left(d+e \sqrt{x}\right)\right)^2+2 b^2 n^2 \left(-2 \text{Li}_3\left(\frac{\sqrt{x} e}{d}+1\right)+2 \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right) \log \left(d+e \sqrt{x}\right)+\log \left(-\frac{e \sqrt{x}}{d}\right) \log ^2\left(d+e \sqrt{x}\right)\right)","4 b n \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+2 \log \left(-\frac{e \sqrt{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2-4 b^2 n^2 \text{Li}_3\left(\frac{\sqrt{x} e}{d}+1\right)",1,"(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2*Log[x] + 2*b*n*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])*((Log[d + e*Sqrt[x]] - Log[1 + (e*Sqrt[x])/d])*Log[x] - 2*PolyLog[2, -((e*Sqrt[x])/d)]) + 2*b^2*n^2*(Log[d + e*Sqrt[x]]^2*Log[-((e*Sqrt[x])/d)] + 2*Log[d + e*Sqrt[x]]*PolyLog[2, 1 + (e*Sqrt[x])/d] - 2*PolyLog[3, 1 + (e*Sqrt[x])/d])","B",1
412,1,188,155,0.1943003,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])^2/x^2,x]","2 \left(b e n \left(\frac{e \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{2 b d^2 n}-\frac{e \log \left(-\frac{e \sqrt{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{d^2}-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{d \sqrt{x}}-\frac{b e n \text{Li}_2\left(\frac{d+e \sqrt{x}}{d}\right)}{d^2}+\frac{b e n \left(\frac{\log (x)}{2 d}-\frac{\log \left(d+e \sqrt{x}\right)}{d}\right)}{d}\right)-\frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{2 x}\right)","-\frac{2 b e^2 n \log \left(1-\frac{d}{d+e \sqrt{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{d^2}-\frac{2 b e n \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{d^2 \sqrt{x}}-\frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{x}+\frac{2 b^2 e^2 n^2 \text{Li}_2\left(\frac{d}{d+e \sqrt{x}}\right)}{d^2}+\frac{b^2 e^2 n^2 \log (x)}{d^2}",1,"2*(-1/2*(a + b*Log[c*(d + e*Sqrt[x])^n])^2/x + b*e*n*(-((a + b*Log[c*(d + e*Sqrt[x])^n])/(d*Sqrt[x])) + (e*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(2*b*d^2*n) - (e*(a + b*Log[c*(d + e*Sqrt[x])^n])*Log[-((e*Sqrt[x])/d)])/d^2 + (b*e*n*(-(Log[d + e*Sqrt[x]]/d) + Log[x]/(2*d)))/d - (b*e*n*PolyLog[2, (d + e*Sqrt[x])/d])/d^2))","A",1
413,1,353,293,0.362208,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])^2/x^3,x]","-\frac{\frac{e \sqrt{x} \left(4 b d^3 n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)-6 b d^2 e n \sqrt{x} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)-6 e^3 x^{3/2} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2+12 b e^3 n x^{3/2} \log \left(-\frac{e \sqrt{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+12 b d e^2 n x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+12 b^2 e^3 n^2 x^{3/2} \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right)+6 b^2 e^3 n^2 x^{3/2} \left(2 \log \left(d+e \sqrt{x}\right)-\log (x)\right)-3 b^2 e^2 n^2 x \left(-2 e \sqrt{x} \log \left(d+e \sqrt{x}\right)+2 d+e \sqrt{x} \log (x)\right)+2 b^2 e n^2 \sqrt{x} \left(2 e^2 x \log \left(d+e \sqrt{x}\right)+d \left(d-2 e \sqrt{x}\right)-e^2 x \log (x)\right)\right)}{d^4}+6 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{12 x^2}","-\frac{b e^4 n \log \left(1-\frac{d}{d+e \sqrt{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{d^4}-\frac{b e^3 n \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{d^4 \sqrt{x}}+\frac{b e^2 n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{2 d^2 x}-\frac{b e n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{3 d x^{3/2}}-\frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{2 x^2}+\frac{b^2 e^4 n^2 \text{Li}_2\left(\frac{d}{d+e \sqrt{x}}\right)}{d^4}-\frac{5 b^2 e^4 n^2 \log \left(d+e \sqrt{x}\right)}{6 d^4}+\frac{11 b^2 e^4 n^2 \log (x)}{12 d^4}+\frac{5 b^2 e^3 n^2}{6 d^3 \sqrt{x}}-\frac{b^2 e^2 n^2}{6 d^2 x}",1,"-1/12*(6*(a + b*Log[c*(d + e*Sqrt[x])^n])^2 + (e*Sqrt[x]*(4*b*d^3*n*(a + b*Log[c*(d + e*Sqrt[x])^n]) - 6*b*d^2*e*n*Sqrt[x]*(a + b*Log[c*(d + e*Sqrt[x])^n]) + 12*b*d*e^2*n*x*(a + b*Log[c*(d + e*Sqrt[x])^n]) - 6*e^3*x^(3/2)*(a + b*Log[c*(d + e*Sqrt[x])^n])^2 + 12*b*e^3*n*x^(3/2)*(a + b*Log[c*(d + e*Sqrt[x])^n])*Log[-((e*Sqrt[x])/d)] + 6*b^2*e^3*n^2*x^(3/2)*(2*Log[d + e*Sqrt[x]] - Log[x]) - 3*b^2*e^2*n^2*x*(2*d - 2*e*Sqrt[x]*Log[d + e*Sqrt[x]] + e*Sqrt[x]*Log[x]) + 2*b^2*e*n^2*Sqrt[x]*(d*(d - 2*e*Sqrt[x]) + 2*e^2*x*Log[d + e*Sqrt[x]] - e^2*x*Log[x]) + 12*b^2*e^3*n^2*x^(3/2)*PolyLog[2, 1 + (e*Sqrt[x])/d]))/d^4)/x^2","A",1
414,1,538,408,0.2944245,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])^2/x^4,x]","-\frac{60 a^2 d^6-60 a^2 e^6 x^3+120 a b d^6 \log \left(c \left(d+e \sqrt{x}\right)^n\right)-120 a b e^6 x^3 \log \left(c \left(d+e \sqrt{x}\right)^n\right)+24 a b d^5 e n \sqrt{x}-30 a b d^4 e^2 n x+40 a b d^3 e^3 n x^{3/2}-60 a b d^2 e^4 n x^2+120 a b e^6 n x^3 \log \left(-\frac{e \sqrt{x}}{d}\right)+120 a b d e^5 n x^{5/2}+60 b^2 d^6 \log ^2\left(c \left(d+e \sqrt{x}\right)^n\right)+24 b^2 d^5 e n \sqrt{x} \log \left(c \left(d+e \sqrt{x}\right)^n\right)-30 b^2 d^4 e^2 n x \log \left(c \left(d+e \sqrt{x}\right)^n\right)+40 b^2 d^3 e^3 n x^{3/2} \log \left(c \left(d+e \sqrt{x}\right)^n\right)-60 b^2 d^2 e^4 n x^2 \log \left(c \left(d+e \sqrt{x}\right)^n\right)-60 b^2 e^6 x^3 \log ^2\left(c \left(d+e \sqrt{x}\right)^n\right)+120 b^2 e^6 n x^3 \log \left(-\frac{e \sqrt{x}}{d}\right) \log \left(c \left(d+e \sqrt{x}\right)^n\right)+120 b^2 d e^5 n x^{5/2} \log \left(c \left(d+e \sqrt{x}\right)^n\right)+6 b^2 d^4 e^2 n^2 x-18 b^2 d^3 e^3 n^2 x^{3/2}+47 b^2 d^2 e^4 n^2 x^2+120 b^2 e^6 n^2 x^3 \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right)+274 b^2 e^6 n^2 x^3 \log \left(d+e \sqrt{x}\right)-154 b^2 d e^5 n^2 x^{5/2}-137 b^2 e^6 n^2 x^3 \log (x)}{180 d^6 x^3}","-\frac{2 b e^6 n \log \left(1-\frac{d}{d+e \sqrt{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{3 d^6}-\frac{2 b e^5 n \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{3 d^6 \sqrt{x}}+\frac{b e^4 n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{3 d^4 x}-\frac{2 b e^3 n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{9 d^3 x^{3/2}}+\frac{b e^2 n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{6 d^2 x^2}-\frac{2 b e n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{15 d x^{5/2}}-\frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{3 x^3}+\frac{2 b^2 e^6 n^2 \text{Li}_2\left(\frac{d}{d+e \sqrt{x}}\right)}{3 d^6}-\frac{77 b^2 e^6 n^2 \log \left(d+e \sqrt{x}\right)}{90 d^6}+\frac{137 b^2 e^6 n^2 \log (x)}{180 d^6}+\frac{77 b^2 e^5 n^2}{90 d^5 \sqrt{x}}-\frac{47 b^2 e^4 n^2}{180 d^4 x}+\frac{b^2 e^3 n^2}{10 d^3 x^{3/2}}-\frac{b^2 e^2 n^2}{30 d^2 x^2}",1,"-1/180*(60*a^2*d^6 + 24*a*b*d^5*e*n*Sqrt[x] - 30*a*b*d^4*e^2*n*x + 6*b^2*d^4*e^2*n^2*x + 40*a*b*d^3*e^3*n*x^(3/2) - 18*b^2*d^3*e^3*n^2*x^(3/2) - 60*a*b*d^2*e^4*n*x^2 + 47*b^2*d^2*e^4*n^2*x^2 + 120*a*b*d*e^5*n*x^(5/2) - 154*b^2*d*e^5*n^2*x^(5/2) - 60*a^2*e^6*x^3 + 274*b^2*e^6*n^2*x^3*Log[d + e*Sqrt[x]] + 120*a*b*d^6*Log[c*(d + e*Sqrt[x])^n] + 24*b^2*d^5*e*n*Sqrt[x]*Log[c*(d + e*Sqrt[x])^n] - 30*b^2*d^4*e^2*n*x*Log[c*(d + e*Sqrt[x])^n] + 40*b^2*d^3*e^3*n*x^(3/2)*Log[c*(d + e*Sqrt[x])^n] - 60*b^2*d^2*e^4*n*x^2*Log[c*(d + e*Sqrt[x])^n] + 120*b^2*d*e^5*n*x^(5/2)*Log[c*(d + e*Sqrt[x])^n] - 120*a*b*e^6*x^3*Log[c*(d + e*Sqrt[x])^n] + 60*b^2*d^6*Log[c*(d + e*Sqrt[x])^n]^2 - 60*b^2*e^6*x^3*Log[c*(d + e*Sqrt[x])^n]^2 + 120*a*b*e^6*n*x^3*Log[-((e*Sqrt[x])/d)] + 120*b^2*e^6*n*x^3*Log[c*(d + e*Sqrt[x])^n]*Log[-((e*Sqrt[x])/d)] - 137*b^2*e^6*n^2*x^3*Log[x] + 120*b^2*e^6*n^2*x^3*PolyLog[2, 1 + (e*Sqrt[x])/d])/(d^6*x^3)","A",1
415,1,577,907,0.4821276,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \, dx","Integrate[x^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^3,x]","\frac{-36000 a^3 \left(d^6-e^6 x^3\right)-60 b \left(1800 a^2 \left(d^6-e^6 x^3\right)-60 a b n \left(147 d^6+60 d^5 e \sqrt{x}-30 d^4 e^2 x+20 d^3 e^3 x^{3/2}-15 d^2 e^4 x^2+12 d e^5 x^{5/2}-10 e^6 x^3\right)+b^2 n^2 \left(13489 d^6+8820 d^5 e \sqrt{x}-2610 d^4 e^2 x+1140 d^3 e^3 x^{3/2}-555 d^2 e^4 x^2+264 d e^5 x^{5/2}-100 e^6 x^3\right)\right) \log \left(c \left(d+e \sqrt{x}\right)^n\right)+1800 a^2 b n \left(147 d^6+60 d^5 e \sqrt{x}-30 d^4 e^2 x+20 d^3 e^3 x^{3/2}-15 d^2 e^4 x^2+12 d e^5 x^{5/2}-10 e^6 x^3\right)-1800 b^2 \left(60 a \left(d^6-e^6 x^3\right)+b n \left(-147 d^6-60 d^5 e \sqrt{x}+30 d^4 e^2 x-20 d^3 e^3 x^{3/2}+15 d^2 e^4 x^2-12 d e^5 x^{5/2}+10 e^6 x^3\right)\right) \log ^2\left(c \left(d+e \sqrt{x}\right)^n\right)+60 a b^2 n^2 \left(8111 d^6-8820 d^5 e \sqrt{x}+2610 d^4 e^2 x-1140 d^3 e^3 x^{3/2}+555 d^2 e^4 x^2-264 d e^5 x^{5/2}+100 e^6 x^3\right)-36000 b^3 \left(d^6-e^6 x^3\right) \log ^3\left(c \left(d+e \sqrt{x}\right)^n\right)+b^3 e n^3 \sqrt{x} \left(809340 d^5-140070 d^4 e \sqrt{x}+41180 d^3 e^2 x-13785 d^2 e^3 x^{3/2}+4368 d e^4 x^2-1000 e^5 x^{5/2}\right)}{108000 e^6}","-\frac{b^3 n^3 \left(d+e \sqrt{x}\right)^6}{108 e^6}+\frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \left(d+e \sqrt{x}\right)^6}{3 e^6}-\frac{b n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \left(d+e \sqrt{x}\right)^6}{6 e^6}+\frac{b^2 n^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \left(d+e \sqrt{x}\right)^6}{18 e^6}+\frac{12 b^3 d n^3 \left(d+e \sqrt{x}\right)^5}{125 e^6}-\frac{2 d \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \left(d+e \sqrt{x}\right)^5}{e^6}+\frac{6 b d n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \left(d+e \sqrt{x}\right)^5}{5 e^6}-\frac{12 b^2 d n^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \left(d+e \sqrt{x}\right)^5}{25 e^6}-\frac{15 b^3 d^2 n^3 \left(d+e \sqrt{x}\right)^4}{32 e^6}+\frac{5 d^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \left(d+e \sqrt{x}\right)^4}{e^6}-\frac{15 b d^2 n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \left(d+e \sqrt{x}\right)^4}{4 e^6}+\frac{15 b^2 d^2 n^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \left(d+e \sqrt{x}\right)^4}{8 e^6}+\frac{40 b^3 d^3 n^3 \left(d+e \sqrt{x}\right)^3}{27 e^6}-\frac{20 d^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \left(d+e \sqrt{x}\right)^3}{3 e^6}+\frac{20 b d^3 n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \left(d+e \sqrt{x}\right)^3}{3 e^6}-\frac{40 b^2 d^3 n^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \left(d+e \sqrt{x}\right)^3}{9 e^6}-\frac{15 b^3 d^4 n^3 \left(d+e \sqrt{x}\right)^2}{4 e^6}+\frac{5 d^4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \left(d+e \sqrt{x}\right)^2}{e^6}-\frac{15 b d^4 n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \left(d+e \sqrt{x}\right)^2}{2 e^6}+\frac{15 b^2 d^4 n^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \left(d+e \sqrt{x}\right)^2}{2 e^6}-\frac{2 d^5 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \left(d+e \sqrt{x}\right)}{e^6}+\frac{6 b d^5 n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \left(d+e \sqrt{x}\right)}{e^6}-\frac{12 b^3 d^5 n^2 \log \left(c \left(d+e \sqrt{x}\right)^n\right) \left(d+e \sqrt{x}\right)}{e^6}+\frac{12 b^3 d^5 n^3 \sqrt{x}}{e^5}-\frac{12 a b^2 d^5 n^2 \sqrt{x}}{e^5}",1,"(b^3*e*n^3*Sqrt[x]*(809340*d^5 - 140070*d^4*e*Sqrt[x] + 41180*d^3*e^2*x - 13785*d^2*e^3*x^(3/2) + 4368*d*e^4*x^2 - 1000*e^5*x^(5/2)) + 1800*a^2*b*n*(147*d^6 + 60*d^5*e*Sqrt[x] - 30*d^4*e^2*x + 20*d^3*e^3*x^(3/2) - 15*d^2*e^4*x^2 + 12*d*e^5*x^(5/2) - 10*e^6*x^3) - 36000*a^3*(d^6 - e^6*x^3) + 60*a*b^2*n^2*(8111*d^6 - 8820*d^5*e*Sqrt[x] + 2610*d^4*e^2*x - 1140*d^3*e^3*x^(3/2) + 555*d^2*e^4*x^2 - 264*d*e^5*x^(5/2) + 100*e^6*x^3) - 60*b*(b^2*n^2*(13489*d^6 + 8820*d^5*e*Sqrt[x] - 2610*d^4*e^2*x + 1140*d^3*e^3*x^(3/2) - 555*d^2*e^4*x^2 + 264*d*e^5*x^(5/2) - 100*e^6*x^3) - 60*a*b*n*(147*d^6 + 60*d^5*e*Sqrt[x] - 30*d^4*e^2*x + 20*d^3*e^3*x^(3/2) - 15*d^2*e^4*x^2 + 12*d*e^5*x^(5/2) - 10*e^6*x^3) + 1800*a^2*(d^6 - e^6*x^3))*Log[c*(d + e*Sqrt[x])^n] - 1800*b^2*(60*a*(d^6 - e^6*x^3) + b*n*(-147*d^6 - 60*d^5*e*Sqrt[x] + 30*d^4*e^2*x - 20*d^3*e^3*x^(3/2) + 15*d^2*e^4*x^2 - 12*d*e^5*x^(5/2) + 10*e^6*x^3))*Log[c*(d + e*Sqrt[x])^n]^2 - 36000*b^3*(d^6 - e^6*x^3)*Log[c*(d + e*Sqrt[x])^n]^3)/(108000*e^6)","A",1
416,1,433,595,0.3054634,"\int x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \, dx","Integrate[x*(a + b*Log[c*(d + e*Sqrt[x])^n])^3,x]","\frac{-288 a^3 \left(d^4-e^4 x^2\right)-12 b \left(72 a^2 \left(d^4-e^4 x^2\right)-12 a b n \left(25 d^4+12 d^3 e \sqrt{x}-6 d^2 e^2 x+4 d e^3 x^{3/2}-3 e^4 x^2\right)+b^2 n^2 \left(415 d^4+300 d^3 e \sqrt{x}-78 d^2 e^2 x+28 d e^3 x^{3/2}-9 e^4 x^2\right)\right) \log \left(c \left(d+e \sqrt{x}\right)^n\right)+72 a^2 b n \left(25 d^4+12 d^3 e \sqrt{x}-6 d^2 e^2 x+4 d e^3 x^{3/2}-3 e^4 x^2\right)-72 b^2 \left(12 a \left(d^4-e^4 x^2\right)+b n \left(-25 d^4-12 d^3 e \sqrt{x}+6 d^2 e^2 x-4 d e^3 x^{3/2}+3 e^4 x^2\right)\right) \log ^2\left(c \left(d+e \sqrt{x}\right)^n\right)+12 a b^2 n^2 \left(161 d^4-300 d^3 e \sqrt{x}+78 d^2 e^2 x-28 d e^3 x^{3/2}+9 e^4 x^2\right)-288 b^3 \left(d^4-e^4 x^2\right) \log ^3\left(c \left(d+e \sqrt{x}\right)^n\right)+b^3 e n^3 \sqrt{x} \left(4980 d^3-690 d^2 e \sqrt{x}+148 d e^2 x-27 e^3 x^{3/2}\right)}{576 e^4}","\frac{9 b^2 d^2 n^2 \left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{2 e^4}+\frac{3 b^2 n^2 \left(d+e \sqrt{x}\right)^4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{16 e^4}-\frac{4 b^2 d n^2 \left(d+e \sqrt{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{3 e^4}-\frac{12 a b^2 d^3 n^2 \sqrt{x}}{e^3}-\frac{2 d^3 \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{e^4}+\frac{6 b d^3 n \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{e^4}+\frac{3 d^2 \left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{e^4}-\frac{9 b d^2 n \left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{2 e^4}+\frac{\left(d+e \sqrt{x}\right)^4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{2 e^4}-\frac{3 b n \left(d+e \sqrt{x}\right)^4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{8 e^4}-\frac{2 d \left(d+e \sqrt{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{e^4}+\frac{2 b d n \left(d+e \sqrt{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{e^4}-\frac{12 b^3 d^3 n^2 \left(d+e \sqrt{x}\right) \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{e^4}+\frac{12 b^3 d^3 n^3 \sqrt{x}}{e^3}-\frac{9 b^3 d^2 n^3 \left(d+e \sqrt{x}\right)^2}{4 e^4}-\frac{3 b^3 n^3 \left(d+e \sqrt{x}\right)^4}{64 e^4}+\frac{4 b^3 d n^3 \left(d+e \sqrt{x}\right)^3}{9 e^4}",1,"(b^3*e*n^3*Sqrt[x]*(4980*d^3 - 690*d^2*e*Sqrt[x] + 148*d*e^2*x - 27*e^3*x^(3/2)) + 72*a^2*b*n*(25*d^4 + 12*d^3*e*Sqrt[x] - 6*d^2*e^2*x + 4*d*e^3*x^(3/2) - 3*e^4*x^2) - 288*a^3*(d^4 - e^4*x^2) + 12*a*b^2*n^2*(161*d^4 - 300*d^3*e*Sqrt[x] + 78*d^2*e^2*x - 28*d*e^3*x^(3/2) + 9*e^4*x^2) - 12*b*(b^2*n^2*(415*d^4 + 300*d^3*e*Sqrt[x] - 78*d^2*e^2*x + 28*d*e^3*x^(3/2) - 9*e^4*x^2) - 12*a*b*n*(25*d^4 + 12*d^3*e*Sqrt[x] - 6*d^2*e^2*x + 4*d*e^3*x^(3/2) - 3*e^4*x^2) + 72*a^2*(d^4 - e^4*x^2))*Log[c*(d + e*Sqrt[x])^n] - 72*b^2*(12*a*(d^4 - e^4*x^2) + b*n*(-25*d^4 - 12*d^3*e*Sqrt[x] + 6*d^2*e^2*x - 4*d*e^3*x^(3/2) + 3*e^4*x^2))*Log[c*(d + e*Sqrt[x])^n]^2 - 288*b^3*(d^4 - e^4*x^2)*Log[c*(d + e*Sqrt[x])^n]^3)/(576*e^4)","A",1
417,1,241,284,0.2117994,"\int \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])^3,x]","\frac{4 \left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3-8 d \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3+24 b d n \left(\left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2-2 b n \left(e \sqrt{x} (a-b n)+b \left(d+e \sqrt{x}\right) \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)\right)-3 b n \left(2 \left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2+b n \left(b e n \left(2 d \sqrt{x}+e x\right)-2 \left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)\right)\right)}{4 e^2}","\frac{3 b^2 n^2 \left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{2 e^2}-\frac{12 a b^2 d n^2 \sqrt{x}}{e}-\frac{3 b n \left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{2 e^2}+\frac{6 b d n \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{e^2}+\frac{\left(d+e \sqrt{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{e^2}-\frac{2 d \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{e^2}-\frac{12 b^3 d n^2 \left(d+e \sqrt{x}\right) \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{e^2}-\frac{3 b^3 n^3 \left(d+e \sqrt{x}\right)^2}{4 e^2}+\frac{12 b^3 d n^3 \sqrt{x}}{e}",1,"(-8*d*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n])^3 + 4*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^3 + 24*b*d*n*((d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n])^2 - 2*b*n*(e*(a - b*n)*Sqrt[x] + b*(d + e*Sqrt[x])*Log[c*(d + e*Sqrt[x])^n])) - 3*b*n*(2*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^2 + b*n*(b*e*n*(2*d*Sqrt[x] + e*x) - 2*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n]))))/(4*e^2)","A",1
418,1,333,135,0.1675345,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{x} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])^3/x,x]","6 b^2 n^2 \left(-2 \text{Li}_3\left(\frac{\sqrt{x} e}{d}+1\right)+2 \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right) \log \left(d+e \sqrt{x}\right)+\log \left(-\frac{e \sqrt{x}}{d}\right) \log ^2\left(d+e \sqrt{x}\right)\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)-b n \log \left(d+e \sqrt{x}\right)\right)+3 b n \left(\log (x) \left(\log \left(d+e \sqrt{x}\right)-\log \left(\frac{e \sqrt{x}}{d}+1\right)\right)-2 \text{Li}_2\left(-\frac{e \sqrt{x}}{d}\right)\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)-b n \log \left(d+e \sqrt{x}\right)\right)^2+\log (x) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)-b n \log \left(d+e \sqrt{x}\right)\right)^3+2 b^3 n^3 \left(6 \text{Li}_4\left(\frac{\sqrt{x} e}{d}+1\right)+3 \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right) \log ^2\left(d+e \sqrt{x}\right)-6 \text{Li}_3\left(\frac{\sqrt{x} e}{d}+1\right) \log \left(d+e \sqrt{x}\right)+\log \left(-\frac{e \sqrt{x}}{d}\right) \log ^3\left(d+e \sqrt{x}\right)\right)","-12 b^2 n^2 \text{Li}_3\left(\frac{\sqrt{x} e}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+6 b n \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2+2 \log \left(-\frac{e \sqrt{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3+12 b^3 n^3 \text{Li}_4\left(\frac{\sqrt{x} e}{d}+1\right)",1,"(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^3*Log[x] + 3*b*n*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2*((Log[d + e*Sqrt[x]] - Log[1 + (e*Sqrt[x])/d])*Log[x] - 2*PolyLog[2, -((e*Sqrt[x])/d)]) + 6*b^2*n^2*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])*(Log[d + e*Sqrt[x]]^2*Log[-((e*Sqrt[x])/d)] + 2*Log[d + e*Sqrt[x]]*PolyLog[2, 1 + (e*Sqrt[x])/d] - 2*PolyLog[3, 1 + (e*Sqrt[x])/d]) + 2*b^3*n^3*(Log[d + e*Sqrt[x]]^3*Log[-((e*Sqrt[x])/d)] + 3*Log[d + e*Sqrt[x]]^2*PolyLog[2, 1 + (e*Sqrt[x])/d] - 6*Log[d + e*Sqrt[x]]*PolyLog[3, 1 + (e*Sqrt[x])/d] + 6*PolyLog[4, 1 + (e*Sqrt[x])/d])","B",1
419,1,536,263,0.7531627,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])^3/x^2,x]","\frac{3 b^2 n^2 \left(-2 e^2 x \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right)-2 e^2 x \left(\log \left(d+e \sqrt{x}\right)-1\right) \log \left(-\frac{e \sqrt{x}}{d}\right)+\left(d+e \sqrt{x}\right) \log \left(d+e \sqrt{x}\right) \left(\left(e \sqrt{x}-d\right) \log \left(d+e \sqrt{x}\right)-2 e \sqrt{x}\right)\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)-b n \log \left(d+e \sqrt{x}\right)\right)-3 b d^2 n \log \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)-b n \log \left(d+e \sqrt{x}\right)\right)^2-d^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)-b n \log \left(d+e \sqrt{x}\right)\right)^3+3 b e^2 n x \log \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)-b n \log \left(d+e \sqrt{x}\right)\right)^2-\frac{3}{2} b e^2 n x \log (x) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)-b n \log \left(d+e \sqrt{x}\right)\right)^2-3 b d e n \sqrt{x} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)-b n \log \left(d+e \sqrt{x}\right)\right)^2+b^3 n^3 \left(6 e^2 x \text{Li}_3\left(\frac{\sqrt{x} e}{d}+1\right)-6 e^2 x \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right) \left(\log \left(d+e \sqrt{x}\right)-1\right)-3 e^2 x \left(\log \left(d+e \sqrt{x}\right)-2\right) \log \left(d+e \sqrt{x}\right) \log \left(-\frac{e \sqrt{x}}{d}\right)+\left(d+e \sqrt{x}\right) \log ^2\left(d+e \sqrt{x}\right) \left(\left(e \sqrt{x}-d\right) \log \left(d+e \sqrt{x}\right)-3 e \sqrt{x}\right)\right)}{d^2 x}","\frac{6 b^2 e^2 n^2 \text{Li}_2\left(\frac{d}{d+e \sqrt{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{d^2}+\frac{6 b^2 e^2 n^2 \log \left(-\frac{e \sqrt{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{d^2}-\frac{3 b e^2 n \log \left(1-\frac{d}{d+e \sqrt{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{d^2}-\frac{3 b e n \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{d^2 \sqrt{x}}-\frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{x}+\frac{6 b^3 e^2 n^3 \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right)}{d^2}+\frac{6 b^3 e^2 n^3 \text{Li}_3\left(\frac{d}{d+e \sqrt{x}}\right)}{d^2}",1,"(-3*b*d*e*n*Sqrt[x]*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2 - 3*b*d^2*n*Log[d + e*Sqrt[x]]*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2 + 3*b*e^2*n*x*Log[d + e*Sqrt[x]]*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2 - d^2*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^3 - (3*b*e^2*n*x*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2*Log[x])/2 + 3*b^2*n^2*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])*((d + e*Sqrt[x])*Log[d + e*Sqrt[x]]*(-2*e*Sqrt[x] + (-d + e*Sqrt[x])*Log[d + e*Sqrt[x]]) - 2*e^2*x*(-1 + Log[d + e*Sqrt[x]])*Log[-((e*Sqrt[x])/d)] - 2*e^2*x*PolyLog[2, 1 + (e*Sqrt[x])/d]) + b^3*n^3*((d + e*Sqrt[x])*Log[d + e*Sqrt[x]]^2*(-3*e*Sqrt[x] + (-d + e*Sqrt[x])*Log[d + e*Sqrt[x]]) - 3*e^2*x*(-2 + Log[d + e*Sqrt[x]])*Log[d + e*Sqrt[x]]*Log[-((e*Sqrt[x])/d)] - 6*e^2*x*(-1 + Log[d + e*Sqrt[x]])*PolyLog[2, 1 + (e*Sqrt[x])/d] + 6*e^2*x*PolyLog[3, 1 + (e*Sqrt[x])/d]))/(d^2*x)","B",1
420,1,841,573,1.1673345,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^n])^3/x^3,x]","-\frac{2 \left(a-b n \log \left(d+e \sqrt{x}\right)+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 d^4+6 b n \log \left(d+e \sqrt{x}\right) \left(a-b n \log \left(d+e \sqrt{x}\right)+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 d^4+2 b e n \sqrt{x} \left(a-b n \log \left(d+e \sqrt{x}\right)+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 d^3-3 b e^2 n x \left(a-b n \log \left(d+e \sqrt{x}\right)+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 d^2+6 b e^3 n x^{3/2} \left(a-b n \log \left(d+e \sqrt{x}\right)+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 d-6 b e^4 n x^2 \log \left(d+e \sqrt{x}\right) \left(a-b n \log \left(d+e \sqrt{x}\right)+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2+3 b e^4 n x^2 \left(a-b n \log \left(d+e \sqrt{x}\right)+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \log (x)-2 b^2 n^2 \left(a-b n \log \left(d+e \sqrt{x}\right)+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \left(-6 x^2 \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right) e^4+x \left(-d^2+5 e \sqrt{x} d+11 e^2 x \log \left(-\frac{e \sqrt{x}}{d}\right)\right) e^2-3 \left(d^4-e^4 x^2\right) \log ^2\left(d+e \sqrt{x}\right)-\log \left(d+e \sqrt{x}\right) \left(11 x^2 e^4+6 x^2 \log \left(-\frac{e \sqrt{x}}{d}\right) e^4+6 d x^{3/2} e^3-3 d^2 x e^2+2 d^3 \sqrt{x} e\right)\right)+b^3 n^3 \left(2 \log ^3\left(d+e \sqrt{x}\right) d^4+2 e \sqrt{x} \log ^2\left(d+e \sqrt{x}\right) d^3+e^2 x \left(2-3 \log \left(d+e \sqrt{x}\right)\right) \log \left(d+e \sqrt{x}\right) d^2+2 e^3 x^{3/2} \left(3 \log ^2\left(d+e \sqrt{x}\right)-5 \log \left(d+e \sqrt{x}\right)+1\right) d+12 e^4 x^2 \left(\log \left(-\frac{e \sqrt{x}}{d}\right)-\log \left(d+e \sqrt{x}\right)\right)+11 e^4 x^2 \left(\log \left(d+e \sqrt{x}\right) \left(\log \left(d+e \sqrt{x}\right)-2 \log \left(-\frac{e \sqrt{x}}{d}\right)\right)-2 \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right)\right)-2 e^4 x^2 \left(\left(\log \left(d+e \sqrt{x}\right)-3 \log \left(-\frac{e \sqrt{x}}{d}\right)\right) \log ^2\left(d+e \sqrt{x}\right)-6 \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right) \log \left(d+e \sqrt{x}\right)+6 \text{Li}_3\left(\frac{\sqrt{x} e}{d}+1\right)\right)\right)}{4 d^4 x^2}","\frac{3 b^2 e^4 n^2 \text{Li}_2\left(\frac{d}{d+e \sqrt{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{d^4}+\frac{5 b^2 e^4 n^2 \log \left(1-\frac{d}{d+e \sqrt{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{2 d^4}+\frac{3 b^2 e^4 n^2 \log \left(-\frac{e \sqrt{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{d^4}+\frac{5 b^2 e^3 n^2 \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{2 d^4 \sqrt{x}}-\frac{b^2 e^2 n^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{2 d^2 x}-\frac{3 b e^4 n \log \left(1-\frac{d}{d+e \sqrt{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{2 d^4}-\frac{3 b e^3 n \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{2 d^4 \sqrt{x}}+\frac{3 b e^2 n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{4 d^2 x}-\frac{b e n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{2 d x^{3/2}}-\frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{2 x^2}-\frac{5 b^3 e^4 n^3 \text{Li}_2\left(\frac{d}{d+e \sqrt{x}}\right)}{2 d^4}+\frac{3 b^3 e^4 n^3 \text{Li}_2\left(\frac{\sqrt{x} e}{d}+1\right)}{d^4}+\frac{3 b^3 e^4 n^3 \text{Li}_3\left(\frac{d}{d+e \sqrt{x}}\right)}{d^4}+\frac{b^3 e^4 n^3 \log \left(d+e \sqrt{x}\right)}{2 d^4}-\frac{3 b^3 e^4 n^3 \log (x)}{2 d^4}-\frac{b^3 e^3 n^3}{2 d^3 \sqrt{x}}",1,"-1/4*(2*b*d^3*e*n*Sqrt[x]*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2 - 3*b*d^2*e^2*n*x*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2 + 6*b*d*e^3*n*x^(3/2)*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2 + 6*b*d^4*n*Log[d + e*Sqrt[x]]*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2 - 6*b*e^4*n*x^2*Log[d + e*Sqrt[x]]*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2 + 2*d^4*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^3 + 3*b*e^4*n*x^2*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])^2*Log[x] - 2*b^2*n^2*(a - b*n*Log[d + e*Sqrt[x]] + b*Log[c*(d + e*Sqrt[x])^n])*(-3*(d^4 - e^4*x^2)*Log[d + e*Sqrt[x]]^2 + e^2*x*(-d^2 + 5*d*e*Sqrt[x] + 11*e^2*x*Log[-((e*Sqrt[x])/d)]) - Log[d + e*Sqrt[x]]*(2*d^3*e*Sqrt[x] - 3*d^2*e^2*x + 6*d*e^3*x^(3/2) + 11*e^4*x^2 + 6*e^4*x^2*Log[-((e*Sqrt[x])/d)]) - 6*e^4*x^2*PolyLog[2, 1 + (e*Sqrt[x])/d]) + b^3*n^3*(d^2*e^2*x*(2 - 3*Log[d + e*Sqrt[x]])*Log[d + e*Sqrt[x]] + 2*d^3*e*Sqrt[x]*Log[d + e*Sqrt[x]]^2 + 2*d^4*Log[d + e*Sqrt[x]]^3 + 2*d*e^3*x^(3/2)*(1 - 5*Log[d + e*Sqrt[x]] + 3*Log[d + e*Sqrt[x]]^2) + 12*e^4*x^2*(-Log[d + e*Sqrt[x]] + Log[-((e*Sqrt[x])/d)]) + 11*e^4*x^2*(Log[d + e*Sqrt[x]]*(Log[d + e*Sqrt[x]] - 2*Log[-((e*Sqrt[x])/d)]) - 2*PolyLog[2, 1 + (e*Sqrt[x])/d]) - 2*e^4*x^2*(Log[d + e*Sqrt[x]]^2*(Log[d + e*Sqrt[x]] - 3*Log[-((e*Sqrt[x])/d)]) - 6*Log[d + e*Sqrt[x]]*PolyLog[2, 1 + (e*Sqrt[x])/d] + 6*PolyLog[3, 1 + (e*Sqrt[x])/d])))/(d^4*x^2)","A",1
421,1,158,171,0.1377037,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \, dx","Integrate[x^3*(a + b*Log[c*(d + e/Sqrt[x])^n]),x]","\frac{a x^4}{4}+\frac{1}{4} b x^4 \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-\frac{1}{4} b e n \left(\frac{e^7 \log \left(d+\frac{e}{\sqrt{x}}\right)}{d^8}+\frac{e^7 \log (x)}{2 d^8}-\frac{e^6 \sqrt{x}}{d^7}+\frac{e^5 x}{2 d^6}-\frac{e^4 x^{3/2}}{3 d^5}+\frac{e^3 x^2}{4 d^4}-\frac{e^2 x^{5/2}}{5 d^3}+\frac{e x^3}{6 d^2}-\frac{x^{7/2}}{7 d}\right)","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)-\frac{b e^8 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{4 d^8}-\frac{b e^8 n \log (x)}{8 d^8}+\frac{b e^7 n \sqrt{x}}{4 d^7}-\frac{b e^6 n x}{8 d^6}+\frac{b e^5 n x^{3/2}}{12 d^5}-\frac{b e^4 n x^2}{16 d^4}+\frac{b e^3 n x^{5/2}}{20 d^3}-\frac{b e^2 n x^3}{24 d^2}+\frac{b e n x^{7/2}}{28 d}",1,"(a*x^4)/4 + (b*x^4*Log[c*(d + e/Sqrt[x])^n])/4 - (b*e*n*(-((e^6*Sqrt[x])/d^7) + (e^5*x)/(2*d^6) - (e^4*x^(3/2))/(3*d^5) + (e^3*x^2)/(4*d^4) - (e^2*x^(5/2))/(5*d^3) + (e*x^3)/(6*d^2) - x^(7/2)/(7*d) + (e^7*Log[d + e/Sqrt[x]])/d^8 + (e^7*Log[x])/(2*d^8)))/4","A",1
422,1,130,139,0.0891203,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*(d + e/Sqrt[x])^n]),x]","\frac{a x^3}{3}+\frac{1}{3} b x^3 \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-\frac{1}{3} b e n \left(\frac{e^5 \log \left(d+\frac{e}{\sqrt{x}}\right)}{d^6}+\frac{e^5 \log (x)}{2 d^6}-\frac{e^4 \sqrt{x}}{d^5}+\frac{e^3 x}{2 d^4}-\frac{e^2 x^{3/2}}{3 d^3}+\frac{e x^2}{4 d^2}-\frac{x^{5/2}}{5 d}\right)","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)-\frac{b e^6 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{3 d^6}-\frac{b e^6 n \log (x)}{6 d^6}+\frac{b e^5 n \sqrt{x}}{3 d^5}-\frac{b e^4 n x}{6 d^4}+\frac{b e^3 n x^{3/2}}{9 d^3}-\frac{b e^2 n x^2}{12 d^2}+\frac{b e n x^{5/2}}{15 d}",1,"(a*x^3)/3 + (b*x^3*Log[c*(d + e/Sqrt[x])^n])/3 - (b*e*n*(-((e^4*Sqrt[x])/d^5) + (e^3*x)/(2*d^4) - (e^2*x^(3/2))/(3*d^3) + (e*x^2)/(4*d^2) - x^(5/2)/(5*d) + (e^5*Log[d + e/Sqrt[x]])/d^6 + (e^5*Log[x])/(2*d^6)))/3","A",1
423,1,102,107,0.0289367,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \, dx","Integrate[x*(a + b*Log[c*(d + e/Sqrt[x])^n]),x]","\frac{a x^2}{2}+\frac{1}{2} b x^2 \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-\frac{1}{2} b e n \left(\frac{e^3 \log \left(d+\frac{e}{\sqrt{x}}\right)}{d^4}+\frac{e^3 \log (x)}{2 d^4}-\frac{e^2 \sqrt{x}}{d^3}+\frac{e x}{2 d^2}-\frac{x^{3/2}}{3 d}\right)","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)-\frac{b e^4 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{2 d^4}-\frac{b e^4 n \log (x)}{4 d^4}+\frac{b e^3 n \sqrt{x}}{2 d^3}-\frac{b e^2 n x}{4 d^2}+\frac{b e n x^{3/2}}{6 d}",1,"(a*x^2)/2 + (b*x^2*Log[c*(d + e/Sqrt[x])^n])/2 - (b*e*n*(-((e^2*Sqrt[x])/d^3) + (e*x)/(2*d^2) - x^(3/2)/(3*d) + (e^3*Log[d + e/Sqrt[x]])/d^4 + (e^3*Log[x])/(2*d^4)))/2","A",1
424,1,62,53,0.0329078,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \, dx","Integrate[a + b*Log[c*(d + e/Sqrt[x])^n],x]","a x+b x \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b e n \left(\frac{e \log \left(d+\frac{e}{\sqrt{x}}\right)}{d^2}+\frac{e \log (x)}{2 d^2}-\frac{\sqrt{x}}{d}\right)","a x+b x \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-\frac{b e^2 n \log \left(d \sqrt{x}+e\right)}{d^2}+\frac{b e n \sqrt{x}}{d}",1,"a*x + b*x*Log[c*(d + e/Sqrt[x])^n] - b*e*n*(-(Sqrt[x]/d) + (e*Log[d + e/Sqrt[x]])/d^2 + (e*Log[x])/(2*d^2))","A",1
425,1,53,51,0.0031498,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{x} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])/x,x]","a \log (x)-2 b \log \left(-\frac{e}{d \sqrt{x}}\right) \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-2 b n \text{Li}_2\left(\frac{d+\frac{e}{\sqrt{x}}}{d}\right)","-2 \log \left(-\frac{e}{d \sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)-2 b n \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right)",1,"-2*b*Log[c*(d + e/Sqrt[x])^n]*Log[-(e/(d*Sqrt[x]))] + a*Log[x] - 2*b*n*PolyLog[2, (d + e/Sqrt[x])/d]","A",1
426,1,68,65,0.0346121,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])/x^2,x]","-\frac{a}{x}-\frac{b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{x}+\frac{b d^2 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{e^2}-\frac{b d n}{e \sqrt{x}}+\frac{b n}{2 x}","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{x}+\frac{b d^2 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{e^2}-\frac{b d n}{e \sqrt{x}}+\frac{b n}{2 x}",1,"-(a/x) + (b*n)/(2*x) - (b*d*n)/(e*Sqrt[x]) + (b*d^2*n*Log[d + e/Sqrt[x]])/e^2 - (b*Log[c*(d + e/Sqrt[x])^n])/x","A",1
427,1,109,104,0.0708751,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])/x^3,x]","-\frac{a}{2 x^2}-\frac{b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{2 x^2}+\frac{b d^4 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{2 e^4}-\frac{b d^3 n}{2 e^3 \sqrt{x}}+\frac{b d^2 n}{4 e^2 x}-\frac{b d n}{6 e x^{3/2}}+\frac{b n}{8 x^2}","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{2 x^2}+\frac{b d^4 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{2 e^4}-\frac{b d^3 n}{2 e^3 \sqrt{x}}+\frac{b d^2 n}{4 e^2 x}-\frac{b d n}{6 e x^{3/2}}+\frac{b n}{8 x^2}",1,"-1/2*a/x^2 + (b*n)/(8*x^2) - (b*d*n)/(6*e*x^(3/2)) + (b*d^2*n)/(4*e^2*x) - (b*d^3*n)/(2*e^3*Sqrt[x]) + (b*d^4*n*Log[d + e/Sqrt[x]])/(2*e^4) - (b*Log[c*(d + e/Sqrt[x])^n])/(2*x^2)","A",1
428,1,133,136,0.0947078,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])/x^4,x]","-\frac{a}{3 x^3}-\frac{b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{3 x^3}+\frac{1}{3} b e n \left(\frac{d^6 \log \left(d+\frac{e}{\sqrt{x}}\right)}{e^7}-\frac{d^5}{e^6 \sqrt{x}}+\frac{d^4}{2 e^5 x}-\frac{d^3}{3 e^4 x^{3/2}}+\frac{d^2}{4 e^3 x^2}-\frac{d}{5 e^2 x^{5/2}}+\frac{1}{6 e x^3}\right)","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{3 x^3}+\frac{b d^6 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{3 e^6}-\frac{b d^5 n}{3 e^5 \sqrt{x}}+\frac{b d^4 n}{6 e^4 x}-\frac{b d^3 n}{9 e^3 x^{3/2}}+\frac{b d^2 n}{12 e^2 x^2}-\frac{b d n}{15 e x^{5/2}}+\frac{b n}{18 x^3}",1,"-1/3*a/x^3 + (b*e*n*(1/(6*e*x^3) - d/(5*e^2*x^(5/2)) + d^2/(4*e^3*x^2) - d^3/(3*e^4*x^(3/2)) + d^4/(2*e^5*x) - d^5/(e^6*Sqrt[x]) + (d^6*Log[d + e/Sqrt[x]])/e^7))/3 - (b*Log[c*(d + e/Sqrt[x])^n])/(3*x^3)","A",1
429,1,540,404,0.2729324,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \, dx","Integrate[x^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^2,x]","\frac{60 a^2 d^6 x^3+120 a b d^6 x^3 \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+24 a b d^5 e n x^{5/2}-30 a b d^4 e^2 n x^2+40 a b d^3 e^3 n x^{3/2}-60 a b d^2 e^4 n x-120 a b e^6 n \log \left(d \sqrt{x}+e\right)+120 a b d e^5 n \sqrt{x}+60 b^2 d^6 x^3 \log ^2\left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+24 b^2 d^5 e n x^{5/2} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-30 b^2 d^4 e^2 n x^2 \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+40 b^2 d^3 e^3 n x^{3/2} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-60 b^2 d^2 e^4 n x \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-120 b^2 e^6 n \log \left(d \sqrt{x}+e\right) \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+120 b^2 d e^5 n \sqrt{x} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+6 b^2 d^4 e^2 n^2 x^2-18 b^2 d^3 e^3 n^2 x^{3/2}+47 b^2 d^2 e^4 n^2 x-120 b^2 e^6 n^2 \text{Li}_2\left(\frac{\sqrt{x} d}{e}+1\right)+60 b^2 e^6 n^2 \log ^2\left(d \sqrt{x}+e\right)+214 b^2 e^6 n^2 \log \left(d+\frac{e}{\sqrt{x}}\right)+60 b^2 e^6 n^2 \log \left(d \sqrt{x}+e\right)-120 b^2 e^6 n^2 \log \left(d \sqrt{x}+e\right) \log \left(-\frac{d \sqrt{x}}{e}\right)-154 b^2 d e^5 n^2 \sqrt{x}+107 b^2 e^6 n^2 \log (x)}{180 d^6}","\frac{2 b e^6 n \log \left(1-\frac{d}{d+\frac{e}{\sqrt{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{3 d^6}+\frac{2 b e^5 n \sqrt{x} \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{3 d^6}-\frac{b e^4 n x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{3 d^4}+\frac{2 b e^3 n x^{3/2} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{9 d^3}-\frac{b e^2 n x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{6 d^2}+\frac{2 b e n x^{5/2} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{15 d}+\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2-\frac{2 b^2 e^6 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt{x}}}\right)}{3 d^6}+\frac{77 b^2 e^6 n^2 \log \left(d+\frac{e}{\sqrt{x}}\right)}{90 d^6}+\frac{137 b^2 e^6 n^2 \log (x)}{180 d^6}-\frac{77 b^2 e^5 n^2 \sqrt{x}}{90 d^5}+\frac{47 b^2 e^4 n^2 x}{180 d^4}-\frac{b^2 e^3 n^2 x^{3/2}}{10 d^3}+\frac{b^2 e^2 n^2 x^2}{30 d^2}",1,"(120*a*b*d*e^5*n*Sqrt[x] - 154*b^2*d*e^5*n^2*Sqrt[x] - 60*a*b*d^2*e^4*n*x + 47*b^2*d^2*e^4*n^2*x + 40*a*b*d^3*e^3*n*x^(3/2) - 18*b^2*d^3*e^3*n^2*x^(3/2) - 30*a*b*d^4*e^2*n*x^2 + 6*b^2*d^4*e^2*n^2*x^2 + 24*a*b*d^5*e*n*x^(5/2) + 60*a^2*d^6*x^3 + 214*b^2*e^6*n^2*Log[d + e/Sqrt[x]] + 120*b^2*d*e^5*n*Sqrt[x]*Log[c*(d + e/Sqrt[x])^n] - 60*b^2*d^2*e^4*n*x*Log[c*(d + e/Sqrt[x])^n] + 40*b^2*d^3*e^3*n*x^(3/2)*Log[c*(d + e/Sqrt[x])^n] - 30*b^2*d^4*e^2*n*x^2*Log[c*(d + e/Sqrt[x])^n] + 24*b^2*d^5*e*n*x^(5/2)*Log[c*(d + e/Sqrt[x])^n] + 120*a*b*d^6*x^3*Log[c*(d + e/Sqrt[x])^n] + 60*b^2*d^6*x^3*Log[c*(d + e/Sqrt[x])^n]^2 - 120*a*b*e^6*n*Log[e + d*Sqrt[x]] + 60*b^2*e^6*n^2*Log[e + d*Sqrt[x]] - 120*b^2*e^6*n*Log[c*(d + e/Sqrt[x])^n]*Log[e + d*Sqrt[x]] + 60*b^2*e^6*n^2*Log[e + d*Sqrt[x]]^2 - 120*b^2*e^6*n^2*Log[e + d*Sqrt[x]]*Log[-((d*Sqrt[x])/e)] + 107*b^2*e^6*n^2*Log[x] - 120*b^2*e^6*n^2*PolyLog[2, 1 + (d*Sqrt[x])/e])/(180*d^6)","A",1
430,1,321,288,0.2320601,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \, dx","Integrate[x*(a + b*Log[c*(d + e/Sqrt[x])^n])^2,x]","\frac{1}{6} \left(\frac{b e n \left(2 a d^3 x^{3/2}-3 a d^2 e x-6 a e^3 \log \left(d \sqrt{x}+e\right)+6 a d e^2 \sqrt{x}+2 b d^3 x^{3/2} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-3 b d^2 e x \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-6 b e^3 \log \left(d \sqrt{x}+e\right) \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+6 b d e^2 \sqrt{x} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+b d^2 e n x-6 b e^3 n \text{Li}_2\left(\frac{\sqrt{x} d}{e}+1\right)+3 b e^3 n \log ^2\left(d \sqrt{x}+e\right)+8 b e^3 n \log \left(d+\frac{e}{\sqrt{x}}\right)+3 b e^3 n \log \left(d \sqrt{x}+e\right)-6 b e^3 n \log \left(d \sqrt{x}+e\right) \log \left(-\frac{d \sqrt{x}}{e}\right)-5 b d e^2 n \sqrt{x}+4 b e^3 n \log (x)\right)}{d^4}+3 x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2\right)","\frac{b e^4 n \log \left(1-\frac{d}{d+\frac{e}{\sqrt{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{d^4}+\frac{b e^3 n \sqrt{x} \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{d^4}-\frac{b e^2 n x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{2 d^2}+\frac{b e n x^{3/2} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{3 d}+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2-\frac{b^2 e^4 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt{x}}}\right)}{d^4}+\frac{5 b^2 e^4 n^2 \log \left(d+\frac{e}{\sqrt{x}}\right)}{6 d^4}+\frac{11 b^2 e^4 n^2 \log (x)}{12 d^4}-\frac{5 b^2 e^3 n^2 \sqrt{x}}{6 d^3}+\frac{b^2 e^2 n^2 x}{6 d^2}",1,"(3*x^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^2 + (b*e*n*(6*a*d*e^2*Sqrt[x] - 5*b*d*e^2*n*Sqrt[x] - 3*a*d^2*e*x + b*d^2*e*n*x + 2*a*d^3*x^(3/2) + 8*b*e^3*n*Log[d + e/Sqrt[x]] + 6*b*d*e^2*Sqrt[x]*Log[c*(d + e/Sqrt[x])^n] - 3*b*d^2*e*x*Log[c*(d + e/Sqrt[x])^n] + 2*b*d^3*x^(3/2)*Log[c*(d + e/Sqrt[x])^n] - 6*a*e^3*Log[e + d*Sqrt[x]] + 3*b*e^3*n*Log[e + d*Sqrt[x]] - 6*b*e^3*Log[c*(d + e/Sqrt[x])^n]*Log[e + d*Sqrt[x]] + 3*b*e^3*n*Log[e + d*Sqrt[x]]^2 - 6*b*e^3*n*Log[e + d*Sqrt[x]]*Log[-((d*Sqrt[x])/e)] + 4*b*e^3*n*Log[x] - 6*b*e^3*n*PolyLog[2, 1 + (d*Sqrt[x])/e]))/d^4)/6","A",1
431,1,170,152,0.1337995,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])^2,x]","\frac{b e n \left(-2 e \log \left(d \sqrt{x}+e\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)+2 a d \sqrt{x}+2 b d \sqrt{x} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+b e n \left(\log \left(d \sqrt{x}+e\right) \left(\log \left(d \sqrt{x}+e\right)-2 \log \left(-\frac{d \sqrt{x}}{e}\right)\right)-2 \text{Li}_2\left(\frac{\sqrt{x} d}{e}+1\right)\right)+b e n \left(2 \log \left(d+\frac{e}{\sqrt{x}}\right)+\log (x)\right)\right)}{d^2}+x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2","\frac{2 b e^2 n \log \left(1-\frac{d}{d+\frac{e}{\sqrt{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{d^2}+\frac{2 b e n \sqrt{x} \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{d^2}+x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2-\frac{2 b^2 e^2 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt{x}}}\right)}{d^2}+\frac{b^2 e^2 n^2 \log (x)}{d^2}",1,"x*(a + b*Log[c*(d + e/Sqrt[x])^n])^2 + (b*e*n*(2*a*d*Sqrt[x] + 2*b*d*Sqrt[x]*Log[c*(d + e/Sqrt[x])^n] - 2*e*(a + b*Log[c*(d + e/Sqrt[x])^n])*Log[e + d*Sqrt[x]] + b*e*n*(2*Log[d + e/Sqrt[x]] + Log[x]) + b*e*n*(Log[e + d*Sqrt[x]]*(Log[e + d*Sqrt[x]] - 2*Log[-((d*Sqrt[x])/e)]) - 2*PolyLog[2, 1 + (d*Sqrt[x])/e])))/d^2","A",1
432,1,386,93,0.361359,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{x} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])^2/x,x]","2 b n \left(2 \text{Li}_2\left(-\frac{e}{d \sqrt{x}}\right)+\log (x) \left(\log \left(d+\frac{e}{\sqrt{x}}\right)-\log \left(\frac{e}{d \sqrt{x}}+1\right)\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)+\log (x) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^2+\frac{1}{12} b^2 n^2 \left(-48 \text{Li}_3\left(\frac{\sqrt{x} d}{e}+1\right)-48 \text{Li}_3\left(-\frac{d \sqrt{x}}{e}\right)+48 \text{Li}_2\left(\frac{\sqrt{x} d}{e}+1\right) \log \left(\frac{e}{d}+\sqrt{x}\right)-48 \text{Li}_2\left(-\frac{d \sqrt{x}}{e}\right) \left(\log \left(d+\frac{e}{\sqrt{x}}\right)-\log \left(\frac{e}{d}+\sqrt{x}\right)\right)+6 \log ^2(x) \log \left(d+\frac{e}{\sqrt{x}}\right)-6 \log ^2(x) \log \left(\frac{d \sqrt{x}}{e}+1\right)+12 \log (x) \log ^2\left(d+\frac{e}{\sqrt{x}}\right)-12 \log (x) \log ^2\left(\frac{e}{d}+\sqrt{x}\right)+24 \log ^2\left(\frac{e}{d}+\sqrt{x}\right) \log \left(-\frac{d \sqrt{x}}{e}\right)-24 \log (x) \log \left(d+\frac{e}{\sqrt{x}}\right) \log \left(\frac{d \sqrt{x}}{e}+1\right)+24 \log (x) \log \left(\frac{e}{d}+\sqrt{x}\right) \log \left(\frac{d \sqrt{x}}{e}+1\right)+\log ^3(x)\right)","-4 b n \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)-2 \log \left(-\frac{e}{d \sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2+4 b^2 n^2 \text{Li}_3\left(\frac{e}{d \sqrt{x}}+1\right)",1,"(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^2*Log[x] + 2*b*n*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])*((Log[d + e/Sqrt[x]] - Log[1 + e/(d*Sqrt[x])])*Log[x] + 2*PolyLog[2, -(e/(d*Sqrt[x]))]) + (b^2*n^2*(24*Log[e/d + Sqrt[x]]^2*Log[-((d*Sqrt[x])/e)] + 12*Log[d + e/Sqrt[x]]^2*Log[x] - 12*Log[e/d + Sqrt[x]]^2*Log[x] - 24*Log[d + e/Sqrt[x]]*Log[1 + (d*Sqrt[x])/e]*Log[x] + 24*Log[e/d + Sqrt[x]]*Log[1 + (d*Sqrt[x])/e]*Log[x] + 6*Log[d + e/Sqrt[x]]*Log[x]^2 - 6*Log[1 + (d*Sqrt[x])/e]*Log[x]^2 + Log[x]^3 + 48*Log[e/d + Sqrt[x]]*PolyLog[2, 1 + (d*Sqrt[x])/e] - 48*(Log[d + e/Sqrt[x]] - Log[e/d + Sqrt[x]])*PolyLog[2, -((d*Sqrt[x])/e)] - 48*PolyLog[3, 1 + (d*Sqrt[x])/e] - 48*PolyLog[3, -((d*Sqrt[x])/e)]))/12","B",1
433,1,298,195,0.3520908,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])^2/x^2,x]","-\frac{\frac{b n \left(-4 d^2 x \log \left(d \sqrt{x}+e\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)-4 d^2 x \log \left(-\frac{e}{d \sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)-2 e^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)+4 a d e \sqrt{x}+4 b d \sqrt{x} \left(d \sqrt{x}+e\right) \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-4 b d^2 n x \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right)+2 b d^2 n x \left(\log \left(d \sqrt{x}+e\right) \left(\log \left(d \sqrt{x}+e\right)-2 \log \left(-\frac{d \sqrt{x}}{e}\right)\right)-2 \text{Li}_2\left(\frac{\sqrt{x} d}{e}+1\right)\right)+b n \left(2 d^2 x \log \left(d+\frac{e}{\sqrt{x}}\right)+e \left(e-2 d \sqrt{x}\right)\right)-4 b d e n \sqrt{x}\right)}{e^2}+2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{2 x}","\frac{b n \left(d+\frac{e}{\sqrt{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{e^2}-\frac{\left(d+\frac{e}{\sqrt{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{e^2}+\frac{2 d \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{e^2}-\frac{4 a b d n}{e \sqrt{x}}-\frac{4 b^2 d n \left(d+\frac{e}{\sqrt{x}}\right) \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{e^2}-\frac{b^2 n^2 \left(d+\frac{e}{\sqrt{x}}\right)^2}{2 e^2}+\frac{4 b^2 d n^2}{e \sqrt{x}}",1,"-1/2*(2*(a + b*Log[c*(d + e/Sqrt[x])^n])^2 + (b*n*(4*a*d*e*Sqrt[x] - 4*b*d*e*n*Sqrt[x] + b*n*(e*(e - 2*d*Sqrt[x]) + 2*d^2*x*Log[d + e/Sqrt[x]]) + 4*b*d*(e + d*Sqrt[x])*Sqrt[x]*Log[c*(d + e/Sqrt[x])^n] - 2*e^2*(a + b*Log[c*(d + e/Sqrt[x])^n]) - 4*d^2*x*(a + b*Log[c*(d + e/Sqrt[x])^n])*Log[e + d*Sqrt[x]] - 4*d^2*x*(a + b*Log[c*(d + e/Sqrt[x])^n])*Log[-(e/(d*Sqrt[x]))] - 4*b*d^2*n*x*PolyLog[2, 1 + e/(d*Sqrt[x])] + 2*b*d^2*n*x*(Log[e + d*Sqrt[x]]*(Log[e + d*Sqrt[x]] - 2*Log[-((d*Sqrt[x])/e)]) - 2*PolyLog[2, 1 + (d*Sqrt[x])/e])))/e^2)/x","C",1
434,1,473,341,0.3907881,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])^2/x^3,x]","-\frac{b n \left(-144 a d^4 x^2 \log \left(d \sqrt{x}+e\right)-144 a d^4 x^2 \log \left(-\frac{e}{d \sqrt{x}}\right)+144 a d^3 e x^{3/2}-72 a d^2 e^2 x+48 a d e^3 \sqrt{x}-36 a e^4+144 b d^4 x^2 \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-144 b d^4 x^2 \log \left(d \sqrt{x}+e\right) \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-144 b d^4 x^2 \log \left(-\frac{e}{d \sqrt{x}}\right) \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+144 b d^3 e x^{3/2} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-72 b d^2 e^2 x \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-36 b e^4 \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+48 b d e^3 \sqrt{x} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-144 b d^4 n x^2 \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right)-144 b d^4 n x^2 \text{Li}_2\left(\frac{\sqrt{x} d}{e}+1\right)+72 b d^4 n x^2 \log ^2\left(d \sqrt{x}+e\right)+156 b d^4 n x^2 \log \left(d+\frac{e}{\sqrt{x}}\right)-144 b d^4 n x^2 \log \left(d \sqrt{x}+e\right) \log \left(-\frac{d \sqrt{x}}{e}\right)-300 b d^3 e n x^{3/2}+78 b d^2 e^2 n x-28 b d e^3 n \sqrt{x}+9 b e^4 n\right)+72 e^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{144 e^4 x^2}","\frac{b d^4 n \log \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{e^4}-\frac{4 b d^3 n \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{e^4}+\frac{3 b d^2 n \left(d+\frac{e}{\sqrt{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{e^4}-\frac{4 b d n \left(d+\frac{e}{\sqrt{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{3 e^4}+\frac{b n \left(d+\frac{e}{\sqrt{x}}\right)^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{4 e^4}-\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{2 x^2}-\frac{b^2 d^4 n^2 \log ^2\left(d+\frac{e}{\sqrt{x}}\right)}{2 e^4}+\frac{4 b^2 d^3 n^2}{e^3 \sqrt{x}}-\frac{3 b^2 d^2 n^2 \left(d+\frac{e}{\sqrt{x}}\right)^2}{2 e^4}+\frac{4 b^2 d n^2 \left(d+\frac{e}{\sqrt{x}}\right)^3}{9 e^4}-\frac{b^2 n^2 \left(d+\frac{e}{\sqrt{x}}\right)^4}{16 e^4}",1,"-1/144*(72*e^4*(a + b*Log[c*(d + e/Sqrt[x])^n])^2 + b*n*(-36*a*e^4 + 9*b*e^4*n + 48*a*d*e^3*Sqrt[x] - 28*b*d*e^3*n*Sqrt[x] - 72*a*d^2*e^2*x + 78*b*d^2*e^2*n*x + 144*a*d^3*e*x^(3/2) - 300*b*d^3*e*n*x^(3/2) + 156*b*d^4*n*x^2*Log[d + e/Sqrt[x]] - 36*b*e^4*Log[c*(d + e/Sqrt[x])^n] + 48*b*d*e^3*Sqrt[x]*Log[c*(d + e/Sqrt[x])^n] - 72*b*d^2*e^2*x*Log[c*(d + e/Sqrt[x])^n] + 144*b*d^3*e*x^(3/2)*Log[c*(d + e/Sqrt[x])^n] + 144*b*d^4*x^2*Log[c*(d + e/Sqrt[x])^n] - 144*a*d^4*x^2*Log[e + d*Sqrt[x]] - 144*b*d^4*x^2*Log[c*(d + e/Sqrt[x])^n]*Log[e + d*Sqrt[x]] + 72*b*d^4*n*x^2*Log[e + d*Sqrt[x]]^2 - 144*a*d^4*x^2*Log[-(e/(d*Sqrt[x]))] - 144*b*d^4*x^2*Log[c*(d + e/Sqrt[x])^n]*Log[-(e/(d*Sqrt[x]))] - 144*b*d^4*n*x^2*Log[e + d*Sqrt[x]]*Log[-((d*Sqrt[x])/e)] - 144*b*d^4*n*x^2*PolyLog[2, 1 + e/(d*Sqrt[x])] - 144*b*d^4*n*x^2*PolyLog[2, 1 + (d*Sqrt[x])/e]))/(e^4*x^2)","C",1
435,1,692,480,0.3507654,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])^2/x^4,x]","\frac{-1800 a^2 e^6-3600 a b e^6 \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+3600 a b d^6 n x^3 \log \left(d \sqrt{x}+e\right)+3600 a b d^6 n x^3 \log \left(-\frac{e}{d \sqrt{x}}\right)-3600 a b d^5 e n x^{5/2}+1800 a b d^4 e^2 n x^2-1200 a b d^3 e^3 n x^{3/2}+900 a b d^2 e^4 n x-720 a b d e^5 n \sqrt{x}+600 a b e^6 n-3600 b^2 d^6 n x^3 \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+3600 b^2 d^6 n x^3 \log \left(d \sqrt{x}+e\right) \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+3600 b^2 d^6 n x^3 \log \left(-\frac{e}{d \sqrt{x}}\right) \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-3600 b^2 d^5 e n x^{5/2} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+1800 b^2 d^4 e^2 n x^2 \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-1200 b^2 d^3 e^3 n x^{3/2} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+900 b^2 d^2 e^4 n x \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-1800 b^2 e^6 \log ^2\left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+600 b^2 e^6 n \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-720 b^2 d e^5 n \sqrt{x} \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+3600 b^2 d^6 n^2 x^3 \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right)+3600 b^2 d^6 n^2 x^3 \text{Li}_2\left(\frac{\sqrt{x} d}{e}+1\right)-1800 b^2 d^6 n^2 x^3 \log ^2\left(d \sqrt{x}+e\right)-5220 b^2 d^6 n^2 x^3 \log \left(d+\frac{e}{\sqrt{x}}\right)+3600 b^2 d^6 n^2 x^3 \log \left(d \sqrt{x}+e\right) \log \left(-\frac{d \sqrt{x}}{e}\right)+8820 b^2 d^5 e n^2 x^{5/2}-2610 b^2 d^4 e^2 n^2 x^2+1140 b^2 d^3 e^3 n^2 x^{3/2}-555 b^2 d^2 e^4 n^2 x+264 b^2 d e^5 n^2 \sqrt{x}-100 b^2 e^6 n^2}{5400 e^6 x^3}","\frac{2 b d^6 n \log \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{3 e^6}-\frac{4 b d^5 n \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{e^6}+\frac{5 b d^4 n \left(d+\frac{e}{\sqrt{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{e^6}-\frac{40 b d^3 n \left(d+\frac{e}{\sqrt{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{9 e^6}+\frac{5 b d^2 n \left(d+\frac{e}{\sqrt{x}}\right)^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{2 e^6}-\frac{4 b d n \left(d+\frac{e}{\sqrt{x}}\right)^5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{5 e^6}+\frac{b n \left(d+\frac{e}{\sqrt{x}}\right)^6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{9 e^6}-\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{3 x^3}-\frac{b^2 d^6 n^2 \log ^2\left(d+\frac{e}{\sqrt{x}}\right)}{3 e^6}+\frac{4 b^2 d^5 n^2}{e^5 \sqrt{x}}-\frac{5 b^2 d^4 n^2 \left(d+\frac{e}{\sqrt{x}}\right)^2}{2 e^6}+\frac{40 b^2 d^3 n^2 \left(d+\frac{e}{\sqrt{x}}\right)^3}{27 e^6}-\frac{5 b^2 d^2 n^2 \left(d+\frac{e}{\sqrt{x}}\right)^4}{8 e^6}+\frac{4 b^2 d n^2 \left(d+\frac{e}{\sqrt{x}}\right)^5}{25 e^6}-\frac{b^2 n^2 \left(d+\frac{e}{\sqrt{x}}\right)^6}{54 e^6}",1,"(-1800*a^2*e^6 + 600*a*b*e^6*n - 100*b^2*e^6*n^2 - 720*a*b*d*e^5*n*Sqrt[x] + 264*b^2*d*e^5*n^2*Sqrt[x] + 900*a*b*d^2*e^4*n*x - 555*b^2*d^2*e^4*n^2*x - 1200*a*b*d^3*e^3*n*x^(3/2) + 1140*b^2*d^3*e^3*n^2*x^(3/2) + 1800*a*b*d^4*e^2*n*x^2 - 2610*b^2*d^4*e^2*n^2*x^2 - 3600*a*b*d^5*e*n*x^(5/2) + 8820*b^2*d^5*e*n^2*x^(5/2) - 5220*b^2*d^6*n^2*x^3*Log[d + e/Sqrt[x]] - 3600*a*b*e^6*Log[c*(d + e/Sqrt[x])^n] + 600*b^2*e^6*n*Log[c*(d + e/Sqrt[x])^n] - 720*b^2*d*e^5*n*Sqrt[x]*Log[c*(d + e/Sqrt[x])^n] + 900*b^2*d^2*e^4*n*x*Log[c*(d + e/Sqrt[x])^n] - 1200*b^2*d^3*e^3*n*x^(3/2)*Log[c*(d + e/Sqrt[x])^n] + 1800*b^2*d^4*e^2*n*x^2*Log[c*(d + e/Sqrt[x])^n] - 3600*b^2*d^5*e*n*x^(5/2)*Log[c*(d + e/Sqrt[x])^n] - 3600*b^2*d^6*n*x^3*Log[c*(d + e/Sqrt[x])^n] - 1800*b^2*e^6*Log[c*(d + e/Sqrt[x])^n]^2 + 3600*a*b*d^6*n*x^3*Log[e + d*Sqrt[x]] + 3600*b^2*d^6*n*x^3*Log[c*(d + e/Sqrt[x])^n]*Log[e + d*Sqrt[x]] - 1800*b^2*d^6*n^2*x^3*Log[e + d*Sqrt[x]]^2 + 3600*a*b*d^6*n*x^3*Log[-(e/(d*Sqrt[x]))] + 3600*b^2*d^6*n*x^3*Log[c*(d + e/Sqrt[x])^n]*Log[-(e/(d*Sqrt[x]))] + 3600*b^2*d^6*n^2*x^3*Log[e + d*Sqrt[x]]*Log[-((d*Sqrt[x])/e)] + 3600*b^2*d^6*n^2*x^3*PolyLog[2, 1 + e/(d*Sqrt[x])] + 3600*b^2*d^6*n^2*x^3*PolyLog[2, 1 + (d*Sqrt[x])/e])/(5400*e^6*x^3)","C",1
436,1,777,569,1.0351804,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3 \, dx","Integrate[x*(a + b*Log[c*(d + e/Sqrt[x])^n])^3,x]","\frac{-2 b^2 n^2 \left(3 \left(e^4-d^4 x^2\right) \log ^2\left(d+\frac{e}{\sqrt{x}}\right)+e^2 \left(d^2 (-x)+11 e^2 \log \left(-\frac{e}{d \sqrt{x}}\right)+5 d e \sqrt{x}\right)-e \log \left(d+\frac{e}{\sqrt{x}}\right) \left(2 d^3 x^{3/2}-3 d^2 e x+6 e^3 \log \left(-\frac{e}{d \sqrt{x}}\right)+6 d e^2 \sqrt{x}+11 e^3\right)-6 e^4 \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)+2 d^4 x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^3+6 b d^4 n x^2 \log \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^2+2 b d^3 e n x^{3/2} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^2-3 b d^2 e^2 n x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^2-6 b e^4 n \log \left(d \sqrt{x}+e\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^2+6 b d e^3 n \sqrt{x} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^2+b^3 n^3 \left(2 d^4 x^2 \log ^3\left(d+\frac{e}{\sqrt{x}}\right)+2 d^3 e x^{3/2} \log ^2\left(d+\frac{e}{\sqrt{x}}\right)+d^2 e^2 x \left(2-3 \log \left(d+\frac{e}{\sqrt{x}}\right)\right) \log \left(d+\frac{e}{\sqrt{x}}\right)-2 e^4 \left(6 \text{Li}_3\left(\frac{e}{d \sqrt{x}}+1\right)-6 \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right) \log \left(d+\frac{e}{\sqrt{x}}\right)+\left(\log \left(d+\frac{e}{\sqrt{x}}\right)-3 \log \left(-\frac{e}{d \sqrt{x}}\right)\right) \log ^2\left(d+\frac{e}{\sqrt{x}}\right)\right)+11 e^4 \left(\log \left(d+\frac{e}{\sqrt{x}}\right) \left(\log \left(d+\frac{e}{\sqrt{x}}\right)-2 \log \left(-\frac{e}{d \sqrt{x}}\right)\right)-2 \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right)\right)+12 e^4 \left(\log \left(-\frac{e}{d \sqrt{x}}\right)-\log \left(d+\frac{e}{\sqrt{x}}\right)\right)+2 d e^3 \sqrt{x} \left(3 \log ^2\left(d+\frac{e}{\sqrt{x}}\right)-5 \log \left(d+\frac{e}{\sqrt{x}}\right)+1\right)\right)}{4 d^4}","-\frac{3 b^2 e^4 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{d^4}-\frac{5 b^2 e^4 n^2 \log \left(1-\frac{d}{d+\frac{e}{\sqrt{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{2 d^4}-\frac{3 b^2 e^4 n^2 \log \left(-\frac{e}{d \sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{d^4}-\frac{5 b^2 e^3 n^2 \sqrt{x} \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{2 d^4}+\frac{b^2 e^2 n^2 x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{2 d^2}+\frac{3 b e^4 n \log \left(1-\frac{d}{d+\frac{e}{\sqrt{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{2 d^4}+\frac{3 b e^3 n \sqrt{x} \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{2 d^4}-\frac{3 b e^2 n x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{4 d^2}+\frac{b e n x^{3/2} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{2 d}+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3+\frac{5 b^3 e^4 n^3 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt{x}}}\right)}{2 d^4}-\frac{3 b^3 e^4 n^3 \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right)}{d^4}-\frac{3 b^3 e^4 n^3 \text{Li}_3\left(\frac{d}{d+\frac{e}{\sqrt{x}}}\right)}{d^4}-\frac{b^3 e^4 n^3 \log \left(d+\frac{e}{\sqrt{x}}\right)}{2 d^4}-\frac{3 b^3 e^4 n^3 \log (x)}{2 d^4}+\frac{b^3 e^3 n^3 \sqrt{x}}{2 d^3}",1,"(6*b*d*e^3*n*Sqrt[x]*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^2 - 3*b*d^2*e^2*n*x*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^2 + 2*b*d^3*e*n*x^(3/2)*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^2 + 6*b*d^4*n*x^2*Log[d + e/Sqrt[x]]*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^2 + 2*d^4*x^2*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^3 - 6*b*e^4*n*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^2*Log[e + d*Sqrt[x]] - 2*b^2*n^2*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])*(3*(e^4 - d^4*x^2)*Log[d + e/Sqrt[x]]^2 + e^2*(5*d*e*Sqrt[x] - d^2*x + 11*e^2*Log[-(e/(d*Sqrt[x]))]) - e*Log[d + e/Sqrt[x]]*(11*e^3 + 6*d*e^2*Sqrt[x] - 3*d^2*e*x + 2*d^3*x^(3/2) + 6*e^3*Log[-(e/(d*Sqrt[x]))]) - 6*e^4*PolyLog[2, 1 + e/(d*Sqrt[x])]) + b^3*n^3*(d^2*e^2*x*(2 - 3*Log[d + e/Sqrt[x]])*Log[d + e/Sqrt[x]] + 2*d^3*e*x^(3/2)*Log[d + e/Sqrt[x]]^2 + 2*d^4*x^2*Log[d + e/Sqrt[x]]^3 + 2*d*e^3*Sqrt[x]*(1 - 5*Log[d + e/Sqrt[x]] + 3*Log[d + e/Sqrt[x]]^2) + 12*e^4*(-Log[d + e/Sqrt[x]] + Log[-(e/(d*Sqrt[x]))]) + 11*e^4*(Log[d + e/Sqrt[x]]*(Log[d + e/Sqrt[x]] - 2*Log[-(e/(d*Sqrt[x]))]) - 2*PolyLog[2, 1 + e/(d*Sqrt[x])]) - 2*e^4*(Log[d + e/Sqrt[x]]^2*(Log[d + e/Sqrt[x]] - 3*Log[-(e/(d*Sqrt[x]))]) - 6*Log[d + e/Sqrt[x]]*PolyLog[2, 1 + e/(d*Sqrt[x])] + 6*PolyLog[3, 1 + e/(d*Sqrt[x])])))/(4*d^4)","A",1
437,1,476,260,0.7294024,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3 \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])^3,x]","\frac{3 b^2 n^2 \left(\left(d^2 x-e^2\right) \log ^2\left(d+\frac{e}{\sqrt{x}}\right)+2 e^2 \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right)-2 e^2 \log \left(-\frac{e}{d \sqrt{x}}\right)+2 e \log \left(d+\frac{e}{\sqrt{x}}\right) \left(e \log \left(-\frac{e}{d \sqrt{x}}\right)+d \sqrt{x}+e\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)+3 b d^2 n x \log \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^2+d^2 x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^3-3 b e^2 n \log \left(d \sqrt{x}+e\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^2+3 b d e n \sqrt{x} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^2+b^3 n^3 \left(\log \left(d+\frac{e}{\sqrt{x}}\right) \left(\left(d^2 x-e^2\right) \log ^2\left(d+\frac{e}{\sqrt{x}}\right)-6 e^2 \log \left(-\frac{e}{d \sqrt{x}}\right)+3 e \log \left(d+\frac{e}{\sqrt{x}}\right) \left(e \log \left(-\frac{e}{d \sqrt{x}}\right)+d \sqrt{x}+e\right)\right)-6 e^2 \text{Li}_3\left(\frac{e}{d \sqrt{x}}+1\right)+6 e^2 \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right) \left(\log \left(d+\frac{e}{\sqrt{x}}\right)-1\right)\right)}{d^2}","-\frac{6 b^2 e^2 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{d^2}-\frac{6 b^2 e^2 n^2 \log \left(-\frac{e}{d \sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{d^2}+\frac{3 b e^2 n \log \left(1-\frac{d}{d+\frac{e}{\sqrt{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{d^2}+\frac{3 b e n \sqrt{x} \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{d^2}+x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3-\frac{6 b^3 e^2 n^3 \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right)}{d^2}-\frac{6 b^3 e^2 n^3 \text{Li}_3\left(\frac{d}{d+\frac{e}{\sqrt{x}}}\right)}{d^2}",1,"(3*b*d*e*n*Sqrt[x]*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^2 + 3*b*d^2*n*x*Log[d + e/Sqrt[x]]*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^2 + d^2*x*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^3 - 3*b*e^2*n*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^2*Log[e + d*Sqrt[x]] + 3*b^2*n^2*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])*((-e^2 + d^2*x)*Log[d + e/Sqrt[x]]^2 - 2*e^2*Log[-(e/(d*Sqrt[x]))] + 2*e*Log[d + e/Sqrt[x]]*(e + d*Sqrt[x] + e*Log[-(e/(d*Sqrt[x]))]) + 2*e^2*PolyLog[2, 1 + e/(d*Sqrt[x])]) + b^3*n^3*(Log[d + e/Sqrt[x]]*((-e^2 + d^2*x)*Log[d + e/Sqrt[x]]^2 - 6*e^2*Log[-(e/(d*Sqrt[x]))] + 3*e*Log[d + e/Sqrt[x]]*(e + d*Sqrt[x] + e*Log[-(e/(d*Sqrt[x]))])) + 6*e^2*(-1 + Log[d + e/Sqrt[x]])*PolyLog[2, 1 + e/(d*Sqrt[x])] - 6*e^2*PolyLog[3, 1 + e/(d*Sqrt[x])]))/d^2","A",1
438,1,532,135,0.3104291,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{x} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])^3/x,x]","6 b^2 n^2 \left(-2 \text{Li}_3\left(\frac{\sqrt{x} d}{e}+1\right)-2 \text{Li}_3\left(-\frac{d \sqrt{x}}{e}\right)+2 \text{Li}_2\left(\frac{\sqrt{x} d}{e}+1\right) \log \left(\frac{e}{d}+\sqrt{x}\right)-2 \text{Li}_2\left(-\frac{d \sqrt{x}}{e}\right) \left(\log \left(d+\frac{e}{\sqrt{x}}\right)-\log \left(\frac{e}{d}+\sqrt{x}\right)\right)+\frac{1}{4} \log ^2(x) \log \left(d+\frac{e}{\sqrt{x}}\right)-\frac{1}{4} \log ^2(x) \log \left(\frac{d \sqrt{x}}{e}+1\right)+\frac{1}{2} \log (x) \log ^2\left(d+\frac{e}{\sqrt{x}}\right)-\frac{1}{2} \log (x) \log ^2\left(\frac{e}{d}+\sqrt{x}\right)+\log ^2\left(\frac{e}{d}+\sqrt{x}\right) \log \left(-\frac{d \sqrt{x}}{e}\right)-\log (x) \log \left(d+\frac{e}{\sqrt{x}}\right) \log \left(\frac{d \sqrt{x}}{e}+1\right)+\log (x) \log \left(\frac{e}{d}+\sqrt{x}\right) \log \left(\frac{d \sqrt{x}}{e}+1\right)+\frac{\log ^3(x)}{24}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)+3 b n \left(2 \text{Li}_2\left(-\frac{e}{d \sqrt{x}}\right)+\log (x) \left(\log \left(d+\frac{e}{\sqrt{x}}\right)-\log \left(\frac{e}{d \sqrt{x}}+1\right)\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^2+\log (x) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt{x}}\right)\right)^3-2 b^3 n^3 \left(6 \text{Li}_4\left(\frac{e}{d \sqrt{x}}+1\right)+3 \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right) \log ^2\left(d+\frac{e}{\sqrt{x}}\right)-6 \text{Li}_3\left(\frac{e}{d \sqrt{x}}+1\right) \log \left(d+\frac{e}{\sqrt{x}}\right)+\log \left(-\frac{e}{d \sqrt{x}}\right) \log ^3\left(d+\frac{e}{\sqrt{x}}\right)\right)","12 b^2 n^2 \text{Li}_3\left(\frac{e}{d \sqrt{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)-6 b n \text{Li}_2\left(\frac{e}{d \sqrt{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2-2 \log \left(-\frac{e}{d \sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3-12 b^3 n^3 \text{Li}_4\left(\frac{e}{d \sqrt{x}}+1\right)",1,"(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^3*Log[x] + 3*b*n*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])^2*((Log[d + e/Sqrt[x]] - Log[1 + e/(d*Sqrt[x])])*Log[x] + 2*PolyLog[2, -(e/(d*Sqrt[x]))]) + 6*b^2*n^2*(a - b*n*Log[d + e/Sqrt[x]] + b*Log[c*(d + e/Sqrt[x])^n])*(Log[e/d + Sqrt[x]]^2*Log[-((d*Sqrt[x])/e)] + (Log[d + e/Sqrt[x]]^2*Log[x])/2 - (Log[e/d + Sqrt[x]]^2*Log[x])/2 - Log[d + e/Sqrt[x]]*Log[1 + (d*Sqrt[x])/e]*Log[x] + Log[e/d + Sqrt[x]]*Log[1 + (d*Sqrt[x])/e]*Log[x] + (Log[d + e/Sqrt[x]]*Log[x]^2)/4 - (Log[1 + (d*Sqrt[x])/e]*Log[x]^2)/4 + Log[x]^3/24 + 2*Log[e/d + Sqrt[x]]*PolyLog[2, 1 + (d*Sqrt[x])/e] - 2*(Log[d + e/Sqrt[x]] - Log[e/d + Sqrt[x]])*PolyLog[2, -((d*Sqrt[x])/e)] - 2*PolyLog[3, 1 + (d*Sqrt[x])/e] - 2*PolyLog[3, -((d*Sqrt[x])/e)]) - 2*b^3*n^3*(Log[d + e/Sqrt[x]]^3*Log[-(e/(d*Sqrt[x]))] + 3*Log[d + e/Sqrt[x]]^2*PolyLog[2, 1 + e/(d*Sqrt[x])] - 6*Log[d + e/Sqrt[x]]*PolyLog[3, 1 + e/(d*Sqrt[x])] + 6*PolyLog[4, 1 + e/(d*Sqrt[x])])","B",1
439,1,558,285,0.6739239,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])^3/x^2,x]","\frac{-4 a^3 e^2-6 b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right) \left(e \left(2 a^2 e-2 a b n \left(e-2 d \sqrt{x}\right)+b^2 n^2 \left(e-6 d \sqrt{x}\right)\right)+2 b d^2 n x (3 b n-2 a) \log \left(d \sqrt{x}+e\right)+b d^2 n x \log (x) (2 a-3 b n)\right)+12 a^2 b d^2 n x \log \left(d \sqrt{x}+e\right)-6 a^2 b d^2 n x \log (x)-12 a^2 b d e n \sqrt{x}+6 a^2 b e^2 n+6 b^2 d^2 n^2 x \log ^2\left(d+\frac{e}{\sqrt{x}}\right) \left(2 a+2 b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+2 b n \log \left(d \sqrt{x}+e\right)-b n \log (x)-3 b n\right)+6 b^2 d^2 n^2 x \log \left(d+\frac{e}{\sqrt{x}}\right) \left(2 \log \left(d \sqrt{x}+e\right)-\log (x)\right) \left(-2 a-2 b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+3 b n\right)+6 b^2 \log ^2\left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right) \left(e \left(b n \left(e-2 d \sqrt{x}\right)-2 a e\right)+2 b d^2 n x \log \left(d \sqrt{x}+e\right)-b d^2 n x \log (x)\right)-36 a b^2 d^2 n^2 x \log \left(d \sqrt{x}+e\right)+18 a b^2 d^2 n^2 x \log (x)+36 a b^2 d e n^2 \sqrt{x}-6 a b^2 e^2 n^2-4 b^3 e^2 \log ^3\left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-8 b^3 d^2 n^3 x \log ^3\left(d+\frac{e}{\sqrt{x}}\right)+42 b^3 d^2 n^3 x \log \left(d \sqrt{x}+e\right)-21 b^3 d^2 n^3 x \log (x)-42 b^3 d e n^3 \sqrt{x}+3 b^3 e^2 n^3}{4 e^2 x}","-\frac{3 b^2 n^2 \left(d+\frac{e}{\sqrt{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{2 e^2}+\frac{12 a b^2 d n^2}{e \sqrt{x}}+\frac{3 b n \left(d+\frac{e}{\sqrt{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{2 e^2}-\frac{6 b d n \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{e^2}-\frac{\left(d+\frac{e}{\sqrt{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{e^2}+\frac{2 d \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{e^2}+\frac{12 b^3 d n^2 \left(d+\frac{e}{\sqrt{x}}\right) \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{e^2}+\frac{3 b^3 n^3 \left(d+\frac{e}{\sqrt{x}}\right)^2}{4 e^2}-\frac{12 b^3 d n^3}{e \sqrt{x}}",1,"(-4*a^3*e^2 + 6*a^2*b*e^2*n - 6*a*b^2*e^2*n^2 + 3*b^3*e^2*n^3 - 12*a^2*b*d*e*n*Sqrt[x] + 36*a*b^2*d*e*n^2*Sqrt[x] - 42*b^3*d*e*n^3*Sqrt[x] - 8*b^3*d^2*n^3*x*Log[d + e/Sqrt[x]]^3 - 4*b^3*e^2*Log[c*(d + e/Sqrt[x])^n]^3 + 12*a^2*b*d^2*n*x*Log[e + d*Sqrt[x]] - 36*a*b^2*d^2*n^2*x*Log[e + d*Sqrt[x]] + 42*b^3*d^2*n^3*x*Log[e + d*Sqrt[x]] + 6*b^2*d^2*n^2*x*Log[d + e/Sqrt[x]]*(-2*a + 3*b*n - 2*b*Log[c*(d + e/Sqrt[x])^n])*(2*Log[e + d*Sqrt[x]] - Log[x]) - 6*a^2*b*d^2*n*x*Log[x] + 18*a*b^2*d^2*n^2*x*Log[x] - 21*b^3*d^2*n^3*x*Log[x] + 6*b^2*d^2*n^2*x*Log[d + e/Sqrt[x]]^2*(2*a - 3*b*n + 2*b*Log[c*(d + e/Sqrt[x])^n] + 2*b*n*Log[e + d*Sqrt[x]] - b*n*Log[x]) + 6*b^2*Log[c*(d + e/Sqrt[x])^n]^2*(e*(-2*a*e + b*n*(e - 2*d*Sqrt[x])) + 2*b*d^2*n*x*Log[e + d*Sqrt[x]] - b*d^2*n*x*Log[x]) - 6*b*Log[c*(d + e/Sqrt[x])^n]*(e*(2*a^2*e + b^2*n^2*(e - 6*d*Sqrt[x]) - 2*a*b*n*(e - 2*d*Sqrt[x])) + 2*b*d^2*n*(-2*a + 3*b*n)*x*Log[e + d*Sqrt[x]] + b*d^2*n*(2*a - 3*b*n)*x*Log[x]))/(4*e^2*x)","A",1
440,1,766,595,1.0959606,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])^3/x^3,x]","\frac{-288 a^3 e^4-12 b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right) \left(72 a^2 e^4+12 b d^4 n x^2 (25 b n-12 a) \log \left(d \sqrt{x}+e\right)+6 b d^4 n x^2 \log (x) (12 a-25 b n)-12 a b e n \left(-12 d^3 x^{3/2}+6 d^2 e x-4 d e^2 \sqrt{x}+3 e^3\right)+b^2 e n^2 \left(-300 d^3 x^{3/2}+78 d^2 e x-28 d e^2 \sqrt{x}+9 e^3\right)\right)+864 a^2 b d^4 n x^2 \log \left(d \sqrt{x}+e\right)-432 a^2 b d^4 n x^2 \log (x)-864 a^2 b d^3 e n x^{3/2}+432 a^2 b d^2 e^2 n x-288 a^2 b d e^3 n \sqrt{x}+216 a^2 b e^4 n+72 b^2 d^4 n^2 x^2 \log ^2\left(d+\frac{e}{\sqrt{x}}\right) \left(12 a+12 b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+12 b n \log \left(d \sqrt{x}+e\right)-6 b n \log (x)-25 b n\right)+72 b^2 d^4 n^2 x^2 \log \left(d+\frac{e}{\sqrt{x}}\right) \left(2 \log \left(d \sqrt{x}+e\right)-\log (x)\right) \left(-12 a-12 b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+25 b n\right)+72 b^2 \log ^2\left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right) \left(e \left(-12 a e^3-12 b d^3 n x^{3/2}+6 b d^2 e n x-4 b d e^2 n \sqrt{x}+3 b e^3 n\right)+12 b d^4 n x^2 \log \left(d \sqrt{x}+e\right)-6 b d^4 n x^2 \log (x)\right)-3600 a b^2 d^4 n^2 x^2 \log \left(d \sqrt{x}+e\right)+1800 a b^2 d^4 n^2 x^2 \log (x)+3600 a b^2 d^3 e n^2 x^{3/2}-936 a b^2 d^2 e^2 n^2 x+336 a b^2 d e^3 n^2 \sqrt{x}-108 a b^2 e^4 n^2-288 b^3 e^4 \log ^3\left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-576 b^3 d^4 n^3 x^2 \log ^3\left(d+\frac{e}{\sqrt{x}}\right)+4980 b^3 d^4 n^3 x^2 \log \left(d \sqrt{x}+e\right)-2490 b^3 d^4 n^3 x^2 \log (x)-4980 b^3 d^3 e n^3 x^{3/2}+690 b^3 d^2 e^2 n^3 x-148 b^3 d e^3 n^3 \sqrt{x}+27 b^3 e^4 n^3}{576 e^4 x^2}","-\frac{9 b^2 d^2 n^2 \left(d+\frac{e}{\sqrt{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{2 e^4}-\frac{3 b^2 n^2 \left(d+\frac{e}{\sqrt{x}}\right)^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{16 e^4}+\frac{4 b^2 d n^2 \left(d+\frac{e}{\sqrt{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{3 e^4}+\frac{12 a b^2 d^3 n^2}{e^3 \sqrt{x}}+\frac{2 d^3 \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{e^4}-\frac{6 b d^3 n \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{e^4}-\frac{3 d^2 \left(d+\frac{e}{\sqrt{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{e^4}+\frac{9 b d^2 n \left(d+\frac{e}{\sqrt{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{2 e^4}-\frac{\left(d+\frac{e}{\sqrt{x}}\right)^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{2 e^4}+\frac{3 b n \left(d+\frac{e}{\sqrt{x}}\right)^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{8 e^4}+\frac{2 d \left(d+\frac{e}{\sqrt{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{e^4}-\frac{2 b d n \left(d+\frac{e}{\sqrt{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{e^4}+\frac{12 b^3 d^3 n^2 \left(d+\frac{e}{\sqrt{x}}\right) \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{e^4}-\frac{12 b^3 d^3 n^3}{e^3 \sqrt{x}}+\frac{9 b^3 d^2 n^3 \left(d+\frac{e}{\sqrt{x}}\right)^2}{4 e^4}+\frac{3 b^3 n^3 \left(d+\frac{e}{\sqrt{x}}\right)^4}{64 e^4}-\frac{4 b^3 d n^3 \left(d+\frac{e}{\sqrt{x}}\right)^3}{9 e^4}",1,"(-288*a^3*e^4 + 216*a^2*b*e^4*n - 108*a*b^2*e^4*n^2 + 27*b^3*e^4*n^3 - 288*a^2*b*d*e^3*n*Sqrt[x] + 336*a*b^2*d*e^3*n^2*Sqrt[x] - 148*b^3*d*e^3*n^3*Sqrt[x] + 432*a^2*b*d^2*e^2*n*x - 936*a*b^2*d^2*e^2*n^2*x + 690*b^3*d^2*e^2*n^3*x - 864*a^2*b*d^3*e*n*x^(3/2) + 3600*a*b^2*d^3*e*n^2*x^(3/2) - 4980*b^3*d^3*e*n^3*x^(3/2) - 576*b^3*d^4*n^3*x^2*Log[d + e/Sqrt[x]]^3 - 288*b^3*e^4*Log[c*(d + e/Sqrt[x])^n]^3 + 864*a^2*b*d^4*n*x^2*Log[e + d*Sqrt[x]] - 3600*a*b^2*d^4*n^2*x^2*Log[e + d*Sqrt[x]] + 4980*b^3*d^4*n^3*x^2*Log[e + d*Sqrt[x]] + 72*b^2*d^4*n^2*x^2*Log[d + e/Sqrt[x]]*(-12*a + 25*b*n - 12*b*Log[c*(d + e/Sqrt[x])^n])*(2*Log[e + d*Sqrt[x]] - Log[x]) - 432*a^2*b*d^4*n*x^2*Log[x] + 1800*a*b^2*d^4*n^2*x^2*Log[x] - 2490*b^3*d^4*n^3*x^2*Log[x] + 72*b^2*d^4*n^2*x^2*Log[d + e/Sqrt[x]]^2*(12*a - 25*b*n + 12*b*Log[c*(d + e/Sqrt[x])^n] + 12*b*n*Log[e + d*Sqrt[x]] - 6*b*n*Log[x]) + 72*b^2*Log[c*(d + e/Sqrt[x])^n]^2*(e*(-12*a*e^3 + 3*b*e^3*n - 4*b*d*e^2*n*Sqrt[x] + 6*b*d^2*e*n*x - 12*b*d^3*n*x^(3/2)) + 12*b*d^4*n*x^2*Log[e + d*Sqrt[x]] - 6*b*d^4*n*x^2*Log[x]) - 12*b*Log[c*(d + e/Sqrt[x])^n]*(72*a^2*e^4 + b^2*e*n^2*(9*e^3 - 28*d*e^2*Sqrt[x] + 78*d^2*e*x - 300*d^3*x^(3/2)) - 12*a*b*e*n*(3*e^3 - 4*d*e^2*Sqrt[x] + 6*d^2*e*x - 12*d^3*x^(3/2)) + 12*b*d^4*n*(-12*a + 25*b*n)*x^2*Log[e + d*Sqrt[x]] + 6*b*d^4*n*(12*a - 25*b*n)*x^2*Log[x]))/(576*e^4*x^2)","A",1
441,1,950,907,1.7945474,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^n])^3/x^4,x]","\frac{-72000 b^3 n^3 x^3 \log ^3\left(d+\frac{e}{\sqrt{x}}\right) d^6+809340 b^3 n^3 x^3 \log \left(\sqrt{x} d+e\right) d^6-529200 a b^2 n^2 x^3 \log \left(\sqrt{x} d+e\right) d^6+108000 a^2 b n x^3 \log \left(\sqrt{x} d+e\right) d^6+5400 b^2 n^2 x^3 \log \left(d+\frac{e}{\sqrt{x}}\right) \left(-20 a+49 b n-20 b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \left(2 \log \left(\sqrt{x} d+e\right)-\log (x)\right) d^6-404670 b^3 n^3 x^3 \log (x) d^6+264600 a b^2 n^2 x^3 \log (x) d^6-54000 a^2 b n x^3 \log (x) d^6+5400 b^2 n^2 x^3 \log ^2\left(d+\frac{e}{\sqrt{x}}\right) \left(20 a-49 b n+20 b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)+20 b n \log \left(\sqrt{x} d+e\right)-10 b n \log (x)\right) d^6-809340 b^3 e n^3 x^{5/2} d^5+529200 a b^2 e n^2 x^{5/2} d^5-108000 a^2 b e n x^{5/2} d^5+140070 b^3 e^2 n^3 x^2 d^4-156600 a b^2 e^2 n^2 x^2 d^4+54000 a^2 b e^2 n x^2 d^4-41180 b^3 e^3 n^3 x^{3/2} d^3+68400 a b^2 e^3 n^2 x^{3/2} d^3-36000 a^2 b e^3 n x^{3/2} d^3+13785 b^3 e^4 n^3 x d^2-33300 a b^2 e^4 n^2 x d^2+27000 a^2 b e^4 n x d^2-4368 b^3 e^5 n^3 \sqrt{x} d+15840 a b^2 e^5 n^2 \sqrt{x} d-21600 a^2 b e^5 n \sqrt{x} d-36000 a^3 e^6+1000 b^3 e^6 n^3-36000 b^3 e^6 \log ^3\left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)-6000 a b^2 e^6 n^2+18000 a^2 b e^6 n+1800 b^2 \log ^2\left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right) \left(60 b n x^3 \log \left(\sqrt{x} d+e\right) d^6-30 b n x^3 \log (x) d^6+e \left(-60 b n x^{5/2} d^5+30 b e n x^2 d^4-20 b e^2 n x^{3/2} d^3+15 b e^3 n x d^2-12 b e^4 n \sqrt{x} d-60 a e^5+10 b e^5 n\right)\right)-60 b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right) \left(180 b n (49 b n-20 a) x^3 \log \left(\sqrt{x} d+e\right) d^6+90 b n (20 a-49 b n) x^3 \log (x) d^6+1800 a^2 e^6+b^2 e n^2 \left(-8820 x^{5/2} d^5+2610 e x^2 d^4-1140 e^2 x^{3/2} d^3+555 e^3 x d^2-264 e^4 \sqrt{x} d+100 e^5\right)-60 a b e n \left(-60 x^{5/2} d^5+30 e x^2 d^4-20 e^2 x^{3/2} d^3+15 e^3 x d^2-12 e^4 \sqrt{x} d+10 e^5\right)\right)}{108000 e^6 x^3}","\frac{b^3 n^3 \left(d+\frac{e}{\sqrt{x}}\right)^6}{108 e^6}-\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt{x}}\right)^6}{3 e^6}+\frac{b n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt{x}}\right)^6}{6 e^6}-\frac{b^2 n^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \left(d+\frac{e}{\sqrt{x}}\right)^6}{18 e^6}-\frac{12 b^3 d n^3 \left(d+\frac{e}{\sqrt{x}}\right)^5}{125 e^6}+\frac{2 d \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt{x}}\right)^5}{e^6}-\frac{6 b d n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt{x}}\right)^5}{5 e^6}+\frac{12 b^2 d n^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \left(d+\frac{e}{\sqrt{x}}\right)^5}{25 e^6}+\frac{15 b^3 d^2 n^3 \left(d+\frac{e}{\sqrt{x}}\right)^4}{32 e^6}-\frac{5 d^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt{x}}\right)^4}{e^6}+\frac{15 b d^2 n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt{x}}\right)^4}{4 e^6}-\frac{15 b^2 d^2 n^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \left(d+\frac{e}{\sqrt{x}}\right)^4}{8 e^6}-\frac{40 b^3 d^3 n^3 \left(d+\frac{e}{\sqrt{x}}\right)^3}{27 e^6}+\frac{20 d^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt{x}}\right)^3}{3 e^6}-\frac{20 b d^3 n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt{x}}\right)^3}{3 e^6}+\frac{40 b^2 d^3 n^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \left(d+\frac{e}{\sqrt{x}}\right)^3}{9 e^6}+\frac{15 b^3 d^4 n^3 \left(d+\frac{e}{\sqrt{x}}\right)^2}{4 e^6}-\frac{5 d^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt{x}}\right)^2}{e^6}+\frac{15 b d^4 n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt{x}}\right)^2}{2 e^6}-\frac{15 b^2 d^4 n^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \left(d+\frac{e}{\sqrt{x}}\right)^2}{2 e^6}+\frac{2 d^5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt{x}}\right)}{e^6}-\frac{6 b d^5 n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt{x}}\right)}{e^6}+\frac{12 b^3 d^5 n^2 \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right) \left(d+\frac{e}{\sqrt{x}}\right)}{e^6}-\frac{12 b^3 d^5 n^3}{e^5 \sqrt{x}}+\frac{12 a b^2 d^5 n^2}{e^5 \sqrt{x}}",1,"(-36000*a^3*e^6 + 18000*a^2*b*e^6*n - 6000*a*b^2*e^6*n^2 + 1000*b^3*e^6*n^3 - 21600*a^2*b*d*e^5*n*Sqrt[x] + 15840*a*b^2*d*e^5*n^2*Sqrt[x] - 4368*b^3*d*e^5*n^3*Sqrt[x] + 27000*a^2*b*d^2*e^4*n*x - 33300*a*b^2*d^2*e^4*n^2*x + 13785*b^3*d^2*e^4*n^3*x - 36000*a^2*b*d^3*e^3*n*x^(3/2) + 68400*a*b^2*d^3*e^3*n^2*x^(3/2) - 41180*b^3*d^3*e^3*n^3*x^(3/2) + 54000*a^2*b*d^4*e^2*n*x^2 - 156600*a*b^2*d^4*e^2*n^2*x^2 + 140070*b^3*d^4*e^2*n^3*x^2 - 108000*a^2*b*d^5*e*n*x^(5/2) + 529200*a*b^2*d^5*e*n^2*x^(5/2) - 809340*b^3*d^5*e*n^3*x^(5/2) - 72000*b^3*d^6*n^3*x^3*Log[d + e/Sqrt[x]]^3 - 36000*b^3*e^6*Log[c*(d + e/Sqrt[x])^n]^3 + 108000*a^2*b*d^6*n*x^3*Log[e + d*Sqrt[x]] - 529200*a*b^2*d^6*n^2*x^3*Log[e + d*Sqrt[x]] + 809340*b^3*d^6*n^3*x^3*Log[e + d*Sqrt[x]] + 5400*b^2*d^6*n^2*x^3*Log[d + e/Sqrt[x]]*(-20*a + 49*b*n - 20*b*Log[c*(d + e/Sqrt[x])^n])*(2*Log[e + d*Sqrt[x]] - Log[x]) - 54000*a^2*b*d^6*n*x^3*Log[x] + 264600*a*b^2*d^6*n^2*x^3*Log[x] - 404670*b^3*d^6*n^3*x^3*Log[x] + 5400*b^2*d^6*n^2*x^3*Log[d + e/Sqrt[x]]^2*(20*a - 49*b*n + 20*b*Log[c*(d + e/Sqrt[x])^n] + 20*b*n*Log[e + d*Sqrt[x]] - 10*b*n*Log[x]) + 1800*b^2*Log[c*(d + e/Sqrt[x])^n]^2*(e*(-60*a*e^5 + 10*b*e^5*n - 12*b*d*e^4*n*Sqrt[x] + 15*b*d^2*e^3*n*x - 20*b*d^3*e^2*n*x^(3/2) + 30*b*d^4*e*n*x^2 - 60*b*d^5*n*x^(5/2)) + 60*b*d^6*n*x^3*Log[e + d*Sqrt[x]] - 30*b*d^6*n*x^3*Log[x]) - 60*b*Log[c*(d + e/Sqrt[x])^n]*(1800*a^2*e^6 + b^2*e*n^2*(100*e^5 - 264*d*e^4*Sqrt[x] + 555*d^2*e^3*x - 1140*d^3*e^2*x^(3/2) + 2610*d^4*e*x^2 - 8820*d^5*x^(5/2)) - 60*a*b*e*n*(10*e^5 - 12*d*e^4*Sqrt[x] + 15*d^2*e^3*x - 20*d^3*e^2*x^(3/2) + 30*d^4*e*x^2 - 60*d^5*x^(5/2)) + 180*b*d^6*n*(-20*a + 49*b*n)*x^3*Log[e + d*Sqrt[x]] + 90*b*d^6*n*(20*a - 49*b*n)*x^3*Log[x]))/(108000*e^6*x^3)","A",1
442,1,219,234,0.2389056,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \, dx","Integrate[x^3*(a + b*Log[c*(d + e*x^(1/3))^n]),x]","\frac{a x^4}{4}+\frac{1}{4} b x^4 \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-\frac{1}{4} b e n \left(\frac{d^{12} \log \left(d+e \sqrt[3]{x}\right)}{e^{13}}-\frac{d^{11} \sqrt[3]{x}}{e^{12}}+\frac{d^{10} x^{2/3}}{2 e^{11}}-\frac{d^9 x}{3 e^{10}}+\frac{d^8 x^{4/3}}{4 e^9}-\frac{d^7 x^{5/3}}{5 e^8}+\frac{d^6 x^2}{6 e^7}-\frac{d^5 x^{7/3}}{7 e^6}+\frac{d^4 x^{8/3}}{8 e^5}-\frac{d^3 x^3}{9 e^4}+\frac{d^2 x^{10/3}}{10 e^3}-\frac{d x^{11/3}}{11 e^2}+\frac{x^4}{12 e}\right)","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)-\frac{b d^{12} n \log \left(d+e \sqrt[3]{x}\right)}{4 e^{12}}+\frac{b d^{11} n \sqrt[3]{x}}{4 e^{11}}-\frac{b d^{10} n x^{2/3}}{8 e^{10}}+\frac{b d^9 n x}{12 e^9}-\frac{b d^8 n x^{4/3}}{16 e^8}+\frac{b d^7 n x^{5/3}}{20 e^7}-\frac{b d^6 n x^2}{24 e^6}+\frac{b d^5 n x^{7/3}}{28 e^5}-\frac{b d^4 n x^{8/3}}{32 e^4}+\frac{b d^3 n x^3}{36 e^3}-\frac{b d^2 n x^{10/3}}{40 e^2}+\frac{b d n x^{11/3}}{44 e}-\frac{1}{48} b n x^4",1,"(a*x^4)/4 - (b*e*n*(-((d^11*x^(1/3))/e^12) + (d^10*x^(2/3))/(2*e^11) - (d^9*x)/(3*e^10) + (d^8*x^(4/3))/(4*e^9) - (d^7*x^(5/3))/(5*e^8) + (d^6*x^2)/(6*e^7) - (d^5*x^(7/3))/(7*e^6) + (d^4*x^(8/3))/(8*e^5) - (d^3*x^3)/(9*e^4) + (d^2*x^(10/3))/(10*e^3) - (d*x^(11/3))/(11*e^2) + x^4/(12*e) + (d^12*Log[d + e*x^(1/3)])/e^13))/4 + (b*x^4*Log[c*(d + e*x^(1/3))^n])/4","A",1
443,1,176,185,0.141236,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*(d + e*x^(1/3))^n]),x]","\frac{a x^3}{3}+\frac{1}{3} b x^3 \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-\frac{1}{3} b e n \left(-\frac{d^9 \log \left(d+e \sqrt[3]{x}\right)}{e^{10}}+\frac{d^8 \sqrt[3]{x}}{e^9}-\frac{d^7 x^{2/3}}{2 e^8}+\frac{d^6 x}{3 e^7}-\frac{d^5 x^{4/3}}{4 e^6}+\frac{d^4 x^{5/3}}{5 e^5}-\frac{d^3 x^2}{6 e^4}+\frac{d^2 x^{7/3}}{7 e^3}-\frac{d x^{8/3}}{8 e^2}+\frac{x^3}{9 e}\right)","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)+\frac{b d^9 n \log \left(d+e \sqrt[3]{x}\right)}{3 e^9}-\frac{b d^8 n \sqrt[3]{x}}{3 e^8}+\frac{b d^7 n x^{2/3}}{6 e^7}-\frac{b d^6 n x}{9 e^6}+\frac{b d^5 n x^{4/3}}{12 e^5}-\frac{b d^4 n x^{5/3}}{15 e^4}+\frac{b d^3 n x^2}{18 e^3}-\frac{b d^2 n x^{7/3}}{21 e^2}+\frac{b d n x^{8/3}}{24 e}-\frac{1}{27} b n x^3",1,"(a*x^3)/3 - (b*e*n*((d^8*x^(1/3))/e^9 - (d^7*x^(2/3))/(2*e^8) + (d^6*x)/(3*e^7) - (d^5*x^(4/3))/(4*e^6) + (d^4*x^(5/3))/(5*e^5) - (d^3*x^2)/(6*e^4) + (d^2*x^(7/3))/(7*e^3) - (d*x^(8/3))/(8*e^2) + x^3/(9*e) - (d^9*Log[d + e*x^(1/3)])/e^10))/3 + (b*x^3*Log[c*(d + e*x^(1/3))^n])/3","A",1
444,1,133,136,0.0988989,"\int x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \, dx","Integrate[x*(a + b*Log[c*(d + e*x^(1/3))^n]),x]","\frac{a x^2}{2}+\frac{1}{2} b x^2 \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-\frac{1}{2} b e n \left(\frac{d^6 \log \left(d+e \sqrt[3]{x}\right)}{e^7}-\frac{d^5 \sqrt[3]{x}}{e^6}+\frac{d^4 x^{2/3}}{2 e^5}-\frac{d^3 x}{3 e^4}+\frac{d^2 x^{4/3}}{4 e^3}-\frac{d x^{5/3}}{5 e^2}+\frac{x^2}{6 e}\right)","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)-\frac{b d^6 n \log \left(d+e \sqrt[3]{x}\right)}{2 e^6}+\frac{b d^5 n \sqrt[3]{x}}{2 e^5}-\frac{b d^4 n x^{2/3}}{4 e^4}+\frac{b d^3 n x}{6 e^3}-\frac{b d^2 n x^{4/3}}{8 e^2}+\frac{b d n x^{5/3}}{10 e}-\frac{1}{12} b n x^2",1,"(a*x^2)/2 - (b*e*n*(-((d^5*x^(1/3))/e^6) + (d^4*x^(2/3))/(2*e^5) - (d^3*x)/(3*e^4) + (d^2*x^(4/3))/(4*e^3) - (d*x^(5/3))/(5*e^2) + x^2/(6*e) + (d^6*Log[d + e*x^(1/3)])/e^7))/2 + (b*x^2*Log[c*(d + e*x^(1/3))^n])/2","A",1
445,1,77,77,0.0440565,"\int \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \, dx","Integrate[a + b*Log[c*(d + e*x^(1/3))^n],x]","a x+b x \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)+\frac{b d^3 n \log \left(d+e \sqrt[3]{x}\right)}{e^3}-\frac{b d^2 n \sqrt[3]{x}}{e^2}+\frac{b d n x^{2/3}}{2 e}-\frac{b n x}{3}","a x+b x \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)+\frac{b d^3 n \log \left(d+e \sqrt[3]{x}\right)}{e^3}-\frac{b d^2 n \sqrt[3]{x}}{e^2}+\frac{b d n x^{2/3}}{2 e}-\frac{b n x}{3}",1,"-((b*d^2*n*x^(1/3))/e^2) + (b*d*n*x^(2/3))/(2*e) + a*x - (b*n*x)/3 + (b*d^3*n*Log[d + e*x^(1/3)])/e^3 + b*x*Log[c*(d + e*x^(1/3))^n]","A",1
446,1,53,51,0.0034497,"\int \frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])/x,x]","a \log (x)+3 b \log \left(-\frac{e \sqrt[3]{x}}{d}\right) \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)+3 b n \text{Li}_2\left(\frac{d+e \sqrt[3]{x}}{d}\right)","3 \log \left(-\frac{e \sqrt[3]{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)+3 b n \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right)",1,"3*b*Log[c*(d + e*x^(1/3))^n]*Log[-((e*x^(1/3))/d)] + a*Log[x] + 3*b*n*PolyLog[2, (d + e*x^(1/3))/d]","A",1
447,1,84,87,0.0368506,"\int \frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])/x^2,x]","-\frac{a}{x}-\frac{b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x}+b e n \left(-\frac{e^2 \log \left(d+e \sqrt[3]{x}\right)}{d^3}+\frac{e^2 \log (x)}{3 d^3}+\frac{e}{d^2 \sqrt[3]{x}}-\frac{1}{2 d x^{2/3}}\right)","-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x}-\frac{b e^3 n \log \left(d+e \sqrt[3]{x}\right)}{d^3}+\frac{b e^3 n \log (x)}{3 d^3}+\frac{b e^2 n}{d^2 \sqrt[3]{x}}-\frac{b e n}{2 d x^{2/3}}",1,"-(a/x) - (b*Log[c*(d + e*x^(1/3))^n])/x + b*e*n*(-1/2*1/(d*x^(2/3)) + e/(d^2*x^(1/3)) - (e^2*Log[d + e*x^(1/3)])/d^3 + (e^2*Log[x])/(3*d^3))","A",1
448,1,134,143,0.145394,"\int \frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])/x^3,x]","-\frac{a}{2 x^2}-\frac{b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{2 x^2}+\frac{1}{2} b e n \left(\frac{e^5 \log \left(d+e \sqrt[3]{x}\right)}{d^6}-\frac{e^5 \log (x)}{3 d^6}-\frac{e^4}{d^5 \sqrt[3]{x}}+\frac{e^3}{2 d^4 x^{2/3}}-\frac{e^2}{3 d^3 x}+\frac{e}{4 d^2 x^{4/3}}-\frac{1}{5 d x^{5/3}}\right)","-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{2 x^2}+\frac{b e^6 n \log \left(d+e \sqrt[3]{x}\right)}{2 d^6}-\frac{b e^6 n \log (x)}{6 d^6}-\frac{b e^5 n}{2 d^5 \sqrt[3]{x}}+\frac{b e^4 n}{4 d^4 x^{2/3}}-\frac{b e^3 n}{6 d^3 x}+\frac{b e^2 n}{8 d^2 x^{4/3}}-\frac{b e n}{10 d x^{5/3}}",1,"-1/2*a/x^2 - (b*Log[c*(d + e*x^(1/3))^n])/(2*x^2) + (b*e*n*(-1/5*1/(d*x^(5/3)) + e/(4*d^2*x^(4/3)) - e^2/(3*d^3*x) + e^3/(2*d^4*x^(2/3)) - e^4/(d^5*x^(1/3)) + (e^5*Log[d + e*x^(1/3)])/d^6 - (e^5*Log[x])/(3*d^6)))/2","A",1
449,1,177,192,0.1975793,"\int \frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])/x^4,x]","-\frac{a}{3 x^3}-\frac{b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{3 x^3}+\frac{1}{3} b e n \left(-\frac{e^8 \log \left(d+e \sqrt[3]{x}\right)}{d^9}+\frac{e^8 \log (x)}{3 d^9}+\frac{e^7}{d^8 \sqrt[3]{x}}-\frac{e^6}{2 d^7 x^{2/3}}+\frac{e^5}{3 d^6 x}-\frac{e^4}{4 d^5 x^{4/3}}+\frac{e^3}{5 d^4 x^{5/3}}-\frac{e^2}{6 d^3 x^2}+\frac{e}{7 d^2 x^{7/3}}-\frac{1}{8 d x^{8/3}}\right)","-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{3 x^3}-\frac{b e^9 n \log \left(d+e \sqrt[3]{x}\right)}{3 d^9}+\frac{b e^9 n \log (x)}{9 d^9}+\frac{b e^8 n}{3 d^8 \sqrt[3]{x}}-\frac{b e^7 n}{6 d^7 x^{2/3}}+\frac{b e^6 n}{9 d^6 x}-\frac{b e^5 n}{12 d^5 x^{4/3}}+\frac{b e^4 n}{15 d^4 x^{5/3}}-\frac{b e^3 n}{18 d^3 x^2}+\frac{b e^2 n}{21 d^2 x^{7/3}}-\frac{b e n}{24 d x^{8/3}}",1,"-1/3*a/x^3 - (b*Log[c*(d + e*x^(1/3))^n])/(3*x^3) + (b*e*n*(-1/8*1/(d*x^(8/3)) + e/(7*d^2*x^(7/3)) - e^2/(6*d^3*x^2) + e^3/(5*d^4*x^(5/3)) - e^4/(4*d^5*x^(4/3)) + e^5/(3*d^6*x) - e^6/(2*d^7*x^(2/3)) + e^7/(d^8*x^(1/3)) - (e^8*Log[d + e*x^(1/3)])/d^9 + (e^8*Log[x])/(3*d^9)))/3","A",1
450,1,411,680,0.5718119,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \, dx","Integrate[x^2*(a + b*Log[c*(d + e*x^(1/3))^n])^2,x]","\frac{e \sqrt[3]{x} \left(3175200 a^2 e^8 x^{8/3}-2520 a b n \left(2520 d^8-1260 d^7 e \sqrt[3]{x}+840 d^6 e^2 x^{2/3}-630 d^5 e^3 x+504 d^4 e^4 x^{4/3}-420 d^3 e^5 x^{5/3}+360 d^2 e^6 x^2-315 d e^7 x^{7/3}+280 e^8 x^{8/3}\right)+b^2 n^2 \left(17965080 d^8-5807340 d^7 e \sqrt[3]{x}+2813160 d^6 e^2 x^{2/3}-1580670 d^5 e^3 x+947016 d^4 e^4 x^{4/3}-577500 d^3 e^5 x^{5/3}+343800 d^2 e^6 x^2-187425 d e^7 x^{7/3}+78400 e^8 x^{8/3}\right)\right)+2520 b \left(2520 a \left(d^9+e^9 x^3\right)-b n \left(7129 d^9+2520 d^8 e \sqrt[3]{x}-1260 d^7 e^2 x^{2/3}+840 d^6 e^3 x-630 d^5 e^4 x^{4/3}+504 d^4 e^5 x^{5/3}-420 d^3 e^6 x^2+360 d^2 e^7 x^{7/3}-315 d e^8 x^{8/3}+280 e^9 x^3\right)\right) \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)+3175200 b^2 \left(d^9+e^9 x^3\right) \log ^2\left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{9525600 e^9}","\frac{2 b d^9 n \log \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{3 e^9}-\frac{6 b d^8 n \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{e^9}+\frac{12 b d^7 n \left(d+e \sqrt[3]{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{e^9}-\frac{56 b d^6 n \left(d+e \sqrt[3]{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{3 e^9}+\frac{21 b d^5 n \left(d+e \sqrt[3]{x}\right)^4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{e^9}-\frac{84 b d^4 n \left(d+e \sqrt[3]{x}\right)^5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{5 e^9}+\frac{28 b d^3 n \left(d+e \sqrt[3]{x}\right)^6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{3 e^9}-\frac{24 b d^2 n \left(d+e \sqrt[3]{x}\right)^7 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{7 e^9}+\frac{3 b d n \left(d+e \sqrt[3]{x}\right)^8 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{4 e^9}-\frac{2 b n \left(d+e \sqrt[3]{x}\right)^9 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{27 e^9}+\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2-\frac{b^2 d^9 n^2 \log ^2\left(d+e \sqrt[3]{x}\right)}{3 e^9}+\frac{6 b^2 d^8 n^2 \sqrt[3]{x}}{e^8}-\frac{6 b^2 d^7 n^2 \left(d+e \sqrt[3]{x}\right)^2}{e^9}+\frac{56 b^2 d^6 n^2 \left(d+e \sqrt[3]{x}\right)^3}{9 e^9}-\frac{21 b^2 d^5 n^2 \left(d+e \sqrt[3]{x}\right)^4}{4 e^9}+\frac{84 b^2 d^4 n^2 \left(d+e \sqrt[3]{x}\right)^5}{25 e^9}-\frac{14 b^2 d^3 n^2 \left(d+e \sqrt[3]{x}\right)^6}{9 e^9}+\frac{24 b^2 d^2 n^2 \left(d+e \sqrt[3]{x}\right)^7}{49 e^9}-\frac{3 b^2 d n^2 \left(d+e \sqrt[3]{x}\right)^8}{32 e^9}+\frac{2 b^2 n^2 \left(d+e \sqrt[3]{x}\right)^9}{243 e^9}",1,"(e*x^(1/3)*(3175200*a^2*e^8*x^(8/3) - 2520*a*b*n*(2520*d^8 - 1260*d^7*e*x^(1/3) + 840*d^6*e^2*x^(2/3) - 630*d^5*e^3*x + 504*d^4*e^4*x^(4/3) - 420*d^3*e^5*x^(5/3) + 360*d^2*e^6*x^2 - 315*d*e^7*x^(7/3) + 280*e^8*x^(8/3)) + b^2*n^2*(17965080*d^8 - 5807340*d^7*e*x^(1/3) + 2813160*d^6*e^2*x^(2/3) - 1580670*d^5*e^3*x + 947016*d^4*e^4*x^(4/3) - 577500*d^3*e^5*x^(5/3) + 343800*d^2*e^6*x^2 - 187425*d*e^7*x^(7/3) + 78400*e^8*x^(8/3))) + 2520*b*(2520*a*(d^9 + e^9*x^3) - b*n*(7129*d^9 + 2520*d^8*e*x^(1/3) - 1260*d^7*e^2*x^(2/3) + 840*d^6*e^3*x - 630*d^5*e^4*x^(4/3) + 504*d^4*e^5*x^(5/3) - 420*d^3*e^6*x^2 + 360*d^2*e^7*x^(7/3) - 315*d*e^8*x^(8/3) + 280*e^9*x^3))*Log[c*(d + e*x^(1/3))^n] + 3175200*b^2*(d^9 + e^9*x^3)*Log[c*(d + e*x^(1/3))^n]^2)/(9525600*e^9)","A",1
451,1,301,480,0.3908992,"\int x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \, dx","Integrate[x*(a + b*Log[c*(d + e*x^(1/3))^n])^2,x]","\frac{e \sqrt[3]{x} \left(1800 a^2 e^5 x^{5/3}+60 a b n \left(60 d^5-30 d^4 e \sqrt[3]{x}+20 d^3 e^2 x^{2/3}-15 d^2 e^3 x+12 d e^4 x^{4/3}-10 e^5 x^{5/3}\right)+b^2 n^2 \left(-8820 d^5+2610 d^4 e \sqrt[3]{x}-1140 d^3 e^2 x^{2/3}+555 d^2 e^3 x-264 d e^4 x^{4/3}+100 e^5 x^{5/3}\right)\right)-60 b \left(60 a \left(d^6-e^6 x^2\right)+b n \left(-147 d^6-60 d^5 e \sqrt[3]{x}+30 d^4 e^2 x^{2/3}-20 d^3 e^3 x+15 d^2 e^4 x^{4/3}-12 d e^5 x^{5/3}+10 e^6 x^2\right)\right) \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-1800 b^2 \left(d^6-e^6 x^2\right) \log ^2\left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{3600 e^6}","-\frac{b d^6 n \log \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{e^6}+\frac{6 b d^5 n \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{e^6}-\frac{15 b d^4 n \left(d+e \sqrt[3]{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{2 e^6}+\frac{20 b d^3 n \left(d+e \sqrt[3]{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{3 e^6}-\frac{15 b d^2 n \left(d+e \sqrt[3]{x}\right)^4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{4 e^6}+\frac{6 b d n \left(d+e \sqrt[3]{x}\right)^5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{5 e^6}-\frac{b n \left(d+e \sqrt[3]{x}\right)^6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{6 e^6}+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2+\frac{b^2 d^6 n^2 \log ^2\left(d+e \sqrt[3]{x}\right)}{2 e^6}-\frac{6 b^2 d^5 n^2 \sqrt[3]{x}}{e^5}+\frac{15 b^2 d^4 n^2 \left(d+e \sqrt[3]{x}\right)^2}{4 e^6}-\frac{20 b^2 d^3 n^2 \left(d+e \sqrt[3]{x}\right)^3}{9 e^6}+\frac{15 b^2 d^2 n^2 \left(d+e \sqrt[3]{x}\right)^4}{16 e^6}-\frac{6 b^2 d n^2 \left(d+e \sqrt[3]{x}\right)^5}{25 e^6}+\frac{b^2 n^2 \left(d+e \sqrt[3]{x}\right)^6}{36 e^6}",1,"(e*x^(1/3)*(1800*a^2*e^5*x^(5/3) + 60*a*b*n*(60*d^5 - 30*d^4*e*x^(1/3) + 20*d^3*e^2*x^(2/3) - 15*d^2*e^3*x + 12*d*e^4*x^(4/3) - 10*e^5*x^(5/3)) + b^2*n^2*(-8820*d^5 + 2610*d^4*e*x^(1/3) - 1140*d^3*e^2*x^(2/3) + 555*d^2*e^3*x - 264*d*e^4*x^(4/3) + 100*e^5*x^(5/3))) - 60*b*(60*a*(d^6 - e^6*x^2) + b*n*(-147*d^6 - 60*d^5*e*x^(1/3) + 30*d^4*e^2*x^(2/3) - 20*d^3*e^3*x + 15*d^2*e^4*x^(4/3) - 12*d*e^5*x^(5/3) + 10*e^6*x^2))*Log[c*(d + e*x^(1/3))^n] - 1800*b^2*(d^6 - e^6*x^2)*Log[c*(d + e*x^(1/3))^n]^2)/(3600*e^6)","A",1
452,1,197,267,0.1315209,"\int \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])^2,x]","\frac{18 a^2 \left(d^3+e^3 x\right)+6 b \left(6 a \left(d^3+e^3 x\right)-b n \left(11 d^3+6 d^2 e \sqrt[3]{x}-3 d e^2 x^{2/3}+2 e^3 x\right)\right) \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)+6 a b n \left(7 d^3-6 d^2 e \sqrt[3]{x}+3 d e^2 x^{2/3}-2 e^3 x\right)+18 b^2 \left(d^3+e^3 x\right) \log ^2\left(c \left(d+e \sqrt[3]{x}\right)^n\right)+b^2 e n^2 \sqrt[3]{x} \left(66 d^2-15 d e \sqrt[3]{x}+4 e^2 x^{2/3}\right)}{18 e^3}","\frac{2 b d^3 n \log \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{e^3}-\frac{6 b d^2 n \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{e^3}+\frac{3 b d n \left(d+e \sqrt[3]{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{e^3}-\frac{2 b n \left(d+e \sqrt[3]{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{3 e^3}+x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2-\frac{b^2 d^3 n^2 \log ^2\left(d+e \sqrt[3]{x}\right)}{e^3}+\frac{6 b^2 d^2 n^2 \sqrt[3]{x}}{e^2}-\frac{3 b^2 d n^2 \left(d+e \sqrt[3]{x}\right)^2}{2 e^3}+\frac{2 b^2 n^2 \left(d+e \sqrt[3]{x}\right)^3}{9 e^3}",1,"(b^2*e*n^2*(66*d^2 - 15*d*e*x^(1/3) + 4*e^2*x^(2/3))*x^(1/3) + 6*a*b*n*(7*d^3 - 6*d^2*e*x^(1/3) + 3*d*e^2*x^(2/3) - 2*e^3*x) + 18*a^2*(d^3 + e^3*x) + 6*b*(6*a*(d^3 + e^3*x) - b*n*(11*d^3 + 6*d^2*e*x^(1/3) - 3*d*e^2*x^(2/3) + 2*e^3*x))*Log[c*(d + e*x^(1/3))^n] + 18*b^2*(d^3 + e^3*x)*Log[c*(d + e*x^(1/3))^n]^2)/(18*e^3)","A",1
453,1,195,93,0.1114148,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{x} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])^2/x,x]","2 b n \left(\log (x) \left(\log \left(d+e \sqrt[3]{x}\right)-\log \left(\frac{e \sqrt[3]{x}}{d}+1\right)\right)-3 \text{Li}_2\left(-\frac{e \sqrt[3]{x}}{d}\right)\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)+\log (x) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)^2+3 b^2 n^2 \left(-2 \text{Li}_3\left(\frac{\sqrt[3]{x} e}{d}+1\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right) \log \left(d+e \sqrt[3]{x}\right)+\log \left(-\frac{e \sqrt[3]{x}}{d}\right) \log ^2\left(d+e \sqrt[3]{x}\right)\right)","6 b n \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)+3 \log \left(-\frac{e \sqrt[3]{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2-6 b^2 n^2 \text{Li}_3\left(\frac{\sqrt[3]{x} e}{d}+1\right)",1,"(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2*Log[x] + 2*b*n*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])*((Log[d + e*x^(1/3)] - Log[1 + (e*x^(1/3))/d])*Log[x] - 3*PolyLog[2, -((e*x^(1/3))/d)]) + 3*b^2*n^2*(Log[d + e*x^(1/3)]^2*Log[-((e*x^(1/3))/d)] + 2*Log[d + e*x^(1/3)]*PolyLog[2, 1 + (e*x^(1/3))/d] - 2*PolyLog[3, 1 + (e*x^(1/3))/d])","B",1
454,1,274,231,0.2308424,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])^2/x^2,x]","3 \left(\frac{2}{3} b e n \left(-\frac{e^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{2 b d^3 n}+\frac{e^2 \log \left(-\frac{e \sqrt[3]{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^3}+\frac{e \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^2 \sqrt[3]{x}}-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{2 d x^{2/3}}+\frac{b e^2 n \text{Li}_2\left(\frac{d+e \sqrt[3]{x}}{d}\right)}{d^3}-\frac{b e^2 n \left(\frac{\log (x)}{3 d}-\frac{\log \left(d+e \sqrt[3]{x}\right)}{d}\right)}{d^2}-\frac{b e n \left(-\frac{e \log \left(d+e \sqrt[3]{x}\right)}{d^2}+\frac{e \log (x)}{3 d^2}+\frac{1}{d \sqrt[3]{x}}\right)}{2 d}\right)-\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{3 x}\right)","\frac{2 b e^3 n \log \left(1-\frac{d}{d+e \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^3}+\frac{2 b e^2 n \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^3 \sqrt[3]{x}}-\frac{b e n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d x^{2/3}}-\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{x}-\frac{2 b^2 e^3 n^2 \text{Li}_2\left(\frac{d}{d+e \sqrt[3]{x}}\right)}{d^3}+\frac{b^2 e^3 n^2 \log \left(d+e \sqrt[3]{x}\right)}{d^3}-\frac{b^2 e^3 n^2 \log (x)}{d^3}-\frac{b^2 e^2 n^2}{d^2 \sqrt[3]{x}}",1,"3*(-1/3*(a + b*Log[c*(d + e*x^(1/3))^n])^2/x + (2*b*e*n*(-1/2*(a + b*Log[c*(d + e*x^(1/3))^n])/(d*x^(2/3)) + (e*(a + b*Log[c*(d + e*x^(1/3))^n]))/(d^2*x^(1/3)) - (e^2*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(2*b*d^3*n) + (e^2*(a + b*Log[c*(d + e*x^(1/3))^n])*Log[-((e*x^(1/3))/d)])/d^3 - (b*e^2*n*(-(Log[d + e*x^(1/3)]/d) + Log[x]/(3*d)))/d^2 - (b*e*n*(1/(d*x^(1/3)) - (e*Log[d + e*x^(1/3)])/d^2 + (e*Log[x])/(3*d^2)))/(2*d) + (b*e^2*n*PolyLog[2, (d + e*x^(1/3))/d])/d^3))/3)","A",1
455,1,533,405,0.2856526,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])^2/x^3,x]","-\frac{180 a^2 d^6+360 a b d^6 \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-360 a b e^6 x^2 \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)+72 a b d^5 e n \sqrt[3]{x}-90 a b d^4 e^2 n x^{2/3}+120 a b d^3 e^3 n x-180 a b d^2 e^4 n x^{4/3}+360 a b e^6 n x^2 \log \left(-\frac{e \sqrt[3]{x}}{d}\right)+360 a b d e^5 n x^{5/3}+180 b^2 d^6 \log ^2\left(c \left(d+e \sqrt[3]{x}\right)^n\right)+72 b^2 d^5 e n \sqrt[3]{x} \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-90 b^2 d^4 e^2 n x^{2/3} \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)+120 b^2 d^3 e^3 n x \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-180 b^2 d^2 e^4 n x^{4/3} \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-180 b^2 e^6 x^2 \log ^2\left(c \left(d+e \sqrt[3]{x}\right)^n\right)+360 b^2 e^6 n x^2 \log \left(-\frac{e \sqrt[3]{x}}{d}\right) \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)+360 b^2 d e^5 n x^{5/3} \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)+18 b^2 d^4 e^2 n^2 x^{2/3}-54 b^2 d^3 e^3 n^2 x+141 b^2 d^2 e^4 n^2 x^{4/3}+360 b^2 e^6 n^2 x^2 \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right)+822 b^2 e^6 n^2 x^2 \log \left(d+e \sqrt[3]{x}\right)-462 b^2 d e^5 n^2 x^{5/3}-274 b^2 e^6 n^2 x^2 \log (x)}{360 d^6 x^2}","-\frac{b e^6 n \log \left(1-\frac{d}{d+e \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^6}-\frac{b e^5 n \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^6 \sqrt[3]{x}}+\frac{b e^4 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{2 d^4 x^{2/3}}-\frac{b e^3 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{3 d^3 x}+\frac{b e^2 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{4 d^2 x^{4/3}}-\frac{b e n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{5 d x^{5/3}}-\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{2 x^2}+\frac{b^2 e^6 n^2 \text{Li}_2\left(\frac{d}{d+e \sqrt[3]{x}}\right)}{d^6}-\frac{77 b^2 e^6 n^2 \log \left(d+e \sqrt[3]{x}\right)}{60 d^6}+\frac{137 b^2 e^6 n^2 \log (x)}{180 d^6}+\frac{77 b^2 e^5 n^2}{60 d^5 \sqrt[3]{x}}-\frac{47 b^2 e^4 n^2}{120 d^4 x^{2/3}}+\frac{3 b^2 e^3 n^2}{20 d^3 x}-\frac{b^2 e^2 n^2}{20 d^2 x^{4/3}}",1,"-1/360*(180*a^2*d^6 + 72*a*b*d^5*e*n*x^(1/3) - 90*a*b*d^4*e^2*n*x^(2/3) + 18*b^2*d^4*e^2*n^2*x^(2/3) + 120*a*b*d^3*e^3*n*x - 54*b^2*d^3*e^3*n^2*x - 180*a*b*d^2*e^4*n*x^(4/3) + 141*b^2*d^2*e^4*n^2*x^(4/3) + 360*a*b*d*e^5*n*x^(5/3) - 462*b^2*d*e^5*n^2*x^(5/3) + 822*b^2*e^6*n^2*x^2*Log[d + e*x^(1/3)] + 360*a*b*d^6*Log[c*(d + e*x^(1/3))^n] + 72*b^2*d^5*e*n*x^(1/3)*Log[c*(d + e*x^(1/3))^n] - 90*b^2*d^4*e^2*n*x^(2/3)*Log[c*(d + e*x^(1/3))^n] + 120*b^2*d^3*e^3*n*x*Log[c*(d + e*x^(1/3))^n] - 180*b^2*d^2*e^4*n*x^(4/3)*Log[c*(d + e*x^(1/3))^n] + 360*b^2*d*e^5*n*x^(5/3)*Log[c*(d + e*x^(1/3))^n] - 360*a*b*e^6*x^2*Log[c*(d + e*x^(1/3))^n] + 180*b^2*d^6*Log[c*(d + e*x^(1/3))^n]^2 - 180*b^2*e^6*x^2*Log[c*(d + e*x^(1/3))^n]^2 + 360*a*b*e^6*n*x^2*Log[-((e*x^(1/3))/d)] + 360*b^2*e^6*n*x^2*Log[c*(d + e*x^(1/3))^n]*Log[-((e*x^(1/3))/d)] - 274*b^2*e^6*n^2*x^2*Log[x] + 360*b^2*e^6*n^2*x^2*PolyLog[2, 1 + (e*x^(1/3))/d])/(d^6*x^2)","A",1
456,1,1009,1835,1.3072093,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \, dx","Integrate[x^3*(a + b*Log[c*(d + e*x^(1/3))^n])^3,x]","\frac{-3550000608000 b^3 \left(d^{12}-e^{12} x^4\right) \log ^3\left(c \left(d+e \sqrt[3]{x}\right)^n\right)-384199200 b^2 \left(27720 a \left(d^{12}-e^{12} x^4\right)+b n \left(-86021 d^{12}-27720 e \sqrt[3]{x} d^{11}+13860 e^2 x^{2/3} d^{10}-9240 e^3 x d^9+6930 e^4 x^{4/3} d^8-5544 e^5 x^{5/3} d^7+4620 e^6 x^2 d^6-3960 e^7 x^{7/3} d^5+3465 e^8 x^{8/3} d^4-3080 e^9 x^3 d^3+2772 e^{10} x^{10/3} d^2-2520 e^{11} x^{11/3} d+2310 e^{12} x^4\right)\right) \log ^2\left(c \left(d+e \sqrt[3]{x}\right)^n\right)-27720 b \left(384199200 \left(d^{12}-e^{12} x^4\right) a^2-27720 b n \left(86021 d^{12}+27720 e \sqrt[3]{x} d^{11}-13860 e^2 x^{2/3} d^{10}+9240 e^3 x d^9-6930 e^4 x^{4/3} d^8+5544 e^5 x^{5/3} d^7-4620 e^6 x^2 d^6+3960 e^7 x^{7/3} d^5-3465 e^8 x^{8/3} d^4+3080 e^9 x^3 d^3-2772 e^{10} x^{10/3} d^2+2520 e^{11} x^{11/3} d-2310 e^{12} x^4\right) a+b^2 n^2 \left(4301068993 d^{12}+2384502120 e \sqrt[3]{x} d^{11}-808051860 e^2 x^{2/3} d^{10}+410634840 e^3 x d^9-243942930 e^4 x^{4/3} d^8+156734424 e^5 x^{5/3} d^7-104998740 e^6 x^2 d^6+71703720 e^7 x^{7/3} d^5-49019355 e^8 x^{8/3} d^4+32900560 e^9 x^3 d^3-21072744 e^{10} x^{10/3} d^2+12171600 e^{11} x^{11/3} d-5336100 e^{12} x^4\right)\right) \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)+e \sqrt[3]{x} \left(3550000608000 a^3 x^{11/3} e^{11}+b^3 n^3 \left(119225632485960 d^{11}-26563616859780 e \sqrt[3]{x} d^{10}+10242678720120 e^2 x^{2/3} d^9-4836309598890 e^3 x d^8+2516628075192 e^4 x^{4/3} d^7-1373077023780 e^5 x^{5/3} d^6+761128152840 e^6 x^2 d^5-417533743935 e^7 x^{7/3} d^4+220161492320 e^8 x^{8/3} d^3-106944990768 e^9 x^3 d^2+44119404000 e^{10} x^{10/3} d-12326391000 e^{11} x^{11/3}\right)-27720 a b^2 n^2 \left(2384502120 d^{11}-808051860 e \sqrt[3]{x} d^{10}+410634840 e^2 x^{2/3} d^9-243942930 e^3 x d^8+156734424 e^4 x^{4/3} d^7-104998740 e^5 x^{5/3} d^6+71703720 e^6 x^2 d^5-49019355 e^7 x^{7/3} d^4+32900560 e^8 x^{8/3} d^3-21072744 e^9 x^3 d^2+12171600 e^{10} x^{10/3} d-5336100 e^{11} x^{11/3}\right)+384199200 a^2 b n \left(27720 d^{11}-13860 e \sqrt[3]{x} d^{10}+9240 e^2 x^{2/3} d^9-6930 e^3 x d^8+5544 e^4 x^{4/3} d^7-4620 e^5 x^{5/3} d^6+3960 e^6 x^2 d^5-3465 e^7 x^{7/3} d^4+3080 e^8 x^{8/3} d^3-2772 e^9 x^3 d^2+2520 e^{10} x^{10/3} d-2310 e^{11} x^{11/3}\right)\right)}{14200002432000 e^{12}}","-\frac{b^3 n^3 \left(d+e \sqrt[3]{x}\right)^{12}}{1152 e^{12}}+\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^{12}}{4 e^{12}}-\frac{b n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^{12}}{16 e^{12}}+\frac{b^2 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^{12}}{96 e^{12}}+\frac{18 b^3 d n^3 \left(d+e \sqrt[3]{x}\right)^{11}}{1331 e^{12}}-\frac{3 d \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^{11}}{e^{12}}+\frac{9 b d n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^{11}}{11 e^{12}}-\frac{18 b^2 d n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^{11}}{121 e^{12}}-\frac{99 b^3 d^2 n^3 \left(d+e \sqrt[3]{x}\right)^{10}}{1000 e^{12}}+\frac{33 d^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^{10}}{2 e^{12}}-\frac{99 b d^2 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^{10}}{20 e^{12}}+\frac{99 b^2 d^2 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^{10}}{100 e^{12}}+\frac{110 b^3 d^3 n^3 \left(d+e \sqrt[3]{x}\right)^9}{243 e^{12}}-\frac{55 d^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^9}{e^{12}}+\frac{55 b d^3 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^9}{3 e^{12}}-\frac{110 b^2 d^3 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^9}{27 e^{12}}-\frac{1485 b^3 d^4 n^3 \left(d+e \sqrt[3]{x}\right)^8}{1024 e^{12}}+\frac{495 d^4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^8}{4 e^{12}}-\frac{1485 b d^4 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^8}{32 e^{12}}+\frac{1485 b^2 d^4 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^8}{128 e^{12}}+\frac{1188 b^3 d^5 n^3 \left(d+e \sqrt[3]{x}\right)^7}{343 e^{12}}-\frac{198 d^5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^7}{e^{12}}+\frac{594 b d^5 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^7}{7 e^{12}}-\frac{1188 b^2 d^5 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^7}{49 e^{12}}-\frac{77 b^3 d^6 n^3 \left(d+e \sqrt[3]{x}\right)^6}{12 e^{12}}+\frac{231 d^6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^6}{e^{12}}-\frac{231 b d^6 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^6}{2 e^{12}}+\frac{77 b^2 d^6 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^6}{2 e^{12}}+\frac{1188 b^3 d^7 n^3 \left(d+e \sqrt[3]{x}\right)^5}{125 e^{12}}-\frac{198 d^7 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^5}{e^{12}}+\frac{594 b d^7 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^5}{5 e^{12}}-\frac{1188 b^2 d^7 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^5}{25 e^{12}}-\frac{1485 b^3 d^8 n^3 \left(d+e \sqrt[3]{x}\right)^4}{128 e^{12}}+\frac{495 d^8 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^4}{4 e^{12}}-\frac{1485 b d^8 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^4}{16 e^{12}}+\frac{1485 b^2 d^8 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^4}{32 e^{12}}+\frac{110 b^3 d^9 n^3 \left(d+e \sqrt[3]{x}\right)^3}{9 e^{12}}-\frac{55 d^9 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^3}{e^{12}}+\frac{55 b d^9 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^3}{e^{12}}-\frac{110 b^2 d^9 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^3}{3 e^{12}}-\frac{99 b^3 d^{10} n^3 \left(d+e \sqrt[3]{x}\right)^2}{8 e^{12}}+\frac{33 d^{10} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^2}{2 e^{12}}-\frac{99 b d^{10} n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^2}{4 e^{12}}+\frac{99 b^2 d^{10} n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^2}{4 e^{12}}-\frac{3 d^{11} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)}{e^{12}}+\frac{9 b d^{11} n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)}{e^{12}}-\frac{18 b^3 d^{11} n^2 \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right) \left(d+e \sqrt[3]{x}\right)}{e^{12}}+\frac{18 b^3 d^{11} n^3 \sqrt[3]{x}}{e^{11}}-\frac{18 a b^2 d^{11} n^2 \sqrt[3]{x}}{e^{11}}",1,"(e*x^(1/3)*(3550000608000*a^3*e^11*x^(11/3) + b^3*n^3*(119225632485960*d^11 - 26563616859780*d^10*e*x^(1/3) + 10242678720120*d^9*e^2*x^(2/3) - 4836309598890*d^8*e^3*x + 2516628075192*d^7*e^4*x^(4/3) - 1373077023780*d^6*e^5*x^(5/3) + 761128152840*d^5*e^6*x^2 - 417533743935*d^4*e^7*x^(7/3) + 220161492320*d^3*e^8*x^(8/3) - 106944990768*d^2*e^9*x^3 + 44119404000*d*e^10*x^(10/3) - 12326391000*e^11*x^(11/3)) - 27720*a*b^2*n^2*(2384502120*d^11 - 808051860*d^10*e*x^(1/3) + 410634840*d^9*e^2*x^(2/3) - 243942930*d^8*e^3*x + 156734424*d^7*e^4*x^(4/3) - 104998740*d^6*e^5*x^(5/3) + 71703720*d^5*e^6*x^2 - 49019355*d^4*e^7*x^(7/3) + 32900560*d^3*e^8*x^(8/3) - 21072744*d^2*e^9*x^3 + 12171600*d*e^10*x^(10/3) - 5336100*e^11*x^(11/3)) + 384199200*a^2*b*n*(27720*d^11 - 13860*d^10*e*x^(1/3) + 9240*d^9*e^2*x^(2/3) - 6930*d^8*e^3*x + 5544*d^7*e^4*x^(4/3) - 4620*d^6*e^5*x^(5/3) + 3960*d^5*e^6*x^2 - 3465*d^4*e^7*x^(7/3) + 3080*d^3*e^8*x^(8/3) - 2772*d^2*e^9*x^3 + 2520*d*e^10*x^(10/3) - 2310*e^11*x^(11/3))) - 27720*b*(b^2*n^2*(4301068993*d^12 + 2384502120*d^11*e*x^(1/3) - 808051860*d^10*e^2*x^(2/3) + 410634840*d^9*e^3*x - 243942930*d^8*e^4*x^(4/3) + 156734424*d^7*e^5*x^(5/3) - 104998740*d^6*e^6*x^2 + 71703720*d^5*e^7*x^(7/3) - 49019355*d^4*e^8*x^(8/3) + 32900560*d^3*e^9*x^3 - 21072744*d^2*e^10*x^(10/3) + 12171600*d*e^11*x^(11/3) - 5336100*e^12*x^4) - 27720*a*b*n*(86021*d^12 + 27720*d^11*e*x^(1/3) - 13860*d^10*e^2*x^(2/3) + 9240*d^9*e^3*x - 6930*d^8*e^4*x^(4/3) + 5544*d^7*e^5*x^(5/3) - 4620*d^6*e^6*x^2 + 3960*d^5*e^7*x^(7/3) - 3465*d^4*e^8*x^(8/3) + 3080*d^3*e^9*x^3 - 2772*d^2*e^10*x^(10/3) + 2520*d*e^11*x^(11/3) - 2310*e^12*x^4) + 384199200*a^2*(d^12 - e^12*x^4))*Log[c*(d + e*x^(1/3))^n] - 384199200*b^2*(27720*a*(d^12 - e^12*x^4) + b*n*(-86021*d^12 - 27720*d^11*e*x^(1/3) + 13860*d^10*e^2*x^(2/3) - 9240*d^9*e^3*x + 6930*d^8*e^4*x^(4/3) - 5544*d^7*e^5*x^(5/3) + 4620*d^6*e^6*x^2 - 3960*d^5*e^7*x^(7/3) + 3465*d^4*e^8*x^(8/3) - 3080*d^3*e^9*x^3 + 2772*d^2*e^10*x^(10/3) - 2520*d*e^11*x^(11/3) + 2310*e^12*x^4))*Log[c*(d + e*x^(1/3))^n]^2 - 3550000608000*b^3*(d^12 - e^12*x^4)*Log[c*(d + e*x^(1/3))^n]^3)/(14200002432000*e^12)","A",1
457,1,808,1357,0.8762221,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \, dx","Integrate[x^2*(a + b*Log[c*(d + e*x^(1/3))^n])^3,x]","\frac{2667168000 \left(d^9+e^9 x^3\right) a^3-3175200 b n \left(7129 d^9+2520 e \sqrt[3]{x} d^8-1260 e^2 x^{2/3} d^7+840 e^3 x d^6-630 e^4 x^{4/3} d^5+504 e^5 x^{5/3} d^4-420 e^6 x^2 d^3+360 e^7 x^{7/3} d^2-315 e^8 x^{8/3} d+280 e^9 x^3\right) a^2-2520 b^2 n^2 \left(26853209 d^9-17965080 e \sqrt[3]{x} d^8+5807340 e^2 x^{2/3} d^7-2813160 e^3 x d^6+1580670 e^4 x^{4/3} d^5-947016 e^5 x^{5/3} d^4+577500 e^6 x^2 d^3-343800 e^7 x^{7/3} d^2+187425 e^8 x^{8/3} d-78400 e^9 x^3\right) a+2667168000 b^3 \left(d^9+e^9 x^3\right) \log ^3\left(c \left(d+e \sqrt[3]{x}\right)^n\right)+3175200 b^2 \left(2520 a \left(d^9+e^9 x^3\right)-b n \left(7129 d^9+2520 e \sqrt[3]{x} d^8-1260 e^2 x^{2/3} d^7+840 e^3 x d^6-630 e^4 x^{4/3} d^5+504 e^5 x^{5/3} d^4-420 e^6 x^2 d^3+360 e^7 x^{7/3} d^2-315 e^8 x^{8/3} d+280 e^9 x^3\right)\right) \log ^2\left(c \left(d+e \sqrt[3]{x}\right)^n\right)+b^3 e n^3 \sqrt[3]{x} \left(-76356985320 d^8+15542491860 e \sqrt[3]{x} d^7-5483495640 e^2 x^{2/3} d^6+2340330930 e^3 x d^5-1075607064 e^4 x^{4/3} d^4+498592500 e^5 x^{5/3} d^3-219465000 e^6 x^2 d^2+83734875 e^7 x^{7/3} d-21952000 e^8 x^{8/3}\right)+2520 b \left(3175200 \left(d^9+e^9 x^3\right) a^2-2520 b n \left(7129 d^9+2520 e \sqrt[3]{x} d^8-1260 e^2 x^{2/3} d^7+840 e^3 x d^6-630 e^4 x^{4/3} d^5+504 e^5 x^{5/3} d^4-420 e^6 x^2 d^3+360 e^7 x^{7/3} d^2-315 e^8 x^{8/3} d+280 e^9 x^3\right) a+b^2 n^2 \left(30300391 d^9+17965080 e \sqrt[3]{x} d^8-5807340 e^2 x^{2/3} d^7+2813160 e^3 x d^6-1580670 e^4 x^{4/3} d^5+947016 e^5 x^{5/3} d^4-577500 e^6 x^2 d^3+343800 e^7 x^{7/3} d^2-187425 e^8 x^{8/3} d+78400 e^9 x^3\right)\right) \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{8001504000 e^9}","-\frac{2 b^3 n^3 \left(d+e \sqrt[3]{x}\right)^9}{729 e^9}+\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^9}{3 e^9}-\frac{b n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^9}{9 e^9}+\frac{2 b^2 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^9}{81 e^9}+\frac{9 b^3 d n^3 \left(d+e \sqrt[3]{x}\right)^8}{256 e^9}-\frac{3 d \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^8}{e^9}+\frac{9 b d n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^8}{8 e^9}-\frac{9 b^2 d n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^8}{32 e^9}-\frac{72 b^3 d^2 n^3 \left(d+e \sqrt[3]{x}\right)^7}{343 e^9}+\frac{12 d^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^7}{e^9}-\frac{36 b d^2 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^7}{7 e^9}+\frac{72 b^2 d^2 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^7}{49 e^9}+\frac{7 b^3 d^3 n^3 \left(d+e \sqrt[3]{x}\right)^6}{9 e^9}-\frac{28 d^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^6}{e^9}+\frac{14 b d^3 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^6}{e^9}-\frac{14 b^2 d^3 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^6}{3 e^9}-\frac{252 b^3 d^4 n^3 \left(d+e \sqrt[3]{x}\right)^5}{125 e^9}+\frac{42 d^4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^5}{e^9}-\frac{126 b d^4 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^5}{5 e^9}+\frac{252 b^2 d^4 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^5}{25 e^9}+\frac{63 b^3 d^5 n^3 \left(d+e \sqrt[3]{x}\right)^4}{16 e^9}-\frac{42 d^5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^4}{e^9}+\frac{63 b d^5 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^4}{2 e^9}-\frac{63 b^2 d^5 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^4}{4 e^9}-\frac{56 b^3 d^6 n^3 \left(d+e \sqrt[3]{x}\right)^3}{9 e^9}+\frac{28 d^6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^3}{e^9}-\frac{28 b d^6 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^3}{e^9}+\frac{56 b^2 d^6 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^3}{3 e^9}+\frac{9 b^3 d^7 n^3 \left(d+e \sqrt[3]{x}\right)^2}{e^9}-\frac{12 d^7 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^2}{e^9}+\frac{18 b d^7 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^2}{e^9}-\frac{18 b^2 d^7 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^2}{e^9}+\frac{3 d^8 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)}{e^9}-\frac{9 b d^8 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)}{e^9}+\frac{18 b^3 d^8 n^2 \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right) \left(d+e \sqrt[3]{x}\right)}{e^9}-\frac{18 b^3 d^8 n^3 \sqrt[3]{x}}{e^8}+\frac{18 a b^2 d^8 n^2 \sqrt[3]{x}}{e^8}",1,"(b^3*e*n^3*x^(1/3)*(-76356985320*d^8 + 15542491860*d^7*e*x^(1/3) - 5483495640*d^6*e^2*x^(2/3) + 2340330930*d^5*e^3*x - 1075607064*d^4*e^4*x^(4/3) + 498592500*d^3*e^5*x^(5/3) - 219465000*d^2*e^6*x^2 + 83734875*d*e^7*x^(7/3) - 21952000*e^8*x^(8/3)) - 2520*a*b^2*n^2*(26853209*d^9 - 17965080*d^8*e*x^(1/3) + 5807340*d^7*e^2*x^(2/3) - 2813160*d^6*e^3*x + 1580670*d^5*e^4*x^(4/3) - 947016*d^4*e^5*x^(5/3) + 577500*d^3*e^6*x^2 - 343800*d^2*e^7*x^(7/3) + 187425*d*e^8*x^(8/3) - 78400*e^9*x^3) + 2667168000*a^3*(d^9 + e^9*x^3) - 3175200*a^2*b*n*(7129*d^9 + 2520*d^8*e*x^(1/3) - 1260*d^7*e^2*x^(2/3) + 840*d^6*e^3*x - 630*d^5*e^4*x^(4/3) + 504*d^4*e^5*x^(5/3) - 420*d^3*e^6*x^2 + 360*d^2*e^7*x^(7/3) - 315*d*e^8*x^(8/3) + 280*e^9*x^3) + 2520*b*(3175200*a^2*(d^9 + e^9*x^3) - 2520*a*b*n*(7129*d^9 + 2520*d^8*e*x^(1/3) - 1260*d^7*e^2*x^(2/3) + 840*d^6*e^3*x - 630*d^5*e^4*x^(4/3) + 504*d^4*e^5*x^(5/3) - 420*d^3*e^6*x^2 + 360*d^2*e^7*x^(7/3) - 315*d*e^8*x^(8/3) + 280*e^9*x^3) + b^2*n^2*(30300391*d^9 + 17965080*d^8*e*x^(1/3) - 5807340*d^7*e^2*x^(2/3) + 2813160*d^6*e^3*x - 1580670*d^5*e^4*x^(4/3) + 947016*d^4*e^5*x^(5/3) - 577500*d^3*e^6*x^2 + 343800*d^2*e^7*x^(7/3) - 187425*d*e^8*x^(8/3) + 78400*e^9*x^3))*Log[c*(d + e*x^(1/3))^n] + 3175200*b^2*(2520*a*(d^9 + e^9*x^3) - b*n*(7129*d^9 + 2520*d^8*e*x^(1/3) - 1260*d^7*e^2*x^(2/3) + 840*d^6*e^3*x - 630*d^5*e^4*x^(4/3) + 504*d^4*e^5*x^(5/3) - 420*d^3*e^6*x^2 + 360*d^2*e^7*x^(7/3) - 315*d*e^8*x^(8/3) + 280*e^9*x^3))*Log[c*(d + e*x^(1/3))^n]^2 + 2667168000*b^3*(d^9 + e^9*x^3)*Log[c*(d + e*x^(1/3))^n]^3)/(8001504000*e^9)","A",1
458,1,589,907,0.5103619,"\int x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \, dx","Integrate[x*(a + b*Log[c*(d + e*x^(1/3))^n])^3,x]","\frac{-36000 a^3 \left(d^6-e^6 x^2\right)-60 b \left(1800 a^2 \left(d^6-e^6 x^2\right)-60 a b n \left(147 d^6+60 d^5 e \sqrt[3]{x}-30 d^4 e^2 x^{2/3}+20 d^3 e^3 x-15 d^2 e^4 x^{4/3}+12 d e^5 x^{5/3}-10 e^6 x^2\right)+b^2 n^2 \left(13489 d^6+8820 d^5 e \sqrt[3]{x}-2610 d^4 e^2 x^{2/3}+1140 d^3 e^3 x-555 d^2 e^4 x^{4/3}+264 d e^5 x^{5/3}-100 e^6 x^2\right)\right) \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)+1800 a^2 b n \left(147 d^6+60 d^5 e \sqrt[3]{x}-30 d^4 e^2 x^{2/3}+20 d^3 e^3 x-15 d^2 e^4 x^{4/3}+12 d e^5 x^{5/3}-10 e^6 x^2\right)-1800 b^2 \left(60 a \left(d^6-e^6 x^2\right)+b n \left(-147 d^6-60 d^5 e \sqrt[3]{x}+30 d^4 e^2 x^{2/3}-20 d^3 e^3 x+15 d^2 e^4 x^{4/3}-12 d e^5 x^{5/3}+10 e^6 x^2\right)\right) \log ^2\left(c \left(d+e \sqrt[3]{x}\right)^n\right)+60 a b^2 n^2 \left(8111 d^6-8820 d^5 e \sqrt[3]{x}+2610 d^4 e^2 x^{2/3}-1140 d^3 e^3 x+555 d^2 e^4 x^{4/3}-264 d e^5 x^{5/3}+100 e^6 x^2\right)-36000 b^3 \left(d^6-e^6 x^2\right) \log ^3\left(c \left(d+e \sqrt[3]{x}\right)^n\right)+b^3 e n^3 \sqrt[3]{x} \left(809340 d^5-140070 d^4 e \sqrt[3]{x}+41180 d^3 e^2 x^{2/3}-13785 d^2 e^3 x+4368 d e^4 x^{4/3}-1000 e^5 x^{5/3}\right)}{72000 e^6}","-\frac{b^3 n^3 \left(d+e \sqrt[3]{x}\right)^6}{72 e^6}+\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^6}{2 e^6}-\frac{b n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^6}{4 e^6}+\frac{b^2 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^6}{12 e^6}+\frac{18 b^3 d n^3 \left(d+e \sqrt[3]{x}\right)^5}{125 e^6}-\frac{3 d \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^5}{e^6}+\frac{9 b d n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^5}{5 e^6}-\frac{18 b^2 d n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^5}{25 e^6}-\frac{45 b^3 d^2 n^3 \left(d+e \sqrt[3]{x}\right)^4}{64 e^6}+\frac{15 d^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^4}{2 e^6}-\frac{45 b d^2 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^4}{8 e^6}+\frac{45 b^2 d^2 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^4}{16 e^6}+\frac{20 b^3 d^3 n^3 \left(d+e \sqrt[3]{x}\right)^3}{9 e^6}-\frac{10 d^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^3}{e^6}+\frac{10 b d^3 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^3}{e^6}-\frac{20 b^2 d^3 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^3}{3 e^6}-\frac{45 b^3 d^4 n^3 \left(d+e \sqrt[3]{x}\right)^2}{8 e^6}+\frac{15 d^4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)^2}{2 e^6}-\frac{45 b d^4 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)^2}{4 e^6}+\frac{45 b^2 d^4 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(d+e \sqrt[3]{x}\right)^2}{4 e^6}-\frac{3 d^5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \left(d+e \sqrt[3]{x}\right)}{e^6}+\frac{9 b d^5 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \left(d+e \sqrt[3]{x}\right)}{e^6}-\frac{18 b^3 d^5 n^2 \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right) \left(d+e \sqrt[3]{x}\right)}{e^6}+\frac{18 b^3 d^5 n^3 \sqrt[3]{x}}{e^5}-\frac{18 a b^2 d^5 n^2 \sqrt[3]{x}}{e^5}",1,"(b^3*e*n^3*x^(1/3)*(809340*d^5 - 140070*d^4*e*x^(1/3) + 41180*d^3*e^2*x^(2/3) - 13785*d^2*e^3*x + 4368*d*e^4*x^(4/3) - 1000*e^5*x^(5/3)) + 1800*a^2*b*n*(147*d^6 + 60*d^5*e*x^(1/3) - 30*d^4*e^2*x^(2/3) + 20*d^3*e^3*x - 15*d^2*e^4*x^(4/3) + 12*d*e^5*x^(5/3) - 10*e^6*x^2) - 36000*a^3*(d^6 - e^6*x^2) + 60*a*b^2*n^2*(8111*d^6 - 8820*d^5*e*x^(1/3) + 2610*d^4*e^2*x^(2/3) - 1140*d^3*e^3*x + 555*d^2*e^4*x^(4/3) - 264*d*e^5*x^(5/3) + 100*e^6*x^2) - 60*b*(b^2*n^2*(13489*d^6 + 8820*d^5*e*x^(1/3) - 2610*d^4*e^2*x^(2/3) + 1140*d^3*e^3*x - 555*d^2*e^4*x^(4/3) + 264*d*e^5*x^(5/3) - 100*e^6*x^2) - 60*a*b*n*(147*d^6 + 60*d^5*e*x^(1/3) - 30*d^4*e^2*x^(2/3) + 20*d^3*e^3*x - 15*d^2*e^4*x^(4/3) + 12*d*e^5*x^(5/3) - 10*e^6*x^2) + 1800*a^2*(d^6 - e^6*x^2))*Log[c*(d + e*x^(1/3))^n] - 1800*b^2*(60*a*(d^6 - e^6*x^2) + b*n*(-147*d^6 - 60*d^5*e*x^(1/3) + 30*d^4*e^2*x^(2/3) - 20*d^3*e^3*x + 15*d^2*e^4*x^(4/3) - 12*d*e^5*x^(5/3) + 10*e^6*x^2))*Log[c*(d + e*x^(1/3))^n]^2 - 36000*b^3*(d^6 - e^6*x^2)*Log[c*(d + e*x^(1/3))^n]^3)/(72000*e^6)","A",1
459,1,362,438,0.2253605,"\int \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])^3,x]","\frac{36 a^3 \left(d^3+e^3 x\right)+6 b \left(d+e \sqrt[3]{x}\right) \left(18 a^2 \left(d^2-d e \sqrt[3]{x}+e^2 x^{2/3}\right)-6 a b n \left(11 d^2-5 d e \sqrt[3]{x}+2 e^2 x^{2/3}\right)+b^2 n^2 \left(85 d^2-19 d e \sqrt[3]{x}+4 e^2 x^{2/3}\right)\right) \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-18 a^2 b n \left(11 d^3+6 d^2 e \sqrt[3]{x}-3 d e^2 x^{2/3}+2 e^3 x\right)+18 b^2 \left(6 a \left(d^3+e^3 x\right)-b n \left(11 d^3+6 d^2 e \sqrt[3]{x}-3 d e^2 x^{2/3}+2 e^3 x\right)\right) \log ^2\left(c \left(d+e \sqrt[3]{x}\right)^n\right)-6 a b^2 n^2 \left(23 d^3-66 d^2 e \sqrt[3]{x}+15 d e^2 x^{2/3}-4 e^3 x\right)+36 b^3 \left(d^3+e^3 x\right) \log ^3\left(c \left(d+e \sqrt[3]{x}\right)^n\right)+b^3 e n^3 \sqrt[3]{x} \left(-510 d^2+57 d e \sqrt[3]{x}-8 e^2 x^{2/3}\right)}{36 e^3}","\frac{2 b^2 n^2 \left(d+e \sqrt[3]{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{3 e^3}-\frac{9 b^2 d n^2 \left(d+e \sqrt[3]{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{2 e^3}+\frac{18 a b^2 d^2 n^2 \sqrt[3]{x}}{e^2}-\frac{9 b d^2 n \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{e^3}+\frac{3 d^2 \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{e^3}-\frac{b n \left(d+e \sqrt[3]{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{e^3}+\frac{9 b d n \left(d+e \sqrt[3]{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{2 e^3}+\frac{\left(d+e \sqrt[3]{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{e^3}-\frac{3 d \left(d+e \sqrt[3]{x}\right)^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{e^3}+\frac{18 b^3 d^2 n^2 \left(d+e \sqrt[3]{x}\right) \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{e^3}-\frac{18 b^3 d^2 n^3 \sqrt[3]{x}}{e^2}-\frac{2 b^3 n^3 \left(d+e \sqrt[3]{x}\right)^3}{9 e^3}+\frac{9 b^3 d n^3 \left(d+e \sqrt[3]{x}\right)^2}{4 e^3}",1,"(b^3*e*n^3*(-510*d^2 + 57*d*e*x^(1/3) - 8*e^2*x^(2/3))*x^(1/3) - 6*a*b^2*n^2*(23*d^3 - 66*d^2*e*x^(1/3) + 15*d*e^2*x^(2/3) - 4*e^3*x) + 36*a^3*(d^3 + e^3*x) - 18*a^2*b*n*(11*d^3 + 6*d^2*e*x^(1/3) - 3*d*e^2*x^(2/3) + 2*e^3*x) + 6*b*(18*a^2*(d^2 - d*e*x^(1/3) + e^2*x^(2/3)) - 6*a*b*n*(11*d^2 - 5*d*e*x^(1/3) + 2*e^2*x^(2/3)) + b^2*n^2*(85*d^2 - 19*d*e*x^(1/3) + 4*e^2*x^(2/3)))*(d + e*x^(1/3))*Log[c*(d + e*x^(1/3))^n] + 18*b^2*(6*a*(d^3 + e^3*x) - b*n*(11*d^3 + 6*d^2*e*x^(1/3) - 3*d*e^2*x^(2/3) + 2*e^3*x))*Log[c*(d + e*x^(1/3))^n]^2 + 36*b^3*(d^3 + e^3*x)*Log[c*(d + e*x^(1/3))^n]^3)/(36*e^3)","A",1
460,1,333,135,0.180739,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{x} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])^3/x,x]","9 b^2 n^2 \left(-2 \text{Li}_3\left(\frac{\sqrt[3]{x} e}{d}+1\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right) \log \left(d+e \sqrt[3]{x}\right)+\log \left(-\frac{e \sqrt[3]{x}}{d}\right) \log ^2\left(d+e \sqrt[3]{x}\right)\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)+3 b n \left(\log (x) \left(\log \left(d+e \sqrt[3]{x}\right)-\log \left(\frac{e \sqrt[3]{x}}{d}+1\right)\right)-3 \text{Li}_2\left(-\frac{e \sqrt[3]{x}}{d}\right)\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)^2+\log (x) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)^3+3 b^3 n^3 \left(6 \text{Li}_4\left(\frac{\sqrt[3]{x} e}{d}+1\right)+3 \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right) \log ^2\left(d+e \sqrt[3]{x}\right)-6 \text{Li}_3\left(\frac{\sqrt[3]{x} e}{d}+1\right) \log \left(d+e \sqrt[3]{x}\right)+\log \left(-\frac{e \sqrt[3]{x}}{d}\right) \log ^3\left(d+e \sqrt[3]{x}\right)\right)","-18 b^2 n^2 \text{Li}_3\left(\frac{\sqrt[3]{x} e}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)+9 b n \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2+3 \log \left(-\frac{e \sqrt[3]{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3+18 b^3 n^3 \text{Li}_4\left(\frac{\sqrt[3]{x} e}{d}+1\right)",1,"(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^3*Log[x] + 3*b*n*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2*((Log[d + e*x^(1/3)] - Log[1 + (e*x^(1/3))/d])*Log[x] - 3*PolyLog[2, -((e*x^(1/3))/d)]) + 9*b^2*n^2*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])*(Log[d + e*x^(1/3)]^2*Log[-((e*x^(1/3))/d)] + 2*Log[d + e*x^(1/3)]*PolyLog[2, 1 + (e*x^(1/3))/d] - 2*PolyLog[3, 1 + (e*x^(1/3))/d]) + 3*b^3*n^3*(Log[d + e*x^(1/3)]^3*Log[-((e*x^(1/3))/d)] + 3*Log[d + e*x^(1/3)]^2*PolyLog[2, 1 + (e*x^(1/3))/d] - 6*Log[d + e*x^(1/3)]*PolyLog[3, 1 + (e*x^(1/3))/d] + 6*PolyLog[4, 1 + (e*x^(1/3))/d])","B",1
461,1,733,439,0.7521055,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])^3/x^2,x]","\frac{-6 b^2 n^2 \left(\left(d^3+e^3 x\right) \log ^2\left(d+e \sqrt[3]{x}\right)+\log \left(d+e \sqrt[3]{x}\right) \left(d^2 e \sqrt[3]{x}-2 e^3 x \log \left(-\frac{e \sqrt[3]{x}}{d}\right)-2 d e^2 x^{2/3}-3 e^3 x\right)-2 e^3 x \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right)+3 e^3 x \log \left(-\frac{e \sqrt[3]{x}}{d}\right)+d e^2 x^{2/3}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)-2 d^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)^3-6 b d^3 n \log \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)^2-3 b d^2 e n \sqrt[3]{x} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)^2-6 b e^3 n x \log \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)^2+2 b e^3 n x \log (x) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)^2+6 b d e^2 n x^{2/3} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)-b n \log \left(d+e \sqrt[3]{x}\right)\right)^2+b^3 n^3 \left(-2 d^3 \log ^3\left(d+e \sqrt[3]{x}\right)-3 d^2 e \sqrt[3]{x} \log ^2\left(d+e \sqrt[3]{x}\right)-12 e^3 x \text{Li}_3\left(\frac{\sqrt[3]{x} e}{d}+1\right)+6 e^3 x \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right) \left(2 \log \left(d+e \sqrt[3]{x}\right)-3\right)-2 e^3 x \log ^3\left(d+e \sqrt[3]{x}\right)+9 e^3 x \log ^2\left(d+e \sqrt[3]{x}\right)+6 e^3 x \log ^2\left(d+e \sqrt[3]{x}\right) \log \left(-\frac{e \sqrt[3]{x}}{d}\right)-6 e^3 x \log \left(d+e \sqrt[3]{x}\right)+6 e^3 x \log \left(-\frac{e \sqrt[3]{x}}{d}\right)-18 e^3 x \log \left(d+e \sqrt[3]{x}\right) \log \left(-\frac{e \sqrt[3]{x}}{d}\right)+6 d e^2 x^{2/3} \log ^2\left(d+e \sqrt[3]{x}\right)-6 d e^2 x^{2/3} \log \left(d+e \sqrt[3]{x}\right)\right)}{2 d^3 x}","-\frac{6 b^2 e^3 n^2 \text{Li}_2\left(\frac{d}{d+e \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^3}-\frac{3 b^2 e^3 n^2 \log \left(1-\frac{d}{d+e \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^3}-\frac{6 b^2 e^3 n^2 \log \left(-\frac{e \sqrt[3]{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^3}-\frac{3 b^2 e^2 n^2 \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^3 \sqrt[3]{x}}+\frac{3 b e^3 n \log \left(1-\frac{d}{d+e \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{d^3}+\frac{3 b e^2 n \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{d^3 \sqrt[3]{x}}-\frac{3 b e n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{2 d x^{2/3}}-\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{x}+\frac{3 b^3 e^3 n^3 \text{Li}_2\left(\frac{d}{d+e \sqrt[3]{x}}\right)}{d^3}-\frac{6 b^3 e^3 n^3 \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right)}{d^3}-\frac{6 b^3 e^3 n^3 \text{Li}_3\left(\frac{d}{d+e \sqrt[3]{x}}\right)}{d^3}+\frac{b^3 e^3 n^3 \log (x)}{d^3}",1,"(-3*b*d^2*e*n*x^(1/3)*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2 + 6*b*d*e^2*n*x^(2/3)*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2 - 6*b*d^3*n*Log[d + e*x^(1/3)]*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2 - 6*b*e^3*n*x*Log[d + e*x^(1/3)]*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2 - 2*d^3*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^3 + 2*b*e^3*n*x*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2*Log[x] - 6*b^2*n^2*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])*(d*e^2*x^(2/3) + (d^3 + e^3*x)*Log[d + e*x^(1/3)]^2 + 3*e^3*x*Log[-((e*x^(1/3))/d)] + Log[d + e*x^(1/3)]*(d^2*e*x^(1/3) - 2*d*e^2*x^(2/3) - 3*e^3*x - 2*e^3*x*Log[-((e*x^(1/3))/d)]) - 2*e^3*x*PolyLog[2, 1 + (e*x^(1/3))/d]) + b^3*n^3*(-6*d*e^2*x^(2/3)*Log[d + e*x^(1/3)] - 6*e^3*x*Log[d + e*x^(1/3)] - 3*d^2*e*x^(1/3)*Log[d + e*x^(1/3)]^2 + 6*d*e^2*x^(2/3)*Log[d + e*x^(1/3)]^2 + 9*e^3*x*Log[d + e*x^(1/3)]^2 - 2*d^3*Log[d + e*x^(1/3)]^3 - 2*e^3*x*Log[d + e*x^(1/3)]^3 + 6*e^3*x*Log[-((e*x^(1/3))/d)] - 18*e^3*x*Log[d + e*x^(1/3)]*Log[-((e*x^(1/3))/d)] + 6*e^3*x*Log[d + e*x^(1/3)]^2*Log[-((e*x^(1/3))/d)] + 6*e^3*x*(-3 + 2*Log[d + e*x^(1/3)])*PolyLog[2, 1 + (e*x^(1/3))/d] - 12*e^3*x*PolyLog[3, 1 + (e*x^(1/3))/d]))/(2*d^3*x)","A",1
462,1,1074,765,1.8717806,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^n])^3/x^3,x]","-\frac{20 \left(a-b n \log \left(d+e \sqrt[3]{x}\right)+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 d^6+60 b n \log \left(d+e \sqrt[3]{x}\right) \left(a-b n \log \left(d+e \sqrt[3]{x}\right)+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 d^6+12 b e n \sqrt[3]{x} \left(a-b n \log \left(d+e \sqrt[3]{x}\right)+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 d^5-15 b e^2 n x^{2/3} \left(a-b n \log \left(d+e \sqrt[3]{x}\right)+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 d^4+20 b e^3 n x \left(a-b n \log \left(d+e \sqrt[3]{x}\right)+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 d^3-30 b e^4 n x^{4/3} \left(a-b n \log \left(d+e \sqrt[3]{x}\right)+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 d^2+60 b e^5 n x^{5/3} \left(a-b n \log \left(d+e \sqrt[3]{x}\right)+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 d-60 b e^6 n x^2 \log \left(d+e \sqrt[3]{x}\right) \left(a-b n \log \left(d+e \sqrt[3]{x}\right)+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2+20 b e^6 n x^2 \left(a-b n \log \left(d+e \sqrt[3]{x}\right)+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \log (x)+b^2 n^2 \left(a-b n \log \left(d+e \sqrt[3]{x}\right)+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \left(-274 x^2 \log \left(-\frac{e \sqrt[3]{x}}{d}\right) e^6+120 x^2 \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right) e^6-154 d x^{5/3} e^5+47 d^2 x^{4/3} e^4-18 d^3 x e^3+6 d^4 x^{2/3} e^2+60 \left(d^6-e^6 x^2\right) \log ^2\left(d+e \sqrt[3]{x}\right)+2 \log \left(d+e \sqrt[3]{x}\right) \left(137 x^2 e^6+60 x^2 \log \left(-\frac{e \sqrt[3]{x}}{d}\right) e^6+60 d x^{5/3} e^5-30 d^2 x^{4/3} e^4+20 d^3 x e^3-15 d^4 x^{2/3} e^2+12 d^5 \sqrt[3]{x} e\right)\right)+b^3 n^3 \left(20 \log ^3\left(d+e \sqrt[3]{x}\right) d^6+12 e \sqrt[3]{x} \log ^2\left(d+e \sqrt[3]{x}\right) d^5+3 e^2 x^{2/3} \left(2-5 \log \left(d+e \sqrt[3]{x}\right)\right) \log \left(d+e \sqrt[3]{x}\right) d^4+2 e^3 x \left(10 \log ^2\left(d+e \sqrt[3]{x}\right)-9 \log \left(d+e \sqrt[3]{x}\right)+1\right) d^3-e^4 x^{4/3} \left(30 \log ^2\left(d+e \sqrt[3]{x}\right)-47 \log \left(d+e \sqrt[3]{x}\right)+12\right) d^2+e^5 x^{5/3} \left(60 \log ^2\left(d+e \sqrt[3]{x}\right)-154 \log \left(d+e \sqrt[3]{x}\right)+71\right) d+225 e^6 x^2 \left(\log \left(-\frac{e \sqrt[3]{x}}{d}\right)-\log \left(d+e \sqrt[3]{x}\right)\right)+137 e^6 x^2 \left(\log \left(d+e \sqrt[3]{x}\right) \left(\log \left(d+e \sqrt[3]{x}\right)-2 \log \left(-\frac{e \sqrt[3]{x}}{d}\right)\right)-2 \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right)\right)-20 e^6 x^2 \left(\left(\log \left(d+e \sqrt[3]{x}\right)-3 \log \left(-\frac{e \sqrt[3]{x}}{d}\right)\right) \log ^2\left(d+e \sqrt[3]{x}\right)-6 \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right) \log \left(d+e \sqrt[3]{x}\right)+6 \text{Li}_3\left(\frac{\sqrt[3]{x} e}{d}+1\right)\right)\right)}{40 d^6 x^2}","\frac{3 b^2 e^6 n^2 \text{Li}_2\left(\frac{d}{d+e \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^6}+\frac{77 b^2 e^6 n^2 \log \left(1-\frac{d}{d+e \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{20 d^6}+\frac{3 b^2 e^6 n^2 \log \left(-\frac{e \sqrt[3]{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^6}+\frac{77 b^2 e^5 n^2 \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{20 d^6 \sqrt[3]{x}}-\frac{47 b^2 e^4 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{40 d^4 x^{2/3}}+\frac{9 b^2 e^3 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{20 d^3 x}-\frac{3 b^2 e^2 n^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{20 d^2 x^{4/3}}-\frac{3 b e^6 n \log \left(1-\frac{d}{d+e \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{2 d^6}-\frac{3 b e^5 n \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{2 d^6 \sqrt[3]{x}}+\frac{3 b e^4 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{4 d^4 x^{2/3}}-\frac{b e^3 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{2 d^3 x}+\frac{3 b e^2 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{8 d^2 x^{4/3}}-\frac{3 b e n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{10 d x^{5/3}}-\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{2 x^2}-\frac{77 b^3 e^6 n^3 \text{Li}_2\left(\frac{d}{d+e \sqrt[3]{x}}\right)}{20 d^6}+\frac{3 b^3 e^6 n^3 \text{Li}_2\left(\frac{\sqrt[3]{x} e}{d}+1\right)}{d^6}+\frac{3 b^3 e^6 n^3 \text{Li}_3\left(\frac{d}{d+e \sqrt[3]{x}}\right)}{d^6}+\frac{71 b^3 e^6 n^3 \log \left(d+e \sqrt[3]{x}\right)}{40 d^6}-\frac{15 b^3 e^6 n^3 \log (x)}{8 d^6}-\frac{71 b^3 e^5 n^3}{40 d^5 \sqrt[3]{x}}+\frac{3 b^3 e^4 n^3}{10 d^4 x^{2/3}}-\frac{b^3 e^3 n^3}{20 d^3 x}",1,"-1/40*(12*b*d^5*e*n*x^(1/3)*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2 - 15*b*d^4*e^2*n*x^(2/3)*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2 + 20*b*d^3*e^3*n*x*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2 - 30*b*d^2*e^4*n*x^(4/3)*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2 + 60*b*d*e^5*n*x^(5/3)*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2 + 60*b*d^6*n*Log[d + e*x^(1/3)]*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2 - 60*b*e^6*n*x^2*Log[d + e*x^(1/3)]*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2 + 20*d^6*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^3 + 20*b*e^6*n*x^2*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])^2*Log[x] + b^2*n^2*(a - b*n*Log[d + e*x^(1/3)] + b*Log[c*(d + e*x^(1/3))^n])*(6*d^4*e^2*x^(2/3) - 18*d^3*e^3*x + 47*d^2*e^4*x^(4/3) - 154*d*e^5*x^(5/3) + 60*(d^6 - e^6*x^2)*Log[d + e*x^(1/3)]^2 - 274*e^6*x^2*Log[-((e*x^(1/3))/d)] + 2*Log[d + e*x^(1/3)]*(12*d^5*e*x^(1/3) - 15*d^4*e^2*x^(2/3) + 20*d^3*e^3*x - 30*d^2*e^4*x^(4/3) + 60*d*e^5*x^(5/3) + 137*e^6*x^2 + 60*e^6*x^2*Log[-((e*x^(1/3))/d)]) + 120*e^6*x^2*PolyLog[2, 1 + (e*x^(1/3))/d]) + b^3*n^3*(3*d^4*e^2*x^(2/3)*(2 - 5*Log[d + e*x^(1/3)])*Log[d + e*x^(1/3)] + 12*d^5*e*x^(1/3)*Log[d + e*x^(1/3)]^2 + 20*d^6*Log[d + e*x^(1/3)]^3 + 2*d^3*e^3*x*(1 - 9*Log[d + e*x^(1/3)] + 10*Log[d + e*x^(1/3)]^2) - d^2*e^4*x^(4/3)*(12 - 47*Log[d + e*x^(1/3)] + 30*Log[d + e*x^(1/3)]^2) + d*e^5*x^(5/3)*(71 - 154*Log[d + e*x^(1/3)] + 60*Log[d + e*x^(1/3)]^2) + 225*e^6*x^2*(-Log[d + e*x^(1/3)] + Log[-((e*x^(1/3))/d)]) + 137*e^6*x^2*(Log[d + e*x^(1/3)]*(Log[d + e*x^(1/3)] - 2*Log[-((e*x^(1/3))/d)]) - 2*PolyLog[2, 1 + (e*x^(1/3))/d]) - 20*e^6*x^2*(Log[d + e*x^(1/3)]^2*(Log[d + e*x^(1/3)] - 3*Log[-((e*x^(1/3))/d)]) - 6*Log[d + e*x^(1/3)]*PolyLog[2, 1 + (e*x^(1/3))/d] + 6*PolyLog[3, 1 + (e*x^(1/3))/d])))/(d^6*x^2)","A",1
463,1,135,138,0.1136802,"\int x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \, dx","Integrate[x^3*(a + b*Log[c*(d + e*x^(2/3))^n]),x]","\frac{a x^4}{4}+\frac{1}{4} b x^4 \log \left(c \left(d+e x^{2/3}\right)^n\right)-\frac{1}{4} b e n \left(\frac{d^6 \log \left(d+e x^{2/3}\right)}{e^7}-\frac{d^5 x^{2/3}}{e^6}+\frac{d^4 x^{4/3}}{2 e^5}-\frac{d^3 x^2}{3 e^4}+\frac{d^2 x^{8/3}}{4 e^3}-\frac{d x^{10/3}}{5 e^2}+\frac{x^4}{6 e}\right)","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)-\frac{b d^6 n \log \left(d+e x^{2/3}\right)}{4 e^6}+\frac{b d^5 n x^{2/3}}{4 e^5}-\frac{b d^4 n x^{4/3}}{8 e^4}+\frac{b d^3 n x^2}{12 e^3}-\frac{b d^2 n x^{8/3}}{16 e^2}+\frac{b d n x^{10/3}}{20 e}-\frac{1}{24} b n x^4",1,"(a*x^4)/4 - (b*e*n*(-((d^5*x^(2/3))/e^6) + (d^4*x^(4/3))/(2*e^5) - (d^3*x^2)/(3*e^4) + (d^2*x^(8/3))/(4*e^3) - (d*x^(10/3))/(5*e^2) + x^4/(6*e) + (d^6*Log[d + e*x^(2/3)])/e^7))/4 + (b*x^4*Log[c*(d + e*x^(2/3))^n])/4","A",1
464,1,135,130,0.1010348,"\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*(d + e*x^(2/3))^n]),x]","\frac{a x^3}{3}+\frac{1}{3} b x^3 \log \left(c \left(d+e x^{2/3}\right)^n\right)+\frac{2 b d^{9/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{3 e^{9/2}}-\frac{2 b d^4 n \sqrt[3]{x}}{3 e^4}+\frac{2 b d^3 n x}{9 e^3}-\frac{2 b d^2 n x^{5/3}}{15 e^2}+\frac{2 b d n x^{7/3}}{21 e}-\frac{2}{27} b n x^3","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+\frac{2 b d^{9/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{3 e^{9/2}}-\frac{2 b d^4 n \sqrt[3]{x}}{3 e^4}+\frac{2 b d^3 n x}{9 e^3}-\frac{2 b d^2 n x^{5/3}}{15 e^2}+\frac{2 b d n x^{7/3}}{21 e}-\frac{2}{27} b n x^3",1,"(-2*b*d^4*n*x^(1/3))/(3*e^4) + (2*b*d^3*n*x)/(9*e^3) - (2*b*d^2*n*x^(5/3))/(15*e^2) + (2*b*d*n*x^(7/3))/(21*e) + (a*x^3)/3 - (2*b*n*x^3)/27 + (2*b*d^(9/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/(3*e^(9/2)) + (b*x^3*Log[c*(d + e*x^(2/3))^n])/3","A",1
465,1,94,89,0.0283141,"\int x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \, dx","Integrate[x*(a + b*Log[c*(d + e*x^(2/3))^n]),x]","\frac{a x^2}{2}+\frac{1}{2} b x^2 \log \left(c \left(d+e x^{2/3}\right)^n\right)+\frac{b d^3 n \log \left(d+e x^{2/3}\right)}{2 e^3}-\frac{b d^2 n x^{2/3}}{2 e^2}+\frac{b d n x^{4/3}}{4 e}-\frac{1}{6} b n x^2","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+\frac{b d^3 n \log \left(d+e x^{2/3}\right)}{2 e^3}-\frac{b d^2 n x^{2/3}}{2 e^2}+\frac{b d n x^{4/3}}{4 e}-\frac{1}{6} b n x^2",1,"-1/2*(b*d^2*n*x^(2/3))/e^2 + (b*d*n*x^(4/3))/(4*e) + (a*x^2)/2 - (b*n*x^2)/6 + (b*d^3*n*Log[d + e*x^(2/3)])/(2*e^3) + (b*x^2*Log[c*(d + e*x^(2/3))^n])/2","A",1
466,1,72,72,0.027386,"\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \, dx","Integrate[a + b*Log[c*(d + e*x^(2/3))^n],x]","a x+b x \log \left(c \left(d+e x^{2/3}\right)^n\right)-\frac{2 b d^{3/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{e^{3/2}}+\frac{2 b d n \sqrt[3]{x}}{e}-\frac{2 b n x}{3}","a x+b x \log \left(c \left(d+e x^{2/3}\right)^n\right)-\frac{2 b d^{3/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{e^{3/2}}+\frac{2 b d n \sqrt[3]{x}}{e}-\frac{2 b n x}{3}",1,"(2*b*d*n*x^(1/3))/e + a*x - (2*b*n*x)/3 - (2*b*d^(3/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/e^(3/2) + b*x*Log[c*(d + e*x^(2/3))^n]","A",1
467,1,55,55,0.0121791,"\int \frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{x} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])/x,x]","a \log (x)+\frac{3}{2} b \left(\log \left(-\frac{e x^{2/3}}{d}\right) \log \left(c \left(d+e x^{2/3}\right)^n\right)+n \text{Li}_2\left(\frac{d+e x^{2/3}}{d}\right)\right)","\frac{3}{2} \log \left(-\frac{e x^{2/3}}{d}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+\frac{3}{2} b n \text{Li}_2\left(\frac{x^{2/3} e}{d}+1\right)",1,"a*Log[x] + (3*b*(Log[c*(d + e*x^(2/3))^n]*Log[-((e*x^(2/3))/d)] + n*PolyLog[2, (d + e*x^(2/3))/d]))/2","A",1
468,1,59,68,0.0181767,"\int \frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])/x^2,x]","-\frac{a}{x}-\frac{b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{x}-\frac{2 b e n \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{e x^{2/3}}{d}\right)}{d \sqrt[3]{x}}","-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{x}-\frac{2 b e^{3/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 b e n}{d \sqrt[3]{x}}",1,"-(a/x) - (2*b*e*n*Hypergeometric2F1[-1/2, 1, 1/2, -((e*x^(2/3))/d)])/(d*x^(1/3)) - (b*Log[c*(d + e*x^(2/3))^n])/x","C",1
469,1,91,94,0.0345879,"\int \frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])/x^3,x]","-\frac{a}{2 x^2}-\frac{b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{2 x^2}+\frac{1}{2} b e n \left(-\frac{e^2 \log \left(d+e x^{2/3}\right)}{d^3}+\frac{2 e^2 \log (x)}{3 d^3}+\frac{e}{d^2 x^{2/3}}-\frac{1}{2 d x^{4/3}}\right)","-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{2 x^2}-\frac{b e^3 n \log \left(d+e x^{2/3}\right)}{2 d^3}+\frac{b e^3 n \log (x)}{3 d^3}+\frac{b e^2 n}{2 d^2 x^{2/3}}-\frac{b e n}{4 d x^{4/3}}",1,"-1/2*a/x^2 - (b*Log[c*(d + e*x^(2/3))^n])/(2*x^2) + (b*e*n*(-1/2*1/(d*x^(4/3)) + e/(d^2*x^(2/3)) - (e^2*Log[d + e*x^(2/3)])/d^3 + (2*e^2*Log[x])/(3*d^3)))/2","A",1
470,1,65,123,0.0140435,"\int \frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])/x^4,x]","-\frac{a}{3 x^3}-\frac{b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{3 x^3}-\frac{2 b e n \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};-\frac{e x^{2/3}}{d}\right)}{21 d x^{7/3}}","-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{3 x^3}+\frac{2 b e^{9/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{3 d^{9/2}}+\frac{2 b e^4 n}{3 d^4 \sqrt[3]{x}}-\frac{2 b e^3 n}{9 d^3 x}+\frac{2 b e^2 n}{15 d^2 x^{5/3}}-\frac{2 b e n}{21 d x^{7/3}}",1,"-1/3*a/x^3 - (2*b*e*n*Hypergeometric2F1[-7/2, 1, -5/2, -((e*x^(2/3))/d)])/(21*d*x^(7/3)) - (b*Log[c*(d + e*x^(2/3))^n])/(3*x^3)","C",1
471,1,328,482,0.3816615,"\int x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \, dx","Integrate[x^3*(a + b*Log[c*(d + e*x^(2/3))^n])^2,x]","\frac{e x^{2/3} \left(1800 a^2 e^5 x^{10/3}+60 a b n \left(60 d^5-30 d^4 e x^{2/3}+20 d^3 e^2 x^{4/3}-15 d^2 e^3 x^2+12 d e^4 x^{8/3}-10 e^5 x^{10/3}\right)+b^2 n^2 \left(-8820 d^5+2610 d^4 e x^{2/3}-1140 d^3 e^2 x^{4/3}+555 d^2 e^3 x^2-264 d e^4 x^{8/3}+100 e^5 x^{10/3}\right)\right)+60 b \left(b n \left(60 d^6+60 d^5 e x^{2/3}-30 d^4 e^2 x^{4/3}+20 d^3 e^3 x^2-15 d^2 e^4 x^{8/3}+12 d e^5 x^{10/3}-10 e^6 x^4\right)-60 a \left(d^6-e^6 x^4\right)\right) \log \left(c \left(d+e x^{2/3}\right)^n\right)-1800 b^2 \left(d^6-e^6 x^4\right) \log ^2\left(c \left(d+e x^{2/3}\right)^n\right)+5220 b^2 d^6 n^2 \log \left(d+e x^{2/3}\right)}{7200 e^6}","-\frac{b d^6 n \log \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{2 e^6}+\frac{3 b d^5 n \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{e^6}-\frac{15 b d^4 n \left(d+e x^{2/3}\right)^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{4 e^6}+\frac{10 b d^3 n \left(d+e x^{2/3}\right)^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{3 e^6}-\frac{15 b d^2 n \left(d+e x^{2/3}\right)^4 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{8 e^6}+\frac{3 b d n \left(d+e x^{2/3}\right)^5 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{5 e^6}-\frac{b n \left(d+e x^{2/3}\right)^6 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{12 e^6}+\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2+\frac{b^2 d^6 n^2 \log ^2\left(d+e x^{2/3}\right)}{4 e^6}-\frac{3 b^2 d^5 n^2 x^{2/3}}{e^5}+\frac{15 b^2 d^4 n^2 \left(d+e x^{2/3}\right)^2}{8 e^6}-\frac{10 b^2 d^3 n^2 \left(d+e x^{2/3}\right)^3}{9 e^6}+\frac{15 b^2 d^2 n^2 \left(d+e x^{2/3}\right)^4}{32 e^6}-\frac{3 b^2 d n^2 \left(d+e x^{2/3}\right)^5}{25 e^6}+\frac{b^2 n^2 \left(d+e x^{2/3}\right)^6}{72 e^6}",1,"(e*x^(2/3)*(1800*a^2*e^5*x^(10/3) + 60*a*b*n*(60*d^5 - 30*d^4*e*x^(2/3) + 20*d^3*e^2*x^(4/3) - 15*d^2*e^3*x^2 + 12*d*e^4*x^(8/3) - 10*e^5*x^(10/3)) + b^2*n^2*(-8820*d^5 + 2610*d^4*e*x^(2/3) - 1140*d^3*e^2*x^(4/3) + 555*d^2*e^3*x^2 - 264*d*e^4*x^(8/3) + 100*e^5*x^(10/3))) + 5220*b^2*d^6*n^2*Log[d + e*x^(2/3)] + 60*b*(b*n*(60*d^6 + 60*d^5*e*x^(2/3) - 30*d^4*e^2*x^(4/3) + 20*d^3*e^3*x^2 - 15*d^2*e^4*x^(8/3) + 12*d*e^5*x^(10/3) - 10*e^6*x^4) - 60*a*(d^6 - e^6*x^4))*Log[c*(d + e*x^(2/3))^n] - 1800*b^2*(d^6 - e^6*x^4)*Log[c*(d + e*x^(2/3))^n]^2)/(7200*e^6)","A",1
472,1,239,275,0.1648403,"\int x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \, dx","Integrate[x*(a + b*Log[c*(d + e*x^(2/3))^n])^2,x]","\frac{18 a^2 d^3+18 a^2 e^3 x^2+6 b \left(6 a \left(d^3+e^3 x^2\right)-b n \left(6 d^3+6 d^2 e x^{2/3}-3 d e^2 x^{4/3}+2 e^3 x^2\right)\right) \log \left(c \left(d+e x^{2/3}\right)^n\right)-36 a b d^2 e n x^{2/3}+18 a b d e^2 n x^{4/3}-12 a b e^3 n x^2+18 b^2 \left(d^3+e^3 x^2\right) \log ^2\left(c \left(d+e x^{2/3}\right)^n\right)-30 b^2 d^3 n^2 \log \left(d+e x^{2/3}\right)+66 b^2 d^2 e n^2 x^{2/3}-15 b^2 d e^2 n^2 x^{4/3}+4 b^2 e^3 n^2 x^2}{36 e^3}","\frac{b d^3 n \log \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{e^3}-\frac{3 b d^2 n \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{e^3}+\frac{3 b d n \left(d+e x^{2/3}\right)^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{2 e^3}-\frac{b n \left(d+e x^{2/3}\right)^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{3 e^3}+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2-\frac{b^2 d^3 n^2 \log ^2\left(d+e x^{2/3}\right)}{2 e^3}+\frac{3 b^2 d^2 n^2 x^{2/3}}{e^2}-\frac{3 b^2 d n^2 \left(d+e x^{2/3}\right)^2}{4 e^3}+\frac{b^2 n^2 \left(d+e x^{2/3}\right)^3}{9 e^3}",1,"(18*a^2*d^3 - 36*a*b*d^2*e*n*x^(2/3) + 66*b^2*d^2*e*n^2*x^(2/3) + 18*a*b*d*e^2*n*x^(4/3) - 15*b^2*d*e^2*n^2*x^(4/3) + 18*a^2*e^3*x^2 - 12*a*b*e^3*n*x^2 + 4*b^2*e^3*n^2*x^2 - 30*b^2*d^3*n^2*Log[d + e*x^(2/3)] + 6*b*(6*a*(d^3 + e^3*x^2) - b*n*(6*d^3 + 6*d^2*e*x^(2/3) - 3*d*e^2*x^(4/3) + 2*e^3*x^2))*Log[c*(d + e*x^(2/3))^n] + 18*b^2*(d^3 + e^3*x^2)*Log[c*(d + e*x^(2/3))^n]^2)/(36*e^3)","A",1
473,1,199,95,0.1238039,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x,x]","2 b n \left(\log (x) \left(\log \left(d+e x^{2/3}\right)-\log \left(\frac{e x^{2/3}}{d}+1\right)\right)-\frac{3}{2} \text{Li}_2\left(-\frac{e x^{2/3}}{d}\right)\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)+\log (x) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2+\frac{3}{2} b^2 n^2 \left(-2 \text{Li}_3\left(\frac{x^{2/3} e}{d}+1\right)+2 \text{Li}_2\left(\frac{x^{2/3} e}{d}+1\right) \log \left(d+e x^{2/3}\right)+\log \left(-\frac{e x^{2/3}}{d}\right) \log ^2\left(d+e x^{2/3}\right)\right)","3 b n \text{Li}_2\left(\frac{x^{2/3} e}{d}+1\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+\frac{3}{2} \log \left(-\frac{e x^{2/3}}{d}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2-3 b^2 n^2 \text{Li}_3\left(\frac{x^{2/3} e}{d}+1\right)",1,"(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2*Log[x] + 2*b*n*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])*((Log[d + e*x^(2/3)] - Log[1 + (e*x^(2/3))/d])*Log[x] - (3*PolyLog[2, -((e*x^(2/3))/d)])/2) + (3*b^2*n^2*(Log[d + e*x^(2/3)]^2*Log[-((e*x^(2/3))/d)] + 2*Log[d + e*x^(2/3)]*PolyLog[2, 1 + (e*x^(2/3))/d] - 2*PolyLog[3, 1 + (e*x^(2/3))/d]))/2","B",1
474,1,264,238,0.314443,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^3,x]","-\frac{\frac{e x^{2/3} \left(3 b d^2 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)-6 b e^2 n x^{4/3} \left(\log \left(-\frac{e x^{2/3}}{d}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+b n \text{Li}_2\left(\frac{x^{2/3} e}{d}+1\right)\right)+3 e^2 x^{4/3} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2-6 b d e n x^{2/3} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)-2 b^2 e^2 n^2 x^{4/3} \left(3 \log \left(d+e x^{2/3}\right)-2 \log (x)\right)+b^2 e n^2 x^{2/3} \left(-3 e x^{2/3} \log \left(d+e x^{2/3}\right)+3 d+2 e x^{2/3} \log (x)\right)\right)}{d^3}+3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{6 x^2}","\frac{b e^3 n \log \left(1-\frac{d}{d+e x^{2/3}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d^3}+\frac{b e^2 n \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d^3 x^{2/3}}-\frac{b e n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{2 d x^{4/3}}-\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{2 x^2}-\frac{b^2 e^3 n^2 \text{Li}_2\left(\frac{d}{d+e x^{2/3}}\right)}{d^3}+\frac{b^2 e^3 n^2 \log \left(d+e x^{2/3}\right)}{2 d^3}-\frac{b^2 e^3 n^2 \log (x)}{d^3}-\frac{b^2 e^2 n^2}{2 d^2 x^{2/3}}",1,"-1/6*(3*(a + b*Log[c*(d + e*x^(2/3))^n])^2 + (e*x^(2/3)*(3*b*d^2*n*(a + b*Log[c*(d + e*x^(2/3))^n]) - 6*b*d*e*n*x^(2/3)*(a + b*Log[c*(d + e*x^(2/3))^n]) + 3*e^2*x^(4/3)*(a + b*Log[c*(d + e*x^(2/3))^n])^2 - 2*b^2*e^2*n^2*x^(4/3)*(3*Log[d + e*x^(2/3)] - 2*Log[x]) + b^2*e*n^2*x^(2/3)*(3*d - 3*e*x^(2/3)*Log[d + e*x^(2/3)] + 2*e*x^(2/3)*Log[x]) - 6*b*e^2*n*x^(4/3)*((a + b*Log[c*(d + e*x^(2/3))^n])*Log[-((e*x^(2/3))/d)] + b*n*PolyLog[2, 1 + (e*x^(2/3))/d])))/d^3)/x^2","A",1
475,1,539,412,0.350253,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^5} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^5,x]","-\frac{180 a^2 d^6+360 a b d^6 \log \left(c \left(d+e x^{2/3}\right)^n\right)-360 a b e^6 x^4 \log \left(c \left(d+e x^{2/3}\right)^n\right)+72 a b d^5 e n x^{2/3}-90 a b d^4 e^2 n x^{4/3}+120 a b d^3 e^3 n x^2-180 a b d^2 e^4 n x^{8/3}+360 a b e^6 n x^4 \log \left(-\frac{e x^{2/3}}{d}\right)+360 a b d e^5 n x^{10/3}+180 b^2 d^6 \log ^2\left(c \left(d+e x^{2/3}\right)^n\right)+72 b^2 d^5 e n x^{2/3} \log \left(c \left(d+e x^{2/3}\right)^n\right)-90 b^2 d^4 e^2 n x^{4/3} \log \left(c \left(d+e x^{2/3}\right)^n\right)+120 b^2 d^3 e^3 n x^2 \log \left(c \left(d+e x^{2/3}\right)^n\right)-180 b^2 d^2 e^4 n x^{8/3} \log \left(c \left(d+e x^{2/3}\right)^n\right)-180 b^2 e^6 x^4 \log ^2\left(c \left(d+e x^{2/3}\right)^n\right)+360 b^2 e^6 n x^4 \log \left(-\frac{e x^{2/3}}{d}\right) \log \left(c \left(d+e x^{2/3}\right)^n\right)+360 b^2 d e^5 n x^{10/3} \log \left(c \left(d+e x^{2/3}\right)^n\right)+18 b^2 d^4 e^2 n^2 x^{4/3}-54 b^2 d^3 e^3 n^2 x^2+141 b^2 d^2 e^4 n^2 x^{8/3}+360 b^2 e^6 n^2 x^4 \text{Li}_2\left(\frac{x^{2/3} e}{d}+1\right)+822 b^2 e^6 n^2 x^4 \log \left(d+e x^{2/3}\right)-462 b^2 d e^5 n^2 x^{10/3}-548 b^2 e^6 n^2 x^4 \log (x)}{720 d^6 x^4}","-\frac{b e^6 n \log \left(1-\frac{d}{d+e x^{2/3}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{2 d^6}-\frac{b e^5 n \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{2 d^6 x^{2/3}}+\frac{b e^4 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{4 d^4 x^{4/3}}-\frac{b e^3 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{6 d^3 x^2}+\frac{b e^2 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{8 d^2 x^{8/3}}-\frac{b e n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{10 d x^{10/3}}-\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{4 x^4}+\frac{b^2 e^6 n^2 \text{Li}_2\left(\frac{d}{d+e x^{2/3}}\right)}{2 d^6}-\frac{77 b^2 e^6 n^2 \log \left(d+e x^{2/3}\right)}{120 d^6}+\frac{137 b^2 e^6 n^2 \log (x)}{180 d^6}+\frac{77 b^2 e^5 n^2}{120 d^5 x^{2/3}}-\frac{47 b^2 e^4 n^2}{240 d^4 x^{4/3}}+\frac{3 b^2 e^3 n^2}{40 d^3 x^2}-\frac{b^2 e^2 n^2}{40 d^2 x^{8/3}}",1,"-1/720*(180*a^2*d^6 + 72*a*b*d^5*e*n*x^(2/3) - 90*a*b*d^4*e^2*n*x^(4/3) + 18*b^2*d^4*e^2*n^2*x^(4/3) + 120*a*b*d^3*e^3*n*x^2 - 54*b^2*d^3*e^3*n^2*x^2 - 180*a*b*d^2*e^4*n*x^(8/3) + 141*b^2*d^2*e^4*n^2*x^(8/3) + 360*a*b*d*e^5*n*x^(10/3) - 462*b^2*d*e^5*n^2*x^(10/3) + 822*b^2*e^6*n^2*x^4*Log[d + e*x^(2/3)] + 360*a*b*d^6*Log[c*(d + e*x^(2/3))^n] + 72*b^2*d^5*e*n*x^(2/3)*Log[c*(d + e*x^(2/3))^n] - 90*b^2*d^4*e^2*n*x^(4/3)*Log[c*(d + e*x^(2/3))^n] + 120*b^2*d^3*e^3*n*x^2*Log[c*(d + e*x^(2/3))^n] - 180*b^2*d^2*e^4*n*x^(8/3)*Log[c*(d + e*x^(2/3))^n] + 360*b^2*d*e^5*n*x^(10/3)*Log[c*(d + e*x^(2/3))^n] - 360*a*b*e^6*x^4*Log[c*(d + e*x^(2/3))^n] + 180*b^2*d^6*Log[c*(d + e*x^(2/3))^n]^2 - 180*b^2*e^6*x^4*Log[c*(d + e*x^(2/3))^n]^2 + 360*a*b*e^6*n*x^4*Log[-((e*x^(2/3))/d)] + 360*b^2*e^6*n*x^4*Log[c*(d + e*x^(2/3))^n]*Log[-((e*x^(2/3))/d)] - 548*b^2*e^6*n^2*x^4*Log[x] + 360*b^2*e^6*n^2*x^4*PolyLog[2, 1 + (e*x^(2/3))/d])/(d^6*x^4)","A",1
476,1,438,547,0.5263014,"\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \, dx","Integrate[x^2*(a + b*Log[c*(d + e*x^(2/3))^n])^2,x]","\frac{\sqrt{e} \sqrt[3]{x} \left(99225 a^2 e^4 x^{8/3}-630 b \left(2 b n \left(315 d^4-105 d^3 e x^{2/3}+63 d^2 e^2 x^{4/3}-45 d e^3 x^2+35 e^4 x^{8/3}\right)-315 a e^4 x^{8/3}\right) \log \left(c \left(d+e x^{2/3}\right)^n\right)-1260 a b n \left(315 d^4-105 d^3 e x^{2/3}+63 d^2 e^2 x^{4/3}-45 d e^3 x^2+35 e^4 x^{8/3}\right)+99225 b^2 e^4 x^{8/3} \log ^2\left(c \left(d+e x^{2/3}\right)^n\right)+8 b^2 n^2 \left(177345 d^4-26040 d^3 e x^{2/3}+9009 d^2 e^2 x^{4/3}-3600 d e^3 x^2+1225 e^4 x^{8/3}\right)\right)+1260 b d^{9/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(315 a+315 b \log \left(c \left(d+e x^{2/3}\right)^n\right)+630 b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)-1126 b n\right)+396900 i b^2 d^{9/2} n^2 \text{Li}_2\left(\frac{i \sqrt{d}+\sqrt{e} \sqrt[3]{x}}{\sqrt{e} \sqrt[3]{x}-i \sqrt{d}}\right)+396900 i b^2 d^{9/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{297675 e^{9/2}}","\frac{4 b d^{9/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{3 e^{9/2}}+\frac{4 b d^3 n x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{9 e^3}-\frac{4 b d^2 n x^{5/3} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{15 e^2}+\frac{4 b d n x^{7/3} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{21 e}+\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2-\frac{4}{27} b n x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)-\frac{4 a b d^4 n \sqrt[3]{x}}{3 e^4}-\frac{4 b^2 d^4 n \sqrt[3]{x} \log \left(c \left(d+e x^{2/3}\right)^n\right)}{3 e^4}+\frac{4 i b^2 d^{9/2} n^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{3 e^{9/2}}+\frac{4 i b^2 d^{9/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{3 e^{9/2}}-\frac{4504 b^2 d^{9/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{945 e^{9/2}}+\frac{8 b^2 d^{9/2} n^2 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{3 e^{9/2}}+\frac{4504 b^2 d^4 n^2 \sqrt[3]{x}}{945 e^4}-\frac{1984 b^2 d^3 n^2 x}{2835 e^3}+\frac{1144 b^2 d^2 n^2 x^{5/3}}{4725 e^2}-\frac{128 b^2 d n^2 x^{7/3}}{1323 e}+\frac{8}{243} b^2 n^2 x^3",1,"((396900*I)*b^2*d^(9/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2 + 1260*b*d^(9/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(315*a - 1126*b*n + 630*b*n*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))] + 315*b*Log[c*(d + e*x^(2/3))^n]) + Sqrt[e]*x^(1/3)*(99225*a^2*e^4*x^(8/3) - 1260*a*b*n*(315*d^4 - 105*d^3*e*x^(2/3) + 63*d^2*e^2*x^(4/3) - 45*d*e^3*x^2 + 35*e^4*x^(8/3)) + 8*b^2*n^2*(177345*d^4 - 26040*d^3*e*x^(2/3) + 9009*d^2*e^2*x^(4/3) - 3600*d*e^3*x^2 + 1225*e^4*x^(8/3)) - 630*b*(-315*a*e^4*x^(8/3) + 2*b*n*(315*d^4 - 105*d^3*e*x^(2/3) + 63*d^2*e^2*x^(4/3) - 45*d*e^3*x^2 + 35*e^4*x^(8/3)))*Log[c*(d + e*x^(2/3))^n] + 99225*b^2*e^4*x^(8/3)*Log[c*(d + e*x^(2/3))^n]^2) + (396900*I)*b^2*d^(9/2)*n^2*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x^(1/3))/((-I)*Sqrt[d] + Sqrt[e]*x^(1/3))])/(297675*e^(9/2))","A",1
477,1,319,364,0.226342,"\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^2,x]","\frac{\sqrt{e} \sqrt[3]{x} \left(9 a^2 e x^{2/3}+6 b \left(3 a e x^{2/3}+6 b d n-2 b e n x^{2/3}\right) \log \left(c \left(d+e x^{2/3}\right)^n\right)+12 a b n \left(3 d-e x^{2/3}\right)+9 b^2 e x^{2/3} \log ^2\left(c \left(d+e x^{2/3}\right)^n\right)+8 b^2 n^2 \left(e x^{2/3}-12 d\right)\right)-12 b d^{3/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(3 a+3 b \log \left(c \left(d+e x^{2/3}\right)^n\right)+6 b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)-8 b n\right)-36 i b^2 d^{3/2} n^2 \text{Li}_2\left(\frac{i \sqrt{d}+\sqrt{e} \sqrt[3]{x}}{\sqrt{e} \sqrt[3]{x}-i \sqrt{d}}\right)-36 i b^2 d^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{9 e^{3/2}}","-\frac{4 b d^{3/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{e^{3/2}}-\frac{4}{3} b n x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2+\frac{4 a b d n \sqrt[3]{x}}{e}+\frac{4 b^2 d n \sqrt[3]{x} \log \left(c \left(d+e x^{2/3}\right)^n\right)}{e}-\frac{4 i b^2 d^{3/2} n^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{e^{3/2}}-\frac{4 i b^2 d^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{e^{3/2}}+\frac{32 b^2 d^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{3 e^{3/2}}-\frac{8 b^2 d^{3/2} n^2 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{e^{3/2}}-\frac{32 b^2 d n^2 \sqrt[3]{x}}{3 e}+\frac{8}{9} b^2 n^2 x",1,"((-36*I)*b^2*d^(3/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2 - 12*b*d^(3/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(3*a - 8*b*n + 6*b*n*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))] + 3*b*Log[c*(d + e*x^(2/3))^n]) + Sqrt[e]*x^(1/3)*(12*a*b*n*(3*d - e*x^(2/3)) + 8*b^2*n^2*(-12*d + e*x^(2/3)) + 9*a^2*e*x^(2/3) + 6*b*(6*b*d*n + 3*a*e*x^(2/3) - 2*b*e*n*x^(2/3))*Log[c*(d + e*x^(2/3))^n] + 9*b^2*e*x^(2/3)*Log[c*(d + e*x^(2/3))^n]^2) - (36*I)*b^2*d^(3/2)*n^2*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x^(1/3))/((-I)*Sqrt[d] + Sqrt[e]*x^(1/3))])/(9*e^(3/2))","A",1
478,1,247,298,0.1923719,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^2,x]","\frac{-4 b e^{3/2} n x \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)+2 b n \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)-2 b n\right)-\sqrt{d} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \left(a d+b d \log \left(c \left(d+e x^{2/3}\right)^n\right)+4 b e n x^{2/3}\right)-4 i b^2 e^{3/2} n^2 x \text{Li}_2\left(\frac{i \sqrt{d}+\sqrt{e} \sqrt[3]{x}}{\sqrt{e} \sqrt[3]{x}-i \sqrt{d}}\right)-4 i b^2 e^{3/2} n^2 x \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{d^{3/2} x}","-\frac{4 b e^{3/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d^{3/2}}-\frac{4 b e n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d \sqrt[3]{x}}-\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x}-\frac{4 i b^2 e^{3/2} n^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{d^{3/2}}-\frac{4 i b^2 e^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{d^{3/2}}+\frac{8 b^2 e^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{8 b^2 e^{3/2} n^2 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{d^{3/2}}",1,"((-4*I)*b^2*e^(3/2)*n^2*x*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2 - 4*b*e^(3/2)*n*x*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a - 2*b*n + 2*b*n*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))] + b*Log[c*(d + e*x^(2/3))^n]) - Sqrt[d]*(a + b*Log[c*(d + e*x^(2/3))^n])*(a*d + 4*b*e*n*x^(2/3) + b*d*Log[c*(d + e*x^(2/3))^n]) - (4*I)*b^2*e^(3/2)*n^2*x*PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x^(1/3))/((-I)*Sqrt[d] + Sqrt[e]*x^(1/3))])/(d^(3/2)*x)","A",1
479,1,473,476,0.550978,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^4,x]","-\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{3 x^3}+\frac{4}{3} b e n \left(\frac{e^{7/2} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d^{9/2}}+\frac{e^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d^4 \sqrt[3]{x}}-\frac{e^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{3 d^3 x}+\frac{e \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{5 d^2 x^{5/3}}-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{7 d x^{7/3}}+\frac{i b e^{7/2} n \left(\text{Li}_2\left(\frac{i \sqrt{d}+\sqrt{e} \sqrt[3]{x}}{\sqrt{e} \sqrt[3]{x}-i \sqrt{d}}\right)+\tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(\tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)-2 i \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)\right)\right)}{d^{9/2}}-\frac{2 b e^{7/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{d^{9/2}}-\frac{2 b e^3 n \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{e x^{2/3}}{d}\right)}{3 d^4 \sqrt[3]{x}}+\frac{2 b e^2 n \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{e x^{2/3}}{d}\right)}{15 d^3 x}-\frac{2 b e n \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{e x^{2/3}}{d}\right)}{35 d^2 x^{5/3}}\right)","\frac{4 b e^{9/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{3 d^{9/2}}+\frac{4 b e^4 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{3 d^4 \sqrt[3]{x}}-\frac{4 b e^3 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{9 d^3 x}+\frac{4 b e^2 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{15 d^2 x^{5/3}}-\frac{4 b e n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{21 d x^{7/3}}-\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{3 x^3}+\frac{4 i b^2 e^{9/2} n^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{3 d^{9/2}}+\frac{4 i b^2 e^{9/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{3 d^{9/2}}-\frac{1408 b^2 e^{9/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{315 d^{9/2}}+\frac{8 b^2 e^{9/2} n^2 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{3 d^{9/2}}-\frac{568 b^2 e^4 n^2}{315 d^4 \sqrt[3]{x}}+\frac{32 b^2 e^3 n^2}{105 d^3 x}-\frac{8 b^2 e^2 n^2}{105 d^2 x^{5/3}}",1,"-1/3*(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^3 + (4*b*e*n*((-2*b*e^(7/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/d^(9/2) - (2*b*e*n*Hypergeometric2F1[-5/2, 1, -3/2, -((e*x^(2/3))/d)])/(35*d^2*x^(5/3)) + (2*b*e^2*n*Hypergeometric2F1[-3/2, 1, -1/2, -((e*x^(2/3))/d)])/(15*d^3*x) - (2*b*e^3*n*Hypergeometric2F1[-1/2, 1, 1/2, -((e*x^(2/3))/d)])/(3*d^4*x^(1/3)) - (a + b*Log[c*(d + e*x^(2/3))^n])/(7*d*x^(7/3)) + (e*(a + b*Log[c*(d + e*x^(2/3))^n]))/(5*d^2*x^(5/3)) - (e^2*(a + b*Log[c*(d + e*x^(2/3))^n]))/(3*d^3*x) + (e^3*(a + b*Log[c*(d + e*x^(2/3))^n]))/(d^4*x^(1/3)) + (e^(7/2)*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*Log[c*(d + e*x^(2/3))^n]))/d^(9/2) + (I*b*e^(7/2)*n*(ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]] - (2*I)*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))]) + PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x^(1/3))/((-I)*Sqrt[d] + Sqrt[e]*x^(1/3))]))/d^(9/2)))/3","C",1
480,1,678,640,1.2355699,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^6} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^6,x]","-\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{5 x^5}+\frac{4}{5} b e n \left(-\frac{e^{13/2} \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d^{15/2}}-\frac{e^6 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d^7 \sqrt[3]{x}}+\frac{e^5 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{3 d^6 x}-\frac{e^4 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{5 d^5 x^{5/3}}+\frac{e^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{7 d^4 x^{7/3}}-\frac{e^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{9 d^3 x^3}+\frac{e \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{11 d^2 x^{11/3}}-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{13 d x^{13/3}}-\frac{i b e^{13/2} n \left(\text{Li}_2\left(\frac{i \sqrt{d}+\sqrt{e} \sqrt[3]{x}}{\sqrt{e} \sqrt[3]{x}-i \sqrt{d}}\right)+\tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(\tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)-2 i \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)\right)\right)}{d^{15/2}}+\frac{2 b e^{13/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{d^{15/2}}+\frac{2 b e^6 n \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{e x^{2/3}}{d}\right)}{3 d^7 \sqrt[3]{x}}-\frac{2 b e^5 n \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{e x^{2/3}}{d}\right)}{15 d^6 x}+\frac{2 b e^4 n \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{e x^{2/3}}{d}\right)}{35 d^5 x^{5/3}}-\frac{2 b e^3 n \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};-\frac{e x^{2/3}}{d}\right)}{63 d^4 x^{7/3}}+\frac{2 b e^2 n \, _2F_1\left(-\frac{9}{2},1;-\frac{7}{2};-\frac{e x^{2/3}}{d}\right)}{99 d^3 x^3}-\frac{2 b e n \, _2F_1\left(-\frac{11}{2},1;-\frac{9}{2};-\frac{e x^{2/3}}{d}\right)}{143 d^2 x^{11/3}}\right)","-\frac{4 b e^{15/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{5 d^{15/2}}-\frac{4 b e^7 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{5 d^7 \sqrt[3]{x}}+\frac{4 b e^6 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{15 d^6 x}-\frac{4 b e^5 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{25 d^5 x^{5/3}}+\frac{4 b e^4 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{35 d^4 x^{7/3}}-\frac{4 b e^3 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{45 d^3 x^3}+\frac{4 b e^2 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{55 d^2 x^{11/3}}-\frac{4 b e n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{65 d x^{13/3}}-\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{5 x^5}-\frac{4 i b^2 e^{15/2} n^2 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{5 d^{15/2}}-\frac{4 i b^2 e^{15/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{5 d^{15/2}}+\frac{704552 b^2 e^{15/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{225225 d^{15/2}}-\frac{8 b^2 e^{15/2} n^2 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{5 d^{15/2}}+\frac{344192 b^2 e^7 n^2}{225225 d^7 \sqrt[3]{x}}-\frac{224072 b^2 e^6 n^2}{675675 d^6 x}+\frac{1216 b^2 e^5 n^2}{9009 d^5 x^{5/3}}-\frac{2872 b^2 e^4 n^2}{45045 d^4 x^{7/3}}+\frac{64 b^2 e^3 n^2}{2145 d^3 x^3}-\frac{8 b^2 e^2 n^2}{715 d^2 x^{11/3}}",1,"-1/5*(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^5 + (4*b*e*n*((2*b*e^(13/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/d^(15/2) - (2*b*e*n*Hypergeometric2F1[-11/2, 1, -9/2, -((e*x^(2/3))/d)])/(143*d^2*x^(11/3)) + (2*b*e^2*n*Hypergeometric2F1[-9/2, 1, -7/2, -((e*x^(2/3))/d)])/(99*d^3*x^3) - (2*b*e^3*n*Hypergeometric2F1[-7/2, 1, -5/2, -((e*x^(2/3))/d)])/(63*d^4*x^(7/3)) + (2*b*e^4*n*Hypergeometric2F1[-5/2, 1, -3/2, -((e*x^(2/3))/d)])/(35*d^5*x^(5/3)) - (2*b*e^5*n*Hypergeometric2F1[-3/2, 1, -1/2, -((e*x^(2/3))/d)])/(15*d^6*x) + (2*b*e^6*n*Hypergeometric2F1[-1/2, 1, 1/2, -((e*x^(2/3))/d)])/(3*d^7*x^(1/3)) - (a + b*Log[c*(d + e*x^(2/3))^n])/(13*d*x^(13/3)) + (e*(a + b*Log[c*(d + e*x^(2/3))^n]))/(11*d^2*x^(11/3)) - (e^2*(a + b*Log[c*(d + e*x^(2/3))^n]))/(9*d^3*x^3) + (e^3*(a + b*Log[c*(d + e*x^(2/3))^n]))/(7*d^4*x^(7/3)) - (e^4*(a + b*Log[c*(d + e*x^(2/3))^n]))/(5*d^5*x^(5/3)) + (e^5*(a + b*Log[c*(d + e*x^(2/3))^n]))/(3*d^6*x) - (e^6*(a + b*Log[c*(d + e*x^(2/3))^n]))/(d^7*x^(1/3)) - (e^(13/2)*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*Log[c*(d + e*x^(2/3))^n]))/d^(15/2) - (I*b*e^(13/2)*n*(ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]] - (2*I)*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))]) + PolyLog[2, (I*Sqrt[d] + Sqrt[e]*x^(1/3))/((-I)*Sqrt[d] + Sqrt[e]*x^(1/3))]))/d^(15/2)))/5","C",1
481,1,598,913,1.0702877,"\int x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \, dx","Integrate[x^3*(a + b*Log[c*(d + e*x^(2/3))^n])^3,x]","\frac{-60 b \left(1800 a^2 \left(d^6-e^6 x^4\right)-60 a b n \left(147 d^6+60 d^5 e x^{2/3}-30 d^4 e^2 x^{4/3}+20 d^3 e^3 x^2-15 d^2 e^4 x^{8/3}+12 d e^5 x^{10/3}-10 e^6 x^4\right)+b^2 n^2 \left(8820 d^6+8820 d^5 e x^{2/3}-2610 d^4 e^2 x^{4/3}+1140 d^3 e^3 x^2-555 d^2 e^4 x^{8/3}+264 d e^5 x^{10/3}-100 e^6 x^4\right)\right) \log \left(c \left(d+e x^{2/3}\right)^n\right)+e x^{2/3} \left(36000 a^3 e^5 x^{10/3}+1800 a^2 b n \left(60 d^5-30 d^4 e x^{2/3}+20 d^3 e^2 x^{4/3}-15 d^2 e^3 x^2+12 d e^4 x^{8/3}-10 e^5 x^{10/3}\right)-60 a b^2 n^2 \left(8820 d^5-2610 d^4 e x^{2/3}+1140 d^3 e^2 x^{4/3}-555 d^2 e^3 x^2+264 d e^4 x^{8/3}-100 e^5 x^{10/3}\right)+b^3 n^3 \left(809340 d^5-140070 d^4 e x^{2/3}+41180 d^3 e^2 x^{4/3}-13785 d^2 e^3 x^2+4368 d e^4 x^{8/3}-1000 e^5 x^{10/3}\right)\right)+1800 b^2 \left(b n \left(147 d^6+60 d^5 e x^{2/3}-30 d^4 e^2 x^{4/3}+20 d^3 e^3 x^2-15 d^2 e^4 x^{8/3}+12 d e^5 x^{10/3}-10 e^6 x^4\right)-60 a \left(d^6-e^6 x^4\right)\right) \log ^2\left(c \left(d+e x^{2/3}\right)^n\right)-36000 b^3 \left(d^6-e^6 x^4\right) \log ^3\left(c \left(d+e x^{2/3}\right)^n\right)-280140 b^3 d^6 n^3 \log \left(d+e x^{2/3}\right)}{144000 e^6}","-\frac{b^3 n^3 \left(d+e x^{2/3}\right)^6}{144 e^6}+\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \left(d+e x^{2/3}\right)^6}{4 e^6}-\frac{b n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \left(d+e x^{2/3}\right)^6}{8 e^6}+\frac{b^2 n^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \left(d+e x^{2/3}\right)^6}{24 e^6}+\frac{9 b^3 d n^3 \left(d+e x^{2/3}\right)^5}{125 e^6}-\frac{3 d \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \left(d+e x^{2/3}\right)^5}{2 e^6}+\frac{9 b d n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \left(d+e x^{2/3}\right)^5}{10 e^6}-\frac{9 b^2 d n^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \left(d+e x^{2/3}\right)^5}{25 e^6}-\frac{45 b^3 d^2 n^3 \left(d+e x^{2/3}\right)^4}{128 e^6}+\frac{15 d^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \left(d+e x^{2/3}\right)^4}{4 e^6}-\frac{45 b d^2 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \left(d+e x^{2/3}\right)^4}{16 e^6}+\frac{45 b^2 d^2 n^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \left(d+e x^{2/3}\right)^4}{32 e^6}+\frac{10 b^3 d^3 n^3 \left(d+e x^{2/3}\right)^3}{9 e^6}-\frac{5 d^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \left(d+e x^{2/3}\right)^3}{e^6}+\frac{5 b d^3 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \left(d+e x^{2/3}\right)^3}{e^6}-\frac{10 b^2 d^3 n^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \left(d+e x^{2/3}\right)^3}{3 e^6}-\frac{45 b^3 d^4 n^3 \left(d+e x^{2/3}\right)^2}{16 e^6}+\frac{15 d^4 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \left(d+e x^{2/3}\right)^2}{4 e^6}-\frac{45 b d^4 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \left(d+e x^{2/3}\right)^2}{8 e^6}+\frac{45 b^2 d^4 n^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \left(d+e x^{2/3}\right)^2}{8 e^6}-\frac{3 d^5 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \left(d+e x^{2/3}\right)}{2 e^6}+\frac{9 b d^5 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \left(d+e x^{2/3}\right)}{2 e^6}-\frac{9 b^3 d^5 n^2 \log \left(c \left(d+e x^{2/3}\right)^n\right) \left(d+e x^{2/3}\right)}{e^6}+\frac{9 b^3 d^5 n^3 x^{2/3}}{e^5}-\frac{9 a b^2 d^5 n^2 x^{2/3}}{e^5}",1,"(e*x^(2/3)*(36000*a^3*e^5*x^(10/3) + b^3*n^3*(809340*d^5 - 140070*d^4*e*x^(2/3) + 41180*d^3*e^2*x^(4/3) - 13785*d^2*e^3*x^2 + 4368*d*e^4*x^(8/3) - 1000*e^5*x^(10/3)) - 60*a*b^2*n^2*(8820*d^5 - 2610*d^4*e*x^(2/3) + 1140*d^3*e^2*x^(4/3) - 555*d^2*e^3*x^2 + 264*d*e^4*x^(8/3) - 100*e^5*x^(10/3)) + 1800*a^2*b*n*(60*d^5 - 30*d^4*e*x^(2/3) + 20*d^3*e^2*x^(4/3) - 15*d^2*e^3*x^2 + 12*d*e^4*x^(8/3) - 10*e^5*x^(10/3))) - 280140*b^3*d^6*n^3*Log[d + e*x^(2/3)] - 60*b*(b^2*n^2*(8820*d^6 + 8820*d^5*e*x^(2/3) - 2610*d^4*e^2*x^(4/3) + 1140*d^3*e^3*x^2 - 555*d^2*e^4*x^(8/3) + 264*d*e^5*x^(10/3) - 100*e^6*x^4) - 60*a*b*n*(147*d^6 + 60*d^5*e*x^(2/3) - 30*d^4*e^2*x^(4/3) + 20*d^3*e^3*x^2 - 15*d^2*e^4*x^(8/3) + 12*d*e^5*x^(10/3) - 10*e^6*x^4) + 1800*a^2*(d^6 - e^6*x^4))*Log[c*(d + e*x^(2/3))^n] + 1800*b^2*(b*n*(147*d^6 + 60*d^5*e*x^(2/3) - 30*d^4*e^2*x^(4/3) + 20*d^3*e^3*x^2 - 15*d^2*e^4*x^(8/3) + 12*d*e^5*x^(10/3) - 10*e^6*x^4) - 60*a*(d^6 - e^6*x^4))*Log[c*(d + e*x^(2/3))^n]^2 - 36000*b^3*(d^6 - e^6*x^4)*Log[c*(d + e*x^(2/3))^n]^3)/(144000*e^6)","A",1
482,1,428,449,0.4295009,"\int x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \, dx","Integrate[x*(a + b*Log[c*(d + e*x^(2/3))^n])^3,x]","\frac{36 a^3 d^3+36 a^3 e^3 x^2+6 b \left(18 a^2 \left(d^3+e^3 x^2\right)-6 a b n \left(11 d^3+6 d^2 e x^{2/3}-3 d e^2 x^{4/3}+2 e^3 x^2\right)+b^2 n^2 \left(66 d^3+66 d^2 e x^{2/3}-15 d e^2 x^{4/3}+4 e^3 x^2\right)\right) \log \left(c \left(d+e x^{2/3}\right)^n\right)-198 a^2 b d^3 n-108 a^2 b d^2 e n x^{2/3}+54 a^2 b d e^2 n x^{4/3}-36 a^2 b e^3 n x^2+18 b^2 \left(6 a \left(d^3+e^3 x^2\right)-b n \left(11 d^3+6 d^2 e x^{2/3}-3 d e^2 x^{4/3}+2 e^3 x^2\right)\right) \log ^2\left(c \left(d+e x^{2/3}\right)^n\right)+396 a b^2 d^2 e n^2 x^{2/3}-90 a b^2 d e^2 n^2 x^{4/3}+24 a b^2 e^3 n^2 x^2+36 b^3 \left(d^3+e^3 x^2\right) \log ^3\left(c \left(d+e x^{2/3}\right)^n\right)+114 b^3 d^3 n^3 \log \left(d+e x^{2/3}\right)-510 b^3 d^2 e n^3 x^{2/3}+57 b^3 d e^2 n^3 x^{4/3}-8 b^3 e^3 n^3 x^2}{72 e^3}","\frac{b^2 n^2 \left(d+e x^{2/3}\right)^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{3 e^3}-\frac{9 b^2 d n^2 \left(d+e x^{2/3}\right)^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{4 e^3}+\frac{9 a b^2 d^2 n^2 x^{2/3}}{e^2}-\frac{9 b d^2 n \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{2 e^3}+\frac{3 d^2 \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{2 e^3}-\frac{b n \left(d+e x^{2/3}\right)^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{2 e^3}+\frac{9 b d n \left(d+e x^{2/3}\right)^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{4 e^3}+\frac{\left(d+e x^{2/3}\right)^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{2 e^3}-\frac{3 d \left(d+e x^{2/3}\right)^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{2 e^3}+\frac{9 b^3 d^2 n^2 \left(d+e x^{2/3}\right) \log \left(c \left(d+e x^{2/3}\right)^n\right)}{e^3}-\frac{9 b^3 d^2 n^3 x^{2/3}}{e^2}-\frac{b^3 n^3 \left(d+e x^{2/3}\right)^3}{9 e^3}+\frac{9 b^3 d n^3 \left(d+e x^{2/3}\right)^2}{8 e^3}",1,"(36*a^3*d^3 - 198*a^2*b*d^3*n - 108*a^2*b*d^2*e*n*x^(2/3) + 396*a*b^2*d^2*e*n^2*x^(2/3) - 510*b^3*d^2*e*n^3*x^(2/3) + 54*a^2*b*d*e^2*n*x^(4/3) - 90*a*b^2*d*e^2*n^2*x^(4/3) + 57*b^3*d*e^2*n^3*x^(4/3) + 36*a^3*e^3*x^2 - 36*a^2*b*e^3*n*x^2 + 24*a*b^2*e^3*n^2*x^2 - 8*b^3*e^3*n^3*x^2 + 114*b^3*d^3*n^3*Log[d + e*x^(2/3)] + 6*b*(18*a^2*(d^3 + e^3*x^2) - 6*a*b*n*(11*d^3 + 6*d^2*e*x^(2/3) - 3*d*e^2*x^(4/3) + 2*e^3*x^2) + b^2*n^2*(66*d^3 + 66*d^2*e*x^(2/3) - 15*d*e^2*x^(4/3) + 4*e^3*x^2))*Log[c*(d + e*x^(2/3))^n] + 18*b^2*(6*a*(d^3 + e^3*x^2) - b*n*(11*d^3 + 6*d^2*e*x^(2/3) - 3*d*e^2*x^(4/3) + 2*e^3*x^2))*Log[c*(d + e*x^(2/3))^n]^2 + 36*b^3*(d^3 + e^3*x^2)*Log[c*(d + e*x^(2/3))^n]^3)/(72*e^3)","A",1
483,1,339,139,0.2591005,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{x} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^3/x,x]","\frac{9}{2} b^2 n^2 \left(-2 \text{Li}_3\left(\frac{x^{2/3} e}{d}+1\right)+2 \text{Li}_2\left(\frac{x^{2/3} e}{d}+1\right) \log \left(d+e x^{2/3}\right)+\log \left(-\frac{e x^{2/3}}{d}\right) \log ^2\left(d+e x^{2/3}\right)\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)+3 b n \left(\log (x) \left(\log \left(d+e x^{2/3}\right)-\log \left(\frac{e x^{2/3}}{d}+1\right)\right)-\frac{3}{2} \text{Li}_2\left(-\frac{e x^{2/3}}{d}\right)\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2+\log (x) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^3+\frac{3}{2} b^3 n^3 \left(6 \text{Li}_4\left(\frac{x^{2/3} e}{d}+1\right)+3 \text{Li}_2\left(\frac{x^{2/3} e}{d}+1\right) \log ^2\left(d+e x^{2/3}\right)-6 \text{Li}_3\left(\frac{x^{2/3} e}{d}+1\right) \log \left(d+e x^{2/3}\right)+\log \left(-\frac{e x^{2/3}}{d}\right) \log ^3\left(d+e x^{2/3}\right)\right)","-9 b^2 n^2 \text{Li}_3\left(\frac{x^{2/3} e}{d}+1\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+\frac{9}{2} b n \text{Li}_2\left(\frac{x^{2/3} e}{d}+1\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2+\frac{3}{2} \log \left(-\frac{e x^{2/3}}{d}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3+9 b^3 n^3 \text{Li}_4\left(\frac{x^{2/3} e}{d}+1\right)",1,"(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^3*Log[x] + 3*b*n*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2*((Log[d + e*x^(2/3)] - Log[1 + (e*x^(2/3))/d])*Log[x] - (3*PolyLog[2, -((e*x^(2/3))/d)])/2) + (9*b^2*n^2*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])*(Log[d + e*x^(2/3)]^2*Log[-((e*x^(2/3))/d)] + 2*Log[d + e*x^(2/3)]*PolyLog[2, 1 + (e*x^(2/3))/d] - 2*PolyLog[3, 1 + (e*x^(2/3))/d]))/2 + (3*b^3*n^3*(Log[d + e*x^(2/3)]^3*Log[-((e*x^(2/3))/d)] + 3*Log[d + e*x^(2/3)]^2*PolyLog[2, 1 + (e*x^(2/3))/d] - 6*Log[d + e*x^(2/3)]*PolyLog[3, 1 + (e*x^(2/3))/d] + 6*PolyLog[4, 1 + (e*x^(2/3))/d]))/2","B",1
484,1,764,451,0.8735585,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^3/x^3,x]","\frac{-6 b^2 n^2 \left(\left(d^3+e^3 x^2\right) \log ^2\left(d+e x^{2/3}\right)+\log \left(d+e x^{2/3}\right) \left(d^2 e x^{2/3}-2 e^3 x^2 \log \left(-\frac{e x^{2/3}}{d}\right)-2 d e^2 x^{4/3}-3 e^3 x^2\right)-2 e^3 x^2 \text{Li}_2\left(\frac{x^{2/3} e}{d}+1\right)+e^2 x^{4/3} \left(3 e x^{2/3} \log \left(-\frac{e x^{2/3}}{d}\right)+d\right)\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)-2 d^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^3-6 b d^3 n \log \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2-3 b d^2 e n x^{2/3} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2-6 b e^3 n x^2 \log \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2+4 b e^3 n x^2 \log (x) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2+6 b d e^2 n x^{4/3} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2+b^3 n^3 \left(-2 d^3 \log ^3\left(d+e x^{2/3}\right)-3 d^2 e x^{2/3} \log ^2\left(d+e x^{2/3}\right)-12 e^3 x^2 \text{Li}_3\left(\frac{x^{2/3} e}{d}+1\right)+6 e^3 x^2 \text{Li}_2\left(\frac{x^{2/3} e}{d}+1\right) \left(2 \log \left(d+e x^{2/3}\right)-3\right)-2 e^3 x^2 \log ^3\left(d+e x^{2/3}\right)+9 e^3 x^2 \log ^2\left(d+e x^{2/3}\right)+6 e^3 x^2 \log ^2\left(d+e x^{2/3}\right) \log \left(-\frac{e x^{2/3}}{d}\right)-6 e^3 x^2 \log \left(d+e x^{2/3}\right)+6 e^3 x^2 \log \left(-\frac{e x^{2/3}}{d}\right)-18 e^3 x^2 \log \left(d+e x^{2/3}\right) \log \left(-\frac{e x^{2/3}}{d}\right)+6 d e^2 x^{4/3} \log ^2\left(d+e x^{2/3}\right)-6 d e^2 x^{4/3} \log \left(d+e x^{2/3}\right)\right)}{4 d^3 x^2}","-\frac{3 b^2 e^3 n^2 \text{Li}_2\left(\frac{d}{d+e x^{2/3}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d^3}-\frac{3 b^2 e^3 n^2 \log \left(1-\frac{d}{d+e x^{2/3}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{2 d^3}-\frac{3 b^2 e^3 n^2 \log \left(-\frac{e x^{2/3}}{d}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d^3}-\frac{3 b^2 e^2 n^2 \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{2 d^3 x^{2/3}}+\frac{3 b e^3 n \log \left(1-\frac{d}{d+e x^{2/3}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{2 d^3}+\frac{3 b e^2 n \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{2 d^3 x^{2/3}}-\frac{3 b e n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{4 d x^{4/3}}-\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{2 x^2}+\frac{3 b^3 e^3 n^3 \text{Li}_2\left(\frac{d}{d+e x^{2/3}}\right)}{2 d^3}-\frac{3 b^3 e^3 n^3 \text{Li}_2\left(\frac{x^{2/3} e}{d}+1\right)}{d^3}-\frac{3 b^3 e^3 n^3 \text{Li}_3\left(\frac{d}{d+e x^{2/3}}\right)}{d^3}+\frac{b^3 e^3 n^3 \log (x)}{d^3}",1,"(-3*b*d^2*e*n*x^(2/3)*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 + 6*b*d*e^2*n*x^(4/3)*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 - 6*b*d^3*n*Log[d + e*x^(2/3)]*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 - 6*b*e^3*n*x^2*Log[d + e*x^(2/3)]*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 - 2*d^3*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^3 + 4*b*e^3*n*x^2*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2*Log[x] - 6*b^2*n^2*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])*((d^3 + e^3*x^2)*Log[d + e*x^(2/3)]^2 + e^2*x^(4/3)*(d + 3*e*x^(2/3)*Log[-((e*x^(2/3))/d)]) + Log[d + e*x^(2/3)]*(d^2*e*x^(2/3) - 2*d*e^2*x^(4/3) - 3*e^3*x^2 - 2*e^3*x^2*Log[-((e*x^(2/3))/d)]) - 2*e^3*x^2*PolyLog[2, 1 + (e*x^(2/3))/d]) + b^3*n^3*(-6*d*e^2*x^(4/3)*Log[d + e*x^(2/3)] - 6*e^3*x^2*Log[d + e*x^(2/3)] - 3*d^2*e*x^(2/3)*Log[d + e*x^(2/3)]^2 + 6*d*e^2*x^(4/3)*Log[d + e*x^(2/3)]^2 + 9*e^3*x^2*Log[d + e*x^(2/3)]^2 - 2*d^3*Log[d + e*x^(2/3)]^3 - 2*e^3*x^2*Log[d + e*x^(2/3)]^3 + 6*e^3*x^2*Log[-((e*x^(2/3))/d)] - 18*e^3*x^2*Log[d + e*x^(2/3)]*Log[-((e*x^(2/3))/d)] + 6*e^3*x^2*Log[d + e*x^(2/3)]^2*Log[-((e*x^(2/3))/d)] + 6*e^3*x^2*(-3 + 2*Log[d + e*x^(2/3)])*PolyLog[2, 1 + (e*x^(2/3))/d] - 12*e^3*x^2*PolyLog[3, 1 + (e*x^(2/3))/d]))/(4*d^3*x^2)","A",1
485,1,3146,794,9.2527226,"\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \, dx","Integrate[x^2*(a + b*Log[c*(d + e*x^(2/3))^n])^3,x]","\text{Result too large to show}","\frac{2 b d^5 n \text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^{2/3} \left(d+e x^{2/3}\right)},x\right)}{3 e^4}-\frac{4504 b^2 d^{9/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{315 e^{9/2}}-\frac{1984 b^2 d^3 n^2 x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{945 e^3}+\frac{1144 b^2 d^2 n^2 x^{5/3} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{1575 e^2}-\frac{128 b^2 d n^2 x^{7/3} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{441 e}+\frac{8}{81} b^2 n^2 x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+\frac{4504 a b^2 d^4 n^2 \sqrt[3]{x}}{315 e^4}-\frac{2 b d^4 n \sqrt[3]{x} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{e^4}+\frac{2 b d^3 n x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{3 e^3}-\frac{2 b d^2 n x^{5/3} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{5 e^2}+\frac{2 b d n x^{7/3} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{7 e}+\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3-\frac{2}{9} b n x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2+\frac{4504 b^3 d^4 n^2 \sqrt[3]{x} \log \left(c \left(d+e x^{2/3}\right)^n\right)}{315 e^4}-\frac{4504 i b^3 d^{9/2} n^3 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{315 e^{9/2}}-\frac{4504 i b^3 d^{9/2} n^3 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{315 e^{9/2}}+\frac{3475504 b^3 d^{9/2} n^3 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{99225 e^{9/2}}-\frac{9008 b^3 d^{9/2} n^3 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{315 e^{9/2}}-\frac{3475504 b^3 d^4 n^3 \sqrt[3]{x}}{99225 e^4}+\frac{637984 b^3 d^3 n^3 x}{297675 e^3}-\frac{221344 b^3 d^2 n^3 x^{5/3}}{496125 e^2}+\frac{3088 b^3 d n^3 x^{7/3}}{27783 e}-\frac{16}{729} b^3 n^3 x^3",0,"(b^3*n^3*x^(1/3)*(32*d^4 - 32*d^4*Sqrt[1 - (d + e*x^(2/3))/d] + 128*d^3*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3)) - 192*d^2*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^2 + 128*d*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^3 - 32*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^4 + 1584*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-7/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^(2/3))/d] - 4536*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-5/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^(2/3))/d] + 3780*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-3/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^(2/3))/d] - 864*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-7/2, 1, 1, 1, 1}, {2, 2, 2, 2}, (d + e*x^(2/3))/d] + 3024*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-5/2, 1, 1, 1, 1}, {2, 2, 2, 2}, (d + e*x^(2/3))/d] - 3780*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-3/2, 1, 1, 1, 1}, {2, 2, 2, 2}, (d + e*x^(2/3))/d] + 1890*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1, 1, 1}, {2, 2, 2, 2}, (d + e*x^(2/3))/d] - 240*d^4*Log[d + e*x^(2/3)] + 240*d^4*Sqrt[1 - (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)] - 672*d^3*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))*Log[d + e*x^(2/3)] + 576*d^2*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^2*Log[d + e*x^(2/3)] - 96*d*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^3*Log[d + e*x^(2/3)] - 48*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^4*Log[d + e*x^(2/3)] - 3780*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-3/2, 1, 1}, {2, 2}, (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)] + 864*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-7/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)] - 3024*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-5/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)] + 3780*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-3/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)] - 1890*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)] + 284*d^4*Log[d + e*x^(2/3)]^2 - 284*d^4*Sqrt[1 - (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)]^2 + 668*d^3*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))*Log[d + e*x^(2/3)]^2 - 552*d^2*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^2*Log[d + e*x^(2/3)]^2 + 236*d*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^3*Log[d + e*x^(2/3)]^2 - 68*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^4*Log[d + e*x^(2/3)]^2 - 1890*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-3/2, 1, 1}, {2, 2}, (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)]^2 + 945*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)]^2 - 70*d^4*Log[d + e*x^(2/3)]^3 + 70*d^4*Sqrt[1 - (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)]^3 - 280*d^3*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))*Log[d + e*x^(2/3)]^3 + 420*d^2*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^2*Log[d + e*x^(2/3)]^3 - 280*d*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^3*Log[d + e*x^(2/3)]^3 + 70*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^4*Log[d + e*x^(2/3)]^3 + 1512*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-5/2, 1, 1}, {2, 2}, (d + e*x^(2/3))/d]*(1 + 3*Log[d + e*x^(2/3)] + Log[d + e*x^(2/3)]^2) - 144*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-7/2, 1, 1}, {2, 2}, (d + e*x^(2/3))/d]*(6 + 11*Log[d + e*x^(2/3)] + 3*Log[d + e*x^(2/3)]^2)))/(210*e^4*Sqrt[1 - (d + e*x^(2/3))/d]) + (b^2*n^2*x^(1/3)*(-120*d^4 + 120*d^4*Sqrt[1 - (d + e*x^(2/3))/d] - 336*d^3*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3)) + 288*d^2*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^2 - 48*d*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^3 - 24*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^4 - 1890*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-3/2, 1, 1}, {2, 2}, (d + e*x^(2/3))/d] + 432*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-7/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^(2/3))/d] - 1512*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-5/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^(2/3))/d] + 1890*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-3/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^(2/3))/d] - 945*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, (d + e*x^(2/3))/d] + 284*d^4*Log[d + e*x^(2/3)] - 284*d^4*Sqrt[1 - (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)] + 668*d^3*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))*Log[d + e*x^(2/3)] - 552*d^2*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^2*Log[d + e*x^(2/3)] + 236*d*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^3*Log[d + e*x^(2/3)] - 68*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^4*Log[d + e*x^(2/3)] - 1890*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-3/2, 1, 1}, {2, 2}, (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)] + 945*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)] - 105*d^4*Log[d + e*x^(2/3)]^2 + 105*d^4*Sqrt[1 - (d + e*x^(2/3))/d]*Log[d + e*x^(2/3)]^2 - 420*d^3*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))*Log[d + e*x^(2/3)]^2 + 630*d^2*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^2*Log[d + e*x^(2/3)]^2 - 420*d*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^3*Log[d + e*x^(2/3)]^2 + 105*Sqrt[1 - (d + e*x^(2/3))/d]*(d + e*x^(2/3))^4*Log[d + e*x^(2/3)]^2 + 756*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-5/2, 1, 1}, {2, 2}, (d + e*x^(2/3))/d]*(3 + 2*Log[d + e*x^(2/3)]) - 72*d^3*(d + e*x^(2/3))*HypergeometricPFQ[{-7/2, 1, 1}, {2, 2}, (d + e*x^(2/3))/d]*(11 + 6*Log[d + e*x^(2/3)]))*(a + b*(-(n*Log[d + e*x^(2/3)]) + Log[c*(d + e*x^(2/3))^n])))/(105*e^4*Sqrt[1 - (d + e*x^(2/3))/d]) - (2*b*d^4*n*x^(1/3)*(a + b*(-(n*Log[d + e*x^(2/3)]) + Log[c*(d + e*x^(2/3))^n]))^2)/e^4 + (2*b*d^3*n*x*(a + b*(-(n*Log[d + e*x^(2/3)]) + Log[c*(d + e*x^(2/3))^n]))^2)/(3*e^3) - (2*b*d^2*n*x^(5/3)*(a + b*(-(n*Log[d + e*x^(2/3)]) + Log[c*(d + e*x^(2/3))^n]))^2)/(5*e^2) + (2*b*d*n*x^(7/3)*(a + b*(-(n*Log[d + e*x^(2/3)]) + Log[c*(d + e*x^(2/3))^n]))^2)/(7*e) + (2*b*d^(9/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*(-(n*Log[d + e*x^(2/3)]) + Log[c*(d + e*x^(2/3))^n]))^2)/e^(9/2) + b*n*x^3*Log[d + e*x^(2/3)]*(a + b*(-(n*Log[d + e*x^(2/3)]) + Log[c*(d + e*x^(2/3))^n]))^2 + (x^3*(a + b*(-(n*Log[d + e*x^(2/3)]) + Log[c*(d + e*x^(2/3))^n]))^2*(3*a - 2*b*n + 3*b*(-(n*Log[d + e*x^(2/3)]) + Log[c*(d + e*x^(2/3))^n])))/9","B",1
486,1,598,486,1.2834495,"\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^3,x]","\frac{3 b^2 n^2 x \left(-a-b \log \left(c \left(d+e x^{2/3}\right)^n\right)+b n \log \left(d+e x^{2/3}\right)\right) \left(3 \left(d+e x^{2/3}\right) \, _4F_3\left(-\frac{1}{2},1,1,1;2,2,2;\frac{x^{2/3} e}{d}+1\right)+\log \left(d+e x^{2/3}\right) \left(\left(d-d \left(-\frac{e x^{2/3}}{d}\right)^{3/2}\right) \log \left(d+e x^{2/3}\right)-3 \left(d+e x^{2/3}\right) \, _3F_2\left(-\frac{1}{2},1,1;2,2;\frac{x^{2/3} e}{d}+1\right)\right)\right)}{d \left(-\frac{e x^{2/3}}{d}\right)^{3/2}}-\frac{b^3 n^3 x \left(\log \left(d+e x^{2/3}\right) \left(18 \left(d+e x^{2/3}\right) \, _4F_3\left(-\frac{1}{2},1,1,1;2,2,2;\frac{x^{2/3} e}{d}+1\right)+\log \left(d+e x^{2/3}\right) \left(2 \left(d-d \left(-\frac{e x^{2/3}}{d}\right)^{3/2}\right) \log \left(d+e x^{2/3}\right)-9 \left(d+e x^{2/3}\right) \, _3F_2\left(-\frac{1}{2},1,1;2,2;\frac{x^{2/3} e}{d}+1\right)\right)\right)-18 \left(d+e x^{2/3}\right) \, _5F_4\left(-\frac{1}{2},1,1,1,1;2,2,2,2;\frac{x^{2/3} e}{d}+1\right)\right)}{2 d \left(-\frac{e x^{2/3}}{d}\right)^{3/2}}-\frac{6 b d^{3/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2}{e^{3/2}}+3 b n x \log \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2+\frac{6 b d n \sqrt[3]{x} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2}{e}+x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)-2 b n\right)","-\frac{2 b d^2 n \text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^{2/3} \left(d+e x^{2/3}\right)},x\right)}{e}+\frac{32 b^2 d^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{e^{3/2}}+\frac{8}{3} b^2 n^2 x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)-\frac{32 a b^2 d n^2 \sqrt[3]{x}}{e}-2 b n x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2+\frac{6 b d n \sqrt[3]{x} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{e}+x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3-\frac{32 b^3 d n^2 \sqrt[3]{x} \log \left(c \left(d+e x^{2/3}\right)^n\right)}{e}+\frac{32 i b^3 d^{3/2} n^3 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{e^{3/2}}+\frac{32 i b^3 d^{3/2} n^3 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{e^{3/2}}-\frac{208 b^3 d^{3/2} n^3 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{3 e^{3/2}}+\frac{64 b^3 d^{3/2} n^3 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{e^{3/2}}+\frac{208 b^3 d n^3 \sqrt[3]{x}}{3 e}-\frac{16}{9} b^3 n^3 x",0,"-1/2*(b^3*n^3*x*(-18*(d + e*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1, 1, 1}, {2, 2, 2, 2}, 1 + (e*x^(2/3))/d] + Log[d + e*x^(2/3)]*(18*(d + e*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, 1 + (e*x^(2/3))/d] + Log[d + e*x^(2/3)]*(-9*(d + e*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, 1 + (e*x^(2/3))/d] + 2*(d - d*(-((e*x^(2/3))/d))^(3/2))*Log[d + e*x^(2/3)]))))/(d*(-((e*x^(2/3))/d))^(3/2)) + (3*b^2*n^2*x*(3*(d + e*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, 1 + (e*x^(2/3))/d] + Log[d + e*x^(2/3)]*(-3*(d + e*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, 1 + (e*x^(2/3))/d] + (d - d*(-((e*x^(2/3))/d))^(3/2))*Log[d + e*x^(2/3)]))*(-a + b*n*Log[d + e*x^(2/3)] - b*Log[c*(d + e*x^(2/3))^n]))/(d*(-((e*x^(2/3))/d))^(3/2)) + (6*b*d*n*x^(1/3)*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2)/e - (6*b*d^(3/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2)/e^(3/2) + 3*b*n*x*Log[d + e*x^(2/3)]*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 + x*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2*(a - 2*b*n - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])","A",1
487,1,646,319,2.6597427,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^3/x^2,x]","-\frac{-3 b^2 n^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right) \left(-6 d \left(d+e x^{2/3}\right) \left(-\frac{e x^{2/3}}{d}\right)^{3/2} \, _4F_3\left(1,1,1,\frac{5}{2};2,2,2;\frac{x^{2/3} e}{d}+1\right)-2 d \log \left(d+e x^{2/3}\right) \left(-4 e x^{2/3} \left(\sqrt{-\frac{e x^{2/3}}{d}}-1\right)+4 d \left(-\frac{e x^{2/3}}{d}\right)^{3/2} \log \left(\frac{1}{2} \left(\sqrt{-\frac{e x^{2/3}}{d}}+1\right)\right)+\left(d-d \left(-\frac{e x^{2/3}}{d}\right)^{3/2}\right) \log \left(d+e x^{2/3}\right)\right)\right)+2 b^3 d n^3 \left(-9 \left(d+e x^{2/3}\right) \left(-\frac{e x^{2/3}}{d}\right)^{3/2} \, _5F_4\left(1,1,1,1,\frac{5}{2};2,2,2,2;\frac{x^{2/3} e}{d}+1\right)+9 \left(d+e x^{2/3}\right) \left(-\frac{e x^{2/3}}{d}\right)^{3/2} \log \left(d+e x^{2/3}\right) \, _4F_3\left(1,1,1,\frac{5}{2};2,2,2;\frac{x^{2/3} e}{d}+1\right)+\left(-6 e x^{2/3} \left(\sqrt{-\frac{e x^{2/3}}{d}}-1\right)+6 d \left(-\frac{e x^{2/3}}{d}\right)^{3/2} \log \left(\frac{1}{2} \left(\sqrt{-\frac{e x^{2/3}}{d}}+1\right)\right)+\left(d-d \left(-\frac{e x^{2/3}}{d}\right)^{3/2}\right) \log \left(d+e x^{2/3}\right)\right) \log ^2\left(d+e x^{2/3}\right)\right)+6 b d^2 n \log \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2+2 d^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^3+12 b \sqrt{d} e^{3/2} n x \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2+12 b d e n x^{2/3} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)-b n \log \left(d+e x^{2/3}\right)\right)^2}{2 d^2 x}","-\frac{2 b e^2 n \text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^{2/3} \left(d+e x^{2/3}\right)},x\right)}{d}+\frac{24 b^2 e^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d^{3/2}}-\frac{6 b e n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{d \sqrt[3]{x}}-\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{x}+\frac{24 i b^3 e^{3/2} n^3 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{d^{3/2}}+\frac{24 i b^3 e^{3/2} n^3 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{d^{3/2}}+\frac{48 b^3 e^{3/2} n^3 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{d^{3/2}}",0,"-1/2*(2*b^3*d*n^3*(-9*(d + e*x^(2/3))*(-((e*x^(2/3))/d))^(3/2)*HypergeometricPFQ[{1, 1, 1, 1, 5/2}, {2, 2, 2, 2}, 1 + (e*x^(2/3))/d] + 9*(d + e*x^(2/3))*(-((e*x^(2/3))/d))^(3/2)*HypergeometricPFQ[{1, 1, 1, 5/2}, {2, 2, 2}, 1 + (e*x^(2/3))/d]*Log[d + e*x^(2/3)] + Log[d + e*x^(2/3)]^2*(-6*e*(-1 + Sqrt[-((e*x^(2/3))/d)])*x^(2/3) + 6*d*(-((e*x^(2/3))/d))^(3/2)*Log[(1 + Sqrt[-((e*x^(2/3))/d)])/2] + (d - d*(-((e*x^(2/3))/d))^(3/2))*Log[d + e*x^(2/3)])) - 3*b^2*n^2*(-6*d*(d + e*x^(2/3))*(-((e*x^(2/3))/d))^(3/2)*HypergeometricPFQ[{1, 1, 1, 5/2}, {2, 2, 2}, 1 + (e*x^(2/3))/d] - 2*d*Log[d + e*x^(2/3)]*(-4*e*(-1 + Sqrt[-((e*x^(2/3))/d)])*x^(2/3) + 4*d*(-((e*x^(2/3))/d))^(3/2)*Log[(1 + Sqrt[-((e*x^(2/3))/d)])/2] + (d - d*(-((e*x^(2/3))/d))^(3/2))*Log[d + e*x^(2/3)]))*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n]) + 12*b*d*e*n*x^(2/3)*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 + 12*b*Sqrt[d]*e^(3/2)*n*x*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 + 6*b*d^2*n*Log[d + e*x^(2/3)]*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 + 2*d^2*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^3)/(d^2*x)","B",1
488,1,803,632,2.936547,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^n])^3/x^4,x]","\frac{-70 \left(a-b n \log \left(d+e x^{2/3}\right)+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 d^5-210 b n \log \left(d+e x^{2/3}\right) \left(a-b n \log \left(d+e x^{2/3}\right)+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 d^5-60 b e n x^{2/3} \left(a-b n \log \left(d+e x^{2/3}\right)+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 d^4+84 b e^2 n x^{4/3} \left(a-b n \log \left(d+e x^{2/3}\right)+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 d^3-140 b e^3 n x^2 \left(a-b n \log \left(d+e x^{2/3}\right)+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 d^2+420 b e^4 n x^{8/3} \left(a-b n \log \left(d+e x^{2/3}\right)+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 d+420 b e^{9/2} n x^3 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a-b n \log \left(d+e x^{2/3}\right)+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \sqrt{d}+35 b^3 n^3 \left(54 \left(d+e x^{2/3}\right) \sqrt{-\frac{e x^{2/3}}{d}} x^{8/3} \, _5F_4\left(1,1,1,1,\frac{11}{2};2,2,2,2;\frac{x^{2/3} e}{d}+1\right) e^4+\log \left(d+e x^{2/3}\right) \left(54 d \left(d+e x^{2/3}\right) \left(-\frac{e x^{2/3}}{d}\right)^{3/2} x^2 \, _4F_3\left(1,1,1,\frac{11}{2};2,2,2;\frac{x^{2/3} e}{d}+1\right) e^3+\log \left(d+e x^{2/3}\right) \left(27 e^4 \left(d+e x^{2/3}\right) \sqrt{-\frac{e x^{2/3}}{d}} x^{8/3} \, _3F_2\left(1,1,\frac{11}{2};2,2;\frac{x^{2/3} e}{d}+1\right)-2 d \left(d^4+e^3 \left(-\frac{e x^{2/3}}{d}\right)^{3/2} x^2 d\right) \log \left(d+e x^{2/3}\right)\right)\right)\right)+\frac{210 b^2 n^2 \left(\log \left(d+e x^{2/3}\right) \left(9 \left(d+e x^{2/3}\right) x^{10/3} \, _3F_2\left(1,1,\frac{11}{2};2,2;\frac{x^{2/3} e}{d}+1\right) e^5+d \left(\sqrt{-\frac{e x^{2/3}}{d}} d^5+e^5 x^{10/3}\right) \log \left(d+e x^{2/3}\right)\right)-9 e^5 \left(d+e x^{2/3}\right) x^{10/3} \, _4F_3\left(1,1,1,\frac{11}{2};2,2,2;\frac{x^{2/3} e}{d}+1\right)\right) \left(-a+b n \log \left(d+e x^{2/3}\right)-b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{\sqrt{-\frac{e x^{2/3}}{d}} d}}{210 d^5 x^3}","\frac{2 b e^5 n \text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^{2/3} \left(d+e x^{2/3}\right)},x\right)}{3 d^4}-\frac{1408 b^2 e^{9/2} n^2 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{105 d^{9/2}}-\frac{568 b^2 e^4 n^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{105 d^4 \sqrt[3]{x}}+\frac{32 b^2 e^3 n^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{35 d^3 x}-\frac{8 b^2 e^2 n^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{35 d^2 x^{5/3}}+\frac{2 b e^4 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{d^4 \sqrt[3]{x}}-\frac{2 b e^3 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{3 d^3 x}+\frac{2 b e^2 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{5 d^2 x^{5/3}}-\frac{2 b e n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{7 d x^{7/3}}-\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{3 x^3}-\frac{1408 i b^3 e^{9/2} n^3 \text{Li}_2\left(1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{105 d^{9/2}}-\frac{1408 i b^3 e^{9/2} n^3 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)^2}{105 d^{9/2}}+\frac{1376 b^3 e^{9/2} n^3 \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{105 d^{9/2}}-\frac{2816 b^3 e^{9/2} n^3 \log \left(\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{105 d^{9/2}}+\frac{16 b^3 e^4 n^3}{7 d^4 \sqrt[3]{x}}-\frac{16 b^3 e^3 n^3}{105 d^3 x}",0,"(35*b^3*n^3*(54*e^4*(d + e*x^(2/3))*Sqrt[-((e*x^(2/3))/d)]*x^(8/3)*HypergeometricPFQ[{1, 1, 1, 1, 11/2}, {2, 2, 2, 2}, 1 + (e*x^(2/3))/d] + Log[d + e*x^(2/3)]*(54*d*e^3*(d + e*x^(2/3))*(-((e*x^(2/3))/d))^(3/2)*x^2*HypergeometricPFQ[{1, 1, 1, 11/2}, {2, 2, 2}, 1 + (e*x^(2/3))/d] + Log[d + e*x^(2/3)]*(27*e^4*(d + e*x^(2/3))*Sqrt[-((e*x^(2/3))/d)]*x^(8/3)*HypergeometricPFQ[{1, 1, 11/2}, {2, 2}, 1 + (e*x^(2/3))/d] - 2*d*(d^4 + d*e^3*(-((e*x^(2/3))/d))^(3/2)*x^2)*Log[d + e*x^(2/3)]))) + (210*b^2*n^2*(-9*e^5*(d + e*x^(2/3))*x^(10/3)*HypergeometricPFQ[{1, 1, 1, 11/2}, {2, 2, 2}, 1 + (e*x^(2/3))/d] + Log[d + e*x^(2/3)]*(9*e^5*(d + e*x^(2/3))*x^(10/3)*HypergeometricPFQ[{1, 1, 11/2}, {2, 2}, 1 + (e*x^(2/3))/d] + d*(d^5*Sqrt[-((e*x^(2/3))/d)] + e^5*x^(10/3))*Log[d + e*x^(2/3)]))*(-a + b*n*Log[d + e*x^(2/3)] - b*Log[c*(d + e*x^(2/3))^n]))/(d*Sqrt[-((e*x^(2/3))/d)]) - 60*b*d^4*e*n*x^(2/3)*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 + 84*b*d^3*e^2*n*x^(4/3)*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 - 140*b*d^2*e^3*n*x^2*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 + 420*b*d*e^4*n*x^(8/3)*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 + 420*b*Sqrt[d]*e^(9/2)*n*x^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 - 210*b*d^5*n*Log[d + e*x^(2/3)]*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^2 - 70*d^5*(a - b*n*Log[d + e*x^(2/3)] + b*Log[c*(d + e*x^(2/3))^n])^3)/(210*d^5*x^3)","A",1
489,1,218,239,0.2383812,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \, dx","Integrate[x^3*(a + b*Log[c*(d + e/x^(1/3))^n]),x]","\frac{a x^4}{4}+\frac{1}{4} b x^4 \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-\frac{1}{4} b e n \left(\frac{e^{11} \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{d^{12}}+\frac{e^{11} \log (x)}{3 d^{12}}-\frac{e^{10} \sqrt[3]{x}}{d^{11}}+\frac{e^9 x^{2/3}}{2 d^{10}}-\frac{e^8 x}{3 d^9}+\frac{e^7 x^{4/3}}{4 d^8}-\frac{e^6 x^{5/3}}{5 d^7}+\frac{e^5 x^2}{6 d^6}-\frac{e^4 x^{7/3}}{7 d^5}+\frac{e^3 x^{8/3}}{8 d^4}-\frac{e^2 x^3}{9 d^3}+\frac{e x^{10/3}}{10 d^2}-\frac{x^{11/3}}{11 d}\right)","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)-\frac{b e^{12} n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{4 d^{12}}-\frac{b e^{12} n \log (x)}{12 d^{12}}+\frac{b e^{11} n \sqrt[3]{x}}{4 d^{11}}-\frac{b e^{10} n x^{2/3}}{8 d^{10}}+\frac{b e^9 n x}{12 d^9}-\frac{b e^8 n x^{4/3}}{16 d^8}+\frac{b e^7 n x^{5/3}}{20 d^7}-\frac{b e^6 n x^2}{24 d^6}+\frac{b e^5 n x^{7/3}}{28 d^5}-\frac{b e^4 n x^{8/3}}{32 d^4}+\frac{b e^3 n x^3}{36 d^3}-\frac{b e^2 n x^{10/3}}{40 d^2}+\frac{b e n x^{11/3}}{44 d}",1,"(a*x^4)/4 + (b*x^4*Log[c*(d + e/x^(1/3))^n])/4 - (b*e*n*(-((e^10*x^(1/3))/d^11) + (e^9*x^(2/3))/(2*d^10) - (e^8*x)/(3*d^9) + (e^7*x^(4/3))/(4*d^8) - (e^6*x^(5/3))/(5*d^7) + (e^5*x^2)/(6*d^6) - (e^4*x^(7/3))/(7*d^5) + (e^3*x^(8/3))/(8*d^4) - (e^2*x^3)/(9*d^3) + (e*x^(10/3))/(10*d^2) - x^(11/3)/(11*d) + (e^11*Log[d + e/x^(1/3)])/d^12 + (e^11*Log[x])/(3*d^12)))/4","A",1
490,1,175,190,0.1345394,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*(d + e/x^(1/3))^n]),x]","\frac{a x^3}{3}+\frac{1}{3} b x^3 \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-\frac{1}{3} b e n \left(-\frac{e^8 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{d^9}-\frac{e^8 \log (x)}{3 d^9}+\frac{e^7 \sqrt[3]{x}}{d^8}-\frac{e^6 x^{2/3}}{2 d^7}+\frac{e^5 x}{3 d^6}-\frac{e^4 x^{4/3}}{4 d^5}+\frac{e^3 x^{5/3}}{5 d^4}-\frac{e^2 x^2}{6 d^3}+\frac{e x^{7/3}}{7 d^2}-\frac{x^{8/3}}{8 d}\right)","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)+\frac{b e^9 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{3 d^9}+\frac{b e^9 n \log (x)}{9 d^9}-\frac{b e^8 n \sqrt[3]{x}}{3 d^8}+\frac{b e^7 n x^{2/3}}{6 d^7}-\frac{b e^6 n x}{9 d^6}+\frac{b e^5 n x^{4/3}}{12 d^5}-\frac{b e^4 n x^{5/3}}{15 d^4}+\frac{b e^3 n x^2}{18 d^3}-\frac{b e^2 n x^{7/3}}{21 d^2}+\frac{b e n x^{8/3}}{24 d}",1,"(a*x^3)/3 + (b*x^3*Log[c*(d + e/x^(1/3))^n])/3 - (b*e*n*((e^7*x^(1/3))/d^8 - (e^6*x^(2/3))/(2*d^7) + (e^5*x)/(3*d^6) - (e^4*x^(4/3))/(4*d^5) + (e^3*x^(5/3))/(5*d^4) - (e^2*x^2)/(6*d^3) + (e*x^(7/3))/(7*d^2) - x^(8/3)/(8*d) - (e^8*Log[d + e/x^(1/3)])/d^9 - (e^8*Log[x])/(3*d^9)))/3","A",1
491,1,132,141,0.0901476,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \, dx","Integrate[x*(a + b*Log[c*(d + e/x^(1/3))^n]),x]","\frac{a x^2}{2}+\frac{1}{2} b x^2 \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-\frac{1}{2} b e n \left(\frac{e^5 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{d^6}+\frac{e^5 \log (x)}{3 d^6}-\frac{e^4 \sqrt[3]{x}}{d^5}+\frac{e^3 x^{2/3}}{2 d^4}-\frac{e^2 x}{3 d^3}+\frac{e x^{4/3}}{4 d^2}-\frac{x^{5/3}}{5 d}\right)","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)-\frac{b e^6 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{2 d^6}-\frac{b e^6 n \log (x)}{6 d^6}+\frac{b e^5 n \sqrt[3]{x}}{2 d^5}-\frac{b e^4 n x^{2/3}}{4 d^4}+\frac{b e^3 n x}{6 d^3}-\frac{b e^2 n x^{4/3}}{8 d^2}+\frac{b e n x^{5/3}}{10 d}",1,"(a*x^2)/2 + (b*x^2*Log[c*(d + e/x^(1/3))^n])/2 - (b*e*n*(-((e^4*x^(1/3))/d^5) + (e^3*x^(2/3))/(2*d^4) - (e^2*x)/(3*d^3) + (e*x^(4/3))/(4*d^2) - x^(5/3)/(5*d) + (e^5*Log[d + e/x^(1/3)])/d^6 + (e^5*Log[x])/(3*d^6)))/2","A",1
492,1,79,70,0.0480846,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \, dx","Integrate[a + b*Log[c*(d + e/x^(1/3))^n],x]","a x+b x \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b e n \left(-\frac{e^2 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{d^3}-\frac{e^2 \log (x)}{3 d^3}+\frac{e \sqrt[3]{x}}{d^2}-\frac{x^{2/3}}{2 d}\right)","a x+b x \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+\frac{b e^3 n \log \left(d \sqrt[3]{x}+e\right)}{d^3}-\frac{b e^2 n \sqrt[3]{x}}{d^2}+\frac{b e n x^{2/3}}{2 d}",1,"a*x + b*x*Log[c*(d + e/x^(1/3))^n] - b*e*n*((e*x^(1/3))/d^2 - x^(2/3)/(2*d) - (e^2*Log[d + e/x^(1/3)])/d^3 - (e^2*Log[x])/(3*d^3))","A",1
493,1,53,51,0.0031911,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{x} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])/x,x]","a \log (x)-3 b \log \left(-\frac{e}{d \sqrt[3]{x}}\right) \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-3 b n \text{Li}_2\left(\frac{d+\frac{e}{\sqrt[3]{x}}}{d}\right)","-3 \log \left(-\frac{e}{d \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)-3 b n \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right)",1,"-3*b*Log[c*(d + e/x^(1/3))^n]*Log[-(e/(d*x^(1/3)))] + a*Log[x] - 3*b*n*PolyLog[2, (d + e/x^(1/3))/d]","A",1
494,1,85,82,0.0365902,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])/x^2,x]","-\frac{a}{x}-\frac{b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{x}-\frac{b d^3 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^3}+\frac{b d^2 n}{e^2 \sqrt[3]{x}}-\frac{b d n}{2 e x^{2/3}}+\frac{b n}{3 x}","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{x}-\frac{b d^3 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^3}+\frac{b d^2 n}{e^2 \sqrt[3]{x}}-\frac{b d n}{2 e x^{2/3}}+\frac{b n}{3 x}",1,"-(a/x) + (b*n)/(3*x) - (b*d*n)/(2*e*x^(2/3)) + (b*d^2*n)/(e^2*x^(1/3)) - (b*d^3*n*Log[d + e/x^(1/3)])/e^3 - (b*Log[c*(d + e/x^(1/3))^n])/x","A",1
495,1,135,138,0.0944756,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])/x^3,x]","-\frac{a}{2 x^2}-\frac{b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{2 x^2}+\frac{1}{2} b e n \left(\frac{d^6 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^7}-\frac{d^5}{e^6 \sqrt[3]{x}}+\frac{d^4}{2 e^5 x^{2/3}}-\frac{d^3}{3 e^4 x}+\frac{d^2}{4 e^3 x^{4/3}}-\frac{d}{5 e^2 x^{5/3}}+\frac{1}{6 e x^2}\right)","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{2 x^2}+\frac{b d^6 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{2 e^6}-\frac{b d^5 n}{2 e^5 \sqrt[3]{x}}+\frac{b d^4 n}{4 e^4 x^{2/3}}-\frac{b d^3 n}{6 e^3 x}+\frac{b d^2 n}{8 e^2 x^{4/3}}-\frac{b d n}{10 e x^{5/3}}+\frac{b n}{12 x^2}",1,"-1/2*a/x^2 + (b*e*n*(1/(6*e*x^2) - d/(5*e^2*x^(5/3)) + d^2/(4*e^3*x^(4/3)) - d^3/(3*e^4*x) + d^4/(2*e^5*x^(2/3)) - d^5/(e^6*x^(1/3)) + (d^6*Log[d + e/x^(1/3)])/e^7))/2 - (b*Log[c*(d + e/x^(1/3))^n])/(2*x^2)","A",1
496,1,178,187,0.1557387,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])/x^4,x]","-\frac{a}{3 x^3}-\frac{b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{3 x^3}+\frac{1}{3} b e n \left(-\frac{d^9 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^{10}}+\frac{d^8}{e^9 \sqrt[3]{x}}-\frac{d^7}{2 e^8 x^{2/3}}+\frac{d^6}{3 e^7 x}-\frac{d^5}{4 e^6 x^{4/3}}+\frac{d^4}{5 e^5 x^{5/3}}-\frac{d^3}{6 e^4 x^2}+\frac{d^2}{7 e^3 x^{7/3}}-\frac{d}{8 e^2 x^{8/3}}+\frac{1}{9 e x^3}\right)","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{3 x^3}-\frac{b d^9 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{3 e^9}+\frac{b d^8 n}{3 e^8 \sqrt[3]{x}}-\frac{b d^7 n}{6 e^7 x^{2/3}}+\frac{b d^6 n}{9 e^6 x}-\frac{b d^5 n}{12 e^5 x^{4/3}}+\frac{b d^4 n}{15 e^4 x^{5/3}}-\frac{b d^3 n}{18 e^3 x^2}+\frac{b d^2 n}{21 e^2 x^{7/3}}-\frac{b d n}{24 e x^{8/3}}+\frac{b n}{27 x^3}",1,"-1/3*a/x^3 + (b*e*n*(1/(9*e*x^3) - d/(8*e^2*x^(8/3)) + d^2/(7*e^3*x^(7/3)) - d^3/(6*e^4*x^2) + d^4/(5*e^5*x^(5/3)) - d^5/(4*e^6*x^(4/3)) + d^6/(3*e^7*x) - d^7/(2*e^8*x^(2/3)) + d^8/(e^9*x^(1/3)) - (d^9*Log[d + e/x^(1/3)])/e^10))/3 - (b*Log[c*(d + e/x^(1/3))^n])/(3*x^3)","A",1
497,1,738,572,0.4373848,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \, dx","Integrate[x^2*(a + b*Log[c*(d + e/x^(1/3))^n])^2,x]","\frac{5040 a^2 d^9 x^3+10080 a b d^9 x^3 \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+1260 a b d^8 e n x^{8/3}-1440 a b d^7 e^2 n x^{7/3}+1680 a b d^6 e^3 n x^2-2016 a b d^5 e^4 n x^{5/3}+2520 a b d^4 e^5 n x^{4/3}-3360 a b d^3 e^6 n x+5040 a b d^2 e^7 n x^{2/3}+10080 a b e^9 n \log \left(d \sqrt[3]{x}+e\right)-10080 a b d e^8 n \sqrt[3]{x}+5040 b^2 d^9 x^3 \log ^2\left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+1260 b^2 d^8 e n x^{8/3} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-1440 b^2 d^7 e^2 n x^{7/3} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+1680 b^2 d^6 e^3 n x^2 \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-2016 b^2 d^5 e^4 n x^{5/3} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+2520 b^2 d^4 e^5 n x^{4/3} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-3360 b^2 d^3 e^6 n x \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+5040 b^2 d^2 e^7 n x^{2/3} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+10080 b^2 e^9 n \log \left(d \sqrt[3]{x}+e\right) \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-10080 b^2 d e^8 n \sqrt[3]{x} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+180 b^2 d^7 e^2 n^2 x^{7/3}-450 b^2 d^6 e^3 n^2 x^2+876 b^2 d^5 e^4 n^2 x^{5/3}-1599 b^2 d^4 e^5 n^2 x^{4/3}+2972 b^2 d^3 e^6 n^2 x-6138 b^2 d^2 e^7 n^2 x^{2/3}+10080 b^2 e^9 n^2 \text{Li}_2\left(\frac{\sqrt[3]{x} d}{e}+1\right)-5040 b^2 e^9 n^2 \log ^2\left(d \sqrt[3]{x}+e\right)-22356 b^2 e^9 n^2 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)-5040 b^2 e^9 n^2 \log \left(d \sqrt[3]{x}+e\right)+10080 b^2 e^9 n^2 \log \left(d \sqrt[3]{x}+e\right) \log \left(-\frac{d \sqrt[3]{x}}{e}\right)+17316 b^2 d e^8 n^2 \sqrt[3]{x}-7452 b^2 e^9 n^2 \log (x)}{15120 d^9}","-\frac{2 b e^9 n \log \left(1-\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{3 d^9}-\frac{2 b e^8 n \sqrt[3]{x} \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{3 d^9}+\frac{b e^7 n x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{3 d^7}-\frac{2 b e^6 n x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{9 d^6}+\frac{b e^5 n x^{4/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{6 d^5}-\frac{2 b e^4 n x^{5/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{15 d^4}+\frac{b e^3 n x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{9 d^3}-\frac{2 b e^2 n x^{7/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{21 d^2}+\frac{b e n x^{8/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{12 d}+\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2+\frac{2 b^2 e^9 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right)}{3 d^9}-\frac{481 b^2 e^9 n^2 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{420 d^9}-\frac{761 b^2 e^9 n^2 \log (x)}{1260 d^9}+\frac{481 b^2 e^8 n^2 \sqrt[3]{x}}{420 d^8}-\frac{341 b^2 e^7 n^2 x^{2/3}}{840 d^7}+\frac{743 b^2 e^6 n^2 x}{3780 d^6}-\frac{533 b^2 e^5 n^2 x^{4/3}}{5040 d^5}+\frac{73 b^2 e^4 n^2 x^{5/3}}{1260 d^4}-\frac{5 b^2 e^3 n^2 x^2}{168 d^3}+\frac{b^2 e^2 n^2 x^{7/3}}{84 d^2}",1,"(-10080*a*b*d*e^8*n*x^(1/3) + 17316*b^2*d*e^8*n^2*x^(1/3) + 5040*a*b*d^2*e^7*n*x^(2/3) - 6138*b^2*d^2*e^7*n^2*x^(2/3) - 3360*a*b*d^3*e^6*n*x + 2972*b^2*d^3*e^6*n^2*x + 2520*a*b*d^4*e^5*n*x^(4/3) - 1599*b^2*d^4*e^5*n^2*x^(4/3) - 2016*a*b*d^5*e^4*n*x^(5/3) + 876*b^2*d^5*e^4*n^2*x^(5/3) + 1680*a*b*d^6*e^3*n*x^2 - 450*b^2*d^6*e^3*n^2*x^2 - 1440*a*b*d^7*e^2*n*x^(7/3) + 180*b^2*d^7*e^2*n^2*x^(7/3) + 1260*a*b*d^8*e*n*x^(8/3) + 5040*a^2*d^9*x^3 - 22356*b^2*e^9*n^2*Log[d + e/x^(1/3)] - 10080*b^2*d*e^8*n*x^(1/3)*Log[c*(d + e/x^(1/3))^n] + 5040*b^2*d^2*e^7*n*x^(2/3)*Log[c*(d + e/x^(1/3))^n] - 3360*b^2*d^3*e^6*n*x*Log[c*(d + e/x^(1/3))^n] + 2520*b^2*d^4*e^5*n*x^(4/3)*Log[c*(d + e/x^(1/3))^n] - 2016*b^2*d^5*e^4*n*x^(5/3)*Log[c*(d + e/x^(1/3))^n] + 1680*b^2*d^6*e^3*n*x^2*Log[c*(d + e/x^(1/3))^n] - 1440*b^2*d^7*e^2*n*x^(7/3)*Log[c*(d + e/x^(1/3))^n] + 1260*b^2*d^8*e*n*x^(8/3)*Log[c*(d + e/x^(1/3))^n] + 10080*a*b*d^9*x^3*Log[c*(d + e/x^(1/3))^n] + 5040*b^2*d^9*x^3*Log[c*(d + e/x^(1/3))^n]^2 + 10080*a*b*e^9*n*Log[e + d*x^(1/3)] - 5040*b^2*e^9*n^2*Log[e + d*x^(1/3)] + 10080*b^2*e^9*n*Log[c*(d + e/x^(1/3))^n]*Log[e + d*x^(1/3)] - 5040*b^2*e^9*n^2*Log[e + d*x^(1/3)]^2 + 10080*b^2*e^9*n^2*Log[e + d*x^(1/3)]*Log[-((d*x^(1/3))/e)] - 7452*b^2*e^9*n^2*Log[x] + 10080*b^2*e^9*n^2*PolyLog[2, 1 + (d*x^(1/3))/e])/(15120*d^9)","A",1
498,1,546,400,0.2458644,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \, dx","Integrate[x*(a + b*Log[c*(d + e/x^(1/3))^n])^2,x]","\frac{180 a^2 d^6 x^2+360 a b d^6 x^2 \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+72 a b d^5 e n x^{5/3}-90 a b d^4 e^2 n x^{4/3}+120 a b d^3 e^3 n x-180 a b d^2 e^4 n x^{2/3}-360 a b e^6 n \log \left(d \sqrt[3]{x}+e\right)+360 a b d e^5 n \sqrt[3]{x}+180 b^2 d^6 x^2 \log ^2\left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+72 b^2 d^5 e n x^{5/3} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-90 b^2 d^4 e^2 n x^{4/3} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+120 b^2 d^3 e^3 n x \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-180 b^2 d^2 e^4 n x^{2/3} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-360 b^2 e^6 n \log \left(d \sqrt[3]{x}+e\right) \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+360 b^2 d e^5 n \sqrt[3]{x} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+18 b^2 d^4 e^2 n^2 x^{4/3}-54 b^2 d^3 e^3 n^2 x+141 b^2 d^2 e^4 n^2 x^{2/3}-360 b^2 e^6 n^2 \text{Li}_2\left(\frac{\sqrt[3]{x} d}{e}+1\right)+180 b^2 e^6 n^2 \log ^2\left(d \sqrt[3]{x}+e\right)+642 b^2 e^6 n^2 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+180 b^2 e^6 n^2 \log \left(d \sqrt[3]{x}+e\right)-360 b^2 e^6 n^2 \log \left(d \sqrt[3]{x}+e\right) \log \left(-\frac{d \sqrt[3]{x}}{e}\right)-462 b^2 d e^5 n^2 \sqrt[3]{x}+214 b^2 e^6 n^2 \log (x)}{360 d^6}","\frac{b e^6 n \log \left(1-\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{d^6}+\frac{b e^5 n \sqrt[3]{x} \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{d^6}-\frac{b e^4 n x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{2 d^4}+\frac{b e^3 n x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{3 d^3}-\frac{b e^2 n x^{4/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{4 d^2}+\frac{b e n x^{5/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{5 d}+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2-\frac{b^2 e^6 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right)}{d^6}+\frac{77 b^2 e^6 n^2 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{60 d^6}+\frac{137 b^2 e^6 n^2 \log (x)}{180 d^6}-\frac{77 b^2 e^5 n^2 \sqrt[3]{x}}{60 d^5}+\frac{47 b^2 e^4 n^2 x^{2/3}}{120 d^4}-\frac{3 b^2 e^3 n^2 x}{20 d^3}+\frac{b^2 e^2 n^2 x^{4/3}}{20 d^2}",1,"(360*a*b*d*e^5*n*x^(1/3) - 462*b^2*d*e^5*n^2*x^(1/3) - 180*a*b*d^2*e^4*n*x^(2/3) + 141*b^2*d^2*e^4*n^2*x^(2/3) + 120*a*b*d^3*e^3*n*x - 54*b^2*d^3*e^3*n^2*x - 90*a*b*d^4*e^2*n*x^(4/3) + 18*b^2*d^4*e^2*n^2*x^(4/3) + 72*a*b*d^5*e*n*x^(5/3) + 180*a^2*d^6*x^2 + 642*b^2*e^6*n^2*Log[d + e/x^(1/3)] + 360*b^2*d*e^5*n*x^(1/3)*Log[c*(d + e/x^(1/3))^n] - 180*b^2*d^2*e^4*n*x^(2/3)*Log[c*(d + e/x^(1/3))^n] + 120*b^2*d^3*e^3*n*x*Log[c*(d + e/x^(1/3))^n] - 90*b^2*d^4*e^2*n*x^(4/3)*Log[c*(d + e/x^(1/3))^n] + 72*b^2*d^5*e*n*x^(5/3)*Log[c*(d + e/x^(1/3))^n] + 360*a*b*d^6*x^2*Log[c*(d + e/x^(1/3))^n] + 180*b^2*d^6*x^2*Log[c*(d + e/x^(1/3))^n]^2 - 360*a*b*e^6*n*Log[e + d*x^(1/3)] + 180*b^2*e^6*n^2*Log[e + d*x^(1/3)] - 360*b^2*e^6*n*Log[c*(d + e/x^(1/3))^n]*Log[e + d*x^(1/3)] + 180*b^2*e^6*n^2*Log[e + d*x^(1/3)]^2 - 360*b^2*e^6*n^2*Log[e + d*x^(1/3)]*Log[-((d*x^(1/3))/e)] + 214*b^2*e^6*n^2*Log[x] - 360*b^2*e^6*n^2*PolyLog[2, 1 + (d*x^(1/3))/e])/(360*d^6)","A",1
499,1,237,227,0.1916061,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])^2,x]","x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2-\frac{b e n \left(-3 d^2 x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)-6 e^2 \log \left(d \sqrt[3]{x}+e\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)+6 a d e \sqrt[3]{x}+6 b d e \sqrt[3]{x} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+3 b e^2 n \left(\log \left(d \sqrt[3]{x}+e\right) \left(\log \left(d \sqrt[3]{x}+e\right)-2 \log \left(-\frac{d \sqrt[3]{x}}{e}\right)\right)-2 \text{Li}_2\left(\frac{\sqrt[3]{x} d}{e}+1\right)\right)+2 b e^2 n \left(3 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+\log (x)\right)+3 b e n \left(e \log \left(d \sqrt[3]{x}+e\right)-d \sqrt[3]{x}\right)\right)}{3 d^3}","-\frac{2 b e^3 n \log \left(1-\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{d^3}-\frac{2 b e^2 n \sqrt[3]{x} \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{d^3}+\frac{b e n x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{d}+x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2+\frac{2 b^2 e^3 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right)}{d^3}-\frac{b^2 e^3 n^2 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{d^3}-\frac{b^2 e^3 n^2 \log (x)}{d^3}+\frac{b^2 e^2 n^2 \sqrt[3]{x}}{d^2}",1,"x*(a + b*Log[c*(d + e/x^(1/3))^n])^2 - (b*e*n*(6*a*d*e*x^(1/3) + 6*b*d*e*x^(1/3)*Log[c*(d + e/x^(1/3))^n] - 3*d^2*x^(2/3)*(a + b*Log[c*(d + e/x^(1/3))^n]) - 6*e^2*(a + b*Log[c*(d + e/x^(1/3))^n])*Log[e + d*x^(1/3)] + 3*b*e*n*(-(d*x^(1/3)) + e*Log[e + d*x^(1/3)]) + 2*b*e^2*n*(3*Log[d + e/x^(1/3)] + Log[x]) + 3*b*e^2*n*(Log[e + d*x^(1/3)]*(Log[e + d*x^(1/3)] - 2*Log[-((d*x^(1/3))/e)]) - 2*PolyLog[2, 1 + (d*x^(1/3))/e])))/(3*d^3)","A",1
500,1,389,93,0.2182791,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{x} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])^2/x,x]","2 b n \left(3 \text{Li}_2\left(-\frac{e}{d \sqrt[3]{x}}\right)+\log (x) \left(\log \left(d+\frac{e}{\sqrt[3]{x}}\right)-\log \left(\frac{e}{d \sqrt[3]{x}}+1\right)\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)+\log (x) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)^2+3 b^2 n^2 \left(\frac{1}{81} \left(-162 \text{Li}_3\left(\frac{\sqrt[3]{x} d}{e}+1\right)-162 \text{Li}_3\left(-\frac{d \sqrt[3]{x}}{e}\right)+9 \log ^2(x) \log \left(d+\frac{e}{\sqrt[3]{x}}\right)-9 \log ^2(x) \log \left(\frac{d \sqrt[3]{x}}{e}+1\right)+27 \log (x) \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)-27 \log (x) \log ^2\left(\frac{e}{d}+\sqrt[3]{x}\right)+81 \log ^2\left(\frac{e}{d}+\sqrt[3]{x}\right) \log \left(-\frac{d \sqrt[3]{x}}{e}\right)-54 \log (x) \log \left(d+\frac{e}{\sqrt[3]{x}}\right) \log \left(\frac{d \sqrt[3]{x}}{e}+1\right)+54 \log (x) \log \left(\frac{e}{d}+\sqrt[3]{x}\right) \log \left(\frac{d \sqrt[3]{x}}{e}+1\right)+\log ^3(x)\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{x} d}{e}+1\right) \log \left(\frac{e}{d}+\sqrt[3]{x}\right)-2 \text{Li}_2\left(-\frac{d \sqrt[3]{x}}{e}\right) \left(\log \left(d+\frac{e}{\sqrt[3]{x}}\right)-\log \left(\frac{e}{d}+\sqrt[3]{x}\right)\right)\right)","-6 b n \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)-3 \log \left(-\frac{e}{d \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2+6 b^2 n^2 \text{Li}_3\left(\frac{e}{d \sqrt[3]{x}}+1\right)",1,"(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2*Log[x] + 2*b*n*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])*((Log[d + e/x^(1/3)] - Log[1 + e/(d*x^(1/3))])*Log[x] + 3*PolyLog[2, -(e/(d*x^(1/3)))]) + 3*b^2*n^2*(2*Log[e/d + x^(1/3)]*PolyLog[2, 1 + (d*x^(1/3))/e] - 2*(Log[d + e/x^(1/3)] - Log[e/d + x^(1/3)])*PolyLog[2, -((d*x^(1/3))/e)] + (81*Log[e/d + x^(1/3)]^2*Log[-((d*x^(1/3))/e)] + 27*Log[d + e/x^(1/3)]^2*Log[x] - 27*Log[e/d + x^(1/3)]^2*Log[x] - 54*Log[d + e/x^(1/3)]*Log[1 + (d*x^(1/3))/e]*Log[x] + 54*Log[e/d + x^(1/3)]*Log[1 + (d*x^(1/3))/e]*Log[x] + 9*Log[d + e/x^(1/3)]*Log[x]^2 - 9*Log[1 + (d*x^(1/3))/e]*Log[x]^2 + Log[x]^3 - 162*PolyLog[3, 1 + (d*x^(1/3))/e] - 162*PolyLog[3, -((d*x^(1/3))/e)])/81)","B",1
501,1,374,269,0.3773548,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])^2/x^2,x]","\frac{\frac{b n \left(-36 d^3 x \log \left(d \sqrt[3]{x}+e\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)-36 d^3 x \log \left(-\frac{e}{d \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)+12 e^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)-18 d e^2 \sqrt[3]{x} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)+36 a d^2 e x^{2/3}+36 b d^2 x^{2/3} \left(d \sqrt[3]{x}+e\right) \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-36 b d^3 n x \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right)-36 b d^3 n x \text{Li}_2\left(\frac{\sqrt[3]{x} d}{e}+1\right)+30 b d^3 n x \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+18 b d^3 n x \log \left(d \sqrt[3]{x}+e\right) \left(\log \left(d \sqrt[3]{x}+e\right)-2 \log \left(-\frac{d \sqrt[3]{x}}{e}\right)\right)-2 b e n \left(6 d^2 x^{2/3}-3 d e \sqrt[3]{x}+2 e^2\right)-36 b d^2 e n x^{2/3}+9 b d e n \sqrt[3]{x} \left(e-2 d \sqrt[3]{x}\right)\right)}{e^3}-18 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{18 x}","-\frac{2 b d^3 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{e^3}+\frac{6 b d^2 n \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{e^3}-\frac{3 b d n \left(d+\frac{e}{\sqrt[3]{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{e^3}+\frac{2 b n \left(d+\frac{e}{\sqrt[3]{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{3 e^3}-\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{x}+\frac{b^2 d^3 n^2 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^3}-\frac{6 b^2 d^2 n^2}{e^2 \sqrt[3]{x}}+\frac{3 b^2 d n^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}{2 e^3}-\frac{2 b^2 n^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^3}{9 e^3}",1,"(-18*(a + b*Log[c*(d + e/x^(1/3))^n])^2 + (b*n*(-2*b*e*n*(2*e^2 - 3*d*e*x^(1/3) + 6*d^2*x^(2/3)) + 9*b*d*e*n*(e - 2*d*x^(1/3))*x^(1/3) + 36*a*d^2*e*x^(2/3) - 36*b*d^2*e*n*x^(2/3) + 30*b*d^3*n*x*Log[d + e/x^(1/3)] + 36*b*d^2*(e + d*x^(1/3))*x^(2/3)*Log[c*(d + e/x^(1/3))^n] + 12*e^3*(a + b*Log[c*(d + e/x^(1/3))^n]) - 18*d*e^2*x^(1/3)*(a + b*Log[c*(d + e/x^(1/3))^n]) - 36*d^3*x*(a + b*Log[c*(d + e/x^(1/3))^n])*Log[e + d*x^(1/3)] - 36*d^3*x*(a + b*Log[c*(d + e/x^(1/3))^n])*Log[-(e/(d*x^(1/3)))] + 18*b*d^3*n*x*Log[e + d*x^(1/3)]*(Log[e + d*x^(1/3)] - 2*Log[-((d*x^(1/3))/e)]) - 36*b*d^3*n*x*PolyLog[2, 1 + e/(d*x^(1/3))] - 36*b*d^3*n*x*PolyLog[2, 1 + (d*x^(1/3))/e]))/e^3)/(18*x)","C",1
502,1,698,479,0.3538316,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])^2/x^3,x]","\frac{-1800 a^2 e^6-3600 a b e^6 \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+3600 a b d^6 n x^2 \log \left(d \sqrt[3]{x}+e\right)+3600 a b d^6 n x^2 \log \left(-\frac{e}{d \sqrt[3]{x}}\right)-3600 a b d^5 e n x^{5/3}+1800 a b d^4 e^2 n x^{4/3}-1200 a b d^3 e^3 n x+900 a b d^2 e^4 n x^{2/3}-720 a b d e^5 n \sqrt[3]{x}+600 a b e^6 n-3600 b^2 d^6 n x^2 \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+3600 b^2 d^6 n x^2 \log \left(d \sqrt[3]{x}+e\right) \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+3600 b^2 d^6 n x^2 \log \left(-\frac{e}{d \sqrt[3]{x}}\right) \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-3600 b^2 d^5 e n x^{5/3} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+1800 b^2 d^4 e^2 n x^{4/3} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-1200 b^2 d^3 e^3 n x \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+900 b^2 d^2 e^4 n x^{2/3} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-1800 b^2 e^6 \log ^2\left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+600 b^2 e^6 n \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-720 b^2 d e^5 n \sqrt[3]{x} \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+3600 b^2 d^6 n^2 x^2 \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right)+3600 b^2 d^6 n^2 x^2 \text{Li}_2\left(\frac{\sqrt[3]{x} d}{e}+1\right)-1800 b^2 d^6 n^2 x^2 \log ^2\left(d \sqrt[3]{x}+e\right)-5220 b^2 d^6 n^2 x^2 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+3600 b^2 d^6 n^2 x^2 \log \left(d \sqrt[3]{x}+e\right) \log \left(-\frac{d \sqrt[3]{x}}{e}\right)+8820 b^2 d^5 e n^2 x^{5/3}-2610 b^2 d^4 e^2 n^2 x^{4/3}+1140 b^2 d^3 e^3 n^2 x-555 b^2 d^2 e^4 n^2 x^{2/3}+264 b^2 d e^5 n^2 \sqrt[3]{x}-100 b^2 e^6 n^2}{3600 e^6 x^2}","\frac{b d^6 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{e^6}-\frac{6 b d^5 n \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{e^6}+\frac{15 b d^4 n \left(d+\frac{e}{\sqrt[3]{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{2 e^6}-\frac{20 b d^3 n \left(d+\frac{e}{\sqrt[3]{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{3 e^6}+\frac{15 b d^2 n \left(d+\frac{e}{\sqrt[3]{x}}\right)^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{4 e^6}-\frac{6 b d n \left(d+\frac{e}{\sqrt[3]{x}}\right)^5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{5 e^6}+\frac{b n \left(d+\frac{e}{\sqrt[3]{x}}\right)^6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{6 e^6}-\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{2 x^2}-\frac{b^2 d^6 n^2 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)}{2 e^6}+\frac{6 b^2 d^5 n^2}{e^5 \sqrt[3]{x}}-\frac{15 b^2 d^4 n^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}{4 e^6}+\frac{20 b^2 d^3 n^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^3}{9 e^6}-\frac{15 b^2 d^2 n^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^4}{16 e^6}+\frac{6 b^2 d n^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^5}{25 e^6}-\frac{b^2 n^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^6}{36 e^6}",1,"(-1800*a^2*e^6 + 600*a*b*e^6*n - 100*b^2*e^6*n^2 - 720*a*b*d*e^5*n*x^(1/3) + 264*b^2*d*e^5*n^2*x^(1/3) + 900*a*b*d^2*e^4*n*x^(2/3) - 555*b^2*d^2*e^4*n^2*x^(2/3) - 1200*a*b*d^3*e^3*n*x + 1140*b^2*d^3*e^3*n^2*x + 1800*a*b*d^4*e^2*n*x^(4/3) - 2610*b^2*d^4*e^2*n^2*x^(4/3) - 3600*a*b*d^5*e*n*x^(5/3) + 8820*b^2*d^5*e*n^2*x^(5/3) - 5220*b^2*d^6*n^2*x^2*Log[d + e/x^(1/3)] - 3600*a*b*e^6*Log[c*(d + e/x^(1/3))^n] + 600*b^2*e^6*n*Log[c*(d + e/x^(1/3))^n] - 720*b^2*d*e^5*n*x^(1/3)*Log[c*(d + e/x^(1/3))^n] + 900*b^2*d^2*e^4*n*x^(2/3)*Log[c*(d + e/x^(1/3))^n] - 1200*b^2*d^3*e^3*n*x*Log[c*(d + e/x^(1/3))^n] + 1800*b^2*d^4*e^2*n*x^(4/3)*Log[c*(d + e/x^(1/3))^n] - 3600*b^2*d^5*e*n*x^(5/3)*Log[c*(d + e/x^(1/3))^n] - 3600*b^2*d^6*n*x^2*Log[c*(d + e/x^(1/3))^n] - 1800*b^2*e^6*Log[c*(d + e/x^(1/3))^n]^2 + 3600*a*b*d^6*n*x^2*Log[e + d*x^(1/3)] + 3600*b^2*d^6*n*x^2*Log[c*(d + e/x^(1/3))^n]*Log[e + d*x^(1/3)] - 1800*b^2*d^6*n^2*x^2*Log[e + d*x^(1/3)]^2 + 3600*a*b*d^6*n*x^2*Log[-(e/(d*x^(1/3)))] + 3600*b^2*d^6*n*x^2*Log[c*(d + e/x^(1/3))^n]*Log[-(e/(d*x^(1/3)))] + 3600*b^2*d^6*n^2*x^2*Log[e + d*x^(1/3)]*Log[-((d*x^(1/3))/e)] + 3600*b^2*d^6*n^2*x^2*PolyLog[2, 1 + e/(d*x^(1/3))] + 3600*b^2*d^6*n^2*x^2*PolyLog[2, 1 + (d*x^(1/3))/e])/(3600*e^6*x^2)","C",1
503,1,1006,759,1.6646744,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3 \, dx","Integrate[x*(a + b*Log[c*(d + e/x^(1/3))^n])^3,x]","\frac{20 x^2 \left(a-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3 d^6+60 b n x^2 \log \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 d^6+12 b e n x^{5/3} \left(a-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 d^5-15 b e^2 n x^{4/3} \left(a-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 d^4+20 b e^3 n x \left(a-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 d^3-30 b e^4 n x^{2/3} \left(a-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 d^2+60 b e^5 n \sqrt[3]{x} \left(a-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 d-60 b e^6 n \left(a-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \log \left(\sqrt[3]{x} d+e\right)+b^2 n^2 \left(a-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \left(-274 \log \left(-\frac{e}{d \sqrt[3]{x}}\right) e^6+120 \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right) e^6+d \sqrt[3]{x} \left(6 x d^3-18 e x^{2/3} d^2+47 e^2 \sqrt[3]{x} d-154 e^3\right) e^2+2 \log \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(12 x^{5/3} d^5-15 e x^{4/3} d^4+20 e^2 x d^3-30 e^3 x^{2/3} d^2+60 e^4 \sqrt[3]{x} d+137 e^5+60 e^5 \log \left(-\frac{e}{d \sqrt[3]{x}}\right)\right) e-60 \left(e^6-d^6 x^2\right) \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)\right)+b^3 n^3 \left(20 x^2 \log ^3\left(d+\frac{e}{\sqrt[3]{x}}\right) d^6+12 e x^{5/3} \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right) d^5+3 e^2 x^{4/3} \left(2-5 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right) \log \left(d+\frac{e}{\sqrt[3]{x}}\right) d^4+2 e^3 x \left(10 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)-9 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+1\right) d^3-e^4 x^{2/3} \left(30 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)-47 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+12\right) d^2+e^5 \sqrt[3]{x} \left(60 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)-154 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+71\right) d+225 e^6 \left(\log \left(-\frac{e}{d \sqrt[3]{x}}\right)-\log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)+137 e^6 \left(\log \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(\log \left(d+\frac{e}{\sqrt[3]{x}}\right)-2 \log \left(-\frac{e}{d \sqrt[3]{x}}\right)\right)-2 \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right)\right)-20 e^6 \left(\left(\log \left(d+\frac{e}{\sqrt[3]{x}}\right)-3 \log \left(-\frac{e}{d \sqrt[3]{x}}\right)\right) \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)-6 \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right) \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+6 \text{Li}_3\left(\frac{e}{d \sqrt[3]{x}}+1\right)\right)\right)}{40 d^6}","-\frac{3 b^2 e^6 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{d^6}-\frac{77 b^2 e^6 n^2 \log \left(1-\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{20 d^6}-\frac{3 b^2 e^6 n^2 \log \left(-\frac{e}{d \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{d^6}-\frac{77 b^2 e^5 n^2 \sqrt[3]{x} \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{20 d^6}+\frac{47 b^2 e^4 n^2 x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{40 d^4}-\frac{9 b^2 e^3 n^2 x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{20 d^3}+\frac{3 b^2 e^2 n^2 x^{4/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{20 d^2}+\frac{3 b e^6 n \log \left(1-\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{2 d^6}+\frac{3 b e^5 n \sqrt[3]{x} \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{2 d^6}-\frac{3 b e^4 n x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{4 d^4}+\frac{b e^3 n x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{2 d^3}-\frac{3 b e^2 n x^{4/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{8 d^2}+\frac{3 b e n x^{5/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{10 d}+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3+\frac{77 b^3 e^6 n^3 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right)}{20 d^6}-\frac{3 b^3 e^6 n^3 \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right)}{d^6}-\frac{3 b^3 e^6 n^3 \text{Li}_3\left(\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right)}{d^6}-\frac{71 b^3 e^6 n^3 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{40 d^6}-\frac{15 b^3 e^6 n^3 \log (x)}{8 d^6}+\frac{71 b^3 e^5 n^3 \sqrt[3]{x}}{40 d^5}-\frac{3 b^3 e^4 n^3 x^{2/3}}{10 d^4}+\frac{b^3 e^3 n^3 x}{20 d^3}",1,"(60*b*d*e^5*n*x^(1/3)*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2 - 30*b*d^2*e^4*n*x^(2/3)*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2 + 20*b*d^3*e^3*n*x*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2 - 15*b*d^4*e^2*n*x^(4/3)*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2 + 12*b*d^5*e*n*x^(5/3)*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2 + 60*b*d^6*n*x^2*Log[d + e/x^(1/3)]*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2 + 20*d^6*x^2*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^3 - 60*b*e^6*n*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2*Log[e + d*x^(1/3)] + b^2*n^2*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])*(d*e^2*x^(1/3)*(-154*e^3 + 47*d*e^2*x^(1/3) - 18*d^2*e*x^(2/3) + 6*d^3*x) - 60*(e^6 - d^6*x^2)*Log[d + e/x^(1/3)]^2 - 274*e^6*Log[-(e/(d*x^(1/3)))] + 2*e*Log[d + e/x^(1/3)]*(137*e^5 + 60*d*e^4*x^(1/3) - 30*d^2*e^3*x^(2/3) + 20*d^3*e^2*x - 15*d^4*e*x^(4/3) + 12*d^5*x^(5/3) + 60*e^5*Log[-(e/(d*x^(1/3)))]) + 120*e^6*PolyLog[2, 1 + e/(d*x^(1/3))]) + b^3*n^3*(3*d^4*e^2*x^(4/3)*(2 - 5*Log[d + e/x^(1/3)])*Log[d + e/x^(1/3)] + 12*d^5*e*x^(5/3)*Log[d + e/x^(1/3)]^2 + 20*d^6*x^2*Log[d + e/x^(1/3)]^3 + 2*d^3*e^3*x*(1 - 9*Log[d + e/x^(1/3)] + 10*Log[d + e/x^(1/3)]^2) - d^2*e^4*x^(2/3)*(12 - 47*Log[d + e/x^(1/3)] + 30*Log[d + e/x^(1/3)]^2) + d*e^5*x^(1/3)*(71 - 154*Log[d + e/x^(1/3)] + 60*Log[d + e/x^(1/3)]^2) + 225*e^6*(-Log[d + e/x^(1/3)] + Log[-(e/(d*x^(1/3)))]) + 137*e^6*(Log[d + e/x^(1/3)]*(Log[d + e/x^(1/3)] - 2*Log[-(e/(d*x^(1/3)))]) - 2*PolyLog[2, 1 + e/(d*x^(1/3))]) - 20*e^6*(Log[d + e/x^(1/3)]^2*(Log[d + e/x^(1/3)] - 3*Log[-(e/(d*x^(1/3)))]) - 6*Log[d + e/x^(1/3)]*PolyLog[2, 1 + e/(d*x^(1/3))] + 6*PolyLog[3, 1 + e/(d*x^(1/3))])))/(40*d^6)","A",1
504,1,675,436,0.7784109,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3 \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])^3,x]","\frac{6 b^2 n^2 \left(\left(d^3 x+e^3\right) \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)+e \log \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(d^2 x^{2/3}-2 e^2 \log \left(-\frac{e}{d \sqrt[3]{x}}\right)-2 d e \sqrt[3]{x}-3 e^2\right)-2 e^3 \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right)+e^2 \left(3 e \log \left(-\frac{e}{d \sqrt[3]{x}}\right)+d \sqrt[3]{x}\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)+2 d^3 x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)^3+6 b d^3 n x \log \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)^2+3 b d^2 e n x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)^2+6 b e^3 n \log \left(d \sqrt[3]{x}+e\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)^2-6 b d e^2 n \sqrt[3]{x} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)^2-b^3 n^3 \left(-2 d^3 x \log ^3\left(d+\frac{e}{\sqrt[3]{x}}\right)-3 d^2 e x^{2/3} \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)-12 e^3 \text{Li}_3\left(\frac{e}{d \sqrt[3]{x}}+1\right)+6 e^3 \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right) \left(2 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)-3\right)-2 e^3 \log ^3\left(d+\frac{e}{\sqrt[3]{x}}\right)+9 e^3 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)+6 e^3 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right) \log \left(-\frac{e}{d \sqrt[3]{x}}\right)-6 e^3 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)-18 e^3 \log \left(d+\frac{e}{\sqrt[3]{x}}\right) \log \left(-\frac{e}{d \sqrt[3]{x}}\right)+6 e^3 \log \left(-\frac{e}{d \sqrt[3]{x}}\right)+6 d e^2 \sqrt[3]{x} \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)-6 d e^2 \sqrt[3]{x} \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{2 d^3}","\frac{6 b^2 e^3 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{d^3}+\frac{3 b^2 e^3 n^2 \log \left(1-\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{d^3}+\frac{6 b^2 e^3 n^2 \log \left(-\frac{e}{d \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{d^3}+\frac{3 b^2 e^2 n^2 \sqrt[3]{x} \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{d^3}-\frac{3 b e^3 n \log \left(1-\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{d^3}-\frac{3 b e^2 n \sqrt[3]{x} \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{d^3}+\frac{3 b e n x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{2 d}+x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3-\frac{3 b^3 e^3 n^3 \text{Li}_2\left(\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right)}{d^3}+\frac{6 b^3 e^3 n^3 \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right)}{d^3}+\frac{6 b^3 e^3 n^3 \text{Li}_3\left(\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right)}{d^3}+\frac{b^3 e^3 n^3 \log (x)}{d^3}",1,"(-6*b*d*e^2*n*x^(1/3)*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2 + 3*b*d^2*e*n*x^(2/3)*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2 + 6*b*d^3*n*x*Log[d + e/x^(1/3)]*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2 + 2*d^3*x*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^3 + 6*b*e^3*n*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2*Log[e + d*x^(1/3)] + 6*b^2*n^2*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])*((e^3 + d^3*x)*Log[d + e/x^(1/3)]^2 + e^2*(d*x^(1/3) + 3*e*Log[-(e/(d*x^(1/3)))]) + e*Log[d + e/x^(1/3)]*(-3*e^2 - 2*d*e*x^(1/3) + d^2*x^(2/3) - 2*e^2*Log[-(e/(d*x^(1/3)))]) - 2*e^3*PolyLog[2, 1 + e/(d*x^(1/3))]) - b^3*n^3*(-6*e^3*Log[d + e/x^(1/3)] - 6*d*e^2*x^(1/3)*Log[d + e/x^(1/3)] + 9*e^3*Log[d + e/x^(1/3)]^2 + 6*d*e^2*x^(1/3)*Log[d + e/x^(1/3)]^2 - 3*d^2*e*x^(2/3)*Log[d + e/x^(1/3)]^2 - 2*e^3*Log[d + e/x^(1/3)]^3 - 2*d^3*x*Log[d + e/x^(1/3)]^3 + 6*e^3*Log[-(e/(d*x^(1/3)))] - 18*e^3*Log[d + e/x^(1/3)]*Log[-(e/(d*x^(1/3)))] + 6*e^3*Log[d + e/x^(1/3)]^2*Log[-(e/(d*x^(1/3)))] + 6*e^3*(-3 + 2*Log[d + e/x^(1/3)])*PolyLog[2, 1 + e/(d*x^(1/3))] - 12*e^3*PolyLog[3, 1 + e/(d*x^(1/3))]))/(2*d^3)","A",1
505,1,527,135,0.324694,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3}{x} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])^3/x,x]","9 b^2 n^2 \left(\frac{1}{81} \left(-162 \text{Li}_3\left(\frac{\sqrt[3]{x} d}{e}+1\right)-162 \text{Li}_3\left(-\frac{d \sqrt[3]{x}}{e}\right)+9 \log ^2(x) \log \left(d+\frac{e}{\sqrt[3]{x}}\right)-9 \log ^2(x) \log \left(\frac{d \sqrt[3]{x}}{e}+1\right)+27 \log (x) \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)-27 \log (x) \log ^2\left(\frac{e}{d}+\sqrt[3]{x}\right)+81 \log ^2\left(\frac{e}{d}+\sqrt[3]{x}\right) \log \left(-\frac{d \sqrt[3]{x}}{e}\right)-54 \log (x) \log \left(d+\frac{e}{\sqrt[3]{x}}\right) \log \left(\frac{d \sqrt[3]{x}}{e}+1\right)+54 \log (x) \log \left(\frac{e}{d}+\sqrt[3]{x}\right) \log \left(\frac{d \sqrt[3]{x}}{e}+1\right)+\log ^3(x)\right)+2 \text{Li}_2\left(\frac{\sqrt[3]{x} d}{e}+1\right) \log \left(\frac{e}{d}+\sqrt[3]{x}\right)-2 \text{Li}_2\left(-\frac{d \sqrt[3]{x}}{e}\right) \left(\log \left(d+\frac{e}{\sqrt[3]{x}}\right)-\log \left(\frac{e}{d}+\sqrt[3]{x}\right)\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)+3 b n \left(3 \text{Li}_2\left(-\frac{e}{d \sqrt[3]{x}}\right)+\log (x) \left(\log \left(d+\frac{e}{\sqrt[3]{x}}\right)-\log \left(\frac{e}{d \sqrt[3]{x}}+1\right)\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)^2+\log (x) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-b n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)^3-3 b^3 n^3 \left(6 \text{Li}_4\left(\frac{e}{d \sqrt[3]{x}}+1\right)+3 \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right) \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)-6 \text{Li}_3\left(\frac{e}{d \sqrt[3]{x}}+1\right) \log \left(d+\frac{e}{\sqrt[3]{x}}\right)+\log \left(-\frac{e}{d \sqrt[3]{x}}\right) \log ^3\left(d+\frac{e}{\sqrt[3]{x}}\right)\right)","18 b^2 n^2 \text{Li}_3\left(\frac{e}{d \sqrt[3]{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)-9 b n \text{Li}_2\left(\frac{e}{d \sqrt[3]{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2-3 \log \left(-\frac{e}{d \sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3-18 b^3 n^3 \text{Li}_4\left(\frac{e}{d \sqrt[3]{x}}+1\right)",1,"(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^3*Log[x] + 3*b*n*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])^2*((Log[d + e/x^(1/3)] - Log[1 + e/(d*x^(1/3))])*Log[x] + 3*PolyLog[2, -(e/(d*x^(1/3)))]) + 9*b^2*n^2*(a - b*n*Log[d + e/x^(1/3)] + b*Log[c*(d + e/x^(1/3))^n])*(2*Log[e/d + x^(1/3)]*PolyLog[2, 1 + (d*x^(1/3))/e] - 2*(Log[d + e/x^(1/3)] - Log[e/d + x^(1/3)])*PolyLog[2, -((d*x^(1/3))/e)] + (81*Log[e/d + x^(1/3)]^2*Log[-((d*x^(1/3))/e)] + 27*Log[d + e/x^(1/3)]^2*Log[x] - 27*Log[e/d + x^(1/3)]^2*Log[x] - 54*Log[d + e/x^(1/3)]*Log[1 + (d*x^(1/3))/e]*Log[x] + 54*Log[e/d + x^(1/3)]*Log[1 + (d*x^(1/3))/e]*Log[x] + 9*Log[d + e/x^(1/3)]*Log[x]^2 - 9*Log[1 + (d*x^(1/3))/e]*Log[x]^2 + Log[x]^3 - 162*PolyLog[3, 1 + (d*x^(1/3))/e] - 162*PolyLog[3, -((d*x^(1/3))/e)])/81) - 3*b^3*n^3*(Log[d + e/x^(1/3)]^3*Log[-(e/(d*x^(1/3)))] + 3*Log[d + e/x^(1/3)]^2*PolyLog[2, 1 + e/(d*x^(1/3))] - 6*Log[d + e/x^(1/3)]*PolyLog[3, 1 + e/(d*x^(1/3))] + 6*PolyLog[4, 1 + e/(d*x^(1/3))])","B",1
506,1,666,438,0.8961527,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])^3/x^2,x]","\frac{-36 a^3 e^3-6 b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right) \left(18 a^2 e^3+6 b d^3 n x (6 a-11 b n) \log \left(d \sqrt[3]{x}+e\right)+2 b d^3 n x \log (x) (11 b n-6 a)-6 a b e n \left(6 d^2 x^{2/3}-3 d e \sqrt[3]{x}+2 e^2\right)+b^2 e n^2 \left(66 d^2 x^{2/3}-15 d e \sqrt[3]{x}+4 e^2\right)\right)-108 a^2 b d^3 n x \log \left(d \sqrt[3]{x}+e\right)+36 a^2 b d^3 n x \log (x)+108 a^2 b d^2 e n x^{2/3}-54 a^2 b d e^2 n \sqrt[3]{x}+36 a^2 b e^3 n-18 b^2 d^3 n^2 x \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right) \left(6 a+6 b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+6 b n \log \left(d \sqrt[3]{x}+e\right)-2 b n \log (x)-11 b n\right)+12 b^2 d^3 n^2 x \log \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(3 \log \left(d \sqrt[3]{x}+e\right)-\log (x)\right) \left(6 a+6 b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-11 b n\right)+18 b^2 \log ^2\left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right) \left(e \left(-6 a e^2+6 b d^2 n x^{2/3}-3 b d e n \sqrt[3]{x}+2 b e^2 n\right)-6 b d^3 n x \log \left(d \sqrt[3]{x}+e\right)+2 b d^3 n x \log (x)\right)+396 a b^2 d^3 n^2 x \log \left(d \sqrt[3]{x}+e\right)-132 a b^2 d^3 n^2 x \log (x)-396 a b^2 d^2 e n^2 x^{2/3}+90 a b^2 d e^2 n^2 \sqrt[3]{x}-24 a b^2 e^3 n^2-36 b^3 e^3 \log ^3\left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+72 b^3 d^3 n^3 x \log ^3\left(d+\frac{e}{\sqrt[3]{x}}\right)-510 b^3 d^3 n^3 x \log \left(d \sqrt[3]{x}+e\right)+170 b^3 d^3 n^3 x \log (x)+510 b^3 d^2 e n^3 x^{2/3}-57 b^3 d e^2 n^3 \sqrt[3]{x}+8 b^3 e^3 n^3}{36 e^3 x}","-\frac{2 b^2 n^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{3 e^3}+\frac{9 b^2 d n^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)}{2 e^3}-\frac{18 a b^2 d^2 n^2}{e^2 \sqrt[3]{x}}+\frac{9 b d^2 n \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{e^3}-\frac{3 d^2 \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3}{e^3}+\frac{b n \left(d+\frac{e}{\sqrt[3]{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{e^3}-\frac{9 b d n \left(d+\frac{e}{\sqrt[3]{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{2 e^3}-\frac{\left(d+\frac{e}{\sqrt[3]{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3}{e^3}+\frac{3 d \left(d+\frac{e}{\sqrt[3]{x}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3}{e^3}-\frac{18 b^3 d^2 n^2 \left(d+\frac{e}{\sqrt[3]{x}}\right) \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{e^3}+\frac{18 b^3 d^2 n^3}{e^2 \sqrt[3]{x}}+\frac{2 b^3 n^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^3}{9 e^3}-\frac{9 b^3 d n^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}{4 e^3}",1,"(-36*a^3*e^3 + 36*a^2*b*e^3*n - 24*a*b^2*e^3*n^2 + 8*b^3*e^3*n^3 - 54*a^2*b*d*e^2*n*x^(1/3) + 90*a*b^2*d*e^2*n^2*x^(1/3) - 57*b^3*d*e^2*n^3*x^(1/3) + 108*a^2*b*d^2*e*n*x^(2/3) - 396*a*b^2*d^2*e*n^2*x^(2/3) + 510*b^3*d^2*e*n^3*x^(2/3) + 72*b^3*d^3*n^3*x*Log[d + e/x^(1/3)]^3 - 36*b^3*e^3*Log[c*(d + e/x^(1/3))^n]^3 - 108*a^2*b*d^3*n*x*Log[e + d*x^(1/3)] + 396*a*b^2*d^3*n^2*x*Log[e + d*x^(1/3)] - 510*b^3*d^3*n^3*x*Log[e + d*x^(1/3)] + 12*b^2*d^3*n^2*x*Log[d + e/x^(1/3)]*(6*a - 11*b*n + 6*b*Log[c*(d + e/x^(1/3))^n])*(3*Log[e + d*x^(1/3)] - Log[x]) + 36*a^2*b*d^3*n*x*Log[x] - 132*a*b^2*d^3*n^2*x*Log[x] + 170*b^3*d^3*n^3*x*Log[x] - 18*b^2*d^3*n^2*x*Log[d + e/x^(1/3)]^2*(6*a - 11*b*n + 6*b*Log[c*(d + e/x^(1/3))^n] + 6*b*n*Log[e + d*x^(1/3)] - 2*b*n*Log[x]) + 18*b^2*Log[c*(d + e/x^(1/3))^n]^2*(e*(-6*a*e^2 + 2*b*e^2*n - 3*b*d*e*n*x^(1/3) + 6*b*d^2*n*x^(2/3)) - 6*b*d^3*n*x*Log[e + d*x^(1/3)] + 2*b*d^3*n*x*Log[x]) - 6*b*Log[c*(d + e/x^(1/3))^n]*(18*a^2*e^3 - 6*a*b*e*n*(2*e^2 - 3*d*e*x^(1/3) + 6*d^2*x^(2/3)) + b^2*e*n^2*(4*e^2 - 15*d*e*x^(1/3) + 66*d^2*x^(2/3)) + 6*b*d^3*n*(6*a - 11*b*n)*x*Log[e + d*x^(1/3)] + 2*b*d^3*n*(-6*a + 11*b*n)*x*Log[x]))/(36*e^3*x)","A",1
507,1,962,907,1.8659866,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^n])^3/x^3,x]","\frac{-72000 b^3 n^3 x^2 \log ^3\left(d+\frac{e}{\sqrt[3]{x}}\right) d^6+809340 b^3 n^3 x^2 \log \left(\sqrt[3]{x} d+e\right) d^6-529200 a b^2 n^2 x^2 \log \left(\sqrt[3]{x} d+e\right) d^6+108000 a^2 b n x^2 \log \left(\sqrt[3]{x} d+e\right) d^6+3600 b^2 n^2 x^2 \log \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(-20 a+49 b n-20 b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \left(3 \log \left(\sqrt[3]{x} d+e\right)-\log (x)\right) d^6-269780 b^3 n^3 x^2 \log (x) d^6+176400 a b^2 n^2 x^2 \log (x) d^6-36000 a^2 b n x^2 \log (x) d^6+1800 b^2 n^2 x^2 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right) \left(60 a-147 b n+60 b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)+60 b n \log \left(\sqrt[3]{x} d+e\right)-20 b n \log (x)\right) d^6-809340 b^3 e n^3 x^{5/3} d^5+529200 a b^2 e n^2 x^{5/3} d^5-108000 a^2 b e n x^{5/3} d^5+140070 b^3 e^2 n^3 x^{4/3} d^4-156600 a b^2 e^2 n^2 x^{4/3} d^4+54000 a^2 b e^2 n x^{4/3} d^4-41180 b^3 e^3 n^3 x d^3+68400 a b^2 e^3 n^2 x d^3-36000 a^2 b e^3 n x d^3+13785 b^3 e^4 n^3 x^{2/3} d^2-33300 a b^2 e^4 n^2 x^{2/3} d^2+27000 a^2 b e^4 n x^{2/3} d^2-4368 b^3 e^5 n^3 \sqrt[3]{x} d+15840 a b^2 e^5 n^2 \sqrt[3]{x} d-21600 a^2 b e^5 n \sqrt[3]{x} d-36000 a^3 e^6+1000 b^3 e^6 n^3-36000 b^3 e^6 \log ^3\left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-6000 a b^2 e^6 n^2+18000 a^2 b e^6 n+1800 b^2 \log ^2\left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right) \left(60 b n x^2 \log \left(\sqrt[3]{x} d+e\right) d^6-20 b n x^2 \log (x) d^6+e \left(-60 b n x^{5/3} d^5+30 b e n x^{4/3} d^4-20 b e^2 n x d^3+15 b e^3 n x^{2/3} d^2-12 b e^4 n \sqrt[3]{x} d-60 a e^5+10 b e^5 n\right)\right)-60 b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right) \left(180 b n (49 b n-20 a) x^2 \log \left(\sqrt[3]{x} d+e\right) d^6+60 b n (20 a-49 b n) x^2 \log (x) d^6+1800 a^2 e^6+b^2 e n^2 \left(-8820 x^{5/3} d^5+2610 e x^{4/3} d^4-1140 e^2 x d^3+555 e^3 x^{2/3} d^2-264 e^4 \sqrt[3]{x} d+100 e^5\right)-60 a b e n \left(-60 x^{5/3} d^5+30 e x^{4/3} d^4-20 e^2 x d^3+15 e^3 x^{2/3} d^2-12 e^4 \sqrt[3]{x} d+10 e^5\right)\right)}{72000 e^6 x^2}","\frac{b^3 n^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^6}{72 e^6}-\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^6}{2 e^6}+\frac{b n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^6}{4 e^6}-\frac{b^2 n^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \left(d+\frac{e}{\sqrt[3]{x}}\right)^6}{12 e^6}-\frac{18 b^3 d n^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^5}{125 e^6}+\frac{3 d \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^5}{e^6}-\frac{9 b d n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^5}{5 e^6}+\frac{18 b^2 d n^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \left(d+\frac{e}{\sqrt[3]{x}}\right)^5}{25 e^6}+\frac{45 b^3 d^2 n^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^4}{64 e^6}-\frac{15 d^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^4}{2 e^6}+\frac{45 b d^2 n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^4}{8 e^6}-\frac{45 b^2 d^2 n^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \left(d+\frac{e}{\sqrt[3]{x}}\right)^4}{16 e^6}-\frac{20 b^3 d^3 n^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^3}{9 e^6}+\frac{10 d^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^3}{e^6}-\frac{10 b d^3 n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^3}{e^6}+\frac{20 b^2 d^3 n^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \left(d+\frac{e}{\sqrt[3]{x}}\right)^3}{3 e^6}+\frac{45 b^3 d^4 n^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}{8 e^6}-\frac{15 d^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}{2 e^6}+\frac{45 b d^4 n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}{4 e^6}-\frac{45 b^2 d^4 n^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}{4 e^6}+\frac{3 d^5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^6}-\frac{9 b d^5 n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^6}+\frac{18 b^3 d^5 n^2 \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right) \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^6}-\frac{18 b^3 d^5 n^3}{e^5 \sqrt[3]{x}}+\frac{18 a b^2 d^5 n^2}{e^5 \sqrt[3]{x}}",1,"(-36000*a^3*e^6 + 18000*a^2*b*e^6*n - 6000*a*b^2*e^6*n^2 + 1000*b^3*e^6*n^3 - 21600*a^2*b*d*e^5*n*x^(1/3) + 15840*a*b^2*d*e^5*n^2*x^(1/3) - 4368*b^3*d*e^5*n^3*x^(1/3) + 27000*a^2*b*d^2*e^4*n*x^(2/3) - 33300*a*b^2*d^2*e^4*n^2*x^(2/3) + 13785*b^3*d^2*e^4*n^3*x^(2/3) - 36000*a^2*b*d^3*e^3*n*x + 68400*a*b^2*d^3*e^3*n^2*x - 41180*b^3*d^3*e^3*n^3*x + 54000*a^2*b*d^4*e^2*n*x^(4/3) - 156600*a*b^2*d^4*e^2*n^2*x^(4/3) + 140070*b^3*d^4*e^2*n^3*x^(4/3) - 108000*a^2*b*d^5*e*n*x^(5/3) + 529200*a*b^2*d^5*e*n^2*x^(5/3) - 809340*b^3*d^5*e*n^3*x^(5/3) - 72000*b^3*d^6*n^3*x^2*Log[d + e/x^(1/3)]^3 - 36000*b^3*e^6*Log[c*(d + e/x^(1/3))^n]^3 + 108000*a^2*b*d^6*n*x^2*Log[e + d*x^(1/3)] - 529200*a*b^2*d^6*n^2*x^2*Log[e + d*x^(1/3)] + 809340*b^3*d^6*n^3*x^2*Log[e + d*x^(1/3)] + 3600*b^2*d^6*n^2*x^2*Log[d + e/x^(1/3)]*(-20*a + 49*b*n - 20*b*Log[c*(d + e/x^(1/3))^n])*(3*Log[e + d*x^(1/3)] - Log[x]) - 36000*a^2*b*d^6*n*x^2*Log[x] + 176400*a*b^2*d^6*n^2*x^2*Log[x] - 269780*b^3*d^6*n^3*x^2*Log[x] + 1800*b^2*d^6*n^2*x^2*Log[d + e/x^(1/3)]^2*(60*a - 147*b*n + 60*b*Log[c*(d + e/x^(1/3))^n] + 60*b*n*Log[e + d*x^(1/3)] - 20*b*n*Log[x]) + 1800*b^2*Log[c*(d + e/x^(1/3))^n]^2*(e*(-60*a*e^5 + 10*b*e^5*n - 12*b*d*e^4*n*x^(1/3) + 15*b*d^2*e^3*n*x^(2/3) - 20*b*d^3*e^2*n*x + 30*b*d^4*e*n*x^(4/3) - 60*b*d^5*n*x^(5/3)) + 60*b*d^6*n*x^2*Log[e + d*x^(1/3)] - 20*b*d^6*n*x^2*Log[x]) - 60*b*Log[c*(d + e/x^(1/3))^n]*(1800*a^2*e^6 + b^2*e*n^2*(100*e^5 - 264*d*e^4*x^(1/3) + 555*d^2*e^3*x^(2/3) - 1140*d^3*e^2*x + 2610*d^4*e*x^(4/3) - 8820*d^5*x^(5/3)) - 60*a*b*e*n*(10*e^5 - 12*d*e^4*x^(1/3) + 15*d^2*e^3*x^(2/3) - 20*d^3*e^2*x + 30*d^4*e*x^(4/3) - 60*d^5*x^(5/3)) + 180*b*d^6*n*(-20*a + 49*b*n)*x^2*Log[e + d*x^(1/3)] + 60*b*d^6*n*(20*a - 49*b*n)*x^2*Log[x]))/(72000*e^6*x^2)","A",1
508,1,134,143,0.116171,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \, dx","Integrate[x^3*(a + b*Log[c*(d + e/x^(2/3))^n]),x]","\frac{a x^4}{4}+\frac{1}{4} b x^4 \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-\frac{1}{4} b e n \left(\frac{e^5 \log \left(d+\frac{e}{x^{2/3}}\right)}{d^6}+\frac{2 e^5 \log (x)}{3 d^6}-\frac{e^4 x^{2/3}}{d^5}+\frac{e^3 x^{4/3}}{2 d^4}-\frac{e^2 x^2}{3 d^3}+\frac{e x^{8/3}}{4 d^2}-\frac{x^{10/3}}{5 d}\right)","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-\frac{b e^6 n \log \left(d+\frac{e}{x^{2/3}}\right)}{4 d^6}-\frac{b e^6 n \log (x)}{6 d^6}+\frac{b e^5 n x^{2/3}}{4 d^5}-\frac{b e^4 n x^{4/3}}{8 d^4}+\frac{b e^3 n x^2}{12 d^3}-\frac{b e^2 n x^{8/3}}{16 d^2}+\frac{b e n x^{10/3}}{20 d}",1,"(a*x^4)/4 + (b*x^4*Log[c*(d + e/x^(2/3))^n])/4 - (b*e*n*(-((e^4*x^(2/3))/d^5) + (e^3*x^(4/3))/(2*d^4) - (e^2*x^2)/(3*d^3) + (e*x^(8/3))/(4*d^2) - x^(10/3)/(5*d) + (e^5*Log[d + e/x^(2/3)])/d^6 + (2*e^5*Log[x])/(3*d^6)))/4","A",1
509,1,65,121,0.015874,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \, dx","Integrate[x^2*(a + b*Log[c*(d + e/x^(2/3))^n]),x]","\frac{a x^3}{3}+\frac{1}{3} b x^3 \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)+\frac{2 b e n x^{7/3} \, _2F_1\left(-\frac{7}{2},1;-\frac{5}{2};-\frac{e}{d x^{2/3}}\right)}{21 d}","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+\frac{2 b e^{9/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{3 d^{9/2}}-\frac{2 b e^4 n \sqrt[3]{x}}{3 d^4}+\frac{2 b e^3 n x}{9 d^3}-\frac{2 b e^2 n x^{5/3}}{15 d^2}+\frac{2 b e n x^{7/3}}{21 d}",1,"(a*x^3)/3 + (2*b*e*n*x^(7/3)*Hypergeometric2F1[-7/2, 1, -5/2, -(e/(d*x^(2/3)))])/(21*d) + (b*x^3*Log[c*(d + e/x^(2/3))^n])/3","C",1
510,1,91,94,0.0245234,"\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \, dx","Integrate[x*(a + b*Log[c*(d + e/x^(2/3))^n]),x]","\frac{a x^2}{2}+\frac{1}{2} b x^2 \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-\frac{1}{2} b e n \left(-\frac{e^2 \log \left(d+\frac{e}{x^{2/3}}\right)}{d^3}-\frac{2 e^2 \log (x)}{3 d^3}+\frac{e x^{2/3}}{d^2}-\frac{x^{4/3}}{2 d}\right)","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+\frac{b e^3 n \log \left(d+\frac{e}{x^{2/3}}\right)}{2 d^3}+\frac{b e^3 n \log (x)}{3 d^3}-\frac{b e^2 n x^{2/3}}{2 d^2}+\frac{b e n x^{4/3}}{4 d}",1,"(a*x^2)/2 + (b*x^2*Log[c*(d + e/x^(2/3))^n])/2 - (b*e*n*((e*x^(2/3))/d^2 - x^(4/3)/(2*d) - (e^2*Log[d + e/x^(2/3)])/d^3 - (2*e^2*Log[x])/(3*d^3)))/2","A",1
511,1,53,65,0.0138264,"\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \, dx","Integrate[a + b*Log[c*(d + e/x^(2/3))^n],x]","a x+b x \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)+\frac{2 b e n \sqrt[3]{x} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{e}{d x^{2/3}}\right)}{d}","a x+b x \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-\frac{2 b e^{3/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{d^{3/2}}+\frac{2 b e n \sqrt[3]{x}}{d}",1,"a*x + (2*b*e*n*x^(1/3)*Hypergeometric2F1[-1/2, 1, 1/2, -(e/(d*x^(2/3)))])/d + b*x*Log[c*(d + e/x^(2/3))^n]","C",1
512,1,55,55,0.011838,"\int \frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{x} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])/x,x]","a \log (x)-\frac{3}{2} b \left(\log \left(-\frac{e}{d x^{2/3}}\right) \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)+n \text{Li}_2\left(\frac{d+\frac{e}{x^{2/3}}}{d}\right)\right)","-\frac{3}{2} \log \left(-\frac{e}{d x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-\frac{3}{2} b n \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right)",1,"a*Log[x] - (3*b*(Log[c*(d + e/x^(2/3))^n]*Log[-(e/(d*x^(2/3)))] + n*PolyLog[2, (d + e/x^(2/3))/d]))/2","A",1
513,1,80,77,0.0504499,"\int \frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])/x^2,x]","-\frac{a}{x}-\frac{b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{x}+\frac{2 b d^{3/2} n \tan ^{-1}\left(\frac{\sqrt{e}}{\sqrt{d} \sqrt[3]{x}}\right)}{e^{3/2}}-\frac{2 b d n}{e \sqrt[3]{x}}+\frac{2 b n}{3 x}","-\frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{x}-\frac{2 b d^{3/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{e^{3/2}}-\frac{2 b d n}{e \sqrt[3]{x}}+\frac{2 b n}{3 x}",1,"-(a/x) + (2*b*n)/(3*x) - (2*b*d*n)/(e*x^(1/3)) + (2*b*d^(3/2)*n*ArcTan[Sqrt[e]/(Sqrt[d]*x^(1/3))])/e^(3/2) - (b*Log[c*(d + e/x^(2/3))^n])/x","A",1
514,1,94,89,0.036403,"\int \frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])/x^3,x]","-\frac{a}{2 x^2}-\frac{b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{2 x^2}-\frac{b d^3 n \log \left(d+\frac{e}{x^{2/3}}\right)}{2 e^3}+\frac{b d^2 n}{2 e^2 x^{2/3}}-\frac{b d n}{4 e x^{4/3}}+\frac{b n}{6 x^2}","-\frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{2 x^2}-\frac{b d^3 n \log \left(d+\frac{e}{x^{2/3}}\right)}{2 e^3}+\frac{b d^2 n}{2 e^2 x^{2/3}}-\frac{b d n}{4 e x^{4/3}}+\frac{b n}{6 x^2}",1,"-1/2*a/x^2 + (b*n)/(6*x^2) - (b*d*n)/(4*e*x^(4/3)) + (b*d^2*n)/(2*e^2*x^(2/3)) - (b*d^3*n*Log[d + e/x^(2/3)])/(2*e^3) - (b*Log[c*(d + e/x^(2/3))^n])/(2*x^2)","A",1
515,1,137,132,0.0660705,"\int \frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])/x^4,x]","-\frac{a}{3 x^3}-\frac{b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{3 x^3}-\frac{2 b d^{9/2} n \tan ^{-1}\left(\frac{\sqrt{e}}{\sqrt{d} \sqrt[3]{x}}\right)}{3 e^{9/2}}+\frac{2 b d^4 n}{3 e^4 \sqrt[3]{x}}-\frac{2 b d^3 n}{9 e^3 x}+\frac{2 b d^2 n}{15 e^2 x^{5/3}}-\frac{2 b d n}{21 e x^{7/3}}+\frac{2 b n}{27 x^3}","-\frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{3 x^3}+\frac{2 b d^{9/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{3 e^{9/2}}+\frac{2 b d^4 n}{3 e^4 \sqrt[3]{x}}-\frac{2 b d^3 n}{9 e^3 x}+\frac{2 b d^2 n}{15 e^2 x^{5/3}}-\frac{2 b d n}{21 e x^{7/3}}+\frac{2 b n}{27 x^3}",1,"-1/3*a/x^3 + (2*b*n)/(27*x^3) - (2*b*d*n)/(21*e*x^(7/3)) + (2*b*d^2*n)/(15*e^2*x^(5/3)) - (2*b*d^3*n)/(9*e^3*x) + (2*b*d^4*n)/(3*e^4*x^(1/3)) - (2*b*d^(9/2)*n*ArcTan[Sqrt[e]/(Sqrt[d]*x^(1/3))])/(3*e^(9/2)) - (b*Log[c*(d + e/x^(2/3))^n])/(3*x^3)","A",1
516,1,968,412,0.4483886,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 \, dx","Integrate[x^3*(a + b*Log[c*(d + e/x^(2/3))^n])^2,x]","\frac{180 a^2 x^4 d^6+180 b^2 x^4 \log ^2\left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d^6+360 a b x^4 \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d^6+72 a b e n x^{10/3} d^5+72 b^2 e n x^{10/3} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d^5+18 b^2 e^2 n^2 x^{8/3} d^4-90 a b e^2 n x^{8/3} d^4-90 b^2 e^2 n x^{8/3} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d^4-54 b^2 e^3 n^2 x^2 d^3+120 a b e^3 n x^2 d^3+120 b^2 e^3 n x^2 \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d^3+141 b^2 e^4 n^2 x^{4/3} d^2-180 a b e^4 n x^{4/3} d^2-180 b^2 e^4 n x^{4/3} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d^2+360 b^2 e^5 n x^{2/3} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d-462 b^2 e^5 n^2 x^{2/3} d+360 a b e^5 n x^{2/3} d+180 b^2 e^6 n^2 \log ^2\left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right)+180 b^2 e^6 n^2 \log ^2\left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right)+822 b^2 e^6 n^2 \log \left(d+\frac{e}{x^{2/3}}\right)-360 a b e^6 n \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right)-360 b^2 e^6 n \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right)-360 a b e^6 n \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right)-360 b^2 e^6 n \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right)+360 b^2 e^6 n^2 \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) \log \left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)+360 b^2 e^6 n^2 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \log \left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right)-720 b^2 e^6 n^2 \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) \log \left(-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)-720 b^2 e^6 n^2 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \log \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)+548 b^2 e^6 n^2 \log (x)-720 b^2 e^6 n^2 \text{Li}_2\left(1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)+360 b^2 e^6 n^2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)+360 b^2 e^6 n^2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right)-720 b^2 e^6 n^2 \text{Li}_2\left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)}{720 d^6}","\frac{b e^6 n \log \left(1-\frac{d}{d+\frac{e}{x^{2/3}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{2 d^6}+\frac{b e^5 n x^{2/3} \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{2 d^6}-\frac{b e^4 n x^{4/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{4 d^4}+\frac{b e^3 n x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{6 d^3}-\frac{b e^2 n x^{8/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{8 d^2}+\frac{b e n x^{10/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{10 d}+\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2-\frac{b^2 e^6 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{x^{2/3}}}\right)}{2 d^6}+\frac{77 b^2 e^6 n^2 \log \left(d+\frac{e}{x^{2/3}}\right)}{120 d^6}+\frac{137 b^2 e^6 n^2 \log (x)}{180 d^6}-\frac{77 b^2 e^5 n^2 x^{2/3}}{120 d^5}+\frac{47 b^2 e^4 n^2 x^{4/3}}{240 d^4}-\frac{3 b^2 e^3 n^2 x^2}{40 d^3}+\frac{b^2 e^2 n^2 x^{8/3}}{40 d^2}",1,"(360*a*b*d*e^5*n*x^(2/3) - 462*b^2*d*e^5*n^2*x^(2/3) - 180*a*b*d^2*e^4*n*x^(4/3) + 141*b^2*d^2*e^4*n^2*x^(4/3) + 120*a*b*d^3*e^3*n*x^2 - 54*b^2*d^3*e^3*n^2*x^2 - 90*a*b*d^4*e^2*n*x^(8/3) + 18*b^2*d^4*e^2*n^2*x^(8/3) + 72*a*b*d^5*e*n*x^(10/3) + 180*a^2*d^6*x^4 + 822*b^2*e^6*n^2*Log[d + e/x^(2/3)] + 360*b^2*d*e^5*n*x^(2/3)*Log[c*(d + e/x^(2/3))^n] - 180*b^2*d^2*e^4*n*x^(4/3)*Log[c*(d + e/x^(2/3))^n] + 120*b^2*d^3*e^3*n*x^2*Log[c*(d + e/x^(2/3))^n] - 90*b^2*d^4*e^2*n*x^(8/3)*Log[c*(d + e/x^(2/3))^n] + 72*b^2*d^5*e*n*x^(10/3)*Log[c*(d + e/x^(2/3))^n] + 360*a*b*d^6*x^4*Log[c*(d + e/x^(2/3))^n] + 180*b^2*d^6*x^4*Log[c*(d + e/x^(2/3))^n]^2 - 360*a*b*e^6*n*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] - 360*b^2*e^6*n*Log[c*(d + e/x^(2/3))^n]*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] + 180*b^2*e^6*n^2*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]^2 - 360*a*b*e^6*n*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] - 360*b^2*e^6*n*Log[c*(d + e/x^(2/3))^n]*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] + 180*b^2*e^6*n^2*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]^2 + 360*b^2*e^6*n^2*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] + 360*b^2*e^6*n^2*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 720*b^2*e^6*n^2*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[-((Sqrt[-d]*x^(1/3))/Sqrt[e])] - 720*b^2*e^6*n^2*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(Sqrt[-d]*x^(1/3))/Sqrt[e]] + 548*b^2*e^6*n^2*Log[x] - 720*b^2*e^6*n^2*PolyLog[2, 1 - (Sqrt[-d]*x^(1/3))/Sqrt[e]] + 360*b^2*e^6*n^2*PolyLog[2, 1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] + 360*b^2*e^6*n^2*PolyLog[2, (1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 720*b^2*e^6*n^2*PolyLog[2, 1 + (Sqrt[-d]*x^(1/3))/Sqrt[e]])/(720*d^6)","B",1
517,1,542,239,0.4606251,"\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 \, dx","Integrate[x*(a + b*Log[c*(d + e/x^(2/3))^n])^2,x]","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2-\frac{b e n \left(-3 d^2 x^{4/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-6 e^2 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-6 e^2 \log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+6 d e x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+3 b e^2 n \left(-4 \text{Li}_2\left(1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)+2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)+\log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \left(\log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}+1\right)\right)-4 \log \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)\right)\right)+3 b e^2 n \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right)-4 \text{Li}_2\left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)+\log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \left(\log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)-4 \log \left(-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)\right)\right)+2 b e^2 n \left(3 \log \left(d+\frac{e}{x^{2/3}}\right)+2 \log (x)\right)+b e n \left(3 e \log \left(d+\frac{e}{x^{2/3}}\right)-3 d x^{2/3}+2 e \log (x)\right)\right)}{6 d^3}","-\frac{b e^3 n \log \left(1-\frac{d}{d+\frac{e}{x^{2/3}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{d^3}-\frac{b e^2 n x^{2/3} \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{d^3}+\frac{b e n x^{4/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{2 d}+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2+\frac{b^2 e^3 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{x^{2/3}}}\right)}{d^3}-\frac{b^2 e^3 n^2 \log \left(d+\frac{e}{x^{2/3}}\right)}{2 d^3}-\frac{b^2 e^3 n^2 \log (x)}{d^3}+\frac{b^2 e^2 n^2 x^{2/3}}{2 d^2}",1,"(x^2*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/2 - (b*e*n*(6*d*e*x^(2/3)*(a + b*Log[c*(d + e/x^(2/3))^n]) - 3*d^2*x^(4/3)*(a + b*Log[c*(d + e/x^(2/3))^n]) - 6*e^2*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] - 6*e^2*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] + 2*b*e^2*n*(3*Log[d + e/x^(2/3)] + 2*Log[x]) + b*e*n*(-3*d*x^(2/3) + 3*e*Log[d + e/x^(2/3)] + 2*e*Log[x]) + 3*b*e^2*n*(Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*(Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] + 2*Log[(1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 4*Log[(Sqrt[-d]*x^(1/3))/Sqrt[e]]) - 4*PolyLog[2, 1 - (Sqrt[-d]*x^(1/3))/Sqrt[e]] + 2*PolyLog[2, 1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])]) + 3*b*e^2*n*(Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*(Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] + 2*Log[1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] - 4*Log[-((Sqrt[-d]*x^(1/3))/Sqrt[e])]) + 2*PolyLog[2, (1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 4*PolyLog[2, 1 + (Sqrt[-d]*x^(1/3))/Sqrt[e]])))/(6*d^3)","B",1
518,1,199,95,0.1528613,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])^2/x,x]","2 b n \left(\frac{3}{2} \text{Li}_2\left(-\frac{e}{d x^{2/3}}\right)+\log (x) \left(\log \left(d+\frac{e}{x^{2/3}}\right)-\log \left(\frac{e}{d x^{2/3}}+1\right)\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)+\log (x) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2-\frac{3}{2} b^2 n^2 \left(-2 \text{Li}_3\left(\frac{e}{d x^{2/3}}+1\right)+2 \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right) \log \left(d+\frac{e}{x^{2/3}}\right)+\log \left(-\frac{e}{d x^{2/3}}\right) \log ^2\left(d+\frac{e}{x^{2/3}}\right)\right)","-3 b n \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-\frac{3}{2} \log \left(-\frac{e}{d x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2+3 b^2 n^2 \text{Li}_3\left(\frac{e}{d x^{2/3}}+1\right)",1,"(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2*Log[x] + 2*b*n*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])*((Log[d + e/x^(2/3)] - Log[1 + e/(d*x^(2/3))])*Log[x] + (3*PolyLog[2, -(e/(d*x^(2/3)))])/2) - (3*b^2*n^2*(Log[d + e/x^(2/3)]^2*Log[-(e/(d*x^(2/3)))] + 2*Log[d + e/x^(2/3)]*PolyLog[2, 1 + e/(d*x^(2/3))] - 2*PolyLog[3, 1 + e/(d*x^(2/3))]))/2","B",1
519,1,691,276,0.5445634,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])^2/x^3,x]","\frac{b n \left(-36 d^3 x^2 \left(\log \left(-\frac{e}{d x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+b n \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right)\right)-36 d^3 x^2 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-36 d^3 x^2 \log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+36 d^2 x^{4/3} \left(e (a-b n)+b \left(d x^{2/3}+e\right) \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+12 e^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-18 d e^2 x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+18 b d^3 n x^2 \left(-4 \text{Li}_2\left(1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)+2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)+\log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \left(\log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}+1\right)\right)-4 \log \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)\right)\right)+18 b d^3 n x^2 \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right)-4 \text{Li}_2\left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)+\log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \left(\log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)-4 \log \left(-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)\right)\right)+9 b d n x^{2/3} \left(2 d^2 x^{4/3} \log \left(d+\frac{e}{x^{2/3}}\right)+e \left(e-2 d x^{2/3}\right)\right)-2 b n \left(e \left(6 d^2 x^{4/3}-3 d e x^{2/3}+2 e^2\right)-6 d^3 x^2 \log \left(d+\frac{e}{x^{2/3}}\right)\right)\right)-18 e^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{36 e^3 x^2}","-\frac{b d^3 n \log \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{e^3}+\frac{3 b d^2 n \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{e^3}-\frac{3 b d n \left(d+\frac{e}{x^{2/3}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{2 e^3}+\frac{b n \left(d+\frac{e}{x^{2/3}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{3 e^3}-\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{2 x^2}+\frac{b^2 d^3 n^2 \log ^2\left(d+\frac{e}{x^{2/3}}\right)}{2 e^3}-\frac{3 b^2 d^2 n^2}{e^2 x^{2/3}}+\frac{3 b^2 d n^2 \left(d+\frac{e}{x^{2/3}}\right)^2}{4 e^3}-\frac{b^2 n^2 \left(d+\frac{e}{x^{2/3}}\right)^3}{9 e^3}",1,"(-18*e^3*(a + b*Log[c*(d + e/x^(2/3))^n])^2 + b*n*(9*b*d*n*x^(2/3)*(e*(e - 2*d*x^(2/3)) + 2*d^2*x^(4/3)*Log[d + e/x^(2/3)]) - 2*b*n*(e*(2*e^2 - 3*d*e*x^(2/3) + 6*d^2*x^(4/3)) - 6*d^3*x^2*Log[d + e/x^(2/3)]) + 12*e^3*(a + b*Log[c*(d + e/x^(2/3))^n]) - 18*d*e^2*x^(2/3)*(a + b*Log[c*(d + e/x^(2/3))^n]) + 36*d^2*x^(4/3)*(e*(a - b*n) + b*(e + d*x^(2/3))*Log[c*(d + e/x^(2/3))^n]) - 36*d^3*x^2*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] - 36*d^3*x^2*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] - 36*d^3*x^2*((a + b*Log[c*(d + e/x^(2/3))^n])*Log[-(e/(d*x^(2/3)))] + b*n*PolyLog[2, 1 + e/(d*x^(2/3))]) + 18*b*d^3*n*x^2*(Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*(Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] + 2*Log[(1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 4*Log[(Sqrt[-d]*x^(1/3))/Sqrt[e]]) - 4*PolyLog[2, 1 - (Sqrt[-d]*x^(1/3))/Sqrt[e]] + 2*PolyLog[2, 1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])]) + 18*b*d^3*n*x^2*(Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*(Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] + 2*Log[1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] - 4*Log[-((Sqrt[-d]*x^(1/3))/Sqrt[e])]) + 2*PolyLog[2, (1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 4*PolyLog[2, 1 + (Sqrt[-d]*x^(1/3))/Sqrt[e]])))/(36*e^3*x^2)","C",1
520,1,1021,482,0.8617881,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x^5} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])^2/x^5,x]","\frac{\frac{b n \left(-1800 b n x^4 \log ^2\left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) d^6-1800 b n x^4 \log ^2\left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) d^6-5220 b n x^4 \log \left(d+\frac{e}{x^{2/3}}\right) d^6-3600 b x^4 \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d^6+3600 a x^4 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) d^6+3600 b x^4 \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) d^6+3600 a x^4 \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) d^6+3600 b x^4 \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) d^6-3600 b n x^4 \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) \log \left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right) d^6-3600 b n x^4 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \log \left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right) d^6+3600 a x^4 \log \left(-\frac{e}{d x^{2/3}}\right) d^6+3600 b x^4 \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) \log \left(-\frac{e}{d x^{2/3}}\right) d^6+7200 b n x^4 \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) \log \left(-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right) d^6+7200 b n x^4 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \log \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right) d^6+3600 b n x^4 \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right) d^6+7200 b n x^4 \text{Li}_2\left(1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right) d^6-3600 b n x^4 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right) d^6-3600 b n x^4 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right) d^6+7200 b n x^4 \text{Li}_2\left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right) d^6-3600 a e x^{10/3} d^5+8820 b e n x^{10/3} d^5-3600 b e x^{10/3} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d^5+1800 a e^2 x^{8/3} d^4-2610 b e^2 n x^{8/3} d^4+1800 b e^2 x^{8/3} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d^4-1200 a e^3 x^2 d^3+1140 b e^3 n x^2 d^3-1200 b e^3 x^2 \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d^3+900 a e^4 x^{4/3} d^2-555 b e^4 n x^{4/3} d^2+900 b e^4 x^{4/3} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d^2-720 b e^5 x^{2/3} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) d-720 a e^5 x^{2/3} d+264 b e^5 n x^{2/3} d+600 a e^6-100 b e^6 n+600 b e^6 \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{e^6}-1800 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{7200 x^4}","\frac{b d^6 n \log \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{2 e^6}-\frac{3 b d^5 n \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{e^6}+\frac{15 b d^4 n \left(d+\frac{e}{x^{2/3}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{4 e^6}-\frac{10 b d^3 n \left(d+\frac{e}{x^{2/3}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{3 e^6}+\frac{15 b d^2 n \left(d+\frac{e}{x^{2/3}}\right)^4 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{8 e^6}-\frac{3 b d n \left(d+\frac{e}{x^{2/3}}\right)^5 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{5 e^6}+\frac{b n \left(d+\frac{e}{x^{2/3}}\right)^6 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{12 e^6}-\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{4 x^4}-\frac{b^2 d^6 n^2 \log ^2\left(d+\frac{e}{x^{2/3}}\right)}{4 e^6}+\frac{3 b^2 d^5 n^2}{e^5 x^{2/3}}-\frac{15 b^2 d^4 n^2 \left(d+\frac{e}{x^{2/3}}\right)^2}{8 e^6}+\frac{10 b^2 d^3 n^2 \left(d+\frac{e}{x^{2/3}}\right)^3}{9 e^6}-\frac{15 b^2 d^2 n^2 \left(d+\frac{e}{x^{2/3}}\right)^4}{32 e^6}+\frac{3 b^2 d n^2 \left(d+\frac{e}{x^{2/3}}\right)^5}{25 e^6}-\frac{b^2 n^2 \left(d+\frac{e}{x^{2/3}}\right)^6}{72 e^6}",1,"(-1800*(a + b*Log[c*(d + e/x^(2/3))^n])^2 + (b*n*(600*a*e^6 - 100*b*e^6*n - 720*a*d*e^5*x^(2/3) + 264*b*d*e^5*n*x^(2/3) + 900*a*d^2*e^4*x^(4/3) - 555*b*d^2*e^4*n*x^(4/3) - 1200*a*d^3*e^3*x^2 + 1140*b*d^3*e^3*n*x^2 + 1800*a*d^4*e^2*x^(8/3) - 2610*b*d^4*e^2*n*x^(8/3) - 3600*a*d^5*e*x^(10/3) + 8820*b*d^5*e*n*x^(10/3) - 5220*b*d^6*n*x^4*Log[d + e/x^(2/3)] + 600*b*e^6*Log[c*(d + e/x^(2/3))^n] - 720*b*d*e^5*x^(2/3)*Log[c*(d + e/x^(2/3))^n] + 900*b*d^2*e^4*x^(4/3)*Log[c*(d + e/x^(2/3))^n] - 1200*b*d^3*e^3*x^2*Log[c*(d + e/x^(2/3))^n] + 1800*b*d^4*e^2*x^(8/3)*Log[c*(d + e/x^(2/3))^n] - 3600*b*d^5*e*x^(10/3)*Log[c*(d + e/x^(2/3))^n] - 3600*b*d^6*x^4*Log[c*(d + e/x^(2/3))^n] + 3600*a*d^6*x^4*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] + 3600*b*d^6*x^4*Log[c*(d + e/x^(2/3))^n]*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] - 1800*b*d^6*n*x^4*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]^2 + 3600*a*d^6*x^4*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] + 3600*b*d^6*x^4*Log[c*(d + e/x^(2/3))^n]*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] - 1800*b*d^6*n*x^4*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]^2 - 3600*b*d^6*n*x^4*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] - 3600*b*d^6*n*x^4*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] + 3600*a*d^6*x^4*Log[-(e/(d*x^(2/3)))] + 3600*b*d^6*x^4*Log[c*(d + e/x^(2/3))^n]*Log[-(e/(d*x^(2/3)))] + 7200*b*d^6*n*x^4*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[-((Sqrt[-d]*x^(1/3))/Sqrt[e])] + 7200*b*d^6*n*x^4*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(Sqrt[-d]*x^(1/3))/Sqrt[e]] + 3600*b*d^6*n*x^4*PolyLog[2, 1 + e/(d*x^(2/3))] + 7200*b*d^6*n*x^4*PolyLog[2, 1 - (Sqrt[-d]*x^(1/3))/Sqrt[e]] - 3600*b*d^6*n*x^4*PolyLog[2, 1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] - 3600*b*d^6*n*x^4*PolyLog[2, (1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] + 7200*b*d^6*n*x^4*PolyLog[2, 1 + (Sqrt[-d]*x^(1/3))/Sqrt[e]]))/e^6)/(7200*x^4)","C",1
521,1,735,490,2.1926082,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 \, dx","Integrate[x^2*(a + b*Log[c*(d + e/x^(2/3))^n])^2,x]","\frac{1}{3} \left(x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2-4 b e n \left(-\frac{e^2 x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{3 d^3}+\frac{e x^{5/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{5 d^2}+\frac{e^{7/2} \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{2 (-d)^{9/2}}-\frac{e^{7/2} \log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{2 (-d)^{9/2}}-\frac{x^{7/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{7 d}+\frac{a e^3 \sqrt[3]{x}}{d^4}+\frac{b e^3 \sqrt[3]{x} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{d^4}-\frac{2 b e^{7/2} n \tan ^{-1}\left(\frac{\sqrt{e}}{\sqrt{d} \sqrt[3]{x}}\right)}{d^{9/2}}-\frac{2 b e^3 n \sqrt[3]{x} \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};-\frac{e}{d x^{2/3}}\right)}{3 d^4}+\frac{2 b e^2 n x \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};-\frac{e}{d x^{2/3}}\right)}{15 d^3}-\frac{2 b e n x^{5/3} \, _2F_1\left(-\frac{5}{2},1;-\frac{3}{2};-\frac{e}{d x^{2/3}}\right)}{35 d^2}-\frac{b e^{7/2} n \left(-4 \text{Li}_2\left(1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)+2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)+\log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \left(\log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}+1\right)\right)-4 \log \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)\right)\right)}{4 (-d)^{9/2}}+\frac{b e^{7/2} n \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right)-4 \text{Li}_2\left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)+\log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \left(\log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)-4 \log \left(-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)\right)\right)}{4 (-d)^{9/2}}\right)\right)","\frac{4 b e^{9/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{3 d^{9/2}}+\frac{4 b e^3 n x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{9 d^3}-\frac{4 b e^2 n x^{5/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{15 d^2}+\frac{4 b e n x^{7/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{21 d}+\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2-\frac{4 a b e^4 n \sqrt[3]{x}}{3 d^4}-\frac{4 b^2 e^4 n \sqrt[3]{x} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{3 d^4}-\frac{4 i b^2 e^{9/2} n^2 \text{Li}_2\left(\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}-1\right)}{3 d^{9/2}}-\frac{4 i b^2 e^{9/2} n^2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)^2}{3 d^{9/2}}-\frac{1408 b^2 e^{9/2} n^2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{315 d^{9/2}}+\frac{8 b^2 e^{9/2} n^2 \log \left(2-\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{3 d^{9/2}}+\frac{568 b^2 e^4 n^2 \sqrt[3]{x}}{315 d^4}-\frac{32 b^2 e^3 n^2 x}{105 d^3}+\frac{8 b^2 e^2 n^2 x^{5/3}}{105 d^2}",1,"(x^3*(a + b*Log[c*(d + e/x^(2/3))^n])^2 - 4*b*e*n*((a*e^3*x^(1/3))/d^4 - (2*b*e^(7/2)*n*ArcTan[Sqrt[e]/(Sqrt[d]*x^(1/3))])/d^(9/2) - (2*b*e*n*x^(5/3)*Hypergeometric2F1[-5/2, 1, -3/2, -(e/(d*x^(2/3)))])/(35*d^2) + (2*b*e^2*n*x*Hypergeometric2F1[-3/2, 1, -1/2, -(e/(d*x^(2/3)))])/(15*d^3) - (2*b*e^3*n*x^(1/3)*Hypergeometric2F1[-1/2, 1, 1/2, -(e/(d*x^(2/3)))])/(3*d^4) + (b*e^3*x^(1/3)*Log[c*(d + e/x^(2/3))^n])/d^4 - (e^2*x*(a + b*Log[c*(d + e/x^(2/3))^n]))/(3*d^3) + (e*x^(5/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(5*d^2) - (x^(7/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(7*d) + (e^(7/2)*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)])/(2*(-d)^(9/2)) - (e^(7/2)*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)])/(2*(-d)^(9/2)) - (b*e^(7/2)*n*(Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*(Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] + 2*Log[(1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 4*Log[(Sqrt[-d]*x^(1/3))/Sqrt[e]]) - 4*PolyLog[2, 1 - (Sqrt[-d]*x^(1/3))/Sqrt[e]] + 2*PolyLog[2, 1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])]))/(4*(-d)^(9/2)) + (b*e^(7/2)*n*(Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*(Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] + 2*Log[1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] - 4*Log[-((Sqrt[-d]*x^(1/3))/Sqrt[e])]) + 2*PolyLog[2, (1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 4*PolyLog[2, 1 + (Sqrt[-d]*x^(1/3))/Sqrt[e]]))/(4*(-d)^(9/2))))/3","C",1
522,1,523,309,1.0693327,"\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])^2,x]","b e n \left(-\frac{2 \sqrt{e} \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{(-d)^{3/2}}+\frac{2 \sqrt{e} \log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{(-d)^{3/2}}+\frac{4 a \sqrt[3]{x}}{d}+\frac{4 b \sqrt[3]{x} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{d}-\frac{8 b \sqrt{e} n \tan ^{-1}\left(\frac{\sqrt{e}}{\sqrt{d} \sqrt[3]{x}}\right)}{d^{3/2}}+\frac{b \sqrt{e} n \left(-4 \text{Li}_2\left(1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)+2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)+\log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \left(\log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}+1\right)\right)-4 \log \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)\right)\right)}{(-d)^{3/2}}+\frac{b d \sqrt{e} n \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right)-4 \text{Li}_2\left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)+\log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \left(\log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)-4 \log \left(-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)\right)\right)}{(-d)^{5/2}}\right)+x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2","-\frac{4 b e^{3/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{d^{3/2}}+x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2+\frac{4 a b e n \sqrt[3]{x}}{d}+\frac{4 b^2 e n \sqrt[3]{x} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{d}+\frac{4 i b^2 e^{3/2} n^2 \text{Li}_2\left(\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}-1\right)}{d^{3/2}}+\frac{4 i b^2 e^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)^2}{d^{3/2}}+\frac{8 b^2 e^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{d^{3/2}}-\frac{8 b^2 e^{3/2} n^2 \log \left(2-\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{d^{3/2}}",1,"x*(a + b*Log[c*(d + e/x^(2/3))^n])^2 + b*e*n*((4*a*x^(1/3))/d - (8*b*Sqrt[e]*n*ArcTan[Sqrt[e]/(Sqrt[d]*x^(1/3))])/d^(3/2) + (4*b*x^(1/3)*Log[c*(d + e/x^(2/3))^n])/d - (2*Sqrt[e]*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)])/(-d)^(3/2) + (2*Sqrt[e]*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)])/(-d)^(3/2) + (b*Sqrt[e]*n*(Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*(Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] + 2*Log[(1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 4*Log[(Sqrt[-d]*x^(1/3))/Sqrt[e]]) - 4*PolyLog[2, 1 - (Sqrt[-d]*x^(1/3))/Sqrt[e]] + 2*PolyLog[2, 1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])]))/(-d)^(3/2) + (b*d*Sqrt[e]*n*(Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*(Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] + 2*Log[1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] - 4*Log[-((Sqrt[-d]*x^(1/3))/Sqrt[e])]) + 2*PolyLog[2, (1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 4*PolyLog[2, 1 + (Sqrt[-d]*x^(1/3))/Sqrt[e]]))/(-d)^(5/2))","A",1
523,1,598,361,1.2723696,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])^2/x^2,x]","\frac{\frac{b n \left(12 e^{3/2} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+18 (-d)^{3/2} x \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+18 d \sqrt{-d} x \log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-36 d \sqrt{e} x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-8 b n \left(3 d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{e}}{\sqrt{d} \sqrt[3]{x}}\right)+\sqrt{e} \left(e-3 d x^{2/3}\right)\right)-72 b d^{3/2} n x \tan ^{-1}\left(\frac{\sqrt{e}}{\sqrt{d} \sqrt[3]{x}}\right)+9 b (-d)^{3/2} n x \left(2 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right)-4 \text{Li}_2\left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)+\log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \left(\log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right)+2 \log \left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)-4 \log \left(-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)\right)\right)+9 b d \sqrt{-d} n x \left(-4 \text{Li}_2\left(1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)+2 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)+\log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \left(\log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right)+2 \log \left(\frac{1}{2} \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}+1\right)\right)-4 \log \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)\right)\right)+72 b d \sqrt{e} n x^{2/3}\right)}{e^{3/2}}-9 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{9 x}","-\frac{4 b d^{3/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{e^{3/2}}-\frac{4 b d n \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{e \sqrt[3]{x}}+\frac{4 b n \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{3 x}-\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x}+\frac{4 i b^2 d^{3/2} n^2 \text{Li}_2\left(\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}-1\right)}{e^{3/2}}+\frac{4 i b^2 d^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)^2}{e^{3/2}}+\frac{32 b^2 d^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{3 e^{3/2}}-\frac{8 b^2 d^{3/2} n^2 \log \left(2-\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{e^{3/2}}+\frac{32 b^2 d n^2}{3 e \sqrt[3]{x}}-\frac{8 b^2 n^2}{9 x}",1,"(-9*(a + b*Log[c*(d + e/x^(2/3))^n])^2 + (b*n*(72*b*d*Sqrt[e]*n*x^(2/3) - 72*b*d^(3/2)*n*x*ArcTan[Sqrt[e]/(Sqrt[d]*x^(1/3))] - 8*b*n*(Sqrt[e]*(e - 3*d*x^(2/3)) + 3*d^(3/2)*x*ArcTan[Sqrt[e]/(Sqrt[d]*x^(1/3))]) + 12*e^(3/2)*(a + b*Log[c*(d + e/x^(2/3))^n]) - 36*d*Sqrt[e]*x^(2/3)*(a + b*Log[c*(d + e/x^(2/3))^n]) + 18*(-d)^(3/2)*x*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] + 18*Sqrt[-d]*d*x*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] + 9*b*Sqrt[-d]*d*n*x*(Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*(Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] + 2*Log[(1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 4*Log[(Sqrt[-d]*x^(1/3))/Sqrt[e]]) - 4*PolyLog[2, 1 - (Sqrt[-d]*x^(1/3))/Sqrt[e]] + 2*PolyLog[2, 1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])]) + 9*b*(-d)^(3/2)*n*x*(Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*(Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] + 2*Log[1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] - 4*Log[-((Sqrt[-d]*x^(1/3))/Sqrt[e])]) + 2*PolyLog[2, (1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] - 4*PolyLog[2, 1 + (Sqrt[-d]*x^(1/3))/Sqrt[e]])))/e^(3/2))/(9*x)","A",1
524,1,1014,773,2.5852673,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3 \, dx","Integrate[x^3*(a + b*Log[c*(d + e/x^(2/3))^n])^3,x]","\frac{20 x^4 \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3 d^6+60 b n x^4 \log \left(d+\frac{e}{x^{2/3}}\right) \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 d^6+12 b e n x^{10/3} \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 d^5-15 b e^2 n x^{8/3} \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 d^4+20 b e^3 n x^2 \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 d^3-30 b e^4 n x^{4/3} \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 d^2+60 b e^5 n x^{2/3} \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 d-60 b e^6 n \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 \log \left(x^{2/3} d+e\right)+b^2 n^2 \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \left(-274 \log \left(-\frac{e}{d x^{2/3}}\right) e^6+120 \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right) e^6+d x^{2/3} \left(6 x^2 d^3-18 e x^{4/3} d^2+47 e^2 x^{2/3} d-154 e^3\right) e^2+2 \log \left(d+\frac{e}{x^{2/3}}\right) \left(12 x^{10/3} d^5-15 e x^{8/3} d^4+20 e^2 x^2 d^3-30 e^3 x^{4/3} d^2+60 e^4 x^{2/3} d+137 e^5+60 e^5 \log \left(-\frac{e}{d x^{2/3}}\right)\right) e-60 \left(e^6-d^6 x^4\right) \log ^2\left(d+\frac{e}{x^{2/3}}\right)\right)+b^3 n^3 \left(20 x^4 \log ^3\left(d+\frac{e}{x^{2/3}}\right) d^6+12 e x^{10/3} \log ^2\left(d+\frac{e}{x^{2/3}}\right) d^5+3 e^2 x^{8/3} \left(2-5 \log \left(d+\frac{e}{x^{2/3}}\right)\right) \log \left(d+\frac{e}{x^{2/3}}\right) d^4+2 e^3 x^2 \left(10 \log ^2\left(d+\frac{e}{x^{2/3}}\right)-9 \log \left(d+\frac{e}{x^{2/3}}\right)+1\right) d^3-e^4 x^{4/3} \left(30 \log ^2\left(d+\frac{e}{x^{2/3}}\right)-47 \log \left(d+\frac{e}{x^{2/3}}\right)+12\right) d^2+e^5 x^{2/3} \left(60 \log ^2\left(d+\frac{e}{x^{2/3}}\right)-154 \log \left(d+\frac{e}{x^{2/3}}\right)+71\right) d+225 e^6 \left(\log \left(-\frac{e}{d x^{2/3}}\right)-\log \left(d+\frac{e}{x^{2/3}}\right)\right)+137 e^6 \left(\log \left(d+\frac{e}{x^{2/3}}\right) \left(\log \left(d+\frac{e}{x^{2/3}}\right)-2 \log \left(-\frac{e}{d x^{2/3}}\right)\right)-2 \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right)\right)-20 e^6 \left(\left(\log \left(d+\frac{e}{x^{2/3}}\right)-3 \log \left(-\frac{e}{d x^{2/3}}\right)\right) \log ^2\left(d+\frac{e}{x^{2/3}}\right)-6 \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right) \log \left(d+\frac{e}{x^{2/3}}\right)+6 \text{Li}_3\left(\frac{e}{d x^{2/3}}+1\right)\right)\right)}{80 d^6}","-\frac{3 b^2 e^6 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{x^{2/3}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{2 d^6}-\frac{77 b^2 e^6 n^2 \log \left(1-\frac{d}{d+\frac{e}{x^{2/3}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{40 d^6}-\frac{3 b^2 e^6 n^2 \log \left(-\frac{e}{d x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{2 d^6}-\frac{77 b^2 e^5 n^2 x^{2/3} \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{40 d^6}+\frac{47 b^2 e^4 n^2 x^{4/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{80 d^4}-\frac{9 b^2 e^3 n^2 x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{40 d^3}+\frac{3 b^2 e^2 n^2 x^{8/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{40 d^2}+\frac{3 b e^6 n \log \left(1-\frac{d}{d+\frac{e}{x^{2/3}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{4 d^6}+\frac{3 b e^5 n x^{2/3} \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{4 d^6}-\frac{3 b e^4 n x^{4/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{8 d^4}+\frac{b e^3 n x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{4 d^3}-\frac{3 b e^2 n x^{8/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{16 d^2}+\frac{3 b e n x^{10/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{20 d}+\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3+\frac{77 b^3 e^6 n^3 \text{Li}_2\left(\frac{d}{d+\frac{e}{x^{2/3}}}\right)}{40 d^6}-\frac{3 b^3 e^6 n^3 \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right)}{2 d^6}-\frac{3 b^3 e^6 n^3 \text{Li}_3\left(\frac{d}{d+\frac{e}{x^{2/3}}}\right)}{2 d^6}-\frac{71 b^3 e^6 n^3 \log \left(d+\frac{e}{x^{2/3}}\right)}{80 d^6}-\frac{15 b^3 e^6 n^3 \log (x)}{8 d^6}+\frac{71 b^3 e^5 n^3 x^{2/3}}{80 d^5}-\frac{3 b^3 e^4 n^3 x^{4/3}}{20 d^4}+\frac{b^3 e^3 n^3 x^2}{40 d^3}",1,"(60*b*d*e^5*n*x^(2/3)*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2 - 30*b*d^2*e^4*n*x^(4/3)*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2 + 20*b*d^3*e^3*n*x^2*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2 - 15*b*d^4*e^2*n*x^(8/3)*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2 + 12*b*d^5*e*n*x^(10/3)*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2 + 60*b*d^6*n*x^4*Log[d + e/x^(2/3)]*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2 + 20*d^6*x^4*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^3 - 60*b*e^6*n*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2*Log[e + d*x^(2/3)] + b^2*n^2*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])*(d*e^2*x^(2/3)*(-154*e^3 + 47*d*e^2*x^(2/3) - 18*d^2*e*x^(4/3) + 6*d^3*x^2) - 60*(e^6 - d^6*x^4)*Log[d + e/x^(2/3)]^2 - 274*e^6*Log[-(e/(d*x^(2/3)))] + 2*e*Log[d + e/x^(2/3)]*(137*e^5 + 60*d*e^4*x^(2/3) - 30*d^2*e^3*x^(4/3) + 20*d^3*e^2*x^2 - 15*d^4*e*x^(8/3) + 12*d^5*x^(10/3) + 60*e^5*Log[-(e/(d*x^(2/3)))]) + 120*e^6*PolyLog[2, 1 + e/(d*x^(2/3))]) + b^3*n^3*(3*d^4*e^2*x^(8/3)*(2 - 5*Log[d + e/x^(2/3)])*Log[d + e/x^(2/3)] + 12*d^5*e*x^(10/3)*Log[d + e/x^(2/3)]^2 + 20*d^6*x^4*Log[d + e/x^(2/3)]^3 + 2*d^3*e^3*x^2*(1 - 9*Log[d + e/x^(2/3)] + 10*Log[d + e/x^(2/3)]^2) - d^2*e^4*x^(4/3)*(12 - 47*Log[d + e/x^(2/3)] + 30*Log[d + e/x^(2/3)]^2) + d*e^5*x^(2/3)*(71 - 154*Log[d + e/x^(2/3)] + 60*Log[d + e/x^(2/3)]^2) + 225*e^6*(-Log[d + e/x^(2/3)] + Log[-(e/(d*x^(2/3)))]) + 137*e^6*(Log[d + e/x^(2/3)]*(Log[d + e/x^(2/3)] - 2*Log[-(e/(d*x^(2/3)))]) - 2*PolyLog[2, 1 + e/(d*x^(2/3))]) - 20*e^6*(Log[d + e/x^(2/3)]^2*(Log[d + e/x^(2/3)] - 3*Log[-(e/(d*x^(2/3)))]) - 6*Log[d + e/x^(2/3)]*PolyLog[2, 1 + e/(d*x^(2/3))] + 6*PolyLog[3, 1 + e/(d*x^(2/3))])))/(80*d^6)","A",1
525,1,683,451,1.4206681,"\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3 \, dx","Integrate[x*(a + b*Log[c*(d + e/x^(2/3))^n])^3,x]","\frac{6 b^2 n^2 \left(\left(d^3 x^2+e^3\right) \log ^2\left(d+\frac{e}{x^{2/3}}\right)+e \log \left(d+\frac{e}{x^{2/3}}\right) \left(d^2 x^{4/3}-2 e^2 \log \left(-\frac{e}{d x^{2/3}}\right)-2 d e x^{2/3}-3 e^2\right)-2 e^3 \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right)+e^2 \left(3 e \log \left(-\frac{e}{d x^{2/3}}\right)+d x^{2/3}\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)+2 d^3 x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^3+6 b d^3 n x^2 \log \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2+3 b d^2 e n x^{4/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2+6 b e^3 n \log \left(d x^{2/3}+e\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2-6 b d e^2 n x^{2/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2-b^3 n^3 \left(-2 d^3 x^2 \log ^3\left(d+\frac{e}{x^{2/3}}\right)-3 d^2 e x^{4/3} \log ^2\left(d+\frac{e}{x^{2/3}}\right)-12 e^3 \text{Li}_3\left(\frac{e}{d x^{2/3}}+1\right)+6 e^3 \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right) \left(2 \log \left(d+\frac{e}{x^{2/3}}\right)-3\right)-2 e^3 \log ^3\left(d+\frac{e}{x^{2/3}}\right)+9 e^3 \log ^2\left(d+\frac{e}{x^{2/3}}\right)+6 e^3 \log ^2\left(d+\frac{e}{x^{2/3}}\right) \log \left(-\frac{e}{d x^{2/3}}\right)-6 e^3 \log \left(d+\frac{e}{x^{2/3}}\right)-18 e^3 \log \left(d+\frac{e}{x^{2/3}}\right) \log \left(-\frac{e}{d x^{2/3}}\right)+6 e^3 \log \left(-\frac{e}{d x^{2/3}}\right)+6 d e^2 x^{2/3} \log ^2\left(d+\frac{e}{x^{2/3}}\right)-6 d e^2 x^{2/3} \log \left(d+\frac{e}{x^{2/3}}\right)\right)}{4 d^3}","\frac{3 b^2 e^3 n^2 \text{Li}_2\left(\frac{d}{d+\frac{e}{x^{2/3}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{d^3}+\frac{3 b^2 e^3 n^2 \log \left(1-\frac{d}{d+\frac{e}{x^{2/3}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{2 d^3}+\frac{3 b^2 e^3 n^2 \log \left(-\frac{e}{d x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{d^3}+\frac{3 b^2 e^2 n^2 x^{2/3} \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{2 d^3}-\frac{3 b e^3 n \log \left(1-\frac{d}{d+\frac{e}{x^{2/3}}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{2 d^3}-\frac{3 b e^2 n x^{2/3} \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{2 d^3}+\frac{3 b e n x^{4/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{4 d}+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3-\frac{3 b^3 e^3 n^3 \text{Li}_2\left(\frac{d}{d+\frac{e}{x^{2/3}}}\right)}{2 d^3}+\frac{3 b^3 e^3 n^3 \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right)}{d^3}+\frac{3 b^3 e^3 n^3 \text{Li}_3\left(\frac{d}{d+\frac{e}{x^{2/3}}}\right)}{d^3}+\frac{b^3 e^3 n^3 \log (x)}{d^3}",1,"(-6*b*d*e^2*n*x^(2/3)*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2 + 3*b*d^2*e*n*x^(4/3)*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2 + 6*b*d^3*n*x^2*Log[d + e/x^(2/3)]*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2 + 2*d^3*x^2*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^3 + 6*b*e^3*n*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2*Log[e + d*x^(2/3)] + 6*b^2*n^2*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])*((e^3 + d^3*x^2)*Log[d + e/x^(2/3)]^2 + e^2*(d*x^(2/3) + 3*e*Log[-(e/(d*x^(2/3)))]) + e*Log[d + e/x^(2/3)]*(-3*e^2 - 2*d*e*x^(2/3) + d^2*x^(4/3) - 2*e^2*Log[-(e/(d*x^(2/3)))]) - 2*e^3*PolyLog[2, 1 + e/(d*x^(2/3))]) - b^3*n^3*(-6*e^3*Log[d + e/x^(2/3)] - 6*d*e^2*x^(2/3)*Log[d + e/x^(2/3)] + 9*e^3*Log[d + e/x^(2/3)]^2 + 6*d*e^2*x^(2/3)*Log[d + e/x^(2/3)]^2 - 3*d^2*e*x^(4/3)*Log[d + e/x^(2/3)]^2 - 2*e^3*Log[d + e/x^(2/3)]^3 - 2*d^3*x^2*Log[d + e/x^(2/3)]^3 + 6*e^3*Log[-(e/(d*x^(2/3)))] - 18*e^3*Log[d + e/x^(2/3)]*Log[-(e/(d*x^(2/3)))] + 6*e^3*Log[d + e/x^(2/3)]^2*Log[-(e/(d*x^(2/3)))] + 6*e^3*(-3 + 2*Log[d + e/x^(2/3)])*PolyLog[2, 1 + e/(d*x^(2/3))] - 12*e^3*PolyLog[3, 1 + e/(d*x^(2/3))]))/(4*d^3)","A",1
526,1,341,139,0.2635387,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{x} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])^3/x,x]","\frac{9}{2} b^2 n^2 \left(-2 \text{Li}_3\left(\frac{e}{d x^{2/3}}+1\right)+2 \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right) \log \left(d+\frac{e}{x^{2/3}}\right)+\log \left(-\frac{e}{d x^{2/3}}\right) \log ^2\left(d+\frac{e}{x^{2/3}}\right)\right) \left(-a-b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)+b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)+3 b n \left(\frac{3}{2} \text{Li}_2\left(-\frac{e}{d x^{2/3}}\right)+\log (x) \left(\log \left(d+\frac{e}{x^{2/3}}\right)-\log \left(\frac{e}{d x^{2/3}}+1\right)\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2+\log (x) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^3-\frac{3}{2} b^3 n^3 \left(6 \text{Li}_4\left(\frac{e}{d x^{2/3}}+1\right)+3 \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right) \log ^2\left(d+\frac{e}{x^{2/3}}\right)-6 \text{Li}_3\left(\frac{e}{d x^{2/3}}+1\right) \log \left(d+\frac{e}{x^{2/3}}\right)+\log \left(-\frac{e}{d x^{2/3}}\right) \log ^3\left(d+\frac{e}{x^{2/3}}\right)\right)","9 b^2 n^2 \text{Li}_3\left(\frac{e}{d x^{2/3}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-\frac{9}{2} b n \text{Li}_2\left(\frac{e}{d x^{2/3}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2-\frac{3}{2} \log \left(-\frac{e}{d x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3-9 b^3 n^3 \text{Li}_4\left(\frac{e}{d x^{2/3}}+1\right)",1,"(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^3*Log[x] + 3*b*n*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2*((Log[d + e/x^(2/3)] - Log[1 + e/(d*x^(2/3))])*Log[x] + (3*PolyLog[2, -(e/(d*x^(2/3)))])/2) + (9*b^2*n^2*(-a + b*n*Log[d + e/x^(2/3)] - b*Log[c*(d + e/x^(2/3))^n])*(Log[d + e/x^(2/3)]^2*Log[-(e/(d*x^(2/3)))] + 2*Log[d + e/x^(2/3)]*PolyLog[2, 1 + e/(d*x^(2/3))] - 2*PolyLog[3, 1 + e/(d*x^(2/3))]))/2 - (3*b^3*n^3*(Log[d + e/x^(2/3)]^3*Log[-(e/(d*x^(2/3)))] + 3*Log[d + e/x^(2/3)]^2*PolyLog[2, 1 + e/(d*x^(2/3))] - 6*Log[d + e/x^(2/3)]*PolyLog[3, 1 + e/(d*x^(2/3))] + 6*PolyLog[4, 1 + e/(d*x^(2/3))]))/2","B",1
527,1,692,449,1.5310495,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])^3/x^3,x]","\frac{-36 a^3 e^3-6 b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) \left(18 a^2 e^3+6 b d^3 n x^2 (6 a-11 b n) \log \left(d x^{2/3}+e\right)+4 b d^3 n x^2 \log (x) (11 b n-6 a)-6 a b e n \left(6 d^2 x^{4/3}-3 d e x^{2/3}+2 e^2\right)+b^2 e n^2 \left(66 d^2 x^{4/3}-15 d e x^{2/3}+4 e^2\right)\right)-108 a^2 b d^3 n x^2 \log \left(d x^{2/3}+e\right)+72 a^2 b d^3 n x^2 \log (x)+108 a^2 b d^2 e n x^{4/3}-54 a^2 b d e^2 n x^{2/3}+36 a^2 b e^3 n-18 b^2 d^3 n^2 x^2 \log ^2\left(d+\frac{e}{x^{2/3}}\right) \left(6 a+6 b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)+6 b n \log \left(d x^{2/3}+e\right)-4 b n \log (x)-11 b n\right)+12 b^2 d^3 n^2 x^2 \log \left(d+\frac{e}{x^{2/3}}\right) \left(3 \log \left(d x^{2/3}+e\right)-2 \log (x)\right) \left(6 a+6 b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-11 b n\right)+18 b^2 \log ^2\left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) \left(e \left(-6 a e^2+6 b d^2 n x^{4/3}-3 b d e n x^{2/3}+2 b e^2 n\right)-6 b d^3 n x^2 \log \left(d x^{2/3}+e\right)+4 b d^3 n x^2 \log (x)\right)+396 a b^2 d^3 n^2 x^2 \log \left(d x^{2/3}+e\right)-264 a b^2 d^3 n^2 x^2 \log (x)-396 a b^2 d^2 e n^2 x^{4/3}+90 a b^2 d e^2 n^2 x^{2/3}-24 a b^2 e^3 n^2-36 b^3 e^3 \log ^3\left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)+72 b^3 d^3 n^3 x^2 \log ^3\left(d+\frac{e}{x^{2/3}}\right)-510 b^3 d^3 n^3 x^2 \log \left(d x^{2/3}+e\right)+340 b^3 d^3 n^3 x^2 \log (x)+510 b^3 d^2 e n^3 x^{4/3}-57 b^3 d e^2 n^3 x^{2/3}+8 b^3 e^3 n^3}{72 e^3 x^2}","-\frac{b^2 n^2 \left(d+\frac{e}{x^{2/3}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{3 e^3}+\frac{9 b^2 d n^2 \left(d+\frac{e}{x^{2/3}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{4 e^3}-\frac{9 a b^2 d^2 n^2}{e^2 x^{2/3}}+\frac{9 b d^2 n \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{2 e^3}-\frac{3 d^2 \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{2 e^3}+\frac{b n \left(d+\frac{e}{x^{2/3}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{2 e^3}-\frac{9 b d n \left(d+\frac{e}{x^{2/3}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{4 e^3}-\frac{\left(d+\frac{e}{x^{2/3}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{2 e^3}+\frac{3 d \left(d+\frac{e}{x^{2/3}}\right)^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{2 e^3}-\frac{9 b^3 d^2 n^2 \left(d+\frac{e}{x^{2/3}}\right) \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{e^3}+\frac{9 b^3 d^2 n^3}{e^2 x^{2/3}}+\frac{b^3 n^3 \left(d+\frac{e}{x^{2/3}}\right)^3}{9 e^3}-\frac{9 b^3 d n^3 \left(d+\frac{e}{x^{2/3}}\right)^2}{8 e^3}",1,"(-36*a^3*e^3 + 36*a^2*b*e^3*n - 24*a*b^2*e^3*n^2 + 8*b^3*e^3*n^3 - 54*a^2*b*d*e^2*n*x^(2/3) + 90*a*b^2*d*e^2*n^2*x^(2/3) - 57*b^3*d*e^2*n^3*x^(2/3) + 108*a^2*b*d^2*e*n*x^(4/3) - 396*a*b^2*d^2*e*n^2*x^(4/3) + 510*b^3*d^2*e*n^3*x^(4/3) + 72*b^3*d^3*n^3*x^2*Log[d + e/x^(2/3)]^3 - 36*b^3*e^3*Log[c*(d + e/x^(2/3))^n]^3 - 108*a^2*b*d^3*n*x^2*Log[e + d*x^(2/3)] + 396*a*b^2*d^3*n^2*x^2*Log[e + d*x^(2/3)] - 510*b^3*d^3*n^3*x^2*Log[e + d*x^(2/3)] + 12*b^2*d^3*n^2*x^2*Log[d + e/x^(2/3)]*(6*a - 11*b*n + 6*b*Log[c*(d + e/x^(2/3))^n])*(3*Log[e + d*x^(2/3)] - 2*Log[x]) + 72*a^2*b*d^3*n*x^2*Log[x] - 264*a*b^2*d^3*n^2*x^2*Log[x] + 340*b^3*d^3*n^3*x^2*Log[x] - 18*b^2*d^3*n^2*x^2*Log[d + e/x^(2/3)]^2*(6*a - 11*b*n + 6*b*Log[c*(d + e/x^(2/3))^n] + 6*b*n*Log[e + d*x^(2/3)] - 4*b*n*Log[x]) + 18*b^2*Log[c*(d + e/x^(2/3))^n]^2*(e*(-6*a*e^2 + 2*b*e^2*n - 3*b*d*e*n*x^(2/3) + 6*b*d^2*n*x^(4/3)) - 6*b*d^3*n*x^2*Log[e + d*x^(2/3)] + 4*b*d^3*n*x^2*Log[x]) - 6*b*Log[c*(d + e/x^(2/3))^n]*(18*a^2*e^3 - 6*a*b*e*n*(2*e^2 - 3*d*e*x^(2/3) + 6*d^2*x^(4/3)) + b^2*e*n^2*(4*e^2 - 15*d*e*x^(2/3) + 66*d^2*x^(4/3)) + 6*b*d^3*n*(6*a - 11*b*n)*x^2*Log[e + d*x^(2/3)] + 4*b*d^3*n*(-6*a + 11*b*n)*x^2*Log[x]))/(72*e^3*x^2)","A",1
528,1,764,1278,4.9526908,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3 \, dx","Integrate[x^2*(a + b*Log[c*(d + e/x^(2/3))^n])^3,x]","-\frac{b^2 n^2 \left(-a-b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)+b n \log \left(d+\frac{e}{x^{2/3}}\right)\right) \left(\log \left(d+\frac{e}{x^{2/3}}\right) \left(9 e^5 \left(d x^{2/3}+e\right) \, _3F_2\left(1,1,\frac{11}{2};2,2;\frac{e}{d x^{2/3}}+1\right)+d x^{2/3} \left(d^5 x^{10/3} \sqrt{-\frac{e}{d x^{2/3}}}+e^5\right) \log \left(d+\frac{e}{x^{2/3}}\right)\right)-9 e^5 \left(d x^{2/3}+e\right) \, _4F_3\left(1,1,1,\frac{11}{2};2,2,2;\frac{e}{d x^{2/3}}+1\right)\right)}{d^6 x \sqrt{-\frac{e}{d x^{2/3}}}}+\frac{b^3 n^3 \left(\log \left(d+\frac{e}{x^{2/3}}\right) \left(\log \left(d+\frac{e}{x^{2/3}}\right) \left(27 e^5 \left(d x^{2/3}+e\right) \, _3F_2\left(1,1,\frac{11}{2};2,2;\frac{e}{d x^{2/3}}+1\right)+2 d x^{2/3} \left(d^5 x^{10/3} \sqrt{-\frac{e}{d x^{2/3}}}+e^5\right) \log \left(d+\frac{e}{x^{2/3}}\right)\right)-54 e^5 \left(d x^{2/3}+e\right) \, _4F_3\left(1,1,1,\frac{11}{2};2,2,2;\frac{e}{d x^{2/3}}+1\right)\right)+54 e^5 \left(d x^{2/3}+e\right) \, _5F_4\left(1,1,1,1,\frac{11}{2};2,2,2,2;\frac{e}{d x^{2/3}}+1\right)\right)}{6 d^6 x \sqrt{-\frac{e}{d x^{2/3}}}}+\frac{2 b e^{9/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2}{d^{9/2}}-\frac{2 b e^4 n \sqrt[3]{x} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2}{d^4}+\frac{2 b e^3 n x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2}{3 d^3}-\frac{2 b e^2 n x^{5/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2}{5 d^2}+\frac{2 b e n x^{7/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2}{7 d}+\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^3+b n x^3 \log \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2","\frac{2 b n \text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{\left(x^{2/3} d+e\right) x^{2/3}},x\right) e^5}{3 d^4}+\frac{568 i b^3 n^3 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)^2 e^{9/2}}{105 d^{9/2}}-\frac{2 b^3 n^3 \log ^2\left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) e^{9/2}}{(-d)^{9/2}}+\frac{2 b^3 n^3 \log ^2\left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) e^{9/2}}{(-d)^{9/2}}+\frac{1376 b^3 n^3 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right) e^{9/2}}{105 d^{9/2}}-\frac{1136 b^3 n^3 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right) \log \left(2-\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\right) e^{9/2}}{105 d^{9/2}}-\frac{568 b^2 n^2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) e^{9/2}}{105 d^{9/2}}+\frac{4 b^2 n^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) e^{9/2}}{(-d)^{9/2}}-\frac{4 b^2 n^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) e^{9/2}}{(-d)^{9/2}}+\frac{4 b^3 n^3 \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) \log \left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right) e^{9/2}}{(-d)^{9/2}}-\frac{4 b^3 n^3 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \log \left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right) e^{9/2}}{(-d)^{9/2}}-\frac{8 b^3 n^3 \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) \log \left(-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right) e^{9/2}}{(-d)^{9/2}}+\frac{8 b^3 n^3 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \log \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right) e^{9/2}}{(-d)^{9/2}}+\frac{568 i b^3 n^3 \text{Li}_2\left(\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}-1\right) e^{9/2}}{105 d^{9/2}}+\frac{8 b^3 n^3 \text{Li}_2\left(1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right) e^{9/2}}{(-d)^{9/2}}-\frac{4 b^3 n^3 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right) e^{9/2}}{(-d)^{9/2}}+\frac{4 b^3 n^3 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right) e^{9/2}}{(-d)^{9/2}}-\frac{8 b^3 n^3 \text{Li}_2\left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right) e^{9/2}}{(-d)^{9/2}}-\frac{2 b n \sqrt[3]{x} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 e^4}{d^4}+\frac{568 b^3 n^2 \sqrt[3]{x} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right) e^4}{105 d^4}-\frac{16 b^3 n^3 \sqrt[3]{x} e^4}{7 d^4}+\frac{568 a b^2 n^2 \sqrt[3]{x} e^4}{105 d^4}+\frac{2 b n x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 e^3}{3 d^3}+\frac{16 b^3 n^3 x e^3}{105 d^3}-\frac{32 b^2 n^2 x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) e^3}{35 d^3}-\frac{2 b n x^{5/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 e^2}{5 d^2}+\frac{8 b^2 n^2 x^{5/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) e^2}{35 d^2}+\frac{2 b n x^{7/3} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 e}{7 d}+\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3",0,"(b^3*n^3*(54*e^5*(e + d*x^(2/3))*HypergeometricPFQ[{1, 1, 1, 1, 11/2}, {2, 2, 2, 2}, 1 + e/(d*x^(2/3))] + Log[d + e/x^(2/3)]*(-54*e^5*(e + d*x^(2/3))*HypergeometricPFQ[{1, 1, 1, 11/2}, {2, 2, 2}, 1 + e/(d*x^(2/3))] + Log[d + e/x^(2/3)]*(27*e^5*(e + d*x^(2/3))*HypergeometricPFQ[{1, 1, 11/2}, {2, 2}, 1 + e/(d*x^(2/3))] + 2*d*x^(2/3)*(e^5 + d^5*Sqrt[-(e/(d*x^(2/3)))]*x^(10/3))*Log[d + e/x^(2/3)]))))/(6*d^6*Sqrt[-(e/(d*x^(2/3)))]*x) - (b^2*n^2*(-9*e^5*(e + d*x^(2/3))*HypergeometricPFQ[{1, 1, 1, 11/2}, {2, 2, 2}, 1 + e/(d*x^(2/3))] + Log[d + e/x^(2/3)]*(9*e^5*(e + d*x^(2/3))*HypergeometricPFQ[{1, 1, 11/2}, {2, 2}, 1 + e/(d*x^(2/3))] + d*x^(2/3)*(e^5 + d^5*Sqrt[-(e/(d*x^(2/3)))]*x^(10/3))*Log[d + e/x^(2/3)]))*(-a + b*n*Log[d + e/x^(2/3)] - b*Log[c*(d + e/x^(2/3))^n]))/(d^6*Sqrt[-(e/(d*x^(2/3)))]*x) - (2*b*e^4*n*x^(1/3)*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/d^4 + (2*b*e^3*n*x*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/(3*d^3) - (2*b*e^2*n*x^(5/3)*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/(5*d^2) + (2*b*e*n*x^(7/3)*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/(7*d) + (2*b*e^(9/2)*n*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/d^(9/2) + b*n*x^3*Log[d + e/x^(2/3)]*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2 + (x^3*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^3)/3","A",1
529,1,475,738,3.2178082,"\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3 \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])^3,x]","\frac{-9 b^2 e n^2 \left(d x^{2/3}+e\right) \sqrt{-\frac{e}{d x^{2/3}}} \, _4F_3\left(1,1,1,\frac{5}{2};2,2,2;\frac{e}{d x^{2/3}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+9 b^3 e n^3 \left(d x^{2/3}+e\right) \sqrt{-\frac{e}{d x^{2/3}}} \, _5F_4\left(1,1,1,1,\frac{5}{2};2,2,2,2;\frac{e}{d x^{2/3}}+1\right)+d x^{2/3} \left(3 b^2 e n^2 \sqrt{-\frac{e}{d x^{2/3}}} \log ^2\left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)+2 b n \log \left(\frac{1}{2} \left(\sqrt{-\frac{e}{d x^{2/3}}}+1\right)\right)+2 b n\right)-12 b^2 e n^2 \sqrt{-\frac{e}{d x^{2/3}}} \left(\log \left(\frac{1}{2} \left(\sqrt{-\frac{e}{d x^{2/3}}}+1\right)\right)+1\right) \log \left(d+\frac{e}{x^{2/3}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)+\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 \left(a d x^{2/3}+b d x^{2/3} \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)+6 b e n\right)-2 b^3 e n^3 \sqrt{-\frac{e}{d x^{2/3}}} \log ^3\left(d+\frac{e}{x^{2/3}}\right)\right)-6 b \sqrt{d} e^{3/2} n \sqrt[3]{x} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)-b n \log \left(d+\frac{e}{x^{2/3}}\right)\right)^2}{d^2 \sqrt[3]{x}}","-\frac{2 b e^2 n \text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x^{2/3} \left(d x^{2/3}+e\right)},x\right)}{d}+\frac{12 b^2 e^{3/2} n^2 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{(-d)^{3/2}}-\frac{12 b^2 e^{3/2} n^2 \log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{(-d)^{3/2}}+\frac{6 b e n \sqrt[3]{x} \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{d}+x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3+\frac{24 b^3 e^{3/2} n^3 \text{Li}_2\left(1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)}{(-d)^{3/2}}-\frac{12 b^3 e^{3/2} n^3 \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)}{(-d)^{3/2}}+\frac{12 b^3 e^{3/2} n^3 \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right)}{(-d)^{3/2}}-\frac{24 b^3 e^{3/2} n^3 \text{Li}_2\left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)}{(-d)^{3/2}}-\frac{6 b^3 e^{3/2} n^3 \log ^2\left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right)}{(-d)^{3/2}}+\frac{6 b^3 e^{3/2} n^3 \log ^2\left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right)}{(-d)^{3/2}}+\frac{12 b^3 e^{3/2} n^3 \log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \log \left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)}{(-d)^{3/2}}-\frac{12 b^3 e^{3/2} n^3 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \log \left(\frac{1}{2} \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}+1\right)\right)}{(-d)^{3/2}}-\frac{24 b^3 e^{3/2} n^3 \log \left(\sqrt{-d} \sqrt[3]{x}+\sqrt{e}\right) \log \left(-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)}{(-d)^{3/2}}+\frac{24 b^3 e^{3/2} n^3 \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \log \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)}{(-d)^{3/2}}",0,"(9*b^3*e*n^3*(e + d*x^(2/3))*Sqrt[-(e/(d*x^(2/3)))]*HypergeometricPFQ[{1, 1, 1, 1, 5/2}, {2, 2, 2, 2}, 1 + e/(d*x^(2/3))] - 9*b^2*e*n^2*(e + d*x^(2/3))*Sqrt[-(e/(d*x^(2/3)))]*HypergeometricPFQ[{1, 1, 1, 5/2}, {2, 2, 2}, 1 + e/(d*x^(2/3))]*(a + b*Log[c*(d + e/x^(2/3))^n]) - 6*b*Sqrt[d]*e^(3/2)*n*x^(1/3)*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2 + d*x^(2/3)*(-2*b^3*e*n^3*Sqrt[-(e/(d*x^(2/3)))]*Log[d + e/x^(2/3)]^3 - 12*b^2*e*n^2*Sqrt[-(e/(d*x^(2/3)))]*(1 + Log[(1 + Sqrt[-(e/(d*x^(2/3)))])/2])*Log[d + e/x^(2/3)]*(a + b*Log[c*(d + e/x^(2/3))^n]) + 3*b^2*e*n^2*Sqrt[-(e/(d*x^(2/3)))]*Log[d + e/x^(2/3)]^2*(a + 2*b*n + 2*b*n*Log[(1 + Sqrt[-(e/(d*x^(2/3)))])/2] + b*Log[c*(d + e/x^(2/3))^n]) + (a + b*Log[c*(d + e/x^(2/3))^n])^2*(6*b*e*n + a*d*x^(2/3) + b*d*x^(2/3)*Log[c*(d + e/x^(2/3))^n])))/(d^2*x^(1/3))","A",1
530,1,1097,483,2.3147517,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])^3/x^2,x]","\frac{b^3 \left(18 \left(x^{2/3} d+e\right) \, _5F_4\left(-\frac{1}{2},1,1,1,1;2,2,2,2;\frac{e}{d x^{2/3}}+1\right)-\log \left(d+\frac{e}{x^{2/3}}\right) \left(18 \left(x^{2/3} d+e\right) \, _4F_3\left(-\frac{1}{2},1,1,1;2,2,2;\frac{e}{d x^{2/3}}+1\right)+\log \left(d+\frac{e}{x^{2/3}}\right) \left(2 \left(x^{2/3} d+e \sqrt{-\frac{e}{d x^{2/3}}}\right) \log \left(d+\frac{e}{x^{2/3}}\right)-9 \left(x^{2/3} d+e\right) \, _3F_2\left(-\frac{1}{2},1,1;2,2;\frac{e}{d x^{2/3}}+1\right)\right)\right)\right) n^3}{2 e \sqrt{-\frac{e}{d x^{2/3}}} x}+\frac{b^2 \left(-a+b n \log \left(d+\frac{e}{x^{2/3}}\right)-b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \left(9 e^{3/2} \log ^2\left(d+\frac{e}{x^{2/3}}\right)-12 e^{3/2} \log \left(d+\frac{e}{x^{2/3}}\right)+18 \sqrt{-d} d x \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \log \left(d+\frac{e}{x^{2/3}}\right)+18 (-d)^{3/2} x \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) \log \left(d+\frac{e}{x^{2/3}}\right)+36 d \sqrt{e} x^{2/3} \log \left(d+\frac{e}{x^{2/3}}\right)+9 (-d)^{3/2} x \log ^2\left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right)+9 \sqrt{-d} d x \log ^2\left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right)+8 e^{3/2}+96 d^{3/2} x \tan ^{-1}\left(\frac{\sqrt{e}}{\sqrt{d} \sqrt[3]{x}}\right)+18 \sqrt{-d} d x \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) \log \left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)+18 (-d)^{3/2} x \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \log \left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right)+36 (-d)^{3/2} x \log \left(\sqrt[3]{x} \sqrt{-d}+\sqrt{e}\right) \log \left(-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)+36 \sqrt{-d} d x \log \left(\sqrt{e}-\sqrt{-d} \sqrt[3]{x}\right) \log \left(\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)+36 \sqrt{-d} d x \text{Li}_2\left(1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)+18 (-d)^{3/2} x \text{Li}_2\left(\frac{1}{2}-\frac{\sqrt{-d} \sqrt[3]{x}}{2 \sqrt{e}}\right)+18 \sqrt{-d} d x \text{Li}_2\left(\frac{1}{2} \left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)\right)+36 (-d)^{3/2} x \text{Li}_2\left(\frac{\sqrt[3]{x} \sqrt{-d}}{\sqrt{e}}+1\right)-96 d \sqrt{e} x^{2/3}\right) n^2}{3 e^{3/2} x}-\frac{6 b d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right) \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 n}{e^{3/2}}-\frac{3 b \log \left(d+\frac{e}{x^{2/3}}\right) \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 n}{x}-\frac{6 b d \left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 n}{e \sqrt[3]{x}}-\frac{\left(a-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 \left(a-2 b n-b n \log \left(d+\frac{e}{x^{2/3}}\right)+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{x}","-\frac{2 b d^2 n \text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x^{2/3} \left(d x^{2/3}+e\right)},x\right)}{e}+\frac{32 b^2 d^{3/2} n^2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{e^{3/2}}+\frac{32 b^2 d n^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{e \sqrt[3]{x}}-\frac{8 b^2 n^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{3 x}-\frac{6 b d n \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{e \sqrt[3]{x}}+\frac{2 b n \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x}-\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{x}-\frac{32 i b^3 d^{3/2} n^3 \text{Li}_2\left(\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}-1\right)}{e^{3/2}}-\frac{32 i b^3 d^{3/2} n^3 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)^2}{e^{3/2}}-\frac{208 b^3 d^{3/2} n^3 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{3 e^{3/2}}+\frac{64 b^3 d^{3/2} n^3 \log \left(2-\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{e^{3/2}}-\frac{208 b^3 d n^3}{3 e \sqrt[3]{x}}+\frac{16 b^3 n^3}{9 x}",0,"(b^3*n^3*(18*(e + d*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1, 1, 1}, {2, 2, 2, 2}, 1 + e/(d*x^(2/3))] - Log[d + e/x^(2/3)]*(18*(e + d*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))] + Log[d + e/x^(2/3)]*(-9*(e + d*x^(2/3))*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, 1 + e/(d*x^(2/3))] + 2*(e*Sqrt[-(e/(d*x^(2/3)))] + d*x^(2/3))*Log[d + e/x^(2/3)]))))/(2*e*Sqrt[-(e/(d*x^(2/3)))]*x) - (6*b*d*n*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/(e*x^(1/3)) - (6*b*d^(3/2)*n*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/e^(3/2) - (3*b*n*Log[d + e/x^(2/3)]*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/x - ((a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2*(a - 2*b*n - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n]))/x + (b^2*n^2*(-a + b*n*Log[d + e/x^(2/3)] - b*Log[c*(d + e/x^(2/3))^n])*(8*e^(3/2) - 96*d*Sqrt[e]*x^(2/3) + 96*d^(3/2)*x*ArcTan[Sqrt[e]/(Sqrt[d]*x^(1/3))] - 12*e^(3/2)*Log[d + e/x^(2/3)] + 36*d*Sqrt[e]*x^(2/3)*Log[d + e/x^(2/3)] + 9*e^(3/2)*Log[d + e/x^(2/3)]^2 + 18*Sqrt[-d]*d*x*Log[d + e/x^(2/3)]*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] + 9*(-d)^(3/2)*x*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]^2 + 18*(-d)^(3/2)*x*Log[d + e/x^(2/3)]*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] + 9*Sqrt[-d]*d*x*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]^2 + 18*Sqrt[-d]*d*x*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] + 18*(-d)^(3/2)*x*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] + 36*(-d)^(3/2)*x*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[-((Sqrt[-d]*x^(1/3))/Sqrt[e])] + 36*Sqrt[-d]*d*x*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(Sqrt[-d]*x^(1/3))/Sqrt[e]] + 36*Sqrt[-d]*d*x*PolyLog[2, 1 - (Sqrt[-d]*x^(1/3))/Sqrt[e]] + 18*(-d)^(3/2)*x*PolyLog[2, 1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] + 18*Sqrt[-d]*d*x*PolyLog[2, (1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] + 36*(-d)^(3/2)*x*PolyLog[2, 1 + (Sqrt[-d]*x^(1/3))/Sqrt[e]]))/(3*e^(3/2)*x)","B",1
531,1,2726,784,8.7050093,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^n])^3/x^4,x]","\text{Result too large to show}","\frac{2 b d^5 n \text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x^{2/3} \left(d x^{2/3}+e\right)},x\right)}{3 e^4}-\frac{4504 b^2 d^{9/2} n^2 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{315 e^{9/2}}-\frac{4504 b^2 d^4 n^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{315 e^4 \sqrt[3]{x}}+\frac{1984 b^2 d^3 n^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{945 e^3 x}-\frac{1144 b^2 d^2 n^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{1575 e^2 x^{5/3}}+\frac{128 b^2 d n^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{441 e x^{7/3}}-\frac{8 b^2 n^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)}{81 x^3}+\frac{2 b d^4 n \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{e^4 \sqrt[3]{x}}-\frac{2 b d^3 n \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{3 e^3 x}+\frac{2 b d^2 n \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{5 e^2 x^{5/3}}-\frac{2 b d n \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{7 e x^{7/3}}-\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{3 x^3}+\frac{2 b n \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{9 x^3}+\frac{4504 i b^3 d^{9/2} n^3 \text{Li}_2\left(\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}-1\right)}{315 e^{9/2}}+\frac{4504 i b^3 d^{9/2} n^3 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)^2}{315 e^{9/2}}+\frac{3475504 b^3 d^{9/2} n^3 \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{99225 e^{9/2}}-\frac{9008 b^3 d^{9/2} n^3 \log \left(2-\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\right) \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{315 e^{9/2}}+\frac{3475504 b^3 d^4 n^3}{99225 e^4 \sqrt[3]{x}}-\frac{637984 b^3 d^3 n^3}{297675 e^3 x}+\frac{221344 b^3 d^2 n^3}{496125 e^2 x^{5/3}}-\frac{3088 b^3 d n^3}{27783 e x^{7/3}}+\frac{16 b^3 n^3}{729 x^3}",0,"(b^3*n^3*(32*e^4*Sqrt[-(e/(d*x^(2/3)))] - 32*d^4*x^(8/3) - 1584*d^3*e*x^2*HypergeometricPFQ[{-7/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))] - 1584*d^4*x^(8/3)*HypergeometricPFQ[{-7/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))] + 4536*d^3*e*x^2*HypergeometricPFQ[{-5/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))] + 4536*d^4*x^(8/3)*HypergeometricPFQ[{-5/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))] - 3780*d^3*e*x^2*HypergeometricPFQ[{-3/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))] - 3780*d^4*x^(8/3)*HypergeometricPFQ[{-3/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))] + 864*d^3*e*x^2*HypergeometricPFQ[{-7/2, 1, 1, 1, 1}, {2, 2, 2, 2}, 1 + e/(d*x^(2/3))] + 864*d^4*x^(8/3)*HypergeometricPFQ[{-7/2, 1, 1, 1, 1}, {2, 2, 2, 2}, 1 + e/(d*x^(2/3))] - 3024*d^3*e*x^2*HypergeometricPFQ[{-5/2, 1, 1, 1, 1}, {2, 2, 2, 2}, 1 + e/(d*x^(2/3))] - 3024*d^4*x^(8/3)*HypergeometricPFQ[{-5/2, 1, 1, 1, 1}, {2, 2, 2, 2}, 1 + e/(d*x^(2/3))] + 3780*d^3*e*x^2*HypergeometricPFQ[{-3/2, 1, 1, 1, 1}, {2, 2, 2, 2}, 1 + e/(d*x^(2/3))] + 3780*d^4*x^(8/3)*HypergeometricPFQ[{-3/2, 1, 1, 1, 1}, {2, 2, 2, 2}, 1 + e/(d*x^(2/3))] - 1890*d^3*e*x^2*HypergeometricPFQ[{-1/2, 1, 1, 1, 1}, {2, 2, 2, 2}, 1 + e/(d*x^(2/3))] - 1890*d^4*x^(8/3)*HypergeometricPFQ[{-1/2, 1, 1, 1, 1}, {2, 2, 2, 2}, 1 + e/(d*x^(2/3))] - (288*e^4*Log[d + e/x^(2/3)])/Sqrt[-(e/(d*x^(2/3)))] + 48*e^4*Sqrt[-(e/(d*x^(2/3)))]*Log[d + e/x^(2/3)] + 240*d^4*x^(8/3)*Log[d + e/x^(2/3)] + 3780*d^3*e*x^2*HypergeometricPFQ[{-3/2, 1, 1}, {2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)] + 3780*d^4*x^(8/3)*HypergeometricPFQ[{-3/2, 1, 1}, {2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)] - 864*d^3*e*x^2*HypergeometricPFQ[{-7/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)] - 864*d^4*x^(8/3)*HypergeometricPFQ[{-7/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)] + 3024*d^3*e*x^2*HypergeometricPFQ[{-5/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)] + 3024*d^4*x^(8/3)*HypergeometricPFQ[{-5/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)] - 3780*d^3*e*x^2*HypergeometricPFQ[{-3/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)] - 3780*d^4*x^(8/3)*HypergeometricPFQ[{-3/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)] + 1890*d^3*e*x^2*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)] + 1890*d^4*x^(8/3)*HypergeometricPFQ[{-1/2, 1, 1, 1}, {2, 2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)] + (252*e^4*Log[d + e/x^(2/3)]^2)/(-(e/(d*x^(2/3))))^(3/2) - (36*e^4*Log[d + e/x^(2/3)]^2)/Sqrt[-(e/(d*x^(2/3)))] + 68*e^4*Sqrt[-(e/(d*x^(2/3)))]*Log[d + e/x^(2/3)]^2 - 284*d^4*x^(8/3)*Log[d + e/x^(2/3)]^2 + 1890*d^3*e*x^2*HypergeometricPFQ[{-3/2, 1, 1}, {2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)]^2 + 1890*d^4*x^(8/3)*HypergeometricPFQ[{-3/2, 1, 1}, {2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)]^2 - 945*d^3*e*x^2*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)]^2 - 945*d^4*x^(8/3)*HypergeometricPFQ[{-1/2, 1, 1}, {2, 2}, 1 + e/(d*x^(2/3))]*Log[d + e/x^(2/3)]^2 - 70*e^4*Sqrt[-(e/(d*x^(2/3)))]*Log[d + e/x^(2/3)]^3 + 70*d^4*x^(8/3)*Log[d + e/x^(2/3)]^3 - 1512*d^3*(e + d*x^(2/3))*x^2*HypergeometricPFQ[{-5/2, 1, 1}, {2, 2}, 1 + e/(d*x^(2/3))]*(1 + 3*Log[d + e/x^(2/3)] + Log[d + e/x^(2/3)]^2) + 144*d^3*(e + d*x^(2/3))*x^2*HypergeometricPFQ[{-7/2, 1, 1}, {2, 2}, 1 + e/(d*x^(2/3))]*(6 + 11*Log[d + e/x^(2/3)] + 3*Log[d + e/x^(2/3)]^2)))/(210*e^4*Sqrt[-(e/(d*x^(2/3)))]*x^3) - (2*b*d*n*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/(7*e*x^(7/3)) + (2*b*d^2*n*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/(5*e^2*x^(5/3)) - (2*b*d^3*n*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/(3*e^3*x) + (2*b*d^4*n*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/(e^4*x^(1/3)) + (2*b*d^(9/2)*n*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/e^(9/2) - (b*n*Log[d + e/x^(2/3)]*(a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2)/x^3 - ((a - b*n*Log[d + e/x^(2/3)] + b*Log[c*(d + e/x^(2/3))^n])^2*(3*a - 2*b*n - 3*b*n*Log[d + e/x^(2/3)] + 3*b*Log[c*(d + e/x^(2/3))^n]))/(9*x^3) + (b^2*n^2*(-a + b*n*Log[d + e/x^(2/3)] - b*Log[c*(d + e/x^(2/3))^n])*(9800*e^(9/2) - 28800*d*e^(7/2)*x^(2/3) + 72072*d^2*e^(5/2)*x^(4/3) - 208320*d^3*e^(3/2)*x^2 + 1418760*d^4*Sqrt[e]*x^(8/3) - 1418760*d^(9/2)*x^3*ArcTan[Sqrt[e]/(Sqrt[d]*x^(1/3))] - 44100*e^(9/2)*Log[d + e/x^(2/3)] + 56700*d*e^(7/2)*x^(2/3)*Log[d + e/x^(2/3)] - 79380*d^2*e^(5/2)*x^(4/3)*Log[d + e/x^(2/3)] + 132300*d^3*e^(3/2)*x^2*Log[d + e/x^(2/3)] - 396900*d^4*Sqrt[e]*x^(8/3)*Log[d + e/x^(2/3)] + 99225*e^(9/2)*Log[d + e/x^(2/3)]^2 - 198450*(-d)^(9/2)*x^3*Log[d + e/x^(2/3)]*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)] + 99225*(-d)^(9/2)*x^3*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]^2 + 198450*(-d)^(9/2)*x^3*Log[d + e/x^(2/3)]*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)] - 99225*(-d)^(9/2)*x^3*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]^2 - 198450*(-d)^(9/2)*x^3*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] + 198450*(-d)^(9/2)*x^3*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] + 396900*(-d)^(9/2)*x^3*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[-((Sqrt[-d]*x^(1/3))/Sqrt[e])] - 396900*(-d)^(9/2)*x^3*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(Sqrt[-d]*x^(1/3))/Sqrt[e]] - 396900*(-d)^(9/2)*x^3*PolyLog[2, 1 - (Sqrt[-d]*x^(1/3))/Sqrt[e]] + 198450*(-d)^(9/2)*x^3*PolyLog[2, 1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])] - 198450*(-d)^(9/2)*x^3*PolyLog[2, (1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2] + 396900*(-d)^(9/2)*x^3*PolyLog[2, 1 + (Sqrt[-d]*x^(1/3))/Sqrt[e]]))/(99225*e^(9/2)*x^3)","B",1
532,1,435,730,1.0170814,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \, dx","Integrate[x^3*(a + b*Log[c*(d + e*Sqrt[x])])^p,x]","\frac{2^{-3 p-2} 105^{-p} e^{-\frac{8 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \left(c^7 d^7 \left(-8^{p+1}\right) 105^p e^{\frac{7 a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)+c^6 d^6 15^p 28^{p+1} e^{\frac{6 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)-c^5 d^5 5^p 56^{p+1} e^{\frac{5 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)+c^4 d^4 3^p 70^{p+1} e^{\frac{4 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)-c^3 d^3 3^p 56^{p+1} e^{\frac{3 a}{b}} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)+c^2 d^2 5^p 28^{p+1} e^{\frac{2 a}{b}} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)-c d 8^{p+1} 15^p e^{a/b} \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)+105^p \Gamma \left(p+1,-\frac{8 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)\right)}{c^8 e^8}","\frac{2^{-3 p-2} e^{-\frac{8 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{8 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^8 e^8}-\frac{2 d 7^{-p} e^{-\frac{7 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^7 e^8}+\frac{7 d^2 6^{-p} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^6 e^8}-\frac{14 d^3 5^{-p} e^{-\frac{5 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^5 e^8}+\frac{35 d^4 2^{-2 p-1} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^4 e^8}-\frac{14 d^5 3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^3 e^8}+\frac{7 d^6 2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^2 e^8}-\frac{2 d^7 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)}{c e^8}",1,"(2^(-2 - 3*p)*(105^p*Gamma[1 + p, (-8*(a + b*Log[c*(d + e*Sqrt[x])]))/b] - 8^(1 + p)*15^p*c*d*E^(a/b)*Gamma[1 + p, (-7*(a + b*Log[c*(d + e*Sqrt[x])]))/b] + 5^p*28^(1 + p)*c^2*d^2*E^((2*a)/b)*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*Sqrt[x])]))/b] - 3^p*56^(1 + p)*c^3*d^3*E^((3*a)/b)*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*Sqrt[x])]))/b] + 3^p*70^(1 + p)*c^4*d^4*E^((4*a)/b)*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*Sqrt[x])]))/b] - 5^p*56^(1 + p)*c^5*d^5*E^((5*a)/b)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*Sqrt[x])]))/b] + 15^p*28^(1 + p)*c^6*d^6*E^((6*a)/b)*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*Sqrt[x])]))/b] - 8^(1 + p)*105^p*c^7*d^7*E^((7*a)/b)*Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])])/b)])*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(105^p*c^8*e^8*E^((8*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p)","A",1
533,1,325,551,0.8964416,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \, dx","Integrate[x^2*(a + b*Log[c*(d + e*Sqrt[x])])^p,x]","\frac{3^{-p-1} 20^{-p} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \left(10^p \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)-c d e^{a/b} \left(2^{2 p+1} 3^{p+1} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)+c d 5^p e^{a/b} \left(c d 2^p e^{a/b} \left(5\ 2^{p+2} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)+c d 3^{p+1} e^{a/b} \left(c d 2^{p+1} e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)-5 \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)\right)\right)-5\ 3^{p+1} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)\right)\right)\right)}{c^6 e^6}","\frac{2^{-p} 3^{-p-1} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^6 e^6}-\frac{2 d 5^{-p} e^{-\frac{5 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^5 e^6}+\frac{5 d^2 4^{-p} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^4 e^6}-\frac{20 d^3 3^{-p-1} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^3 e^6}+\frac{5 d^4 2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^2 e^6}-\frac{2 d^5 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)}{c e^6}",1,"(3^(-1 - p)*(10^p*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*Sqrt[x])]))/b] - c*d*E^(a/b)*(2^(1 + 2*p)*3^(1 + p)*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*Sqrt[x])]))/b] + 5^p*c*d*E^(a/b)*(-5*3^(1 + p)*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*Sqrt[x])]))/b] + 2^p*c*d*E^(a/b)*(5*2^(2 + p)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*Sqrt[x])]))/b] + 3^(1 + p)*c*d*E^(a/b)*(-5*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*Sqrt[x])]))/b] + 2^(1 + p)*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])])/b)])))))*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(20^p*c^6*e^6*E^((6*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p)","A",1
534,1,229,360,0.4341856,"\int x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e*Sqrt[x])])^p,x]","\frac{2^{-2 p-1} 3^{-p} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \left(3^p \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)-c d 2^{p+1} e^{a/b} \left(2^{p+1} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)+c d 3^p e^{a/b} \left(c d 2^{p+1} e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)-3 \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)\right)\right)\right)}{c^4 e^4}","\frac{2^{-2 p-1} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^4 e^4}-\frac{2 d 3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^3 e^4}+\frac{3 d^2 2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^2 e^4}-\frac{2 d^3 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)}{c e^4}",1,"(2^(-1 - 2*p)*(3^p*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*Sqrt[x])]))/b] - 2^(1 + p)*c*d*E^(a/b)*(2^(1 + p)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*Sqrt[x])]))/b] + 3^p*c*d*E^(a/b)*(-3*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*Sqrt[x])]))/b] + 2^(1 + p)*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])])/b)])))*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(3^p*c^4*e^4*E^((4*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p)","A",1
535,1,130,174,0.1294315,"\int \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])])^p,x]","\frac{2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \left(\Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)-c d 2^{p+1} e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)\right)}{c^2 e^2}","\frac{2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)}{b}\right)}{c^2 e^2}-\frac{2 d e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)}{c e^2}",1,"((Gamma[1 + p, (-2*(a + b*Log[c*(d + e*Sqrt[x])]))/b] - 2^(1 + p)*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])])/b)])*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(2^p*c^2*e^2*E^((2*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p)","A",1
536,0,0,25,0.2722844,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e*Sqrt[x])])^p/x, x]","A",-1
537,0,0,25,0.5015291,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])])^p/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p}{x^2},x\right)",0,"Integrate[(a + b*Log[c*(d + e*Sqrt[x])])^p/x^2, x]","A",-1
538,0,0,907,0.5678678,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","Integrate[x^3*(a + b*Log[c*(d + e*Sqrt[x])^2])^p,x]","\int x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","\frac{2^{-2 (p+1)} e^{-\frac{4 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p}}{c^4 e^8}-\frac{2^{p+1} 7^{-p} d e^{-\frac{7 a}{2 b}} \left(d+e \sqrt{x}\right)^7 \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p}}{e^8 \left(c \left(d+e \sqrt{x}\right)^2\right)^{7/2}}+\frac{7\ 3^{-p} d^2 e^{-\frac{3 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p}}{c^3 e^8}-\frac{7\ 2^{p+1} 5^{-p} d^3 e^{-\frac{5 a}{2 b}} \left(d+e \sqrt{x}\right)^5 \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p}}{e^8 \left(c \left(d+e \sqrt{x}\right)^2\right)^{5/2}}+\frac{35\ 2^{-p-1} d^4 e^{-\frac{2 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p}}{c^2 e^8}-\frac{7\ 2^{p+1} 3^{-p} d^5 e^{-\frac{3 a}{2 b}} \left(d+e \sqrt{x}\right)^3 \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p}}{e^8 \left(c \left(d+e \sqrt{x}\right)^2\right)^{3/2}}+\frac{7 d^6 e^{-\frac{a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p}}{c e^8}-\frac{2^{p+1} d^7 e^{-\frac{a}{2 b}} \left(d+e \sqrt{x}\right) \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p}}{e^8 \sqrt{c \left(d+e \sqrt{x}\right)^2}}",1,"Integrate[x^3*(a + b*Log[c*(d + e*Sqrt[x])^2])^p, x]","F",-1
539,0,0,677,0.3868545,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","Integrate[x^2*(a + b*Log[c*(d + e*Sqrt[x])^2])^p,x]","\int x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","\frac{3^{-p-1} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{b}\right)}{c^3 e^6}+\frac{5 d^2 2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{b}\right)}{c^2 e^6}-\frac{d^5 2^{p+1} e^{-\frac{a}{2 b}} \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{2 b}\right)}{e^6 \sqrt{c \left(d+e \sqrt{x}\right)^2}}+\frac{5 d^4 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)}{c e^6}-\frac{5 d^3 2^{p+2} 3^{-p-1} e^{-\frac{3 a}{2 b}} \left(d+e \sqrt{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{2 b}\right)}{e^6 \left(c \left(d+e \sqrt{x}\right)^2\right)^{3/2}}-\frac{d 2^{p+1} 5^{-p} e^{-\frac{5 a}{2 b}} \left(d+e \sqrt{x}\right)^5 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{2 b}\right)}{e^6 \left(c \left(d+e \sqrt{x}\right)^2\right)^{5/2}}",1,"Integrate[x^2*(a + b*Log[c*(d + e*Sqrt[x])^2])^p, x]","F",-1
540,0,0,445,0.2486848,"\int x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e*Sqrt[x])^2])^p,x]","\int x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","\frac{2^{-p-1} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{b}\right)}{c^2 e^4}-\frac{d^3 2^{p+1} e^{-\frac{a}{2 b}} \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{2 b}\right)}{e^4 \sqrt{c \left(d+e \sqrt{x}\right)^2}}+\frac{3 d^2 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)}{c e^4}-\frac{d 2^{p+1} 3^{-p} e^{-\frac{3 a}{2 b}} \left(d+e \sqrt{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)}{2 b}\right)}{e^4 \left(c \left(d+e \sqrt{x}\right)^2\right)^{3/2}}",1,"Integrate[x*(a + b*Log[c*(d + e*Sqrt[x])^2])^p, x]","F",-1
541,0,0,213,0.1242841,"\int \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^2])^p,x]","\int \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","\frac{e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)}{c e^2}-\frac{d 2^{p+1} e^{-\frac{a}{2 b}} \left(d+e \sqrt{x}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{2 b}\right)}{e^2 \sqrt{c \left(d+e \sqrt{x}\right)^2}}",1,"Integrate[(a + b*Log[c*(d + e*Sqrt[x])^2])^p, x]","F",-1
542,0,0,27,0.12003,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^2])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e*Sqrt[x])^2])^p/x, x]","A",-1
543,0,0,27,0.1189675,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*Sqrt[x])^2])^p/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p}{x^2},x\right)",0,"Integrate[(a + b*Log[c*(d + e*Sqrt[x])^2])^p/x^2, x]","A",-1
544,0,0,23,1.1630233,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e/Sqrt[x])])^p,x]","\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \, dx","\text{Int}\left(x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p,x\right)",0,"Integrate[x*(a + b*Log[c*(d + e/Sqrt[x])])^p, x]","A",-1
545,0,0,21,0.2444406,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])])^p,x]","\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \, dx","\text{Int}\left(\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p,x\right)",0,"Integrate[(a + b*Log[c*(d + e/Sqrt[x])])^p, x]","A",-1
546,0,0,25,0.3305973,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e/Sqrt[x])])^p/x, x]","A",-1
547,1,131,175,0.1760652,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])])^p/x^2,x]","\frac{2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p} \left(c d 2^{p+1} e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)-\Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)\right)}{c^2 e^2}","\frac{2 d e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)}{c e^2}-\frac{2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)}{c^2 e^2}",1,"((-Gamma[1 + p, (-2*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + 2^(1 + p)*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e/Sqrt[x])])/b)])*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(2^p*c^2*e^2*E^((2*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p)","A",1
548,1,325,552,0.7922861,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])])^p/x^4,x]","\frac{3^{-p-1} 20^{-p} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p} \left(c d e^{a/b} \left(2^{2 p+1} 3^{p+1} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)+c d 5^p e^{a/b} \left(c d 2^p e^{a/b} \left(5\ 2^{p+2} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)+c d 3^{p+1} e^{a/b} \left(c d 2^{p+1} e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)-5 \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)\right)\right)-5\ 3^{p+1} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)\right)\right)-10^p \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)\right)}{c^6 e^6}","-\frac{2^{-p} 3^{-p-1} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)}{c^6 e^6}+\frac{2 d 5^{-p} e^{-\frac{5 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)}{c^5 e^6}-\frac{5 d^2 4^{-p} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)}{c^4 e^6}+\frac{20 d^3 3^{-p-1} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)}{c^3 e^6}-\frac{5 d^4 2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)}{c^2 e^6}+\frac{2 d^5 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)}{c e^6}",1,"(3^(-1 - p)*(-(10^p*Gamma[1 + p, (-6*(a + b*Log[c*(d + e/Sqrt[x])]))/b]) + c*d*E^(a/b)*(2^(1 + 2*p)*3^(1 + p)*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + 5^p*c*d*E^(a/b)*(-5*3^(1 + p)*Gamma[1 + p, (-4*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + 2^p*c*d*E^(a/b)*(5*2^(2 + p)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + 3^(1 + p)*c*d*E^(a/b)*(-5*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + 2^(1 + p)*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e/Sqrt[x])])/b)])))))*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(20^p*c^6*e^6*E^((6*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p)","A",1
549,1,525,926,3.3134335,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p}{x^6} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])])^p/x^6,x]","\frac{5^{-p-1} 504^{-p} e^{-\frac{10 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p} \left(c d e^{a/b} \left(2^{3 p+1} 5^{p+1} 7^p \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)+c d e^{a/b} \left(c d 2^p e^{a/b} \left(2^{2 p+3} 3^{2 p+1} 5^{p+1} \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)+c d 7^p e^{a/b} \left(c d e^{a/b} \left(7\ 36^{p+1} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)+c d 3^p 5^{p+1} e^{a/b} \left(c d 2^p e^{a/b} \left(3\ 2^{p+3} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)+c d 3^p e^{a/b} \left(c d 2^{p+1} e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)-9 \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)\right)\right)-14\ 3^{p+1} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)\right)\right)-7\ 30^{p+1} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)\right)\right)-7^p 45^{p+1} \Gamma \left(p+1,-\frac{8 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)\right)\right)-252^p \Gamma \left(p+1,-\frac{10 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right)\right)}{c^{10} e^{10}}","-\frac{2^{-p} 5^{-p-1} e^{-\frac{10 a}{b}} \Gamma \left(p+1,-\frac{10 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p}}{c^{10} e^{10}}+\frac{2\ 9^{-p} d e^{-\frac{9 a}{b}} \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p}}{c^9 e^{10}}-\frac{9\ 8^{-p} d^2 e^{-\frac{8 a}{b}} \Gamma \left(p+1,-\frac{8 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p}}{c^8 e^{10}}+\frac{24\ 7^{-p} d^3 e^{-\frac{7 a}{b}} \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p}}{c^7 e^{10}}-\frac{7\ 6^{1-p} d^4 e^{-\frac{6 a}{b}} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p}}{c^6 e^{10}}+\frac{252\ 5^{-p-1} d^5 e^{-\frac{5 a}{b}} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p}}{c^5 e^{10}}-\frac{21\ 2^{1-2 p} d^6 e^{-\frac{4 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p}}{c^4 e^{10}}+\frac{8\ 3^{1-p} d^7 e^{-\frac{3 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p}}{c^3 e^{10}}-\frac{9\ 2^{-p} d^8 e^{-\frac{2 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p}}{c^2 e^{10}}+\frac{2 d^9 e^{-\frac{a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)^{-p}}{c e^{10}}",1,"(5^(-1 - p)*(-(252^p*Gamma[1 + p, (-10*(a + b*Log[c*(d + e/Sqrt[x])]))/b]) + c*d*E^(a/b)*(2^(1 + 3*p)*5^(1 + p)*7^p*Gamma[1 + p, (-9*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + c*d*E^(a/b)*(-(7^p*45^(1 + p)*Gamma[1 + p, (-8*(a + b*Log[c*(d + e/Sqrt[x])]))/b]) + 2^p*c*d*E^(a/b)*(2^(3 + 2*p)*3^(1 + 2*p)*5^(1 + p)*Gamma[1 + p, (-7*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + 7^p*c*d*E^(a/b)*(-7*30^(1 + p)*Gamma[1 + p, (-6*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + c*d*E^(a/b)*(7*36^(1 + p)*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + 3^p*5^(1 + p)*c*d*E^(a/b)*(-14*3^(1 + p)*Gamma[1 + p, (-4*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + 2^p*c*d*E^(a/b)*(3*2^(3 + p)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + 3^p*c*d*E^(a/b)*(-9*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/Sqrt[x])]))/b] + 2^(1 + p)*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e/Sqrt[x])])/b)])))))))))*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(504^p*c^10*e^10*E^((10*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p)","A",1
550,0,0,25,0.232979,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e/Sqrt[x])^2])^p,x]","\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \, dx","\text{Int}\left(x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p,x\right)",0,"Integrate[x*(a + b*Log[c*(d + e/Sqrt[x])^2])^p, x]","A",-1
551,0,0,23,0.1072808,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^2])^p,x]","\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \, dx","\text{Int}\left(\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p,x\right)",0,"Integrate[(a + b*Log[c*(d + e/Sqrt[x])^2])^p, x]","A",-1
552,0,0,27,0.1719283,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^2])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e/Sqrt[x])^2])^p/x, x]","A",-1
553,0,0,216,0.1365976,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^2])^p/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x^2} \, dx","\frac{d 2^{p+1} e^{-\frac{a}{2 b}} \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,\frac{-a-b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{2 b}\right)}{e^2 \sqrt{c \left(d+\frac{e}{\sqrt{x}}\right)^2}}-\frac{e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)}{c e^2}",1,"Integrate[(a + b*Log[c*(d + e/Sqrt[x])^2])^p/x^2, x]","F",-1
554,0,0,676,0.1440728,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^2])^p/x^4,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x^4} \, dx","-\frac{3^{-p-1} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{b}\right)}{c^3 e^6}-\frac{5 d^2 2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{b}\right)}{c^2 e^6}+\frac{d^5 2^{p+1} e^{-\frac{a}{2 b}} \left(d+\frac{e}{\sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{2 b}\right)}{e^6 \sqrt{c \left(d+\frac{e}{\sqrt{x}}\right)^2}}-\frac{5 d^4 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)}{c e^6}+\frac{5 d^3 2^{p+2} 3^{-p-1} e^{-\frac{3 a}{2 b}} \left(d+\frac{e}{\sqrt{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{2 b}\right)}{e^6 \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)^{3/2}}+\frac{d 2^{p+1} 5^{-p} e^{-\frac{5 a}{2 b}} \left(d+\frac{e}{\sqrt{x}}\right)^5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{2 b}\right)}{e^6 \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)^{5/2}}",1,"Integrate[(a + b*Log[c*(d + e/Sqrt[x])^2])^p/x^4, x]","F",-1
555,0,0,1141,0.1461845,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x^6} \, dx","Integrate[(a + b*Log[c*(d + e/Sqrt[x])^2])^p/x^6,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x^6} \, dx","-\frac{5^{-p-1} e^{-\frac{5 a}{b}} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p}}{c^5 e^{10}}+\frac{2^{p+1} 9^{-p} d e^{-\frac{9 a}{2 b}} \left(d+\frac{e}{\sqrt{x}}\right)^9 \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p}}{e^{10} \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)^{9/2}}-\frac{9\ 4^{-p} d^2 e^{-\frac{4 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p}}{c^4 e^{10}}+\frac{3\ 2^{p+3} 7^{-p} d^3 e^{-\frac{7 a}{2 b}} \left(d+\frac{e}{\sqrt{x}}\right)^7 \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p}}{e^{10} \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)^{7/2}}-\frac{14\ 3^{1-p} d^4 e^{-\frac{3 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p}}{c^3 e^{10}}+\frac{63\ 2^{p+2} 5^{-p-1} d^5 e^{-\frac{5 a}{2 b}} \left(d+\frac{e}{\sqrt{x}}\right)^5 \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p}}{e^{10} \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)^{5/2}}-\frac{21\ 2^{1-p} d^6 e^{-\frac{2 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p}}{c^2 e^{10}}+\frac{2^{p+3} 3^{1-p} d^7 e^{-\frac{3 a}{2 b}} \left(d+\frac{e}{\sqrt{x}}\right)^3 \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p}}{e^{10} \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)^{3/2}}-\frac{9 d^8 e^{-\frac{a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p}}{c e^{10}}+\frac{2^{p+1} d^9 e^{-\frac{a}{2 b}} \left(d+\frac{e}{\sqrt{x}}\right) \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{2 b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)^{-p}}{e^{10} \sqrt{c \left(d+\frac{e}{\sqrt{x}}\right)^2}}",1,"Integrate[(a + b*Log[c*(d + e/Sqrt[x])^2])^p/x^6, x]","F",-1
556,1,670,1121,2.7067117,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \, dx","Integrate[x^3*(a + b*Log[c*(d + e*x^(1/3))])^p,x]","-\frac{2^{-3 p-2} 3465^{-p} e^{-\frac{12 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \left(c^2 d^2 e^{\frac{2 a}{b}} \left(c^2 d^2 e^{\frac{2 a}{b}} \left(c^7 d^7 2^{3 p+2} 3^{2 p+1} 385^p e^{\frac{7 a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)-c^6 d^6 6^{2 p+1} 11^{p+1} 35^p e^{\frac{6 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)+c^5 d^5 2^{3 p+2} 21^p 55^{p+1} e^{\frac{5 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)-c^4 d^4 14^p 495^{p+1} e^{\frac{4 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)+c^3 d^3 7^p 792^{p+1} e^{\frac{3 a}{b}} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)-c^2 d^2 5^p 924^{p+1} e^{\frac{2 a}{b}} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)+c d 5^p 792^{p+1} e^{a/b} \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)-7^p 495^{p+1} \Gamma \left(p+1,-\frac{8 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)\right)+c d 2^{3 p+2} 7^p 55^{p+1} e^{a/b} \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)-6^{2 p+1} 7^p 11^{p+1} \Gamma \left(p+1,-\frac{10 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)\right)+c d 2^{3 p+2} 3^{2 p+1} 35^p e^{a/b} \Gamma \left(p+1,-\frac{11 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)-2310^p \Gamma \left(p+1,-\frac{12 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)\right)}{c^{12} e^{12}}","\frac{3^{-p} 4^{-p-1} e^{-\frac{12 a}{b}} \Gamma \left(p+1,-\frac{12 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^{12} e^{12}}-\frac{3\ 11^{-p} d e^{-\frac{11 a}{b}} \Gamma \left(p+1,-\frac{11 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^{11} e^{12}}+\frac{33\ 2^{-p-1} 5^{-p} d^2 e^{-\frac{10 a}{b}} \Gamma \left(p+1,-\frac{10 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^{10} e^{12}}-\frac{55\ 9^{-p} d^3 e^{-\frac{9 a}{b}} \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^9 e^{12}}+\frac{495\ 2^{-3 p-2} d^4 e^{-\frac{8 a}{b}} \Gamma \left(p+1,-\frac{8 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^8 e^{12}}-\frac{198\ 7^{-p} d^5 e^{-\frac{7 a}{b}} \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^7 e^{12}}+\frac{77\ 2^{-p} 3^{1-p} d^6 e^{-\frac{6 a}{b}} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^6 e^{12}}-\frac{198\ 5^{-p} d^7 e^{-\frac{5 a}{b}} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^5 e^{12}}+\frac{495\ 4^{-p-1} d^8 e^{-\frac{4 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^4 e^{12}}-\frac{55\ 3^{-p} d^9 e^{-\frac{3 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^3 e^{12}}+\frac{33\ 2^{-p-1} d^{10} e^{-\frac{2 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^2 e^{12}}-\frac{3 d^{11} e^{-\frac{a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c e^{12}}",1,"-((2^(-2 - 3*p)*(-(2310^p*Gamma[1 + p, (-12*(a + b*Log[c*(d + e*x^(1/3))]))/b]) + 2^(2 + 3*p)*3^(1 + 2*p)*35^p*c*d*E^(a/b)*Gamma[1 + p, (-11*(a + b*Log[c*(d + e*x^(1/3))]))/b] + c^2*d^2*E^((2*a)/b)*(-(6^(1 + 2*p)*7^p*11^(1 + p)*Gamma[1 + p, (-10*(a + b*Log[c*(d + e*x^(1/3))]))/b]) + 2^(2 + 3*p)*7^p*55^(1 + p)*c*d*E^(a/b)*Gamma[1 + p, (-9*(a + b*Log[c*(d + e*x^(1/3))]))/b] + c^2*d^2*E^((2*a)/b)*(-(7^p*495^(1 + p)*Gamma[1 + p, (-8*(a + b*Log[c*(d + e*x^(1/3))]))/b]) + 5^p*792^(1 + p)*c*d*E^(a/b)*Gamma[1 + p, (-7*(a + b*Log[c*(d + e*x^(1/3))]))/b] - 5^p*924^(1 + p)*c^2*d^2*E^((2*a)/b)*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 7^p*792^(1 + p)*c^3*d^3*E^((3*a)/b)*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(1/3))]))/b] - 14^p*495^(1 + p)*c^4*d^4*E^((4*a)/b)*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 2^(2 + 3*p)*21^p*55^(1 + p)*c^5*d^5*E^((5*a)/b)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))]))/b] - 6^(1 + 2*p)*11^(1 + p)*35^p*c^6*d^6*E^((6*a)/b)*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 2^(2 + 3*p)*3^(1 + 2*p)*385^p*c^7*d^7*E^((7*a)/b)*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))])/b)])))*(a + b*Log[c*(d + e*x^(1/3))])^p)/(3465^p*c^12*e^12*E^((12*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p))","A",1
557,1,501,831,1.0008207,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \, dx","Integrate[x^2*(a + b*Log[c*(d + e*x^(1/3))])^p,x]","\frac{3^{-2 p-1} 280^{-p} e^{-\frac{9 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \left(c^8 d^8 9^{p+1} 280^p e^{\frac{8 a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)-c^7 d^7 35^p 36^{p+1} e^{\frac{7 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)+c^6 d^6 2^{3 p+2} 5^p 21^{p+1} e^{\frac{6 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)-c^5 d^5 5^p 126^{p+1} e^{\frac{5 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)+c^4 d^4 2^{3 p+1} 63^{p+1} e^{\frac{4 a}{b}} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)-c^3 d^3 5^p 84^{p+1} e^{\frac{3 a}{b}} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)+c^2 d^2 2^{3 p+2} 5^p 9^{p+1} e^{\frac{2 a}{b}} \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)-c d 9^{p+1} 35^p e^{a/b} \Gamma \left(p+1,-\frac{8 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)+280^p \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)\right)}{c^9 e^9}","\frac{3^{-2 p-1} e^{-\frac{9 a}{b}} \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^9 e^9}-\frac{3\ 8^{-p} d e^{-\frac{8 a}{b}} \Gamma \left(p+1,-\frac{8 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^8 e^9}+\frac{12\ 7^{-p} d^2 e^{-\frac{7 a}{b}} \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^7 e^9}-\frac{7\ 2^{2-p} 3^{-p} d^3 e^{-\frac{6 a}{b}} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^6 e^9}+\frac{42\ 5^{-p} d^4 e^{-\frac{5 a}{b}} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^5 e^9}-\frac{21\ 2^{1-2 p} d^5 e^{-\frac{4 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^4 e^9}+\frac{28\ 3^{-p} d^6 e^{-\frac{3 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^3 e^9}-\frac{3\ 2^{2-p} d^7 e^{-\frac{2 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c^2 e^9}+\frac{3 d^8 e^{-\frac{a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p}}{c e^9}",1,"(3^(-1 - 2*p)*(280^p*Gamma[1 + p, (-9*(a + b*Log[c*(d + e*x^(1/3))]))/b] - 9^(1 + p)*35^p*c*d*E^(a/b)*Gamma[1 + p, (-8*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 2^(2 + 3*p)*5^p*9^(1 + p)*c^2*d^2*E^((2*a)/b)*Gamma[1 + p, (-7*(a + b*Log[c*(d + e*x^(1/3))]))/b] - 5^p*84^(1 + p)*c^3*d^3*E^((3*a)/b)*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 2^(1 + 3*p)*63^(1 + p)*c^4*d^4*E^((4*a)/b)*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(1/3))]))/b] - 5^p*126^(1 + p)*c^5*d^5*E^((5*a)/b)*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 2^(2 + 3*p)*5^p*21^(1 + p)*c^6*d^6*E^((6*a)/b)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))]))/b] - 35^p*36^(1 + p)*c^7*d^7*E^((7*a)/b)*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 9^(1 + p)*280^p*c^8*d^8*E^((8*a)/b)*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))])/b)])*(a + b*Log[c*(d + e*x^(1/3))])^p)/(280^p*c^9*e^9*E^((9*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p)","A",1
558,1,325,553,0.9506401,"\int x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e*x^(1/3))])^p,x]","\frac{2^{-2 p-1} 15^{-p} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \left(10^p \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)-c d e^{a/b} \left(2^{2 p+1} 3^{p+1} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)+c d 5^p e^{a/b} \left(c d 2^p e^{a/b} \left(5\ 2^{p+2} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)+c d 3^{p+1} e^{a/b} \left(c d 2^{p+1} e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)-5 \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)\right)\right)-5\ 3^{p+1} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)\right)\right)\right)}{c^6 e^6}","\frac{2^{-p-1} 3^{-p} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)}{c^6 e^6}-\frac{3 d 5^{-p} e^{-\frac{5 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)}{c^5 e^6}+\frac{15 d^2 2^{-2 p-1} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)}{c^4 e^6}-\frac{10 d^3 3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)}{c^3 e^6}+\frac{15 d^4 2^{-p-1} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)}{c^2 e^6}-\frac{3 d^5 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)}{c e^6}",1,"(2^(-1 - 2*p)*(10^p*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*x^(1/3))]))/b] - c*d*E^(a/b)*(2^(1 + 2*p)*3^(1 + p)*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 5^p*c*d*E^(a/b)*(-5*3^(1 + p)*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 2^p*c*d*E^(a/b)*(5*2^(2 + p)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 3^(1 + p)*c*d*E^(a/b)*(-5*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 2^(1 + p)*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))])/b)])))))*(a + b*Log[c*(d + e*x^(1/3))])^p)/(15^p*c^6*e^6*E^((6*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p)","A",1
559,1,174,266,0.2063033,"\int \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))])^p,x]","\frac{6^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \left(2^p \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)+c d 3^{p+1} e^{a/b} \left(c d 2^p e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)-\Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)\right)\right)}{c^3 e^3}","\frac{3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)}{c^3 e^3}-\frac{3 d 2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)}{b}\right)}{c^2 e^3}+\frac{3 d^2 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)}{c e^3}",1,"((2^p*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 3^(1 + p)*c*d*E^(a/b)*(-Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(1/3))]))/b] + 2^p*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))])/b)]))*(a + b*Log[c*(d + e*x^(1/3))])^p)/(6^p*c^3*e^3*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p)","A",1
560,0,0,25,0.2610458,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(1/3))])^p/x, x]","A",-1
561,0,0,25,0.6217024,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))])^p/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p}{x^2},x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(1/3))])^p/x^2, x]","A",-1
562,0,0,1363,0.7073636,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","Integrate[x^3*(a + b*Log[c*(d + e*x^(1/3))^2])^p,x]","\int x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","\frac{2^{-p-2} 3^{-p} e^{-\frac{6 a}{b}} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{c^6 e^{12}}-\frac{3 \left(\frac{2}{11}\right)^p d e^{-\frac{11 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^{11} \Gamma \left(p+1,-\frac{11 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{e^{12} \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{11/2}}+\frac{33\ 5^{-p} d^2 e^{-\frac{5 a}{b}} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{2 c^5 e^{12}}-\frac{55 \left(\frac{2}{9}\right)^p d^3 e^{-\frac{9 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^9 \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{e^{12} \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{9/2}}+\frac{495\ 2^{-2 (p+1)} d^4 e^{-\frac{4 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{c^4 e^{12}}-\frac{99\ 2^{p+1} 7^{-p} d^5 e^{-\frac{7 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^7 \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{e^{12} \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{7/2}}+\frac{77\ 3^{1-p} d^6 e^{-\frac{3 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{c^3 e^{12}}-\frac{99\ 2^{p+1} 5^{-p} d^7 e^{-\frac{5 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^5 \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{e^{12} \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{5/2}}+\frac{495\ 2^{-p-2} d^8 e^{-\frac{2 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{c^2 e^{12}}-\frac{55 \left(\frac{2}{3}\right)^p d^9 e^{-\frac{3 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^3 \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{e^{12} \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{3/2}}+\frac{33 d^{10} e^{-\frac{a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{2 c e^{12}}-\frac{3\ 2^p d^{11} e^{-\frac{a}{2 b}} \left(d+e \sqrt[3]{x}\right) \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{e^{12} \sqrt{c \left(d+e \sqrt[3]{x}\right)^2}}",1,"Integrate[x^3*(a + b*Log[c*(d + e*x^(1/3))^2])^p, x]","F",-1
563,0,0,1035,0.5044332,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","Integrate[x^2*(a + b*Log[c*(d + e*x^(1/3))^2])^p,x]","\int x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","\frac{2^p 3^{-2 p-1} e^{-\frac{9 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^9 \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{e^9 \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{9/2}}-\frac{3\ 4^{-p} d e^{-\frac{4 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{c^4 e^9}+\frac{3\ 2^{p+2} 7^{-p} d^2 e^{-\frac{7 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^7 \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{e^9 \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{7/2}}-\frac{28\ 3^{-p} d^3 e^{-\frac{3 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{c^3 e^9}+\frac{21\ 2^{p+1} 5^{-p} d^4 e^{-\frac{5 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^5 \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{e^9 \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{5/2}}-\frac{21\ 2^{1-p} d^5 e^{-\frac{2 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{c^2 e^9}+\frac{7\ 2^{p+2} 3^{-p} d^6 e^{-\frac{3 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^3 \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{e^9 \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{3/2}}-\frac{12 d^7 e^{-\frac{a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{c e^9}+\frac{3\ 2^p d^8 e^{-\frac{a}{2 b}} \left(d+e \sqrt[3]{x}\right) \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{2 b}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p}}{e^9 \sqrt{c \left(d+e \sqrt[3]{x}\right)^2}}",1,"Integrate[x^2*(a + b*Log[c*(d + e*x^(1/3))^2])^p, x]","F",-1
564,0,0,673,0.371277,"\int x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e*x^(1/3))^2])^p,x]","\int x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","\frac{3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{b}\right)}{2 c^3 e^6}+\frac{15 d^2 2^{-p-1} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{b}\right)}{c^2 e^6}-\frac{3 d^5 2^p e^{-\frac{a}{2 b}} \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{2 b}\right)}{e^6 \sqrt{c \left(d+e \sqrt[3]{x}\right)^2}}+\frac{15 d^4 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)}{2 c e^6}-\frac{5 d^3 2^{p+1} 3^{-p} e^{-\frac{3 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right)}{e^6 \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{3/2}}-\frac{3 d \left(\frac{2}{5}\right)^p e^{-\frac{5 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right)}{e^6 \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{5/2}}",1,"Integrate[x*(a + b*Log[c*(d + e*x^(1/3))^2])^p, x]","F",-1
565,0,0,338,0.136249,"\int \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^2])^p,x]","\int \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","\frac{3 d^2 2^p e^{-\frac{a}{2 b}} \left(d+e \sqrt[3]{x}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{2 b}\right)}{e^3 \sqrt{c \left(d+e \sqrt[3]{x}\right)^2}}+\frac{\left(\frac{2}{3}\right)^p e^{-\frac{3 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)}{2 b}\right)}{e^3 \left(c \left(d+e \sqrt[3]{x}\right)^2\right)^{3/2}}-\frac{3 d e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)}{c e^3}",1,"Integrate[(a + b*Log[c*(d + e*x^(1/3))^2])^p, x]","F",-1
566,0,0,27,0.1212328,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^2])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(1/3))^2])^p/x, x]","A",-1
567,0,0,27,0.1217816,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x^(1/3))^2])^p/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p}{x^2},x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(1/3))^2])^p/x^2, x]","A",-1
568,1,325,557,0.9424393,"\int x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \, dx","Integrate[x^3*(a + b*Log[c*(d + e*x^(2/3))])^p,x]","\frac{4^{-p-1} 15^{-p} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)^{-p} \left(10^p \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)-c d e^{a/b} \left(2^{2 p+1} 3^{p+1} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)+c d 5^p e^{a/b} \left(c d 2^p e^{a/b} \left(5\ 2^{p+2} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)+c d 3^{p+1} e^{a/b} \left(c d 2^{p+1} e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)-5 \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)\right)\right)-5\ 3^{p+1} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)\right)\right)\right)}{c^6 e^6}","\frac{2^{-p-2} 3^{-p} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)}{c^6 e^6}-\frac{3 d 5^{-p} e^{-\frac{5 a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)}{2 c^5 e^6}+\frac{15 d^2 2^{-2 (p+1)} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)}{c^4 e^6}-\frac{5 d^3 3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)}{c^3 e^6}+\frac{15 d^4 2^{-p-2} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)}{c^2 e^6}-\frac{3 d^5 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)}{2 c e^6}",1,"(4^(-1 - p)*(10^p*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*x^(2/3))]))/b] - c*d*E^(a/b)*(2^(1 + 2*p)*3^(1 + p)*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(2/3))]))/b] + 5^p*c*d*E^(a/b)*(-5*3^(1 + p)*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*x^(2/3))]))/b] + 2^p*c*d*E^(a/b)*(5*2^(2 + p)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(2/3))]))/b] + 3^(1 + p)*c*d*E^(a/b)*(-5*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(2/3))]))/b] + 2^(1 + p)*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(2/3))])/b)])))))*(a + b*Log[c*(d + e*x^(2/3))])^p)/(15^p*c^6*e^6*E^((6*a)/b)*(-((a + b*Log[c*(d + e*x^(2/3))])/b))^p)","A",1
569,1,181,273,0.2164303,"\int x \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e*x^(2/3))])^p,x]","\frac{2^{-p-1} 3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)^{-p} \left(2^p \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)+c d 3^{p+1} e^{a/b} \left(c d 2^p e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)-\Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)\right)\right)}{c^3 e^3}","\frac{3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)}{2 c^3 e^3}-\frac{3 d 2^{-p-1} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)}{b}\right)}{c^2 e^3}+\frac{3 d^2 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)}{2 c e^3}",1,"(2^(-1 - p)*(2^p*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(2/3))]))/b] + 3^(1 + p)*c*d*E^(a/b)*(-Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(2/3))]))/b] + 2^p*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(2/3))])/b)]))*(a + b*Log[c*(d + e*x^(2/3))])^p)/(3^p*c^3*e^3*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(2/3))])/b))^p)","A",1
570,0,0,25,0.2985099,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(2/3))])^p/x, x]","A",-1
571,0,0,25,0.6239767,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))])^p/x^3,x]","\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x^3} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x^3},x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(2/3))])^p/x^3, x]","A",-1
572,0,0,25,0.7419095,"\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \, dx","Integrate[x^2*(a + b*Log[c*(d + e*x^(2/3))])^p,x]","\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \, dx","\text{Int}\left(x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p,x\right)",0,"Integrate[x^2*(a + b*Log[c*(d + e*x^(2/3))])^p, x]","A",-1
573,0,0,21,0.1782794,"\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))])^p,x]","\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \, dx","\text{Int}\left(\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p,x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(2/3))])^p, x]","A",-1
574,0,0,25,0.4904843,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))])^p/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x^2},x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(2/3))])^p/x^2, x]","A",-1
575,0,0,678,0.5211043,"\int x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","Integrate[x^3*(a + b*Log[c*(d + e*x^(2/3))^2])^p,x]","\int x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","\frac{3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)}{b}\right)}{4 c^3 e^6}+\frac{15 d^2 2^{-p-2} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)}{b}\right)}{c^2 e^6}-\frac{3 d^5 2^{p-1} e^{-\frac{a}{2 b}} \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,\frac{-a-b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{2 b}\right)}{e^6 \sqrt{c \left(d+e x^{2/3}\right)^2}}+\frac{15 d^4 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{b}\right)}{4 c e^6}-\frac{5 d^3 \left(\frac{2}{3}\right)^p e^{-\frac{3 a}{2 b}} \left(d+e x^{2/3}\right)^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)}{2 b}\right)}{e^6 \left(c \left(d+e x^{2/3}\right)^2\right)^{3/2}}-\frac{3 d 2^{p-1} 5^{-p} e^{-\frac{5 a}{2 b}} \left(d+e x^{2/3}\right)^5 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)}{2 b}\right)}{e^6 \left(c \left(d+e x^{2/3}\right)^2\right)^{5/2}}",1,"Integrate[x^3*(a + b*Log[c*(d + e*x^(2/3))^2])^p, x]","F",-1
576,0,0,350,0.3002223,"\int x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e*x^(2/3))^2])^p,x]","\int x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","\frac{3 d^2 2^{p-1} e^{-\frac{a}{2 b}} \left(d+e x^{2/3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,\frac{-a-b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{2 b}\right)}{e^3 \sqrt{c \left(d+e x^{2/3}\right)^2}}+\frac{2^{p-1} 3^{-p} e^{-\frac{3 a}{2 b}} \left(d+e x^{2/3}\right)^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)}{2 b}\right)}{e^3 \left(c \left(d+e x^{2/3}\right)^2\right)^{3/2}}-\frac{3 d e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)}{b}\right)}{2 c e^3}",1,"Integrate[x*(a + b*Log[c*(d + e*x^(2/3))^2])^p, x]","F",-1
577,0,0,27,0.1624899,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^2])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(2/3))^2])^p/x, x]","A",-1
578,0,0,27,0.1588868,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^2])^p/x^3,x]","\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x^3} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x^3},x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(2/3))^2])^p/x^3, x]","A",-1
579,0,0,27,0.1830423,"\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","Integrate[x^2*(a + b*Log[c*(d + e*x^(2/3))^2])^p,x]","\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","\text{Int}\left(x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p,x\right)",0,"Integrate[x^2*(a + b*Log[c*(d + e*x^(2/3))^2])^p, x]","A",-1
580,0,0,23,0.0970633,"\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^2])^p,x]","\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","\text{Int}\left(\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p,x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(2/3))^2])^p, x]","A",-1
581,0,0,27,0.1293142,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e*x^(2/3))^2])^p/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x^2},x\right)",0,"Integrate[(a + b*Log[c*(d + e*x^(2/3))^2])^p/x^2, x]","A",-1
582,0,0,23,1.7053617,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e/x^(1/3))])^p,x]","\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \, dx","\text{Int}\left(x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p,x\right)",0,"Integrate[x*(a + b*Log[c*(d + e/x^(1/3))])^p, x]","A",-1
583,0,0,21,0.2866306,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))])^p,x]","\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \, dx","\text{Int}\left(\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p,x\right)",0,"Integrate[(a + b*Log[c*(d + e/x^(1/3))])^p, x]","A",-1
584,0,0,25,0.3302729,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e/x^(1/3))])^p/x, x]","A",-1
585,1,175,267,0.2498531,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))])^p/x^2,x]","-\frac{6^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \left(2^p \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)+c d 3^{p+1} e^{a/b} \left(c d 2^p e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)-\Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)\right)\right)}{c^3 e^3}","-\frac{3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)}{c^3 e^3}+\frac{3 d 2^{-p} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)}{c^2 e^3}-\frac{3 d^2 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)}{c e^3}",1,"-(((2^p*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/x^(1/3))]))/b] + 3^(1 + p)*c*d*E^(a/b)*(-Gamma[1 + p, (-2*(a + b*Log[c*(d + e/x^(1/3))]))/b] + 2^p*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e/x^(1/3))])/b)]))*(a + b*Log[c*(d + e/x^(1/3))])^p)/(6^p*c^3*e^3*E^((3*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p))","A",1
586,1,325,554,0.7913336,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))])^p/x^3,x]","\frac{2^{-2 p-1} 15^{-p} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \left(c d e^{a/b} \left(2^{2 p+1} 3^{p+1} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)+c d 5^p e^{a/b} \left(c d 2^p e^{a/b} \left(5\ 2^{p+2} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)+c d 3^{p+1} e^{a/b} \left(c d 2^{p+1} e^{a/b} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)-5 \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)\right)\right)-5\ 3^{p+1} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)\right)\right)-10^p \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)\right)}{c^6 e^6}","-\frac{2^{-p-1} 3^{-p} e^{-\frac{6 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)}{c^6 e^6}+\frac{3 d 5^{-p} e^{-\frac{5 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)}{c^5 e^6}-\frac{15 d^2 2^{-2 p-1} e^{-\frac{4 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)}{c^4 e^6}+\frac{10 d^3 3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)}{c^3 e^6}-\frac{15 d^4 2^{-p-1} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)}{c^2 e^6}+\frac{3 d^5 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)}{c e^6}",1,"(2^(-1 - 2*p)*(-(10^p*Gamma[1 + p, (-6*(a + b*Log[c*(d + e/x^(1/3))]))/b]) + c*d*E^(a/b)*(2^(1 + 2*p)*3^(1 + p)*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/x^(1/3))]))/b] + 5^p*c*d*E^(a/b)*(-5*3^(1 + p)*Gamma[1 + p, (-4*(a + b*Log[c*(d + e/x^(1/3))]))/b] + 2^p*c*d*E^(a/b)*(5*2^(2 + p)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/x^(1/3))]))/b] + 3^(1 + p)*c*d*E^(a/b)*(-5*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/x^(1/3))]))/b] + 2^(1 + p)*c*d*E^(a/b)*Gamma[1 + p, -((a + b*Log[c*(d + e/x^(1/3))])/b)])))))*(a + b*Log[c*(d + e/x^(1/3))])^p)/(15^p*c^6*e^6*E^((6*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p)","A",1
587,1,502,832,0.8668092,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))])^p/x^4,x]","-\frac{3^{-2 p-1} 280^{-p} e^{-\frac{9 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p} \left(c^8 d^8 9^{p+1} 280^p e^{\frac{8 a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)-c^7 d^7 35^p 36^{p+1} e^{\frac{7 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)+c^6 d^6 2^{3 p+2} 5^p 21^{p+1} e^{\frac{6 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)-c^5 d^5 5^p 126^{p+1} e^{\frac{5 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)+c^4 d^4 2^{3 p+1} 63^{p+1} e^{\frac{4 a}{b}} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)-c^3 d^3 5^p 84^{p+1} e^{\frac{3 a}{b}} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)+c^2 d^2 2^{3 p+2} 5^p 9^{p+1} e^{\frac{2 a}{b}} \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)-c d 9^{p+1} 35^p e^{a/b} \Gamma \left(p+1,-\frac{8 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)+280^p \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right)\right)}{c^9 e^9}","-\frac{3^{-2 p-1} e^{-\frac{9 a}{b}} \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p}}{c^9 e^9}+\frac{3\ 8^{-p} d e^{-\frac{8 a}{b}} \Gamma \left(p+1,-\frac{8 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p}}{c^8 e^9}-\frac{12\ 7^{-p} d^2 e^{-\frac{7 a}{b}} \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p}}{c^7 e^9}+\frac{7\ 2^{2-p} 3^{-p} d^3 e^{-\frac{6 a}{b}} \Gamma \left(p+1,-\frac{6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p}}{c^6 e^9}-\frac{42\ 5^{-p} d^4 e^{-\frac{5 a}{b}} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p}}{c^5 e^9}+\frac{21\ 2^{1-2 p} d^5 e^{-\frac{4 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p}}{c^4 e^9}-\frac{28\ 3^{-p} d^6 e^{-\frac{3 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p}}{c^3 e^9}+\frac{3\ 2^{2-p} d^7 e^{-\frac{2 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p}}{c^2 e^9}-\frac{3 d^8 e^{-\frac{a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)^{-p}}{c e^9}",1,"-((3^(-1 - 2*p)*(280^p*Gamma[1 + p, (-9*(a + b*Log[c*(d + e/x^(1/3))]))/b] - 9^(1 + p)*35^p*c*d*E^(a/b)*Gamma[1 + p, (-8*(a + b*Log[c*(d + e/x^(1/3))]))/b] + 2^(2 + 3*p)*5^p*9^(1 + p)*c^2*d^2*E^((2*a)/b)*Gamma[1 + p, (-7*(a + b*Log[c*(d + e/x^(1/3))]))/b] - 5^p*84^(1 + p)*c^3*d^3*E^((3*a)/b)*Gamma[1 + p, (-6*(a + b*Log[c*(d + e/x^(1/3))]))/b] + 2^(1 + 3*p)*63^(1 + p)*c^4*d^4*E^((4*a)/b)*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/x^(1/3))]))/b] - 5^p*126^(1 + p)*c^5*d^5*E^((5*a)/b)*Gamma[1 + p, (-4*(a + b*Log[c*(d + e/x^(1/3))]))/b] + 2^(2 + 3*p)*5^p*21^(1 + p)*c^6*d^6*E^((6*a)/b)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/x^(1/3))]))/b] - 35^p*36^(1 + p)*c^7*d^7*E^((7*a)/b)*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/x^(1/3))]))/b] + 9^(1 + p)*280^p*c^8*d^8*E^((8*a)/b)*Gamma[1 + p, -((a + b*Log[c*(d + e/x^(1/3))])/b)])*(a + b*Log[c*(d + e/x^(1/3))])^p)/(280^p*c^9*e^9*E^((9*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p))","A",1
588,0,0,25,0.2419352,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e/x^(1/3))^2])^p,x]","\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \, dx","\text{Int}\left(x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p,x\right)",0,"Integrate[x*(a + b*Log[c*(d + e/x^(1/3))^2])^p, x]","A",-1
589,0,0,23,0.1161966,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^2])^p,x]","\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \, dx","\text{Int}\left(\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p,x\right)",0,"Integrate[(a + b*Log[c*(d + e/x^(1/3))^2])^p, x]","A",-1
590,0,0,27,0.172545,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^2])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e/x^(1/3))^2])^p/x, x]","A",-1
591,0,0,342,0.1464773,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^2])^p/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x^2} \, dx","-\frac{3 d^2 2^p e^{-\frac{a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,\frac{-a-b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{2 b}\right)}{e^3 \sqrt{c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}}-\frac{\left(\frac{2}{3}\right)^p e^{-\frac{3 a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{2 b}\right)}{e^3 \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)^{3/2}}+\frac{3 d e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)}{c e^3}",1,"Integrate[(a + b*Log[c*(d + e/x^(1/3))^2])^p/x^2, x]","F",-1
592,0,0,673,0.1417894,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x^3} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^2])^p/x^3,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x^3} \, dx","-\frac{3^{-p} e^{-\frac{3 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{b}\right)}{2 c^3 e^6}-\frac{15 d^2 2^{-p-1} e^{-\frac{2 a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{b}\right)}{c^2 e^6}+\frac{3 d^5 2^p e^{-\frac{a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{2 b}\right)}{e^6 \sqrt{c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}}-\frac{15 d^4 e^{-\frac{a}{b}} \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)}{2 c e^6}+\frac{5 d^3 2^{p+1} 3^{-p} e^{-\frac{3 a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right)^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{2 b}\right)}{e^6 \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)^{3/2}}+\frac{3 d \left(\frac{2}{5}\right)^p e^{-\frac{5 a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right)^5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p} \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{2 b}\right)}{e^6 \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)^{5/2}}",1,"Integrate[(a + b*Log[c*(d + e/x^(1/3))^2])^p/x^3, x]","F",-1
593,0,0,1036,0.1388064,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x^4} \, dx","Integrate[(a + b*Log[c*(d + e/x^(1/3))^2])^p/x^4,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x^4} \, dx","-\frac{2^p 3^{-2 p-1} e^{-\frac{9 a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right)^9 \Gamma \left(p+1,-\frac{9 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p}}{e^9 \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)^{9/2}}+\frac{3\ 4^{-p} d e^{-\frac{4 a}{b}} \Gamma \left(p+1,-\frac{4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p}}{c^4 e^9}-\frac{3\ 2^{p+2} 7^{-p} d^2 e^{-\frac{7 a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right)^7 \Gamma \left(p+1,-\frac{7 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p}}{e^9 \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)^{7/2}}+\frac{28\ 3^{-p} d^3 e^{-\frac{3 a}{b}} \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p}}{c^3 e^9}-\frac{21\ 2^{p+1} 5^{-p} d^4 e^{-\frac{5 a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right)^5 \Gamma \left(p+1,-\frac{5 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p}}{e^9 \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)^{5/2}}+\frac{21\ 2^{1-p} d^5 e^{-\frac{2 a}{b}} \Gamma \left(p+1,-\frac{2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p}}{c^2 e^9}-\frac{7\ 2^{p+2} 3^{-p} d^6 e^{-\frac{3 a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right)^3 \Gamma \left(p+1,-\frac{3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)}{2 b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p}}{e^9 \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)^{3/2}}+\frac{12 d^7 e^{-\frac{a}{b}} \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p}}{c e^9}-\frac{3\ 2^p d^8 e^{-\frac{a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right) \Gamma \left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{2 b}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)}{b}\right)^{-p}}{e^9 \sqrt{c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}}",1,"Integrate[(a + b*Log[c*(d + e/x^(1/3))^2])^p/x^4, x]","F",-1
594,0,0,25,1.4967881,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","Integrate[x^3*(a + b*Log[c*(d + e/x^(2/3))])^p,x]","\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","\text{Int}\left(x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p,x\right)",0,"Integrate[x^3*(a + b*Log[c*(d + e/x^(2/3))])^p, x]","A",-1
595,0,0,25,0.7533703,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","Integrate[x^2*(a + b*Log[c*(d + e/x^(2/3))])^p,x]","\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","\text{Int}\left(x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p,x\right)",0,"Integrate[x^2*(a + b*Log[c*(d + e/x^(2/3))])^p, x]","A",-1
596,0,0,23,0.8218598,"\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e/x^(2/3))])^p,x]","\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","\text{Int}\left(x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p,x\right)",0,"Integrate[x*(a + b*Log[c*(d + e/x^(2/3))])^p, x]","A",-1
597,0,0,21,0.2688695,"\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))])^p,x]","\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","\text{Int}\left(\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p,x\right)",0,"Integrate[(a + b*Log[c*(d + e/x^(2/3))])^p, x]","A",-1
598,0,0,25,0.5145147,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e/x^(2/3))])^p/x, x]","A",-1
599,0,0,25,0.5156517,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))])^p/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p}{x^2},x\right)",0,"Integrate[(a + b*Log[c*(d + e/x^(2/3))])^p/x^2, x]","A",-1
600,0,0,27,0.3053786,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","Integrate[x^3*(a + b*Log[c*(d + e/x^(2/3))^2])^p,x]","\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","\text{Int}\left(x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p,x\right)",0,"Integrate[x^3*(a + b*Log[c*(d + e/x^(2/3))^2])^p, x]","A",-1
601,0,0,27,0.2116648,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","Integrate[x^2*(a + b*Log[c*(d + e/x^(2/3))^2])^p,x]","\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","\text{Int}\left(x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p,x\right)",0,"Integrate[x^2*(a + b*Log[c*(d + e/x^(2/3))^2])^p, x]","A",-1
602,0,0,25,0.251623,"\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","Integrate[x*(a + b*Log[c*(d + e/x^(2/3))^2])^p,x]","\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","\text{Int}\left(x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p,x\right)",0,"Integrate[x*(a + b*Log[c*(d + e/x^(2/3))^2])^p, x]","A",-1
603,0,0,23,0.1186956,"\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^2])^p,x]","\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","\text{Int}\left(\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p,x\right)",0,"Integrate[(a + b*Log[c*(d + e/x^(2/3))^2])^p, x]","A",-1
604,0,0,27,0.174739,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p}{x} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^2])^p/x,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p}{x} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p}{x},x\right)",0,"Integrate[(a + b*Log[c*(d + e/x^(2/3))^2])^p/x, x]","A",-1
605,0,0,27,0.1510468,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p}{x^2} \, dx","Integrate[(a + b*Log[c*(d + e/x^(2/3))^2])^p/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p}{x^2},x\right)",0,"Integrate[(a + b*Log[c*(d + e/x^(2/3))^2])^p/x^2, x]","A",-1
606,1,344,631,0.4729705,"\int \frac{(f+g x) \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{\sqrt{h x}} \, dx","Integrate[((f + g*x)*(a + b*Log[c*(d + e*x^2)^p]))/Sqrt[h*x],x]","\frac{2 \sqrt{x} \left(\frac{1}{3} g x^{3/2} \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)+a f \sqrt{x}+b f \sqrt{x} \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 b g p \left(2 \sqrt[4]{-d} e^{3/4} x^{3/2}-3 d \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)+3 d \tanh ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)\right)}{9 \sqrt[4]{-d} e^{3/4}}-\frac{b f p \left(\sqrt{2} \sqrt[4]{d} \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)-\sqrt{2} \sqrt[4]{d} \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)+2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)-2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)+8 \sqrt[4]{e} \sqrt{x}\right)}{2 \sqrt[4]{e}}\right)}{\sqrt{h x}}","\frac{2 g (h x)^{3/2} \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{3 h^2}+\frac{2 a f \sqrt{h x}}{h}+\frac{2 b f \sqrt{h x} \log \left(c \left(d+e x^2\right)^p\right)}{h}+\frac{\sqrt{2} b d^{3/4} g p \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{3 e^{3/4} \sqrt{h}}-\frac{\sqrt{2} b d^{3/4} g p \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{3 e^{3/4} \sqrt{h}}-\frac{2 \sqrt{2} b d^{3/4} g p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{3 e^{3/4} \sqrt{h}}+\frac{2 \sqrt{2} b d^{3/4} g p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{3 e^{3/4} \sqrt{h}}-\frac{\sqrt{2} b \sqrt[4]{d} f p \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{\sqrt[4]{e} \sqrt{h}}+\frac{\sqrt{2} b \sqrt[4]{d} f p \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{\sqrt[4]{e} \sqrt{h}}-\frac{2 \sqrt{2} b \sqrt[4]{d} f p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{\sqrt[4]{e} \sqrt{h}}+\frac{2 \sqrt{2} b \sqrt[4]{d} f p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{\sqrt[4]{e} \sqrt{h}}-\frac{8 b f p \sqrt{h x}}{h}-\frac{8 b g p (h x)^{3/2}}{9 h^2}",1,"(2*Sqrt[x]*(a*f*Sqrt[x] - (2*b*g*p*(2*(-d)^(1/4)*e^(3/4)*x^(3/2) - 3*d*ArcTan[(e^(1/4)*Sqrt[x])/(-d)^(1/4)] + 3*d*ArcTanh[(e^(1/4)*Sqrt[x])/(-d)^(1/4)]))/(9*(-d)^(1/4)*e^(3/4)) - (b*f*p*(8*e^(1/4)*Sqrt[x] + 2*Sqrt[2]*d^(1/4)*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] - 2*Sqrt[2]*d^(1/4)*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + Sqrt[2]*d^(1/4)*Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] - Sqrt[2]*d^(1/4)*Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x]))/(2*e^(1/4)) + b*f*Sqrt[x]*Log[c*(d + e*x^2)^p] + (g*x^(3/2)*(a + b*Log[c*(d + e*x^2)^p]))/3))/Sqrt[h*x]","A",1
607,1,316,603,0.4845148,"\int \frac{(f+g x) \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{(h x)^{3/2}} \, dx","Integrate[((f + g*x)*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(3/2),x]","\frac{2 x^{3/2} \left(-\frac{f \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{\sqrt{x}}+a g \sqrt{x}+b g \sqrt{x} \log \left(c \left(d+e x^2\right)^p\right)+\frac{2 b \sqrt[4]{e} f p \left(\tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)+\tanh ^{-1}\left(\frac{d \sqrt[4]{e} \sqrt{x}}{(-d)^{5/4}}\right)\right)}{\sqrt[4]{-d}}-\frac{b g p \left(\sqrt{2} \sqrt[4]{d} \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)-\sqrt{2} \sqrt[4]{d} \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)+2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)-2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)+8 \sqrt[4]{e} \sqrt{x}\right)}{2 \sqrt[4]{e}}\right)}{(h x)^{3/2}}","-\frac{2 f \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{h \sqrt{h x}}+\frac{2 a g \sqrt{h x}}{h^2}+\frac{2 b g \sqrt{h x} \log \left(c \left(d+e x^2\right)^p\right)}{h^2}+\frac{\sqrt{2} b \sqrt[4]{e} f p \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{\sqrt[4]{d} h^{3/2}}-\frac{\sqrt{2} b \sqrt[4]{e} f p \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{\sqrt[4]{d} h^{3/2}}-\frac{2 \sqrt{2} b \sqrt[4]{e} f p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{\sqrt[4]{d} h^{3/2}}+\frac{2 \sqrt{2} b \sqrt[4]{e} f p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{\sqrt[4]{d} h^{3/2}}-\frac{\sqrt{2} b \sqrt[4]{d} g p \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{\sqrt[4]{e} h^{3/2}}+\frac{\sqrt{2} b \sqrt[4]{d} g p \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{\sqrt[4]{e} h^{3/2}}-\frac{2 \sqrt{2} b \sqrt[4]{d} g p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{\sqrt[4]{e} h^{3/2}}+\frac{2 \sqrt{2} b \sqrt[4]{d} g p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{\sqrt[4]{e} h^{3/2}}-\frac{8 b g p \sqrt{h x}}{h^2}",1,"(2*x^(3/2)*(a*g*Sqrt[x] + (2*b*e^(1/4)*f*p*(ArcTan[(e^(1/4)*Sqrt[x])/(-d)^(1/4)] + ArcTanh[(d*e^(1/4)*Sqrt[x])/(-d)^(5/4)]))/(-d)^(1/4) - (b*g*p*(8*e^(1/4)*Sqrt[x] + 2*Sqrt[2]*d^(1/4)*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] - 2*Sqrt[2]*d^(1/4)*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + Sqrt[2]*d^(1/4)*Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] - Sqrt[2]*d^(1/4)*Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x]))/(2*e^(1/4)) + b*g*Sqrt[x]*Log[c*(d + e*x^2)^p] - (f*(a + b*Log[c*(d + e*x^2)^p]))/Sqrt[x]))/(h*x)^(3/2)","A",1
608,1,271,588,0.4435169,"\int \frac{(f+g x) \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{(h x)^{5/2}} \, dx","Integrate[((f + g*x)*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(5/2),x]","\frac{2 x^{5/2} \left(-\frac{f \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{3 x^{3/2}}-\frac{g \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{\sqrt{x}}-\frac{b e^{3/4} f p \left(\log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)-\log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)+2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)-2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)\right)}{3 \sqrt{2} d^{3/4}}+\frac{2 b \sqrt[4]{e} g p \left(\tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)+\tanh ^{-1}\left(\frac{d \sqrt[4]{e} \sqrt{x}}{(-d)^{5/4}}\right)\right)}{\sqrt[4]{-d}}\right)}{(h x)^{5/2}}","-\frac{2 f \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{3 h (h x)^{3/2}}-\frac{2 g \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{h^2 \sqrt{h x}}-\frac{\sqrt{2} b e^{3/4} f p \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{3 d^{3/4} h^{5/2}}+\frac{\sqrt{2} b e^{3/4} f p \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{3 d^{3/4} h^{5/2}}-\frac{2 \sqrt{2} b e^{3/4} f p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{3 d^{3/4} h^{5/2}}+\frac{2 \sqrt{2} b e^{3/4} f p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{3 d^{3/4} h^{5/2}}+\frac{\sqrt{2} b \sqrt[4]{e} g p \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{\sqrt[4]{d} h^{5/2}}-\frac{\sqrt{2} b \sqrt[4]{e} g p \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{\sqrt[4]{d} h^{5/2}}-\frac{2 \sqrt{2} b \sqrt[4]{e} g p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{\sqrt[4]{d} h^{5/2}}+\frac{2 \sqrt{2} b \sqrt[4]{e} g p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{\sqrt[4]{d} h^{5/2}}",1,"(2*x^(5/2)*((2*b*e^(1/4)*g*p*(ArcTan[(e^(1/4)*Sqrt[x])/(-d)^(1/4)] + ArcTanh[(d*e^(1/4)*Sqrt[x])/(-d)^(5/4)]))/(-d)^(1/4) - (b*e^(3/4)*f*p*(2*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] - 2*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] - Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x]))/(3*Sqrt[2]*d^(3/4)) - (f*(a + b*Log[c*(d + e*x^2)^p]))/(3*x^(3/2)) - (g*(a + b*Log[c*(d + e*x^2)^p]))/Sqrt[x]))/(h*x)^(5/2)","A",1
609,1,309,620,0.1948731,"\int \frac{(f+g x) \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{(h x)^{7/2}} \, dx","Integrate[((f + g*x)*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(7/2),x]","\frac{2 x^{7/2} \left(-\frac{f \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{5 x^{5/2}}-\frac{g \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{3 x^{3/2}}-\frac{1}{6} b g p \left(\frac{\frac{\sqrt{2} e^{3/4} \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)}{\sqrt[4]{d}}-\frac{\sqrt{2} e^{3/4} \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)}{\sqrt[4]{d}}}{\sqrt{d}}+\frac{2 \left(\frac{\sqrt{2} e^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)}{\sqrt[4]{d}}-\frac{\sqrt{2} e^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)}{\sqrt[4]{d}}\right)}{\sqrt{d}}\right)-\frac{4 b e f p \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};-\frac{e x^2}{d}\right)}{5 d \sqrt{x}}\right)}{(h x)^{7/2}}","-\frac{2 f \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{5 h (h x)^{5/2}}-\frac{2 g \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{3 h^2 (h x)^{3/2}}-\frac{\sqrt{2} b e^{5/4} f p \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{5 d^{5/4} h^{7/2}}+\frac{\sqrt{2} b e^{5/4} f p \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{5 d^{5/4} h^{7/2}}+\frac{2 \sqrt{2} b e^{5/4} f p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{5 d^{5/4} h^{7/2}}-\frac{2 \sqrt{2} b e^{5/4} f p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{5 d^{5/4} h^{7/2}}-\frac{\sqrt{2} b e^{3/4} g p \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{3 d^{3/4} h^{7/2}}+\frac{\sqrt{2} b e^{3/4} g p \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{3 d^{3/4} h^{7/2}}-\frac{2 \sqrt{2} b e^{3/4} g p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{3 d^{3/4} h^{7/2}}+\frac{2 \sqrt{2} b e^{3/4} g p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{3 d^{3/4} h^{7/2}}-\frac{8 b e f p}{5 d h^3 \sqrt{h x}}",1,"(2*x^(7/2)*((-4*b*e*f*p*Hypergeometric2F1[-1/4, 1, 3/4, -((e*x^2)/d)])/(5*d*Sqrt[x]) - (b*g*p*((2*((Sqrt[2]*e^(3/4)*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)])/d^(1/4) - (Sqrt[2]*e^(3/4)*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)])/d^(1/4)))/Sqrt[d] + ((Sqrt[2]*e^(3/4)*Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x])/d^(1/4) - (Sqrt[2]*e^(3/4)*Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x])/d^(1/4))/Sqrt[d]))/6 - (f*(a + b*Log[c*(d + e*x^2)^p]))/(5*x^(5/2)) - (g*(a + b*Log[c*(d + e*x^2)^p]))/(3*x^(3/2))))/(h*x)^(7/2)","C",1
610,1,100,641,0.0716249,"\int \frac{(f+g x) \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{(h x)^{9/2}} \, dx","Integrate[((f + g*x)*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(9/2),x]","-\frac{2 \sqrt{h x} \left(3 d (5 f+7 g x) \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)+20 b e f p x^2 \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};-\frac{e x^2}{d}\right)+84 b e g p x^3 \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};-\frac{e x^2}{d}\right)\right)}{105 d h^5 x^4}","-\frac{2 f \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{7 h (h x)^{7/2}}-\frac{2 g \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{5 h^2 (h x)^{5/2}}+\frac{\sqrt{2} b e^{7/4} f p \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{7 d^{7/4} h^{9/2}}-\frac{\sqrt{2} b e^{7/4} f p \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{7 d^{7/4} h^{9/2}}+\frac{2 \sqrt{2} b e^{7/4} f p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{7 d^{7/4} h^{9/2}}-\frac{2 \sqrt{2} b e^{7/4} f p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{7 d^{7/4} h^{9/2}}-\frac{\sqrt{2} b e^{5/4} g p \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{5 d^{5/4} h^{9/2}}+\frac{\sqrt{2} b e^{5/4} g p \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}+\sqrt{d} \sqrt{h}+\sqrt{e} \sqrt{h} x\right)}{5 d^{5/4} h^{9/2}}+\frac{2 \sqrt{2} b e^{5/4} g p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{5 d^{5/4} h^{9/2}}-\frac{2 \sqrt{2} b e^{5/4} g p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{5 d^{5/4} h^{9/2}}-\frac{8 b e f p}{21 d h^3 (h x)^{3/2}}-\frac{8 b e g p}{5 d h^4 \sqrt{h x}}",1,"(-2*Sqrt[h*x]*(20*b*e*f*p*x^2*Hypergeometric2F1[-3/4, 1, 1/4, -((e*x^2)/d)] + 84*b*e*g*p*x^3*Hypergeometric2F1[-1/4, 1, 3/4, -((e*x^2)/d)] + 3*d*(5*f + 7*g*x)*(a + b*Log[c*(d + e*x^2)^p])))/(105*d*h^5*x^4)","C",1
611,1,588,1002,1.4807696,"\int \frac{(f+g x)^2 \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{\sqrt{h x}} \, dx","Integrate[((f + g*x)^2*(a + b*Log[c*(d + e*x^2)^p]))/Sqrt[h*x],x]","\frac{2 \sqrt{x} \left(\frac{2}{3} f g x^{3/2} \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)+\frac{1}{5} g^2 x^{5/2} \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)+a f^2 \sqrt{x}+b f^2 \sqrt{x} \log \left(c \left(d+e x^2\right)^p\right)-\frac{b g^2 p \left(-5 \sqrt{2} d^{5/4} \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)+5 \sqrt{2} d^{5/4} \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)-10 \sqrt{2} d^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)+10 \sqrt{2} d^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)-40 d \sqrt[4]{e} \sqrt{x}+8 e^{5/4} x^{5/2}\right)}{50 e^{5/4}}-\frac{4 b f g p \left(2 \sqrt[4]{-d} e^{3/4} x^{3/2}-3 d \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)+3 d \tanh ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)\right)}{9 \sqrt[4]{-d} e^{3/4}}-\frac{b f^2 p \left(\sqrt{2} \sqrt[4]{d} \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)-\sqrt{2} \sqrt[4]{d} \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)+2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)-2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)+8 \sqrt[4]{e} \sqrt{x}\right)}{2 \sqrt[4]{e}}\right)}{\sqrt{h x}}","-\frac{8 b g^2 p (h x)^{5/2}}{25 h^3}+\frac{2 g^2 \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right) (h x)^{5/2}}{5 h^3}-\frac{16 b f g p (h x)^{3/2}}{9 h^2}+\frac{4 f g \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right) (h x)^{3/2}}{3 h^2}-\frac{8 b f^2 p \sqrt{h x}}{h}+\frac{8 b d g^2 p \sqrt{h x}}{5 e h}+\frac{2 b f^2 \log \left(c \left(e x^2+d\right)^p\right) \sqrt{h x}}{h}+\frac{2 a f^2 \sqrt{h x}}{h}-\frac{2 \sqrt{2} b \sqrt[4]{d} f^2 p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{\sqrt[4]{e} \sqrt{h}}+\frac{2 \sqrt{2} b d^{5/4} g^2 p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{5 e^{5/4} \sqrt{h}}-\frac{4 \sqrt{2} b d^{3/4} f g p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{3 e^{3/4} \sqrt{h}}+\frac{2 \sqrt{2} b \sqrt[4]{d} f^2 p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{\sqrt[4]{e} \sqrt{h}}-\frac{2 \sqrt{2} b d^{5/4} g^2 p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{5 e^{5/4} \sqrt{h}}+\frac{4 \sqrt{2} b d^{3/4} f g p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{3 e^{3/4} \sqrt{h}}-\frac{\sqrt{2} b \sqrt[4]{d} f^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{\sqrt[4]{e} \sqrt{h}}+\frac{\sqrt{2} b d^{5/4} g^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{5 e^{5/4} \sqrt{h}}+\frac{2 \sqrt{2} b d^{3/4} f g p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{3 e^{3/4} \sqrt{h}}+\frac{\sqrt{2} b \sqrt[4]{d} f^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{\sqrt[4]{e} \sqrt{h}}-\frac{\sqrt{2} b d^{5/4} g^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{5 e^{5/4} \sqrt{h}}-\frac{2 \sqrt{2} b d^{3/4} f g p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{3 e^{3/4} \sqrt{h}}",1,"(2*Sqrt[x]*(a*f^2*Sqrt[x] - (4*b*f*g*p*(2*(-d)^(1/4)*e^(3/4)*x^(3/2) - 3*d*ArcTan[(e^(1/4)*Sqrt[x])/(-d)^(1/4)] + 3*d*ArcTanh[(e^(1/4)*Sqrt[x])/(-d)^(1/4)]))/(9*(-d)^(1/4)*e^(3/4)) - (b*f^2*p*(8*e^(1/4)*Sqrt[x] + 2*Sqrt[2]*d^(1/4)*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] - 2*Sqrt[2]*d^(1/4)*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + Sqrt[2]*d^(1/4)*Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] - Sqrt[2]*d^(1/4)*Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x]))/(2*e^(1/4)) - (b*g^2*p*(-40*d*e^(1/4)*Sqrt[x] + 8*e^(5/4)*x^(5/2) - 10*Sqrt[2]*d^(5/4)*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + 10*Sqrt[2]*d^(5/4)*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] - 5*Sqrt[2]*d^(5/4)*Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] + 5*Sqrt[2]*d^(5/4)*Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x]))/(50*e^(5/4)) + b*f^2*Sqrt[x]*Log[c*(d + e*x^2)^p] + (2*f*g*x^(3/2)*(a + b*Log[c*(d + e*x^2)^p]))/3 + (g^2*x^(5/2)*(a + b*Log[c*(d + e*x^2)^p]))/5))/Sqrt[h*x]","A",1
612,1,436,949,0.8718614,"\int \frac{(f+g x)^2 \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{(h x)^{3/2}} \, dx","Integrate[((f + g*x)^2*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(3/2),x]","\frac{2 x^{3/2} \left(-\frac{f^2 \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{\sqrt{x}}+\frac{1}{3} g^2 x^{3/2} \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)+2 a f g \sqrt{x}+2 b f g \sqrt{x} \log \left(c \left(d+e x^2\right)^p\right)-\frac{2 b g^2 p \left(2 \sqrt[4]{-d} e^{3/4} x^{3/2}-3 d \tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)+3 d \tanh ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)\right)}{9 \sqrt[4]{-d} e^{3/4}}+\frac{2 b \sqrt[4]{e} f^2 p \left(\tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)+\tanh ^{-1}\left(\frac{d \sqrt[4]{e} \sqrt{x}}{(-d)^{5/4}}\right)\right)}{\sqrt[4]{-d}}-\frac{b f g p \left(\sqrt{2} \sqrt[4]{d} \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)-\sqrt{2} \sqrt[4]{d} \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)+2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)-2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)+8 \sqrt[4]{e} \sqrt{x}\right)}{\sqrt[4]{e}}\right)}{(h x)^{3/2}}","-\frac{2 \sqrt{2} b \sqrt[4]{e} p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right) f^2}{\sqrt[4]{d} h^{3/2}}+\frac{2 \sqrt{2} b \sqrt[4]{e} p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right) f^2}{\sqrt[4]{d} h^{3/2}}-\frac{2 \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right) f^2}{h \sqrt{h x}}+\frac{\sqrt{2} b \sqrt[4]{e} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f^2}{\sqrt[4]{d} h^{3/2}}-\frac{\sqrt{2} b \sqrt[4]{e} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f^2}{\sqrt[4]{d} h^{3/2}}-\frac{4 \sqrt{2} b \sqrt[4]{d} g p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right) f}{\sqrt[4]{e} h^{3/2}}+\frac{4 \sqrt{2} b \sqrt[4]{d} g p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right) f}{\sqrt[4]{e} h^{3/2}}+\frac{4 b g \sqrt{h x} \log \left(c \left(e x^2+d\right)^p\right) f}{h^2}-\frac{2 \sqrt{2} b \sqrt[4]{d} g p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f}{\sqrt[4]{e} h^{3/2}}+\frac{2 \sqrt{2} b \sqrt[4]{d} g p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f}{\sqrt[4]{e} h^{3/2}}-\frac{16 b g p \sqrt{h x} f}{h^2}+\frac{4 a g \sqrt{h x} f}{h^2}-\frac{8 b g^2 p (h x)^{3/2}}{9 h^3}-\frac{2 \sqrt{2} b d^{3/4} g^2 p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{3 e^{3/4} h^{3/2}}+\frac{2 \sqrt{2} b d^{3/4} g^2 p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{3 e^{3/4} h^{3/2}}+\frac{2 g^2 (h x)^{3/2} \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)}{3 h^3}+\frac{\sqrt{2} b d^{3/4} g^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{3 e^{3/4} h^{3/2}}-\frac{\sqrt{2} b d^{3/4} g^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{3 e^{3/4} h^{3/2}}",1,"(2*x^(3/2)*(2*a*f*g*Sqrt[x] - (2*b*g^2*p*(2*(-d)^(1/4)*e^(3/4)*x^(3/2) - 3*d*ArcTan[(e^(1/4)*Sqrt[x])/(-d)^(1/4)] + 3*d*ArcTanh[(e^(1/4)*Sqrt[x])/(-d)^(1/4)]))/(9*(-d)^(1/4)*e^(3/4)) + (2*b*e^(1/4)*f^2*p*(ArcTan[(e^(1/4)*Sqrt[x])/(-d)^(1/4)] + ArcTanh[(d*e^(1/4)*Sqrt[x])/(-d)^(5/4)]))/(-d)^(1/4) - (b*f*g*p*(8*e^(1/4)*Sqrt[x] + 2*Sqrt[2]*d^(1/4)*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] - 2*Sqrt[2]*d^(1/4)*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + Sqrt[2]*d^(1/4)*Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] - Sqrt[2]*d^(1/4)*Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x]))/e^(1/4) + 2*b*f*g*Sqrt[x]*Log[c*(d + e*x^2)^p] - (f^2*(a + b*Log[c*(d + e*x^2)^p]))/Sqrt[x] + (g^2*x^(3/2)*(a + b*Log[c*(d + e*x^2)^p]))/3))/(h*x)^(3/2)","A",1
613,1,503,932,0.9829062,"\int \frac{(f+g x)^2 \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{(h x)^{5/2}} \, dx","Integrate[((f + g*x)^2*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(5/2),x]","\frac{2 x^{5/2} \left(-\frac{f^2 \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{3 x^{3/2}}-\frac{2 f g \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{\sqrt{x}}+a g^2 \sqrt{x}+b g^2 \sqrt{x} \log \left(c \left(d+e x^2\right)^p\right)-\frac{b e^{3/4} f^2 p \left(\log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)-\log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)+2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)-2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)\right)}{3 \sqrt{2} d^{3/4}}+\frac{4 b \sqrt[4]{e} f g p \left(\tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)+\tanh ^{-1}\left(\frac{d \sqrt[4]{e} \sqrt{x}}{(-d)^{5/4}}\right)\right)}{\sqrt[4]{-d}}-\frac{b g^2 p \left(\sqrt{2} \sqrt[4]{d} \log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)-\sqrt{2} \sqrt[4]{d} \log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)+2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)-2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)+8 \sqrt[4]{e} \sqrt{x}\right)}{2 \sqrt[4]{e}}\right)}{(h x)^{5/2}}","-\frac{2 \sqrt{2} b e^{3/4} p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right) f^2}{3 d^{3/4} h^{5/2}}+\frac{2 \sqrt{2} b e^{3/4} p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right) f^2}{3 d^{3/4} h^{5/2}}-\frac{2 \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right) f^2}{3 h (h x)^{3/2}}-\frac{\sqrt{2} b e^{3/4} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f^2}{3 d^{3/4} h^{5/2}}+\frac{\sqrt{2} b e^{3/4} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f^2}{3 d^{3/4} h^{5/2}}-\frac{4 \sqrt{2} b \sqrt[4]{e} g p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right) f}{\sqrt[4]{d} h^{5/2}}+\frac{4 \sqrt{2} b \sqrt[4]{e} g p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right) f}{\sqrt[4]{d} h^{5/2}}-\frac{4 g \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right) f}{h^2 \sqrt{h x}}+\frac{2 \sqrt{2} b \sqrt[4]{e} g p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f}{\sqrt[4]{d} h^{5/2}}-\frac{2 \sqrt{2} b \sqrt[4]{e} g p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f}{\sqrt[4]{d} h^{5/2}}-\frac{2 \sqrt{2} b \sqrt[4]{d} g^2 p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{\sqrt[4]{e} h^{5/2}}+\frac{2 \sqrt{2} b \sqrt[4]{d} g^2 p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{\sqrt[4]{e} h^{5/2}}+\frac{2 b g^2 \sqrt{h x} \log \left(c \left(e x^2+d\right)^p\right)}{h^3}-\frac{\sqrt{2} b \sqrt[4]{d} g^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{\sqrt[4]{e} h^{5/2}}+\frac{\sqrt{2} b \sqrt[4]{d} g^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{\sqrt[4]{e} h^{5/2}}-\frac{8 b g^2 p \sqrt{h x}}{h^3}+\frac{2 a g^2 \sqrt{h x}}{h^3}",1,"(2*x^(5/2)*(a*g^2*Sqrt[x] + (4*b*e^(1/4)*f*g*p*(ArcTan[(e^(1/4)*Sqrt[x])/(-d)^(1/4)] + ArcTanh[(d*e^(1/4)*Sqrt[x])/(-d)^(5/4)]))/(-d)^(1/4) - (b*e^(3/4)*f^2*p*(2*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] - 2*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] - Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x]))/(3*Sqrt[2]*d^(3/4)) - (b*g^2*p*(8*e^(1/4)*Sqrt[x] + 2*Sqrt[2]*d^(1/4)*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] - 2*Sqrt[2]*d^(1/4)*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + Sqrt[2]*d^(1/4)*Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] - Sqrt[2]*d^(1/4)*Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x]))/(2*e^(1/4)) + b*g^2*Sqrt[x]*Log[c*(d + e*x^2)^p] - (f^2*(a + b*Log[c*(d + e*x^2)^p]))/(3*x^(3/2)) - (2*f*g*(a + b*Log[c*(d + e*x^2)^p]))/Sqrt[x]))/(h*x)^(5/2)","A",1
614,1,340,935,1.0825379,"\int \frac{(f+g x)^2 \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{(h x)^{7/2}} \, dx","Integrate[((f + g*x)^2*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(7/2),x]","\frac{2 x^{7/2} \left(-\frac{f^2 \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{5 x^{5/2}}-\frac{2 f g \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{3 x^{3/2}}-\frac{g^2 \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{\sqrt{x}}-\frac{\sqrt{2} b e^{3/4} f g p \left(\log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)-\log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)+2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)-2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)\right)}{3 d^{3/4}}-\frac{4 b e f^2 p \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};-\frac{e x^2}{d}\right)}{5 d \sqrt{x}}+\frac{2 b \sqrt[4]{e} g^2 p \left(\tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)+\tanh ^{-1}\left(\frac{d \sqrt[4]{e} \sqrt{x}}{(-d)^{5/4}}\right)\right)}{\sqrt[4]{-d}}\right)}{(h x)^{7/2}}","\frac{2 \sqrt{2} b e^{5/4} p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right) f^2}{5 d^{5/4} h^{7/2}}-\frac{2 \sqrt{2} b e^{5/4} p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right) f^2}{5 d^{5/4} h^{7/2}}-\frac{2 \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right) f^2}{5 h (h x)^{5/2}}-\frac{\sqrt{2} b e^{5/4} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f^2}{5 d^{5/4} h^{7/2}}+\frac{\sqrt{2} b e^{5/4} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f^2}{5 d^{5/4} h^{7/2}}-\frac{8 b e p f^2}{5 d h^3 \sqrt{h x}}-\frac{4 \sqrt{2} b e^{3/4} g p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right) f}{3 d^{3/4} h^{7/2}}+\frac{4 \sqrt{2} b e^{3/4} g p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right) f}{3 d^{3/4} h^{7/2}}-\frac{4 g \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right) f}{3 h^2 (h x)^{3/2}}-\frac{2 \sqrt{2} b e^{3/4} g p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f}{3 d^{3/4} h^{7/2}}+\frac{2 \sqrt{2} b e^{3/4} g p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f}{3 d^{3/4} h^{7/2}}-\frac{2 \sqrt{2} b \sqrt[4]{e} g^2 p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{\sqrt[4]{d} h^{7/2}}+\frac{2 \sqrt{2} b \sqrt[4]{e} g^2 p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{\sqrt[4]{d} h^{7/2}}-\frac{2 g^2 \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)}{h^3 \sqrt{h x}}+\frac{\sqrt{2} b \sqrt[4]{e} g^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{\sqrt[4]{d} h^{7/2}}-\frac{\sqrt{2} b \sqrt[4]{e} g^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{\sqrt[4]{d} h^{7/2}}",1,"(2*x^(7/2)*((2*b*e^(1/4)*g^2*p*(ArcTan[(e^(1/4)*Sqrt[x])/(-d)^(1/4)] + ArcTanh[(d*e^(1/4)*Sqrt[x])/(-d)^(5/4)]))/(-d)^(1/4) - (4*b*e*f^2*p*Hypergeometric2F1[-1/4, 1, 3/4, -((e*x^2)/d)])/(5*d*Sqrt[x]) - (Sqrt[2]*b*e^(3/4)*f*g*p*(2*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] - 2*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] - Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x]))/(3*d^(3/4)) - (f^2*(a + b*Log[c*(d + e*x^2)^p]))/(5*x^(5/2)) - (2*f*g*(a + b*Log[c*(d + e*x^2)^p]))/(3*x^(3/2)) - (g^2*(a + b*Log[c*(d + e*x^2)^p]))/Sqrt[x]))/(h*x)^(7/2)","C",1
615,1,294,968,0.2685097,"\int \frac{(f+g x)^2 \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{(h x)^{9/2}} \, dx","Integrate[((f + g*x)^2*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(9/2),x]","\frac{x \left(-30 d f^2 \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)-84 d f g x \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)-70 d g^2 x^2 \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)-35 \sqrt{2} b \sqrt[4]{d} e^{3/4} g^2 p x^{7/2} \left(\log \left(-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)-\log \left(\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}+\sqrt{e} x\right)+2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)-2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)\right)-40 b e f^2 p x^2 \, _2F_1\left(-\frac{3}{4},1;\frac{1}{4};-\frac{e x^2}{d}\right)-336 b e f g p x^3 \, _2F_1\left(-\frac{1}{4},1;\frac{3}{4};-\frac{e x^2}{d}\right)\right)}{105 d (h x)^{9/2}}","\frac{2 \sqrt{2} b e^{7/4} p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right) f^2}{7 d^{7/4} h^{9/2}}-\frac{2 \sqrt{2} b e^{7/4} p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right) f^2}{7 d^{7/4} h^{9/2}}-\frac{2 \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right) f^2}{7 h (h x)^{7/2}}+\frac{\sqrt{2} b e^{7/4} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f^2}{7 d^{7/4} h^{9/2}}-\frac{\sqrt{2} b e^{7/4} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f^2}{7 d^{7/4} h^{9/2}}-\frac{8 b e p f^2}{21 d h^3 (h x)^{3/2}}+\frac{4 \sqrt{2} b e^{5/4} g p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right) f}{5 d^{5/4} h^{9/2}}-\frac{4 \sqrt{2} b e^{5/4} g p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right) f}{5 d^{5/4} h^{9/2}}-\frac{4 g \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right) f}{5 h^2 (h x)^{5/2}}-\frac{2 \sqrt{2} b e^{5/4} g p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f}{5 d^{5/4} h^{9/2}}+\frac{2 \sqrt{2} b e^{5/4} g p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right) f}{5 d^{5/4} h^{9/2}}-\frac{16 b e g p f}{5 d h^4 \sqrt{h x}}-\frac{2 \sqrt{2} b e^{3/4} g^2 p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{3 d^{3/4} h^{9/2}}+\frac{2 \sqrt{2} b e^{3/4} g^2 p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{3 d^{3/4} h^{9/2}}-\frac{2 g^2 \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)}{3 h^3 (h x)^{3/2}}-\frac{\sqrt{2} b e^{3/4} g^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{3 d^{3/4} h^{9/2}}+\frac{\sqrt{2} b e^{3/4} g^2 p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{3 d^{3/4} h^{9/2}}",1,"(x*(-40*b*e*f^2*p*x^2*Hypergeometric2F1[-3/4, 1, 1/4, -((e*x^2)/d)] - 336*b*e*f*g*p*x^3*Hypergeometric2F1[-1/4, 1, 3/4, -((e*x^2)/d)] - 35*Sqrt[2]*b*d^(1/4)*e^(3/4)*g^2*p*x^(7/2)*(2*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] - 2*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] - Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x]) - 30*d*f^2*(a + b*Log[c*(d + e*x^2)^p]) - 84*d*f*g*x*(a + b*Log[c*(d + e*x^2)^p]) - 70*d*g^2*x^2*(a + b*Log[c*(d + e*x^2)^p])))/(105*d*(h*x)^(9/2))","C",1
616,1,1471,1680,1.4061825,"\int \frac{\sqrt{h x} \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{f+g x} \, dx","Integrate[(Sqrt[h*x]*(a + b*Log[c*(d + e*x^2)^p]))/(f + g*x),x]","\frac{\sqrt{h x} \left(2 \sqrt{g} \sqrt{x} a-\frac{b \sqrt{g} p \left(2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}\right)-2 \sqrt{2} \sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{x}}{\sqrt[4]{d}}+1\right)+\sqrt{2} \sqrt[4]{d} \log \left(\sqrt{e} x-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}\right)-\sqrt{2} \sqrt[4]{d} \log \left(\sqrt{e} x+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{x}+\sqrt{d}\right)+8 \sqrt[4]{e} \sqrt{x}\right)}{\sqrt[4]{e}}+2 b \sqrt{g} \sqrt{x} \log \left(c \left(e x^2+d\right)^p\right)+\sqrt{-f} \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right) \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)-\sqrt{-f} \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right) \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)-b \sqrt{-f} p \left(\log \left(\frac{\sqrt{g} \left(\sqrt[4]{-d}-\sqrt[4]{e} \sqrt{x}\right)}{\sqrt[4]{-d} \sqrt{g}-\sqrt[4]{e} \sqrt{-f}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(i \sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{i \sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(\sqrt[4]{e} \sqrt{x}+i \sqrt[4]{-d}\right)}{\sqrt[4]{e} \sqrt{-f}+i \sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(\sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-\sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-i \sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+i \sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right)\right)+b \sqrt{-f} p \left(\log \left(\frac{\sqrt{g} \left(\sqrt[4]{-d}-\sqrt[4]{e} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(\sqrt[4]{-d}-i \sqrt[4]{e} \sqrt{x}\right)}{i \sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(i \sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{\sqrt[4]{-d} \sqrt{g}-i \sqrt[4]{e} \sqrt{-f}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(\sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{\sqrt[4]{-d} \sqrt{g}-\sqrt[4]{e} \sqrt{-f}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-\sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-i \sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+i \sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right)\right)\right)}{g^{3/2} \sqrt{x}}","\frac{2 \sqrt{h x} a}{g}-\frac{2 \sqrt{2} b \sqrt[4]{d} \sqrt{h} p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{\sqrt[4]{e} g}+\frac{2 \sqrt{2} b \sqrt[4]{d} \sqrt{h} p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{\sqrt[4]{e} g}+\frac{2 b \sqrt{h x} \log \left(c \left(e x^2+d\right)^p\right)}{g}-\frac{2 \sqrt{f} \sqrt{h} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)}{g^{3/2}}-\frac{\sqrt{2} b \sqrt[4]{d} \sqrt{h} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{\sqrt[4]{e} g}+\frac{\sqrt{2} b \sqrt[4]{d} \sqrt{h} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{\sqrt[4]{e} g}-\frac{8 b \sqrt{f} \sqrt{h} p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{h}}{\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}}\right)}{g^{3/2}}+\frac{2 b \sqrt{f} \sqrt{h} p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}-i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{g^{3/2}}+\frac{2 b \sqrt{f} \sqrt{h} p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}-\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{g^{3/2}}+\frac{2 b \sqrt{f} \sqrt{h} p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}+i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{g^{3/2}}+\frac{2 b \sqrt{f} \sqrt{h} p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}+\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{g^{3/2}}+\frac{4 i b \sqrt{f} \sqrt{h} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{h}}{\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}}\right)}{g^{3/2}}-\frac{i b \sqrt{f} \sqrt{h} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}-i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{g^{3/2}}-\frac{i b \sqrt{f} \sqrt{h} p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}-\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}+1\right)}{g^{3/2}}-\frac{i b \sqrt{f} \sqrt{h} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}+i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{g^{3/2}}-\frac{i b \sqrt{f} \sqrt{h} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}+\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{g^{3/2}}-\frac{8 b p \sqrt{h x}}{g}",1,"(Sqrt[h*x]*(2*a*Sqrt[g]*Sqrt[x] - (b*Sqrt[g]*p*(8*e^(1/4)*Sqrt[x] + 2*Sqrt[2]*d^(1/4)*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] - 2*Sqrt[2]*d^(1/4)*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[x])/d^(1/4)] + Sqrt[2]*d^(1/4)*Log[Sqrt[d] - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x] - Sqrt[2]*d^(1/4)*Log[Sqrt[d] + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[x] + Sqrt[e]*x]))/e^(1/4) + 2*b*Sqrt[g]*Sqrt[x]*Log[c*(d + e*x^2)^p] + Sqrt[-f]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]]*(a + b*Log[c*(d + e*x^2)^p]) - Sqrt[-f]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]]*(a + b*Log[c*(d + e*x^2)^p]) - b*Sqrt[-f]*p*(Log[(Sqrt[g]*((-d)^(1/4) - e^(1/4)*Sqrt[x]))/(-(e^(1/4)*Sqrt[-f]) + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*((-d)^(1/4) + I*e^(1/4)*Sqrt[x]))/(I*e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*(I*(-d)^(1/4) + e^(1/4)*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + I*(-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*((-d)^(1/4) + e^(1/4)*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] + PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - (-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - I*(-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + I*(-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]) + b*Sqrt[-f]*p*(Log[(Sqrt[g]*((-d)^(1/4) - e^(1/4)*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*((-d)^(1/4) - I*e^(1/4)*Sqrt[x]))/(I*e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*((-d)^(1/4) + I*e^(1/4)*Sqrt[x]))/((-I)*e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*((-d)^(1/4) + e^(1/4)*Sqrt[x]))/(-(e^(1/4)*Sqrt[-f]) + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - (-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - I*(-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + I*(-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])])))/(g^(3/2)*Sqrt[x])","A",1
617,1,1297,1361,0.3945984,"\int \frac{a+b \log \left(c \left(d+e x^2\right)^p\right)}{\sqrt{h x} (f+g x)} \, dx","Integrate[(a + b*Log[c*(d + e*x^2)^p])/(Sqrt[h*x]*(f + g*x)),x]","\frac{\sqrt{x} \left(a \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)-b p \log \left(\frac{\sqrt{g} \left(\sqrt[4]{-d}-\sqrt[4]{e} \sqrt{x}\right)}{\sqrt[4]{-d} \sqrt{g}-\sqrt[4]{e} \sqrt{-f}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)-b p \log \left(\frac{\sqrt{g} \left(i \sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{i \sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)-b p \log \left(\frac{\sqrt{g} \left(\sqrt[4]{e} \sqrt{x}+i \sqrt[4]{-d}\right)}{\sqrt[4]{e} \sqrt{-f}+i \sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)-b p \log \left(\frac{\sqrt{g} \left(\sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)+b \log \left(c \left(e x^2+d\right)^p\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)-a \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+b p \log \left(\frac{\sqrt{g} \left(\sqrt[4]{-d}-\sqrt[4]{e} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+b p \log \left(\frac{\sqrt{g} \left(\sqrt[4]{-d}-i \sqrt[4]{e} \sqrt{x}\right)}{i \sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+b p \log \left(\frac{\sqrt{g} \left(i \sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{\sqrt[4]{-d} \sqrt{g}-i \sqrt[4]{e} \sqrt{-f}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+b p \log \left(\frac{\sqrt{g} \left(\sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{\sqrt[4]{-d} \sqrt{g}-\sqrt[4]{e} \sqrt{-f}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)-b \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right) \log \left(c \left(e x^2+d\right)^p\right)-b p \text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-\sqrt[4]{-d} \sqrt{g}}\right)-b p \text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-i \sqrt[4]{-d} \sqrt{g}}\right)-b p \text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+i \sqrt[4]{-d} \sqrt{g}}\right)-b p \text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right)+b p \text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-\sqrt[4]{-d} \sqrt{g}}\right)+b p \text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-i \sqrt[4]{-d} \sqrt{g}}\right)+b p \text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+i \sqrt[4]{-d} \sqrt{g}}\right)+b p \text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right)\right)}{\sqrt{-f} \sqrt{g} \sqrt{h x}}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)}{\sqrt{f} \sqrt{g} \sqrt{h}}+\frac{8 b p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{h}}{\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}}\right)}{\sqrt{f} \sqrt{g} \sqrt{h}}-\frac{2 b p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}-i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{\sqrt{f} \sqrt{g} \sqrt{h}}-\frac{2 b p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}-\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{\sqrt{f} \sqrt{g} \sqrt{h}}-\frac{2 b p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}+i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{\sqrt{f} \sqrt{g} \sqrt{h}}-\frac{2 b p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}+\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{\sqrt{f} \sqrt{g} \sqrt{h}}-\frac{4 i b p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{h}}{\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}}\right)}{\sqrt{f} \sqrt{g} \sqrt{h}}+\frac{i b p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}-i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{\sqrt{f} \sqrt{g} \sqrt{h}}+\frac{i b p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}-\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}+1\right)}{\sqrt{f} \sqrt{g} \sqrt{h}}+\frac{i b p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}+i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{\sqrt{f} \sqrt{g} \sqrt{h}}+\frac{i b p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}+\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{\sqrt{f} \sqrt{g} \sqrt{h}}",1,"(Sqrt[x]*(a*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] - b*p*Log[(Sqrt[g]*((-d)^(1/4) - e^(1/4)*Sqrt[x]))/(-(e^(1/4)*Sqrt[-f]) + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] - b*p*Log[(Sqrt[g]*((-d)^(1/4) + I*e^(1/4)*Sqrt[x]))/(I*e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] - b*p*Log[(Sqrt[g]*(I*(-d)^(1/4) + e^(1/4)*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + I*(-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] - b*p*Log[(Sqrt[g]*((-d)^(1/4) + e^(1/4)*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] - a*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + b*p*Log[(Sqrt[g]*((-d)^(1/4) - e^(1/4)*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + b*p*Log[(Sqrt[g]*((-d)^(1/4) - I*e^(1/4)*Sqrt[x]))/(I*e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + b*p*Log[(Sqrt[g]*((-d)^(1/4) + I*e^(1/4)*Sqrt[x]))/((-I)*e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + b*p*Log[(Sqrt[g]*((-d)^(1/4) + e^(1/4)*Sqrt[x]))/(-(e^(1/4)*Sqrt[-f]) + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + b*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]]*Log[c*(d + e*x^2)^p] - b*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]]*Log[c*(d + e*x^2)^p] - b*p*PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - (-d)^(1/4)*Sqrt[g])] - b*p*PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - I*(-d)^(1/4)*Sqrt[g])] - b*p*PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + I*(-d)^(1/4)*Sqrt[g])] - b*p*PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])] + b*p*PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - (-d)^(1/4)*Sqrt[g])] + b*p*PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - I*(-d)^(1/4)*Sqrt[g])] + b*p*PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + I*(-d)^(1/4)*Sqrt[g])] + b*p*PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]))/(Sqrt[-f]*Sqrt[g]*Sqrt[h*x])","A",1
618,1,1336,1659,1.616683,"\int \frac{a+b \log \left(c \left(d+e x^2\right)^p\right)}{(h x)^{3/2} (f+g x)} \, dx","Integrate[(a + b*Log[c*(d + e*x^2)^p])/((h*x)^(3/2)*(f + g*x)),x]","\frac{x^{3/2} \left(\frac{4 b \sqrt[4]{e} p \left(\tan ^{-1}\left(\frac{\sqrt[4]{e} \sqrt{x}}{\sqrt[4]{-d}}\right)+\tanh ^{-1}\left(\frac{d \sqrt[4]{e} \sqrt{x}}{(-d)^{5/4}}\right)\right)}{\sqrt[4]{-d}}+\frac{f \sqrt{g} \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right) \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)}{(-f)^{3/2}}+\frac{\sqrt{g} \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right) \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)}{\sqrt{-f}}-\frac{2 \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)}{\sqrt{x}}+\frac{b \sqrt{g} p \left(\log \left(\frac{\sqrt{g} \left(\sqrt[4]{-d}-\sqrt[4]{e} \sqrt{x}\right)}{\sqrt[4]{-d} \sqrt{g}-\sqrt[4]{e} \sqrt{-f}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(i \sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{i \sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(\sqrt[4]{e} \sqrt{x}+i \sqrt[4]{-d}\right)}{\sqrt[4]{e} \sqrt{-f}+i \sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(\sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-\sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-i \sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+i \sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}-\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right)\right)}{\sqrt{-f}}+\frac{b f \sqrt{g} p \left(\log \left(\frac{\sqrt{g} \left(\sqrt[4]{-d}-\sqrt[4]{e} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(\sqrt[4]{-d}-i \sqrt[4]{e} \sqrt{x}\right)}{i \sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(i \sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{\sqrt[4]{-d} \sqrt{g}-i \sqrt[4]{e} \sqrt{-f}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+\log \left(\frac{\sqrt{g} \left(\sqrt[4]{e} \sqrt{x}+\sqrt[4]{-d}\right)}{\sqrt[4]{-d} \sqrt{g}-\sqrt[4]{e} \sqrt{-f}}\right) \log \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-\sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}-i \sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+i \sqrt[4]{-d} \sqrt{g}}\right)+\text{Li}_2\left(\frac{\sqrt[4]{e} \left(\sqrt{-f}+\sqrt{g} \sqrt{x}\right)}{\sqrt[4]{e} \sqrt{-f}+\sqrt[4]{-d} \sqrt{g}}\right)\right)}{(-f)^{3/2}}\right)}{f (h x)^{3/2}}","-\frac{2 \sqrt{2} b \sqrt[4]{e} p \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}\right)}{\sqrt[4]{d} f h^{3/2}}+\frac{2 \sqrt{2} b \sqrt[4]{e} p \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{e} \sqrt{h x}}{\sqrt[4]{d} \sqrt{h}}+1\right)}{\sqrt[4]{d} f h^{3/2}}-\frac{2 \sqrt{g} \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)}{f^{3/2} h^{3/2}}-\frac{2 \left(a+b \log \left(c \left(e x^2+d\right)^p\right)\right)}{f h \sqrt{h x}}+\frac{\sqrt{2} b \sqrt[4]{e} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}-\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{\sqrt[4]{d} f h^{3/2}}-\frac{\sqrt{2} b \sqrt[4]{e} p \log \left(\sqrt{e} \sqrt{h} x+\sqrt{d} \sqrt{h}+\sqrt{2} \sqrt[4]{d} \sqrt[4]{e} \sqrt{h x}\right)}{\sqrt[4]{d} f h^{3/2}}-\frac{8 b \sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{h}}{\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}}\right)}{f^{3/2} h^{3/2}}+\frac{2 b \sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}-i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{f^{3/2} h^{3/2}}+\frac{2 b \sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}-\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{f^{3/2} h^{3/2}}+\frac{2 b \sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}+i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{f^{3/2} h^{3/2}}+\frac{2 b \sqrt{g} p \tan ^{-1}\left(\frac{\sqrt{g} \sqrt{h x}}{\sqrt{f} \sqrt{h}}\right) \log \left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}+\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{f^{3/2} h^{3/2}}+\frac{4 i b \sqrt{g} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{h}}{\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}}\right)}{f^{3/2} h^{3/2}}-\frac{i b \sqrt{g} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}-i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{f^{3/2} h^{3/2}}-\frac{i b \sqrt{g} p \text{Li}_2\left(\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}-\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}-\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}+1\right)}{f^{3/2} h^{3/2}}-\frac{i b \sqrt{g} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \sqrt{h} \left(\sqrt[4]{-d} \sqrt{-h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(\sqrt[4]{-d} \sqrt{g} \sqrt{-h}+i \sqrt[4]{e} \sqrt{f} \sqrt{h}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{f^{3/2} h^{3/2}}-\frac{i b \sqrt{g} p \text{Li}_2\left(1-\frac{2 \sqrt{f} \sqrt{g} \left(\sqrt[4]{-d} \sqrt{h}+\sqrt[4]{e} \sqrt{h x}\right)}{\left(i \sqrt[4]{e} \sqrt{f}+\sqrt[4]{-d} \sqrt{g}\right) \left(\sqrt{f} \sqrt{h}-i \sqrt{g} \sqrt{h x}\right)}\right)}{f^{3/2} h^{3/2}}",1,"(x^(3/2)*((4*b*e^(1/4)*p*(ArcTan[(e^(1/4)*Sqrt[x])/(-d)^(1/4)] + ArcTanh[(d*e^(1/4)*Sqrt[x])/(-d)^(5/4)]))/(-d)^(1/4) - (2*(a + b*Log[c*(d + e*x^2)^p]))/Sqrt[x] + (f*Sqrt[g]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]]*(a + b*Log[c*(d + e*x^2)^p]))/(-f)^(3/2) + (Sqrt[g]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]]*(a + b*Log[c*(d + e*x^2)^p]))/Sqrt[-f] + (b*Sqrt[g]*p*(Log[(Sqrt[g]*((-d)^(1/4) - e^(1/4)*Sqrt[x]))/(-(e^(1/4)*Sqrt[-f]) + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*((-d)^(1/4) + I*e^(1/4)*Sqrt[x]))/(I*e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*(I*(-d)^(1/4) + e^(1/4)*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + I*(-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*((-d)^(1/4) + e^(1/4)*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] - Sqrt[g]*Sqrt[x]] + PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - (-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - I*(-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + I*(-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] - Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]))/Sqrt[-f] + (b*f*Sqrt[g]*p*(Log[(Sqrt[g]*((-d)^(1/4) - e^(1/4)*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*((-d)^(1/4) - I*e^(1/4)*Sqrt[x]))/(I*e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*((-d)^(1/4) + I*e^(1/4)*Sqrt[x]))/((-I)*e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + Log[(Sqrt[g]*((-d)^(1/4) + e^(1/4)*Sqrt[x]))/(-(e^(1/4)*Sqrt[-f]) + (-d)^(1/4)*Sqrt[g])]*Log[Sqrt[-f] + Sqrt[g]*Sqrt[x]] + PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - (-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] - I*(-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + I*(-d)^(1/4)*Sqrt[g])] + PolyLog[2, (e^(1/4)*(Sqrt[-f] + Sqrt[g]*Sqrt[x]))/(e^(1/4)*Sqrt[-f] + (-d)^(1/4)*Sqrt[g])]))/(-f)^(3/2)))/(f*(h*x)^(3/2))","A",1
619,1,33,33,0.0116693,"\int \frac{\log \left(f x^p\right) \log \left(1+e x^m\right)}{x} \, dx","Integrate[(Log[f*x^p]*Log[1 + e*x^m])/x,x]","\frac{p \text{Li}_3\left(-e x^m\right)}{m^2}-\frac{\text{Li}_2\left(-e x^m\right) \log \left(f x^p\right)}{m}","\frac{p \text{Li}_3\left(-e x^m\right)}{m^2}-\frac{\text{Li}_2\left(-e x^m\right) \log \left(f x^p\right)}{m}",1,"-((Log[f*x^p]*PolyLog[2, -(e*x^m)])/m) + (p*PolyLog[3, -(e*x^m)])/m^2","A",1
620,1,210,75,0.140531,"\int \frac{x^{-1+m} \log ^2\left(f x^p\right)}{d+e x^m} \, dx","Integrate[(x^(-1 + m)*Log[f*x^p]^2)/(d + e*x^m),x]","\frac{3 m^2 \log ^2\left(f x^p\right) \log \left(d+e x^m\right)+6 m p \left(p \log (x)-\log \left(f x^p\right)\right) \text{Li}_2\left(\frac{e x^m}{d}+1\right)-6 m p \log \left(f x^p\right) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)+3 m^2 p^2 \log ^2(x) \log \left(\frac{d x^{-m}}{e}+1\right)-3 m^2 p^2 \log ^2(x) \log \left(d+e x^m\right)-6 p^2 \text{Li}_3\left(-\frac{d x^{-m}}{e}\right)-6 m p^2 \log (x) \text{Li}_2\left(-\frac{d x^{-m}}{e}\right)+6 m p^2 \log (x) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)+m^3 p^2 \log ^3(x)}{3 e m^3}","\frac{2 p \log \left(f x^p\right) \text{Li}_2\left(-\frac{e x^m}{d}\right)}{e m^2}+\frac{\log ^2\left(f x^p\right) \log \left(\frac{e x^m}{d}+1\right)}{e m}-\frac{2 p^2 \text{Li}_3\left(-\frac{e x^m}{d}\right)}{e m^3}",1,"(m^3*p^2*Log[x]^3 + 3*m^2*p^2*Log[x]^2*Log[1 + d/(e*x^m)] - 3*m^2*p^2*Log[x]^2*Log[d + e*x^m] + 6*m*p^2*Log[x]*Log[-((e*x^m)/d)]*Log[d + e*x^m] - 6*m*p*Log[-((e*x^m)/d)]*Log[f*x^p]*Log[d + e*x^m] + 3*m^2*Log[f*x^p]^2*Log[d + e*x^m] - 6*m*p^2*Log[x]*PolyLog[2, -(d/(e*x^m))] + 6*m*p*(p*Log[x] - Log[f*x^p])*PolyLog[2, 1 + (e*x^m)/d] - 6*p^2*PolyLog[3, -(d/(e*x^m))])/(3*e*m^3)","B",1
621,1,659,161,0.2784514,"\int \frac{\log ^3\left(f x^p\right) \left(a+b \log \left(c \left(d+e x^m\right)^n\right)\right)}{x} \, dx","Integrate[(Log[f*x^p]^3*(a + b*Log[c*(d + e*x^m)^n]))/x,x]","\frac{a \log ^4\left(f x^p\right)}{4 p}+b p^2 \log ^3(x) \log \left(f x^p\right) \log \left(c \left(d+e x^m\right)^n\right)+b \log (x) \log ^3\left(f x^p\right) \log \left(c \left(d+e x^m\right)^n\right)-\frac{3}{2} b p \log ^2(x) \log ^2\left(f x^p\right) \log \left(c \left(d+e x^m\right)^n\right)-\frac{1}{4} b p^3 \log ^4(x) \log \left(c \left(d+e x^m\right)^n\right)+\frac{6 b n p^2 \log \left(f x^p\right) \text{Li}_4\left(-\frac{d x^{-m}}{e}\right)}{m^3}+\frac{3 b n p \log ^2\left(f x^p\right) \text{Li}_3\left(-\frac{d x^{-m}}{e}\right)}{m^2}+\frac{b n p \log (x) \left(3 \log ^2\left(f x^p\right)-3 p \log (x) \log \left(f x^p\right)+p^2 \log ^2(x)\right) \text{Li}_2\left(-\frac{d x^{-m}}{e}\right)}{m}+2 b n p^2 \log ^3(x) \log \left(f x^p\right) \log \left(\frac{d x^{-m}}{e}+1\right)-3 b n p^2 \log ^3(x) \log \left(f x^p\right) \log \left(d+e x^m\right)+\frac{3 b n p^2 \log ^2(x) \log \left(f x^p\right) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)}{m}-\frac{b n \left(p \log (x)-\log \left(f x^p\right)\right)^3 \text{Li}_2\left(\frac{e x^m}{d}+1\right)}{m}-\frac{3}{2} b n p \log ^2(x) \log ^2\left(f x^p\right) \log \left(\frac{d x^{-m}}{e}+1\right)-b n \log (x) \log ^3\left(f x^p\right) \log \left(d+e x^m\right)+\frac{b n \log ^3\left(f x^p\right) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)}{m}+3 b n p \log ^2(x) \log ^2\left(f x^p\right) \log \left(d+e x^m\right)-\frac{3 b n p \log (x) \log ^2\left(f x^p\right) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)}{m}+\frac{6 b n p^3 \text{Li}_5\left(-\frac{d x^{-m}}{e}\right)}{m^4}-\frac{3}{4} b n p^3 \log ^4(x) \log \left(\frac{d x^{-m}}{e}+1\right)+b n p^3 \log ^4(x) \log \left(d+e x^m\right)-\frac{b n p^3 \log ^3(x) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)}{m}+\frac{3}{4} b m n p^2 \log ^4(x) \log \left(f x^p\right)-\frac{1}{2} b m n p \log ^3(x) \log ^2\left(f x^p\right)-\frac{3}{10} b m n p^3 \log ^5(x)","\frac{\log ^4\left(f x^p\right) \left(a+b \log \left(c \left(d+e x^m\right)^n\right)\right)}{4 p}-\frac{6 b n p^2 \log \left(f x^p\right) \text{Li}_4\left(-\frac{e x^m}{d}\right)}{m^3}+\frac{3 b n p \log ^2\left(f x^p\right) \text{Li}_3\left(-\frac{e x^m}{d}\right)}{m^2}-\frac{b n \log ^3\left(f x^p\right) \text{Li}_2\left(-\frac{e x^m}{d}\right)}{m}-\frac{b n \log ^4\left(f x^p\right) \log \left(\frac{e x^m}{d}+1\right)}{4 p}+\frac{6 b n p^3 \text{Li}_5\left(-\frac{e x^m}{d}\right)}{m^4}",1,"(-3*b*m*n*p^3*Log[x]^5)/10 + (3*b*m*n*p^2*Log[x]^4*Log[f*x^p])/4 - (b*m*n*p*Log[x]^3*Log[f*x^p]^2)/2 + (a*Log[f*x^p]^4)/(4*p) - (3*b*n*p^3*Log[x]^4*Log[1 + d/(e*x^m)])/4 + 2*b*n*p^2*Log[x]^3*Log[f*x^p]*Log[1 + d/(e*x^m)] - (3*b*n*p*Log[x]^2*Log[f*x^p]^2*Log[1 + d/(e*x^m)])/2 + b*n*p^3*Log[x]^4*Log[d + e*x^m] - (b*n*p^3*Log[x]^3*Log[-((e*x^m)/d)]*Log[d + e*x^m])/m - 3*b*n*p^2*Log[x]^3*Log[f*x^p]*Log[d + e*x^m] + (3*b*n*p^2*Log[x]^2*Log[-((e*x^m)/d)]*Log[f*x^p]*Log[d + e*x^m])/m + 3*b*n*p*Log[x]^2*Log[f*x^p]^2*Log[d + e*x^m] - (3*b*n*p*Log[x]*Log[-((e*x^m)/d)]*Log[f*x^p]^2*Log[d + e*x^m])/m - b*n*Log[x]*Log[f*x^p]^3*Log[d + e*x^m] + (b*n*Log[-((e*x^m)/d)]*Log[f*x^p]^3*Log[d + e*x^m])/m - (b*p^3*Log[x]^4*Log[c*(d + e*x^m)^n])/4 + b*p^2*Log[x]^3*Log[f*x^p]*Log[c*(d + e*x^m)^n] - (3*b*p*Log[x]^2*Log[f*x^p]^2*Log[c*(d + e*x^m)^n])/2 + b*Log[x]*Log[f*x^p]^3*Log[c*(d + e*x^m)^n] + (b*n*p*Log[x]*(p^2*Log[x]^2 - 3*p*Log[x]*Log[f*x^p] + 3*Log[f*x^p]^2)*PolyLog[2, -(d/(e*x^m))])/m - (b*n*(p*Log[x] - Log[f*x^p])^3*PolyLog[2, 1 + (e*x^m)/d])/m + (3*b*n*p*Log[f*x^p]^2*PolyLog[3, -(d/(e*x^m))])/m^2 + (6*b*n*p^2*Log[f*x^p]*PolyLog[4, -(d/(e*x^m))])/m^3 + (6*b*n*p^3*PolyLog[5, -(d/(e*x^m))])/m^4","B",1
622,1,456,132,0.2479878,"\int \frac{\log ^2\left(f x^p\right) \left(a+b \log \left(c \left(d+e x^m\right)^n\right)\right)}{x} \, dx","Integrate[(Log[f*x^p]^2*(a + b*Log[c*(d + e*x^m)^n]))/x,x]","\frac{a \log ^3\left(f x^p\right)}{3 p}-b p \log ^2(x) \log \left(f x^p\right) \log \left(c \left(d+e x^m\right)^n\right)+b \log (x) \log ^2\left(f x^p\right) \log \left(c \left(d+e x^m\right)^n\right)+\frac{1}{3} b p^2 \log ^3(x) \log \left(c \left(d+e x^m\right)^n\right)+\frac{2 b n p \log \left(f x^p\right) \text{Li}_3\left(-\frac{d x^{-m}}{e}\right)}{m^2}-\frac{b n p \log (x) \left(p \log (x)-2 \log \left(f x^p\right)\right) \text{Li}_2\left(-\frac{d x^{-m}}{e}\right)}{m}+\frac{b n \left(\log \left(f x^p\right)-p \log (x)\right)^2 \text{Li}_2\left(\frac{e x^m}{d}+1\right)}{m}-b n p \log ^2(x) \log \left(f x^p\right) \log \left(\frac{d x^{-m}}{e}+1\right)+2 b n p \log ^2(x) \log \left(f x^p\right) \log \left(d+e x^m\right)-b n \log (x) \log ^2\left(f x^p\right) \log \left(d+e x^m\right)+\frac{b n \log ^2\left(f x^p\right) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)}{m}-\frac{2 b n p \log (x) \log \left(f x^p\right) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)}{m}+\frac{2 b n p^2 \text{Li}_4\left(-\frac{d x^{-m}}{e}\right)}{m^3}+\frac{2}{3} b n p^2 \log ^3(x) \log \left(\frac{d x^{-m}}{e}+1\right)-b n p^2 \log ^3(x) \log \left(d+e x^m\right)+\frac{b n p^2 \log ^2(x) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)}{m}-\frac{1}{3} b m n p \log ^3(x) \log \left(f x^p\right)+\frac{1}{4} b m n p^2 \log ^4(x)","\frac{\log ^3\left(f x^p\right) \left(a+b \log \left(c \left(d+e x^m\right)^n\right)\right)}{3 p}+\frac{2 b n p \log \left(f x^p\right) \text{Li}_3\left(-\frac{e x^m}{d}\right)}{m^2}-\frac{b n \log ^2\left(f x^p\right) \text{Li}_2\left(-\frac{e x^m}{d}\right)}{m}-\frac{b n \log ^3\left(f x^p\right) \log \left(\frac{e x^m}{d}+1\right)}{3 p}-\frac{2 b n p^2 \text{Li}_4\left(-\frac{e x^m}{d}\right)}{m^3}",1,"(b*m*n*p^2*Log[x]^4)/4 - (b*m*n*p*Log[x]^3*Log[f*x^p])/3 + (a*Log[f*x^p]^3)/(3*p) + (2*b*n*p^2*Log[x]^3*Log[1 + d/(e*x^m)])/3 - b*n*p*Log[x]^2*Log[f*x^p]*Log[1 + d/(e*x^m)] - b*n*p^2*Log[x]^3*Log[d + e*x^m] + (b*n*p^2*Log[x]^2*Log[-((e*x^m)/d)]*Log[d + e*x^m])/m + 2*b*n*p*Log[x]^2*Log[f*x^p]*Log[d + e*x^m] - (2*b*n*p*Log[x]*Log[-((e*x^m)/d)]*Log[f*x^p]*Log[d + e*x^m])/m - b*n*Log[x]*Log[f*x^p]^2*Log[d + e*x^m] + (b*n*Log[-((e*x^m)/d)]*Log[f*x^p]^2*Log[d + e*x^m])/m + (b*p^2*Log[x]^3*Log[c*(d + e*x^m)^n])/3 - b*p*Log[x]^2*Log[f*x^p]*Log[c*(d + e*x^m)^n] + b*Log[x]*Log[f*x^p]^2*Log[c*(d + e*x^m)^n] - (b*n*p*Log[x]*(p*Log[x] - 2*Log[f*x^p])*PolyLog[2, -(d/(e*x^m))])/m + (b*n*(-(p*Log[x]) + Log[f*x^p])^2*PolyLog[2, 1 + (e*x^m)/d])/m + (2*b*n*p*Log[f*x^p]*PolyLog[3, -(d/(e*x^m))])/m^2 + (2*b*n*p^2*PolyLog[4, -(d/(e*x^m))])/m^3","B",1
623,1,265,102,0.192956,"\int \frac{\log \left(f x^p\right) \left(a+b \log \left(c \left(d+e x^m\right)^n\right)\right)}{x} \, dx","Integrate[(Log[f*x^p]*(a + b*Log[c*(d + e*x^m)^n]))/x,x]","\frac{a \log ^2\left(f x^p\right)}{2 p}+b \log (x) \log \left(f x^p\right) \log \left(c \left(d+e x^m\right)^n\right)-\frac{1}{2} b p \log ^2(x) \log \left(c \left(d+e x^m\right)^n\right)-\frac{b n \left(p \log (x)-\log \left(f x^p\right)\right) \text{Li}_2\left(\frac{e x^m}{d}+1\right)}{m}-b n \log (x) \log \left(f x^p\right) \log \left(d+e x^m\right)+\frac{b n \log \left(f x^p\right) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)}{m}+\frac{b n p \text{Li}_3\left(-\frac{d x^{-m}}{e}\right)}{m^2}+\frac{b n p \log (x) \text{Li}_2\left(-\frac{d x^{-m}}{e}\right)}{m}-\frac{1}{2} b n p \log ^2(x) \log \left(\frac{d x^{-m}}{e}+1\right)+b n p \log ^2(x) \log \left(d+e x^m\right)-\frac{b n p \log (x) \log \left(-\frac{e x^m}{d}\right) \log \left(d+e x^m\right)}{m}-\frac{1}{6} b m n p \log ^3(x)","\frac{\log ^2\left(f x^p\right) \left(a+b \log \left(c \left(d+e x^m\right)^n\right)\right)}{2 p}-\frac{b n \log \left(f x^p\right) \text{Li}_2\left(-\frac{e x^m}{d}\right)}{m}-\frac{b n \log ^2\left(f x^p\right) \log \left(\frac{e x^m}{d}+1\right)}{2 p}+\frac{b n p \text{Li}_3\left(-\frac{e x^m}{d}\right)}{m^2}",1,"-1/6*(b*m*n*p*Log[x]^3) + (a*Log[f*x^p]^2)/(2*p) - (b*n*p*Log[x]^2*Log[1 + d/(e*x^m)])/2 + b*n*p*Log[x]^2*Log[d + e*x^m] - (b*n*p*Log[x]*Log[-((e*x^m)/d)]*Log[d + e*x^m])/m - b*n*Log[x]*Log[f*x^p]*Log[d + e*x^m] + (b*n*Log[-((e*x^m)/d)]*Log[f*x^p]*Log[d + e*x^m])/m - (b*p*Log[x]^2*Log[c*(d + e*x^m)^n])/2 + b*Log[x]*Log[f*x^p]*Log[c*(d + e*x^m)^n] + (b*n*p*Log[x]*PolyLog[2, -(d/(e*x^m))])/m - (b*n*(p*Log[x] - Log[f*x^p])*PolyLog[2, 1 + (e*x^m)/d])/m + (b*n*p*PolyLog[3, -(d/(e*x^m))])/m^2","B",1
624,1,49,49,0.0150454,"\int \frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{x} \, dx","Integrate[(a + b*Log[c*(d + e*x^m)^n])/x,x]","a \log (x)+\frac{b \left(\log \left(-\frac{e x^m}{d}\right) \log \left(c \left(d+e x^m\right)^n\right)+n \text{Li}_2\left(\frac{e x^m+d}{d}\right)\right)}{m}","\frac{\log \left(-\frac{e x^m}{d}\right) \left(a+b \log \left(c \left(d+e x^m\right)^n\right)\right)}{m}+\frac{b n \text{Li}_2\left(\frac{e x^m}{d}+1\right)}{m}",1,"a*Log[x] + (b*(Log[-((e*x^m)/d)]*Log[c*(d + e*x^m)^n] + n*PolyLog[2, (d + e*x^m)/d]))/m","A",1
625,0,0,42,0.5617957,"\int \frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{x \log \left(f x^p\right)} \, dx","Integrate[(a + b*Log[c*(d + e*x^m)^n])/(x*Log[f*x^p]),x]","\int \frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{x \log \left(f x^p\right)} \, dx","b \text{Int}\left(\frac{\log \left(c \left(d+e x^m\right)^n\right)}{x \log \left(f x^p\right)},x\right)+\frac{a \log \left(\log \left(f x^p\right)\right)}{p}",0,"Integrate[(a + b*Log[c*(d + e*x^m)^n])/(x*Log[f*x^p]), x]","A",-1
626,0,0,64,2.1586721,"\int \frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{x \log ^2\left(f x^p\right)} \, dx","Integrate[(a + b*Log[c*(d + e*x^m)^n])/(x*Log[f*x^p]^2),x]","\int \frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{x \log ^2\left(f x^p\right)} \, dx","\frac{b e m n \text{Int}\left(\frac{x^{m-1}}{\left(d+e x^m\right) \log \left(f x^p\right)},x\right)}{p}-\frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{p \log \left(f x^p\right)}",0,"Integrate[(a + b*Log[c*(d + e*x^m)^n])/(x*Log[f*x^p]^2), x]","A",-1
627,0,0,69,11.0605859,"\int \frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{x \log ^3\left(f x^p\right)} \, dx","Integrate[(a + b*Log[c*(d + e*x^m)^n])/(x*Log[f*x^p]^3),x]","\int \frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{x \log ^3\left(f x^p\right)} \, dx","\frac{b e m n \text{Int}\left(\frac{x^{m-1}}{\left(d+e x^m\right) \log ^2\left(f x^p\right)},x\right)}{2 p}-\frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{2 p \log ^2\left(f x^p\right)}",0,"Integrate[(a + b*Log[c*(d + e*x^m)^n])/(x*Log[f*x^p]^3), x]","A",-1
628,1,65,76,0.0275238,"\int \log \left(c \left(d+e (f+g x)^p\right)^q\right) \, dx","Integrate[Log[c*(d + e*(f + g*x)^p)^q],x]","\frac{(f+g x) \log \left(c \left(d+e (f+g x)^p\right)^q\right)}{g}+\frac{p q (f+g x) \, _2F_1\left(1,\frac{1}{p};1+\frac{1}{p};-\frac{e (f+g x)^p}{d}\right)}{g}-p q x","\frac{(f+g x) \log \left(c \left(d+e (f+g x)^p\right)^q\right)}{g}-\frac{e p q (f+g x)^{p+1} \, _2F_1\left(1,1+\frac{1}{p};2+\frac{1}{p};-\frac{e (f+g x)^p}{d}\right)}{d g (p+1)}",1,"-(p*q*x) + (p*q*(f + g*x)*Hypergeometric2F1[1, p^(-1), 1 + p^(-1), -((e*(f + g*x)^p)/d)])/g + ((f + g*x)*Log[c*(d + e*(f + g*x)^p)^q])/g","A",1
629,1,147,169,0.1041201,"\int \log \left(c \left(d+e (f+g x)^3\right)^q\right) \, dx","Integrate[Log[c*(d + e*(f + g*x)^3)^q],x]","\frac{(f+g x) \log \left(c \left(d+e (f+g x)^3\right)^q\right)}{g}+\frac{\sqrt[3]{d} q \left(-\log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} (f+g x)+e^{2/3} (f+g x)^2\right)+2 \log \left(\sqrt[3]{d}+\sqrt[3]{e} (f+g x)\right)+2 \sqrt{3} \tan ^{-1}\left(\frac{2 \sqrt[3]{e} (f+g x)-\sqrt[3]{d}}{\sqrt{3} \sqrt[3]{d}}\right)\right)}{2 \sqrt[3]{e} g}-3 q x","\frac{(f+g x) \log \left(c \left(d+e (f+g x)^3\right)^q\right)}{g}-\frac{\sqrt[3]{d} q \log \left(d^{2/3}-\sqrt[3]{d} \sqrt[3]{e} (f+g x)+e^{2/3} (f+g x)^2\right)}{2 \sqrt[3]{e} g}+\frac{\sqrt[3]{d} q \log \left(\sqrt[3]{d}+\sqrt[3]{e} (f+g x)\right)}{\sqrt[3]{e} g}-\frac{\sqrt{3} \sqrt[3]{d} q \tan ^{-1}\left(\frac{\sqrt[3]{d}-2 \sqrt[3]{e} (f+g x)}{\sqrt{3} \sqrt[3]{d}}\right)}{\sqrt[3]{e} g}-3 q x",1,"-3*q*x + (d^(1/3)*q*(2*Sqrt[3]*ArcTan[(-d^(1/3) + 2*e^(1/3)*(f + g*x))/(Sqrt[3]*d^(1/3))] + 2*Log[d^(1/3) + e^(1/3)*(f + g*x)] - Log[d^(2/3) - d^(1/3)*e^(1/3)*(f + g*x) + e^(2/3)*(f + g*x)^2]))/(2*e^(1/3)*g) + ((f + g*x)*Log[c*(d + e*(f + g*x)^3)^q])/g","A",1
630,1,63,63,0.035207,"\int \log \left(c \left(d+e (f+g x)^2\right)^q\right) \, dx","Integrate[Log[c*(d + e*(f + g*x)^2)^q],x]","\frac{(f+g x) \log \left(c \left(d+e (f+g x)^2\right)^q\right)}{g}+\frac{2 \sqrt{d} q \tan ^{-1}\left(\frac{\sqrt{e} (f+g x)}{\sqrt{d}}\right)}{\sqrt{e} g}-2 q x","\frac{(f+g x) \log \left(c \left(d+e (f+g x)^2\right)^q\right)}{g}+\frac{2 \sqrt{d} q \tan ^{-1}\left(\frac{\sqrt{e} (f+g x)}{\sqrt{d}}\right)}{\sqrt{e} g}-2 q x",1,"-2*q*x + (2*Sqrt[d]*q*ArcTan[(Sqrt[e]*(f + g*x))/Sqrt[d]])/(Sqrt[e]*g) + ((f + g*x)*Log[c*(d + e*(f + g*x)^2)^q])/g","A",1
631,1,47,35,0.0321289,"\int \log \left(c (d+e (f+g x))^q\right) \, dx","Integrate[Log[c*(d + e*(f + g*x))^q],x]","\frac{(f+g x) \log \left(c (d+e (f+g x))^q\right)}{g}+\frac{d q \log (d+e f+e g x)}{e g}-q x","\frac{(d+e f+e g x) \log \left(c (d+e (f+g x))^q\right)}{e g}-q x",1,"-(q*x) + (d*q*Log[d + e*f + e*g*x])/(e*g) + ((f + g*x)*Log[c*(d + e*(f + g*x))^q])/g","A",1
632,1,56,45,0.0491628,"\int \log \left(c \left(d+\frac{e}{f+g x}\right)^q\right) \, dx","Integrate[Log[c*(d + e/(f + g*x))^q],x]","\frac{d g x \log \left(c \left(d+\frac{e}{f+g x}\right)^q\right)+q (d f+e) \log (d f+d g x+e)-d f q \log (f+g x)}{d g}","\frac{(f+g x) \log \left(c \left(d+\frac{e}{f+g x}\right)^q\right)}{g}+\frac{e q \log (d (f+g x)+e)}{d g}",1,"(-(d*f*q*Log[f + g*x]) + (e + d*f)*q*Log[e + d*f + d*g*x] + d*g*x*Log[c*(d + e/(f + g*x))^q])/(d*g)","A",1
633,1,61,59,0.0480322,"\int \log \left(c \left(d+\frac{e}{(f+g x)^2}\right)^q\right) \, dx","Integrate[Log[c*(d + e/(f + g*x)^2)^q],x]","\frac{(f+g x) \log \left(c \left(d+\frac{e}{(f+g x)^2}\right)^q\right)}{g}-\frac{2 \sqrt{e} q \tan ^{-1}\left(\frac{\sqrt{e}}{\sqrt{d} (f+g x)}\right)}{\sqrt{d} g}","\frac{(f+g x) \log \left(c \left(d+\frac{e}{(f+g x)^2}\right)^q\right)}{g}+\frac{2 \sqrt{e} q \tan ^{-1}\left(\frac{\sqrt{d} (f+g x)}{\sqrt{e}}\right)}{\sqrt{d} g}",1,"(-2*Sqrt[e]*q*ArcTan[Sqrt[e]/(Sqrt[d]*(f + g*x))])/(Sqrt[d]*g) + ((f + g*x)*Log[c*(d + e/(f + g*x)^2)^q])/g","A",1
634,1,66,165,0.3272277,"\int \log \left(c \left(d+\frac{e}{(f+g x)^3}\right)^q\right) \, dx","Integrate[Log[c*(d + e/(f + g*x)^3)^q],x]","\frac{(f+g x) \log \left(c \left(d+\frac{e}{(f+g x)^3}\right)^q\right)}{g}-\frac{3 e q \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};-\frac{e}{d (f+g x)^3}\right)}{2 d g (f+g x)^2}","\frac{(f+g x) \log \left(c \left(d+\frac{e}{(f+g x)^3}\right)^q\right)}{g}-\frac{\sqrt[3]{e} q \log \left(d^{2/3} (f+g x)^2-\sqrt[3]{d} \sqrt[3]{e} (f+g x)+e^{2/3}\right)}{2 \sqrt[3]{d} g}+\frac{\sqrt[3]{e} q \log \left(\sqrt[3]{d} (f+g x)+\sqrt[3]{e}\right)}{\sqrt[3]{d} g}-\frac{\sqrt{3} \sqrt[3]{e} q \tan ^{-1}\left(\frac{\sqrt[3]{e}-2 \sqrt[3]{d} (f+g x)}{\sqrt{3} \sqrt[3]{e}}\right)}{\sqrt[3]{d} g}",1,"(-3*e*q*Hypergeometric2F1[2/3, 1, 5/3, -(e/(d*(f + g*x)^3))])/(2*d*g*(f + g*x)^2) + ((f + g*x)*Log[c*(d + e/(f + g*x)^3)^q])/g","C",1
635,0,0,25,0.4201769,"\int \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^n \, dx","Integrate[(a + b*Log[c*(d + e/(f + g*x))^p])^n,x]","\int \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^n \, dx","\text{Int}\left(\left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^n,x\right)",0,"Integrate[(a + b*Log[c*(d + e/(f + g*x))^p])^n, x]","A",-1
636,1,739,221,1.4182645,"\int \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^4 \, dx","Integrate[(a + b*Log[c*(d + e/(f + g*x))^p])^4,x]","\frac{4 b^3 p^3 \left(6 e \text{Li}_3\left(\frac{e}{d f+d g x}+1\right)-6 e \text{Li}_2\left(\frac{e}{d f+d g x}+1\right) \log \left(d+\frac{e}{f+g x}\right)+\left((d f+d g x+e) \log \left(d+\frac{e}{f+g x}\right)-3 e \log \left(-\frac{e}{d f+d g x}\right)\right) \log ^2\left(d+\frac{e}{f+g x}\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)-b p \log \left(d+\frac{e}{f+g x}\right)\right)+6 b^2 p^2 \left(-d f \left(\log \left(-\frac{e}{d f+d g x}\right) \left(\log \left(-\frac{e}{d f+d g x}\right)+2 \log \left(\frac{d f+d g x+e}{e}\right)\right)-2 \text{Li}_2\left(-\frac{d (f+g x)}{e}\right)\right)+(d f+e) \left(2 \text{Li}_2\left(\frac{e+d f+d g x}{e}\right)+\left(2 \log \left(-\frac{d (f+g x)}{e}\right)-\log (d f+d g x+e)\right) \log (d f+d g x+e)\right)+d g x \log ^2\left(\frac{d f+d g x+e}{f+g x}\right)+2 d f \log \left(-\frac{e}{d f+d g x}\right) \log \left(\frac{d f+d g x+e}{f+g x}\right)+2 (d f+e) \log (d f+d g x+e) \log \left(\frac{d f+d g x+e}{f+g x}\right)\right) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)-b p \log \left(d+\frac{e}{f+g x}\right)\right)^2-4 b p \left(-(d f+e) \log (d f+d g x+e)-d g x \log \left(\frac{d f+d g x+e}{f+g x}\right)+d f \log (f+g x)\right) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)-b p \log \left(d+\frac{e}{f+g x}\right)\right)^3+d g x \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)-b p \log \left(d+\frac{e}{f+g x}\right)\right)^4-b^4 p^4 \left(24 e \text{Li}_4\left(\frac{e}{d f+d g x}+1\right)+12 e \text{Li}_2\left(\frac{e}{d f+d g x}+1\right) \log ^2\left(d+\frac{e}{f+g x}\right)-24 e \text{Li}_3\left(\frac{e}{d f+d g x}+1\right) \log \left(d+\frac{e}{f+g x}\right)-e \log ^4\left(d+\frac{e}{f+g x}\right)-d f \log ^4\left(d+\frac{e}{f+g x}\right)-d g x \log ^4\left(d+\frac{e}{f+g x}\right)+4 e \log \left(-\frac{e}{d f+d g x}\right) \log ^3\left(d+\frac{e}{f+g x}\right)\right)}{d g}","\frac{24 b^3 e p^3 \text{Li}_3\left(\frac{e}{d (f+g x)}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)}{d g}-\frac{12 b^2 e p^2 \text{Li}_2\left(\frac{e}{d (f+g x)}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^2}{d g}-\frac{4 b e p \log \left(-\frac{e}{d (f+g x)}\right) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^3}{d g}+\frac{(d (f+g x)+e) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^4}{d g}-\frac{24 b^4 e p^4 \text{Li}_4\left(\frac{e}{d (f+g x)}+1\right)}{d g}",1,"(-4*b*p*(d*f*Log[f + g*x] - (e + d*f)*Log[e + d*f + d*g*x] - d*g*x*Log[(e + d*f + d*g*x)/(f + g*x)])*(a - b*p*Log[d + e/(f + g*x)] + b*Log[c*(d + e/(f + g*x))^p])^3 + d*g*x*(a - b*p*Log[d + e/(f + g*x)] + b*Log[c*(d + e/(f + g*x))^p])^4 + 6*b^2*p^2*(a - b*p*Log[d + e/(f + g*x)] + b*Log[c*(d + e/(f + g*x))^p])^2*(2*d*f*Log[-(e/(d*f + d*g*x))]*Log[(e + d*f + d*g*x)/(f + g*x)] + 2*(e + d*f)*Log[e + d*f + d*g*x]*Log[(e + d*f + d*g*x)/(f + g*x)] + d*g*x*Log[(e + d*f + d*g*x)/(f + g*x)]^2 - d*f*(Log[-(e/(d*f + d*g*x))]*(Log[-(e/(d*f + d*g*x))] + 2*Log[(e + d*f + d*g*x)/e]) - 2*PolyLog[2, -((d*(f + g*x))/e)]) + (e + d*f)*((2*Log[-((d*(f + g*x))/e)] - Log[e + d*f + d*g*x])*Log[e + d*f + d*g*x] + 2*PolyLog[2, (e + d*f + d*g*x)/e])) + 4*b^3*p^3*(a - b*p*Log[d + e/(f + g*x)] + b*Log[c*(d + e/(f + g*x))^p])*(Log[d + e/(f + g*x)]^2*(-3*e*Log[-(e/(d*f + d*g*x))] + (e + d*f + d*g*x)*Log[d + e/(f + g*x)]) - 6*e*Log[d + e/(f + g*x)]*PolyLog[2, 1 + e/(d*f + d*g*x)] + 6*e*PolyLog[3, 1 + e/(d*f + d*g*x)]) - b^4*p^4*(4*e*Log[-(e/(d*f + d*g*x))]*Log[d + e/(f + g*x)]^3 - e*Log[d + e/(f + g*x)]^4 - d*f*Log[d + e/(f + g*x)]^4 - d*g*x*Log[d + e/(f + g*x)]^4 + 12*e*Log[d + e/(f + g*x)]^2*PolyLog[2, 1 + e/(d*f + d*g*x)] - 24*e*Log[d + e/(f + g*x)]*PolyLog[3, 1 + e/(d*f + d*g*x)] + 24*e*PolyLog[4, 1 + e/(d*f + d*g*x)]))/(d*g)","B",1
637,1,415,168,0.7241477,"\int \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^3 \, dx","Integrate[(a + b*Log[c*(d + e/(f + g*x))^p])^3,x]","\frac{3 b^2 p^2 \left(2 e \text{Li}_2\left(\frac{d (f+g x)}{e}+1\right)+d (f+g x) \log ^2\left(d+\frac{e}{f+g x}\right)+e \left(2 \log \left(-\frac{d (f+g x)}{e}\right)-\log (d f+d g x+e)+2 \log \left(d+\frac{e}{f+g x}\right)\right) \log (d (f+g x)+e)\right) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)-b p \log \left(d+\frac{e}{f+g x}\right)\right)+3 b d p (f+g x) \log \left(d+\frac{e}{f+g x}\right) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)-b p \log \left(d+\frac{e}{f+g x}\right)\right)^2+3 b e p \log (d (f+g x)+e) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)-b p \log \left(d+\frac{e}{f+g x}\right)\right)^2+d (f+g x) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)-b p \log \left(d+\frac{e}{f+g x}\right)\right)^3+b^3 p^3 \left(6 e \text{Li}_3\left(\frac{e}{d f+d g x}+1\right)-6 e \text{Li}_2\left(\frac{e}{d f+d g x}+1\right) \log \left(d+\frac{e}{f+g x}\right)+\left((d f+d g x+e) \log \left(d+\frac{e}{f+g x}\right)-3 e \log \left(-\frac{e}{d f+d g x}\right)\right) \log ^2\left(d+\frac{e}{f+g x}\right)\right)}{d g}","-\frac{6 b^2 e p^2 \text{Li}_2\left(\frac{e}{d (f+g x)}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)}{d g}-\frac{3 b e p \log \left(-\frac{e}{d (f+g x)}\right) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^2}{d g}+\frac{(d (f+g x)+e) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^3}{d g}+\frac{6 b^3 e p^3 \text{Li}_3\left(\frac{e}{d (f+g x)}+1\right)}{d g}",1,"(3*b*d*p*(f + g*x)*Log[d + e/(f + g*x)]*(a - b*p*Log[d + e/(f + g*x)] + b*Log[c*(d + e/(f + g*x))^p])^2 + d*(f + g*x)*(a - b*p*Log[d + e/(f + g*x)] + b*Log[c*(d + e/(f + g*x))^p])^3 + 3*b*e*p*(a - b*p*Log[d + e/(f + g*x)] + b*Log[c*(d + e/(f + g*x))^p])^2*Log[e + d*(f + g*x)] + 3*b^2*p^2*(a - b*p*Log[d + e/(f + g*x)] + b*Log[c*(d + e/(f + g*x))^p])*(d*(f + g*x)*Log[d + e/(f + g*x)]^2 + e*(2*Log[-((d*(f + g*x))/e)] - Log[e + d*f + d*g*x] + 2*Log[d + e/(f + g*x)])*Log[e + d*(f + g*x)] + 2*e*PolyLog[2, 1 + (d*(f + g*x))/e]) + b^3*p^3*(Log[d + e/(f + g*x)]^2*(-3*e*Log[-(e/(d*f + d*g*x))] + (e + d*f + d*g*x)*Log[d + e/(f + g*x)]) - 6*e*Log[d + e/(f + g*x)]*PolyLog[2, 1 + e/(d*f + d*g*x)] + 6*e*PolyLog[3, 1 + e/(d*f + d*g*x)]))/(d*g)","B",1
638,1,219,115,0.2646766,"\int \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^2 \, dx","Integrate[(a + b*Log[c*(d + e/(f + g*x))^p])^2,x]","x \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^2-\frac{b p \left(2 d f \log (f+g x) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)-2 (d f+e) \log (d (f+g x)+e) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)+b d f p \left(\log (f+g x) \left(\log (f+g x)-2 \log \left(\frac{d f+d g x+e}{e}\right)\right)-2 \text{Li}_2\left(-\frac{d (f+g x)}{e}\right)\right)-b p (d f+e) \left(2 \text{Li}_2\left(\frac{e+d f+d g x}{e}\right)+\left(2 \log \left(-\frac{d (f+g x)}{e}\right)-\log (d f+d g x+e)\right) \log (d (f+g x)+e)\right)\right)}{d g}","-\frac{2 b e p \log \left(-\frac{e}{d (f+g x)}\right) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)}{d g}+\frac{(d (f+g x)+e) \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^2}{d g}-\frac{2 b^2 e p^2 \text{Li}_2\left(\frac{e}{d (f+g x)}+1\right)}{d g}",1,"x*(a + b*Log[c*(d + e/(f + g*x))^p])^2 - (b*p*(2*d*f*Log[f + g*x]*(a + b*Log[c*(d + e/(f + g*x))^p]) - 2*(e + d*f)*(a + b*Log[c*(d + e/(f + g*x))^p])*Log[e + d*(f + g*x)] + b*d*f*p*(Log[f + g*x]*(Log[f + g*x] - 2*Log[(e + d*f + d*g*x)/e]) - 2*PolyLog[2, -((d*(f + g*x))/e)]) - b*(e + d*f)*p*((2*Log[-((d*(f + g*x))/e)] - Log[e + d*f + d*g*x])*Log[e + d*(f + g*x)] + 2*PolyLog[2, (e + d*f + d*g*x)/e])))/(d*g)","A",1
639,1,70,50,0.0424507,"\int \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right) \, dx","Integrate[a + b*Log[c*(d + e/(f + g*x))^p],x]","a x+b x \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)-b e g p \left(\frac{f \log (f+g x)}{e g^2}-\frac{(d f+e) \log (d f+d g x+e)}{d e g^2}\right)","a x+\frac{b (f+g x) \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)}{g}+\frac{b e p \log (d (f+g x)+e)}{d g}",1,"a*x - b*e*g*p*((f*Log[f + g*x])/(e*g^2) - ((e + d*f)*Log[e + d*f + d*g*x])/(d*e*g^2)) + b*x*Log[c*(d + e/(f + g*x))^p]","A",1
640,0,0,25,0.5557168,"\int \frac{1}{a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)} \, dx","Integrate[(a + b*Log[c*(d + e/(f + g*x))^p])^(-1),x]","\int \frac{1}{a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)} \, dx","\text{Int}\left(\frac{1}{a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)},x\right)",0,"Integrate[(a + b*Log[c*(d + e/(f + g*x))^p])^(-1), x]","A",-1
641,0,0,25,0.8756612,"\int \frac{1}{\left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^2} \, dx","Integrate[(a + b*Log[c*(d + e/(f + g*x))^p])^(-2),x]","\int \frac{1}{\left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^2} \, dx","\text{Int}\left(\frac{1}{\left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^2},x\right)",0,"Integrate[(a + b*Log[c*(d + e/(f + g*x))^p])^(-2), x]","A",-1