1,1,80,0,0.0465048,"\int x^4 \log \left(c \left(a+b x^2\right)^p\right) \, dx","Int[x^4*Log[c*(a + b*x^2)^p],x]","-\frac{2 a^2 p x}{5 b^2}+\frac{2 a^{5/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{5 b^{5/2}}+\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}","-\frac{2 a^2 p x}{5 b^2}+\frac{2 a^{5/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{5 b^{5/2}}+\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,"(-2*a^2*p*x)/(5*b^2) + (2*a*p*x^3)/(15*b) - (2*p*x^5)/25 + (2*a^(5/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(5*b^(5/2)) + (x^5*Log[c*(a + b*x^2)^p])/5","A",4,3,16,0.1875,1,"{2455, 302, 205}"
2,1,59,0,0.0492964,"\int x^3 \log \left(c \left(a+b x^2\right)^p\right) \, dx","Int[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",4,3,16,0.1875,1,"{2454, 2395, 43}"
3,1,66,0,0.036543,"\int x^2 \log \left(c \left(a+b x^2\right)^p\right) \, dx","Int[x^2*Log[c*(a + b*x^2)^p],x]","-\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}","-\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,"(2*a*p*x)/(3*b) - (2*p*x^3)/9 - (2*a^(3/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(3*b^(3/2)) + (x^3*Log[c*(a + b*x^2)^p])/3","A",4,3,16,0.1875,1,"{2455, 302, 205}"
4,1,35,0,0.0244695,"\int x \log \left(c \left(a+b x^2\right)^p\right) \, dx","Int[x*Log[c*(a + b*x^2)^p],x]","\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}","\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)/2 + ((a + b*x^2)*Log[c*(a + b*x^2)^p])/(2*b)","A",3,3,14,0.2143,1,"{2454, 2389, 2295}"
5,1,45,0,0.0183606,"\int \log \left(c \left(a+b x^2\right)^p\right) \, dx","Int[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",3,3,12,0.2500,1,"{2448, 321, 205}"
6,1,44,0,0.045528,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x} \, dx","Int[Log[c*(a + b*x^2)^p]/x,x]","\frac{1}{2} p \text{PolyLog}\left(2,\frac{b x^2}{a}+1\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{PolyLog}\left(2,\frac{b x^2}{a}+1\right)+\frac{1}{2} \log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)",1,"(Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p])/2 + (p*PolyLog[2, 1 + (b*x^2)/a])/2","A",3,3,16,0.1875,1,"{2454, 2394, 2315}"
7,1,44,0,0.0204981,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^2} \, dx","Int[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",2,2,16,0.1250,1,"{2455, 205}"
8,1,45,0,0.037124,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^3} \, dx","Int[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",5,5,16,0.3125,1,"{2454, 2395, 36, 29, 31}"
9,1,60,0,0.0295252,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^4} \, dx","Int[Log[c*(a + b*x^2)^p]/x^4,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}","-\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)/(3*a*x) - (2*b^(3/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(3*a^(3/2)) - Log[c*(a + b*x^2)^p]/(3*x^3)","A",3,3,16,0.1875,1,"{2455, 325, 205}"
10,1,64,0,0.0520589,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^5} \, dx","Int[Log[c*(a + b*x^2)^p]/x^5,x]","\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}","\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)/(4*a*x^2) - (b^2*p*Log[x])/(2*a^2) + (b^2*p*Log[a + b*x^2])/(4*a^2) - Log[c*(a + b*x^2)^p]/(4*x^4)","A",4,3,16,0.1875,1,"{2454, 2395, 44}"
11,1,74,0,0.0365117,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^6} \, dx","Int[Log[c*(a + b*x^2)^p]/x^6,x]","\frac{2 b^2 p}{5 a^2 x}+\frac{2 b^{5/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{5 a^{5/2}}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{5 x^5}-\frac{2 b p}{15 a x^3}","\frac{2 b^2 p}{5 a^2 x}+\frac{2 b^{5/2} p \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{5 a^{5/2}}-\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)/(15*a*x^3) + (2*b^2*p)/(5*a^2*x) + (2*b^(5/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(5*a^(5/2)) - Log[c*(a + b*x^2)^p]/(5*x^5)","A",4,3,16,0.1875,1,"{2455, 325, 205}"
12,1,78,0,0.0601039,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^7} \, dx","Int[Log[c*(a + b*x^2)^p]/x^7,x]","\frac{b^2 p}{6 a^2 x^2}-\frac{b^3 p \log \left(a+b x^2\right)}{6 a^3}+\frac{b^3 p \log (x)}{3 a^3}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{6 x^6}-\frac{b p}{12 a x^4}","\frac{b^2 p}{6 a^2 x^2}-\frac{b^3 p \log \left(a+b x^2\right)}{6 a^3}+\frac{b^3 p \log (x)}{3 a^3}-\frac{\log \left(c \left(a+b x^2\right)^p\right)}{6 x^6}-\frac{b p}{12 a x^4}",1,"-(b*p)/(12*a*x^4) + (b^2*p)/(6*a^2*x^2) + (b^3*p*Log[x])/(3*a^3) - (b^3*p*Log[a + b*x^2])/(6*a^3) - Log[c*(a + b*x^2)^p]/(6*x^6)","A",4,3,16,0.1875,1,"{2454, 2395, 44}"
13,1,59,0,0.0494319,"\int x^5 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Int[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",4,3,16,0.1875,1,"{2454, 2395, 43}"
14,1,159,0,0.1290386,"\int x^4 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Int[x^4*Log[c*(a + b*x^3)^p],x]","-\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}","-\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 + (Sqrt[3]*a^(5/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(5*b^(5/3)) + (a^(5/3)*p*Log[a^(1/3) + b^(1/3)*x])/(5*b^(5/3)) - (a^(5/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(10*b^(5/3)) + (x^5*Log[c*(a + b*x^3)^p])/5","A",9,8,16,0.5000,1,"{2455, 302, 292, 31, 634, 617, 204, 628}"
15,1,157,0,0.1144584,"\int x^3 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Int[x^3*Log[c*(a + b*x^3)^p],x]","\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}","\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,"(3*a*p*x)/(4*b) - (3*p*x^4)/16 + (Sqrt[3]*a^(4/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(4*b^(4/3)) - (a^(4/3)*p*Log[a^(1/3) + b^(1/3)*x])/(4*b^(4/3)) + (a^(4/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(8*b^(4/3)) + (x^4*Log[c*(a + b*x^3)^p])/4","A",9,8,16,0.5000,1,"{2455, 302, 200, 31, 634, 617, 204, 628}"
16,1,35,0,0.0291231,"\int x^2 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Int[x^2*Log[c*(a + b*x^3)^p],x]","\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}","\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)/3 + ((a + b*x^3)*Log[c*(a + b*x^3)^p])/(3*b)","A",3,3,16,0.1875,1,"{2454, 2389, 2295}"
17,1,147,0,0.0846344,"\int x \log \left(c \left(a+b x^3\right)^p\right) \, dx","Int[x*Log[c*(a + b*x^3)^p],x]","\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}","\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 - (Sqrt[3]*a^(2/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(2*b^(2/3)) - (a^(2/3)*p*Log[a^(1/3) + b^(1/3)*x])/(2*b^(2/3)) + (a^(2/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(4*b^(2/3)) + (x^2*Log[c*(a + b*x^3)^p])/2","A",8,8,14,0.5714,1,"{2455, 321, 292, 31, 634, 617, 204, 628}"
18,1,133,0,0.081811,"\int \log \left(c \left(a+b x^3\right)^p\right) \, dx","Int[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{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\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[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/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",8,8,12,0.6667,1,"{2448, 321, 200, 31, 634, 617, 204, 628}"
19,1,44,0,0.0477984,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x} \, dx","Int[Log[c*(a + b*x^3)^p]/x,x]","\frac{1}{3} p \text{PolyLog}\left(2,\frac{b x^3}{a}+1\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{PolyLog}\left(2,\frac{b x^3}{a}+1\right)+\frac{1}{3} \log \left(-\frac{b x^3}{a}\right) \log \left(c \left(a+b x^3\right)^p\right)",1,"(Log[-((b*x^3)/a)]*Log[c*(a + b*x^3)^p])/3 + (p*PolyLog[2, 1 + (b*x^3)/a])/3","A",3,3,16,0.1875,1,"{2454, 2394, 2315}"
20,1,133,0,0.0777852,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^2} \, dx","Int[Log[c*(a + b*x^3)^p]/x^2,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}}","\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,"-((Sqrt[3]*b^(1/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/a^(1/3)) - (b^(1/3)*p*Log[a^(1/3) + b^(1/3)*x])/a^(1/3) + (b^(1/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(2*a^(1/3)) - Log[c*(a + b*x^3)^p]/x","A",7,7,16,0.4375,1,"{2455, 292, 31, 634, 617, 204, 628}"
21,1,139,0,0.0747968,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^3} \, dx","Int[Log[c*(a + b*x^3)^p]/x^3,x]","-\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}","-\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,"-(Sqrt[3]*b^(2/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(2*a^(2/3)) + (b^(2/3)*p*Log[a^(1/3) + b^(1/3)*x])/(2*a^(2/3)) - (b^(2/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(4*a^(2/3)) - Log[c*(a + b*x^3)^p]/(2*x^2)","A",7,7,16,0.4375,1,"{2455, 200, 31, 634, 617, 204, 628}"
22,1,45,0,0.0385288,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^4} \, dx","Int[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",5,5,16,0.3125,1,"{2454, 2395, 36, 29, 31}"
23,1,151,0,0.0945938,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^5} \, dx","Int[Log[c*(a + b*x^3)^p]/x^5,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}","-\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)/(4*a*x) + (Sqrt[3]*b^(4/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(4*a^(4/3)) + (b^(4/3)*p*Log[a^(1/3) + b^(1/3)*x])/(4*a^(4/3)) - (b^(4/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(8*a^(4/3)) - Log[c*(a + b*x^3)^p]/(4*x^4)","A",8,8,16,0.5000,1,"{2455, 325, 292, 31, 634, 617, 204, 628}"
24,1,151,0,0.0911043,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^6} \, dx","Int[Log[c*(a + b*x^3)^p]/x^6,x]","\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}","\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)/(10*a*x^2) + (Sqrt[3]*b^(5/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(5*a^(5/3)) - (b^(5/3)*p*Log[a^(1/3) + b^(1/3)*x])/(5*a^(5/3)) + (b^(5/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(10*a^(5/3)) - Log[c*(a + b*x^3)^p]/(5*x^5)","A",8,8,16,0.5000,1,"{2455, 325, 200, 31, 634, 617, 204, 628}"
25,1,64,0,0.051364,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^7} \, dx","Int[Log[c*(a + b*x^3)^p]/x^7,x]","\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}","\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)/(6*a*x^3) - (b^2*p*Log[x])/(2*a^2) + (b^2*p*Log[a + b*x^3])/(6*a^2) - Log[c*(a + b*x^3)^p]/(6*x^6)","A",4,3,16,0.1875,1,"{2454, 2395, 44}"
26,1,89,0,0.0549788,"\int x^4 \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Int[x^4*Log[c*(a + b/x)^p],x]","\frac{b^3 p x^2}{10 a^3}-\frac{b^2 p x^3}{15 a^2}-\frac{b^4 p x}{5 a^4}+\frac{b^5 p \log (a x+b)}{5 a^5}+\frac{1}{5} x^5 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p x^4}{20 a}","\frac{b^3 p x^2}{10 a^3}-\frac{b^2 p x^3}{15 a^2}-\frac{b^4 p x}{5 a^4}+\frac{b^5 p \log (a x+b)}{5 a^5}+\frac{1}{5} x^5 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p x^4}{20 a}",1,"-(b^4*p*x)/(5*a^4) + (b^3*p*x^2)/(10*a^3) - (b^2*p*x^3)/(15*a^2) + (b*p*x^4)/(20*a) + (x^5*Log[c*(a + b/x)^p])/5 + (b^5*p*Log[b + a*x])/(5*a^5)","A",4,3,16,0.1875,1,"{2455, 263, 43}"
27,1,75,0,0.040069,"\int x^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Int[x^3*Log[c*(a + b/x)^p],x]","-\frac{b^2 p x^2}{8 a^2}+\frac{b^3 p x}{4 a^3}-\frac{b^4 p \log (a x+b)}{4 a^4}+\frac{1}{4} x^4 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p x^3}{12 a}","-\frac{b^2 p x^2}{8 a^2}+\frac{b^3 p x}{4 a^3}-\frac{b^4 p \log (a x+b)}{4 a^4}+\frac{1}{4} x^4 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p x^3}{12 a}",1,"(b^3*p*x)/(4*a^3) - (b^2*p*x^2)/(8*a^2) + (b*p*x^3)/(12*a) + (x^4*Log[c*(a + b/x)^p])/4 - (b^4*p*Log[b + a*x])/(4*a^4)","A",4,3,16,0.1875,1,"{2455, 263, 43}"
28,1,61,0,0.0316943,"\int x^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Int[x^2*Log[c*(a + b/x)^p],x]","-\frac{b^2 p x}{3 a^2}+\frac{b^3 p \log (a x+b)}{3 a^3}+\frac{1}{3} x^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p x^2}{6 a}","-\frac{b^2 p x}{3 a^2}+\frac{b^3 p \log (a x+b)}{3 a^3}+\frac{1}{3} x^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p x^2}{6 a}",1,"-(b^2*p*x)/(3*a^2) + (b*p*x^2)/(6*a) + (x^3*Log[c*(a + b/x)^p])/3 + (b^3*p*Log[b + a*x])/(3*a^3)","A",4,3,16,0.1875,1,"{2455, 263, 43}"
29,1,47,0,0.0210677,"\int x \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Int[x*Log[c*(a + b/x)^p],x]","-\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}","-\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,"(b*p*x)/(2*a) + (x^2*Log[c*(a + b/x)^p])/2 - (b^2*p*Log[b + a*x])/(2*a^2)","A",4,3,14,0.2143,1,"{2455, 193, 43}"
30,1,27,0,0.0087283,"\int \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Int[Log[c*(a + b/x)^p],x]","x \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p \log (a x+b)}{a}","x \log \left(c \left(a+\frac{b}{x}\right)^p\right)+\frac{b p \log (a x+b)}{a}",1,"x*Log[c*(a + b/x)^p] + (b*p*Log[b + a*x])/a","A",3,3,12,0.2500,1,"{2448, 263, 31}"
31,1,40,0,0.0370085,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x} \, dx","Int[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{PolyLog}\left(2,\frac{b}{a x}+1\right)","\log \left(-\frac{b}{a x}\right) \left(-\log \left(c \left(a+\frac{b}{x}\right)^p\right)\right)-p \text{PolyLog}\left(2,\frac{b}{a x}+1\right)",1,"-(Log[c*(a + b/x)^p]*Log[-(b/(a*x))]) - p*PolyLog[2, 1 + b/(a*x)]","A",3,3,16,0.1875,1,"{2454, 2394, 2315}"
32,1,30,0,0.0211428,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^2} \, dx","Int[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",3,3,16,0.1875,1,"{2454, 2389, 2295}"
33,1,59,0,0.0354572,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^3} \, dx","Int[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",4,3,16,0.1875,1,"{2454, 2395, 43}"
34,1,73,0,0.0501546,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^4} \, dx","Int[Log[c*(a + b/x)^p]/x^4,x]","\frac{a^2 p}{3 b^2 x}-\frac{a^3 p \log \left(a+\frac{b}{x}\right)}{3 b^3}-\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^2 p}{3 b^2 x}-\frac{a^3 p \log \left(a+\frac{b}{x}\right)}{3 b^3}-\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",4,3,16,0.1875,1,"{2454, 2395, 43}"
35,1,87,0,0.0560602,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^5} \, dx","Int[Log[c*(a + b/x)^p]/x^5,x]","\frac{a^2 p}{8 b^2 x^2}-\frac{a^3 p}{4 b^3 x}+\frac{a^4 p \log \left(a+\frac{b}{x}\right)}{4 b^4}-\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^2 p}{8 b^2 x^2}-\frac{a^3 p}{4 b^3 x}+\frac{a^4 p \log \left(a+\frac{b}{x}\right)}{4 b^4}-\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",4,3,16,0.1875,1,"{2454, 2395, 43}"
36,1,72,0,0.0375931,"\int x^4 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Int[x^4*Log[c*(a + b/x^2)^p],x]","-\frac{2 b^2 p x}{5 a^2}+\frac{2 b^{5/2} p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{5 a^{5/2}}+\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}","-\frac{2 b^2 p x}{5 a^2}+\frac{2 b^{5/2} p \tan ^{-1}\left(\frac{\sqrt{a} x}{\sqrt{b}}\right)}{5 a^{5/2}}+\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^2*p*x)/(5*a^2) + (2*b*p*x^3)/(15*a) + (2*b^(5/2)*p*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(5*a^(5/2)) + (x^5*Log[c*(a + b/x^2)^p])/5","A",5,4,16,0.2500,1,"{2455, 263, 302, 205}"
37,1,51,0,0.0335074,"\int x^3 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Int[x^3*Log[c*(a + b/x^2)^p],x]","-\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}","-\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,"(b*p*x^2)/(4*a) + (x^4*Log[c*(a + b/x^2)^p])/4 - (b^2*p*Log[b + a*x^2])/(4*a^2)","A",5,4,16,0.2500,1,"{2455, 263, 266, 43}"
38,1,58,0,0.0270836,"\int x^2 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Int[x^2*Log[c*(a + b/x^2)^p],x]","-\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}","-\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)/(3*a) - (2*b^(3/2)*p*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(3*a^(3/2)) + (x^3*Log[c*(a + b/x^2)^p])/3","A",4,4,16,0.2500,1,"{2455, 193, 321, 205}"
39,1,37,0,0.0144121,"\int x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Int[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 x^2+b\right)}{2 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,"(x^2*Log[c*(a + b/x^2)^p])/2 + (b*p*Log[b + a*x^2])/(2*a)","A",3,3,14,0.2143,1,"{2455, 263, 260}"
40,1,41,0,0.0148343,"\int \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Int[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{a} x}{\sqrt{b}}\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[a]*x)/Sqrt[b]])/Sqrt[a] + x*Log[c*(a + b/x^2)^p]","A",3,3,12,0.2500,1,"{2448, 263, 205}"
41,1,44,0,0.040415,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x} \, dx","Int[Log[c*(a + b/x^2)^p]/x,x]","-\frac{1}{2} p \text{PolyLog}\left(2,\frac{b}{a x^2}+1\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{PolyLog}\left(2,\frac{b}{a x^2}+1\right)-\frac{1}{2} \log \left(-\frac{b}{a x^2}\right) \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)",1,"-(Log[c*(a + b/x^2)^p]*Log[-(b/(a*x^2))])/2 - (p*PolyLog[2, 1 + b/(a*x^2)])/2","A",3,3,16,0.1875,1,"{2454, 2394, 2315}"
42,1,50,0,0.0271548,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x^2} \, dx","Int[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{a} x}{\sqrt{b}}\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[a]*x)/Sqrt[b]])/Sqrt[b] - Log[c*(a + b/x^2)^p]/x","A",4,4,16,0.2500,1,"{2455, 263, 325, 205}"
43,1,35,0,0.0259068,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x^3} \, dx","Int[Log[c*(a + b/x^2)^p]/x^3,x]","\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}","\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/(2*x^2) - ((a + b/x^2)*Log[c*(a + b/x^2)^p])/(2*b)","A",3,3,16,0.1875,1,"{2454, 2389, 2295}"
44,1,68,0,0.0355895,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x^4} \, dx","Int[Log[c*(a + b/x^2)^p]/x^4,x]","-\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}","-\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[a]*x)/Sqrt[b]])/(3*b^(3/2)) - Log[c*(a + b/x^2)^p]/(3*x^3)","A",5,4,16,0.2500,1,"{2455, 263, 325, 205}"
45,1,8,0,0.0077864,"\int \frac{\log \left(1+\frac{b}{x}\right)}{x} \, dx","Int[Log[1 + b/x]/x,x]","\text{PolyLog}\left(2,-\frac{b}{x}\right)","\text{PolyLog}\left(2,-\frac{b}{x}\right)",1,"PolyLog[2, -(b/x)]","A",1,1,12,0.08333,1,"{2391}"
46,1,153,0,0.1175541,"\int x^3 \log \left(c \left(a+b \sqrt{x}\right)^p\right) \, dx","Int[x^3*Log[c*(a + b*Sqrt[x])^p],x]","\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{a^7 p \sqrt{x}}{4 b^7}-\frac{a^6 p x}{8 b^6}-\frac{a^8 p \log \left(a+b \sqrt{x}\right)}{4 b^8}+\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}","\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{a^7 p \sqrt{x}}{4 b^7}-\frac{a^6 p x}{8 b^6}-\frac{a^8 p \log \left(a+b \sqrt{x}\right)}{4 b^8}+\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,"(a^7*p*Sqrt[x])/(4*b^7) - (a^6*p*x)/(8*b^6) + (a^5*p*x^(3/2))/(12*b^5) - (a^4*p*x^2)/(16*b^4) + (a^3*p*x^(5/2))/(20*b^3) - (a^2*p*x^3)/(24*b^2) + (a*p*x^(7/2))/(28*b) - (p*x^4)/32 - (a^8*p*Log[a + b*Sqrt[x]])/(4*b^8) + (x^4*Log[c*(a + b*Sqrt[x])^p])/4","A",4,3,18,0.1667,1,"{2454, 2395, 43}"
47,1,123,0,0.0880257,"\int x^2 \log \left(c \left(a+b \sqrt{x}\right)^p\right) \, dx","Int[x^2*Log[c*(a + b*Sqrt[x])^p],x]","\frac{a^3 p x^{3/2}}{9 b^3}-\frac{a^2 p x^2}{12 b^2}+\frac{a^5 p \sqrt{x}}{3 b^5}-\frac{a^4 p x}{6 b^4}-\frac{a^6 p \log \left(a+b \sqrt{x}\right)}{3 b^6}+\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}","\frac{a^3 p x^{3/2}}{9 b^3}-\frac{a^2 p x^2}{12 b^2}+\frac{a^5 p \sqrt{x}}{3 b^5}-\frac{a^4 p x}{6 b^4}-\frac{a^6 p \log \left(a+b \sqrt{x}\right)}{3 b^6}+\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,"(a^5*p*Sqrt[x])/(3*b^5) - (a^4*p*x)/(6*b^4) + (a^3*p*x^(3/2))/(9*b^3) - (a^2*p*x^2)/(12*b^2) + (a*p*x^(5/2))/(15*b) - (p*x^3)/18 - (a^6*p*Log[a + b*Sqrt[x]])/(3*b^6) + (x^3*Log[c*(a + b*Sqrt[x])^p])/3","A",4,3,18,0.1667,1,"{2454, 2395, 43}"
48,1,93,0,0.0602953,"\int x \log \left(c \left(a+b \sqrt{x}\right)^p\right) \, dx","Int[x*Log[c*(a + b*Sqrt[x])^p],x]","\frac{a^3 p \sqrt{x}}{2 b^3}-\frac{a^2 p x}{4 b^2}-\frac{a^4 p \log \left(a+b \sqrt{x}\right)}{2 b^4}+\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}","\frac{a^3 p \sqrt{x}}{2 b^3}-\frac{a^2 p x}{4 b^2}-\frac{a^4 p \log \left(a+b \sqrt{x}\right)}{2 b^4}+\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,"(a^3*p*Sqrt[x])/(2*b^3) - (a^2*p*x)/(4*b^2) + (a*p*x^(3/2))/(6*b) - (p*x^2)/8 - (a^4*p*Log[a + b*Sqrt[x]])/(2*b^4) + (x^2*Log[c*(a + b*Sqrt[x])^p])/2","A",4,3,16,0.1875,1,"{2454, 2395, 43}"
49,1,53,0,0.0283768,"\int \log \left(c \left(a+b \sqrt{x}\right)^p\right) \, dx","Int[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",4,3,14,0.2143,1,"{2448, 266, 43}"
50,1,46,0,0.0404115,"\int \frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{x} \, dx","Int[Log[c*(a + b*Sqrt[x])^p]/x,x]","2 p \text{PolyLog}\left(2,\frac{b \sqrt{x}}{a}+1\right)+2 \log \left(-\frac{b \sqrt{x}}{a}\right) \log \left(c \left(a+b \sqrt{x}\right)^p\right)","2 p \text{PolyLog}\left(2,\frac{b \sqrt{x}}{a}+1\right)+2 \log \left(-\frac{b \sqrt{x}}{a}\right) \log \left(c \left(a+b \sqrt{x}\right)^p\right)",1,"2*Log[c*(a + b*Sqrt[x])^p]*Log[-((b*Sqrt[x])/a)] + 2*p*PolyLog[2, 1 + (b*Sqrt[x])/a]","A",3,3,18,0.1667,1,"{2454, 2394, 2315}"
51,1,63,0,0.0452999,"\int \frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{x^2} \, dx","Int[Log[c*(a + b*Sqrt[x])^p]/x^2,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}}","\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,"-((b*p)/(a*Sqrt[x])) + (b^2*p*Log[a + b*Sqrt[x]])/a^2 - Log[c*(a + b*Sqrt[x])^p]/x - (b^2*p*Log[x])/(2*a^2)","A",4,3,18,0.1667,1,"{2454, 2395, 44}"
52,1,100,0,0.0632133,"\int \frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{x^3} \, dx","Int[Log[c*(a + b*Sqrt[x])^p]/x^3,x]","-\frac{b^3 p}{2 a^3 \sqrt{x}}+\frac{b^2 p}{4 a^2 x}+\frac{b^4 p \log \left(a+b \sqrt{x}\right)}{2 a^4}-\frac{b^4 p \log (x)}{4 a^4}-\frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{2 x^2}-\frac{b p}{6 a x^{3/2}}","-\frac{b^3 p}{2 a^3 \sqrt{x}}+\frac{b^2 p}{4 a^2 x}+\frac{b^4 p \log \left(a+b \sqrt{x}\right)}{2 a^4}-\frac{b^4 p \log (x)}{4 a^4}-\frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{2 x^2}-\frac{b p}{6 a x^{3/2}}",1,"-(b*p)/(6*a*x^(3/2)) + (b^2*p)/(4*a^2*x) - (b^3*p)/(2*a^3*Sqrt[x]) + (b^4*p*Log[a + b*Sqrt[x]])/(2*a^4) - Log[c*(a + b*Sqrt[x])^p]/(2*x^2) - (b^4*p*Log[x])/(4*a^4)","A",4,3,18,0.1667,1,"{2454, 2395, 44}"
53,1,130,0,0.0794123,"\int \frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{x^4} \, dx","Int[Log[c*(a + b*Sqrt[x])^p]/x^4,x]","-\frac{b^3 p}{9 a^3 x^{3/2}}+\frac{b^2 p}{12 a^2 x^2}-\frac{b^5 p}{3 a^5 \sqrt{x}}+\frac{b^4 p}{6 a^4 x}+\frac{b^6 p \log \left(a+b \sqrt{x}\right)}{3 a^6}-\frac{b^6 p \log (x)}{6 a^6}-\frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{3 x^3}-\frac{b p}{15 a x^{5/2}}","-\frac{b^3 p}{9 a^3 x^{3/2}}+\frac{b^2 p}{12 a^2 x^2}-\frac{b^5 p}{3 a^5 \sqrt{x}}+\frac{b^4 p}{6 a^4 x}+\frac{b^6 p \log \left(a+b \sqrt{x}\right)}{3 a^6}-\frac{b^6 p \log (x)}{6 a^6}-\frac{\log \left(c \left(a+b \sqrt{x}\right)^p\right)}{3 x^3}-\frac{b p}{15 a x^{5/2}}",1,"-(b*p)/(15*a*x^(5/2)) + (b^2*p)/(12*a^2*x^2) - (b^3*p)/(9*a^3*x^(3/2)) + (b^4*p)/(6*a^4*x) - (b^5*p)/(3*a^5*Sqrt[x]) + (b^6*p*Log[a + b*Sqrt[x]])/(3*a^6) - Log[c*(a + b*Sqrt[x])^p]/(3*x^3) - (b^6*p*Log[x])/(6*a^6)","A",4,3,18,0.1667,1,"{2454, 2395, 44}"
54,1,32,0,0.0180764,"\int \frac{\log \left(a+b \sqrt{x}\right)}{\sqrt{x}} \, dx","Int[Log[a + b*Sqrt[x]]/Sqrt[x],x]","\frac{2 \left(a+b \sqrt{x}\right) \log \left(a+b \sqrt{x}\right)}{b}-2 \sqrt{x}","\frac{2 \left(a+b \sqrt{x}\right) \log \left(a+b \sqrt{x}\right)}{b}-2 \sqrt{x}",1,"-2*Sqrt[x] + (2*(a + b*Sqrt[x])*Log[a + b*Sqrt[x]])/b","A",3,3,16,0.1875,1,"{2454, 2389, 2295}"
55,1,81,0,0.0437643,"\int (f x)^m \log \left(c \left(d+e x^3\right)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e*x^3)^p],x]","\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)}","\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,"(-3*e*p*(f*x)^(4 + m)*Hypergeometric2F1[1, (4 + m)/3, (7 + m)/3, -((e*x^3)/d)])/(d*f^4*(1 + m)*(4 + m)) + ((f*x)^(1 + m)*Log[c*(d + e*x^3)^p])/(f*(1 + m))","A",3,3,18,0.1667,1,"{2455, 16, 364}"
56,1,81,0,0.0418747,"\int (f x)^m \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e*x^2)^p],x]","\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)}","\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,"(-2*e*p*(f*x)^(3 + m)*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, -((e*x^2)/d)])/(d*f^3*(1 + m)*(3 + m)) + ((f*x)^(1 + m)*Log[c*(d + e*x^2)^p])/(f*(1 + m))","A",3,3,18,0.1667,1,"{2455, 16, 364}"
57,1,69,0,0.0293683,"\int (f x)^m \log \left(c (d+e x)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e*x)^p],x]","\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)}","\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,"-((e*p*(f*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, -((e*x)/d)])/(d*f^2*(1 + m)*(2 + m))) + ((f*x)^(1 + m)*Log[c*(d + e*x)^p])/(f*(1 + m))","A",2,2,16,0.1250,1,"{2395, 64}"
58,1,67,0,0.040617,"\int (f x)^m \log \left(c \left(d+\frac{e}{x}\right)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e/x)^p],x]","\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)}","\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,"(e*p*(f*x)^m*Hypergeometric2F1[1, -m, 1 - m, -(e/(d*x))])/(d*m*(1 + m)) + ((f*x)^(1 + m)*Log[c*(d + e/x)^p])/(f*(1 + m))","A",4,4,18,0.2222,1,"{2455, 16, 339, 64}"
59,1,82,0,0.0544225,"\int (f x)^m \log \left(c \left(d+\frac{e}{x^2}\right)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e/x^2)^p],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)}","\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,"(-2*e*f*p*(f*x)^(-1 + m)*Hypergeometric2F1[1, (1 - m)/2, (3 - m)/2, -(e/(d*x^2))])/(d*(1 - m^2)) + ((f*x)^(1 + m)*Log[c*(d + e/x^2)^p])/(f*(1 + m))","A",4,4,18,0.2222,1,"{2455, 16, 339, 364}"
60,1,85,0,0.0605074,"\int (f x)^m \log \left(c \left(d+\frac{e}{x^3}\right)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e/x^3)^p],x]","\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)}","\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,"(-3*e*f^2*p*(f*x)^(-2 + m)*Hypergeometric2F1[1, (2 - m)/3, (5 - m)/3, -(e/(d*x^3))])/(d*(2 + m - m^2)) + ((f*x)^(1 + m)*Log[c*(d + e/x^3)^p])/(f*(1 + m))","A",4,4,18,0.2222,1,"{2455, 16, 339, 364}"
61,1,83,0,0.0505886,"\int (f x)^m \log \left(c \left(d+e \sqrt{x}\right)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e*Sqrt[x])^p],x]","\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)}","\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,"-((e*p*x^(3/2)*(f*x)^m*Hypergeometric2F1[1, 3 + 2*m, 2*(2 + m), -((e*Sqrt[x])/d)])/(d*(3 + 5*m + 2*m^2))) + ((f*x)^(1 + m)*Log[c*(d + e*Sqrt[x])^p])/(f*(1 + m))","A",4,4,20,0.2000,1,"{2455, 20, 341, 64}"
62,1,70,0,0.0422632,"\int (f x)^m \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e/Sqrt[x])^p],x]","\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}","\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,"(p*x*(f*x)^m*Hypergeometric2F1[1, 2*(1 + m), 3 + 2*m, -((d*Sqrt[x])/e)])/(2*(1 + m)^2) + ((f*x)^(1 + m)*Log[c*(d + e/Sqrt[x])^p])/(f*(1 + m))","A",5,5,20,0.2500,1,"{2455, 20, 263, 341, 64}"
63,1,87,0,0.0434718,"\int (f x)^m \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e*x^n)^p],x]","\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)}","\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,"-((e*n*p*x^(1 + n)*(f*x)^m*Hypergeometric2F1[1, (1 + m + n)/n, (1 + m + 2*n)/n, -((e*x^n)/d)])/(d*(1 + m)*(1 + m + n))) + ((f*x)^(1 + m)*Log[c*(d + e*x^n)^p])/(f*(1 + m))","A",3,3,18,0.1667,1,"{2455, 20, 364}"
64,1,141,0,0.0772847,"\int (f x)^{-1+3 n} \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f*x)^(-1 + 3*n)*Log[c*(d + e*x^n)^p],x]","\frac{(f x)^{3 n} \log \left(c \left(d+e x^n\right)^p\right)}{3 f n}-\frac{d^2 p x^{-2 n} (f x)^{3 n}}{3 e^2 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 p x^{-n} (f x)^{3 n}}{6 e f n}-\frac{p (f x)^{3 n}}{9 f n}","\frac{(f x)^{3 n} \log \left(c \left(d+e x^n\right)^p\right)}{3 f n}-\frac{d^2 p x^{-2 n} (f x)^{3 n}}{3 e^2 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 p x^{-n} (f x)^{3 n}}{6 e f n}-\frac{p (f x)^{3 n}}{9 f n}",1,"-(p*(f*x)^(3*n))/(9*f*n) - (d^2*p*(f*x)^(3*n))/(3*e^2*f*n*x^(2*n)) + (d*p*(f*x)^(3*n))/(6*e*f*n*x^n) + (d^3*p*(f*x)^(3*n)*Log[d + e*x^n])/(3*e^3*f*n*x^(3*n)) + ((f*x)^(3*n)*Log[c*(d + e*x^n)^p])/(3*f*n)","A",5,4,22,0.1818,1,"{2455, 20, 266, 43}"
65,1,112,0,0.0571477,"\int (f x)^{-1+2 n} \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f*x)^(-1 + 2*n)*Log[c*(d + e*x^n)^p],x]","\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}","\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,"-(p*(f*x)^(2*n))/(4*f*n) + (d*p*(f*x)^(2*n))/(2*e*f*n*x^n) - (d^2*p*(f*x)^(2*n)*Log[d + e*x^n])/(2*e^2*f*n*x^(2*n)) + ((f*x)^(2*n)*Log[c*(d + e*x^n)^p])/(2*f*n)","A",5,4,22,0.1818,1,"{2455, 20, 266, 43}"
66,1,69,0,0.0428553,"\int (f x)^{-1+n} \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f*x)^(-1 + n)*Log[c*(d + e*x^n)^p],x]","\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}","\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,"-((p*(f*x)^n)/(f*n)) + (d*p*(f*x)^n*Log[d + e*x^n])/(e*f*n*x^n) + ((f*x)^n*Log[c*(d + e*x^n)^p])/(f*n)","A",5,4,20,0.2000,1,"{2455, 20, 266, 43}"
67,1,50,0,0.0467335,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{f x} \, dx","Int[Log[c*(d + e*x^n)^p]/(f*x),x]","\frac{p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\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{PolyLog}\left(2,\frac{e x^n}{d}+1\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}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/(f*n) + (p*PolyLog[2, 1 + (e*x^n)/d])/(f*n)","A",4,4,19,0.2105,1,"{12, 2454, 2394, 2315}"
68,1,80,0,0.0356827,"\int (f x)^{-1-n} \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f*x)^(-1 - n)*Log[c*(d + e*x^n)^p],x]","-\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}","-\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*p*x^n*Log[x])/(d*f*(f*x)^n) - (e*p*x^n*Log[d + e*x^n])/(d*f*n*(f*x)^n) - Log[c*(d + e*x^n)^p]/(f*n*(f*x)^n)","A",6,6,22,0.2727,1,"{2455, 19, 266, 36, 29, 31}"
69,1,120,0,0.0578244,"\int (f x)^{-1-2 n} \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f*x)^(-1 - 2*n)*Log[c*(d + e*x^n)^p],x]","-\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}","-\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,"-(e*p*x^n)/(2*d*f*n*(f*x)^(2*n)) - (e^2*p*x^(2*n)*Log[x])/(2*d^2*f*(f*x)^(2*n)) + (e^2*p*x^(2*n)*Log[d + e*x^n])/(2*d^2*f*n*(f*x)^(2*n)) - Log[c*(d + e*x^n)^p]/(2*f*n*(f*x)^(2*n))","A",5,4,22,0.1818,1,"{2455, 20, 266, 44}"
70,1,65,0,0.0280675,"\int x^2 \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[x^2*Log[c*(d + e*x^n)^p],x]","\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)}","\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,"-(e*n*p*x^(3 + n)*Hypergeometric2F1[1, (3 + n)/n, 2 + 3/n, -((e*x^n)/d)])/(3*d*(3 + n)) + (x^3*Log[c*(d + e*x^n)^p])/3","A",2,2,16,0.1250,1,"{2455, 364}"
71,1,65,0,0.0241193,"\int x \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[x*Log[c*(d + e*x^n)^p],x]","\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)}","\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,"-(e*n*p*x^(2 + n)*Hypergeometric2F1[1, (2 + n)/n, 2*(1 + n^(-1)), -((e*x^n)/d)])/(2*d*(2 + n)) + (x^2*Log[c*(d + e*x^n)^p])/2","A",2,2,14,0.1429,1,"{2455, 364}"
72,1,54,0,0.0202858,"\int \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[Log[c*(d + e*x^n)^p],x]","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)}","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,"-((e*n*p*x^(1 + n)*Hypergeometric2F1[1, 1 + n^(-1), 2 + n^(-1), -((e*x^n)/d)])/(d*(1 + n))) + x*Log[c*(d + e*x^n)^p]","A",2,2,12,0.1667,1,"{2448, 364}"
73,1,44,0,0.0398748,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[Log[c*(d + e*x^n)^p]/x,x]","\frac{p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\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{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (p*PolyLog[2, 1 + (e*x^n)/d])/n","A",3,3,16,0.1875,1,"{2454, 2394, 2315}"
74,1,66,0,0.0315251,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x^2} \, dx","Int[Log[c*(d + e*x^n)^p]/x^2,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)}","-\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^(-1 + 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",2,2,16,0.1250,1,"{2455, 364}"
75,1,72,0,0.0307312,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x^3} \, dx","Int[Log[c*(d + e*x^n)^p]/x^3,x]","-\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)}","-\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^(-2 + n)*Hypergeometric2F1[1, -((2 - n)/n), 2*(1 - n^(-1)), -((e*x^n)/d)])/(2*d*(2 - n)) - Log[c*(d + e*x^n)^p]/(2*x^2)","A",2,2,16,0.1250,1,"{2455, 364}"
76,1,70,0,0.0293658,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x^4} \, dx","Int[Log[c*(d + e*x^n)^p]/x^4,x]","-\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)}","-\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^(-3 + n)*Hypergeometric2F1[1, -((3 - n)/n), 2 - 3/n, -((e*x^n)/d)])/(3*d*(3 - n)) - Log[c*(d + e*x^n)^p]/(3*x^3)","A",2,2,16,0.1250,1,"{2455, 364}"
77,1,175,0,0.2985636,"\int x^5 \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Int[x^5*Log[c*(a + b*x^2)^p]^2,x]","-\frac{1}{18} p \left(\frac{18 a^2 \left(a+b x^2\right)}{b^3}-\frac{6 a^3 \log \left(a+b x^2\right)}{b^3}-\frac{9 a \left(a+b x^2\right)^2}{b^3}+\frac{2 \left(a+b x^2\right)^3}{b^3}\right) \log \left(c \left(a+b x^2\right)^p\right)+\frac{a^2 p^2 x^2}{b^2}-\frac{a^3 p^2 \log ^2\left(a+b x^2\right)}{6 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)","-\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^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^2 p^2 x^2}{b^2}-\frac{a^3 p^2 \log ^2\left(a+b x^2\right)}{6 b^3}-\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,"(a^2*p^2*x^2)/b^2 - (a*p^2*(a + b*x^2)^2)/(4*b^3) + (p^2*(a + b*x^2)^3)/(27*b^3) - (a^3*p^2*Log[a + b*x^2]^2)/(6*b^3) - (p*((18*a^2*(a + b*x^2))/b^3 - (9*a*(a + b*x^2)^2)/b^3 + (2*(a + b*x^2)^3)/b^3 - (6*a^3*Log[a + b*x^2])/b^3)*Log[c*(a + b*x^2)^p])/18 + (x^6*Log[c*(a + b*x^2)^p]^2)/6","A",8,8,18,0.4444,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
78,1,145,0,0.1533452,"\int x^3 \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Int[x^3*Log[c*(a + b*x^2)^p]^2,x]","\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}","\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,"-((a*p^2*x^2)/b) + (p^2*(a + b*x^2)^2)/(8*b^2) + (a*p*(a + b*x^2)*Log[c*(a + b*x^2)^p])/b^2 - (p*(a + b*x^2)^2*Log[c*(a + b*x^2)^p])/(4*b^2) - (a*(a + b*x^2)*Log[c*(a + b*x^2)^p]^2)/(2*b^2) + ((a + b*x^2)^2*Log[c*(a + b*x^2)^p]^2)/(4*b^2)","A",9,8,18,0.4444,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
79,1,61,0,0.0503193,"\int x \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Int[x*Log[c*(a + b*x^2)^p]^2,x]","\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","\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,"p^2*x^2 - (p*(a + b*x^2)*Log[c*(a + b*x^2)^p])/b + ((a + b*x^2)*Log[c*(a + b*x^2)^p]^2)/(2*b)","A",4,4,16,0.2500,1,"{2454, 2389, 2296, 2295}"
80,1,72,0,0.1127513,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x} \, dx","Int[Log[c*(a + b*x^2)^p]^2/x,x]","p \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)+p^2 \left(-\text{PolyLog}\left(3,\frac{b x^2}{a}+1\right)\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 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)+p^2 \left(-\text{PolyLog}\left(3,\frac{b x^2}{a}+1\right)\right)+\frac{1}{2} \log \left(-\frac{b x^2}{a}\right) \log ^2\left(c \left(a+b x^2\right)^p\right)",1,"(Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p]^2)/2 + p*Log[c*(a + b*x^2)^p]*PolyLog[2, 1 + (b*x^2)/a] - p^2*PolyLog[3, 1 + (b*x^2)/a]","A",5,5,18,0.2778,1,"{2454, 2396, 2433, 2374, 6589}"
81,1,80,0,0.0838589,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^3} \, dx","Int[Log[c*(a + b*x^2)^p]^2/x^3,x]","\frac{b p^2 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\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{PolyLog}\left(2,\frac{b x^2}{a}+1\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}",1,"(b*p*Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p])/a - ((a + b*x^2)*Log[c*(a + b*x^2)^p]^2)/(2*a*x^2) + (b*p^2*PolyLog[2, 1 + (b*x^2)/a])/a","A",4,4,18,0.2222,1,"{2454, 2397, 2394, 2315}"
82,1,147,0,0.2687232,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^5} \, dx","Int[Log[c*(a + b*x^2)^p]^2/x^5,x]","-\frac{b^2 p^2 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{2 a^2}+\frac{b^2 \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 a^2}-\frac{b^2 p \log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\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}","\frac{b^2 p^2 \text{PolyLog}\left(2,\frac{a}{a+b x^2}\right)}{2 a^2}-\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 \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,"(b^2*p^2*Log[x])/a^2 - (b*p*(a + b*x^2)*Log[c*(a + b*x^2)^p])/(2*a^2*x^2) - (b^2*p*Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p])/(2*a^2) + (b^2*Log[c*(a + b*x^2)^p]^2)/(4*a^2) - Log[c*(a + b*x^2)^p]^2/(4*x^4) - (b^2*p^2*PolyLog[2, 1 + (b*x^2)/a])/(2*a^2)","A",10,10,18,0.5556,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31}"
83,1,211,0,0.4072359,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^7} \, dx","Int[Log[c*(a + b*x^2)^p]^2/x^7,x]","\frac{b^3 p^2 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{3 a^3}-\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^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{b^3 p^2 \log \left(a+b x^2\right)}{6 a^3}-\frac{b^3 p^2 \log (x)}{a^3}-\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^2 \text{PolyLog}\left(2,\frac{a}{a+b x^2}\right)}{3 a^3}+\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^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{b^3 p^2 \log \left(a+b x^2\right)}{6 a^3}-\frac{b^3 p^2 \log (x)}{a^3}-\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,"-(b^2*p^2)/(6*a^2*x^2) - (b^3*p^2*Log[x])/a^3 + (b^3*p^2*Log[a + b*x^2])/(6*a^3) - (b*p*Log[c*(a + b*x^2)^p])/(6*a*x^4) + (b^2*p*(a + b*x^2)*Log[c*(a + b*x^2)^p])/(3*a^3*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, 1 + (b*x^2)/a])/(3*a^3)","A",14,12,18,0.6667,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
84,1,336,0,0.4079805,"\int x^4 \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Int[x^4*Log[c*(a + b*x^2)^p]^2,x]","\frac{4 i a^{5/2} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\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{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{184 a^2 p^2 x}{75 b^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{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}","\frac{4 i a^{5/2} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\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{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{184 a^2 p^2 x}{75 b^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{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,"(184*a^2*p^2*x)/(75*b^2) - (64*a*p^2*x^3)/(225*b) + (8*p^2*x^5)/125 - (184*a^(5/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(75*b^(5/2)) + (((4*I)/5)*a^(5/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/b^(5/2) + (8*a^(5/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/(5*b^(5/2)) - (4*a^2*p*x*Log[c*(a + b*x^2)^p])/(5*b^2) + (4*a*p*x^3*Log[c*(a + b*x^2)^p])/(15*b) - (4*p*x^5*Log[c*(a + b*x^2)^p])/25 + (4*a^(5/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p])/(5*b^(5/2)) + (x^5*Log[c*(a + b*x^2)^p]^2)/5 + (((4*I)/5)*a^(5/2)*p^2*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/b^(5/2)","A",20,13,18,0.7222,1,"{2457, 2476, 2448, 321, 205, 2455, 302, 2470, 12, 4920, 4854, 2402, 2315}"
85,1,294,0,0.3227651,"\int x^2 \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Int[x^2*Log[c*(a + b*x^2)^p]^2,x]","-\frac{4 i a^{3/2} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)}{3 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 \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{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{4 a p x \log \left(c \left(a+b x^2\right)^p\right)}{3 b}-\frac{32 a p^2 x}{9 b}+\frac{8 p^2 x^3}{27}","-\frac{4 i a^{3/2} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)}{3 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 \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{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{4 a p x \log \left(c \left(a+b x^2\right)^p\right)}{3 b}-\frac{32 a p^2 x}{9 b}+\frac{8 p^2 x^3}{27}",1,"(-32*a*p^2*x)/(9*b) + (8*p^2*x^3)/27 + (32*a^(3/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(9*b^(3/2)) - (((4*I)/3)*a^(3/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/b^(3/2) - (8*a^(3/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/(3*b^(3/2)) + (4*a*p*x*Log[c*(a + b*x^2)^p])/(3*b) - (4*p*x^3*Log[c*(a + b*x^2)^p])/9 - (4*a^(3/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p])/(3*b^(3/2)) + (x^3*Log[c*(a + b*x^2)^p]^2)/3 - (((4*I)/3)*a^(3/2)*p^2*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/b^(3/2)","A",16,13,18,0.7222,1,"{2457, 2476, 2448, 321, 205, 2455, 302, 2470, 12, 4920, 4854, 2402, 2315}"
86,1,237,0,0.2674971,"\int \log ^2\left(c \left(a+b x^2\right)^p\right) \, dx","Int[Log[c*(a + b*x^2)^p]^2,x]","\frac{4 i \sqrt{a} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)}{\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 \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","\frac{4 i \sqrt{a} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)}{\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 \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,"8*p^2*x - (8*Sqrt[a]*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[b] + ((4*I)*Sqrt[a]*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/Sqrt[b] + (8*Sqrt[a]*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/Sqrt[b] - 4*p*x*Log[c*(a + b*x^2)^p] + (4*Sqrt[a]*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p])/Sqrt[b] + x*Log[c*(a + b*x^2)^p]^2 + ((4*I)*Sqrt[a]*p^2*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/Sqrt[b]","A",12,11,14,0.7857,1,"{2450, 2476, 2448, 321, 205, 2470, 12, 4920, 4854, 2402, 2315}"
87,1,190,0,0.1687991,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^2} \, dx","Int[Log[c*(a + b*x^2)^p]^2/x^2,x]","\frac{4 i \sqrt{b} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)}{\sqrt{a}}-\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 \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}}","\frac{4 i \sqrt{b} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)}{\sqrt{a}}-\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 \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*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/Sqrt[a] + (8*Sqrt[b]*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/Sqrt[a] + (4*Sqrt[b]*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p])/Sqrt[a] - Log[c*(a + b*x^2)^p]^2/x + ((4*I)*Sqrt[b]*p^2*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/Sqrt[a]","A",7,8,18,0.4444,1,"{2457, 205, 2470, 12, 4920, 4854, 2402, 2315}"
88,1,254,0,0.2850701,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^4} \, dx","Int[Log[c*(a + b*x^2)^p]^2/x^4,x]","-\frac{4 i b^{3/2} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)}{3 a^{3/2}}-\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 \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{\log ^2\left(c \left(a+b x^2\right)^p\right)}{3 x^3}-\frac{4 b p \log \left(c \left(a+b x^2\right)^p\right)}{3 a x}","-\frac{4 i b^{3/2} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)}{3 a^{3/2}}-\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 \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{\log ^2\left(c \left(a+b x^2\right)^p\right)}{3 x^3}-\frac{4 b p \log \left(c \left(a+b x^2\right)^p\right)}{3 a x}",1,"(8*b^(3/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(3*a^(3/2)) - (((4*I)/3)*b^(3/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/a^(3/2) - (8*b^(3/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/(3*a^(3/2)) - (4*b*p*Log[c*(a + b*x^2)^p])/(3*a*x) - (4*b^(3/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p])/(3*a^(3/2)) - Log[c*(a + b*x^2)^p]^2/(3*x^3) - (((4*I)/3)*b^(3/2)*p^2*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/a^(3/2)","A",11,10,18,0.5556,1,"{2457, 2476, 2455, 205, 2470, 12, 4920, 4854, 2402, 2315}"
89,1,296,0,0.3203502,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^6} \, dx","Int[Log[c*(a + b*x^2)^p]^2/x^6,x]","\frac{4 i b^{5/2} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\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{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{8 b^2 p^2}{15 a^2 x}+\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{\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}","\frac{4 i b^{5/2} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\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{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{8 b^2 p^2}{15 a^2 x}+\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{\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,"(-8*b^2*p^2)/(15*a^2*x) - (32*b^(5/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(15*a^(5/2)) + (((4*I)/5)*b^(5/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/a^(5/2) + (8*b^(5/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/(5*a^(5/2)) - (4*b*p*Log[c*(a + b*x^2)^p])/(15*a*x^3) + (4*b^2*p*Log[c*(a + b*x^2)^p])/(5*a^2*x) + (4*b^(5/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p])/(5*a^(5/2)) - Log[c*(a + b*x^2)^p]^2/(5*x^5) + (((4*I)/5)*b^(5/2)*p^2*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/a^(5/2)","A",14,11,18,0.6111,1,"{2457, 2476, 2455, 325, 205, 2470, 12, 4920, 4854, 2402, 2315}"
90,1,338,0,0.3767269,"\int \frac{\log ^2\left(c \left(a+b x^2\right)^p\right)}{x^8} \, dx","Int[Log[c*(a + b*x^2)^p]^2/x^8,x]","-\frac{4 i b^{7/2} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\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{4 b^2 p \log \left(c \left(a+b x^2\right)^p\right)}{21 a^2 x^3}-\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{8 b^2 p^2}{105 a^2 x^3}+\frac{64 b^3 p^2}{105 a^3 x}-\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{\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}","-\frac{4 i b^{7/2} p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\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{4 b^2 p \log \left(c \left(a+b x^2\right)^p\right)}{21 a^2 x^3}-\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{8 b^2 p^2}{105 a^2 x^3}+\frac{64 b^3 p^2}{105 a^3 x}-\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{\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,"(-8*b^2*p^2)/(105*a^2*x^3) + (64*b^3*p^2)/(105*a^3*x) + (184*b^(7/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(105*a^(7/2)) - (((4*I)/7)*b^(7/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/a^(7/2) - (8*b^(7/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/(7*a^(7/2)) - (4*b*p*Log[c*(a + b*x^2)^p])/(35*a*x^5) + (4*b^2*p*Log[c*(a + b*x^2)^p])/(21*a^2*x^3) - (4*b^3*p*Log[c*(a + b*x^2)^p])/(7*a^3*x) - (4*b^(7/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p])/(7*a^(7/2)) - Log[c*(a + b*x^2)^p]^2/(7*x^7) - (((4*I)/7)*b^(7/2)*p^2*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/a^(7/2)","A",18,11,18,0.6111,1,"{2457, 2476, 2455, 325, 205, 2470, 12, 4920, 4854, 2402, 2315}"
91,1,334,0,0.3579686,"\int x^5 \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","Int[x^5*Log[c*(a + b*x^2)^p]^3,x]","\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{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{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^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{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{\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^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}","\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{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{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^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{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{\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^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,"(-3*a^2*p^3*x^2)/b^2 + (3*a*p^3*(a + b*x^2)^2)/(8*b^3) - (p^3*(a + b*x^2)^3)/(27*b^3) + (3*a^2*p^2*(a + b*x^2)*Log[c*(a + b*x^2)^p])/b^3 - (3*a*p^2*(a + b*x^2)^2*Log[c*(a + b*x^2)^p])/(4*b^3) + (p^2*(a + b*x^2)^3*Log[c*(a + b*x^2)^p])/(9*b^3) - (3*a^2*p*(a + b*x^2)*Log[c*(a + b*x^2)^p]^2)/(2*b^3) + (3*a*p*(a + b*x^2)^2*Log[c*(a + b*x^2)^p]^2)/(4*b^3) - (p*(a + b*x^2)^3*Log[c*(a + b*x^2)^p]^2)/(6*b^3) + (a^2*(a + b*x^2)*Log[c*(a + b*x^2)^p]^3)/(2*b^3) - (a*(a + b*x^2)^2*Log[c*(a + b*x^2)^p]^3)/(2*b^3) + ((a + b*x^2)^3*Log[c*(a + b*x^2)^p]^3)/(6*b^3)","A",15,8,18,0.4444,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
92,1,211,0,0.2053365,"\int x^3 \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","Int[x^3*Log[c*(a + b*x^2)^p]^3,x]","\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{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{\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^3 \left(a+b x^2\right)^2}{16 b^2}+\frac{3 a p^3 x^2}{b}","\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{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{\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^3 \left(a+b x^2\right)^2}{16 b^2}+\frac{3 a p^3 x^2}{b}",1,"(3*a*p^3*x^2)/b - (3*p^3*(a + b*x^2)^2)/(16*b^2) - (3*a*p^2*(a + b*x^2)*Log[c*(a + b*x^2)^p])/b^2 + (3*p^2*(a + b*x^2)^2*Log[c*(a + b*x^2)^p])/(8*b^2) + (3*a*p*(a + b*x^2)*Log[c*(a + b*x^2)^p]^2)/(2*b^2) - (3*p*(a + b*x^2)^2*Log[c*(a + b*x^2)^p]^2)/(8*b^2) - (a*(a + b*x^2)*Log[c*(a + b*x^2)^p]^3)/(2*b^2) + ((a + b*x^2)^2*Log[c*(a + b*x^2)^p]^3)/(4*b^2)","A",11,8,18,0.4444,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
93,1,93,0,0.0656985,"\int x \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","Int[x*Log[c*(a + b*x^2)^p]^3,x]","\frac{3 p^2 \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b}-\frac{3 p \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 b}+\frac{\left(a+b x^2\right) \log ^3\left(c \left(a+b x^2\right)^p\right)}{2 b}-3 p^3 x^2","\frac{3 p^2 \left(a+b x^2\right) \log \left(c \left(a+b x^2\right)^p\right)}{b}-\frac{3 p \left(a+b x^2\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 b}+\frac{\left(a+b x^2\right) \log ^3\left(c \left(a+b x^2\right)^p\right)}{2 b}-3 p^3 x^2",1,"-3*p^3*x^2 + (3*p^2*(a + b*x^2)*Log[c*(a + b*x^2)^p])/b - (3*p*(a + b*x^2)*Log[c*(a + b*x^2)^p]^2)/(2*b) + ((a + b*x^2)*Log[c*(a + b*x^2)^p]^3)/(2*b)","A",5,4,16,0.2500,1,"{2454, 2389, 2296, 2295}"
94,1,106,0,0.1614113,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x} \, dx","Int[Log[c*(a + b*x^2)^p]^3/x,x]","-3 p^2 \text{PolyLog}\left(3,\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)+\frac{3}{2} p \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right) \log ^2\left(c \left(a+b x^2\right)^p\right)+3 p^3 \text{PolyLog}\left(4,\frac{b x^2}{a}+1\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^2 \text{PolyLog}\left(3,\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)+\frac{3}{2} p \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right) \log ^2\left(c \left(a+b x^2\right)^p\right)+3 p^3 \text{PolyLog}\left(4,\frac{b x^2}{a}+1\right)+\frac{1}{2} \log \left(-\frac{b x^2}{a}\right) \log ^3\left(c \left(a+b x^2\right)^p\right)",1,"(Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p]^3)/2 + (3*p*Log[c*(a + b*x^2)^p]^2*PolyLog[2, 1 + (b*x^2)/a])/2 - 3*p^2*Log[c*(a + b*x^2)^p]*PolyLog[3, 1 + (b*x^2)/a] + 3*p^3*PolyLog[4, 1 + (b*x^2)/a]","A",6,6,18,0.3333,1,"{2454, 2396, 2433, 2374, 2383, 6589}"
95,1,119,0,0.1454452,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^3} \, dx","Int[Log[c*(a + b*x^2)^p]^3/x^3,x]","\frac{3 b p^2 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)}{a}-\frac{3 b p^3 \text{PolyLog}\left(3,\frac{b x^2}{a}+1\right)}{a}+\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{\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^2 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)}{a}-\frac{3 b p^3 \text{PolyLog}\left(3,\frac{b x^2}{a}+1\right)}{a}+\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{\left(a+b x^2\right) \log ^3\left(c \left(a+b x^2\right)^p\right)}{2 a x^2}",1,"(3*b*p*Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p]^2)/(2*a) - ((a + b*x^2)*Log[c*(a + b*x^2)^p]^3)/(2*a*x^2) + (3*b*p^2*Log[c*(a + b*x^2)^p]*PolyLog[2, 1 + (b*x^2)/a])/a - (3*b*p^3*PolyLog[3, 1 + (b*x^2)/a])/a","A",6,6,18,0.3333,1,"{2454, 2397, 2396, 2433, 2374, 6589}"
96,1,236,0,0.4337357,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^5} \, dx","Int[Log[c*(a + b*x^2)^p]^3/x^5,x]","-\frac{3 b^2 p^2 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 a^2}+\frac{3 b^2 p^3 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{2 a^2}+\frac{3 b^2 p^3 \text{PolyLog}\left(3,\frac{b x^2}{a}+1\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(-\frac{b x^2}{a}\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 a^2}+\frac{b^2 \log ^3\left(c \left(a+b x^2\right)^p\right)}{4 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}","\frac{3 b^2 p^2 \text{PolyLog}\left(2,\frac{a}{a+b x^2}\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 a^2}+\frac{3 b^2 p^3 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{2 a^2}+\frac{3 b^2 p^3 \text{PolyLog}\left(3,\frac{a}{a+b x^2}\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 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,"(3*b^2*p^2*Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p])/(2*a^2) - (3*b*p*(a + b*x^2)*Log[c*(a + b*x^2)^p]^2)/(4*a^2*x^2) - (3*b^2*p*Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p]^2)/(4*a^2) + (b^2*Log[c*(a + b*x^2)^p]^3)/(4*a^2) - Log[c*(a + b*x^2)^p]^3/(4*x^4) + (3*b^2*p^3*PolyLog[2, 1 + (b*x^2)/a])/(2*a^2) - (3*b^2*p^2*Log[c*(a + b*x^2)^p]*PolyLog[2, 1 + (b*x^2)/a])/(2*a^2) + (3*b^2*p^3*PolyLog[3, 1 + (b*x^2)/a])/(2*a^2)","A",13,12,18,0.6667,1,"{2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391}"
97,1,331,0,0.7449867,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^7} \, dx","Int[Log[c*(a + b*x^2)^p]^3/x^7,x]","\frac{b^3 p^2 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right) \log \left(c \left(a+b x^2\right)^p\right)}{a^3}-\frac{3 b^3 p^3 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{2 a^3}-\frac{b^3 p^3 \text{PolyLog}\left(3,\frac{b x^2}{a}+1\right)}{a^3}-\frac{3 b^3 p^2 \log \left(-\frac{b x^2}{a}\right) \log \left(c \left(a+b x^2\right)^p\right)}{2 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^3 \log ^3\left(c \left(a+b x^2\right)^p\right)}{6 a^3}+\frac{b^3 p \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 a^3}+\frac{b^3 p \log \left(-\frac{b x^2}{a}\right) \log ^2\left(c \left(a+b x^2\right)^p\right)}{2 a^3}+\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{b^3 p^3 \log (x)}{a^3}-\frac{b p \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 a x^4}-\frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{6 x^6}","-\frac{b^3 p^2 \text{PolyLog}\left(2,\frac{a}{a+b x^2}\right) \log \left(c \left(a+b x^2\right)^p\right)}{a^3}+\frac{b^3 p^3 \text{PolyLog}\left(2,\frac{a}{a+b x^2}\right)}{2 a^3}-\frac{b^3 p^3 \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{a^3}-\frac{b^3 p^3 \text{PolyLog}\left(3,\frac{a}{a+b x^2}\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^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^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^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{b^3 p^3 \log (x)}{a^3}-\frac{b p \log ^2\left(c \left(a+b x^2\right)^p\right)}{4 a x^4}-\frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{6 x^6}",1,"(b^3*p^3*Log[x])/a^3 - (b^2*p^2*(a + b*x^2)*Log[c*(a + b*x^2)^p])/(2*a^3*x^2) - (3*b^3*p^2*Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p])/(2*a^3) + (b^3*p*Log[c*(a + b*x^2)^p]^2)/(4*a^3) - (b*p*Log[c*(a + b*x^2)^p]^2)/(4*a*x^4) + (b^2*p*(a + b*x^2)*Log[c*(a + b*x^2)^p]^2)/(2*a^3*x^2) + (b^3*p*Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p]^2)/(2*a^3) - (b^3*Log[c*(a + b*x^2)^p]^3)/(6*a^3) - Log[c*(a + b*x^2)^p]^3/(6*x^6) - (3*b^3*p^3*PolyLog[2, 1 + (b*x^2)/a])/(2*a^3) + (b^3*p^2*Log[c*(a + b*x^2)^p]*PolyLog[2, 1 + (b*x^2)/a])/a^3 - (b^3*p^3*PolyLog[3, 1 + (b*x^2)/a])/a^3","A",22,16,18,0.8889,1,"{2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31}"
98,0,0,0,0.8339473,"\int x^2 \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","Int[x^2*Log[c*(a + b*x^2)^p]^3,x]","\int x^2 \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","\frac{32 i a^{3/2} p^3 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)}{3 b^{3/2}}-\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 \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{8}{9} p^2 x^3 \log \left(c \left(a+b x^2\right)^p\right)-\frac{32 a p^2 x \log \left(c \left(a+b x^2\right)^p\right)}{3 b}-\frac{2}{3} p x^3 \log ^2\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{208 a p^3 x}{9 b}-\frac{16}{27} p^3 x^3",0,"(208*a*p^3*x)/(9*b) - (16*p^3*x^3)/27 - (208*a^(3/2)*p^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(9*b^(3/2)) + (((32*I)/3)*a^(3/2)*p^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/b^(3/2) + (64*a^(3/2)*p^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/(3*b^(3/2)) - (32*a*p^2*x*Log[c*(a + b*x^2)^p])/(3*b) + (8*p^2*x^3*Log[c*(a + b*x^2)^p])/9 + (32*a^(3/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p])/(3*b^(3/2)) + (2*a*p*x*Log[c*(a + b*x^2)^p]^2)/b - (2*p*x^3*Log[c*(a + b*x^2)^p]^2)/3 + (x^3*Log[c*(a + b*x^2)^p]^3)/3 + (((32*I)/3)*a^(3/2)*p^3*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/b^(3/2) - (2*a^2*p*Defer[Int][Log[c*(a + b*x^2)^p]^2/(a + b*x^2), x])/b","A",0,0,0,0,-1,"{}"
99,0,0,0,0.4343497,"\int \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","Int[Log[c*(a + b*x^2)^p]^3,x]","\int \log ^3\left(c \left(a+b x^2\right)^p\right) \, dx","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)-\frac{24 i \sqrt{a} p^3 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)}{\sqrt{b}}+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}}-6 p x \log ^2\left(c \left(a+b x^2\right)^p\right)+x \log ^3\left(c \left(a+b x^2\right)^p\right)-\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,"-48*p^3*x + (48*Sqrt[a]*p^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[b] - ((24*I)*Sqrt[a]*p^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/Sqrt[b] - (48*Sqrt[a]*p^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/Sqrt[b] + 24*p^2*x*Log[c*(a + b*x^2)^p] - (24*Sqrt[a]*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p])/Sqrt[b] - 6*p*x*Log[c*(a + b*x^2)^p]^2 + x*Log[c*(a + b*x^2)^p]^3 - ((24*I)*Sqrt[a]*p^3*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/Sqrt[b] + 6*a*p*Defer[Int][Log[c*(a + b*x^2)^p]^2/(a + b*x^2), x]","A",0,0,0,0,-1,"{}"
100,0,0,0,0.0450119,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^2} \, dx","Int[Log[c*(a + b*x^2)^p]^3/x^2,x]","\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^2} \, dx","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,"-(Log[c*(a + b*x^2)^p]^3/x) + 6*b*p*Defer[Int][Log[c*(a + b*x^2)^p]^2/(a + b*x^2), x]","A",0,0,0,0,-1,"{}"
101,0,0,0,0.3507786,"\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^4} \, dx","Int[Log[c*(a + b*x^2)^p]^3/x^4,x]","\int \frac{\log ^3\left(c \left(a+b x^2\right)^p\right)}{x^4} \, dx","\frac{8 i b^{3/2} p^3 \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\right)}{a^{3/2}}-\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 \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,"((8*I)*b^(3/2)*p^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/a^(3/2) + (16*b^(3/2)*p^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/a^(3/2) + (8*b^(3/2)*p^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^p])/a^(3/2) - (2*b*p*Log[c*(a + b*x^2)^p]^2)/(a*x) - Log[c*(a + b*x^2)^p]^3/(3*x^3) + ((8*I)*b^(3/2)*p^3*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/a^(3/2) - (2*b^2*p*Defer[Int][Log[c*(a + b*x^2)^p]^2/(a + b*x^2), x])/a","A",0,0,0,0,-1,"{}"
102,1,107,0,0.1544337,"\int \frac{x^3}{\log \left(c \left(a+b x^2\right)^p\right)} \, dx","Int[x^3/Log[c*(a + b*x^2)^p],x]","\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}","\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,"-(a*(a + b*x^2)*ExpIntegralEi[Log[c*(a + b*x^2)^p]/p])/(2*b^2*p*(c*(a + b*x^2)^p)^p^(-1)) + ((a + b*x^2)^2*ExpIntegralEi[(2*Log[c*(a + b*x^2)^p])/p])/(2*b^2*p*(c*(a + b*x^2)^p)^(2/p))","A",9,7,18,0.3889,1,"{2454, 2399, 2389, 2300, 2178, 2390, 2310}"
103,1,51,0,0.0576011,"\int \frac{x}{\log \left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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",4,4,16,0.2500,1,"{2454, 2389, 2300, 2178}"
104,0,0,0,0.0171699,"\int \frac{1}{x \log \left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x*Log[c*(a + b*x^2)^p]), x]","A",0,0,0,0,-1,"{}"
105,0,0,0,0.0173301,"\int \frac{1}{x^3 \log \left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^3*Log[c*(a + b*x^2)^p]), x]","A",0,0,0,0,-1,"{}"
106,0,0,0,0.0177013,"\int \frac{x^2}{\log \left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][x^2/Log[c*(a + b*x^2)^p], x]","A",0,0,0,0,-1,"{}"
107,0,0,0,0.0035811,"\int \frac{1}{\log \left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][Log[c*(a + b*x^2)^p]^(-1), x]","A",0,0,0,0,-1,"{}"
108,0,0,0,0.0177068,"\int \frac{1}{x^2 \log \left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^2*Log[c*(a + b*x^2)^p]), x]","A",0,0,0,0,-1,"{}"
109,1,138,0,0.2066151,"\int \frac{x^3}{\log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[x^3/Log[c*(a + b*x^2)^p]^2,x]","\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)}","\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,"-(a*(a + b*x^2)*ExpIntegralEi[Log[c*(a + b*x^2)^p]/p])/(2*b^2*p^2*(c*(a + b*x^2)^p)^p^(-1)) + ((a + b*x^2)^2*ExpIntegralEi[(2*Log[c*(a + b*x^2)^p])/p])/(b^2*p^2*(c*(a + b*x^2)^p)^(2/p)) - (x^2*(a + b*x^2))/(2*b*p*Log[c*(a + b*x^2)^p])","A",13,8,18,0.4444,1,"{2454, 2400, 2399, 2389, 2300, 2178, 2390, 2310}"
110,1,83,0,0.0720991,"\int \frac{x}{\log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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} \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)}","\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,"((a + b*x^2)*ExpIntegralEi[Log[c*(a + b*x^2)^p]/p])/(2*b*p^2*(c*(a + b*x^2)^p)^p^(-1)) - (a + b*x^2)/(2*b*p*Log[c*(a + b*x^2)^p])","A",5,5,16,0.3125,1,"{2454, 2389, 2297, 2300, 2178}"
111,0,0,0,0.0157959,"\int \frac{1}{x \log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x*Log[c*(a + b*x^2)^p]^2), x]","A",0,0,0,0,-1,"{}"
112,0,0,0,0.0172644,"\int \frac{1}{x^3 \log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^3*Log[c*(a + b*x^2)^p]^2), x]","A",0,0,0,0,-1,"{}"
113,0,0,0,0.0168387,"\int \frac{x^2}{\log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][x^2/Log[c*(a + b*x^2)^p]^2, x]","A",0,0,0,0,-1,"{}"
114,0,0,0,0.0035547,"\int \frac{1}{\log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][Log[c*(a + b*x^2)^p]^(-2), x]","A",0,0,0,0,-1,"{}"
115,0,0,0,0.0165008,"\int \frac{1}{x^2 \log ^2\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^2*Log[c*(a + b*x^2)^p]^2), x]","A",0,0,0,0,-1,"{}"
116,1,204,0,0.2885152,"\int \frac{x^3}{\log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[x^3/Log[c*(a + b*x^2)^p]^3,x]","\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)}","\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,"-(a*(a + b*x^2)*ExpIntegralEi[Log[c*(a + b*x^2)^p]/p])/(4*b^2*p^3*(c*(a + b*x^2)^p)^p^(-1)) + ((a + b*x^2)^2*ExpIntegralEi[(2*Log[c*(a + b*x^2)^p])/p])/(b^2*p^3*(c*(a + b*x^2)^p)^(2/p)) - (x^2*(a + b*x^2))/(4*b*p*Log[c*(a + b*x^2)^p]^2) - (a*(a + b*x^2))/(4*b^2*p^2*Log[c*(a + b*x^2)^p]) - (x^2*(a + b*x^2))/(2*b*p^2*Log[c*(a + b*x^2)^p])","A",18,9,18,0.5000,1,"{2454, 2400, 2399, 2389, 2300, 2178, 2390, 2310, 2297}"
117,1,114,0,0.0931416,"\int \frac{x}{\log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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} \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)}","\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,"((a + b*x^2)*ExpIntegralEi[Log[c*(a + b*x^2)^p]/p])/(4*b*p^3*(c*(a + b*x^2)^p)^p^(-1)) - (a + b*x^2)/(4*b*p*Log[c*(a + b*x^2)^p]^2) - (a + b*x^2)/(4*b*p^2*Log[c*(a + b*x^2)^p])","A",6,5,16,0.3125,1,"{2454, 2389, 2297, 2300, 2178}"
118,0,0,0,0.0163287,"\int \frac{1}{x \log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x*Log[c*(a + b*x^2)^p]^3), x]","A",0,0,0,0,-1,"{}"
119,0,0,0,0.0168112,"\int \frac{1}{x^3 \log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^3*Log[c*(a + b*x^2)^p]^3), x]","A",0,0,0,0,-1,"{}"
120,0,0,0,0.0169869,"\int \frac{x^2}{\log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][x^2/Log[c*(a + b*x^2)^p]^3, x]","A",0,0,0,0,-1,"{}"
121,0,0,0,0.0039762,"\int \frac{1}{\log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][Log[c*(a + b*x^2)^p]^(-3), x]","A",0,0,0,0,-1,"{}"
122,0,0,0,0.0167578,"\int \frac{1}{x^2 \log ^3\left(c \left(a+b x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^2*Log[c*(a + b*x^2)^p]^3), x]","A",0,0,0,0,-1,"{}"
123,1,45,0,0.0954564,"\int \frac{x^3}{\log \left(c \left(a+b x^2\right)\right)} \, dx","Int[x^3/Log[c*(a + b*x^2)],x]","\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}","\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,"ExpIntegralEi[2*Log[c*(a + b*x^2)]]/(2*b^2*c^2) - (a*LogIntegral[c*(a + b*x^2)])/(2*b^2*c)","A",8,7,16,0.4375,1,"{2454, 2399, 2389, 2298, 2390, 2309, 2178}"
124,1,20,0,0.0271766,"\int \frac{x}{\log \left(c \left(a+b x^2\right)\right)} \, dx","Int[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",3,3,14,0.2143,1,"{2454, 2389, 2298}"
125,1,71,0,0.1251995,"\int \frac{x^3}{\log ^2\left(c \left(a+b x^2\right)\right)} \, dx","Int[x^3/Log[c*(a + b*x^2)]^2,x]","\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)}","\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,"ExpIntegralEi[2*Log[c*(a + b*x^2)]]/(b^2*c^2) - (x^2*(a + b*x^2))/(2*b*Log[c*(a + b*x^2)]) - (a*LogIntegral[c*(a + b*x^2)])/(2*b^2*c)","A",11,8,16,0.5000,1,"{2454, 2400, 2399, 2389, 2298, 2390, 2309, 2178}"
126,1,47,0,0.0430946,"\int \frac{x}{\log ^2\left(c \left(a+b x^2\right)\right)} \, dx","Int[x/Log[c*(a + b*x^2)]^2,x]","\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)}","\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)/(2*b*Log[c*(a + b*x^2)]) + LogIntegral[c*(a + b*x^2)]/(2*b*c)","A",4,4,14,0.2857,1,"{2454, 2389, 2297, 2298}"
127,1,127,0,0.1701531,"\int \frac{x^3}{\log ^3\left(c \left(a+b x^2\right)\right)} \, dx","Int[x^3/Log[c*(a + b*x^2)]^3,x]","\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)}","\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,"ExpIntegralEi[2*Log[c*(a + b*x^2)]]/(b^2*c^2) - (x^2*(a + b*x^2))/(4*b*Log[c*(a + b*x^2)]^2) - (a*(a + b*x^2))/(4*b^2*Log[c*(a + b*x^2)]) - (x^2*(a + b*x^2))/(2*b*Log[c*(a + b*x^2)]) - (a*LogIntegral[c*(a + b*x^2)])/(4*b^2*c)","A",15,9,16,0.5625,1,"{2454, 2400, 2399, 2389, 2298, 2390, 2309, 2178, 2297}"
128,1,73,0,0.0592836,"\int \frac{x}{\log ^3\left(c \left(a+b x^2\right)\right)} \, dx","Int[x/Log[c*(a + b*x^2)]^3,x]","\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)}","\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)/(4*b*Log[c*(a + b*x^2)]^2) - (a + b*x^2)/(4*b*Log[c*(a + b*x^2)]) + LogIntegral[c*(a + b*x^2)]/(4*b*c)","A",5,4,14,0.2857,1,"{2454, 2389, 2297, 2298}"
129,1,150,0,0.1561202,"\int x^5 \log ^2\left(c \left(d+e x^3\right)^p\right) \, dx","Int[x^5*Log[c*(d + e*x^3)^p]^2,x]","\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}","\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,"(-2*d*p^2*x^3)/(3*e) + (p^2*(d + e*x^3)^2)/(12*e^2) + (2*d*p*(d + e*x^3)*Log[c*(d + e*x^3)^p])/(3*e^2) - (p*(d + e*x^3)^2*Log[c*(d + e*x^3)^p])/(6*e^2) - (d*(d + e*x^3)*Log[c*(d + e*x^3)^p]^2)/(3*e^2) + ((d + e*x^3)^2*Log[c*(d + e*x^3)^p]^2)/(6*e^2)","A",9,8,18,0.4444,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
130,1,66,0,0.0556588,"\int x^2 \log ^2\left(c \left(d+e x^3\right)^p\right) \, dx","Int[x^2*Log[c*(d + e*x^3)^p]^2,x]","\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}","\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,"(2*p^2*x^3)/3 - (2*p*(d + e*x^3)*Log[c*(d + e*x^3)^p])/(3*e) + ((d + e*x^3)*Log[c*(d + e*x^3)^p]^2)/(3*e)","A",4,4,18,0.2222,1,"{2454, 2389, 2296, 2295}"
131,1,77,0,0.1083941,"\int \frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x} \, dx","Int[Log[c*(d + e*x^3)^p]^2/x,x]","\frac{2}{3} p \text{PolyLog}\left(2,\frac{e x^3}{d}+1\right) \log \left(c \left(d+e x^3\right)^p\right)-\frac{2}{3} p^2 \text{PolyLog}\left(3,\frac{e x^3}{d}+1\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 \text{PolyLog}\left(2,\frac{e x^3}{d}+1\right) \log \left(c \left(d+e x^3\right)^p\right)-\frac{2}{3} p^2 \text{PolyLog}\left(3,\frac{e x^3}{d}+1\right)+\frac{1}{3} \log \left(-\frac{e x^3}{d}\right) \log ^2\left(c \left(d+e x^3\right)^p\right)",1,"(Log[-((e*x^3)/d)]*Log[c*(d + e*x^3)^p]^2)/3 + (2*p*Log[c*(d + e*x^3)^p]*PolyLog[2, 1 + (e*x^3)/d])/3 - (2*p^2*PolyLog[3, 1 + (e*x^3)/d])/3","A",5,5,18,0.2778,1,"{2454, 2396, 2433, 2374, 6589}"
132,1,86,0,0.0841468,"\int \frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x^4} \, dx","Int[Log[c*(d + e*x^3)^p]^2/x^4,x]","\frac{2 e p^2 \text{PolyLog}\left(2,\frac{e x^3}{d}+1\right)}{3 d}-\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{PolyLog}\left(2,\frac{e x^3}{d}+1\right)}{3 d}-\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}",1,"(2*e*p*Log[-((e*x^3)/d)]*Log[c*(d + e*x^3)^p])/(3*d) - ((d + e*x^3)*Log[c*(d + e*x^3)^p]^2)/(3*d*x^3) + (2*e*p^2*PolyLog[2, 1 + (e*x^3)/d])/(3*d)","A",4,4,18,0.2222,1,"{2454, 2397, 2394, 2315}"
133,1,1300,0,1.9198729,"\int x \log ^2\left(c \left(d+e x^3\right)^p\right) \, dx","Int[x*Log[c*(d + e*x^3)^p]^2,x]","\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{(-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(\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{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{\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{PolyLog}\left(2,\frac{\sqrt[3]{e} x+\sqrt[3]{d}}{\left(1+\sqrt[3]{-1}\right) \sqrt[3]{d}}\right) p^2}{e^{2/3}}+\frac{d^{2/3} \text{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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) p^2}{e^{2/3}}+\frac{(-1)^{2/3} d^{2/3} \text{PolyLog}\left(2,\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{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)","\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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,"(9*p^2*x^2)/4 + (3*Sqrt[3]*d^(2/3)*p^2*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(2*e^(2/3)) + (3*d^(2/3)*p^2*Log[d^(1/3) + e^(1/3)*x])/(2*e^(2/3)) + (d^(2/3)*p^2*Log[d^(1/3) + e^(1/3)*x]^2)/(2*e^(2/3)) + (d^(2/3)*p^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^(2/3) - ((-1)^(1/3)*d^(2/3)*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^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*Log[d^(1/3) - (-1)^(1/3)*e^(1/3)*x]^2)/(2*e^(2/3)) + ((-1)^(2/3)*d^(2/3)*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^(2/3) + ((-1)^(2/3)*d^(2/3)*p^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^(2/3) + ((-1)^(2/3)*d^(2/3)*p^2*Log[d^(1/3) + (-1)^(2/3)*e^(1/3)*x]^2)/(2*e^(2/3)) - ((-1)^(2/3)*d^(2/3)*p^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)/((1 + (-1)^(1/3))*d^(1/3))])/e^(2/3) + (d^(2/3)*p^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^(2/3) - ((-1)^(1/3)*d^(2/3)*p^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^(2/3) - (3*d^(2/3)*p^2*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(4*e^(2/3)) - (3*p*x^2*Log[c*(d + e*x^3)^p])/2 - (d^(2/3)*p*Log[d^(1/3) + e^(1/3)*x]*Log[c*(d + e*x^3)^p])/e^(2/3) + ((-1)^(1/3)*d^(2/3)*p*Log[d^(1/3) - (-1)^(1/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/e^(2/3) - ((-1)^(2/3)*d^(2/3)*p*Log[d^(1/3) + (-1)^(2/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/e^(2/3) + (x^2*Log[c*(d + e*x^3)^p]^2)/2 + (d^(2/3)*p^2*PolyLog[2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/e^(2/3) + (d^(2/3)*p^2*PolyLog[2, (2*(d^(1/3) + e^(1/3)*x))/((3 - I*Sqrt[3])*d^(1/3))])/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*PolyLog[2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))])/e^(2/3) - ((-1)^(1/3)*d^(2/3)*p^2*PolyLog[2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/e^(2/3) - ((-1)^(2/3)*d^(2/3)*p^2*PolyLog[2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))])/e^(2/3) + ((-1)^(2/3)*d^(2/3)*p^2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))])/e^(2/3)","A",49,19,16,1.187,1,"{2457, 2476, 2455, 321, 292, 31, 634, 617, 204, 628, 2462, 260, 2416, 2390, 2301, 2394, 2393, 2391, 12}"
134,1,1310,0,1.7910475,"\int \log ^2\left(c \left(d+e x^3\right)^p\right) \, dx","Int[Log[c*(d + e*x^3)^p]^2,x]","-\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]{-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(\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}}-\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 (-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{PolyLog}\left(2,\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]{d} \text{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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) p^2}{\sqrt[3]{e}}+\frac{2 \sqrt[3]{-1} \sqrt[3]{d} \text{PolyLog}\left(2,\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}}-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)","-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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,"18*p^2*x + (6*Sqrt[3]*d^(1/3)*p^2*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/e^(1/3) - (d^(1/3)*p^2*Log[-d^(1/3) - e^(1/3)*x]^2)/e^(1/3) - (6*d^(1/3)*p^2*Log[d^(1/3) + e^(1/3)*x])/e^(1/3) - (2*d^(1/3)*p^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*(-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) - ((-1)^(2/3)*d^(1/3)*p^2*Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]^2)/e^(1/3) + (2*(-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*(-1)^(1/3)*d^(1/3)*p^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) + ((-1)^(1/3)*d^(1/3)*p^2*Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]^2)/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p^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)/((1 + (-1)^(1/3))*d^(1/3))])/e^(1/3) - (2*d^(1/3)*p^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*(-1)^(2/3)*d^(1/3)*p^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) + (3*d^(1/3)*p^2*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/e^(1/3) - 6*p*x*Log[c*(d + e*x^3)^p] + (2*d^(1/3)*p*Log[-d^(1/3) - e^(1/3)*x]*Log[c*(d + e*x^3)^p])/e^(1/3) + (2*(-1)^(2/3)*d^(1/3)*p*Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p*Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/e^(1/3) + x*Log[c*(d + e*x^3)^p]^2 - (2*d^(1/3)*p^2*PolyLog[2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/e^(1/3) - (2*d^(1/3)*p^2*PolyLog[2, (2*(d^(1/3) + e^(1/3)*x))/((3 - I*Sqrt[3])*d^(1/3))])/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*PolyLog[2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))])/e^(1/3) - (2*(-1)^(2/3)*d^(1/3)*p^2*PolyLog[2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/e^(1/3) - (2*(-1)^(1/3)*d^(1/3)*p^2*PolyLog[2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))])/e^(1/3) + (2*(-1)^(1/3)*d^(1/3)*p^2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))])/e^(1/3)","A",49,20,14,1.429,1,"{2450, 2476, 2448, 321, 200, 31, 634, 617, 204, 628, 2471, 2462, 260, 2416, 2390, 2301, 2394, 2393, 2391, 12}"
135,1,1143,0,1.3277405,"\int \frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x^2} \, dx","Int[Log[c*(d + e*x^3)^p]^2/x^2,x]","\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 (-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(\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(\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 \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{PolyLog}\left(2,\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 \sqrt[3]{e} \text{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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) p^2}{\sqrt[3]{d}}+\frac{2 (-1)^{2/3} \sqrt[3]{e} \text{PolyLog}\left(2,\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]{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}","\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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,"(e^(1/3)*p^2*Log[d^(1/3) + e^(1/3)*x]^2)/d^(1/3) + (2*e^(1/3)*p^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)))])/d^(1/3) - (2*(-1)^(1/3)*e^(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])/d^(1/3) - ((-1)^(1/3)*e^(1/3)*p^2*Log[d^(1/3) - (-1)^(1/3)*e^(1/3)*x]^2)/d^(1/3) + (2*(-1)^(2/3)*e^(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])/d^(1/3) + (2*(-1)^(2/3)*e^(1/3)*p^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])/d^(1/3) + ((-1)^(2/3)*e^(1/3)*p^2*Log[d^(1/3) + (-1)^(2/3)*e^(1/3)*x]^2)/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p^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)/((1 + (-1)^(1/3))*d^(1/3))])/d^(1/3) + (2*e^(1/3)*p^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))])/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^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)))])/d^(1/3) - (2*e^(1/3)*p*Log[d^(1/3) + e^(1/3)*x]*Log[c*(d + e*x^3)^p])/d^(1/3) + (2*(-1)^(1/3)*e^(1/3)*p*Log[d^(1/3) - (-1)^(1/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p*Log[d^(1/3) + (-1)^(2/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/d^(1/3) - Log[c*(d + e*x^3)^p]^2/x + (2*e^(1/3)*p^2*PolyLog[2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/d^(1/3) + (2*e^(1/3)*p^2*PolyLog[2, (2*(d^(1/3) + e^(1/3)*x))/((3 - I*Sqrt[3])*d^(1/3))])/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*PolyLog[2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))])/d^(1/3) - (2*(-1)^(1/3)*e^(1/3)*p^2*PolyLog[2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/d^(1/3) - (2*(-1)^(2/3)*e^(1/3)*p^2*PolyLog[2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))])/d^(1/3) + (2*(-1)^(2/3)*e^(1/3)*p^2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))])/d^(1/3)","A",39,11,18,0.6111,1,"{2457, 2476, 2462, 260, 2416, 2390, 2301, 2394, 2393, 2391, 12}"
136,1,1176,0,1.3444827,"\int \frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x^3} \, dx","Int[Log[c*(d + e*x^3)^p]^2/x^3,x]","-\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{\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(\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(\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{(-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{PolyLog}\left(2,\frac{\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} \text{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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) p^2}{d^{2/3}}+\frac{\sqrt[3]{-1} e^{2/3} \text{PolyLog}\left(2,\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{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}","-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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,"-(e^(2/3)*p^2*Log[-d^(1/3) - e^(1/3)*x]^2)/(2*d^(2/3)) - (e^(2/3)*p^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)))])/d^(2/3) - ((-1)^(2/3)*e^(2/3)*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])/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]^2)/(2*d^(2/3)) + ((-1)^(1/3)*e^(2/3)*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])/d^(2/3) + ((-1)^(1/3)*e^(2/3)*p^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])/d^(2/3) + ((-1)^(1/3)*e^(2/3)*p^2*Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]^2)/(2*d^(2/3)) - ((-1)^(1/3)*e^(2/3)*p^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)/((1 + (-1)^(1/3))*d^(1/3))])/d^(2/3) - (e^(2/3)*p^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))])/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^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)))])/d^(2/3) + (e^(2/3)*p*Log[-d^(1/3) - e^(1/3)*x]*Log[c*(d + e*x^3)^p])/d^(2/3) + ((-1)^(2/3)*e^(2/3)*p*Log[-d^(1/3) + (-1)^(1/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/d^(2/3) - ((-1)^(1/3)*e^(2/3)*p*Log[-d^(1/3) - (-1)^(2/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/d^(2/3) - Log[c*(d + e*x^3)^p]^2/(2*x^2) - (e^(2/3)*p^2*PolyLog[2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/d^(2/3) - (e^(2/3)*p^2*PolyLog[2, (2*(d^(1/3) + e^(1/3)*x))/((3 - I*Sqrt[3])*d^(1/3))])/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*PolyLog[2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))])/d^(2/3) - ((-1)^(2/3)*e^(2/3)*p^2*PolyLog[2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/d^(2/3) - ((-1)^(1/3)*e^(2/3)*p^2*PolyLog[2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))])/d^(2/3) + ((-1)^(1/3)*e^(2/3)*p^2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))])/d^(2/3)","A",39,11,18,0.6111,1,"{2457, 2471, 2462, 260, 2416, 2390, 2301, 2394, 2393, 2391, 12}"
137,1,1334,0,1.723456,"\int \frac{\log ^2\left(c \left(d+e x^3\right)^p\right)}{x^5} \, dx","Int[Log[c*(d + e*x^3)^p]^2/x^5,x]","-\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{(-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(\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(\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{\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{PolyLog}\left(2,\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{e^{4/3} \text{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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) p^2}{2 d^{4/3}}-\frac{(-1)^{2/3} e^{4/3} \text{PolyLog}\left(2,\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{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}","-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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,"(-3*Sqrt[3]*e^(4/3)*p^2*ArcTan[(d^(1/3) - 2*e^(1/3)*x)/(Sqrt[3]*d^(1/3))])/(2*d^(4/3)) - (3*e^(4/3)*p^2*Log[d^(1/3) + e^(1/3)*x])/(2*d^(4/3)) - (e^(4/3)*p^2*Log[d^(1/3) + e^(1/3)*x]^2)/(4*d^(4/3)) - (e^(4/3)*p^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)))])/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*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])/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*Log[d^(1/3) - (-1)^(1/3)*e^(1/3)*x]^2)/(4*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*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])/(2*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^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*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*Log[d^(1/3) + (-1)^(2/3)*e^(1/3)*x]^2)/(4*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p^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)/((1 + (-1)^(1/3))*d^(1/3))])/(2*d^(4/3)) - (e^(4/3)*p^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))])/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^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)))])/(2*d^(4/3)) + (3*e^(4/3)*p^2*Log[d^(2/3) - d^(1/3)*e^(1/3)*x + e^(2/3)*x^2])/(4*d^(4/3)) - (3*e*p*Log[c*(d + e*x^3)^p])/(2*d*x) + (e^(4/3)*p*Log[d^(1/3) + e^(1/3)*x]*Log[c*(d + e*x^3)^p])/(2*d^(4/3)) - ((-1)^(1/3)*e^(4/3)*p*Log[d^(1/3) - (-1)^(1/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/(2*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p*Log[d^(1/3) + (-1)^(2/3)*e^(1/3)*x]*Log[c*(d + e*x^3)^p])/(2*d^(4/3)) - Log[c*(d + e*x^3)^p]^2/(4*x^4) - (e^(4/3)*p^2*PolyLog[2, (d^(1/3) + e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/(2*d^(4/3)) - (e^(4/3)*p^2*PolyLog[2, (2*(d^(1/3) + e^(1/3)*x))/((3 - I*Sqrt[3])*d^(1/3))])/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*PolyLog[2, -(((-1)^(1/3)*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((1 - (-1)^(2/3))*d^(1/3)))])/(2*d^(4/3)) + ((-1)^(1/3)*e^(4/3)*p^2*PolyLog[2, (d^(1/3) - (-1)^(1/3)*e^(1/3)*x)/((1 + (-1)^(1/3))*d^(1/3))])/(2*d^(4/3)) + ((-1)^(2/3)*e^(4/3)*p^2*PolyLog[2, ((-1)^(1/3)*(d^(1/3) - (-1)^(1/3)*e^(1/3)*x))/((1 + (-1)^(1/3))*d^(1/3))])/(2*d^(4/3)) - ((-1)^(2/3)*e^(4/3)*p^2*PolyLog[2, (d^(1/3) + (-1)^(2/3)*e^(1/3)*x)/((1 - (-1)^(2/3))*d^(1/3))])/(2*d^(4/3))","A",48,18,18,1.000,1,"{2457, 2476, 2455, 292, 31, 634, 617, 204, 628, 2462, 260, 2416, 2390, 2301, 2394, 2393, 2391, 12}"
138,1,164,0,0.2374252,"\int \frac{x^8}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Int[x^8/Log[c*(d + e*x^3)^p],x]","\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}","\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^2*(d + e*x^3)*ExpIntegralEi[Log[c*(d + e*x^3)^p]/p])/(3*e^3*p*(c*(d + e*x^3)^p)^p^(-1)) - (2*d*(d + e*x^3)^2*ExpIntegralEi[(2*Log[c*(d + e*x^3)^p])/p])/(3*e^3*p*(c*(d + e*x^3)^p)^(2/p)) + ((d + e*x^3)^3*ExpIntegralEi[(3*Log[c*(d + e*x^3)^p])/p])/(3*e^3*p*(c*(d + e*x^3)^p)^(3/p))","A",12,7,18,0.3889,1,"{2454, 2399, 2389, 2300, 2178, 2390, 2310}"
139,1,107,0,0.1473692,"\int \frac{x^5}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Int[x^5/Log[c*(d + e*x^3)^p],x]","\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}","\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,"-(d*(d + e*x^3)*ExpIntegralEi[Log[c*(d + e*x^3)^p]/p])/(3*e^2*p*(c*(d + e*x^3)^p)^p^(-1)) + ((d + e*x^3)^2*ExpIntegralEi[(2*Log[c*(d + e*x^3)^p])/p])/(3*e^2*p*(c*(d + e*x^3)^p)^(2/p))","A",9,7,18,0.3889,1,"{2454, 2399, 2389, 2300, 2178, 2390, 2310}"
140,1,51,0,0.0623186,"\int \frac{x^2}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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",4,4,18,0.2222,1,"{2454, 2389, 2300, 2178}"
141,0,0,0,0.0168213,"\int \frac{1}{x \log \left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x*Log[c*(d + e*x^3)^p]), x]","A",0,0,0,0,-1,"{}"
142,0,0,0,0.0177668,"\int \frac{1}{x^4 \log \left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^4*Log[c*(d + e*x^3)^p]), x]","A",0,0,0,0,-1,"{}"
143,0,0,0,0.0181132,"\int \frac{x^3}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][x^3/Log[c*(d + e*x^3)^p], x]","A",0,0,0,0,-1,"{}"
144,0,0,0,0.0097062,"\int \frac{x}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][x/Log[c*(d + e*x^3)^p], x]","A",0,0,0,0,-1,"{}"
145,0,0,0,0.0035738,"\int \frac{1}{\log \left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^3)^p]^(-1), x]","A",0,0,0,0,-1,"{}"
146,0,0,0,0.0172972,"\int \frac{1}{x^2 \log \left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^2*Log[c*(d + e*x^3)^p]), x]","A",0,0,0,0,-1,"{}"
147,0,0,0,0.0184043,"\int \frac{1}{x^3 \log \left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^3*Log[c*(d + e*x^3)^p]), x]","A",0,0,0,0,-1,"{}"
148,1,195,0,0.3809373,"\int \frac{x^8}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Int[x^8/Log[c*(d + e*x^3)^p]^2,x]","\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)}","\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^2*(d + e*x^3)*ExpIntegralEi[Log[c*(d + e*x^3)^p]/p])/(3*e^3*p^2*(c*(d + e*x^3)^p)^p^(-1)) - (4*d*(d + e*x^3)^2*ExpIntegralEi[(2*Log[c*(d + e*x^3)^p])/p])/(3*e^3*p^2*(c*(d + e*x^3)^p)^(2/p)) + ((d + e*x^3)^3*ExpIntegralEi[(3*Log[c*(d + e*x^3)^p])/p])/(e^3*p^2*(c*(d + e*x^3)^p)^(3/p)) - (x^6*(d + e*x^3))/(3*e*p*Log[c*(d + e*x^3)^p])","A",21,8,18,0.4444,1,"{2454, 2400, 2399, 2389, 2300, 2178, 2390, 2310}"
149,1,141,0,0.2078045,"\int \frac{x^5}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Int[x^5/Log[c*(d + e*x^3)^p]^2,x]","\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)}","\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,"-(d*(d + e*x^3)*ExpIntegralEi[Log[c*(d + e*x^3)^p]/p])/(3*e^2*p^2*(c*(d + e*x^3)^p)^p^(-1)) + (2*(d + e*x^3)^2*ExpIntegralEi[(2*Log[c*(d + e*x^3)^p])/p])/(3*e^2*p^2*(c*(d + e*x^3)^p)^(2/p)) - (x^3*(d + e*x^3))/(3*e*p*Log[c*(d + e*x^3)^p])","A",13,8,18,0.4444,1,"{2454, 2400, 2399, 2389, 2300, 2178, 2390, 2310}"
150,1,83,0,0.0820962,"\int \frac{x^2}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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} \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)}","\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,"((d + e*x^3)*ExpIntegralEi[Log[c*(d + e*x^3)^p]/p])/(3*e*p^2*(c*(d + e*x^3)^p)^p^(-1)) - (d + e*x^3)/(3*e*p*Log[c*(d + e*x^3)^p])","A",5,5,18,0.2778,1,"{2454, 2389, 2297, 2300, 2178}"
151,0,0,0,0.0162048,"\int \frac{1}{x \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x*Log[c*(d + e*x^3)^p]^2), x]","A",0,0,0,0,-1,"{}"
152,0,0,0,0.0168459,"\int \frac{1}{x^4 \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^4*Log[c*(d + e*x^3)^p]^2), x]","A",0,0,0,0,-1,"{}"
153,0,0,0,0.0173569,"\int \frac{x^3}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][x^3/Log[c*(d + e*x^3)^p]^2, x]","A",0,0,0,0,-1,"{}"
154,0,0,0,0.0095794,"\int \frac{x}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][x/Log[c*(d + e*x^3)^p]^2, x]","A",0,0,0,0,-1,"{}"
155,0,0,0,0.0035729,"\int \frac{1}{\log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^3)^p]^(-2), x]","A",0,0,0,0,-1,"{}"
156,0,0,0,0.0171222,"\int \frac{1}{x^2 \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^2*Log[c*(d + e*x^3)^p]^2), x]","A",0,0,0,0,-1,"{}"
157,0,0,0,0.0166394,"\int \frac{1}{x^3 \log ^2\left(c \left(d+e x^3\right)^p\right)} \, dx","Int[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,"Defer[Int][1/(x^3*Log[c*(d + e*x^3)^p]^2), x]","A",0,0,0,0,-1,"{}"
158,0,0,0,0.1180393,"\int (f x)^m \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e*x^2)^p]^3,x]","\int (f x)^m \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","\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)^(1 + m)*Log[c*(d + e*x^2)^p]^3)/(f*(1 + m)) - (6*e*p*Defer[Int][((f*x)^(2 + m)*Log[c*(d + e*x^2)^p]^2)/(d + e*x^2), x])/(f^2*(1 + m))","A",0,0,0,0,-1,"{}"
159,0,0,0,0.0889901,"\int (f x)^m \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e*x^2)^p]^2,x]","\int (f x)^m \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","\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)^(1 + m)*Log[c*(d + e*x^2)^p]^2)/(f*(1 + m)) - (4*e*p*Defer[Int][((f*x)^(2 + m)*Log[c*(d + e*x^2)^p])/(d + e*x^2), x])/(f^2*(1 + m))","A",0,0,0,0,-1,"{}"
160,1,81,0,0.0429515,"\int (f x)^m \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f*x)^m*Log[c*(d + e*x^2)^p],x]","\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)}","\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,"(-2*e*p*(f*x)^(3 + m)*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, -((e*x^2)/d)])/(d*f^3*(1 + m)*(3 + m)) + ((f*x)^(1 + m)*Log[c*(d + e*x^2)^p])/(f*(1 + m))","A",3,3,18,0.1667,1,"{2455, 16, 364}"
161,0,0,0,0.0181375,"\int \frac{(f x)^m}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","Int[(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,"Defer[Int][(f*x)^m/Log[c*(d + e*x^2)^p], x]","A",0,0,0,0,-1,"{}"
162,0,0,0,0.017193,"\int \frac{(f x)^m}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Int[(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,"Defer[Int][(f*x)^m/Log[c*(d + e*x^2)^p]^2, x]","A",0,0,0,0,-1,"{}"
163,1,278,0,0.3208281,"\int (f x)^{-1+3 n} \log ^2\left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f*x)^(-1 + 3*n)*Log[c*(d + e*x^n)^p]^2,x]","-\frac{p x^{1-3 n} (f x)^{3 n-1} \left(\frac{18 d^2 \left(d+e x^n\right)}{e^3}-\frac{6 d^3 \log \left(d+e x^n\right)}{e^3}-\frac{9 d \left(d+e x^n\right)^2}{e^3}+\frac{2 \left(d+e x^n\right)^3}{e^3}\right) \log \left(c \left(d+e x^n\right)^p\right)}{9 n}+\frac{x (f x)^{3 n-1} \log ^2\left(c \left(d+e x^n\right)^p\right)}{3 n}+\frac{2 d^2 p^2 x^{1-2 n} (f x)^{3 n-1}}{e^2 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 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}","-\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 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 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{2 d^2 p^2 x^{1-2 n} (f x)^{3 n-1}}{e^2 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 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,"(2*d^2*p^2*x^(1 - 2*n)*(f*x)^(-1 + 3*n))/(e^2*n) - (d*p^2*x^(1 - 3*n)*(f*x)^(-1 + 3*n)*(d + e*x^n)^2)/(2*e^3*n) + (2*p^2*x^(1 - 3*n)*(f*x)^(-1 + 3*n)*(d + e*x^n)^3)/(27*e^3*n) - (d^3*p^2*x^(1 - 3*n)*(f*x)^(-1 + 3*n)*Log[d + e*x^n]^2)/(3*e^3*n) - (p*x^(1 - 3*n)*(f*x)^(-1 + 3*n)*((18*d^2*(d + e*x^n))/e^3 - (9*d*(d + e*x^n)^2)/e^3 + (2*(d + e*x^n)^3)/e^3 - (6*d^3*Log[d + e*x^n])/e^3)*Log[c*(d + e*x^n)^p])/(9*n) + (x*(f*x)^(-1 + 3*n)*Log[c*(d + e*x^n)^p]^2)/(3*n)","A",9,9,24,0.3750,1,"{2456, 2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
164,1,255,0,0.1872185,"\int (f x)^{-1+2 n} \log ^2\left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f*x)^(-1 + 2*n)*Log[c*(d + e*x^n)^p]^2,x]","\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}","\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,"(-2*d*p^2*x^(1 - n)*(f*x)^(-1 + 2*n))/(e*n) + (p^2*x^(1 - 2*n)*(f*x)^(-1 + 2*n)*(d + e*x^n)^2)/(4*e^2*n) + (2*d*p*x^(1 - 2*n)*(f*x)^(-1 + 2*n)*(d + e*x^n)*Log[c*(d + e*x^n)^p])/(e^2*n) - (p*x^(1 - 2*n)*(f*x)^(-1 + 2*n)*(d + e*x^n)^2*Log[c*(d + e*x^n)^p])/(2*e^2*n) - (d*x^(1 - 2*n)*(f*x)^(-1 + 2*n)*(d + e*x^n)*Log[c*(d + e*x^n)^p]^2)/(e^2*n) + (x^(1 - 2*n)*(f*x)^(-1 + 2*n)*(d + e*x^n)^2*Log[c*(d + e*x^n)^p]^2)/(2*e^2*n)","A",10,9,24,0.3750,1,"{2456, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
165,1,101,0,0.0810466,"\int (f x)^{-1+n} \log ^2\left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f*x)^(-1 + n)*Log[c*(d + e*x^n)^p]^2,x]","\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}","\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,"(2*p^2*x*(f*x)^(-1 + n))/n - (2*p*x^(1 - n)*(f*x)^(-1 + n)*(d + e*x^n)*Log[c*(d + e*x^n)^p])/(e*n) + (x^(1 - n)*(f*x)^(-1 + n)*(d + e*x^n)*Log[c*(d + e*x^n)^p]^2)/(e*n)","A",5,5,22,0.2273,1,"{2456, 2454, 2389, 2296, 2295}"
166,1,88,0,0.1139379,"\int \frac{\log ^2\left(c \left(d+e x^n\right)^p\right)}{f x} \, dx","Int[Log[c*(d + e*x^n)^p]^2/(f*x),x]","\frac{2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right) \log \left(c \left(d+e x^n\right)^p\right)}{f n}-\frac{2 p^2 \text{PolyLog}\left(3,\frac{e x^n}{d}+1\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 \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right) \log \left(c \left(d+e x^n\right)^p\right)}{f n}-\frac{2 p^2 \text{PolyLog}\left(3,\frac{e x^n}{d}+1\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}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p]^2)/(f*n) + (2*p*Log[c*(d + e*x^n)^p]*PolyLog[2, 1 + (e*x^n)/d])/(f*n) - (2*p^2*PolyLog[3, 1 + (e*x^n)/d])/(f*n)","A",6,6,21,0.2857,1,"{12, 2454, 2396, 2433, 2374, 6589}"
167,1,124,0,0.1112775,"\int (f x)^{-1-n} \log ^2\left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f*x)^(-1 - n)*Log[c*(d + e*x^n)^p]^2,x]","\frac{2 e p^2 x^{n+1} (f x)^{-n-1} \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{d 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{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{d 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}",1,"(2*e*p*x^(1 + n)*(f*x)^(-1 - n)*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/(d*n) - (x*(f*x)^(-1 - n)*(d + e*x^n)*Log[c*(d + e*x^n)^p]^2)/(d*n) + (2*e*p^2*x^(1 + n)*(f*x)^(-1 - n)*PolyLog[2, 1 + (e*x^n)/d])/(d*n)","A",5,5,24,0.2083,1,"{2456, 2454, 2397, 2394, 2315}"
168,1,238,0,0.3163487,"\int (f x)^{-1-2 n} \log ^2\left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f*x)^(-1 - 2*n)*Log[c*(d + e*x^n)^p]^2,x]","-\frac{e^2 p^2 x^{2 n+1} (f x)^{-2 n-1} \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{d^2 n}+\frac{e^2 x^{2 n+1} (f x)^{-2 n-1} \log ^2\left(c \left(d+e x^n\right)^p\right)}{2 d^2 n}-\frac{e^2 p x^{2 n+1} (f x)^{-2 n-1} \log \left(-\frac{e x^n}{d}\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} \log (x) (f x)^{-2 n-1}}{d^2}","\frac{e^2 p^2 x^{2 n+1} (f x)^{-2 n-1} \text{PolyLog}\left(2,\frac{d}{d+e x^n}\right)}{d^2 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} \log (x) (f x)^{-2 n-1}}{d^2}",1,"(e^2*p^2*x^(1 + 2*n)*(f*x)^(-1 - 2*n)*Log[x])/d^2 - (e*p*x^(1 + n)*(f*x)^(-1 - 2*n)*(d + e*x^n)*Log[c*(d + e*x^n)^p])/(d^2*n) - (e^2*p*x^(1 + 2*n)*(f*x)^(-1 - 2*n)*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/(d^2*n) - (x*(f*x)^(-1 - 2*n)*Log[c*(d + e*x^n)^p]^2)/(2*n) + (e^2*x^(1 + 2*n)*(f*x)^(-1 - 2*n)*Log[c*(d + e*x^n)^p]^2)/(2*d^2*n) - (e^2*p^2*x^(1 + 2*n)*(f*x)^(-1 - 2*n)*PolyLog[2, 1 + (e*x^n)/d])/(d^2*n)","A",11,11,24,0.4583,1,"{2456, 2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31}"
169,1,13,0,0.0086505,"\int \frac{\log \left(1+e x^n\right)}{x} \, dx","Int[Log[1 + e*x^n]/x,x]","-\frac{\text{PolyLog}\left(2,-e x^n\right)}{n}","-\frac{\text{PolyLog}\left(2,-e x^n\right)}{n}",1,"-(PolyLog[2, -(e*x^n)]/n)","A",1,1,12,0.08333,1,"{2391}"
170,1,21,0,0.027229,"\int \frac{\log \left(2+e x^n\right)}{x} \, dx","Int[Log[2 + e*x^n]/x,x]","\log (2) \log (x)-\frac{\text{PolyLog}\left(2,-\frac{e x^n}{2}\right)}{n}","\log (2) \log (x)-\frac{\text{PolyLog}\left(2,-\frac{e x^n}{2}\right)}{n}",1,"Log[2]*Log[x] - PolyLog[2, -(e*x^n)/2]/n","A",3,3,12,0.2500,1,"{2454, 2392, 2391}"
171,1,21,0,0.0284914,"\int \frac{\log \left(2 \left(3+e x^n\right)\right)}{x} \, dx","Int[Log[2*(3 + e*x^n)]/x,x]","\log (6) \log (x)-\frac{\text{PolyLog}\left(2,-\frac{e x^n}{3}\right)}{n}","\log (6) \log (x)-\frac{\text{PolyLog}\left(2,-\frac{e x^n}{3}\right)}{n}",1,"Log[6]*Log[x] - PolyLog[2, -(e*x^n)/3]/n","A",3,3,14,0.2143,1,"{2454, 2392, 2391}"
172,1,41,0,0.0392548,"\int \frac{\log \left(c \left(d+e x^n\right)\right)}{x} \, dx","Int[Log[c*(d + e*x^n)]/x,x]","\frac{\text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)\right)}{n}","\frac{\text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)\right)}{n}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)])/n + PolyLog[2, 1 + (e*x^n)/d]/n","A",3,3,14,0.2143,1,"{2454, 2394, 2315}"
173,1,44,0,0.0397916,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[Log[c*(d + e*x^n)^p]/x,x]","\frac{p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\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{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (p*PolyLog[2, 1 + (e*x^n)/d])/n","A",3,3,16,0.1875,1,"{2454, 2394, 2315}"
174,1,79,0,0.1001758,"\int \frac{\log ^2\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[Log[c*(d + e*x^n)^p]^2/x,x]","\frac{2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}-\frac{2 p^2 \text{PolyLog}\left(3,\frac{e x^n}{d}+1\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 \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}-\frac{2 p^2 \text{PolyLog}\left(3,\frac{e x^n}{d}+1\right)}{n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log ^2\left(c \left(d+e x^n\right)^p\right)}{n}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p]^2)/n + (2*p*Log[c*(d + e*x^n)^p]*PolyLog[2, 1 + (e*x^n)/d])/n - (2*p^2*PolyLog[3, 1 + (e*x^n)/d])/n","A",5,5,18,0.2778,1,"{2454, 2396, 2433, 2374, 6589}"
175,1,113,0,0.1484538,"\int \frac{\log ^3\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[Log[c*(d + e*x^n)^p]^3/x,x]","-\frac{6 p^2 \text{PolyLog}\left(3,\frac{e x^n}{d}+1\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{3 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right) \log ^2\left(c \left(d+e x^n\right)^p\right)}{n}+\frac{6 p^3 \text{PolyLog}\left(4,\frac{e x^n}{d}+1\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^2 \text{PolyLog}\left(3,\frac{e x^n}{d}+1\right) \log \left(c \left(d+e x^n\right)^p\right)}{n}+\frac{3 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right) \log ^2\left(c \left(d+e x^n\right)^p\right)}{n}+\frac{6 p^3 \text{PolyLog}\left(4,\frac{e x^n}{d}+1\right)}{n}+\frac{\log \left(-\frac{e x^n}{d}\right) \log ^3\left(c \left(d+e x^n\right)^p\right)}{n}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p]^3)/n + (3*p*Log[c*(d + e*x^n)^p]^2*PolyLog[2, 1 + (e*x^n)/d])/n - (6*p^2*Log[c*(d + e*x^n)^p]*PolyLog[3, 1 + (e*x^n)/d])/n + (6*p^3*PolyLog[4, 1 + (e*x^n)/d])/n","A",6,6,18,0.3333,1,"{2454, 2396, 2433, 2374, 2383, 6589}"
176,1,140,0,0.0772138,"\int (d+e x)^3 \log \left(c (a+b x)^p\right) \, dx","Int[(d + e*x)^3*Log[c*(a + b*x)^p],x]","-\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{p (b d-a e)^4 \log (a+b x)}{4 b^4 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}","-\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{p (b d-a e)^4 \log (a+b x)}{4 b^4 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,"-((b*d - a*e)^3*p*x)/(4*b^3) - ((b*d - a*e)^2*p*(d + e*x)^2)/(8*b^2*e) - ((b*d - a*e)*p*(d + e*x)^3)/(12*b*e) - (p*(d + e*x)^4)/(16*e) - ((b*d - a*e)^4*p*Log[a + b*x])/(4*b^4*e) + ((d + e*x)^4*Log[c*(a + b*x)^p])/(4*e)","A",3,2,18,0.1111,1,"{2395, 43}"
177,1,112,0,0.073292,"\int (d+e x)^2 \log \left(c (a+b x)^p\right) \, dx","Int[(d + e*x)^2*Log[c*(a + b*x)^p],x]","-\frac{p x (b d-a e)^2}{3 b^2}-\frac{p (b d-a e)^3 \log (a+b x)}{3 b^3 e}+\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}","-\frac{p x (b d-a e)^2}{3 b^2}-\frac{p (b d-a e)^3 \log (a+b x)}{3 b^3 e}+\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,"-((b*d - a*e)^2*p*x)/(3*b^2) - ((b*d - a*e)*p*(d + e*x)^2)/(6*b*e) - (p*(d + e*x)^3)/(9*e) - ((b*d - a*e)^3*p*Log[a + b*x])/(3*b^3*e) + ((d + e*x)^3*Log[c*(a + b*x)^p])/(3*e)","A",3,2,18,0.1111,1,"{2395, 43}"
178,1,84,0,0.0371142,"\int (d+e x) \log \left(c (a+b x)^p\right) \, dx","Int[(d + e*x)*Log[c*(a + b*x)^p],x]","-\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}","-\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,"-((b*d - a*e)*p*x)/(2*b) - (p*(d + e*x)^2)/(4*e) - ((b*d - a*e)^2*p*Log[a + b*x])/(2*b^2*e) + ((d + e*x)^2*Log[c*(a + b*x)^p])/(2*e)","A",3,2,16,0.1250,1,"{2395, 43}"
179,1,24,0,0.0090786,"\int \log \left(c (a+b x)^p\right) \, dx","Int[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",2,2,10,0.2000,1,"{2389, 2295}"
180,1,58,0,0.0504011,"\int \frac{\log \left(c (a+b x)^p\right)}{d+e x} \, dx","Int[Log[c*(a + b*x)^p]/(d + e*x),x]","\frac{p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\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{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{e}+\frac{\log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e 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",3,3,18,0.1667,1,"{2394, 2393, 2391}"
181,1,68,0,0.0274055,"\int \frac{\log \left(c (a+b x)^p\right)}{(d+e x)^2} \, dx","Int[Log[c*(a + b*x)^p]/(d + e*x)^2,x]","-\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)}","-\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,"(b*p*Log[a + b*x])/(e*(b*d - a*e)) - Log[c*(a + b*x)^p]/(e*(d + e*x)) - (b*p*Log[d + e*x])/(e*(b*d - a*e))","A",4,3,18,0.1667,1,"{2395, 36, 31}"
182,1,105,0,0.0588471,"\int \frac{\log \left(c (a+b x)^p\right)}{(d+e x)^3} \, dx","Int[Log[c*(a + b*x)^p]/(d + e*x)^3,x]","\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)}","\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,"(b*p)/(2*e*(b*d - a*e)*(d + e*x)) + (b^2*p*Log[a + b*x])/(2*e*(b*d - a*e)^2) - Log[c*(a + b*x)^p]/(2*e*(d + e*x)^2) - (b^2*p*Log[d + e*x])/(2*e*(b*d - a*e)^2)","A",3,2,18,0.1111,1,"{2395, 44}"
183,1,133,0,0.0773629,"\int \frac{\log \left(c (a+b x)^p\right)}{(d+e x)^4} \, dx","Int[Log[c*(a + b*x)^p]/(d + e*x)^4,x]","\frac{b^2 p}{3 e (d+e x) (b d-a e)^2}+\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{\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)}","\frac{b^2 p}{3 e (d+e x) (b d-a e)^2}+\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{\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,"(b*p)/(6*e*(b*d - a*e)*(d + e*x)^2) + (b^2*p)/(3*e*(b*d - a*e)^2*(d + e*x)) + (b^3*p*Log[a + b*x])/(3*e*(b*d - a*e)^3) - Log[c*(a + b*x)^p]/(3*e*(d + e*x)^3) - (b^3*p*Log[d + e*x])/(3*e*(b*d - a*e)^3)","A",3,2,18,0.1111,1,"{2395, 44}"
184,1,178,0,0.163456,"\int (d+e x)^3 \log \left(c \left(a+b x^2\right)^p\right) \, dx","Int[(d + e*x)^3*Log[c*(a + b*x^2)^p],x]","-\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","-\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,"(-2*d*(b*d^2 - a*e^2)*p*x)/b - (e*(6*b*d^2 - a*e^2)*p*x^2)/(4*b) - (2*d*e^2*p*x^3)/3 - (e^3*p*x^4)/8 + (2*Sqrt[a]*d*(b*d^2 - a*e^2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(3/2) - ((b^2*d^4 - 6*a*b*d^2*e^2 + a^2*e^4)*p*Log[a + b*x^2])/(4*b^2*e) + ((d + e*x)^4*Log[c*(a + b*x^2)^p])/(4*e)","A",6,5,20,0.2500,1,"{2463, 801, 635, 205, 260}"
185,1,141,0,0.1321586,"\int (d+e x)^2 \log \left(c \left(a+b x^2\right)^p\right) \, dx","Int[(d + e*x)^2*Log[c*(a + b*x^2)^p],x]","\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","\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,"(-2*(3*b*d^2 - a*e^2)*p*x)/(3*b) - d*e*p*x^2 - (2*e^2*p*x^3)/9 + (2*Sqrt[a]*(3*b*d^2 - a*e^2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(3*b^(3/2)) - (d*(b*d^2 - 3*a*e^2)*p*Log[a + b*x^2])/(3*b*e) + ((d + e*x)^3*Log[c*(a + b*x^2)^p])/(3*e)","A",6,5,20,0.2500,1,"{2463, 801, 635, 205, 260}"
186,1,99,0,0.078563,"\int (d+e x) \log \left(c \left(a+b x^2\right)^p\right) \, dx","Int[(d + e*x)*Log[c*(a + b*x^2)^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","\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 - (e*p*x^2)/2 + (2*Sqrt[a]*d*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/Sqrt[b] - ((b*d^2 - a*e^2)*p*Log[a + b*x^2])/(2*b*e) + ((d + e*x)^2*Log[c*(a + b*x^2)^p])/(2*e)","A",6,5,18,0.2778,1,"{2463, 801, 635, 205, 260}"
187,1,45,0,0.0190329,"\int \log \left(c \left(a+b x^2\right)^p\right) \, dx","Int[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",3,3,12,0.2500,1,"{2448, 321, 205}"
188,1,201,0,0.2663164,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{d+e x} \, dx","Int[Log[c*(a + b*x^2)^p]/(d + e*x),x]","-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+b x^2\right)^p\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{p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+b x^2\right)^p\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",9,6,20,0.3000,1,"{2462, 260, 2416, 2394, 2393, 2391}"
189,1,119,0,0.0901617,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{(d+e x)^2} \, dx","Int[Log[c*(a + b*x^2)^p]/(d + e*x)^2,x]","-\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}","-\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]*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(b*d^2 + a*e^2) - (2*b*d*p*Log[d + e*x])/(e*(b*d^2 + a*e^2)) + (b*d*p*Log[a + b*x^2])/(e*(b*d^2 + a*e^2)) - Log[c*(a + b*x^2)^p]/(e*(d + e*x))","A",6,5,20,0.2500,1,"{2463, 801, 635, 205, 260}"
190,1,174,0,0.1449845,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{(d+e x)^3} \, dx","Int[Log[c*(a + b*x^2)^p]/(d + e*x)^3,x]","\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}","\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*d*p)/(e*(b*d^2 + a*e^2)*(d + e*x)) + (2*Sqrt[a]*b^(3/2)*d*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(b*d^2 + a*e^2)^2 - (b*(b*d^2 - a*e^2)*p*Log[d + e*x])/(e*(b*d^2 + a*e^2)^2) + (b*(b*d^2 - a*e^2)*p*Log[a + b*x^2])/(2*e*(b*d^2 + a*e^2)^2) - Log[c*(a + b*x^2)^p]/(2*e*(d + e*x)^2)","A",6,5,20,0.2500,1,"{2463, 801, 635, 205, 260}"
191,1,320,0,0.7417169,"\int (d+e x)^3 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Int[(d + e*x)^3*Log[c*(a + b*x^3)^p],x]","-\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","-\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*(4*b*d^3 - a*e^3)*p*x)/(4*b) - (9*d^2*e*p*x^2)/4 - d*e^2*p*x^3 - (3*e^3*p*x^4)/16 - (Sqrt[3]*a^(1/3)*(4*b*d^3 + 6*a^(1/3)*b^(2/3)*d^2*e - a*e^3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(4*b^(4/3)) + (a^(1/3)*(4*b*d^3 - 6*a^(1/3)*b^(2/3)*d^2*e - a*e^3)*p*Log[a^(1/3) + b^(1/3)*x])/(4*b^(4/3)) - (a^(1/3)*(4*b*d^3 - 6*a^(1/3)*b^(2/3)*d^2*e - a*e^3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(8*b^(4/3)) - (d*(b*d^3 - 4*a*e^3)*p*Log[a + b*x^3])/(4*b*e) + ((d + e*x)^4*Log[c*(a + b*x^3)^p])/(4*e)","A",13,11,20,0.5500,1,"{2463, 1836, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
192,1,250,0,0.482857,"\int (d+e x)^2 \log \left(c \left(a+b x^3\right)^p\right) \, dx","Int[(d + e*x)^2*Log[c*(a + b*x^3)^p],x]","-\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","-\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,"-3*d^2*p*x - (3*d*e*p*x^2)/2 - (e^2*p*x^3)/3 - (Sqrt[3]*a^(1/3)*d*(b^(1/3)*d + a^(1/3)*e)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/b^(2/3) + (a^(1/3)*d*(b^(1/3)*d - a^(1/3)*e)*p*Log[a^(1/3) + b^(1/3)*x])/b^(2/3) - (a^(1/3)*d*(b^(1/3)*d - a^(1/3)*e)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(2*b^(2/3)) - ((b*d^3 - a*e^3)*p*Log[a + b*x^3])/(3*b*e) + ((d + e*x)^3*Log[c*(a + b*x^3)^p])/(3*e)","A",12,11,20,0.5500,1,"{2463, 1836, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
193,1,229,0,0.3172498,"\int (d+e x) \log \left(c \left(a+b x^3\right)^p\right) \, dx","Int[(d + e*x)*Log[c*(a + b*x^3)^p],x]","-\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","-\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)*(2*b^(1/3)*d + a^(1/3)*e)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(2*b^(2/3)) + (a^(1/3)*(2*b^(1/3)*d - a^(1/3)*e)*p*Log[a^(1/3) + b^(1/3)*x])/(2*b^(2/3)) - (a^(1/3)*(2*b^(1/3)*d - a^(1/3)*e)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(4*b^(2/3)) - (d^2*p*Log[a + b*x^3])/(2*e) + ((d + e*x)^2*Log[c*(a + b*x^3)^p])/(2*e)","A",11,10,18,0.5556,1,"{2463, 1887, 1871, 1860, 31, 634, 617, 204, 628, 260}"
194,1,133,0,0.0866253,"\int \log \left(c \left(a+b x^3\right)^p\right) \, dx","Int[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{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\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[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/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",8,8,12,0.6667,1,"{2448, 321, 200, 31, 634, 617, 204, 628}"
195,1,308,0,0.5168302,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{d+e x} \, dx","Int[Log[c*(a + b*x^3)^p]/(d + e*x),x]","-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+b x^3\right)^p\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}","-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+b x^3\right)^p\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[-((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])/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",12,6,20,0.3000,1,"{2462, 260, 2416, 2394, 2393, 2391}"
196,1,292,0,0.5494615,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{(d+e x)^2} \, dx","Int[Log[c*(a + b*x^3)^p]/(d + e*x)^2,x]","-\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{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)}+\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{\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{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)}+\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}",1,"-((Sqrt[3]*a^(1/3)*b^(1/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(b^(2/3)*d^2 + a^(1/3)*b^(1/3)*d*e + a^(2/3)*e^2)) + (a^(1/3)*b^(1/3)*(b^(1/3)*d + a^(1/3)*e)*p*Log[a^(1/3) + b^(1/3)*x])/(b*d^3 - a*e^3) - (3*b*d^2*p*Log[d + e*x])/(e*(b*d^3 - a*e^3)) - (a^(1/3)*b^(1/3)*(b^(1/3)*d + a^(1/3)*e)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(2*(b*d^3 - a*e^3)) + (b*d^2*p*Log[a + b*x^3])/(e*(b*d^3 - a*e^3)) - Log[c*(a + b*x^3)^p]/(e*(d + e*x))","A",11,10,20,0.5000,1,"{2463, 6725, 1871, 1860, 31, 634, 617, 204, 628, 260}"
197,1,391,0,0.712848,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{(d+e x)^3} \, dx","Int[Log[c*(a + b*x^3)^p]/(d + e*x)^3,x]","-\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^2 p}{2 e (d+e x) \left(b d^3-a e^3\right)}-\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{\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^2 p}{2 e (d+e x) \left(b d^3-a e^3\right)}-\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}",1,"(3*b*d^2*p)/(2*e*(b*d^3 - a*e^3)*(d + e*x)) - (Sqrt[3]*a^(1/3)*b^(2/3)*(2*b*d^3 - 3*a^(1/3)*b^(2/3)*d^2*e + a*e^3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(2*(b*d^3 - a*e^3)^2) + (a^(1/3)*b^(2/3)*(2*b*d^3 + 3*a^(1/3)*b^(2/3)*d^2*e + a*e^3)*p*Log[a^(1/3) + b^(1/3)*x])/(2*(b*d^3 - a*e^3)^2) - (3*b*d*(b*d^3 + 2*a*e^3)*p*Log[d + e*x])/(2*e*(b*d^3 - a*e^3)^2) - (a^(1/3)*b^(2/3)*(2*b*d^3 + 3*a^(1/3)*b^(2/3)*d^2*e + a*e^3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(4*(b*d^3 - a*e^3)^2) + (b*d*(b*d^3 + 2*a*e^3)*p*Log[a + b*x^3])/(2*e*(b*d^3 - a*e^3)^2) - Log[c*(a + b*x^3)^p]/(2*e*(d + e*x)^2)","A",11,10,20,0.5000,1,"{2463, 6725, 1871, 1860, 31, 634, 617, 204, 628, 260}"
198,1,139,0,0.125612,"\int (d+e x)^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Int[(d + e*x)^3*Log[c*(a + b/x)^p],x]","\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{b e^2 p x^2 (4 a d-b e)}{8 a^2}-\frac{p (a d-b e)^4 \log (a x+b)}{4 a^4 e}+\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}","\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{b e^2 p x^2 (4 a d-b e)}{8 a^2}-\frac{p (a d-b e)^4 \log (a x+b)}{4 a^4 e}+\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*(6*a^2*d^2 - 4*a*b*d*e + b^2*e^2)*p*x)/(4*a^3) + (b*e^2*(4*a*d - b*e)*p*x^2)/(8*a^2) + (b*e^3*p*x^3)/(12*a) + ((d + e*x)^4*Log[c*(a + b/x)^p])/(4*e) + (d^4*p*Log[x])/(4*e) - ((a*d - b*e)^4*p*Log[b + a*x])/(4*a^4*e)","A",4,3,20,0.1500,1,"{2463, 514, 72}"
199,1,102,0,0.093517,"\int (d+e x)^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Int[(d + e*x)^2*Log[c*(a + b/x)^p],x]","\frac{b e p x (3 a d-b e)}{3 a^2}-\frac{p (a d-b e)^3 \log (a x+b)}{3 a^3 e}+\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}","\frac{b e p x (3 a d-b e)}{3 a^2}-\frac{p (a d-b e)^3 \log (a x+b)}{3 a^3 e}+\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,"(b*e*(3*a*d - b*e)*p*x)/(3*a^2) + (b*e^2*p*x^2)/(6*a) + ((d + e*x)^3*Log[c*(a + b/x)^p])/(3*e) + (d^3*p*Log[x])/(3*e) - ((a*d - b*e)^3*p*Log[b + a*x])/(3*a^3*e)","A",4,3,20,0.1500,1,"{2463, 514, 72}"
200,1,78,0,0.0561594,"\int (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Int[(d + e*x)*Log[c*(a + b/x)^p],x]","-\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}","-\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*e*p*x)/(2*a) + ((d + e*x)^2*Log[c*(a + b/x)^p])/(2*e) + (d^2*p*Log[x])/(2*e) - ((a*d - b*e)^2*p*Log[b + a*x])/(2*a^2*e)","A",4,3,18,0.1667,1,"{2463, 514, 72}"
201,1,113,0,0.1575689,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d+e x} \, dx","Int[Log[c*(a + b/x)^p]/(d + e*x),x]","-\frac{p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{e}+\frac{p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{e}+\frac{p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}","-\frac{p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{e}+\frac{p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\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, (a*(d + e*x))/(a*d - b*e)])/e + (p*PolyLog[2, 1 + (e*x)/d])/e","A",8,7,20,0.3500,1,"{2462, 260, 2416, 2394, 2315, 2393, 2391}"
202,1,81,0,0.0774764,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{(d+e x)^2} \, dx","Int[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",4,3,20,0.1500,1,"{2463, 514, 72}"
203,1,127,0,0.1185395,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{(d+e x)^3} \, dx","Int[Log[c*(a + b/x)^p]/(d + e*x)^3,x]","\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}","\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*p)/(2*d*(a*d - b*e)*(d + e*x)) - Log[c*(a + b/x)^p]/(2*e*(d + e*x)^2) - (p*Log[x])/(2*d^2*e) + (a^2*p*Log[b + a*x])/(2*e*(a*d - b*e)^2) - (b*(2*a*d - b*e)*p*Log[d + e*x])/(2*d^2*(a*d - b*e)^2)","A",4,3,20,0.1500,1,"{2463, 514, 72}"
204,1,175,0,0.1715205,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{(d+e x)^4} \, dx","Int[Log[c*(a + b/x)^p]/(d + e*x)^4,x]","-\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{a^3 p \log (a x+b)}{3 e (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}","-\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{a^3 p \log (a x+b)}{3 e (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*p)/(6*d*(a*d - b*e)*(d + e*x)^2) + (b*(2*a*d - b*e)*p)/(3*d^2*(a*d - b*e)^2*(d + e*x)) - Log[c*(a + b/x)^p]/(3*e*(d + e*x)^3) - (p*Log[x])/(3*d^3*e) + (a^3*p*Log[b + a*x])/(3*e*(a*d - b*e)^3) - (b*(3*a^2*d^2 - 3*a*b*d*e + b^2*e^2)*p*Log[d + e*x])/(3*d^3*(a*d - b*e)^3)","A",4,3,20,0.1500,1,"{2463, 514, 72}"
205,1,105,0,0.166766,"\int \frac{\log \left(a+\frac{b}{x}\right)}{c+d x} \, dx","Int[Log[a + b/x]/(c + d*x),x]","-\frac{\text{PolyLog}\left(2,\frac{a (c+d x)}{a c-b d}\right)}{d}+\frac{\text{PolyLog}\left(2,\frac{d x}{c}+1\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{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{d}","-\frac{\text{PolyLog}\left(2,\frac{a (c+d x)}{a c-b d}\right)}{d}+\frac{\text{PolyLog}\left(2,\frac{d x}{c}+1\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{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{d}",1,"(Log[a + b/x]*Log[c + d*x])/d + (Log[-((d*x)/c)]*Log[c + d*x])/d - (Log[-((d*(b + a*x))/(a*c - b*d))]*Log[c + d*x])/d - PolyLog[2, (a*(c + d*x))/(a*c - b*d)]/d + PolyLog[2, 1 + (d*x)/c]/d","A",8,7,16,0.4375,1,"{2462, 260, 2416, 2394, 2315, 2393, 2391}"
206,1,301,0,0.7555881,"\int (d+e x)^m \log \left(c \left(a+b x^3\right)^p\right) \, dx","Int[(d + e*x)^m*Log[c*(a + b*x^3)^p],x]","\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)}","\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,"(b^(1/3)*p*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)])/(e*(b^(1/3)*d - a^(1/3)*e)*(1 + m)*(2 + m)) + (b^(1/3)*p*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)])/(e*(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)*(1 + m)*(2 + m)) + (b^(1/3)*p*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)])/(e*(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)*(1 + m)*(2 + m)) + ((d + e*x)^(1 + m)*Log[c*(a + b*x^3)^p])/(e*(1 + m))","A",6,3,20,0.1500,1,"{2463, 6725, 68}"
207,1,205,0,0.247979,"\int (d+e x)^m \log \left(c \left(a+b x^2\right)^p\right) \, dx","Int[(d + e*x)^m*Log[c*(a + b*x^2)^p],x]","\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)}","\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,"(Sqrt[b]*p*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)])/(e*(Sqrt[b]*d - Sqrt[-a]*e)*(1 + m)*(2 + m)) + (Sqrt[b]*p*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)])/(e*(Sqrt[b]*d + Sqrt[-a]*e)*(1 + m)*(2 + m)) + ((d + e*x)^(1 + m)*Log[c*(a + b*x^2)^p])/(e*(1 + m))","A",5,3,20,0.1500,1,"{2463, 831, 68}"
208,1,89,0,0.045602,"\int (d+e x)^m \log \left(c (a+b x)^p\right) \, dx","Int[(d + e*x)^m*Log[c*(a + b*x)^p],x]","\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)}","\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,"(b*p*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (b*(d + e*x))/(b*d - a*e)])/(e*(b*d - a*e)*(1 + m)*(2 + m)) + ((d + e*x)^(1 + m)*Log[c*(a + b*x)^p])/(e*(1 + m))","A",2,2,18,0.1111,1,"{2395, 68}"
209,1,135,0,0.0926796,"\int (d+e x)^m \log \left(c \left(a+\frac{b}{x}\right)^p\right) \, dx","Int[(d + e*x)^m*Log[c*(a + b/x)^p],x]","\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)}","\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,"(a*p*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (a*(d + e*x))/(a*d - b*e)])/(e*(a*d - b*e)*(1 + m)*(2 + m)) - (p*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, 1 + (e*x)/d])/(d*e*(2 + 3*m + m^2)) + ((d + e*x)^(1 + m)*Log[c*(a + b/x)^p])/(e*(1 + m))","A",5,5,20,0.2500,1,"{2463, 514, 86, 65, 68}"
210,1,257,0,0.5327418,"\int (d+e x)^m \log \left(c \left(a+\frac{b}{x^2}\right)^p\right) \, dx","Int[(d + e*x)^m*Log[c*(a + b/x^2)^p],x]","\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)}","\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,"(Sqrt[-a]*p*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)])/(e*(Sqrt[-a]*d - Sqrt[b]*e)*(1 + m)*(2 + m)) + (Sqrt[-a]*p*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)])/(e*(Sqrt[-a]*d + Sqrt[b]*e)*(1 + m)*(2 + m)) - (2*p*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, 1 + (e*x)/d])/(d*e*(2 + 3*m + m^2)) + ((d + e*x)^(1 + m)*Log[c*(a + b/x^2)^p])/(e*(1 + m))","A",9,6,20,0.3000,1,"{2463, 1570, 961, 65, 831, 68}"
211,0,0,0,0.0110441,"\int (f+g x)^m \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[(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,"Defer[Int][(f + g*x)^m*Log[c*(d + e*x^n)^p], x]","A",0,0,0,0,-1,"{}"
212,1,234,0,0.232796,"\int (f+g x)^3 \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[(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)}{4 g}-\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{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{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)}","\frac{(f+g x)^4 \log \left(c \left(d+e x^n\right)^p\right)}{4 g}-\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{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{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*f^3*n*p*x^(1 + n)*Hypergeometric2F1[1, 1 + n^(-1), 2 + n^(-1), -((e*x^n)/d)])/(d*(1 + n))) - (3*e*f^2*g*n*p*x^(2 + n)*Hypergeometric2F1[1, (2 + n)/n, 2*(1 + n^(-1)), -((e*x^n)/d)])/(2*d*(2 + n)) - (e*f*g^2*n*p*x^(3 + n)*Hypergeometric2F1[1, (3 + n)/n, 2 + 3/n, -((e*x^n)/d)])/(d*(3 + n)) - (e*g^3*n*p*x^(4 + n)*Hypergeometric2F1[1, (4 + n)/n, 2*(1 + 2/n), -((e*x^n)/d)])/(4*d*(4 + n)) - (f^4*p*Log[d + e*x^n])/(4*g) + ((f + g*x)^4*Log[c*(d + e*x^n)^p])/(4*g)","A",8,4,20,0.2000,1,"{2463, 1844, 260, 364}"
213,1,181,0,0.176117,"\int (f+g x)^2 \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[(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)}{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)}","\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*f^2*n*p*x^(1 + n)*Hypergeometric2F1[1, 1 + n^(-1), 2 + n^(-1), -((e*x^n)/d)])/(d*(1 + n))) - (e*f*g*n*p*x^(2 + n)*Hypergeometric2F1[1, (2 + n)/n, 2*(1 + n^(-1)), -((e*x^n)/d)])/(d*(2 + n)) - (e*g^2*n*p*x^(3 + n)*Hypergeometric2F1[1, (3 + n)/n, 2 + 3/n, -((e*x^n)/d)])/(3*d*(3 + n)) - (f^3*p*Log[d + e*x^n])/(3*g) + ((f + g*x)^3*Log[c*(d + e*x^n)^p])/(3*g)","A",7,4,20,0.2000,1,"{2463, 1844, 260, 364}"
214,1,132,0,0.1356161,"\int (f+g x) \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[(f + g*x)*Log[c*(d + e*x^n)^p],x]","\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)}","\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^(-1), 2 + n^(-1), -((e*x^n)/d)])/(d*(1 + n))) - (e*g*n*p*x^(2 + n)*Hypergeometric2F1[1, (2 + n)/n, 2*(1 + n^(-1)), -((e*x^n)/d)])/(2*d*(2 + n)) - (f^2*p*Log[d + e*x^n])/(2*g) + ((f + g*x)^2*Log[c*(d + e*x^n)^p])/(2*g)","A",6,4,18,0.2222,1,"{2463, 1844, 260, 364}"
215,1,54,0,0.0168512,"\int \log \left(c \left(d+e x^n\right)^p\right) \, dx","Int[Log[c*(d + e*x^n)^p],x]","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)}","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,"-((e*n*p*x^(1 + n)*Hypergeometric2F1[1, 1 + n^(-1), 2 + n^(-1), -((e*x^n)/d)])/(d*(1 + n))) + x*Log[c*(d + e*x^n)^p]","A",2,2,12,0.1667,1,"{2448, 364}"
216,0,0,0,0.0124176,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{f+g x} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^n)^p]/(f + g*x), x]","A",0,0,0,0,-1,"{}"
217,0,0,0,0.0122881,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{(f+g x)^2} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^n)^p]/(f + g*x)^2, x]","A",0,0,0,0,-1,"{}"
218,0,0,0,0.0122042,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{(f+g x)^3} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^n)^p]/(f + g*x)^3, x]","A",0,0,0,0,-1,"{}"
219,1,250,0,0.2458567,"\int \frac{x^3 \log \left(c (a+b x)^p\right)}{d+e x} \, dx","Int[(x^3*Log[c*(a + b*x)^p])/(d + e*x),x]","-\frac{d^3 p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{e^4}+\frac{a^2 d p \log (a+b x)}{2 b^2 e^2}-\frac{a^2 p x}{3 b^2 e}+\frac{a^3 p \log (a+b x)}{3 b^3 e}+\frac{d^2 (a+b x) \log \left(c (a+b x)^p\right)}{b e^3}-\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 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{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}","-\frac{d^3 p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{e^4}+\frac{a^2 d p \log (a+b x)}{2 b^2 e^2}-\frac{a^2 p x}{3 b^2 e}+\frac{a^3 p \log (a+b x)}{3 b^3 e}+\frac{d^2 (a+b x) \log \left(c (a+b x)^p\right)}{b e^3}-\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 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{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,"-((d^2*p*x)/e^3) - (a*d*p*x)/(2*b*e^2) - (a^2*p*x)/(3*b^2*e) + (d*p*x^2)/(4*e^2) + (a*p*x^2)/(6*b*e) - (p*x^3)/(9*e) + (a^2*d*p*Log[a + b*x])/(2*b^2*e^2) + (a^3*p*Log[a + b*x])/(3*b^3*e) - (d*x^2*Log[c*(a + b*x)^p])/(2*e^2) + (x^3*Log[c*(a + b*x)^p])/(3*e) + (d^2*(a + b*x)*Log[c*(a + b*x)^p])/(b*e^3) - (d^3*Log[c*(a + b*x)^p]*Log[(b*(d + e*x))/(b*d - a*e)])/e^4 - (d^3*p*PolyLog[2, -((e*(a + b*x))/(b*d - a*e))])/e^4","A",13,8,21,0.3810,1,"{43, 2416, 2389, 2295, 2395, 2394, 2393, 2391}"
220,1,159,0,0.1670798,"\int \frac{x^2 \log \left(c (a+b x)^p\right)}{d+e x} \, dx","Int[(x^2*Log[c*(a + b*x)^p])/(d + e*x),x]","\frac{d^2 p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{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{a p x}{2 b e}+\frac{d p x}{e^2}-\frac{p x^2}{4 e}","\frac{d^2 p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{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{a p x}{2 b e}+\frac{d p x}{e^2}-\frac{p x^2}{4 e}",1,"(d*p*x)/e^2 + (a*p*x)/(2*b*e) - (p*x^2)/(4*e) - (a^2*p*Log[a + b*x])/(2*b^2*e) + (x^2*Log[c*(a + b*x)^p])/(2*e) - (d*(a + b*x)*Log[c*(a + b*x)^p])/(b*e^2) + (d^2*Log[c*(a + b*x)^p]*Log[(b*(d + e*x))/(b*d - a*e)])/e^3 + (d^2*p*PolyLog[2, -((e*(a + b*x))/(b*d - a*e))])/e^3","A",10,8,21,0.3810,1,"{43, 2416, 2389, 2295, 2395, 2394, 2393, 2391}"
221,1,91,0,0.107653,"\int \frac{x \log \left(c (a+b x)^p\right)}{d+e x} \, dx","Int[(x*Log[c*(a + b*x)^p])/(d + e*x),x]","-\frac{d p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{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{p x}{e}","-\frac{d p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{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{p x}{e}",1,"-((p*x)/e) + ((a + b*x)*Log[c*(a + b*x)^p])/(b*e) - (d*Log[c*(a + b*x)^p]*Log[(b*(d + e*x))/(b*d - a*e)])/e^2 - (d*p*PolyLog[2, -((e*(a + b*x))/(b*d - a*e))])/e^2","A",7,7,19,0.3684,1,"{43, 2416, 2389, 2295, 2394, 2393, 2391}"
222,1,58,0,0.0429506,"\int \frac{\log \left(c (a+b x)^p\right)}{d+e x} \, dx","Int[Log[c*(a + b*x)^p]/(d + e*x),x]","\frac{p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\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{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{e}+\frac{\log \left(c (a+b x)^p\right) \log \left(\frac{b (d+e 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",3,3,18,0.1667,1,"{2394, 2393, 2391}"
223,1,97,0,0.1226985,"\int \frac{\log \left(c (a+b x)^p\right)}{x (d+e x)} \, dx","Int[Log[c*(a + b*x)^p]/(x*(d + e*x)),x]","-\frac{p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{b x}{a}+1\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{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{b x}{a}+1\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}",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, -((e*(a + b*x))/(b*d - a*e))])/d + (p*PolyLog[2, 1 + (b*x)/a])/d","A",7,8,21,0.3810,1,"{36, 29, 31, 2416, 2394, 2315, 2393, 2391}"
224,1,146,0,0.166364,"\int \frac{\log \left(c (a+b x)^p\right)}{x^2 (d+e x)} \, dx","Int[Log[c*(a + b*x)^p]/(x^2*(d + e*x)),x]","\frac{e p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{d^2}-\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{b p \log (x)}{a d}-\frac{b p \log (a+b x)}{a d}","\frac{e p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{d^2}-\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{b p \log (x)}{a d}-\frac{b p \log (a+b x)}{a d}",1,"(b*p*Log[x])/(a*d) - (b*p*Log[a + b*x])/(a*d) - Log[c*(a + b*x)^p]/(d*x) - (e*Log[-((b*x)/a)]*Log[c*(a + b*x)^p])/d^2 + (e*Log[c*(a + b*x)^p]*Log[(b*(d + e*x))/(b*d - a*e)])/d^2 + (e*p*PolyLog[2, -((e*(a + b*x))/(b*d - a*e))])/d^2 - (e*p*PolyLog[2, 1 + (b*x)/a])/d^2","A",11,10,21,0.4762,1,"{44, 2416, 2395, 36, 29, 31, 2394, 2315, 2393, 2391}"
225,1,227,0,0.2226144,"\int \frac{\log \left(c (a+b x)^p\right)}{x^3 (d+e x)} \, dx","Int[Log[c*(a + b*x)^p]/(x^3*(d + e*x)),x]","-\frac{e^2 p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{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{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}","-\frac{e^2 p \text{PolyLog}\left(2,-\frac{e (a+b x)}{b d-a e}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{b x}{a}+1\right)}{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{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,"-(b*p)/(2*a*d*x) - (b^2*p*Log[x])/(2*a^2*d) - (b*e*p*Log[x])/(a*d^2) + (b^2*p*Log[a + b*x])/(2*a^2*d) + (b*e*p*Log[a + b*x])/(a*d^2) - Log[c*(a + b*x)^p]/(2*d*x^2) + (e*Log[c*(a + b*x)^p])/(d^2*x) + (e^2*Log[-((b*x)/a)]*Log[c*(a + b*x)^p])/d^3 - (e^2*Log[c*(a + b*x)^p]*Log[(b*(d + e*x))/(b*d - a*e)])/d^3 - (e^2*p*PolyLog[2, -((e*(a + b*x))/(b*d - a*e))])/d^3 + (e^2*p*PolyLog[2, 1 + (b*x)/a])/d^3","A",14,10,21,0.4762,1,"{44, 2416, 2395, 36, 29, 31, 2394, 2315, 2393, 2391}"
226,1,394,0,0.426393,"\int \frac{x^3 \log \left(c \left(a+b x^2\right)^p\right)}{d+e x} \, dx","Int[(x^3*Log[c*(a + b*x^2)^p])/(d + e*x),x]","\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^4}+\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{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 \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}","\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^4}+\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{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 \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,"(-2*d^2*p*x)/e^3 + (2*a*p*x)/(3*b*e) + (d*p*x^2)/(2*e^2) - (2*p*x^3)/(9*e) + (2*Sqrt[a]*d^2*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[b]*e^3) - (2*a^(3/2)*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(3*b^(3/2)*e) + (d^3*p*Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)]*Log[d + e*x])/e^4 + (d^3*p*Log[-((e*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*d - Sqrt[-a]*e))]*Log[d + e*x])/e^4 + (d^2*x*Log[c*(a + b*x^2)^p])/e^3 + (x^3*Log[c*(a + b*x^2)^p])/(3*e) - (d*(a + b*x^2)*Log[c*(a + b*x^2)^p])/(2*b*e^2) - (d^3*Log[d + e*x]*Log[c*(a + b*x^2)^p])/e^4 + (d^3*p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)])/e^4 + (d^3*p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)])/e^4","A",21,15,23,0.6522,1,"{2466, 2448, 321, 205, 2454, 2389, 2295, 2455, 302, 2462, 260, 2416, 2394, 2393, 2391}"
227,1,313,0,0.3342363,"\int \frac{x^2 \log \left(c \left(a+b x^2\right)^p\right)}{d+e x} \, dx","Int[(x^2*Log[c*(a + b*x^2)^p])/(d + e*x),x]","-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^3}-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{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 \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}","-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^3}-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{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 \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,"(2*d*p*x)/e^2 - (p*x^2)/(2*e) - (2*Sqrt[a]*d*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[b]*e^2) - (d^2*p*Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)]*Log[d + e*x])/e^3 - (d^2*p*Log[-((e*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*d - Sqrt[-a]*e))]*Log[d + e*x])/e^3 - (d*x*Log[c*(a + b*x^2)^p])/e^2 + ((a + b*x^2)*Log[c*(a + b*x^2)^p])/(2*b*e) + (d^2*Log[d + e*x]*Log[c*(a + b*x^2)^p])/e^3 - (d^2*p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)])/e^3 - (d^2*p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)])/e^3","A",17,13,23,0.5652,1,"{2466, 2448, 321, 205, 2454, 2389, 2295, 2462, 260, 2416, 2394, 2393, 2391}"
228,1,256,0,0.2733361,"\int \frac{x \log \left(c \left(a+b x^2\right)^p\right)}{d+e x} \, dx","Int[(x*Log[c*(a + b*x^2)^p])/(d + e*x),x]","\frac{d p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^2}+\frac{d p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\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 \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}","\frac{d p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e^2}+\frac{d p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\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 \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*p*x)/e + (2*Sqrt[a]*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[b]*e) + (d*p*Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)]*Log[d + e*x])/e^2 + (d*p*Log[-((e*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*d - Sqrt[-a]*e))]*Log[d + e*x])/e^2 + (x*Log[c*(a + b*x^2)^p])/e - (d*Log[d + e*x]*Log[c*(a + b*x^2)^p])/e^2 + (d*p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)])/e^2 + (d*p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)])/e^2","A",14,10,21,0.4762,1,"{2466, 2448, 321, 205, 2462, 260, 2416, 2394, 2393, 2391}"
229,1,201,0,0.1849898,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{d+e x} \, dx","Int[Log[c*(a + b*x^2)^p]/(d + e*x),x]","-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+b x^2\right)^p\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{p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+b x^2\right)^p\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",9,6,20,0.3000,1,"{2462, 260, 2416, 2394, 2393, 2391}"
230,1,247,0,0.3025245,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x (d+e x)} \, dx","Int[Log[c*(a + b*x^2)^p]/(x*(d + e*x)),x]","\frac{p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{2 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 \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{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{2 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 \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}",1,"(p*Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)]*Log[d + e*x])/d + (p*Log[-((e*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*d - Sqrt[-a]*e))]*Log[d + e*x])/d + (Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p])/(2*d) - (Log[d + e*x]*Log[c*(a + b*x^2)^p])/d + (p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)])/d + (p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)])/d + (p*PolyLog[2, 1 + (b*x^2)/a])/(2*d)","A",14,9,23,0.3913,1,"{2466, 2454, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
231,1,306,0,0.3501568,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^2 (d+e x)} \, dx","Int[Log[c*(a + b*x^2)^p]/(x^2*(d + e*x)),x]","-\frac{e p \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{2 d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{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 \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}","-\frac{e p \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{2 d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{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 \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,"(2*Sqrt[b]*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*d) - (e*p*Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)]*Log[d + e*x])/d^2 - (e*p*Log[-((e*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*d - Sqrt[-a]*e))]*Log[d + e*x])/d^2 - Log[c*(a + b*x^2)^p]/(d*x) - (e*Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p])/(2*d^2) + (e*Log[d + e*x]*Log[c*(a + b*x^2)^p])/d^2 - (e*p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)])/d^2 - (e*p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)])/d^2 - (e*p*PolyLog[2, 1 + (b*x^2)/a])/(2*d^2)","A",16,11,23,0.4783,1,"{2466, 2455, 205, 2454, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
232,1,371,0,0.3948176,"\int \frac{\log \left(c \left(a+b x^2\right)^p\right)}{x^3 (d+e x)} \, dx","Int[Log[c*(a + b*x^2)^p]/(x^3*(d + e*x)),x]","\frac{e^2 p \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{2 d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{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 \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}","\frac{e^2 p \text{PolyLog}\left(2,\frac{b x^2}{a}+1\right)}{2 d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{b} d-\sqrt{-a} e}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt{b} (d+e x)}{\sqrt{-a} e+\sqrt{b} d}\right)}{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 \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,"(-2*Sqrt[b]*e*p*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*d^2) + (b*p*Log[x])/(a*d) + (e^2*p*Log[(e*(Sqrt[-a] - Sqrt[b]*x))/(Sqrt[b]*d + Sqrt[-a]*e)]*Log[d + e*x])/d^3 + (e^2*p*Log[-((e*(Sqrt[-a] + Sqrt[b]*x))/(Sqrt[b]*d - Sqrt[-a]*e))]*Log[d + e*x])/d^3 - (b*p*Log[a + b*x^2])/(2*a*d) - Log[c*(a + b*x^2)^p]/(2*d*x^2) + (e*Log[c*(a + b*x^2)^p])/(d^2*x) + (e^2*Log[-((b*x^2)/a)]*Log[c*(a + b*x^2)^p])/(2*d^3) - (e^2*Log[d + e*x]*Log[c*(a + b*x^2)^p])/d^3 + (e^2*p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d - Sqrt[-a]*e)])/d^3 + (e^2*p*PolyLog[2, (Sqrt[b]*(d + e*x))/(Sqrt[b]*d + Sqrt[-a]*e)])/d^3 + (e^2*p*PolyLog[2, 1 + (b*x^2)/a])/(2*d^3)","A",21,15,23,0.6522,1,"{2466, 2454, 2395, 36, 29, 31, 2455, 205, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
233,1,692,0,0.891271,"\int \frac{x^3 \log \left(c \left(a+b x^3\right)^p\right)}{d+e x} \, dx","Int[(x^3*Log[c*(a + b*x^3)^p])/(d + e*x),x]","\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^4}+\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e^4}+\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{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 \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}","\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^4}+\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e^4}+\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{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 \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,"(-3*d^2*p*x)/e^3 + (3*d*p*x^2)/(4*e^2) - (p*x^3)/(3*e) - (Sqrt[3]*a^(1/3)*d^2*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(b^(1/3)*e^3) + (Sqrt[3]*a^(2/3)*d*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(2*b^(2/3)*e^2) + (a^(1/3)*d^2*p*Log[a^(1/3) + b^(1/3)*x])/(b^(1/3)*e^3) + (a^(2/3)*d*p*Log[a^(1/3) + b^(1/3)*x])/(2*b^(2/3)*e^2) + (d^3*p*Log[-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e))]*Log[d + e*x])/e^4 + (d^3*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])/e^4 + (d^3*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^4 - (a^(1/3)*d^2*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(2*b^(1/3)*e^3) - (a^(2/3)*d*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(4*b^(2/3)*e^2) + (d^2*x*Log[c*(a + b*x^3)^p])/e^3 - (d*x^2*Log[c*(a + b*x^3)^p])/(2*e^2) + ((a + b*x^3)*Log[c*(a + b*x^3)^p])/(3*b*e) - (d^3*Log[d + e*x]*Log[c*(a + b*x^3)^p])/e^4 + (d^3*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)])/e^4 + (d^3*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)])/e^4 + (d^3*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)])/e^4","A",33,20,23,0.8696,1,"{2466, 2448, 321, 200, 31, 634, 617, 204, 628, 2455, 292, 2454, 2389, 2295, 2462, 260, 2416, 2394, 2393, 2391}"
234,1,643,0,0.7744399,"\int \frac{x^2 \log \left(c \left(a+b x^3\right)^p\right)}{d+e x} \, dx","Int[(x^2*Log[c*(a + b*x^3)^p])/(d + e*x),x]","-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^3}-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e^3}-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{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 \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}","-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^3}-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e^3}-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{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 \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,"(3*d*p*x)/e^2 - (3*p*x^2)/(4*e) + (Sqrt[3]*a^(1/3)*d*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(b^(1/3)*e^2) - (Sqrt[3]*a^(2/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(2*b^(2/3)*e) - (a^(1/3)*d*p*Log[a^(1/3) + b^(1/3)*x])/(b^(1/3)*e^2) - (a^(2/3)*p*Log[a^(1/3) + b^(1/3)*x])/(2*b^(2/3)*e) - (d^2*p*Log[-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e))]*Log[d + e*x])/e^3 - (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])/e^3 - (d^2*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^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)*e^2) + (a^(2/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(4*b^(2/3)*e) - (d*x*Log[c*(a + b*x^3)^p])/e^2 + (x^2*Log[c*(a + b*x^3)^p])/(2*e) + (d^2*Log[d + e*x]*Log[c*(a + b*x^3)^p])/e^3 - (d^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)])/e^3 - (d^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)])/e^3 - (d^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)])/e^3","A",30,17,23,0.7391,1,"{2466, 2448, 321, 200, 31, 634, 617, 204, 628, 2455, 292, 2462, 260, 2416, 2394, 2393, 2391}"
235,1,457,0,0.6315223,"\int \frac{x \log \left(c \left(a+b x^3\right)^p\right)}{d+e x} \, dx","Int[(x*Log[c*(a + b*x^3)^p])/(d + e*x),x]","\frac{d p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^2}+\frac{d p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e^2}+\frac{d p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{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 \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}","\frac{d p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e^2}+\frac{d p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e^2}+\frac{d p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{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 \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,"(-3*p*x)/e - (Sqrt[3]*a^(1/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(b^(1/3)*e) + (a^(1/3)*p*Log[a^(1/3) + b^(1/3)*x])/(b^(1/3)*e) + (d*p*Log[-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e))]*Log[d + e*x])/e^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])/e^2 + (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])/e^2 - (a^(1/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(2*b^(1/3)*e) + (x*Log[c*(a + b*x^3)^p])/e - (d*Log[d + e*x]*Log[c*(a + b*x^3)^p])/e^2 + (d*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)])/e^2 + (d*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)])/e^2 + (d*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)])/e^2","A",22,15,21,0.7143,1,"{2466, 2448, 321, 200, 31, 634, 617, 204, 628, 2462, 260, 2416, 2394, 2393, 2391}"
236,1,308,0,0.3873831,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{d+e x} \, dx","Int[Log[c*(a + b*x^3)^p]/(d + e*x),x]","-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+b x^3\right)^p\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}","-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+b x^3\right)^p\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[-((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])/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",12,6,20,0.3000,1,"{2462, 260, 2416, 2394, 2393, 2391}"
237,1,352,0,0.5649333,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x (d+e x)} \, dx","Int[Log[c*(a + b*x^3)^p]/(x*(d + e*x)),x]","\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{b x^3}{a}+1\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 \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{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{b x^3}{a}+1\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 \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}",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[-((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])/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, 1 + (b*x^3)/a])/(3*d)","A",17,9,23,0.3913,1,"{2466, 2454, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
238,1,510,0,0.6774973,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^2 (d+e x)} \, dx","Int[Log[c*(a + b*x^3)^p]/(x^2*(d + e*x)),x]","-\frac{e p \text{PolyLog}\left(2,\frac{b x^3}{a}+1\right)}{3 d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d^2}+\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 \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}","-\frac{e p \text{PolyLog}\left(2,\frac{b x^3}{a}+1\right)}{3 d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{d^2}+\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 \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,"-((Sqrt[3]*b^(1/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(a^(1/3)*d)) - (b^(1/3)*p*Log[a^(1/3) + b^(1/3)*x])/(a^(1/3)*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[-((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])/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 + (b^(1/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(2*a^(1/3)*d) - 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, 1 + (b*x^3)/a])/(3*d^2)","A",24,16,23,0.6957,1,"{2466, 2455, 292, 31, 634, 617, 204, 628, 2454, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
239,1,674,0,0.7932705,"\int \frac{\log \left(c \left(a+b x^3\right)^p\right)}{x^3 (d+e x)} \, dx","Int[Log[c*(a + b*x^3)^p]/(x^3*(d + e*x)),x]","\frac{e^2 p \text{PolyLog}\left(2,\frac{b x^3}{a}+1\right)}{3 d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{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 \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}","\frac{e^2 p \text{PolyLog}\left(2,\frac{b x^3}{a}+1\right)}{3 d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-\sqrt[3]{a} e}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{-1} \sqrt[3]{a} e+\sqrt[3]{b} d}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{b} (d+e x)}{\sqrt[3]{b} d-(-1)^{2/3} \sqrt[3]{a} e}\right)}{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 \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,"-(Sqrt[3]*b^(2/3)*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(2*a^(2/3)*d) + (Sqrt[3]*b^(1/3)*e*p*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(a^(1/3)*d^2) + (b^(2/3)*p*Log[a^(1/3) + b^(1/3)*x])/(2*a^(2/3)*d) + (b^(1/3)*e*p*Log[a^(1/3) + b^(1/3)*x])/(a^(1/3)*d^2) + (e^2*p*Log[-((e*(a^(1/3) + b^(1/3)*x))/(b^(1/3)*d - a^(1/3)*e))]*Log[d + e*x])/d^3 + (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])/d^3 + (e^2*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^3 - (b^(2/3)*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(4*a^(2/3)*d) - (b^(1/3)*e*p*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(2*a^(1/3)*d^2) - Log[c*(a + b*x^3)^p]/(2*d*x^2) + (e*Log[c*(a + b*x^3)^p])/(d^2*x) + (e^2*Log[-((b*x^3)/a)]*Log[c*(a + b*x^3)^p])/(3*d^3) - (e^2*Log[d + e*x]*Log[c*(a + b*x^3)^p])/d^3 + (e^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - a^(1/3)*e)])/d^3 + (e^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d + (-1)^(1/3)*a^(1/3)*e)])/d^3 + (e^2*p*PolyLog[2, (b^(1/3)*(d + e*x))/(b^(1/3)*d - (-1)^(2/3)*a^(1/3)*e)])/d^3 + (e^2*p*PolyLog[2, 1 + (b*x^3)/a])/(3*d^3)","A",31,17,23,0.7391,1,"{2466, 2455, 200, 31, 634, 617, 204, 628, 292, 2454, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
240,1,297,0,0.3214642,"\int \frac{x^3 \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d+e x} \, dx","Int[(x^3*Log[c*(a + b/x)^p])/(d + e*x),x]","\frac{d^3 p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{e^4}-\frac{d^3 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e^4}+\frac{b^2 d p \log (a x+b)}{2 a^2 e^2}-\frac{b^2 p x}{3 a^2 e}+\frac{b^3 p \log (a x+b)}{3 a^3 e}+\frac{d^2 x \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e^3}-\frac{d^3 \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e^4}-\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{b d^2 p \log (a x+b)}{a e^3}+\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 p x}{2 a e^2}+\frac{b p x^2}{6 a e}-\frac{d^3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^4}","\frac{d^3 p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{e^4}-\frac{d^3 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e^4}+\frac{b^2 d p \log (a x+b)}{2 a^2 e^2}-\frac{b^2 p x}{3 a^2 e}+\frac{b^3 p \log (a x+b)}{3 a^3 e}+\frac{d^2 x \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e^3}-\frac{d^3 \log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e^4}-\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{b d^2 p \log (a x+b)}{a e^3}+\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 p x}{2 a e^2}+\frac{b p x^2}{6 a e}-\frac{d^3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^4}",1,"-(b*d*p*x)/(2*a*e^2) - (b^2*p*x)/(3*a^2*e) + (b*p*x^2)/(6*a*e) + (d^2*x*Log[c*(a + b/x)^p])/e^3 - (d*x^2*Log[c*(a + b/x)^p])/(2*e^2) + (x^3*Log[c*(a + b/x)^p])/(3*e) + (b*d^2*p*Log[b + a*x])/(a*e^3) + (b^2*d*p*Log[b + a*x])/(2*a^2*e^2) + (b^3*p*Log[b + a*x])/(3*a^3*e) - (d^3*Log[c*(a + b/x)^p]*Log[d + e*x])/e^4 - (d^3*p*Log[-((e*x)/d)]*Log[d + e*x])/e^4 + (d^3*p*Log[-((e*(b + a*x))/(a*d - b*e))]*Log[d + e*x])/e^4 + (d^3*p*PolyLog[2, (a*(d + e*x))/(a*d - b*e)])/e^4 - (d^3*p*PolyLog[2, 1 + (e*x)/d])/e^4","A",21,14,23,0.6087,1,"{2466, 2448, 263, 31, 2455, 193, 43, 2462, 260, 2416, 2394, 2315, 2393, 2391}"
241,1,219,0,0.2655515,"\int \frac{x^2 \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d+e x} \, dx","Int[(x^2*Log[c*(a + b/x)^p])/(d + e*x),x]","-\frac{d^2 p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{e^3}+\frac{d^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^3}","-\frac{d^2 p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{e^3}+\frac{d^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^3}",1,"(b*p*x)/(2*a*e) - (d*x*Log[c*(a + b/x)^p])/e^2 + (x^2*Log[c*(a + b/x)^p])/(2*e) - (b*d*p*Log[b + a*x])/(a*e^2) - (b^2*p*Log[b + a*x])/(2*a^2*e) + (d^2*Log[c*(a + b/x)^p]*Log[d + e*x])/e^3 + (d^2*p*Log[-((e*x)/d)]*Log[d + e*x])/e^3 - (d^2*p*Log[-((e*(b + a*x))/(a*d - b*e))]*Log[d + e*x])/e^3 - (d^2*p*PolyLog[2, (a*(d + e*x))/(a*d - b*e)])/e^3 + (d^2*p*PolyLog[2, 1 + (e*x)/d])/e^3","A",17,14,23,0.6087,1,"{2466, 2448, 263, 31, 2455, 193, 43, 2462, 260, 2416, 2394, 2315, 2393, 2391}"
242,1,151,0,0.2122872,"\int \frac{x \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d+e x} \, dx","Int[(x*Log[c*(a + b/x)^p])/(d + e*x),x]","\frac{d p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{e^2}-\frac{d p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e^2}-\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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^2}","\frac{d p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{e^2}-\frac{d p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e^2}-\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 \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 \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[b + a*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])/e^2 + (d*p*Log[-((e*(b + a*x))/(a*d - b*e))]*Log[d + e*x])/e^2 + (d*p*PolyLog[2, (a*(d + e*x))/(a*d - b*e)])/e^2 - (d*p*PolyLog[2, 1 + (e*x)/d])/e^2","A",13,11,21,0.5238,1,"{2466, 2448, 263, 31, 2462, 260, 2416, 2394, 2315, 2393, 2391}"
243,1,113,0,0.1468832,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{d+e x} \, dx","Int[Log[c*(a + b/x)^p]/(d + e*x),x]","-\frac{p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{e}+\frac{p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{e}+\frac{p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}","-\frac{p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{e}+\frac{p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x}\right)^p\right)}{e}-\frac{p \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\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, (a*(d + e*x))/(a*d - b*e)])/e + (p*PolyLog[2, 1 + (e*x)/d])/e","A",8,7,20,0.3500,1,"{2462, 260, 2416, 2394, 2315, 2393, 2391}"
244,1,159,0,0.2460788,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x (d+e x)} \, dx","Int[Log[c*(a + b/x)^p]/(x*(d + e*x)),x]","\frac{p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{d}-\frac{p \text{PolyLog}\left(2,\frac{b}{a x}+1\right)}{d}-\frac{p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{d}-\frac{p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d}","\frac{p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{d}-\frac{p \text{PolyLog}\left(2,\frac{b}{a x}+1\right)}{d}-\frac{p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\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))])/d) - (Log[c*(a + b/x)^p]*Log[d + e*x])/d - (p*Log[-((e*x)/d)]*Log[d + e*x])/d + (p*Log[-((e*(b + a*x))/(a*d - b*e))]*Log[d + e*x])/d - (p*PolyLog[2, 1 + b/(a*x)])/d + (p*PolyLog[2, (a*(d + e*x))/(a*d - b*e)])/d - (p*PolyLog[2, 1 + (e*x)/d])/d","A",13,9,23,0.3913,1,"{2466, 2454, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
245,1,198,0,0.2770571,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^2 (d+e x)} \, dx","Int[Log[c*(a + b/x)^p]/(x^2*(d + e*x)),x]","\frac{e p \text{PolyLog}\left(2,\frac{b}{a x}+1\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{d^2}+\frac{e p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{d^2}+\frac{e p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^2}+\frac{p}{d x}","\frac{e p \text{PolyLog}\left(2,\frac{b}{a x}+1\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{d^2}+\frac{e p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \log (d+e x) \log \left(-\frac{e (a x+b)}{a d-b e}\right)}{d^2}+\frac{e p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^2}+\frac{p}{d x}",1,"p/(d*x) - ((a + b/x)*Log[c*(a + b/x)^p])/(b*d) + (e*Log[c*(a + b/x)^p]*Log[-(b/(a*x))])/d^2 + (e*Log[c*(a + b/x)^p]*Log[d + e*x])/d^2 + (e*p*Log[-((e*x)/d)]*Log[d + e*x])/d^2 - (e*p*Log[-((e*(b + a*x))/(a*d - b*e))]*Log[d + e*x])/d^2 + (e*p*PolyLog[2, 1 + b/(a*x)])/d^2 - (e*p*PolyLog[2, (a*(d + e*x))/(a*d - b*e)])/d^2 + (e*p*PolyLog[2, 1 + (e*x)/d])/d^2","A",16,11,23,0.4783,1,"{2466, 2454, 2389, 2295, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
246,1,287,0,0.3294903,"\int \frac{\log \left(c \left(a+\frac{b}{x}\right)^p\right)}{x^3 (d+e x)} \, dx","Int[Log[c*(a + b/x)^p]/(x^3*(d + e*x)),x]","-\frac{e^2 p \text{PolyLog}\left(2,\frac{b}{a x}+1\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{d^3}-\frac{e^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \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}","-\frac{e^2 p \text{PolyLog}\left(2,\frac{b}{a x}+1\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{a (d+e x)}{a d-b e}\right)}{d^3}-\frac{e^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \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,"p/(4*d*x^2) - (a*p)/(2*b*d*x) - (e*p)/(d^2*x) + (a^2*p*Log[a + b/x])/(2*b^2*d) + (e*(a + b/x)*Log[c*(a + b/x)^p])/(b*d^2) - Log[c*(a + b/x)^p]/(2*d*x^2) - (e^2*Log[c*(a + b/x)^p]*Log[-(b/(a*x))])/d^3 - (e^2*Log[c*(a + b/x)^p]*Log[d + e*x])/d^3 - (e^2*p*Log[-((e*x)/d)]*Log[d + e*x])/d^3 + (e^2*p*Log[-((e*(b + a*x))/(a*d - b*e))]*Log[d + e*x])/d^3 - (e^2*p*PolyLog[2, 1 + b/(a*x)])/d^3 + (e^2*p*PolyLog[2, (a*(d + e*x))/(a*d - b*e)])/d^3 - (e^2*p*PolyLog[2, 1 + (e*x)/d])/d^3","A",20,13,23,0.5652,1,"{2466, 2454, 2395, 43, 2389, 2295, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
247,1,421,0,0.5859274,"\int \frac{x^3 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d+e x} \, dx","Int[(x^3*Log[c*(a + b/x^2)^p])/(d + e*x),x]","\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^4}+\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^4}-\frac{2 d^3 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^4}","\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^4}+\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^4}-\frac{2 d^3 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^4}",1,"(2*b*p*x)/(3*a*e) + (2*Sqrt[b]*d^2*p*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(Sqrt[a]*e^3) - (2*b^(3/2)*p*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(3*a^(3/2)*e) + (d^2*x*Log[c*(a + b/x^2)^p])/e^3 - (d*x^2*Log[c*(a + b/x^2)^p])/(2*e^2) + (x^3*Log[c*(a + b/x^2)^p])/(3*e) - (d^3*Log[c*(a + b/x^2)^p]*Log[d + e*x])/e^4 - (2*d^3*p*Log[-((e*x)/d)]*Log[d + e*x])/e^4 + (d^3*p*Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x])/e^4 + (d^3*p*Log[-((e*(Sqrt[b] + Sqrt[-a]*x))/(Sqrt[-a]*d - Sqrt[b]*e))]*Log[d + e*x])/e^4 - (b*d*p*Log[b + a*x^2])/(2*a*e^2) + (d^3*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)])/e^4 + (d^3*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)])/e^4 - (2*d^3*p*PolyLog[2, 1 + (e*x)/d])/e^4","A",25,14,23,0.6087,1,"{2466, 2448, 263, 205, 2455, 260, 193, 321, 2462, 2416, 2394, 2315, 2393, 2391}"
248,1,353,0,0.4920041,"\int \frac{x^2 \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d+e x} \, dx","Int[(x^2*Log[c*(a + b/x^2)^p])/(d + e*x),x]","-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^3}-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^3}+\frac{2 d^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^3}","-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^3}-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^3}+\frac{2 d^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^3}",1,"(-2*Sqrt[b]*d*p*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(Sqrt[a]*e^2) - (d*x*Log[c*(a + b/x^2)^p])/e^2 + (x^2*Log[c*(a + b/x^2)^p])/(2*e) + (d^2*Log[c*(a + b/x^2)^p]*Log[d + e*x])/e^3 + (2*d^2*p*Log[-((e*x)/d)]*Log[d + e*x])/e^3 - (d^2*p*Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x])/e^3 - (d^2*p*Log[-((e*(Sqrt[b] + Sqrt[-a]*x))/(Sqrt[-a]*d - Sqrt[b]*e))]*Log[d + e*x])/e^3 + (b*p*Log[b + a*x^2])/(2*a*e) - (d^2*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)])/e^3 - (d^2*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)])/e^3 + (2*d^2*p*PolyLog[2, 1 + (e*x)/d])/e^3","A",21,12,23,0.5217,1,"{2466, 2448, 263, 205, 2455, 260, 2462, 2416, 2394, 2315, 2393, 2391}"
249,1,291,0,0.4380898,"\int \frac{x \log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d+e x} \, dx","Int[(x*Log[c*(a + b/x^2)^p])/(d + e*x),x]","\frac{d p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^2}+\frac{d p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^2}-\frac{2 d p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^2}","\frac{d p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e^2}+\frac{d p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e^2}-\frac{2 d p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^2}",1,"(2*Sqrt[b]*p*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(Sqrt[a]*e) + (x*Log[c*(a + b/x^2)^p])/e - (d*Log[c*(a + b/x^2)^p]*Log[d + e*x])/e^2 - (2*d*p*Log[-((e*x)/d)]*Log[d + e*x])/e^2 + (d*p*Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x])/e^2 + (d*p*Log[-((e*(Sqrt[b] + Sqrt[-a]*x))/(Sqrt[-a]*d - Sqrt[b]*e))]*Log[d + e*x])/e^2 + (d*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)])/e^2 + (d*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)])/e^2 - (2*d*p*PolyLog[2, 1 + (e*x)/d])/e^2","A",18,11,21,0.5238,1,"{2466, 2448, 263, 205, 2462, 260, 2416, 2394, 2315, 2393, 2391}"
250,1,241,0,0.3342938,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{d+e x} \, dx","Int[Log[c*(a + b/x^2)^p]/(d + e*x),x]","-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e}+\frac{2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}","-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{e}+\frac{2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x^2}\right)^p\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 \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 - (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 + (2*p*PolyLog[2, 1 + (e*x)/d])/e","A",13,7,20,0.3500,1,"{2462, 260, 2416, 2394, 2315, 2393, 2391}"
251,1,287,0,0.4609662,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x (d+e x)} \, dx","Int[Log[c*(a + b/x^2)^p]/(x*(d + e*x)),x]","\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d}-\frac{p \text{PolyLog}\left(2,\frac{b}{a x^2}+1\right)}{2 d}-\frac{2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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{2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d}","\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d}-\frac{p \text{PolyLog}\left(2,\frac{b}{a x^2}+1\right)}{2 d}-\frac{2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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{2 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d}",1,"-(Log[c*(a + b/x^2)^p]*Log[-(b/(a*x^2))])/(2*d) - (Log[c*(a + b/x^2)^p]*Log[d + e*x])/d - (2*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, 1 + b/(a*x^2)])/(2*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)])/d - (2*p*PolyLog[2, 1 + (e*x)/d])/d","A",18,9,23,0.3913,1,"{2466, 2454, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
252,1,357,0,0.5068592,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x^2 (d+e x)} \, dx","Int[Log[c*(a + b/x^2)^p]/(x^2*(d + e*x)),x]","\frac{e p \text{PolyLog}\left(2,\frac{b}{a x^2}+1\right)}{2 d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d^2}+\frac{2 e p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^2}+\frac{2 p}{d x}","\frac{e p \text{PolyLog}\left(2,\frac{b}{a x^2}+1\right)}{2 d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d^2}+\frac{2 e p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^2}+\frac{2 p}{d x}",1,"(2*p)/(d*x) + (2*Sqrt[a]*p*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(Sqrt[b]*d) - Log[c*(a + b/x^2)^p]/(d*x) + (e*Log[c*(a + b/x^2)^p]*Log[-(b/(a*x^2))])/(2*d^2) + (e*Log[c*(a + b/x^2)^p]*Log[d + e*x])/d^2 + (2*e*p*Log[-((e*x)/d)]*Log[d + e*x])/d^2 - (e*p*Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x])/d^2 - (e*p*Log[-((e*(Sqrt[b] + Sqrt[-a]*x))/(Sqrt[-a]*d - Sqrt[b]*e))]*Log[d + e*x])/d^2 + (e*p*PolyLog[2, 1 + b/(a*x^2)])/(2*d^2) - (e*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)])/d^2 - (e*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)])/d^2 + (2*e*p*PolyLog[2, 1 + (e*x)/d])/d^2","A",22,13,23,0.5652,1,"{2466, 2455, 263, 325, 205, 2454, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
253,1,414,0,0.5469808,"\int \frac{\log \left(c \left(a+\frac{b}{x^2}\right)^p\right)}{x^3 (d+e x)} \, dx","Int[Log[c*(a + b/x^2)^p]/(x^3*(d + e*x)),x]","-\frac{e^2 p \text{PolyLog}\left(2,\frac{b}{a x^2}+1\right)}{2 d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d^3}-\frac{2 e^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \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}","-\frac{e^2 p \text{PolyLog}\left(2,\frac{b}{a x^2}+1\right)}{2 d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d-\sqrt{b} e}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt{-a} (d+e x)}{\sqrt{-a} d+\sqrt{b} e}\right)}{d^3}-\frac{2 e^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \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,"p/(2*d*x^2) - (2*e*p)/(d^2*x) - (2*Sqrt[a]*e*p*ArcTan[(Sqrt[a]*x)/Sqrt[b]])/(Sqrt[b]*d^2) - ((a + b/x^2)*Log[c*(a + b/x^2)^p])/(2*b*d) + (e*Log[c*(a + b/x^2)^p])/(d^2*x) - (e^2*Log[c*(a + b/x^2)^p]*Log[-(b/(a*x^2))])/(2*d^3) - (e^2*Log[c*(a + b/x^2)^p]*Log[d + e*x])/d^3 - (2*e^2*p*Log[-((e*x)/d)]*Log[d + e*x])/d^3 + (e^2*p*Log[(e*(Sqrt[b] - Sqrt[-a]*x))/(Sqrt[-a]*d + Sqrt[b]*e)]*Log[d + e*x])/d^3 + (e^2*p*Log[-((e*(Sqrt[b] + Sqrt[-a]*x))/(Sqrt[-a]*d - Sqrt[b]*e))]*Log[d + e*x])/d^3 - (e^2*p*PolyLog[2, 1 + b/(a*x^2)])/(2*d^3) + (e^2*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d - Sqrt[b]*e)])/d^3 + (e^2*p*PolyLog[2, (Sqrt[-a]*(d + e*x))/(Sqrt[-a]*d + Sqrt[b]*e)])/d^3 - (2*e^2*p*PolyLog[2, 1 + (e*x)/d])/d^3","A",25,15,23,0.6522,1,"{2466, 2454, 2389, 2295, 2455, 263, 325, 205, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
254,1,714,0,0.9212982,"\int \frac{x^3 \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d+e x} \, dx","Int[(x^3*Log[c*(a + b/x^3)^p])/(d + e*x),x]","\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^4}+\frac{d^3 p \text{PolyLog}\left(2,\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{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^4}-\frac{3 d^3 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e^4}-\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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^4}","\frac{d^3 p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^4}+\frac{d^3 p \text{PolyLog}\left(2,\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{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^4}-\frac{3 d^3 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e^4}-\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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^4}",1,"-((Sqrt[3]*b^(1/3)*d^2*p*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(a^(1/3)*e^3)) + (Sqrt[3]*b^(2/3)*d*p*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(2*a^(2/3)*e^2) + (d^2*x*Log[c*(a + b/x^3)^p])/e^3 - (d*x^2*Log[c*(a + b/x^3)^p])/(2*e^2) + (x^3*Log[c*(a + b/x^3)^p])/(3*e) + (b^(1/3)*d^2*p*Log[b^(1/3) + a^(1/3)*x])/(a^(1/3)*e^3) + (b^(2/3)*d*p*Log[b^(1/3) + a^(1/3)*x])/(2*a^(2/3)*e^2) - (d^3*Log[c*(a + b/x^3)^p]*Log[d + e*x])/e^4 - (3*d^3*p*Log[-((e*x)/d)]*Log[d + e*x])/e^4 + (d^3*p*Log[-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e))]*Log[d + e*x])/e^4 + (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])/e^4 + (d^3*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^4 - (b^(1/3)*d^2*p*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(2*a^(1/3)*e^3) - (b^(2/3)*d*p*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(4*a^(2/3)*e^2) + (b*p*Log[b + a*x^3])/(3*a*e) + (d^3*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)])/e^4 + (d^3*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)])/e^4 + (d^3*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)])/e^4 - (3*d^3*p*PolyLog[2, 1 + (e*x)/d])/e^4","A",37,18,23,0.7826,1,"{2466, 2448, 263, 200, 31, 634, 617, 204, 628, 2455, 292, 260, 2462, 2416, 2394, 2315, 2393, 2391}"
255,1,666,0,0.7305734,"\int \frac{x^2 \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d+e x} \, dx","Int[(x^2*Log[c*(a + b/x^3)^p])/(d + e*x),x]","-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^3}-\frac{d^2 p \text{PolyLog}\left(2,\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{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^3}+\frac{3 d^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e^3}+\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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^3}","-\frac{d^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^3}-\frac{d^2 p \text{PolyLog}\left(2,\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{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^3}+\frac{3 d^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e^3}+\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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^3}",1,"(Sqrt[3]*b^(1/3)*d*p*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(a^(1/3)*e^2) - (Sqrt[3]*b^(2/3)*p*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(2*a^(2/3)*e) - (d*x*Log[c*(a + b/x^3)^p])/e^2 + (x^2*Log[c*(a + b/x^3)^p])/(2*e) - (b^(1/3)*d*p*Log[b^(1/3) + a^(1/3)*x])/(a^(1/3)*e^2) - (b^(2/3)*p*Log[b^(1/3) + a^(1/3)*x])/(2*a^(2/3)*e) + (d^2*Log[c*(a + b/x^3)^p]*Log[d + e*x])/e^3 + (3*d^2*p*Log[-((e*x)/d)]*Log[d + e*x])/e^3 - (d^2*p*Log[-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e))]*Log[d + e*x])/e^3 - (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])/e^3 - (d^2*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 + (b^(1/3)*d*p*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(2*a^(1/3)*e^2) + (b^(2/3)*p*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(4*a^(2/3)*e) - (d^2*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)])/e^3 - (d^2*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)])/e^3 - (d^2*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)])/e^3 + (3*d^2*p*PolyLog[2, 1 + (e*x)/d])/e^3","A",34,18,23,0.7826,1,"{2466, 2448, 263, 200, 31, 634, 617, 204, 628, 2455, 292, 2462, 260, 2416, 2394, 2315, 2393, 2391}"
256,1,488,0,0.601154,"\int \frac{x \log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d+e x} \, dx","Int[(x*Log[c*(a + b/x^3)^p])/(d + e*x),x]","\frac{d p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^2}+\frac{d p \text{PolyLog}\left(2,\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{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^2}-\frac{3 d p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^2}","\frac{d p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e^2}+\frac{d p \text{PolyLog}\left(2,\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{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e^2}-\frac{3 d p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e^2}",1,"-((Sqrt[3]*b^(1/3)*p*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(a^(1/3)*e)) + (x*Log[c*(a + b/x^3)^p])/e + (b^(1/3)*p*Log[b^(1/3) + a^(1/3)*x])/(a^(1/3)*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[-((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^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 - (b^(1/3)*p*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(2*a^(1/3)*e) + (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 - (3*d*p*PolyLog[2, 1 + (e*x)/d])/e^2","A",26,16,21,0.7619,1,"{2466, 2448, 263, 200, 31, 634, 617, 204, 628, 2462, 260, 2416, 2394, 2315, 2393, 2391}"
257,1,344,0,0.409433,"\int \frac{\log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{d+e x} \, dx","Int[Log[c*(a + b/x^3)^p]/(d + e*x),x]","-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e}+\frac{3 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{e}","-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{e}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{e}+\frac{3 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{e}+\frac{\log (d+e x) \log \left(c \left(a+\frac{b}{x^3}\right)^p\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 \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[-((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*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 - (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 + (3*p*PolyLog[2, 1 + (e*x)/d])/e","A",16,7,20,0.3500,1,"{2462, 260, 2416, 2394, 2315, 2393, 2391}"
258,1,388,0,0.538067,"\int \frac{\log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{x (d+e x)} \, dx","Int[Log[c*(a + b/x^3)^p]/(x*(d + e*x)),x]","\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d}-\frac{p \text{PolyLog}\left(2,\frac{b}{a x^3}+1\right)}{3 d}-\frac{3 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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{3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d}","\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d+\sqrt[3]{-1} \sqrt[3]{b} e}\right)}{d}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d}-\frac{p \text{PolyLog}\left(2,\frac{b}{a x^3}+1\right)}{3 d}-\frac{3 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{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 \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{3 p \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d}",1,"-(Log[c*(a + b/x^3)^p]*Log[-(b/(a*x^3))])/(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[-((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])/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, 1 + b/(a*x^3)])/(3*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 - (3*p*PolyLog[2, 1 + (e*x)/d])/d","A",21,9,23,0.3913,1,"{2466, 2454, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
259,1,557,0,0.6683868,"\int \frac{\log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{x^2 (d+e x)} \, dx","Int[Log[c*(a + b/x^3)^p]/(x^2*(d + e*x)),x]","\frac{e p \text{PolyLog}\left(2,\frac{b}{a x^3}+1\right)}{3 d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\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{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d^2}+\frac{3 e p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d^2}+\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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^2}+\frac{3 p}{d x}","\frac{e p \text{PolyLog}\left(2,\frac{b}{a x^3}+1\right)}{3 d^2}-\frac{e p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d^2}-\frac{e p \text{PolyLog}\left(2,\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{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d^2}+\frac{3 e p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d^2}+\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 \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 \log \left(-\frac{e x}{d}\right) \log (d+e x)}{d^2}+\frac{3 p}{d x}",1,"(3*p)/(d*x) - (Sqrt[3]*a^(1/3)*p*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(b^(1/3)*d) - Log[c*(a + b/x^3)^p]/(d*x) + (e*Log[c*(a + b/x^3)^p]*Log[-(b/(a*x^3))])/(3*d^2) - (a^(1/3)*p*Log[b^(1/3) + a^(1/3)*x])/(b^(1/3)*d) + (e*Log[c*(a + b/x^3)^p]*Log[d + e*x])/d^2 + (3*e*p*Log[-((e*x)/d)]*Log[d + e*x])/d^2 - (e*p*Log[-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e))]*Log[d + e*x])/d^2 - (e*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])/d^2 - (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])/d^2 + (a^(1/3)*p*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(2*b^(1/3)*d) + (e*p*PolyLog[2, 1 + b/(a*x^3)])/(3*d^2) - (e*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)])/d^2 - (e*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)])/d^2 - (e*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)])/d^2 + (3*e*p*PolyLog[2, 1 + (e*x)/d])/d^2","A",30,18,23,0.7826,1,"{2466, 2455, 263, 325, 292, 31, 634, 617, 204, 628, 2454, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
260,1,737,0,0.7951491,"\int \frac{\log \left(c \left(a+\frac{b}{x^3}\right)^p\right)}{x^3 (d+e x)} \, dx","Int[Log[c*(a + b/x^3)^p]/(x^3*(d + e*x)),x]","-\frac{e^2 p \text{PolyLog}\left(2,\frac{b}{a x^3}+1\right)}{3 d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\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{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d^3}-\frac{3 e^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d^3}-\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 \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 \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}","-\frac{e^2 p \text{PolyLog}\left(2,\frac{b}{a x^3}+1\right)}{3 d^3}+\frac{e^2 p \text{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-\sqrt[3]{b} e}\right)}{d^3}+\frac{e^2 p \text{PolyLog}\left(2,\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{PolyLog}\left(2,\frac{\sqrt[3]{a} (d+e x)}{\sqrt[3]{a} d-(-1)^{2/3} \sqrt[3]{b} e}\right)}{d^3}-\frac{3 e^2 p \text{PolyLog}\left(2,\frac{e x}{d}+1\right)}{d^3}-\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 \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 \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,"(3*p)/(4*d*x^2) - (3*e*p)/(d^2*x) - (Sqrt[3]*a^(2/3)*p*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(2*b^(2/3)*d) + (Sqrt[3]*a^(1/3)*e*p*ArcTan[(b^(1/3) - 2*a^(1/3)*x)/(Sqrt[3]*b^(1/3))])/(b^(1/3)*d^2) - Log[c*(a + b/x^3)^p]/(2*d*x^2) + (e*Log[c*(a + b/x^3)^p])/(d^2*x) - (e^2*Log[c*(a + b/x^3)^p]*Log[-(b/(a*x^3))])/(3*d^3) + (a^(2/3)*p*Log[b^(1/3) + a^(1/3)*x])/(2*b^(2/3)*d) + (a^(1/3)*e*p*Log[b^(1/3) + a^(1/3)*x])/(b^(1/3)*d^2) - (e^2*Log[c*(a + b/x^3)^p]*Log[d + e*x])/d^3 - (3*e^2*p*Log[-((e*x)/d)]*Log[d + e*x])/d^3 + (e^2*p*Log[-((e*(b^(1/3) + a^(1/3)*x))/(a^(1/3)*d - b^(1/3)*e))]*Log[d + e*x])/d^3 + (e^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])/d^3 + (e^2*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^3 - (a^(2/3)*p*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(4*b^(2/3)*d) - (a^(1/3)*e*p*Log[b^(2/3) - a^(1/3)*b^(1/3)*x + a^(2/3)*x^2])/(2*b^(1/3)*d^2) - (e^2*p*PolyLog[2, 1 + b/(a*x^3)])/(3*d^3) + (e^2*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - b^(1/3)*e)])/d^3 + (e^2*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d + (-1)^(1/3)*b^(1/3)*e)])/d^3 + (e^2*p*PolyLog[2, (a^(1/3)*(d + e*x))/(a^(1/3)*d - (-1)^(2/3)*b^(1/3)*e)])/d^3 - (3*e^2*p*PolyLog[2, 1 + (e*x)/d])/d^3","A",39,19,23,0.8261,1,"{2466, 2455, 263, 325, 200, 31, 634, 617, 204, 628, 292, 2454, 2394, 2315, 2462, 260, 2416, 2393, 2391}"
261,1,749,0,0.9309863,"\int \frac{\log \left(c \left(d+e x^3\right)^p\right)}{f+g x^2} \, dx","Int[Log[c*(d + e*x^3)^p]/(f + g*x^2),x]","\frac{i p \text{PolyLog}\left(2,1-\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)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1+\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)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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)}{2 \sqrt{f} \sqrt{g}}-\frac{3 i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \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+e x^3\right)^p\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[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 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}}","\frac{i p \text{PolyLog}\left(2,1-\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)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1+\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)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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)}{2 \sqrt{f} \sqrt{g}}-\frac{3 i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \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+e x^3\right)^p\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[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 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,"(3*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(d^(1/3) + e^(1/3)*x))/((I*e^(1/3)*Sqrt[f] + d^(1/3)*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[((-2*I)*Sqrt[f]*Sqrt[g]*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((e^(1/3)*Sqrt[f] + (-1)^(1/6)*d^(1/3)*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*(-1)^(5/6)*Sqrt[f]*Sqrt[g]*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((e^(1/3)*Sqrt[f] + (-1)^(5/6)*d^(1/3)*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + (ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^3)^p])/(Sqrt[f]*Sqrt[g]) - (((3*I)/2)*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(d^(1/3) + e^(1/3)*x))/((I*e^(1/3)*Sqrt[f] + d^(1/3)*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 + ((2*I)*Sqrt[f]*Sqrt[g]*((-1)^(2/3)*d^(1/3) + e^(1/3)*x))/((e^(1/3)*Sqrt[f] + (-1)^(1/6)*d^(1/3)*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 - (2*(-1)^(5/6)*Sqrt[f]*Sqrt[g]*(d^(1/3) + (-1)^(2/3)*e^(1/3)*x))/((e^(1/3)*Sqrt[f] + (-1)^(5/6)*d^(1/3)*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g])","A",16,9,22,0.4091,1,"{205, 2470, 12, 260, 6725, 4856, 2402, 2315, 2447}"
262,1,533,0,0.5092214,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Int[Log[c*(d + e*x^2)^p]/(f + g*x^2),x]","\frac{i p \text{PolyLog}\left(2,1+\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} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\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{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{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}}","\frac{i p \text{PolyLog}\left(2,1+\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} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\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{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{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,"(2*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + (ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/(Sqrt[f]*Sqrt[g]) - (I*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g])","A",12,8,22,0.3636,1,"{205, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
263,1,229,0,0.2286809,"\int \frac{\log \left(c (d+e x)^p\right)}{f+g x^2} \, dx","Int[Log[c*(d + e*x)^p]/(f + g*x^2),x]","-\frac{p \text{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{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)}{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{PolyLog}\left(2,-\frac{\sqrt{g} (d+e x)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt{g} (d+e x)}{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)}{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}}",1,"(Log[c*(d + e*x)^p]*Log[(e*(Sqrt[-f] - Sqrt[g]*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*Sqrt[-f]*Sqrt[g]) - (Log[c*(d + e*x)^p]*Log[(e*(Sqrt[-f] + Sqrt[g]*x))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, -((Sqrt[g]*(d + e*x))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (Sqrt[g]*(d + e*x))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*Sqrt[-f]*Sqrt[g])","A",8,4,20,0.2000,1,"{2409, 2394, 2393, 2391}"
264,1,360,0,0.4366013,"\int \frac{\log \left(c \left(d+\frac{e}{x}\right)^p\right)}{f+g x^2} \, dx","Int[Log[c*(d + e/x)^p]/(f + g*x^2),x]","\frac{i p \text{PolyLog}\left(2,1-\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)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,-\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \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{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{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}}","\frac{i p \text{PolyLog}\left(2,1-\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)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,-\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{2 \sqrt{f} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \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{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{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,"(ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e/x)^p])/(Sqrt[f]*Sqrt[g]) + (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(e + d*x))/((I*d*Sqrt[f] + e*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, ((-I)*Sqrt[g]*x)/Sqrt[f]])/(Sqrt[f]*Sqrt[g]) - ((I/2)*p*PolyLog[2, (I*Sqrt[g]*x)/Sqrt[f]])/(Sqrt[f]*Sqrt[g]) - ((I/2)*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(e + d*x))/((I*d*Sqrt[f] + e*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g])","A",12,12,22,0.5455,1,"{205, 2470, 12, 260, 6688, 4876, 4848, 2391, 4856, 2402, 2315, 2447}"
265,1,597,0,0.8385803,"\int \frac{\log \left(c \left(d+\frac{e}{x^2}\right)^p\right)}{f+g x^2} \, dx","Int[Log[c*(d + e/x^2)^p]/(f + g*x^2),x]","\frac{i p \text{PolyLog}\left(2,1+\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)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,-\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\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{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{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}}","\frac{i p \text{PolyLog}\left(2,1+\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)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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)}{2 \sqrt{f} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,-\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,\frac{i \sqrt{g} x}{\sqrt{f}}\right)}{\sqrt{f} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\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{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{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,"(ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e/x^2)^p])/(Sqrt[f]*Sqrt[g]) + (2*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[e] - Sqrt[-d]*x))/((I*Sqrt[-d]*Sqrt[f] - Sqrt[e]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[e] + Sqrt[-d]*x))/((I*Sqrt[-d]*Sqrt[f] + Sqrt[e]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + (I*p*PolyLog[2, ((-I)*Sqrt[g]*x)/Sqrt[f]])/(Sqrt[f]*Sqrt[g]) - (I*p*PolyLog[2, (I*Sqrt[g]*x)/Sqrt[f]])/(Sqrt[f]*Sqrt[g]) - (I*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[e] - Sqrt[-d]*x))/((I*Sqrt[-d]*Sqrt[f] - Sqrt[e]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[e] + Sqrt[-d]*x))/((I*Sqrt[-d]*Sqrt[f] + Sqrt[e]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g])","A",18,12,22,0.5455,1,"{205, 2470, 12, 260, 6688, 4928, 4848, 2391, 4856, 2402, 2315, 2447}"
266,1,541,0,0.8132149,"\int \frac{\log \left(c \left(d+e \sqrt{x}\right)^p\right)}{f+g x^2} \, dx","Int[Log[c*(d + e*Sqrt[x])^p]/(f + g*x^2),x]","-\frac{p \text{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\frac{\sqrt[4]{g} \left(d+e \sqrt{x}\right)}{d \sqrt[4]{g}+e \sqrt{-\sqrt{-f}}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt[4]{g} \left(d+e \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)}{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{PolyLog}\left(2,-\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{PolyLog}\left(2,-\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{PolyLog}\left(2,\frac{\sqrt[4]{g} \left(d+e \sqrt{x}\right)}{d \sqrt[4]{g}+e \sqrt{-\sqrt{-f}}}\right)}{2 \sqrt{-f} \sqrt{g}}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt[4]{g} \left(d+e \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)}{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}}",1,"-(Log[c*(d + e*Sqrt[x])^p]*Log[(e*(Sqrt[-Sqrt[-f]] - g^(1/4)*Sqrt[x]))/(e*Sqrt[-Sqrt[-f]] + d*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (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))])/(2*Sqrt[-f]*Sqrt[g]) - (Log[c*(d + e*Sqrt[x])^p]*Log[(e*(Sqrt[-Sqrt[-f]] + g^(1/4)*Sqrt[x]))/(e*Sqrt[-Sqrt[-f]] - d*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (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))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, -((g^(1/4)*(d + e*Sqrt[x]))/(e*Sqrt[-Sqrt[-f]] - d*g^(1/4)))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, -((g^(1/4)*(d + e*Sqrt[x]))/(e*(-f)^(1/4) - d*g^(1/4)))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (g^(1/4)*(d + e*Sqrt[x]))/(e*Sqrt[-Sqrt[-f]] + d*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, (g^(1/4)*(d + e*Sqrt[x]))/(e*(-f)^(1/4) + d*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g])","A",19,8,24,0.3333,1,"{2472, 275, 205, 2416, 260, 2394, 2393, 2391}"
267,1,561,0,1.107128,"\int \frac{\log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^p\right)}{f+g x^2} \, dx","Int[Log[c*(d + e/Sqrt[x])^p]/(f + g*x^2),x]","-\frac{p \text{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{\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}}",1,"-(Log[c*(d + e/Sqrt[x])^p]*Log[(e*(g^(1/4) - Sqrt[-Sqrt[-f]]/Sqrt[x]))/(d*Sqrt[-Sqrt[-f]] + e*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (Log[c*(d + e/Sqrt[x])^p]*Log[-((e*(g^(1/4) + Sqrt[-Sqrt[-f]]/Sqrt[x]))/(d*Sqrt[-Sqrt[-f]] - e*g^(1/4)))])/(2*Sqrt[-f]*Sqrt[g]) + (Log[c*(d + e/Sqrt[x])^p]*Log[(e*(g^(1/4) - (-f)^(1/4)/Sqrt[x]))/(d*(-f)^(1/4) + e*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (Log[c*(d + e/Sqrt[x])^p]*Log[-((e*(g^(1/4) + (-f)^(1/4)/Sqrt[x]))/(d*(-f)^(1/4) - e*g^(1/4)))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (Sqrt[-Sqrt[-f]]*(d + e/Sqrt[x]))/(d*Sqrt[-Sqrt[-f]] - e*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, ((-f)^(1/4)*(d + e/Sqrt[x]))/(d*(-f)^(1/4) - e*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) - (p*PolyLog[2, (Sqrt[-Sqrt[-f]]*(d + e/Sqrt[x]))/(d*Sqrt[-Sqrt[-f]] + e*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g]) + (p*PolyLog[2, ((-f)^(1/4)*(d + e/Sqrt[x]))/(d*(-f)^(1/4) + e*g^(1/4))])/(2*Sqrt[-f]*Sqrt[g])","A",20,10,24,0.4167,1,"{2472, 2475, 263, 275, 205, 2416, 260, 2394, 2393, 2391}"
268,1,338,0,0.2589658,"\int \left(f+g x^2\right)^3 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^2)^3*Log[c*(d + e*x^2)^p],x]","f^2 g x^3 \log \left(c \left(d+e x^2\right)^p\right)+f^3 x \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^2 f g^2 p x}{5 e^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^2 g^3 p x^3}{21 e^2}+\frac{2 d^3 g^3 p x}{7 e^3}-\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 f^2 g p x}{e}+\frac{2 \sqrt{d} f^3 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{2 d f g^2 p x^3}{5 e}+\frac{2 d g^3 p x^5}{35 e}-\frac{2}{3} f^2 g p x^3-2 f^3 p x-\frac{6}{25} f g^2 p x^5-\frac{2}{49} g^3 p x^7","f^2 g x^3 \log \left(c \left(d+e x^2\right)^p\right)+f^3 x \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^2 f g^2 p x}{5 e^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^2 g^3 p x^3}{21 e^2}+\frac{2 d^3 g^3 p x}{7 e^3}-\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 f^2 g p x}{e}+\frac{2 \sqrt{d} f^3 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{2 d f g^2 p x^3}{5 e}+\frac{2 d g^3 p x^5}{35 e}-\frac{2}{3} f^2 g p x^3-2 f^3 p x-\frac{6}{25} f g^2 p x^5-\frac{2}{49} g^3 p x^7",1,"-2*f^3*p*x + (2*d*f^2*g*p*x)/e - (6*d^2*f*g^2*p*x)/(5*e^2) + (2*d^3*g^3*p*x)/(7*e^3) - (2*f^2*g*p*x^3)/3 + (2*d*f*g^2*p*x^3)/(5*e) - (2*d^2*g^3*p*x^3)/(21*e^2) - (6*f*g^2*p*x^5)/25 + (2*d*g^3*p*x^5)/(35*e) - (2*g^3*p*x^7)/49 + (2*Sqrt[d]*f^3*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (2*d^(3/2)*f^2*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/e^(3/2) + (6*d^(5/2)*f*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(5*e^(5/2)) - (2*d^(7/2)*g^3*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(7*e^(7/2)) + f^3*x*Log[c*(d + e*x^2)^p] + f^2*g*x^3*Log[c*(d + e*x^2)^p] + (3*f*g^2*x^5*Log[c*(d + e*x^2)^p])/5 + (g^3*x^7*Log[c*(d + e*x^2)^p])/7","A",17,6,22,0.2727,1,"{2471, 2448, 321, 205, 2455, 302}"
269,1,221,0,0.1706128,"\int \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","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^2 g^2 p x}{5 e^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 \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","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^2 g^2 p x}{5 e^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 \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,"-2*f^2*p*x + (4*d*f*g*p*x)/(3*e) - (2*d^2*g^2*p*x)/(5*e^2) - (4*f*g*p*x^3)/9 + (2*d*g^2*p*x^3)/(15*e) - (2*g^2*p*x^5)/25 + (2*Sqrt[d]*f^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (4*d^(3/2)*f*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*e^(3/2)) + (2*d^(5/2)*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(5*e^(5/2)) + f^2*x*Log[c*(d + e*x^2)^p] + (2*f*g*x^3*Log[c*(d + e*x^2)^p])/3 + (g^2*x^5*Log[c*(d + e*x^2)^p])/5","A",13,6,22,0.2727,1,"{2471, 2448, 321, 205, 2455, 302}"
270,1,117,0,0.0869666,"\int \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[(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",9,6,20,0.3000,1,"{2471, 2448, 321, 205, 2455, 302}"
271,1,533,0,0.4585881,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Int[Log[c*(d + e*x^2)^p]/(f + g*x^2),x]","\frac{i p \text{PolyLog}\left(2,1+\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} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\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{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{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}}","\frac{i p \text{PolyLog}\left(2,1+\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} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\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{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{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,"(2*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + (ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/(Sqrt[f]*Sqrt[g]) - (I*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g])","A",12,8,22,0.3636,1,"{205, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
272,1,751,0,1.0239357,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Int[Log[c*(d + e*x^2)^p]/(f + g*x^2)^2,x]","\frac{i p \text{PolyLog}\left(2,1+\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)}{4 f^{3/2} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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)}{4 f^{3/2} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 f^{3/2} \sqrt{g}}+\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{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{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}}","\frac{i p \text{PolyLog}\left(2,1+\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)}{4 f^{3/2} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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)}{4 f^{3/2} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 f^{3/2} \sqrt{g}}+\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{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{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,"(Sqrt[d]*Sqrt[e]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(f*(e*f - d*g)) - (e*p*Log[Sqrt[-f] - Sqrt[g]*x])/(2*Sqrt[-f]*Sqrt[g]*(e*f - d*g)) + (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(f^(3/2)*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(2*f^(3/2)*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(2*f^(3/2)*Sqrt[g]) + (e*p*Log[Sqrt[-f] + Sqrt[g]*x])/(2*Sqrt[-f]*Sqrt[g]*(e*f - d*g)) - Log[c*(d + e*x^2)^p]/(4*f*Sqrt[g]*(Sqrt[-f] - Sqrt[g]*x)) + Log[c*(d + e*x^2)^p]/(4*f*Sqrt[g]*(Sqrt[-f] + Sqrt[g]*x)) + (ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/(2*f^(3/2)*Sqrt[g]) - ((I/2)*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(f^(3/2)*Sqrt[g]) + ((I/4)*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(f^(3/2)*Sqrt[g]) + ((I/4)*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(f^(3/2)*Sqrt[g])","A",26,13,22,0.5909,1,"{2471, 2463, 801, 635, 205, 260, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
273,1,945,0,1.251212,"\int \left(f+g x^2\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^2)^2*Log[c*(d + e*x^2)^p]^2,x]","\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{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}+\frac{4 i d^{5/2} g^2 p^2 \text{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{3 e^{3/2}}","\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{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}+\frac{4 i d^{5/2} g^2 p^2 \text{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{3 e^{3/2}}",1,"8*f^2*p^2*x - (64*d*f*g*p^2*x)/(9*e) + (184*d^2*g^2*p^2*x)/(75*e^2) + (16*f*g*p^2*x^3)/27 - (64*d*g^2*p^2*x^3)/(225*e) + (8*g^2*p^2*x^5)/125 - (8*Sqrt[d]*f^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] + (64*d^(3/2)*f*g*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(9*e^(3/2)) - (184*d^(5/2)*g^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(75*e^(5/2)) + ((4*I)*Sqrt[d]*f^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/Sqrt[e] - (((8*I)/3)*d^(3/2)*f*g*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/e^(3/2) + (((4*I)/5)*d^(5/2)*g^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/e^(5/2) + (8*Sqrt[d]*f^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] - (16*d^(3/2)*f*g*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/(3*e^(3/2)) + (8*d^(5/2)*g^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/(5*e^(5/2)) - 4*f^2*p*x*Log[c*(d + e*x^2)^p] + (8*d*f*g*p*x*Log[c*(d + e*x^2)^p])/(3*e) - (4*d^2*g^2*p*x*Log[c*(d + e*x^2)^p])/(5*e^2) - (8*f*g*p*x^3*Log[c*(d + e*x^2)^p])/9 + (4*d*g^2*p*x^3*Log[c*(d + e*x^2)^p])/(15*e) - (4*g^2*p*x^5*Log[c*(d + e*x^2)^p])/25 + (4*Sqrt[d]*f^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/Sqrt[e] - (8*d^(3/2)*f*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/(3*e^(3/2)) + (4*d^(5/2)*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/(5*e^(5/2)) + f^2*x*Log[c*(d + e*x^2)^p]^2 + (2*f*g*x^3*Log[c*(d + e*x^2)^p]^2)/3 + (g^2*x^5*Log[c*(d + e*x^2)^p]^2)/5 + ((4*I)*Sqrt[d]*f^2*p^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] - (((8*I)/3)*d^(3/2)*f*g*p^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/e^(3/2) + (((4*I)/5)*d^(5/2)*g^2*p^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/e^(5/2)","A",50,15,24,0.6250,1,"{2471, 2450, 2476, 2448, 321, 205, 2470, 12, 4920, 4854, 2402, 2315, 2457, 2455, 302}"
274,1,548,0,0.7198113,"\int \left(f+g x^2\right) \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^2)*Log[c*(d + e*x^2)^p]^2,x]","-\frac{4 i d^{3/2} g p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right)}{3 e^{3/2}}+\frac{4 i \sqrt{d} f p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right)}{\sqrt{e}}-\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{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 d g p x \log \left(c \left(d+e x^2\right)^p\right)}{3 e}-\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 \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","-\frac{4 i d^{3/2} g p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right)}{3 e^{3/2}}+\frac{4 i \sqrt{d} f p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right)}{\sqrt{e}}-\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{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 d g p x \log \left(c \left(d+e x^2\right)^p\right)}{3 e}-\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 \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,"8*f*p^2*x - (32*d*g*p^2*x)/(9*e) + (8*g*p^2*x^3)/27 - (8*Sqrt[d]*f*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] + (32*d^(3/2)*g*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(9*e^(3/2)) + ((4*I)*Sqrt[d]*f*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/Sqrt[e] - (((4*I)/3)*d^(3/2)*g*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/e^(3/2) + (8*Sqrt[d]*f*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] - (8*d^(3/2)*g*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/(3*e^(3/2)) - 4*f*p*x*Log[c*(d + e*x^2)^p] + (4*d*g*p*x*Log[c*(d + e*x^2)^p])/(3*e) - (4*g*p*x^3*Log[c*(d + e*x^2)^p])/9 + (4*Sqrt[d]*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/Sqrt[e] - (4*d^(3/2)*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/(3*e^(3/2)) + f*x*Log[c*(d + e*x^2)^p]^2 + (g*x^3*Log[c*(d + e*x^2)^p]^2)/3 + ((4*I)*Sqrt[d]*f*p^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] - (((4*I)/3)*d^(3/2)*g*p^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/e^(3/2)","A",30,15,22,0.6818,1,"{2471, 2450, 2476, 2448, 321, 205, 2470, 12, 4920, 4854, 2402, 2315, 2457, 2455, 302}"
275,0,0,0,0.0287186,"\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^2)^p]^2/(f + g*x^2), x]","A",0,0,0,0,-1,"{}"
276,0,0,0,0.0262376,"\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^2)^p]^2/(f + g*x^2)^2, x]","A",0,0,0,0,-1,"{}"
277,0,0,0,1.3860414,"\int \left(f+g x^2\right) \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^2)*Log[c*(d + e*x^2)^p]^3,x]","\int \left(f+g x^2\right) \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","-\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 i d^{3/2} g p^3 \text{PolyLog}\left(2,-\frac{\sqrt{d}-i \sqrt{e} x}{\sqrt{d}+i \sqrt{e} x}\right)}{3 e^{3/2}}-\frac{24 i \sqrt{d} f p^3 \text{PolyLog}\left(2,-\frac{\sqrt{d}-i \sqrt{e} x}{\sqrt{d}+i \sqrt{e} x}\right)}{\sqrt{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}}-6 f p x \log ^2\left(c \left(d+e x^2\right)^p\right)+f x \log ^3\left(c \left(d+e x^2\right)^p\right)+\frac{8}{9} g p^2 x^3 \log \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{2}{3} g p x^3 \log ^2\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{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 \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,"-48*f*p^3*x + (208*d*g*p^3*x)/(9*e) - (16*g*p^3*x^3)/27 + (48*Sqrt[d]*f*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (208*d^(3/2)*g*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(9*e^(3/2)) - ((24*I)*Sqrt[d]*f*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/Sqrt[e] + (((32*I)/3)*d^(3/2)*g*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/e^(3/2) - (48*Sqrt[d]*f*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] + (64*d^(3/2)*g*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/(3*e^(3/2)) + 24*f*p^2*x*Log[c*(d + e*x^2)^p] - (32*d*g*p^2*x*Log[c*(d + e*x^2)^p])/(3*e) + (8*g*p^2*x^3*Log[c*(d + e*x^2)^p])/9 - (24*Sqrt[d]*f*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/Sqrt[e] + (32*d^(3/2)*g*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/(3*e^(3/2)) - 6*f*p*x*Log[c*(d + e*x^2)^p]^2 + (2*d*g*p*x*Log[c*(d + e*x^2)^p]^2)/e - (2*g*p*x^3*Log[c*(d + e*x^2)^p]^2)/3 + f*x*Log[c*(d + e*x^2)^p]^3 + (g*x^3*Log[c*(d + e*x^2)^p]^3)/3 - ((24*I)*Sqrt[d]*f*p^3*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] + (((32*I)/3)*d^(3/2)*g*p^3*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/e^(3/2) + 6*d*f*p*Defer[Int][Log[c*(d + e*x^2)^p]^2/(d + e*x^2), x] - (2*d^2*g*p*Defer[Int][Log[c*(d + e*x^2)^p]^2/(d + e*x^2), x])/e","A",0,0,0,0,-1,"{}"
278,0,0,0,0.0266382,"\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^2)^p]^3/(f + g*x^2), x]","A",0,0,0,0,-1,"{}"
279,0,0,0,0.0259536,"\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^2)^p]^3/(f + g*x^2)^2, x]","A",0,0,0,0,-1,"{}"
280,0,0,0,0.0244526,"\int \frac{\left(f+g x^2\right)^2}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","Int[(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,"Defer[Int][(f + g*x^2)^2/Log[c*(d + e*x^2)^p], x]","A",0,0,0,0,-1,"{}"
281,0,0,0,0.0143442,"\int \frac{f+g x^2}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","Int[(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,"Defer[Int][(f + g*x^2)/Log[c*(d + e*x^2)^p], x]","A",0,0,0,0,-1,"{}"
282,0,0,0,0.0278251,"\int \frac{1}{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/((f + g*x^2)*Log[c*(d + e*x^2)^p]), x]","A",0,0,0,0,-1,"{}"
283,0,0,0,0.0266515,"\int \frac{1}{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/((f + g*x^2)^2*Log[c*(d + e*x^2)^p]), x]","A",0,0,0,0,-1,"{}"
284,0,0,0,0.0240136,"\int \frac{\left(f+g x^2\right)^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Int[(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,"Defer[Int][(f + g*x^2)^2/Log[c*(d + e*x^2)^p]^2, x]","A",0,0,0,0,-1,"{}"
285,0,0,0,0.0133854,"\int \frac{f+g x^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Int[(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,"Defer[Int][(f + g*x^2)/Log[c*(d + e*x^2)^p]^2, x]","A",0,0,0,0,-1,"{}"
286,0,0,0,0.0263288,"\int \frac{1}{\left(f+g x^2\right) \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/((f + g*x^2)*Log[c*(d + e*x^2)^p]^2), x]","A",0,0,0,0,-1,"{}"
287,0,0,0,0.0247196,"\int \frac{1}{\left(f+g x^2\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/((f + g*x^2)^2*Log[c*(d + e*x^2)^p]^2), x]","A",0,0,0,0,-1,"{}"
288,1,366,0,0.3078972,"\int \left(f+g x^3\right)^3 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^3)^3*Log[c*(d + e*x^2)^p],x]","\frac{3}{4} f^2 g x^4 \log \left(c \left(d+e x^2\right)^p\right)+f^3 x \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{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{6 d^3 f g^2 p x}{7 e^3}-\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^2 g^3 p x^6}{30 e^2}+\frac{d^3 g^3 p x^4}{20 e^3}-\frac{d^4 g^3 p x^2}{10 e^4}+\frac{d^5 g^3 p \log \left(d+e x^2\right)}{10 e^5}+\frac{3 d f^2 g p x^2}{4 e}+\frac{2 \sqrt{d} f^3 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{6 d f g^2 p x^5}{35 e}+\frac{d g^3 p x^8}{40 e}-\frac{3}{8} f^2 g p x^4-2 f^3 p x-\frac{6}{49} f g^2 p x^7-\frac{1}{50} g^3 p x^{10}","\frac{3}{4} f^2 g x^4 \log \left(c \left(d+e x^2\right)^p\right)+f^3 x \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{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{6 d^3 f g^2 p x}{7 e^3}-\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^2 g^3 p x^6}{30 e^2}+\frac{d^3 g^3 p x^4}{20 e^3}-\frac{d^4 g^3 p x^2}{10 e^4}+\frac{d^5 g^3 p \log \left(d+e x^2\right)}{10 e^5}+\frac{3 d f^2 g p x^2}{4 e}+\frac{2 \sqrt{d} f^3 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{e}}+\frac{6 d f g^2 p x^5}{35 e}+\frac{d g^3 p x^8}{40 e}-\frac{3}{8} f^2 g p x^4-2 f^3 p x-\frac{6}{49} f g^2 p x^7-\frac{1}{50} g^3 p x^{10}",1,"-2*f^3*p*x + (6*d^3*f*g^2*p*x)/(7*e^3) + (3*d*f^2*g*p*x^2)/(4*e) - (d^4*g^3*p*x^2)/(10*e^4) - (2*d^2*f*g^2*p*x^3)/(7*e^2) - (3*f^2*g*p*x^4)/8 + (d^3*g^3*p*x^4)/(20*e^3) + (6*d*f*g^2*p*x^5)/(35*e) - (d^2*g^3*p*x^6)/(30*e^2) - (6*f*g^2*p*x^7)/49 + (d*g^3*p*x^8)/(40*e) - (g^3*p*x^10)/50 + (2*Sqrt[d]*f^3*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (6*d^(7/2)*f*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(7*e^(7/2)) - (3*d^2*f^2*g*p*Log[d + e*x^2])/(4*e^2) + (d^5*g^3*p*Log[d + e*x^2])/(10*e^5) + f^3*x*Log[c*(d + e*x^2)^p] + (3*f^2*g*x^4*Log[c*(d + e*x^2)^p])/4 + (3*f*g^2*x^7*Log[c*(d + e*x^2)^p])/7 + (g^3*x^10*Log[c*(d + e*x^2)^p])/10","A",17,9,22,0.4091,1,"{2471, 2448, 321, 205, 2454, 2395, 43, 2455, 302}"
289,1,231,0,0.1767453,"\int \left(f+g x^3\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^3)^2*Log[c*(d + e*x^2)^p],x]","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{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 d^3 g^2 p x}{7 e^3}-\frac{2 d^{7/2} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{7 e^{7/2}}+\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","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{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 d^3 g^2 p x}{7 e^3}-\frac{2 d^{7/2} g^2 p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{7 e^{7/2}}+\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,"-2*f^2*p*x + (2*d^3*g^2*p*x)/(7*e^3) + (d*f*g*p*x^2)/(2*e) - (2*d^2*g^2*p*x^3)/(21*e^2) - (f*g*p*x^4)/4 + (2*d*g^2*p*x^5)/(35*e) - (2*g^2*p*x^7)/49 + (2*Sqrt[d]*f^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (2*d^(7/2)*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) + f^2*x*Log[c*(d + e*x^2)^p] + (f*g*x^4*Log[c*(d + e*x^2)^p])/2 + (g^2*x^7*Log[c*(d + e*x^2)^p])/7","A",13,9,22,0.4091,1,"{2471, 2448, 321, 205, 2454, 2395, 43, 2455, 302}"
290,1,110,0,0.0974112,"\int \left(f+g x^3\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[(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",9,7,20,0.3500,1,"{2471, 2448, 321, 205, 2454, 2395, 43}"
291,1,1165,0,1.6036059,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{f+g x^3} \, dx","Int[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)}{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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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])/(3*f^(2/3)*g^(1/3)) - (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])/(3*f^(2/3)*g^(1/3)) - ((-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])/(3*f^(2/3)*g^(1/3)) - ((-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])/(3*f^(2/3)*g^(1/3)) + ((-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])/(3*f^(2/3)*g^(1/3)) + ((-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])/(3*f^(2/3)*g^(1/3)) + (Log[-f^(1/3) - g^(1/3)*x]*Log[c*(d + e*x^2)^p])/(3*f^(2/3)*g^(1/3)) + ((-1)^(2/3)*Log[-f^(1/3) + (-1)^(1/3)*g^(1/3)*x]*Log[c*(d + e*x^2)^p])/(3*f^(2/3)*g^(1/3)) - ((-1)^(1/3)*Log[-f^(1/3) - (-1)^(2/3)*g^(1/3)*x]*Log[c*(d + e*x^2)^p])/(3*f^(2/3)*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))])/(3*f^(2/3)*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))])/(3*f^(2/3)*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))])/(3*f^(2/3)*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))])/(3*f^(2/3)*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)) + ((-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",29,7,22,0.3182,1,"{2471, 2462, 260, 2416, 2394, 2393, 2391}"
292,1,1863,0,2.8870132,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^3\right)^2} \, dx","Int[Log[c*(d + e*x^2)^p]/(f + g*x^3)^2,x]","\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(i \left(i-\sqrt{3}\right) g^{2/3} d+2 e f^{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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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}}","\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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,"(2*Sqrt[d]*Sqrt[e]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(9*f^(4/3)*(e*f^(2/3) + d*g^(2/3))) + (2*(-1)^(2/3)*Sqrt[d]*Sqrt[e]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/((1 + (-1)^(1/3))^4*f^(4/3)*(e*f^(2/3) + (-1)^(2/3)*d*g^(2/3))) + (4*Sqrt[d]*Sqrt[e]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(9*f^(4/3)*(2*e*f^(2/3) + I*(I - Sqrt[3])*d*g^(2/3))) - (2*e*p*Log[f^(1/3) + g^(1/3)*x])/(9*f*(e*f^(2/3) + d*g^(2/3))*g^(1/3)) - (2*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])/(9*f^(5/3)*g^(1/3)) - (2*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])/(9*f^(5/3)*g^(1/3)) + (2*(-1)^(1/3)*e*p*Log[f^(1/3) - (-1)^(1/3)*g^(1/3)*x])/((1 + (-1)^(1/3))^4*f*(e*f^(2/3) + (-1)^(2/3)*d*g^(2/3))*g^(1/3)) + ((2*I)*Sqrt[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)^(1/3))^5*f^(5/3)*g^(1/3)) + ((2*I)*Sqrt[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)^(1/3))^5*f^(5/3)*g^(1/3)) + (4*(-1)^(1/3)*e*p*Log[f^(1/3) + (-1)^(2/3)*g^(1/3)*x])/(9*f*(2*e*f^(2/3) - (1 + I*Sqrt[3])*d*g^(2/3))*g^(1/3)) - (2*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)^(1/3))^4*f^(5/3)*g^(1/3)) - (2*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)^(1/3))^4*f^(5/3)*g^(1/3)) + (e*p*Log[d + e*x^2])/(9*f*(e*f^(2/3) + d*g^(2/3))*g^(1/3)) - ((-1)^(1/3)*e*p*Log[d + e*x^2])/((1 + (-1)^(1/3))^4*f*(e*f^(2/3) + (-1)^(2/3)*d*g^(2/3))*g^(1/3)) - (2*(-1)^(1/3)*e*p*Log[d + e*x^2])/(9*f*(2*e*f^(2/3) - (1 + I*Sqrt[3])*d*g^(2/3))*g^(1/3)) - Log[c*(d + e*x^2)^p]/(9*f^(4/3)*g^(1/3)*(f^(1/3) + g^(1/3)*x)) - Log[c*(d + e*x^2)^p]/((1 + (-1)^(1/3))^4*f^(4/3)*g^(1/3)*((-1)^(2/3)*f^(1/3) + g^(1/3)*x)) + ((-1)^(1/3)*Log[c*(d + e*x^2)^p])/(9*f^(4/3)*g^(1/3)*(f^(1/3) + (-1)^(2/3)*g^(1/3)*x)) + (2*Log[f^(1/3) + g^(1/3)*x]*Log[c*(d + e*x^2)^p])/(9*f^(5/3)*g^(1/3)) - ((2*I)*Sqrt[3]*Log[-f^(1/3) + (-1)^(1/3)*g^(1/3)*x]*Log[c*(d + e*x^2)^p])/((1 + (-1)^(1/3))^5*f^(5/3)*g^(1/3)) + (2*Log[f^(1/3) + (-1)^(2/3)*g^(1/3)*x]*Log[c*(d + e*x^2)^p])/((1 + (-1)^(1/3))^4*f^(5/3)*g^(1/3)) - (2*p*PolyLog[2, (Sqrt[e]*(f^(1/3) + g^(1/3)*x))/(Sqrt[e]*f^(1/3) - Sqrt[-d]*g^(1/3))])/(9*f^(5/3)*g^(1/3)) - (2*p*PolyLog[2, (Sqrt[e]*(f^(1/3) + g^(1/3)*x))/(Sqrt[e]*f^(1/3) + Sqrt[-d]*g^(1/3))])/(9*f^(5/3)*g^(1/3)) + ((2*I)*Sqrt[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)^(1/3))^5*f^(5/3)*g^(1/3)) + ((2*I)*Sqrt[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)^(1/3))^5*f^(5/3)*g^(1/3)) - (2*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)^(1/3))^4*f^(5/3)*g^(1/3)) - (2*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)^(1/3))^4*f^(5/3)*g^(1/3))","A",47,11,22,0.5000,1,"{2471, 2463, 801, 635, 205, 260, 2462, 2416, 2394, 2393, 2391}"
293,1,1139,0,1.6415309,"\int \left(f+g x^3\right)^3 \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^3)^3*Log[c*(d + e*x^2)^p]^2,x]","\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{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{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{1}{300} g^3 p \left(-\frac{60 \log \left(e x^2+d\right) d^5}{e^5}+\frac{300 \left(e x^2+d\right) d^4}{e^5}-\frac{300 \left(e x^2+d\right)^2 d^3}{e^5}+\frac{200 \left(e x^2+d\right)^3 d^2}{e^5}-\frac{75 \left(e x^2+d\right)^4 d}{e^5}+\frac{12 \left(e x^2+d\right)^5}{e^5}\right) \log \left(c \left(e x^2+d\right)^p\right)+\frac{4 i \sqrt{d} f^3 p^2 \text{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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) - (3*d*f^2*g*p^2*x^2)/e + (d^4*g^3*p^2*x^2)/e^4 + (568*d^2*f*g^2*p^2*x^3)/(735*e^2) - (288*d*f*g^2*p^2*x^5)/(1225*e) + (24*f*g^2*p^2*x^7)/343 + (3*f^2*g*p^2*(d + e*x^2)^2)/(8*e^2) - (d^3*g^3*p^2*(d + e*x^2)^2)/(2*e^5) + (2*d^2*g^3*p^2*(d + e*x^2)^3)/(9*e^5) - (d*g^3*p^2*(d + e*x^2)^4)/(16*e^5) + (g^3*p^2*(d + e*x^2)^5)/(125*e^5) - (8*Sqrt[d]*f^3*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] + (1408*d^(7/2)*f*g^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(245*e^(7/2)) + ((4*I)*Sqrt[d]*f^3*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/Sqrt[e] - (((12*I)/7)*d^(7/2)*f*g^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/e^(7/2) + (8*Sqrt[d]*f^3*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] - (24*d^(7/2)*f*g^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/(7*e^(7/2)) - (d^5*g^3*p^2*Log[d + e*x^2]^2)/(10*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) - (4*d^2*f*g^2*p*x^3*Log[c*(d + e*x^2)^p])/(7*e^2) + (12*d*f*g^2*p*x^5*Log[c*(d + e*x^2)^p])/(35*e) - (12*f*g^2*p*x^7*Log[c*(d + e*x^2)^p])/49 + (3*d*f^2*g*p*(d + e*x^2)*Log[c*(d + e*x^2)^p])/e^2 - (3*f^2*g*p*(d + e*x^2)^2*Log[c*(d + e*x^2)^p])/(4*e^2) + (4*Sqrt[d]*f^3*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/Sqrt[e] - (12*d^(7/2)*f*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/(7*e^(7/2)) - (g^3*p*((300*d^4*(d + e*x^2))/e^5 - (300*d^3*(d + e*x^2)^2)/e^5 + (200*d^2*(d + e*x^2)^3)/e^5 - (75*d*(d + e*x^2)^4)/e^5 + (12*(d + e*x^2)^5)/e^5 - (60*d^5*Log[d + e*x^2])/e^5)*Log[c*(d + e*x^2)^p])/300 + f^3*x*Log[c*(d + e*x^2)^p]^2 + (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 - (3*d*f^2*g*(d + e*x^2)*Log[c*(d + e*x^2)^p]^2)/(2*e^2) + (3*f^2*g*(d + e*x^2)^2*Log[c*(d + e*x^2)^p]^2)/(4*e^2) + ((4*I)*Sqrt[d]*f^3*p^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] - (((12*I)/7)*d^(7/2)*f*g^2*p^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/e^(7/2)","A",55,29,24,1.208,1,"{2471, 2450, 2476, 2448, 321, 205, 2470, 12, 4920, 4854, 2402, 2315, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2457, 2455, 302, 2398, 2411, 43, 2334, 14, 2301}"
294,1,835,0,1.0792251,"\int \left(f+g x^3\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^3)^2*Log[c*(d + e*x^2)^p]^2,x]","\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{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}-\frac{4 i d^{7/2} g^2 p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{7 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{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}-\frac{4 i d^{7/2} g^2 p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{7 e^{7/2}}",1,"8*f^2*p^2*x - (1408*d^3*g^2*p^2*x)/(735*e^3) - (2*d*f*g*p^2*x^2)/e + (568*d^2*g^2*p^2*x^3)/(2205*e^2) - (96*d*g^2*p^2*x^5)/(1225*e) + (8*g^2*p^2*x^7)/343 + (f*g*p^2*(d + e*x^2)^2)/(4*e^2) - (8*Sqrt[d]*f^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] + (1408*d^(7/2)*g^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(735*e^(7/2)) + ((4*I)*Sqrt[d]*f^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/Sqrt[e] - (((4*I)/7)*d^(7/2)*g^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/e^(7/2) + (8*Sqrt[d]*f^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] - (8*d^(7/2)*g^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/(7*e^(7/2)) - 4*f^2*p*x*Log[c*(d + e*x^2)^p] + (4*d^3*g^2*p*x*Log[c*(d + e*x^2)^p])/(7*e^3) - (4*d^2*g^2*p*x^3*Log[c*(d + e*x^2)^p])/(21*e^2) + (4*d*g^2*p*x^5*Log[c*(d + e*x^2)^p])/(35*e) - (4*g^2*p*x^7*Log[c*(d + e*x^2)^p])/49 + (2*d*f*g*p*(d + e*x^2)*Log[c*(d + e*x^2)^p])/e^2 - (f*g*p*(d + e*x^2)^2*Log[c*(d + e*x^2)^p])/(2*e^2) + (4*Sqrt[d]*f^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/Sqrt[e] - (4*d^(7/2)*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/(7*e^(7/2)) + f^2*x*Log[c*(d + e*x^2)^p]^2 + (g^2*x^7*Log[c*(d + e*x^2)^p]^2)/7 - (d*f*g*(d + e*x^2)*Log[c*(d + e*x^2)^p]^2)/e^2 + (f*g*(d + e*x^2)^2*Log[c*(d + e*x^2)^p]^2)/(2*e^2) + ((4*I)*Sqrt[d]*f^2*p^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] - (((4*I)/7)*d^(7/2)*g^2*p^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/e^(7/2)","A",47,23,24,0.9583,1,"{2471, 2450, 2476, 2448, 321, 205, 2470, 12, 4920, 4854, 2402, 2315, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304, 2457, 2455, 302}"
295,1,395,0,0.5068872,"\int \left(f+g x^3\right) \log ^2\left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^3)*Log[c*(d + e*x^2)^p]^2,x]","\frac{4 i \sqrt{d} f p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right)}{\sqrt{e}}+\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 \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","\frac{4 i \sqrt{d} f p^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right)}{\sqrt{e}}+\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 \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 - (d*g*p^2*x^2)/e + (g*p^2*(d + e*x^2)^2)/(8*e^2) - (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*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] - 4*f*p*x*Log[c*(d + e*x^2)^p] + (d*g*p*(d + e*x^2)*Log[c*(d + e*x^2)^p])/e^2 - (g*p*(d + e*x^2)^2*Log[c*(d + e*x^2)^p])/(4*e^2) + (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 - (d*g*(d + e*x^2)*Log[c*(d + e*x^2)^p]^2)/(2*e^2) + (g*(d + e*x^2)^2*Log[c*(d + e*x^2)^p]^2)/(4*e^2) + ((4*I)*Sqrt[d]*f*p^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e]","A",23,20,22,0.9091,1,"{2471, 2450, 2476, 2448, 321, 205, 2470, 12, 4920, 4854, 2402, 2315, 2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
296,0,0,0,0.0269754,"\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{f+g x^3} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^2)^p]^2/(f + g*x^3), x]","A",0,0,0,0,-1,"{}"
297,0,0,0,0.0255872,"\int \frac{\log ^2\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^3\right)^2} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^2)^p]^2/(f + g*x^3)^2, x]","A",0,0,0,0,-1,"{}"
298,0,0,0,2.6493678,"\int \left(f+g x^3\right)^2 \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^3)^2*Log[c*(d + e*x^2)^p]^3,x]","\int \left(f+g x^3\right)^2 \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","-\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{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{i \sqrt{e} x+\sqrt{d}}\right)}{\sqrt{e}}+\frac{1408 i d^{7/2} g^2 p^3 \text{PolyLog}\left(2,1-\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,"-48*f^2*p^3*x + (351136*d^3*g^2*p^3*x)/(25725*e^3) + (6*d*f*g*p^3*x^2)/e - (55456*d^2*g^2*p^3*x^3)/(77175*e^2) + (5232*d*g^2*p^3*x^5)/(42875*e) - (48*g^2*p^3*x^7)/2401 - (3*f*g*p^3*(d + e*x^2)^2)/(8*e^2) + (48*Sqrt[d]*f^2*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (351136*d^(7/2)*g^2*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(25725*e^(7/2)) - ((24*I)*Sqrt[d]*f^2*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/Sqrt[e] + (((1408*I)/245)*d^(7/2)*g^2*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/e^(7/2) - (48*Sqrt[d]*f^2*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] + (2816*d^(7/2)*g^2*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/(245*e^(7/2)) + 24*f^2*p^2*x*Log[c*(d + e*x^2)^p] - (1408*d^3*g^2*p^2*x*Log[c*(d + e*x^2)^p])/(245*e^3) + (568*d^2*g^2*p^2*x^3*Log[c*(d + e*x^2)^p])/(735*e^2) - (288*d*g^2*p^2*x^5*Log[c*(d + e*x^2)^p])/(1225*e) + (24*g^2*p^2*x^7*Log[c*(d + e*x^2)^p])/343 - (6*d*f*g*p^2*(d + e*x^2)*Log[c*(d + e*x^2)^p])/e^2 + (3*f*g*p^2*(d + e*x^2)^2*Log[c*(d + e*x^2)^p])/(4*e^2) - (24*Sqrt[d]*f^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/Sqrt[e] + (1408*d^(7/2)*g^2*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/(245*e^(7/2)) - 6*f^2*p*x*Log[c*(d + e*x^2)^p]^2 + (6*d^3*g^2*p*x*Log[c*(d + e*x^2)^p]^2)/(7*e^3) - (2*d^2*g^2*p*x^3*Log[c*(d + e*x^2)^p]^2)/(7*e^2) + (6*d*g^2*p*x^5*Log[c*(d + e*x^2)^p]^2)/(35*e) - (6*g^2*p*x^7*Log[c*(d + e*x^2)^p]^2)/49 + (3*d*f*g*p*(d + e*x^2)*Log[c*(d + e*x^2)^p]^2)/e^2 - (3*f*g*p*(d + e*x^2)^2*Log[c*(d + e*x^2)^p]^2)/(4*e^2) + f^2*x*Log[c*(d + e*x^2)^p]^3 + (g^2*x^7*Log[c*(d + e*x^2)^p]^3)/7 - (d*f*g*(d + e*x^2)*Log[c*(d + e*x^2)^p]^3)/e^2 + (f*g*(d + e*x^2)^2*Log[c*(d + e*x^2)^p]^3)/(2*e^2) - ((24*I)*Sqrt[d]*f^2*p^3*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] + (((1408*I)/245)*d^(7/2)*g^2*p^3*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/e^(7/2) + 6*d*f^2*p*Defer[Int][Log[c*(d + e*x^2)^p]^2/(d + e*x^2), x] - (6*d^4*g^2*p*Defer[Int][Log[c*(d + e*x^2)^p]^2/(d + e*x^2), x])/(7*e^3)","A",0,0,0,0,-1,"{}"
299,0,0,0,0.7676161,"\int \left(f+g x^3\right) \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^3)*Log[c*(d + e*x^2)^p]^3,x]","\int \left(f+g x^3\right) \log ^3\left(c \left(d+e x^2\right)^p\right) \, dx","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{24 i \sqrt{d} f p^3 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} x}\right)}{\sqrt{e}}+\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{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}+\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}+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}}-6 f p x \log ^2\left(c \left(d+e x^2\right)^p\right)+f x \log ^3\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 \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,"-48*f*p^3*x + (3*d*g*p^3*x^2)/e - (3*g*p^3*(d + e*x^2)^2)/(16*e^2) + (48*Sqrt[d]*f*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - ((24*I)*Sqrt[d]*f*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]^2)/Sqrt[e] - (48*Sqrt[d]*f*p^3*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] + 24*f*p^2*x*Log[c*(d + e*x^2)^p] - (3*d*g*p^2*(d + e*x^2)*Log[c*(d + e*x^2)^p])/e^2 + (3*g*p^2*(d + e*x^2)^2*Log[c*(d + e*x^2)^p])/(8*e^2) - (24*Sqrt[d]*f*p^2*ArcTan[(Sqrt[e]*x)/Sqrt[d]]*Log[c*(d + e*x^2)^p])/Sqrt[e] - 6*f*p*x*Log[c*(d + e*x^2)^p]^2 + (3*d*g*p*(d + e*x^2)*Log[c*(d + e*x^2)^p]^2)/(2*e^2) - (3*g*p*(d + e*x^2)^2*Log[c*(d + e*x^2)^p]^2)/(8*e^2) + f*x*Log[c*(d + e*x^2)^p]^3 - (d*g*(d + e*x^2)*Log[c*(d + e*x^2)^p]^3)/(2*e^2) + (g*(d + e*x^2)^2*Log[c*(d + e*x^2)^p]^3)/(4*e^2) - ((24*I)*Sqrt[d]*f*p^3*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x)])/Sqrt[e] + 6*d*f*p*Defer[Int][Log[c*(d + e*x^2)^p]^2/(d + e*x^2), x]","A",0,0,0,0,-1,"{}"
300,0,0,0,0.0280148,"\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{f+g x^3} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^2)^p]^3/(f + g*x^3), x]","A",0,0,0,0,-1,"{}"
301,0,0,0,0.0259449,"\int \frac{\log ^3\left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^3\right)^2} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^2)^p]^3/(f + g*x^3)^2, x]","A",0,0,0,0,-1,"{}"
302,0,0,0,0.0244984,"\int \frac{\left(f+g x^3\right)^2}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","Int[(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,"Defer[Int][(f + g*x^3)^2/Log[c*(d + e*x^2)^p], x]","A",0,0,0,0,-1,"{}"
303,0,0,0,0.0143791,"\int \frac{f+g x^3}{\log \left(c \left(d+e x^2\right)^p\right)} \, dx","Int[(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,"Defer[Int][(f + g*x^3)/Log[c*(d + e*x^2)^p], x]","A",0,0,0,0,-1,"{}"
304,0,0,0,0.0293051,"\int \frac{1}{\left(f+g x^3\right) \log \left(c \left(d+e x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/((f + g*x^3)*Log[c*(d + e*x^2)^p]), x]","A",0,0,0,0,-1,"{}"
305,0,0,0,0.0267897,"\int \frac{1}{\left(f+g x^3\right)^2 \log \left(c \left(d+e x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/((f + g*x^3)^2*Log[c*(d + e*x^2)^p]), x]","A",0,0,0,0,-1,"{}"
306,0,0,0,0.0232582,"\int \frac{\left(f+g x^3\right)^2}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Int[(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,"Defer[Int][(f + g*x^3)^2/Log[c*(d + e*x^2)^p]^2, x]","A",0,0,0,0,-1,"{}"
307,0,0,0,0.0141798,"\int \frac{f+g x^3}{\log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Int[(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,"Defer[Int][(f + g*x^3)/Log[c*(d + e*x^2)^p]^2, x]","A",0,0,0,0,-1,"{}"
308,0,0,0,0.0284273,"\int \frac{1}{\left(f+g x^3\right) \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/((f + g*x^3)*Log[c*(d + e*x^2)^p]^2), x]","A",0,0,0,0,-1,"{}"
309,0,0,0,0.0263193,"\int \frac{1}{\left(f+g x^3\right)^2 \log ^2\left(c \left(d+e x^2\right)^p\right)} \, dx","Int[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,"Defer[Int][1/((f + g*x^3)^2*Log[c*(d + e*x^2)^p]^2), x]","A",0,0,0,0,-1,"{}"
310,1,142,0,0.2286799,"\int x^5 \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[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^2 p x^2 (4 e f-3 d g)}{24 e^3}+\frac{d^3 p (4 e f-3 d g) \log \left(d+e x^2\right)}{24 e^4}+\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","\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^2 p x^2 (4 e f-3 d g)}{24 e^3}+\frac{d^3 p (4 e f-3 d g) \log \left(d+e x^2\right)}{24 e^4}+\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,"-(d^2*(4*e*f - 3*d*g)*p*x^2)/(24*e^3) + (d*(4*e*f - 3*d*g)*p*x^4)/(48*e^2) - ((4*e*f - 3*d*g)*p*x^6)/(72*e) - (g*p*x^8)/32 + (d^3*(4*e*f - 3*d*g)*p*Log[d + e*x^2])/(24*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",5,5,23,0.2174,1,"{2475, 43, 2414, 12, 77}"
311,1,119,0,0.1785472,"\int x^3 \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[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^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","\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*(3*e*f - 2*d*g)*p*x^2)/(12*e^2) - ((3*e*f - 2*d*g)*p*x^4)/(24*e) - (g*p*x^6)/18 - (d^2*(3*e*f - 2*d*g)*p*Log[d + e*x^2])/(12*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",5,5,23,0.2174,1,"{2475, 43, 2414, 12, 77}"
312,1,94,0,0.0928483,"\int x \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[x*(f + g*x^2)*Log[c*(d + e*x^2)^p],x]","\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}","\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,"-((e*f - d*g)*p*x^2)/(4*e) - (p*(f + g*x^2)^2)/(8*g) - ((e*f - d*g)^2*p*Log[d + e*x^2])/(4*e^2*g) + ((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/(4*g)","A",4,3,21,0.1429,1,"{2475, 2395, 43}"
313,1,82,0,0.111122,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x} \, dx","Int[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x,x]","\frac{1}{2} f p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\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} g p x^2","\frac{1}{2} f p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\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} g p x^2",1,"-(g*p*x^2)/2 + (g*(d + e*x^2)*Log[c*(d + e*x^2)^p])/(2*e) + (f*Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p])/2 + (f*p*PolyLog[2, 1 + (e*x^2)/d])/2","A",7,7,23,0.3043,1,"{2475, 43, 2416, 2389, 2295, 2394, 2315}"
314,1,93,0,0.1268354,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^3} \, dx","Int[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x^3,x]","\frac{1}{2} g p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\right)-\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{PolyLog}\left(2,\frac{e x^2}{d}+1\right)-\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}",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])/2 + (g*p*PolyLog[2, 1 + (e*x^2)/d])/2","A",9,9,23,0.3913,1,"{2475, 43, 2416, 2395, 36, 29, 31, 2394, 2315}"
315,1,93,0,0.1373834,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^5} \, dx","Int[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x^5,x]","-\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}","-\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*f*p)/(4*d*x^2) - (e*(e*f - 2*d*g)*p*Log[x])/(2*d^2) + ((e*f - d*g)^2*p*Log[d + e*x^2])/(4*d^2*f) - ((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/(4*f*x^4)","A",5,5,23,0.2174,1,"{2475, 37, 2414, 12, 88}"
316,1,125,0,0.1629687,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^7} \, dx","Int[((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{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}","-\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*f*p)/(12*d*x^4) + (e*(2*e*f - 3*d*g)*p)/(12*d^2*x^2) + (e^2*(2*e*f - 3*d*g)*p*Log[x])/(6*d^3) - (e^2*(2*e*f - 3*d*g)*p*Log[d + e*x^2])/(12*d^3) - (f*Log[c*(d + e*x^2)^p])/(6*x^6) - (g*Log[c*(d + e*x^2)^p])/(4*x^4)","A",5,5,23,0.2174,1,"{2475, 43, 2414, 12, 77}"
317,1,148,0,0.2023689,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^9} \, dx","Int[((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{e^2 p (3 e f-4 d g)}{24 d^3 x^2}+\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 p (3 e f-4 d g)}{48 d^2 x^4}-\frac{e f p}{24 d x^6}","-\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^2 p (3 e f-4 d g)}{24 d^3 x^2}+\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 p (3 e f-4 d g)}{48 d^2 x^4}-\frac{e f p}{24 d x^6}",1,"-(e*f*p)/(24*d*x^6) + (e*(3*e*f - 4*d*g)*p)/(48*d^2*x^4) - (e^2*(3*e*f - 4*d*g)*p)/(24*d^3*x^2) - (e^3*(3*e*f - 4*d*g)*p*Log[x])/(12*d^4) + (e^3*(3*e*f - 4*d*g)*p*Log[d + e*x^2])/(24*d^4) - (f*Log[c*(d + e*x^2)^p])/(8*x^8) - (g*Log[c*(d + e*x^2)^p])/(6*x^6)","A",5,5,23,0.2174,1,"{2475, 43, 2414, 12, 77}"
318,1,154,0,0.1299551,"\int x^2 \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[x^2*(f + g*x^2)*Log[c*(d + e*x^2)^p],x]","\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^2 g p x}{5 e^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 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","\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^2 g p x}{5 e^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 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,"(2*d*f*p*x)/(3*e) - (2*d^2*g*p*x)/(5*e^2) - (2*f*p*x^3)/9 + (2*d*g*p*x^3)/(15*e) - (2*g*p*x^5)/25 - (2*d^(3/2)*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*e^(3/2)) + (2*d^(5/2)*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(5*e^(5/2)) + (f*x^3*Log[c*(d + e*x^2)^p])/3 + (g*x^5*Log[c*(d + e*x^2)^p])/5","A",10,4,23,0.1739,1,"{2476, 2455, 302, 205}"
319,1,117,0,0.0856192,"\int \left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[(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",9,6,20,0.3000,1,"{2471, 2448, 321, 205, 2455, 302}"
320,1,93,0,0.0838046,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^2} \, dx","Int[((f + g*x^2)*Log[c*(d + e*x^2)^p])/x^2,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 \sqrt{e} f p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\sqrt{d}}+\frac{2 \sqrt{d} g p \tan ^{-1}\left(\frac{\sqrt{e} x}{\sqrt{d}}\right)}{\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*Sqrt[e]*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[d] + (2*Sqrt[d]*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (f*Log[c*(d + e*x^2)^p])/x + g*x*Log[c*(d + e*x^2)^p]","A",7,5,23,0.2174,1,"{2476, 2448, 321, 205, 2455}"
321,1,108,0,0.0998344,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^4} \, dx","Int[((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^{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}}","-\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*e*f*p)/(3*d*x) - (2*e^(3/2)*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*d^(3/2)) + (2*Sqrt[e]*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[d] - (f*Log[c*(d + e*x^2)^p])/(3*x^3) - (g*Log[c*(d + e*x^2)^p])/x","A",7,4,23,0.1739,1,"{2476, 2455, 325, 205}"
322,1,140,0,0.1214022,"\int \frac{\left(f+g x^2\right) \log \left(c \left(d+e x^2\right)^p\right)}{x^6} \, dx","Int[((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^2 f p}{5 d^2 x}+\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 f p}{15 d x^3}-\frac{2 e g p}{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^2 f p}{5 d^2 x}+\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 f p}{15 d x^3}-\frac{2 e g p}{3 d x}",1,"(-2*e*f*p)/(15*d*x^3) + (2*e^2*f*p)/(5*d^2*x) - (2*e*g*p)/(3*d*x) + (2*e^(5/2)*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(5*d^(5/2)) - (2*e^(3/2)*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*d^(3/2)) - (f*Log[c*(d + e*x^2)^p])/(5*x^5) - (g*Log[c*(d + e*x^2)^p])/(3*x^3)","A",9,4,23,0.1739,1,"{2476, 2455, 325, 205}"
323,1,251,0,0.4706985,"\int x^5 \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[x^5*(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","\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{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{d^2 p x^2 (e f-d g)^2}{2 e^4}-\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}","\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{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{d^2 p x^2 (e f-d g)^2}{2 e^4}-\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,"-(d^2*(e*f - d*g)^2*p*x^2)/(2*e^4) + (d*(e*f - 2*d*g)*(e*f - d*g)*p*(d + e*x^2)^2)/(4*e^5) - ((e^2*f^2 - 6*d*e*f*g + 6*d^2*g^2)*p*(d + e*x^2)^3)/(18*e^5) - (g*(e*f - 2*d*g)*p*(d + e*x^2)^4)/(16*e^5) - (g^2*p*(d + e*x^2)^5)/(50*e^5) + (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) + (f^2*x^6*Log[c*(d + e*x^2)^p])/6 + (f*g*x^8*Log[c*(d + e*x^2)^p])/4 + (g^2*x^10*Log[c*(d + e*x^2)^p])/10","A",5,5,25,0.2000,1,"{2475, 43, 2414, 12, 893}"
324,1,210,0,0.3605552,"\int x^3 \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[x^3*(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","\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{d p x^2 (e f-d g)^2}{2 e^3}-\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{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{d p x^2 (e f-d g)^2}{2 e^3}-\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}",1,"(d*(e*f - d*g)^2*p*x^2)/(2*e^3) - ((e*f - 3*d*g)*(e*f - d*g)*p*(d + e*x^2)^2)/(8*e^4) - (g*(2*e*f - 3*d*g)*p*(d + e*x^2)^3)/(18*e^4) - (g^2*p*(d + e*x^2)^4)/(32*e^4) - (d^2*(6*e^2*f^2 - 8*d*e*f*g + 3*d^2*g^2)*p*Log[d + e*x^2])/(24*e^4) + (f^2*x^4*Log[c*(d + e*x^2)^p])/4 + (f*g*x^6*Log[c*(d + e*x^2)^p])/3 + (g^2*x^8*Log[c*(d + e*x^2)^p])/8","A",5,5,25,0.2000,1,"{2475, 43, 2414, 12, 893}"
325,1,124,0,0.1409232,"\int x \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[x*(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","\frac{\left(f+g x^2\right)^3 \log \left(c \left(d+e x^2\right)^p\right)}{6 g}-\frac{p x^2 (e f-d g)^2}{6 e^2}-\frac{p (e f-d g)^3 \log \left(d+e x^2\right)}{6 e^3 g}-\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}","\frac{\left(f+g x^2\right)^3 \log \left(c \left(d+e x^2\right)^p\right)}{6 g}-\frac{p x^2 (e f-d g)^2}{6 e^2}-\frac{p (e f-d g)^3 \log \left(d+e x^2\right)}{6 e^3 g}-\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,"-((e*f - d*g)^2*p*x^2)/(6*e^2) - ((e*f - d*g)*p*(f + g*x^2)^2)/(12*e*g) - (p*(f + g*x^2)^3)/(18*g) - ((e*f - d*g)^3*p*Log[d + e*x^2])/(6*e^3*g) + ((f + g*x^2)^3*Log[c*(d + e*x^2)^p])/(6*g)","A",4,3,23,0.1304,1,"{2475, 2395, 43}"
326,1,153,0,0.2029649,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x} \, dx","Int[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x,x]","\frac{1}{2} f^2 p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\right)+\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{d g^2 p x^2}{4 e}-f g p x^2-\frac{1}{8} g^2 p x^4","\frac{1}{2} f^2 p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\right)+\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{d g^2 p x^2}{4 e}-f g p x^2-\frac{1}{8} g^2 p x^4",1,"-(f*g*p*x^2) + (d*g^2*p*x^2)/(4*e) - (g^2*p*x^4)/8 - (d^2*g^2*p*Log[d + e*x^2])/(4*e^2) + (g^2*x^4*Log[c*(d + e*x^2)^p])/4 + (f*g*(d + e*x^2)*Log[c*(d + e*x^2)^p])/e + (f^2*Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p])/2 + (f^2*p*PolyLog[2, 1 + (e*x^2)/d])/2","A",10,8,25,0.3200,1,"{2475, 43, 2416, 2389, 2295, 2394, 2315, 2395}"
327,1,135,0,0.1931421,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^3} \, dx","Int[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^3,x]","f g p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\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}-\frac{1}{2} g^2 p x^2","f g p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\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}-\frac{1}{2} g^2 p x^2",1,"-(g^2*p*x^2)/2 + (e*f^2*p*Log[x])/d - (e*f^2*p*Log[d + e*x^2])/(2*d) - (f^2*Log[c*(d + e*x^2)^p])/(2*x^2) + (g^2*(d + e*x^2)*Log[c*(d + e*x^2)^p])/(2*e) + f*g*Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p] + f*g*p*PolyLog[2, 1 + (e*x^2)/d]","A",11,11,25,0.4400,1,"{2475, 43, 2416, 2389, 2295, 2395, 36, 29, 31, 2394, 2315}"
328,1,172,0,0.2234548,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^5} \, dx","Int[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^5,x]","\frac{1}{2} g^2 p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\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{PolyLog}\left(2,\frac{e x^2}{d}+1\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}",1,"-(e*f^2*p)/(4*d*x^2) - (e^2*f^2*p*Log[x])/(2*d^2) + (2*e*f*g*p*Log[x])/d + (e^2*f^2*p*Log[d + e*x^2])/(4*d^2) - (e*f*g*p*Log[d + e*x^2])/d - (f^2*Log[c*(d + e*x^2)^p])/(4*x^4) - (f*g*Log[c*(d + e*x^2)^p])/x^2 + (g^2*Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p])/2 + (g^2*p*PolyLog[2, 1 + (e*x^2)/d])/2","A",12,10,25,0.4000,1,"{2475, 43, 2416, 2395, 44, 36, 29, 31, 2394, 2315}"
329,1,130,0,0.208371,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^7} \, dx","Int[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^7,x]","-\frac{\left(f+g x^2\right)^3 \log \left(c \left(d+e x^2\right)^p\right)}{6 f x^6}+\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 p (e f-3 d g)}{6 d^2 x^2}-\frac{p (e f-d g)^3 \log \left(d+e x^2\right)}{6 d^3 f}-\frac{e f^2 p}{12 d x^4}","-\frac{\left(f+g x^2\right)^3 \log \left(c \left(d+e x^2\right)^p\right)}{6 f x^6}+\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 p (e f-3 d g)}{6 d^2 x^2}-\frac{p (e f-d g)^3 \log \left(d+e x^2\right)}{6 d^3 f}-\frac{e f^2 p}{12 d x^4}",1,"-(e*f^2*p)/(12*d*x^4) + (e*f*(e*f - 3*d*g)*p)/(6*d^2*x^2) + (e*(e^2*f^2 - 3*d*e*f*g + 3*d^2*g^2)*p*Log[x])/(3*d^3) - ((e*f - d*g)^3*p*Log[d + e*x^2])/(6*d^3*f) - ((f + g*x^2)^3*Log[c*(d + e*x^2)^p])/(6*f*x^6)","A",5,5,25,0.2000,1,"{2475, 37, 2414, 12, 88}"
330,1,216,0,0.2897026,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^9} \, dx","Int[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^9,x]","-\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 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^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 f p (3 e f-8 d g)}{48 d^2 x^4}-\frac{e f^2 p}{24 d x^6}","-\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 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^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 f p (3 e f-8 d g)}{48 d^2 x^4}-\frac{e f^2 p}{24 d x^6}",1,"-(e*f^2*p)/(24*d*x^6) + (e*f*(3*e*f - 8*d*g)*p)/(48*d^2*x^4) - (e*(3*e^2*f^2 - 8*d*e*f*g + 6*d^2*g^2)*p)/(24*d^3*x^2) - (e^2*(3*e^2*f^2 - 8*d*e*f*g + 6*d^2*g^2)*p*Log[x])/(12*d^4) + (e^2*(3*e^2*f^2 - 8*d*e*f*g + 6*d^2*g^2)*p*Log[d + e*x^2])/(24*d^4) - (f^2*Log[c*(d + e*x^2)^p])/(8*x^8) - (f*g*Log[c*(d + e*x^2)^p])/(3*x^6) - (g^2*Log[c*(d + e*x^2)^p])/(4*x^4)","A",5,5,25,0.2000,1,"{2475, 43, 2414, 12, 893}"
331,1,253,0,0.3334182,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^{11}} \, dx","Int[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^11,x]","-\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^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^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 f p (2 e f-5 d g)}{60 d^2 x^6}-\frac{e f^2 p}{40 d x^8}","-\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^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^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 f p (2 e f-5 d g)}{60 d^2 x^6}-\frac{e f^2 p}{40 d x^8}",1,"-(e*f^2*p)/(40*d*x^8) + (e*f*(2*e*f - 5*d*g)*p)/(60*d^2*x^6) - (e*(6*e^2*f^2 - 15*d*e*f*g + 10*d^2*g^2)*p)/(120*d^3*x^4) + (e^2*(6*e^2*f^2 - 15*d*e*f*g + 10*d^2*g^2)*p)/(60*d^4*x^2) + (e^3*(6*e^2*f^2 - 15*d*e*f*g + 10*d^2*g^2)*p*Log[x])/(30*d^5) - (e^3*(6*e^2*f^2 - 15*d*e*f*g + 10*d^2*g^2)*p*Log[d + e*x^2])/(60*d^5) - (f^2*Log[c*(d + e*x^2)^p])/(10*x^10) - (f*g*Log[c*(d + e*x^2)^p])/(4*x^8) - (g^2*Log[c*(d + e*x^2)^p])/(6*x^6)","A",5,5,25,0.2000,1,"{2475, 43, 2414, 12, 893}"
332,1,278,0,0.2364721,"\int x^2 \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[x^2*(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","\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^2 f g p x}{5 e^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^2 g^2 p x^3}{21 e^2}+\frac{2 d^3 g^2 p x}{7 e^3}-\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 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","\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^2 f g p x}{5 e^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^2 g^2 p x^3}{21 e^2}+\frac{2 d^3 g^2 p x}{7 e^3}-\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 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,"(2*d*f^2*p*x)/(3*e) - (4*d^2*f*g*p*x)/(5*e^2) + (2*d^3*g^2*p*x)/(7*e^3) - (2*f^2*p*x^3)/9 + (4*d*f*g*p*x^3)/(15*e) - (2*d^2*g^2*p*x^3)/(21*e^2) - (4*f*g*p*x^5)/25 + (2*d*g^2*p*x^5)/(35*e) - (2*g^2*p*x^7)/49 - (2*d^(3/2)*f^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*e^(3/2)) + (4*d^(5/2)*f*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(5*e^(5/2)) - (2*d^(7/2)*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(7*e^(7/2)) + (f^2*x^3*Log[c*(d + e*x^2)^p])/3 + (2*f*g*x^5*Log[c*(d + e*x^2)^p])/5 + (g^2*x^7*Log[c*(d + e*x^2)^p])/7","A",14,4,25,0.1600,1,"{2476, 2455, 302, 205}"
333,1,221,0,0.1628787,"\int \left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right) \, dx","Int[(f + g*x^2)^2*Log[c*(d + e*x^2)^p],x]","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^2 g^2 p x}{5 e^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 \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","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^2 g^2 p x}{5 e^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 \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,"-2*f^2*p*x + (4*d*f*g*p*x)/(3*e) - (2*d^2*g^2*p*x)/(5*e^2) - (4*f*g*p*x^3)/9 + (2*d*g^2*p*x^3)/(15*e) - (2*g^2*p*x^5)/25 + (2*Sqrt[d]*f^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (4*d^(3/2)*f*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*e^(3/2)) + (2*d^(5/2)*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(5*e^(5/2)) + f^2*x*Log[c*(d + e*x^2)^p] + (2*f*g*x^3*Log[c*(d + e*x^2)^p])/3 + (g^2*x^5*Log[c*(d + e*x^2)^p])/5","A",13,6,22,0.2727,1,"{2471, 2448, 321, 205, 2455, 302}"
334,1,178,0,0.1552544,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^2} \, dx","Int[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^2,x]","-\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","-\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,"-4*f*g*p*x + (2*d*g^2*p*x)/(3*e) - (2*g^2*p*x^3)/9 + (2*Sqrt[e]*f^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[d] + (4*Sqrt[d]*f*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (2*d^(3/2)*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*e^(3/2)) - (f^2*Log[c*(d + e*x^2)^p])/x + 2*f*g*x*Log[c*(d + e*x^2)^p] + (g^2*x^3*Log[c*(d + e*x^2)^p])/3","A",11,6,25,0.2400,1,"{2476, 2448, 321, 205, 2455, 302}"
335,1,169,0,0.146754,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^4} \, dx","Int[((f + g*x^2)^2*Log[c*(d + e*x^2)^p])/x^4,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","-\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*e*f^2*p)/(3*d*x) - 2*g^2*p*x - (2*e^(3/2)*f^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*d^(3/2)) + (4*Sqrt[e]*f*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[d] + (2*Sqrt[d]*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[e] - (f^2*Log[c*(d + e*x^2)^p])/(3*x^3) - (2*f*g*Log[c*(d + e*x^2)^p])/x + g^2*x*Log[c*(d + e*x^2)^p]","A",10,6,25,0.2400,1,"{2476, 2448, 321, 205, 2455, 325}"
336,1,200,0,0.1707218,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^6} \, dx","Int[((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^2 f^2 p}{5 d^2 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 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}}","-\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^2 f^2 p}{5 d^2 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 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*e*f^2*p)/(15*d*x^3) + (2*e^2*f^2*p)/(5*d^2*x) - (4*e*f*g*p)/(3*d*x) + (2*e^(5/2)*f^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(5*d^(5/2)) - (4*e^(3/2)*f*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*d^(3/2)) + (2*Sqrt[e]*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/Sqrt[d] - (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","A",11,4,25,0.1600,1,"{2476, 2455, 325, 205}"
337,1,252,0,0.2064526,"\int \frac{\left(f+g x^2\right)^2 \log \left(c \left(d+e x^2\right)^p\right)}{x^8} \, dx","Int[((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^2 f^2 p}{21 d^2 x^3}-\frac{2 e^3 f^2 p}{7 d^3 x}-\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^2 f g p}{5 d^2 x}+\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 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}","-\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^2 f^2 p}{21 d^2 x^3}-\frac{2 e^3 f^2 p}{7 d^3 x}-\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^2 f g p}{5 d^2 x}+\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 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)/(35*d*x^5) + (2*e^2*f^2*p)/(21*d^2*x^3) - (4*e*f*g*p)/(15*d*x^3) - (2*e^3*f^2*p)/(7*d^3*x) + (4*e^2*f*g*p)/(5*d^2*x) - (2*e*g^2*p)/(3*d*x) - (2*e^(7/2)*f^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(7*d^(7/2)) + (4*e^(5/2)*f*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(5*d^(5/2)) - (2*e^(3/2)*g^2*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*d^(3/2)) - (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)","A",14,4,25,0.1600,1,"{2476, 2455, 325, 205}"
338,1,188,0,0.2759343,"\int \frac{x^5 \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Int[(x^5*Log[c*(d + e*x^2)^p])/(f + g*x^2),x]","\frac{f^2 p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{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{d p x^2}{4 e g}+\frac{f p x^2}{2 g^2}-\frac{p x^4}{8 g}","\frac{f^2 p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{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{d p x^2}{4 e g}+\frac{f p x^2}{2 g^2}-\frac{p x^4}{8 g}",1,"(f*p*x^2)/(2*g^2) + (d*p*x^2)/(4*e*g) - (p*x^4)/(8*g) - (d^2*p*Log[d + e*x^2])/(4*e^2*g) + (x^4*Log[c*(d + e*x^2)^p])/(4*g) - (f*(d + e*x^2)*Log[c*(d + e*x^2)^p])/(2*e*g^2) + (f^2*Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)])/(2*g^3) + (f^2*p*PolyLog[2, -((g*(d + e*x^2))/(e*f - d*g))])/(2*g^3)","A",11,9,25,0.3600,1,"{2475, 43, 2416, 2389, 2295, 2395, 2394, 2393, 2391}"
339,1,112,0,0.1877005,"\int \frac{x^3 \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Int[(x^3*Log[c*(d + e*x^2)^p])/(f + g*x^2),x]","-\frac{f p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{2 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{p x^2}{2 g}","-\frac{f p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{2 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{p x^2}{2 g}",1,"-(p*x^2)/(2*g) + ((d + e*x^2)*Log[c*(d + e*x^2)^p])/(2*e*g) - (f*Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)])/(2*g^2) - (f*p*PolyLog[2, -((g*(d + e*x^2))/(e*f - d*g))])/(2*g^2)","A",8,8,25,0.3200,1,"{2475, 43, 2416, 2389, 2295, 2394, 2393, 2391}"
340,1,70,0,0.09544,"\int \frac{x \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Int[(x*Log[c*(d + e*x^2)^p])/(f + g*x^2),x]","\frac{p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\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{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\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}",1,"(Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)])/(2*g) + (p*PolyLog[2, -((g*(d + e*x^2))/(e*f - d*g))])/(2*g)","A",4,4,23,0.1739,1,"{2475, 2394, 2393, 2391}"
341,1,119,0,0.2063256,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x \left(f+g x^2\right)} \, dx","Int[Log[c*(d + e*x^2)^p]/(x*(f + g*x^2)),x]","-\frac{p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{2 f}+\frac{p \text{PolyLog}\left(2,\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{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{2 f}+\frac{p \text{PolyLog}\left(2,\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}",1,"(Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p])/(2*f) - (Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)])/(2*f) - (p*PolyLog[2, -((g*(d + e*x^2))/(e*f - d*g))])/(2*f) + (p*PolyLog[2, 1 + (e*x^2)/d])/(2*f)","A",8,9,25,0.3600,1,"{2475, 36, 29, 31, 2416, 2394, 2315, 2393, 2391}"
342,1,176,0,0.2666199,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x^3 \left(f+g x^2\right)} \, dx","Int[Log[c*(d + e*x^2)^p]/(x^3*(f + g*x^2)),x]","\frac{g p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{2 f^2}-\frac{g p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\right)}{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{e p \log \left(d+e x^2\right)}{2 d f}+\frac{e p \log (x)}{d f}","\frac{g p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{2 f^2}-\frac{g p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\right)}{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{e p \log \left(d+e x^2\right)}{2 d f}+\frac{e p \log (x)}{d f}",1,"(e*p*Log[x])/(d*f) - (e*p*Log[d + e*x^2])/(2*d*f) - Log[c*(d + e*x^2)^p]/(2*f*x^2) - (g*Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p])/(2*f^2) + (g*Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)])/(2*f^2) + (g*p*PolyLog[2, -((g*(d + e*x^2))/(e*f - d*g))])/(2*f^2) - (g*p*PolyLog[2, 1 + (e*x^2)/d])/(2*f^2)","A",12,11,25,0.4400,1,"{2475, 44, 2416, 2395, 36, 29, 31, 2394, 2315, 2393, 2391}"
343,1,667,0,0.7179446,"\int \frac{x^4 \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Int[(x^4*Log[c*(d + e*x^2)^p])/(f + g*x^2),x]","\frac{i f^{3/2} p \text{PolyLog}\left(2,1+\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 g^{5/2}}+\frac{i f^{3/2} p \text{PolyLog}\left(2,1-\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 g^{5/2}}-\frac{i f^{3/2} p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{g^{5/2}}+\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{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{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}","\frac{i f^{3/2} p \text{PolyLog}\left(2,1+\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 g^{5/2}}+\frac{i f^{3/2} p \text{PolyLog}\left(2,1-\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 g^{5/2}}-\frac{i f^{3/2} p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{g^{5/2}}+\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{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{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*f*p*x)/g^2 + (2*d*p*x)/(3*e*g) - (2*p*x^3)/(9*g) - (2*Sqrt[d]*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[e]*g^2) - (2*d^(3/2)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*e^(3/2)*g) + (2*f^(3/2)*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/g^(5/2) - (f^(3/2)*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/g^(5/2) - (f^(3/2)*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/g^(5/2) - (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*f^(3/2)*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/g^(5/2) + ((I/2)*f^(3/2)*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/g^(5/2) + ((I/2)*f^(3/2)*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/g^(5/2)","A",21,13,25,0.5200,1,"{2476, 2448, 321, 205, 2455, 302, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
344,1,585,0,0.5941256,"\int \frac{x^2 \log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Int[(x^2*Log[c*(d + e*x^2)^p])/(f + g*x^2),x]","-\frac{i \sqrt{f} p \text{PolyLog}\left(2,1+\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 g^{3/2}}-\frac{i \sqrt{f} p \text{PolyLog}\left(2,1-\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 g^{3/2}}+\frac{i \sqrt{f} p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{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{\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{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}","-\frac{i \sqrt{f} p \text{PolyLog}\left(2,1+\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 g^{3/2}}-\frac{i \sqrt{f} p \text{PolyLog}\left(2,1-\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 g^{3/2}}+\frac{i \sqrt{f} p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{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{\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{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,"(-2*p*x)/g + (2*Sqrt[d]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[e]*g) - (2*Sqrt[f]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/g^(3/2) + (Sqrt[f]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/g^(3/2) + (Sqrt[f]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/g^(3/2) + (x*Log[c*(d + e*x^2)^p])/g - (Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/g^(3/2) + (I*Sqrt[f]*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/g^(3/2) - ((I/2)*Sqrt[f]*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/g^(3/2) - ((I/2)*Sqrt[f]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/g^(3/2)","A",17,11,25,0.4400,1,"{2476, 2448, 321, 205, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
345,1,533,0,0.4254352,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{f+g x^2} \, dx","Int[Log[c*(d + e*x^2)^p]/(f + g*x^2),x]","\frac{i p \text{PolyLog}\left(2,1+\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} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\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{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{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}}","\frac{i p \text{PolyLog}\left(2,1+\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} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{\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{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{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,"(2*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + (ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/(Sqrt[f]*Sqrt[g]) - (I*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g]) + ((I/2)*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*Sqrt[g])","A",12,8,22,0.3636,1,"{205, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
346,1,581,0,0.5969576,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x^2 \left(f+g x^2\right)} \, dx","Int[Log[c*(d + e*x^2)^p]/(x^2*(f + g*x^2)),x]","-\frac{i \sqrt{g} p \text{PolyLog}\left(2,1+\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}}-\frac{i \sqrt{g} p \text{PolyLog}\left(2,1-\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}}+\frac{i \sqrt{g} p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{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{\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{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}}","-\frac{i \sqrt{g} p \text{PolyLog}\left(2,1+\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}}-\frac{i \sqrt{g} p \text{PolyLog}\left(2,1-\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}}+\frac{i \sqrt{g} p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{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{\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{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,"(2*Sqrt[e]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*f) - (2*Sqrt[g]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/f^(3/2) + (Sqrt[g]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/f^(3/2) + (Sqrt[g]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/f^(3/2) - Log[c*(d + e*x^2)^p]/(f*x) - (Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/f^(3/2) + (I*Sqrt[g]*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/f^(3/2) - ((I/2)*Sqrt[g]*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/f^(3/2) - ((I/2)*Sqrt[g]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/f^(3/2)","A",16,10,25,0.4000,1,"{2476, 2455, 205, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
347,1,651,0,0.6498229,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x^4 \left(f+g x^2\right)} \, dx","Int[Log[c*(d + e*x^2)^p]/(x^4*(f + g*x^2)),x]","\frac{i g^{3/2} p \text{PolyLog}\left(2,1+\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^{5/2}}+\frac{i g^{3/2} p \text{PolyLog}\left(2,1-\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^{5/2}}-\frac{i g^{3/2} p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{f^{5/2}}+\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{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{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}}","\frac{i g^{3/2} p \text{PolyLog}\left(2,1+\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^{5/2}}+\frac{i g^{3/2} p \text{PolyLog}\left(2,1-\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^{5/2}}-\frac{i g^{3/2} p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{f^{5/2}}+\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{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{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*e*p)/(3*d*f*x) - (2*e^(3/2)*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(3*d^(3/2)*f) - (2*Sqrt[e]*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*f^2) + (2*g^(3/2)*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/f^(5/2) - (g^(3/2)*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/f^(5/2) - (g^(3/2)*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/f^(5/2) - 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) - (I*g^(3/2)*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/f^(5/2) + ((I/2)*g^(3/2)*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/f^(5/2) + ((I/2)*g^(3/2)*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/f^(5/2)","A",19,11,25,0.4400,1,"{2476, 2455, 325, 205, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
348,1,199,0,0.2834168,"\int \frac{x^5 \log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Int[(x^5*Log[c*(d + e*x^2)^p])/(f + g*x^2)^2,x]","-\frac{f p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{g^3}-\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{p x^2}{2 g^2}","-\frac{f p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{g^3}-\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{p x^2}{2 g^2}",1,"-(p*x^2)/(2*g^2) + (e*f^2*p*Log[d + e*x^2])/(2*g^3*(e*f - d*g)) + ((d + e*x^2)*Log[c*(d + e*x^2)^p])/(2*e*g^2) - (f^2*Log[c*(d + e*x^2)^p])/(2*g^3*(f + g*x^2)) - (e*f^2*p*Log[f + g*x^2])/(2*g^3*(e*f - d*g)) - (f*Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)])/g^3 - (f*p*PolyLog[2, -((g*(d + e*x^2))/(e*f - d*g))])/g^3","A",12,11,25,0.4400,1,"{2475, 43, 2416, 2389, 2295, 2395, 36, 31, 2394, 2393, 2391}"
349,1,155,0,0.2212047,"\int \frac{x^3 \log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Int[(x^3*Log[c*(d + e*x^2)^p])/(f + g*x^2)^2,x]","\frac{p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{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{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)}","\frac{p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{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{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])/(2*g^2*(e*f - d*g)) + (f*Log[c*(d + e*x^2)^p])/(2*g^2*(f + g*x^2)) + (e*f*p*Log[f + g*x^2])/(2*g^2*(e*f - d*g)) + (Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)])/(2*g^2) + (p*PolyLog[2, -((g*(d + e*x^2))/(e*f - d*g))])/(2*g^2)","A",10,9,25,0.3600,1,"{2475, 43, 2416, 2395, 36, 31, 2394, 2393, 2391}"
350,1,83,0,0.074348,"\int \frac{x \log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Int[(x*Log[c*(d + e*x^2)^p])/(f + g*x^2)^2,x]","-\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)}","-\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,"(e*p*Log[d + e*x^2])/(2*g*(e*f - d*g)) - Log[c*(d + e*x^2)^p]/(2*g*(f + g*x^2)) - (e*p*Log[f + g*x^2])/(2*g*(e*f - d*g))","A",5,4,23,0.1739,1,"{2475, 2395, 36, 31}"
351,1,201,0,0.2825182,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x \left(f+g x^2\right)^2} \, dx","Int[Log[c*(d + e*x^2)^p]/(x*(f + g*x^2)^2),x]","-\frac{p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{2 f^2}+\frac{p \text{PolyLog}\left(2,\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{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)}","-\frac{p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{2 f^2}+\frac{p \text{PolyLog}\left(2,\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{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*p*Log[d + e*x^2])/(2*f*(e*f - d*g)) + Log[c*(d + e*x^2)^p]/(2*f*(f + g*x^2)) + (Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p])/(2*f^2) + (e*p*Log[f + g*x^2])/(2*f*(e*f - d*g)) - (Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)])/(2*f^2) - (p*PolyLog[2, -((g*(d + e*x^2))/(e*f - d*g))])/(2*f^2) + (p*PolyLog[2, 1 + (e*x^2)/d])/(2*f^2)","A",12,10,25,0.4000,1,"{2475, 44, 2416, 2394, 2315, 2395, 36, 31, 2393, 2391}"
352,1,251,0,0.3408786,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x^3 \left(f+g x^2\right)^2} \, dx","Int[Log[c*(d + e*x^2)^p]/(x^3*(f + g*x^2)^2),x]","\frac{g p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{f^3}-\frac{g p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\right)}{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)}{2 f^2 \left(f+g x^2\right)}+\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{\log \left(c \left(d+e x^2\right)^p\right)}{2 f^2 x^2}+\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}","\frac{g p \text{PolyLog}\left(2,-\frac{g \left(d+e x^2\right)}{e f-d g}\right)}{f^3}-\frac{g p \text{PolyLog}\left(2,\frac{e x^2}{d}+1\right)}{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)}{2 f^2 \left(f+g x^2\right)}+\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{\log \left(c \left(d+e x^2\right)^p\right)}{2 f^2 x^2}+\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*p*Log[x])/(d*f^2) - (e*p*Log[d + e*x^2])/(2*d*f^2) + (e*g*p*Log[d + e*x^2])/(2*f^2*(e*f - d*g)) - Log[c*(d + e*x^2)^p]/(2*f^2*x^2) - (g*Log[c*(d + e*x^2)^p])/(2*f^2*(f + g*x^2)) - (g*Log[-((e*x^2)/d)]*Log[c*(d + e*x^2)^p])/f^3 - (e*g*p*Log[f + g*x^2])/(2*f^2*(e*f - d*g)) + (g*Log[c*(d + e*x^2)^p]*Log[(e*(f + g*x^2))/(e*f - d*g)])/f^3 + (g*p*PolyLog[2, -((g*(d + e*x^2))/(e*f - d*g))])/f^3 - (g*p*PolyLog[2, 1 + (e*x^2)/d])/f^3","A",16,11,25,0.4400,1,"{2475, 44, 2416, 2395, 36, 29, 31, 2394, 2315, 2393, 2391}"
353,1,802,0,1.6875603,"\int \frac{x^4 \log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Int[(x^4*Log[c*(d + e*x^2)^p])/(f + g*x^2)^2,x]","-\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{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 g^{5/2}}-\frac{3 i \sqrt{f} p \text{PolyLog}\left(2,\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{PolyLog}\left(2,1-\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}}","-\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{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 g^{5/2}}-\frac{3 i \sqrt{f} p \text{PolyLog}\left(2,\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{PolyLog}\left(2,1-\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,"(-2*p*x)/g^2 + (2*Sqrt[d]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[e]*g^2) + (Sqrt[d]*Sqrt[e]*f*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(g^2*(e*f - d*g)) - (e*(-f)^(3/2)*p*Log[Sqrt[-f] - Sqrt[g]*x])/(2*g^(5/2)*(e*f - d*g)) - (3*Sqrt[f]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/g^(5/2) + (3*Sqrt[f]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(2*g^(5/2)) + (3*Sqrt[f]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(2*g^(5/2)) + (e*(-f)^(3/2)*p*Log[Sqrt[-f] + Sqrt[g]*x])/(2*g^(5/2)*(e*f - d*g)) + (x*Log[c*(d + e*x^2)^p])/g^2 - (f*Log[c*(d + e*x^2)^p])/(4*g^(5/2)*(Sqrt[-f] - Sqrt[g]*x)) + (f*Log[c*(d + e*x^2)^p])/(4*g^(5/2)*(Sqrt[-f] + Sqrt[g]*x)) - (3*Sqrt[f]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/(2*g^(5/2)) + (((3*I)/2)*Sqrt[f]*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/g^(5/2) - (((3*I)/4)*Sqrt[f]*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/g^(5/2) - (((3*I)/4)*Sqrt[f]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/g^(5/2)","A",43,16,25,0.6400,1,"{2476, 2448, 321, 205, 2471, 2463, 801, 635, 260, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
354,1,746,0,1.5125352,"\int \frac{x^2 \log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Int[(x^2*Log[c*(d + e*x^2)^p])/(f + g*x^2)^2,x]","\frac{i p \text{PolyLog}\left(2,1+\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)}{4 \sqrt{f} g^{3/2}}+\frac{i p \text{PolyLog}\left(2,1-\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)}{4 \sqrt{f} g^{3/2}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 \sqrt{f} g^{3/2}}+\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{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{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}}","\frac{i p \text{PolyLog}\left(2,1+\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)}{4 \sqrt{f} g^{3/2}}+\frac{i p \text{PolyLog}\left(2,1-\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)}{4 \sqrt{f} g^{3/2}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 \sqrt{f} g^{3/2}}+\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{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{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,"-((Sqrt[d]*Sqrt[e]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(g*(e*f - d*g))) - (e*Sqrt[-f]*p*Log[Sqrt[-f] - Sqrt[g]*x])/(2*g^(3/2)*(e*f - d*g)) + (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*g^(3/2)) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(2*Sqrt[f]*g^(3/2)) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(2*Sqrt[f]*g^(3/2)) + (e*Sqrt[-f]*p*Log[Sqrt[-f] + Sqrt[g]*x])/(2*g^(3/2)*(e*f - d*g)) + Log[c*(d + e*x^2)^p]/(4*g^(3/2)*(Sqrt[-f] - Sqrt[g]*x)) - Log[c*(d + e*x^2)^p]/(4*g^(3/2)*(Sqrt[-f] + Sqrt[g]*x)) + (ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/(2*Sqrt[f]*g^(3/2)) - ((I/2)*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(Sqrt[f]*g^(3/2)) + ((I/4)*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*g^(3/2)) + ((I/4)*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(Sqrt[f]*g^(3/2))","A",40,14,25,0.5600,1,"{2476, 2471, 2463, 801, 635, 205, 260, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
355,1,751,0,0.8245983,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{\left(f+g x^2\right)^2} \, dx","Int[Log[c*(d + e*x^2)^p]/(f + g*x^2)^2,x]","\frac{i p \text{PolyLog}\left(2,1+\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)}{4 f^{3/2} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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)}{4 f^{3/2} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 f^{3/2} \sqrt{g}}+\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{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{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}}","\frac{i p \text{PolyLog}\left(2,1+\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)}{4 f^{3/2} \sqrt{g}}+\frac{i p \text{PolyLog}\left(2,1-\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)}{4 f^{3/2} \sqrt{g}}-\frac{i p \text{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 f^{3/2} \sqrt{g}}+\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{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{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,"(Sqrt[d]*Sqrt[e]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(f*(e*f - d*g)) - (e*p*Log[Sqrt[-f] - Sqrt[g]*x])/(2*Sqrt[-f]*Sqrt[g]*(e*f - d*g)) + (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(f^(3/2)*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(2*f^(3/2)*Sqrt[g]) - (p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(2*f^(3/2)*Sqrt[g]) + (e*p*Log[Sqrt[-f] + Sqrt[g]*x])/(2*Sqrt[-f]*Sqrt[g]*(e*f - d*g)) - Log[c*(d + e*x^2)^p]/(4*f*Sqrt[g]*(Sqrt[-f] - Sqrt[g]*x)) + Log[c*(d + e*x^2)^p]/(4*f*Sqrt[g]*(Sqrt[-f] + Sqrt[g]*x)) + (ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/(2*f^(3/2)*Sqrt[g]) - ((I/2)*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/(f^(3/2)*Sqrt[g]) + ((I/4)*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(f^(3/2)*Sqrt[g]) + ((I/4)*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(f^(3/2)*Sqrt[g])","A",26,13,22,0.5909,1,"{2471, 2463, 801, 635, 205, 260, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
356,1,803,0,1.541663,"\int \frac{\log \left(c \left(d+e x^2\right)^p\right)}{x^2 \left(f+g x^2\right)^2} \, dx","Int[Log[c*(d + e*x^2)^p]/(x^2*(f + g*x^2)^2),x]","-\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{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 f^{5/2}}-\frac{3 i \sqrt{g} p \text{PolyLog}\left(2,\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{PolyLog}\left(2,1-\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}}","-\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{PolyLog}\left(2,1-\frac{2 \sqrt{f}}{\sqrt{f}-i \sqrt{g} x}\right)}{2 f^{5/2}}-\frac{3 i \sqrt{g} p \text{PolyLog}\left(2,\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{PolyLog}\left(2,1-\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,"(2*Sqrt[e]*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(Sqrt[d]*f^2) - (Sqrt[d]*Sqrt[e]*g*p*ArcTan[(Sqrt[e]*x)/Sqrt[d]])/(f^2*(e*f - d*g)) - (e*Sqrt[g]*p*Log[Sqrt[-f] - Sqrt[g]*x])/(2*(-f)^(3/2)*(e*f - d*g)) - (3*Sqrt[g]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/f^(5/2) + (3*Sqrt[g]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(-2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(2*f^(5/2)) + (3*Sqrt[g]*p*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[(2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/(2*f^(5/2)) + (e*Sqrt[g]*p*Log[Sqrt[-f] + Sqrt[g]*x])/(2*(-f)^(3/2)*(e*f - d*g)) - Log[c*(d + e*x^2)^p]/(f^2*x) + (Sqrt[g]*Log[c*(d + e*x^2)^p])/(4*f^2*(Sqrt[-f] - Sqrt[g]*x)) - (Sqrt[g]*Log[c*(d + e*x^2)^p])/(4*f^2*(Sqrt[-f] + Sqrt[g]*x)) - (3*Sqrt[g]*ArcTan[(Sqrt[g]*x)/Sqrt[f]]*Log[c*(d + e*x^2)^p])/(2*f^(5/2)) + (((3*I)/2)*Sqrt[g]*p*PolyLog[2, 1 - (2*Sqrt[f])/(Sqrt[f] - I*Sqrt[g]*x)])/f^(5/2) - (((3*I)/4)*Sqrt[g]*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] - Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] - Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/f^(5/2) - (((3*I)/4)*Sqrt[g]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*(Sqrt[-d] + Sqrt[e]*x))/((I*Sqrt[e]*Sqrt[f] + Sqrt[-d]*Sqrt[g])*(Sqrt[f] - I*Sqrt[g]*x))])/f^(5/2)","A",42,15,25,0.6000,1,"{2476, 2455, 205, 2471, 2463, 801, 635, 260, 2470, 12, 4928, 4856, 2402, 2315, 2447}"
357,1,163,0,0.1454705,"\int \frac{\log \left(c \left(a+b x^2\right)^n\right)}{a+b x^2} \, dx","Int[Log[c*(a + b*x^2)^n]/(a + b*x^2),x]","\frac{i n \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\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 \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}}","\frac{i n \text{PolyLog}\left(2,1-\frac{2 \sqrt{a}}{\sqrt{a}+i \sqrt{b} x}\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 \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,"(I*n*ArcTan[(Sqrt[b]*x)/Sqrt[a]]^2)/(Sqrt[a]*Sqrt[b]) + (2*n*ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[(2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/(Sqrt[a]*Sqrt[b]) + (ArcTan[(Sqrt[b]*x)/Sqrt[a]]*Log[c*(a + b*x^2)^n])/(Sqrt[a]*Sqrt[b]) + (I*n*PolyLog[2, 1 - (2*Sqrt[a])/(Sqrt[a] + I*Sqrt[b]*x)])/(Sqrt[a]*Sqrt[b])","A",6,7,22,0.3182,1,"{205, 2470, 12, 4920, 4854, 2402, 2315}"
358,1,239,0,0.28966,"\int \frac{\log \left(1-x^2\right)}{2-x^2} \, dx","Int[Log[1 - x^2]/(2 - x^2),x]","-\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{2}}{x+\sqrt{2}}\right)}{\sqrt{2}}+\frac{\text{PolyLog}\left(2,\frac{4 (1-x)}{\left(2-\sqrt{2}\right) \left(x+\sqrt{2}\right)}+1\right)}{2 \sqrt{2}}+\frac{\text{PolyLog}\left(2,1-\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}}","-\frac{\text{PolyLog}\left(2,1-\frac{2 \sqrt{2}}{x+\sqrt{2}}\right)}{\sqrt{2}}+\frac{\text{PolyLog}\left(2,\frac{4 (1-x)}{\left(2-\sqrt{2}\right) \left(x+\sqrt{2}\right)}+1\right)}{2 \sqrt{2}}+\frac{\text{PolyLog}\left(2,1-\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,"Sqrt[2]*ArcTanh[x/Sqrt[2]]*Log[(2*Sqrt[2])/(Sqrt[2] + x)] - (ArcTanh[x/Sqrt[2]]*Log[(-4*(1 - x))/((2 - Sqrt[2])*(Sqrt[2] + x))])/Sqrt[2] - (ArcTanh[x/Sqrt[2]]*Log[(4*(1 + x))/((2 + Sqrt[2])*(Sqrt[2] + x))])/Sqrt[2] + (ArcTanh[x/Sqrt[2]]*Log[1 - x^2])/Sqrt[2] - PolyLog[2, 1 - (2*Sqrt[2])/(Sqrt[2] + x)]/Sqrt[2] + PolyLog[2, 1 + (4*(1 - x))/((2 - Sqrt[2])*(Sqrt[2] + x))]/(2*Sqrt[2]) + PolyLog[2, 1 - (4*(1 + x))/((2 + Sqrt[2])*(Sqrt[2] + x))]/(2*Sqrt[2])","A",12,8,18,0.4444,1,"{206, 2470, 12, 5992, 5920, 2402, 2315, 2447}"
359,1,217,0,0.2530169,"\int \frac{\log \left(d+e x^2\right)}{1-x^2} \, dx","Int[Log[d + e*x^2]/(1 - x^2),x]","\frac{1}{2} \text{PolyLog}\left(2,1-\frac{2 \left(\sqrt{-d}-\sqrt{e} x\right)}{(x+1) \left(\sqrt{-d}-\sqrt{e}\right)}\right)+\frac{1}{2} \text{PolyLog}\left(2,1-\frac{2 \left(\sqrt{-d}+\sqrt{e} x\right)}{(x+1) \left(\sqrt{-d}+\sqrt{e}\right)}\right)-\text{PolyLog}\left(2,1-\frac{2}{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)+2 \log \left(\frac{2}{x+1}\right) \tanh ^{-1}(x)","\frac{1}{2} \text{PolyLog}\left(2,1-\frac{2 \left(\sqrt{-d}-\sqrt{e} x\right)}{(x+1) \left(\sqrt{-d}-\sqrt{e}\right)}\right)+\frac{1}{2} \text{PolyLog}\left(2,1-\frac{2 \left(\sqrt{-d}+\sqrt{e} x\right)}{(x+1) \left(\sqrt{-d}+\sqrt{e}\right)}\right)-\text{PolyLog}\left(2,1-\frac{2}{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)+2 \log \left(\frac{2}{x+1}\right) \tanh ^{-1}(x)",1,"2*ArcTanh[x]*Log[2/(1 + x)] - ArcTanh[x]*Log[(2*(Sqrt[-d] - Sqrt[e]*x))/((Sqrt[-d] - Sqrt[e])*(1 + x))] - ArcTanh[x]*Log[(2*(Sqrt[-d] + Sqrt[e]*x))/((Sqrt[-d] + Sqrt[e])*(1 + x))] + ArcTanh[x]*Log[d + e*x^2] - PolyLog[2, 1 - 2/(1 + x)] + PolyLog[2, 1 - (2*(Sqrt[-d] - Sqrt[e]*x))/((Sqrt[-d] - Sqrt[e])*(1 + x))]/2 + PolyLog[2, 1 - (2*(Sqrt[-d] + Sqrt[e]*x))/((Sqrt[-d] + Sqrt[e])*(1 + x))]/2","A",11,7,18,0.3889,1,"{206, 2470, 5992, 5920, 2402, 2315, 2447}"
360,1,144,0,0.1709981,"\int \frac{\left(f+g x^{3 n}\right) \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((f + g*x^(3*n))*Log[c*(d + e*x^n)^p])/x,x]","\frac{f p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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^2 g p x^n}{3 e^2 n}+\frac{d^3 g p \log \left(d+e x^n\right)}{3 e^3 n}+\frac{d g p x^{2 n}}{6 e n}-\frac{g p x^{3 n}}{9 n}","\frac{f p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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^2 g p x^n}{3 e^2 n}+\frac{d^3 g p \log \left(d+e x^n\right)}{3 e^3 n}+\frac{d g p x^{2 n}}{6 e n}-\frac{g p x^{3 n}}{9 n}",1,"-(d^2*g*p*x^n)/(3*e^2*n) + (d*g*p*x^(2*n))/(6*e*n) - (g*p*x^(3*n))/(9*n) + (d^3*g*p*Log[d + e*x^n])/(3*e^3*n) + (g*x^(3*n)*Log[c*(d + e*x^n)^p])/(3*n) + (f*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (f*p*PolyLog[2, 1 + (e*x^n)/d])/n","A",8,7,25,0.2800,1,"{2475, 14, 2416, 2394, 2315, 2395, 43}"
361,1,124,0,0.1420979,"\int \frac{\left(f+g x^{2 n}\right) \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((f + g*x^(2*n))*Log[c*(d + e*x^n)^p])/x,x]","\frac{f p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{d g p x^n}{2 e n}-\frac{g p x^{2 n}}{4 n}","\frac{f p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{d g p x^n}{2 e n}-\frac{g p x^{2 n}}{4 n}",1,"(d*g*p*x^n)/(2*e*n) - (g*p*x^(2*n))/(4*n) - (d^2*g*p*Log[d + e*x^n])/(2*e^2*n) + (g*x^(2*n)*Log[c*(d + e*x^n)^p])/(2*n) + (f*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (f*p*PolyLog[2, 1 + (e*x^n)/d])/n","A",8,7,25,0.2800,1,"{2475, 14, 2416, 2394, 2315, 2395, 43}"
362,1,83,0,0.10986,"\int \frac{\left(f+g x^n\right) \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((f + g*x^n)*Log[c*(d + e*x^n)^p])/x,x]","\frac{f p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{g p x^n}{n}","\frac{f p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{g p x^n}{n}",1,"-((g*p*x^n)/n) + (g*(d + e*x^n)*Log[c*(d + e*x^n)^p])/(e*n) + (f*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (f*p*PolyLog[2, 1 + (e*x^n)/d])/n","A",7,7,23,0.3043,1,"{2475, 43, 2416, 2389, 2295, 2394, 2315}"
363,1,97,0,0.1405338,"\int \frac{\left(f+g x^{-n}\right) \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((f + g/x^n)*Log[c*(d + e*x^n)^p])/x,x]","\frac{f p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{e g p \log \left(d+e x^n\right)}{d n}+\frac{e g p \log (x)}{d}","\frac{f p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{e g p \log \left(d+e x^n\right)}{d n}+\frac{e g p \log (x)}{d}",1,"(e*g*p*Log[x])/d - (e*g*p*Log[d + e*x^n])/(d*n) - (g*Log[c*(d + e*x^n)^p])/(n*x^n) + (f*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (f*p*PolyLog[2, 1 + (e*x^n)/d])/n","A",9,9,25,0.3600,1,"{2475, 14, 2416, 2395, 36, 29, 31, 2394, 2315}"
364,1,126,0,0.1692078,"\int \frac{\left(f+g x^{-2 n}\right) \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((f + g/x^(2*n))*Log[c*(d + e*x^n)^p])/x,x]","\frac{f p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{e g p x^{-n}}{2 d n}","\frac{f p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{e g p x^{-n}}{2 d n}",1,"-(e*g*p)/(2*d*n*x^n) - (e^2*g*p*Log[x])/(2*d^2) + (e^2*g*p*Log[d + e*x^n])/(2*d^2*n) - (g*Log[c*(d + e*x^n)^p])/(2*n*x^(2*n)) + (f*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (f*p*PolyLog[2, 1 + (e*x^n)/d])/n","A",8,7,25,0.2800,1,"{2475, 14, 2416, 2395, 44, 2394, 2315}"
365,1,327,0,0.3257448,"\int \frac{\left(f+g x^{3 n}\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((f + g*x^(3*n))^2*Log[c*(d + e*x^n)^p])/x,x]","\frac{f^2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{2 d^2 f g p x^n}{3 e^2 n}+\frac{2 d^3 f g p \log \left(d+e x^n\right)}{3 e^3 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{d^3 g^2 p x^{3 n}}{18 e^3 n}-\frac{d^2 g^2 p x^{4 n}}{24 e^2 n}-\frac{d^6 g^2 p \log \left(d+e x^n\right)}{6 e^6 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}","\frac{f^2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{2 d^2 f g p x^n}{3 e^2 n}+\frac{2 d^3 f g p \log \left(d+e x^n\right)}{3 e^3 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{d^3 g^2 p x^{3 n}}{18 e^3 n}-\frac{d^2 g^2 p x^{4 n}}{24 e^2 n}-\frac{d^6 g^2 p \log \left(d+e x^n\right)}{6 e^6 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,"(-2*d^2*f*g*p*x^n)/(3*e^2*n) + (d^5*g^2*p*x^n)/(6*e^5*n) + (d*f*g*p*x^(2*n))/(3*e*n) - (d^4*g^2*p*x^(2*n))/(12*e^4*n) - (2*f*g*p*x^(3*n))/(9*n) + (d^3*g^2*p*x^(3*n))/(18*e^3*n) - (d^2*g^2*p*x^(4*n))/(24*e^2*n) + (d*g^2*p*x^(5*n))/(30*e*n) - (g^2*p*x^(6*n))/(36*n) + (2*d^3*f*g*p*Log[d + e*x^n])/(3*e^3*n) - (d^6*g^2*p*Log[d + e*x^n])/(6*e^6*n) + (2*f*g*x^(3*n)*Log[c*(d + e*x^n)^p])/(3*n) + (g^2*x^(6*n)*Log[c*(d + e*x^n)^p])/(6*n) + (f^2*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (f^2*p*PolyLog[2, 1 + (e*x^n)/d])/n","A",11,7,27,0.2593,1,"{2475, 266, 43, 2416, 2394, 2315, 2395}"
366,1,254,0,0.2673908,"\int \frac{\left(f+g x^{2 n}\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((f + g*x^(2*n))^2*Log[c*(d + e*x^n)^p])/x,x]","\frac{f^2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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^2 f g p \log \left(d+e x^n\right)}{e^2 n}+\frac{d^3 g^2 p x^n}{4 e^3 n}-\frac{d^2 g^2 p x^{2 n}}{8 e^2 n}-\frac{d^4 g^2 p \log \left(d+e x^n\right)}{4 e^4 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}","\frac{f^2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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^2 f g p \log \left(d+e x^n\right)}{e^2 n}+\frac{d^3 g^2 p x^n}{4 e^3 n}-\frac{d^2 g^2 p x^{2 n}}{8 e^2 n}-\frac{d^4 g^2 p \log \left(d+e x^n\right)}{4 e^4 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,"(d*f*g*p*x^n)/(e*n) + (d^3*g^2*p*x^n)/(4*e^3*n) - (f*g*p*x^(2*n))/(2*n) - (d^2*g^2*p*x^(2*n))/(8*e^2*n) + (d*g^2*p*x^(3*n))/(12*e*n) - (g^2*p*x^(4*n))/(16*n) - (d^2*f*g*p*Log[d + e*x^n])/(e^2*n) - (d^4*g^2*p*Log[d + e*x^n])/(4*e^4*n) + (f*g*x^(2*n)*Log[c*(d + e*x^n)^p])/n + (g^2*x^(4*n)*Log[c*(d + e*x^n)^p])/(4*n) + (f^2*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (f^2*p*PolyLog[2, 1 + (e*x^n)/d])/n","A",11,7,27,0.2593,1,"{2475, 266, 43, 2416, 2394, 2315, 2395}"
367,1,176,0,0.1967581,"\int \frac{\left(f+g x^n\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((f + g*x^n)^2*Log[c*(d + e*x^n)^p])/x,x]","\frac{f^2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{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}","\frac{f^2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{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,"(-2*f*g*p*x^n)/n + (d*g^2*p*x^n)/(2*e*n) - (g^2*p*x^(2*n))/(4*n) - (d^2*g^2*p*Log[d + e*x^n])/(2*e^2*n) + (g^2*x^(2*n)*Log[c*(d + e*x^n)^p])/(2*n) + (2*f*g*(d + e*x^n)*Log[c*(d + e*x^n)^p])/(e*n) + (f^2*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (f^2*p*PolyLog[2, 1 + (e*x^n)/d])/n","A",10,8,25,0.3200,1,"{2475, 43, 2416, 2389, 2295, 2394, 2315, 2395}"
368,1,193,0,0.242307,"\int \frac{\left(f+g x^{-n}\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((f + g/x^n)^2*Log[c*(d + e*x^n)^p])/x,x]","\frac{f^2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{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}","\frac{f^2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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{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,"-(e*g^2*p)/(2*d*n*x^n) + (2*e*f*g*p*Log[x])/d - (e^2*g^2*p*Log[x])/(2*d^2) - (2*e*f*g*p*Log[d + e*x^n])/(d*n) + (e^2*g^2*p*Log[d + e*x^n])/(2*d^2*n) - (g^2*Log[c*(d + e*x^n)^p])/(2*n*x^(2*n)) - (2*f*g*Log[c*(d + e*x^n)^p])/(n*x^n) + (f^2*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (f^2*p*PolyLog[2, 1 + (e*x^n)/d])/n","A",12,11,27,0.4074,1,"{2475, 263, 43, 2416, 2395, 44, 36, 29, 31, 2394, 2315}"
369,1,257,0,0.3172137,"\int \frac{\left(f+g x^{-2 n}\right)^2 \log \left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((f + g/x^(2*n))^2*Log[c*(d + e*x^n)^p])/x,x]","\frac{f^2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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^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{e^3 g^2 p x^{-n}}{4 d^3 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 f g p x^{-n}}{d n}-\frac{e g^2 p x^{-3 n}}{12 d n}","\frac{f^2 p \text{PolyLog}\left(2,\frac{e x^n}{d}+1\right)}{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^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{e^3 g^2 p x^{-n}}{4 d^3 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 f g p x^{-n}}{d n}-\frac{e g^2 p x^{-3 n}}{12 d n}",1,"-(e*g^2*p)/(12*d*n*x^(3*n)) + (e^2*g^2*p)/(8*d^2*n*x^(2*n)) - (e*f*g*p)/(d*n*x^n) - (e^3*g^2*p)/(4*d^3*n*x^n) - (e^2*f*g*p*Log[x])/d^2 - (e^4*g^2*p*Log[x])/(4*d^4) + (e^2*f*g*p*Log[d + e*x^n])/(d^2*n) + (e^4*g^2*p*Log[d + e*x^n])/(4*d^4*n) - (g^2*Log[c*(d + e*x^n)^p])/(4*n*x^(4*n)) - (f*g*Log[c*(d + e*x^n)^p])/(n*x^(2*n)) + (f^2*Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/n + (f^2*p*PolyLog[2, 1 + (e*x^n)/d])/n","A",11,9,27,0.3333,1,"{2475, 263, 266, 43, 2416, 2395, 44, 2394, 2315}"
370,1,266,0,0.4236641,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{2 n}\right)} \, dx","Int[Log[c*(d + e*x^n)^p]/(x*(f + g*x^(2*n))),x]","-\frac{p \text{PolyLog}\left(2,-\frac{\sqrt{g} \left(d+e x^n\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f n}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{g} \left(d+e x^n\right)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f n}+\frac{p \text{PolyLog}\left(2,\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(\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{PolyLog}\left(2,-\frac{\sqrt{g} \left(d+e x^n\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f n}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{g} \left(d+e x^n\right)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f n}+\frac{p \text{PolyLog}\left(2,\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(\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}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/(f*n) - (Log[c*(d + e*x^n)^p]*Log[(e*(Sqrt[-f] - Sqrt[g]*x^n))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f*n) - (Log[c*(d + e*x^n)^p]*Log[(e*(Sqrt[-f] + Sqrt[g]*x^n))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f*n) - (p*PolyLog[2, -((Sqrt[g]*(d + e*x^n))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*f*n) - (p*PolyLog[2, (Sqrt[g]*(d + e*x^n))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f*n) + (p*PolyLog[2, 1 + (e*x^n)/d])/(f*n)","A",13,11,27,0.4074,1,"{2475, 266, 36, 29, 31, 2416, 2394, 2315, 260, 2393, 2391}"
371,1,121,0,0.1951714,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^n\right)} \, dx","Int[Log[c*(d + e*x^n)^p]/(x*(f + g*x^n)),x]","-\frac{p \text{PolyLog}\left(2,-\frac{g \left(d+e x^n\right)}{e f-d g}\right)}{f n}+\frac{p \text{PolyLog}\left(2,\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{PolyLog}\left(2,-\frac{g \left(d+e x^n\right)}{e f-d g}\right)}{f n}+\frac{p \text{PolyLog}\left(2,\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}",1,"(Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/(f*n) - (Log[c*(d + e*x^n)^p]*Log[(e*(f + g*x^n))/(e*f - d*g)])/(f*n) - (p*PolyLog[2, -((g*(d + e*x^n))/(e*f - d*g))])/(f*n) + (p*PolyLog[2, 1 + (e*x^n)/d])/(f*n)","A",8,9,25,0.3600,1,"{2475, 36, 29, 31, 2416, 2394, 2315, 2393, 2391}"
372,1,70,0,0.1636247,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-n}\right)} \, dx","Int[Log[c*(d + e*x^n)^p]/(x*(f + g/x^n)),x]","\frac{p \text{PolyLog}\left(2,\frac{f \left(d+e x^n\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{PolyLog}\left(2,\frac{f \left(d+e x^n\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}",1,"(Log[c*(d + e*x^n)^p]*Log[-((e*(g + f*x^n))/(d*f - e*g))])/(f*n) + (p*PolyLog[2, (f*(d + e*x^n))/(d*f - e*g)])/(f*n)","A",5,5,27,0.1852,1,"{2475, 2412, 2394, 2393, 2391}"
373,1,221,0,0.4120203,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-2 n}\right)} \, dx","Int[Log[c*(d + e*x^n)^p]/(x*(f + g/x^(2*n))),x]","\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-f} \left(d+e x^n\right)}{d \sqrt{-f}-e \sqrt{g}}\right)}{2 f n}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-f} \left(d+e 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{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{PolyLog}\left(2,\frac{\sqrt{-f} \left(d+e x^n\right)}{d \sqrt{-f}-e \sqrt{g}}\right)}{2 f n}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-f} \left(d+e 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{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}",1,"(Log[c*(d + e*x^n)^p]*Log[(e*(Sqrt[g] - Sqrt[-f]*x^n))/(d*Sqrt[-f] + e*Sqrt[g])])/(2*f*n) + (Log[c*(d + e*x^n)^p]*Log[-((e*(Sqrt[g] + Sqrt[-f]*x^n))/(d*Sqrt[-f] - e*Sqrt[g]))])/(2*f*n) + (p*PolyLog[2, (Sqrt[-f]*(d + e*x^n))/(d*Sqrt[-f] - e*Sqrt[g])])/(2*f*n) + (p*PolyLog[2, (Sqrt[-f]*(d + e*x^n))/(d*Sqrt[-f] + e*Sqrt[g])])/(2*f*n)","A",9,7,27,0.2593,1,"{2475, 263, 260, 2416, 2394, 2393, 2391}"
374,1,419,0,0.5651024,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{2 n}\right)^2} \, dx","Int[Log[c*(d + e*x^n)^p]/(x*(f + g*x^(2*n))^2),x]","-\frac{p \text{PolyLog}\left(2,-\frac{\sqrt{g} \left(d+e x^n\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2 n}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{g} \left(d+e x^n\right)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f^2 n}+\frac{p \text{PolyLog}\left(2,\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(\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(d+e x^n\right)}{2 f 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{p \text{PolyLog}\left(2,-\frac{\sqrt{g} \left(d+e x^n\right)}{e \sqrt{-f}-d \sqrt{g}}\right)}{2 f^2 n}-\frac{p \text{PolyLog}\left(2,\frac{\sqrt{g} \left(d+e x^n\right)}{d \sqrt{g}+e \sqrt{-f}}\right)}{2 f^2 n}+\frac{p \text{PolyLog}\left(2,\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(\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(d+e x^n\right)}{2 f 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)}",1,"-(d*e*Sqrt[g]*p*ArcTan[(Sqrt[g]*x^n)/Sqrt[f]])/(2*f^(3/2)*(e^2*f + d^2*g)*n) - (e^2*p*Log[d + e*x^n])/(2*f*(e^2*f + d^2*g)*n) + Log[c*(d + e*x^n)^p]/(2*f*n*(f + g*x^(2*n))) + (Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/(f^2*n) - (Log[c*(d + e*x^n)^p]*Log[(e*(Sqrt[-f] - Sqrt[g]*x^n))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2*n) - (Log[c*(d + e*x^n)^p]*Log[(e*(Sqrt[-f] + Sqrt[g]*x^n))/(e*Sqrt[-f] - d*Sqrt[g])])/(2*f^2*n) + (e^2*p*Log[f + g*x^(2*n)])/(4*f*(e^2*f + d^2*g)*n) - (p*PolyLog[2, -((Sqrt[g]*(d + e*x^n))/(e*Sqrt[-f] - d*Sqrt[g]))])/(2*f^2*n) - (p*PolyLog[2, (Sqrt[g]*(d + e*x^n))/(e*Sqrt[-f] + d*Sqrt[g])])/(2*f^2*n) + (p*PolyLog[2, 1 + (e*x^n)/d])/(f^2*n)","A",19,14,27,0.5185,1,"{2475, 266, 44, 2416, 2394, 2315, 2413, 706, 31, 635, 205, 260, 2393, 2391}"
375,1,204,0,0.2681446,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^n\right)^2} \, dx","Int[Log[c*(d + e*x^n)^p]/(x*(f + g*x^n)^2),x]","-\frac{p \text{PolyLog}\left(2,-\frac{g \left(d+e x^n\right)}{e f-d g}\right)}{f^2 n}+\frac{p \text{PolyLog}\left(2,\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{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)}","-\frac{p \text{PolyLog}\left(2,-\frac{g \left(d+e x^n\right)}{e f-d g}\right)}{f^2 n}+\frac{p \text{PolyLog}\left(2,\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{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*p*Log[d + e*x^n])/(f*(e*f - d*g)*n)) + Log[c*(d + e*x^n)^p]/(f*n*(f + g*x^n)) + (Log[-((e*x^n)/d)]*Log[c*(d + e*x^n)^p])/(f^2*n) + (e*p*Log[f + g*x^n])/(f*(e*f - d*g)*n) - (Log[c*(d + e*x^n)^p]*Log[(e*(f + g*x^n))/(e*f - d*g)])/(f^2*n) - (p*PolyLog[2, -((g*(d + e*x^n))/(e*f - d*g))])/(f^2*n) + (p*PolyLog[2, 1 + (e*x^n)/d])/(f^2*n)","A",12,10,25,0.4000,1,"{2475, 44, 2416, 2394, 2315, 2395, 36, 31, 2393, 2391}"
376,1,156,0,0.2775771,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-n}\right)^2} \, dx","Int[Log[c*(d + e*x^n)^p]/(x*(f + g/x^n)^2),x]","\frac{p \text{PolyLog}\left(2,\frac{f \left(d+e x^n\right)}{d f-e g}\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{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)}","\frac{p \text{PolyLog}\left(2,\frac{f \left(d+e x^n\right)}{d f-e g}\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{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,"(e*g*p*Log[d + e*x^n])/(f^2*(d*f - e*g)*n) + (g*Log[c*(d + e*x^n)^p])/(f^2*n*(g + f*x^n)) - (e*g*p*Log[g + f*x^n])/(f^2*(d*f - e*g)*n) + (Log[c*(d + e*x^n)^p]*Log[-((e*(g + f*x^n))/(d*f - e*g))])/(f^2*n) + (p*PolyLog[2, (f*(d + e*x^n))/(d*f - e*g)])/(f^2*n)","A",10,10,27,0.3704,1,"{2475, 263, 43, 2416, 2395, 36, 31, 2394, 2393, 2391}"
377,1,377,0,0.6086576,"\int \frac{\log \left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-2 n}\right)^2} \, dx","Int[Log[c*(d + e*x^n)^p]/(x*(f + g/x^(2*n))^2),x]","\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-f} \left(d+e x^n\right)}{d \sqrt{-f}-e \sqrt{g}}\right)}{2 f^2 n}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-f} \left(d+e x^n\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{\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{e^2 g p \log \left(d+e x^n\right)}{2 f^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{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{p \text{PolyLog}\left(2,\frac{\sqrt{-f} \left(d+e x^n\right)}{d \sqrt{-f}-e \sqrt{g}}\right)}{2 f^2 n}+\frac{p \text{PolyLog}\left(2,\frac{\sqrt{-f} \left(d+e x^n\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{\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{e^2 g p \log \left(d+e x^n\right)}{2 f^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{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)}",1,"-(d*e*Sqrt[g]*p*ArcTan[(Sqrt[f]*x^n)/Sqrt[g]])/(2*f^(3/2)*(d^2*f + e^2*g)*n) - (e^2*g*p*Log[d + e*x^n])/(2*f^2*(d^2*f + e^2*g)*n) + (g*Log[c*(d + e*x^n)^p])/(2*f^2*n*(g + f*x^(2*n))) + (Log[c*(d + e*x^n)^p]*Log[(e*(Sqrt[g] - Sqrt[-f]*x^n))/(d*Sqrt[-f] + e*Sqrt[g])])/(2*f^2*n) + (Log[c*(d + e*x^n)^p]*Log[-((e*(Sqrt[g] + Sqrt[-f]*x^n))/(d*Sqrt[-f] - e*Sqrt[g]))])/(2*f^2*n) + (e^2*g*p*Log[g + f*x^(2*n)])/(4*f^2*(d^2*f + e^2*g)*n) + (p*PolyLog[2, (Sqrt[-f]*(d + e*x^n))/(d*Sqrt[-f] - e*Sqrt[g])])/(2*f^2*n) + (p*PolyLog[2, (Sqrt[-f]*(d + e*x^n))/(d*Sqrt[-f] + e*Sqrt[g])])/(2*f^2*n)","A",17,14,27,0.5185,1,"{2475, 263, 266, 43, 2416, 2413, 706, 31, 635, 205, 260, 2394, 2393, 2391}"
378,1,25,0,0.1570726,"\int \frac{\log \left(c \left(d+e x^n\right)\right)}{x \left(c e-(1-c d) x^{-n}\right)} \, dx","Int[Log[c*(d + e*x^n)]/(x*(c*e - (1 - c*d)/x^n)),x]","-\frac{\text{PolyLog}\left(2,1-c \left(d+e x^n\right)\right)}{c e n}","-\frac{\text{PolyLog}\left(2,1-c \left(d+e x^n\right)\right)}{c e n}",1,"-(PolyLog[2, 1 - c*(d + e*x^n)]/(c*e*n))","A",4,4,33,0.1212,1,"{2475, 2412, 2393, 2391}"
379,1,25,0,0.0985,"\int \frac{x^{-1+n} \log \left(c \left(d+e x^n\right)\right)}{-1+c d+c e x^n} \, dx","Int[(x^(-1 + n)*Log[c*(d + e*x^n)])/(-1 + c*d + c*e*x^n),x]","-\frac{\text{PolyLog}\left(2,1-c \left(d+e x^n\right)\right)}{c e n}","-\frac{\text{PolyLog}\left(2,1-c \left(d+e x^n\right)\right)}{c e n}",1,"-(PolyLog[2, 1 - c*(d + e*x^n)]/(c*e*n))","A",3,3,29,0.1034,1,"{2475, 2393, 2391}"
380,1,26,0,0.1553775,"\int \frac{\log \left(c \left(d+e x^{-n}\right)\right)}{x \left(c e-(1-c d) x^n\right)} \, dx","Int[Log[c*(d + e/x^n)]/(x*(c*e - (1 - c*d)*x^n)),x]","\frac{\text{PolyLog}\left(2,1-c \left(d+e x^{-n}\right)\right)}{c e n}","\frac{\text{PolyLog}\left(2,1-c \left(d+e x^{-n}\right)\right)}{c e n}",1,"PolyLog[2, 1 - c*(d + e/x^n)]/(c*e*n)","A",4,4,33,0.1212,1,"{2475, 2412, 2393, 2391}"
381,0,0,0,0.0845421,"\int \frac{\left(f+g x^{2 n}\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((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","\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} \text{Gamma}\left(q+1,-\frac{2 \log \left(c \left(d+e x^n\right)^p\right)}{p}\right)}{e^4 n}-\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} \text{Gamma}\left(q+1,-\frac{\log \left(c \left(d+e x^n\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} \text{Gamma}\left(q+1,-\frac{2 \log \left(c \left(d+e x^n\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} \text{Gamma}\left(q+1,-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)}{e^2 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} \text{Gamma}\left(q+1,-\frac{4 \log \left(c \left(d+e x^n\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} \text{Gamma}\left(q+1,-\frac{3 \log \left(c \left(d+e x^n\right)^p\right)}{p}\right)}{e^4 n}+f^2 \text{Int}\left(\frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x},x\right)",0,"Defer[Int][((f + g*x^(2*n))^2*Log[c*(d + e*x^n)^p]^q)/x, x]","A",0,0,0,0,-1,"{}"
382,0,0,0,0.0791144,"\int \frac{\left(f+g x^n\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((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","\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} \text{Gamma}\left(q+1,-\frac{2 \log \left(c \left(d+e x^n\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} \text{Gamma}\left(q+1,-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)}{e^2 n}+f^2 \text{Int}\left(\frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x},x\right)+\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} \text{Gamma}\left(q+1,-\frac{\log \left(c \left(d+e x^n\right)^p\right)}{p}\right)}{e n}",0,"Defer[Int][((f + g*x^n)^2*Log[c*(d + e*x^n)^p]^q)/x, x]","A",0,0,0,0,-1,"{}"
383,0,0,0,0.1070683,"\int \frac{\left(f+g x^{-n}\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((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,"Defer[Int][((f + g/x^n)^2*Log[c*(d + e*x^n)^p]^q)/x, x]","A",0,0,0,0,-1,"{}"
384,0,0,0,0.1096337,"\int \frac{\left(f+g x^{-2 n}\right)^2 \log ^q\left(c \left(d+e x^n\right)^p\right)}{x} \, dx","Int[((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,"Defer[Int][((f + g/x^(2*n))^2*Log[c*(d + e*x^n)^p]^q)/x, x]","A",0,0,0,0,-1,"{}"
385,0,0,0,0.0905777,"\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{2 n}\right)} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^n)^p]^q/(x*(f + g*x^(2*n))), x]","A",0,0,0,0,-1,"{}"
386,0,0,0,0.0861844,"\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^n\right)} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^n)^p]^q/(x*(f + g*x^n)), x]","A",0,0,0,0,-1,"{}"
387,0,0,0,0.1054804,"\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-n}\right)} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^n)^p]^q/(x*(f + g/x^n)), x]","A",0,0,0,0,-1,"{}"
388,0,0,0,0.1101997,"\int \frac{\log ^q\left(c \left(d+e x^n\right)^p\right)}{x \left(f+g x^{-2 n}\right)} \, dx","Int[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,"Defer[Int][Log[c*(d + e*x^n)^p]^q/(x*(f + g/x^(2*n))), x]","A",0,0,0,0,-1,"{}"
389,1,69,0,0.1244918,"\int \frac{\log (x) \log \left(d+e x^m\right)}{x} \, dx","Int[(Log[x]*Log[d + e*x^m])/x,x]","\frac{\text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{m^2}-\frac{\log (x) \text{PolyLog}\left(2,-\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)","\frac{\text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{m^2}-\frac{\log (x) \text{PolyLog}\left(2,-\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,"(Log[x]^2*Log[d + e*x^m])/2 - (Log[x]^2*Log[1 + (e*x^m)/d])/2 - (Log[x]*PolyLog[2, -((e*x^m)/d)])/m + PolyLog[3, -((e*x^m)/d)]/m^2","A",4,4,14,0.2857,1,"{2375, 2337, 2374, 6589}"
390,1,12,0,0.0095414,"\int \frac{\log \left(\frac{a+x}{x}\right)}{x} \, dx","Int[Log[(a + x)/x]/x,x]","\text{PolyLog}\left(2,1-\frac{a+x}{x}\right)","\text{PolyLog}\left(2,-\frac{a}{x}\right)",1,"PolyLog[2, 1 - (a + x)/x]","A",1,1,12,0.08333,1,"{2447}"
391,1,12,0,0.0184693,"\int \frac{\log \left(\frac{a+x^2}{x^2}\right)}{x} \, dx","Int[Log[(a + x^2)/x^2]/x,x]","\frac{1}{2} \text{PolyLog}\left(2,-\frac{a}{x^2}\right)","\frac{1}{2} \text{PolyLog}\left(2,-\frac{a}{x^2}\right)",1,"PolyLog[2, -(a/x^2)]/2","A",2,2,14,0.1429,1,"{2461, 2391}"
392,1,14,0,0.0188247,"\int \frac{\log \left(x^{-n} \left(a+x^n\right)\right)}{x} \, dx","Int[Log[(a + x^n)/x^n]/x,x]","\frac{\text{PolyLog}\left(2,-a x^{-n}\right)}{n}","\frac{\text{PolyLog}\left(2,-a x^{-n}\right)}{n}",1,"PolyLog[2, -(a/x^n)]/n","A",2,2,16,0.1250,1,"{2461, 2391}"
393,1,35,0,0.055865,"\int \frac{\log \left(\frac{a+b x}{x}\right)}{x} \, dx","Int[Log[(a + b*x)/x]/x,x]","-\text{PolyLog}\left(2,\frac{a}{b x}+1\right)-\log \left(\frac{a}{x}+b\right) \log \left(-\frac{a}{b x}\right)","-\text{PolyLog}\left(2,\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, 1 + a/(b*x)]","A",4,4,14,0.2857,1,"{2461, 2454, 2394, 2315}"
394,1,39,0,0.0470272,"\int \frac{\log \left(\frac{a+b x^2}{x^2}\right)}{x} \, dx","Int[Log[(a + b*x^2)/x^2]/x,x]","-\frac{1}{2} \text{PolyLog}\left(2,\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)","-\frac{1}{2} \text{PolyLog}\left(2,\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,"-(Log[b + a/x^2]*Log[-(a/(b*x^2))])/2 - PolyLog[2, 1 + a/(b*x^2)]/2","A",4,4,16,0.2500,1,"{2461, 2454, 2394, 2315}"
395,1,47,0,0.0503694,"\int \frac{\log \left(x^{-n} \left(a+b x^n\right)\right)}{x} \, dx","Int[Log[(a + b*x^n)/x^n]/x,x]","-\frac{\text{PolyLog}\left(2,\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}","-\frac{\text{PolyLog}\left(2,\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])/n) - PolyLog[2, 1 + a/(b*x^n)]/n","A",4,4,18,0.2222,1,"{2461, 2454, 2394, 2315}"
396,1,105,0,0.1679462,"\int \frac{\log \left(\frac{a+b x}{x}\right)}{c+d x} \, dx","Int[Log[(a + b*x)/x]/(c + d*x),x]","-\frac{\text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d}+\frac{\text{PolyLog}\left(2,\frac{d x}{c}+1\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{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{d}","-\frac{\text{PolyLog}\left(2,\frac{b (c+d x)}{b c-a d}\right)}{d}+\frac{\text{PolyLog}\left(2,\frac{d x}{c}+1\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{\log \left(-\frac{d x}{c}\right) \log (c+d x)}{d}",1,"(Log[b + a/x]*Log[c + d*x])/d + (Log[-((d*x)/c)]*Log[c + d*x])/d - (Log[-((d*(a + b*x))/(b*c - a*d))]*Log[c + d*x])/d - PolyLog[2, (b*(c + d*x))/(b*c - a*d)]/d + PolyLog[2, 1 + (d*x)/c]/d","A",9,8,18,0.4444,1,"{2465, 2462, 260, 2416, 2394, 2315, 2393, 2391}"
397,1,227,0,0.3783624,"\int \frac{\log \left(\frac{a+b x^2}{x^2}\right)}{c+d x} \, dx","Int[Log[(a + b*x^2)/x^2]/(c + d*x),x]","-\frac{\text{PolyLog}\left(2,\frac{\sqrt{b} (c+d x)}{\sqrt{b} c-\sqrt{-a} d}\right)}{d}-\frac{\text{PolyLog}\left(2,\frac{\sqrt{b} (c+d x)}{\sqrt{-a} d+\sqrt{b} c}\right)}{d}+\frac{2 \text{PolyLog}\left(2,\frac{d x}{c}+1\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 \log \left(-\frac{d x}{c}\right) \log (c+d x)}{d}","-\frac{\text{PolyLog}\left(2,\frac{\sqrt{b} (c+d x)}{\sqrt{b} c-\sqrt{-a} d}\right)}{d}-\frac{\text{PolyLog}\left(2,\frac{\sqrt{b} (c+d x)}{\sqrt{-a} d+\sqrt{b} c}\right)}{d}+\frac{2 \text{PolyLog}\left(2,\frac{d x}{c}+1\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 \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 - 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 + (2*PolyLog[2, 1 + (d*x)/c])/d","A",14,8,20,0.4000,1,"{2465, 2462, 260, 2416, 2394, 2315, 2393, 2391}"
398,0,0,0,0.0257867,"\int \frac{\log \left(x^{-n} \left(a+b x^n\right)\right)}{c+d x} \, dx","Int[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,"Defer[Int][Log[b + a/x^n]/(c + d*x), x]","A",0,0,0,0,-1,"{}"
399,1,92,0,0.0499879,"\int (f x)^q \left(a+b \log \left(c \left(d+e x^m\right)^n\right)\right) \, dx","Int[(f*x)^q*(a + b*Log[c*(d + e*x^m)^n]),x]","\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)}","\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,"-((b*e*m*n*x^(1 + m)*(f*x)^q*Hypergeometric2F1[1, (1 + m + q)/m, (1 + 2*m + q)/m, -((e*x^m)/d)])/(d*(1 + q)*(1 + m + q))) + ((f*x)^(1 + q)*(a + b*Log[c*(d + e*x^m)^n]))/(f*(1 + q))","A",3,3,22,0.1364,1,"{2455, 20, 364}"
400,1,166,0,0.1360793,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \, dx","Int[x^3*(a + b*Log[c*(d + e*Sqrt[x])^n]),x]","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+\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^7 n \sqrt{x}}{4 e^7}-\frac{b d^6 n x}{8 e^6}-\frac{b d^8 n \log \left(d+e \sqrt{x}\right)}{4 e^8}+\frac{b d n x^{7/2}}{28 e}-\frac{1}{32} b n x^4","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+\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^7 n \sqrt{x}}{4 e^7}-\frac{b d^6 n x}{8 e^6}-\frac{b d^8 n \log \left(d+e \sqrt{x}\right)}{4 e^8}+\frac{b d n x^{7/2}}{28 e}-\frac{1}{32} b n x^4",1,"(b*d^7*n*Sqrt[x])/(4*e^7) - (b*d^6*n*x)/(8*e^6) + (b*d^5*n*x^(3/2))/(12*e^5) - (b*d^4*n*x^2)/(16*e^4) + (b*d^3*n*x^(5/2))/(20*e^3) - (b*d^2*n*x^3)/(24*e^2) + (b*d*n*x^(7/2))/(28*e) - (b*n*x^4)/32 - (b*d^8*n*Log[d + e*Sqrt[x]])/(4*e^8) + (x^4*(a + b*Log[c*(d + e*Sqrt[x])^n]))/4","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
401,1,134,0,0.0993512,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \, dx","Int[x^2*(a + b*Log[c*(d + e*Sqrt[x])^n]),x]","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+\frac{b d^3 n x^{3/2}}{9 e^3}-\frac{b d^2 n x^2}{12 e^2}+\frac{b d^5 n \sqrt{x}}{3 e^5}-\frac{b d^4 n x}{6 e^4}-\frac{b d^6 n \log \left(d+e \sqrt{x}\right)}{3 e^6}+\frac{b d n x^{5/2}}{15 e}-\frac{1}{18} b n x^3","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+\frac{b d^3 n x^{3/2}}{9 e^3}-\frac{b d^2 n x^2}{12 e^2}+\frac{b d^5 n \sqrt{x}}{3 e^5}-\frac{b d^4 n x}{6 e^4}-\frac{b d^6 n \log \left(d+e \sqrt{x}\right)}{3 e^6}+\frac{b d n x^{5/2}}{15 e}-\frac{1}{18} b n x^3",1,"(b*d^5*n*Sqrt[x])/(3*e^5) - (b*d^4*n*x)/(6*e^4) + (b*d^3*n*x^(3/2))/(9*e^3) - (b*d^2*n*x^2)/(12*e^2) + (b*d*n*x^(5/2))/(15*e) - (b*n*x^3)/18 - (b*d^6*n*Log[d + e*Sqrt[x]])/(3*e^6) + (x^3*(a + b*Log[c*(d + e*Sqrt[x])^n]))/3","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
402,1,102,0,0.0721291,"\int x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \, dx","Int[x*(a + b*Log[c*(d + e*Sqrt[x])^n]),x]","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+\frac{b d^3 n \sqrt{x}}{2 e^3}-\frac{b d^2 n x}{4 e^2}-\frac{b d^4 n \log \left(d+e \sqrt{x}\right)}{2 e^4}+\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^3 n \sqrt{x}}{2 e^3}-\frac{b d^2 n x}{4 e^2}-\frac{b d^4 n \log \left(d+e \sqrt{x}\right)}{2 e^4}+\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) - (b*n*x^2)/8 - (b*d^4*n*Log[d + e*Sqrt[x]])/(2*e^4) + (x^2*(a + b*Log[c*(d + e*Sqrt[x])^n]))/2","A",4,3,20,0.1500,1,"{2454, 2395, 43}"
403,1,60,0,0.040151,"\int \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right) \, dx","Int[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",5,3,18,0.1667,1,"{2448, 266, 43}"
404,1,51,0,0.0484987,"\int \frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{x} \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])/x,x]","2 b n \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\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{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\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)",1,"2*(a + b*Log[c*(d + e*Sqrt[x])^n])*Log[-((e*Sqrt[x])/d)] + 2*b*n*PolyLog[2, 1 + (e*Sqrt[x])/d]","A",3,3,22,0.1364,1,"{2454, 2394, 2315}"
405,1,70,0,0.0577774,"\int \frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{x^2} \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])/x^2,x]","-\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}}","-\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,"-((b*e*n)/(d*Sqrt[x])) + (b*e^2*n*Log[d + e*Sqrt[x]])/d^2 - (a + b*Log[c*(d + e*Sqrt[x])^n])/x - (b*e^2*n*Log[x])/(2*d^2)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
406,1,109,0,0.0742414,"\int \frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{x^3} \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])/x^3,x]","-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{2 x^2}-\frac{b e^3 n}{2 d^3 \sqrt{x}}+\frac{b e^2 n}{4 d^2 x}+\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 n}{6 d x^{3/2}}","-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{2 x^2}-\frac{b e^3 n}{2 d^3 \sqrt{x}}+\frac{b e^2 n}{4 d^2 x}+\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 n}{6 d x^{3/2}}",1,"-(b*e*n)/(6*d*x^(3/2)) + (b*e^2*n)/(4*d^2*x) - (b*e^3*n)/(2*d^3*Sqrt[x]) + (b*e^4*n*Log[d + e*Sqrt[x]])/(2*d^4) - (a + b*Log[c*(d + e*Sqrt[x])^n])/(2*x^2) - (b*e^4*n*Log[x])/(4*d^4)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
407,1,141,0,0.0921506,"\int \frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{x^4} \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])/x^4,x]","-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{3 x^3}-\frac{b e^3 n}{9 d^3 x^{3/2}}+\frac{b e^2 n}{12 d^2 x^2}-\frac{b e^5 n}{3 d^5 \sqrt{x}}+\frac{b e^4 n}{6 d^4 x}+\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 n}{15 d x^{5/2}}","-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)}{3 x^3}-\frac{b e^3 n}{9 d^3 x^{3/2}}+\frac{b e^2 n}{12 d^2 x^2}-\frac{b e^5 n}{3 d^5 \sqrt{x}}+\frac{b e^4 n}{6 d^4 x}+\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 n}{15 d x^{5/2}}",1,"-(b*e*n)/(15*d*x^(5/2)) + (b*e^2*n)/(12*d^2*x^2) - (b*e^3*n)/(9*d^3*x^(3/2)) + (b*e^4*n)/(6*d^4*x) - (b*e^5*n)/(3*d^5*Sqrt[x]) + (b*e^6*n*Log[d + e*Sqrt[x]])/(3*d^6) - (a + b*Log[c*(d + e*Sqrt[x])^n])/(3*x^3) - (b*e^6*n*Log[x])/(6*d^6)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
408,1,355,0,0.4763726,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \, dx","Int[x^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^2,x]","\frac{1}{90} b n \left(\frac{360 d^5 \left(d+e \sqrt{x}\right)}{e^6}-\frac{450 d^4 \left(d+e \sqrt{x}\right)^2}{e^6}+\frac{400 d^3 \left(d+e \sqrt{x}\right)^3}{e^6}-\frac{225 d^2 \left(d+e \sqrt{x}\right)^4}{e^6}-\frac{60 d^6 \log \left(d+e \sqrt{x}\right)}{e^6}+\frac{72 d \left(d+e \sqrt{x}\right)^5}{e^6}-\frac{10 \left(d+e \sqrt{x}\right)^6}{e^6}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2-\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{b^2 d^6 n^2 \log ^2\left(d+e \sqrt{x}\right)}{3 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}","-\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{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{b^2 d^6 n^2 \log ^2\left(d+e \sqrt{x}\right)}{3 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,"(5*b^2*d^4*n^2*(d + e*Sqrt[x])^2)/(2*e^6) - (40*b^2*d^3*n^2*(d + e*Sqrt[x])^3)/(27*e^6) + (5*b^2*d^2*n^2*(d + e*Sqrt[x])^4)/(8*e^6) - (4*b^2*d*n^2*(d + e*Sqrt[x])^5)/(25*e^6) + (b^2*n^2*(d + e*Sqrt[x])^6)/(54*e^6) - (4*b^2*d^5*n^2*Sqrt[x])/e^5 + (b^2*d^6*n^2*Log[d + e*Sqrt[x]]^2)/(3*e^6) + (b*n*((360*d^5*(d + e*Sqrt[x]))/e^6 - (450*d^4*(d + e*Sqrt[x])^2)/e^6 + (400*d^3*(d + e*Sqrt[x])^3)/e^6 - (225*d^2*(d + e*Sqrt[x])^4)/e^6 + (72*d*(d + e*Sqrt[x])^5)/e^6 - (10*(d + e*Sqrt[x])^6)/e^6 - (60*d^6*Log[d + e*Sqrt[x]])/e^6)*(a + b*Log[c*(d + e*Sqrt[x])^n]))/90 + (x^3*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/3","A",8,8,24,0.3333,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
409,1,263,0,0.3610318,"\int x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \, dx","Int[x*(a + b*Log[c*(d + e*Sqrt[x])^n])^2,x]","\frac{1}{12} b n \left(\frac{48 d^3 \left(d+e \sqrt{x}\right)}{e^4}-\frac{36 d^2 \left(d+e \sqrt{x}\right)^2}{e^4}-\frac{12 d^4 \log \left(d+e \sqrt{x}\right)}{e^4}+\frac{16 d \left(d+e \sqrt{x}\right)^3}{e^4}-\frac{3 \left(d+e \sqrt{x}\right)^4}{e^4}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2-\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{b^2 d^4 n^2 \log ^2\left(d+e \sqrt{x}\right)}{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}","-\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{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{b^2 d^4 n^2 \log ^2\left(d+e \sqrt{x}\right)}{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,"(3*b^2*d^2*n^2*(d + e*Sqrt[x])^2)/(2*e^4) - (4*b^2*d*n^2*(d + e*Sqrt[x])^3)/(9*e^4) + (b^2*n^2*(d + e*Sqrt[x])^4)/(16*e^4) - (4*b^2*d^3*n^2*Sqrt[x])/e^3 + (b^2*d^4*n^2*Log[d + e*Sqrt[x]]^2)/(2*e^4) + (b*n*((48*d^3*(d + e*Sqrt[x]))/e^4 - (36*d^2*(d + e*Sqrt[x])^2)/e^4 + (16*d*(d + e*Sqrt[x])^3)/e^4 - (3*(d + e*Sqrt[x])^4)/e^4 - (12*d^4*Log[d + e*Sqrt[x]])/e^4)*(a + b*Log[c*(d + e*Sqrt[x])^n]))/12 + (x^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/2","A",8,8,22,0.3636,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
410,1,195,0,0.1835519,"\int \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2 \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])^2,x]","-\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}","-\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,"(b^2*n^2*(d + e*Sqrt[x])^2)/(2*e^2) + (4*a*b*d*n*Sqrt[x])/e - (4*b^2*d*n^2*Sqrt[x])/e + (4*b^2*d*n*(d + e*Sqrt[x])*Log[c*(d + e*Sqrt[x])^n])/e^2 - (b*n*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n]))/e^2 - (2*d*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/e^2 + ((d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/e^2","A",10,8,20,0.4000,1,"{2451, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
411,1,93,0,0.1303252,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{x} \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])^2/x,x]","4 b n \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)-4 b^2 n^2 \text{PolyLog}\left(3,\frac{e \sqrt{x}}{d}+1\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 n \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)-4 b^2 n^2 \text{PolyLog}\left(3,\frac{e \sqrt{x}}{d}+1\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",1,"2*(a + b*Log[c*(d + e*Sqrt[x])^n])^2*Log[-((e*Sqrt[x])/d)] + 4*b*n*(a + b*Log[c*(d + e*Sqrt[x])^n])*PolyLog[2, 1 + (e*Sqrt[x])/d] - 4*b^2*n^2*PolyLog[3, 1 + (e*Sqrt[x])/d]","A",5,5,24,0.2083,1,"{2454, 2396, 2433, 2374, 6589}"
412,1,176,0,0.3512401,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{x^2} \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])^2/x^2,x]","-\frac{2 b^2 e^2 n^2 \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right)}{d^2}+\frac{e^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{d^2}-\frac{2 b e^2 n \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{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{b^2 e^2 n^2 \log (x)}{d^2}","\frac{2 b^2 e^2 n^2 \text{PolyLog}\left(2,\frac{d}{d+e \sqrt{x}}\right)}{d^2}-\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{b^2 e^2 n^2 \log (x)}{d^2}",1,"(-2*b*e*n*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(d^2*Sqrt[x]) + (e^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/d^2 - (a + b*Log[c*(d + e*Sqrt[x])^n])^2/x - (2*b*e^2*n*(a + b*Log[c*(d + e*Sqrt[x])^n])*Log[-((e*Sqrt[x])/d)])/d^2 + (b^2*e^2*n^2*Log[x])/d^2 - (2*b^2*e^2*n^2*PolyLog[2, 1 + (e*Sqrt[x])/d])/d^2","A",10,10,24,0.4167,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31}"
413,1,318,0,0.6672089,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{x^3} \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])^2/x^3,x]","-\frac{b^2 e^4 n^2 \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right)}{d^4}+\frac{e^4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{2 d^4}-\frac{b e^4 n \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{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{5 b^2 e^3 n^2}{6 d^3 \sqrt{x}}-\frac{b^2 e^2 n^2}{6 d^2 x}-\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{b^2 e^4 n^2 \text{PolyLog}\left(2,\frac{d}{d+e \sqrt{x}}\right)}{d^4}-\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{5 b^2 e^3 n^2}{6 d^3 \sqrt{x}}-\frac{b^2 e^2 n^2}{6 d^2 x}-\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}",1,"-(b^2*e^2*n^2)/(6*d^2*x) + (5*b^2*e^3*n^2)/(6*d^3*Sqrt[x]) - (5*b^2*e^4*n^2*Log[d + e*Sqrt[x]])/(6*d^4) - (b*e*n*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(3*d*x^(3/2)) + (b*e^2*n*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(2*d^2*x) - (b*e^3*n*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(d^4*Sqrt[x]) + (e^4*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(2*d^4) - (a + b*Log[c*(d + e*Sqrt[x])^n])^2/(2*x^2) - (b*e^4*n*(a + b*Log[c*(d + e*Sqrt[x])^n])*Log[-((e*Sqrt[x])/d)])/d^4 + (11*b^2*e^4*n^2*Log[x])/(12*d^4) - (b^2*e^4*n^2*PolyLog[2, 1 + (e*Sqrt[x])/d])/d^4","A",18,12,24,0.5000,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
414,1,432,0,1.0336074,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{x^4} \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])^2/x^4,x]","-\frac{2 b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right)}{3 d^6}-\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{e^6 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{3 d^6}-\frac{2 b e^6 n \log \left(-\frac{e \sqrt{x}}{d}\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 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{b^2 e^3 n^2}{10 d^3 x^{3/2}}-\frac{b^2 e^2 n^2}{30 d^2 x^2}+\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{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{2 b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{d}{d+e \sqrt{x}}\right)}{3 d^6}-\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^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 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{b^2 e^3 n^2}{10 d^3 x^{3/2}}-\frac{b^2 e^2 n^2}{30 d^2 x^2}+\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{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}",1,"-(b^2*e^2*n^2)/(30*d^2*x^2) + (b^2*e^3*n^2)/(10*d^3*x^(3/2)) - (47*b^2*e^4*n^2)/(180*d^4*x) + (77*b^2*e^5*n^2)/(90*d^5*Sqrt[x]) - (77*b^2*e^6*n^2*Log[d + e*Sqrt[x]])/(90*d^6) - (2*b*e*n*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(15*d*x^(5/2)) + (b*e^2*n*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(6*d^2*x^2) - (2*b*e^3*n*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(9*d^3*x^(3/2)) + (b*e^4*n*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(3*d^4*x) - (2*b*e^5*n*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(3*d^6*Sqrt[x]) + (e^6*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(3*d^6) - (a + b*Log[c*(d + e*Sqrt[x])^n])^2/(3*x^3) - (2*b*e^6*n*(a + b*Log[c*(d + e*Sqrt[x])^n])*Log[-((e*Sqrt[x])/d)])/(3*d^6) + (137*b^2*e^6*n^2*Log[x])/(180*d^6) - (2*b^2*e^6*n^2*PolyLog[2, 1 + (e*Sqrt[x])/d])/(3*d^6)","A",26,12,24,0.5000,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
415,1,907,0,1.0070775,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \, dx","Int[x^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^3,x]","-\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}","-\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,"(-15*b^3*d^4*n^3*(d + e*Sqrt[x])^2)/(4*e^6) + (40*b^3*d^3*n^3*(d + e*Sqrt[x])^3)/(27*e^6) - (15*b^3*d^2*n^3*(d + e*Sqrt[x])^4)/(32*e^6) + (12*b^3*d*n^3*(d + e*Sqrt[x])^5)/(125*e^6) - (b^3*n^3*(d + e*Sqrt[x])^6)/(108*e^6) - (12*a*b^2*d^5*n^2*Sqrt[x])/e^5 + (12*b^3*d^5*n^3*Sqrt[x])/e^5 - (12*b^3*d^5*n^2*(d + e*Sqrt[x])*Log[c*(d + e*Sqrt[x])^n])/e^6 + (15*b^2*d^4*n^2*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(2*e^6) - (40*b^2*d^3*n^2*(d + e*Sqrt[x])^3*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(9*e^6) + (15*b^2*d^2*n^2*(d + e*Sqrt[x])^4*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(8*e^6) - (12*b^2*d*n^2*(d + e*Sqrt[x])^5*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(25*e^6) + (b^2*n^2*(d + e*Sqrt[x])^6*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(18*e^6) + (6*b*d^5*n*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/e^6 - (15*b*d^4*n*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(2*e^6) + (20*b*d^3*n*(d + e*Sqrt[x])^3*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(3*e^6) - (15*b*d^2*n*(d + e*Sqrt[x])^4*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(4*e^6) + (6*b*d*n*(d + e*Sqrt[x])^5*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(5*e^6) - (b*n*(d + e*Sqrt[x])^6*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(6*e^6) - (2*d^5*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/e^6 + (5*d^4*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/e^6 - (20*d^3*(d + e*Sqrt[x])^3*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/(3*e^6) + (5*d^2*(d + e*Sqrt[x])^4*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/e^6 - (2*d*(d + e*Sqrt[x])^5*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/e^6 + ((d + e*Sqrt[x])^6*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/(3*e^6)","A",28,8,24,0.3333,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
416,1,595,0,0.619151,"\int x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \, dx","Int[x*(a + b*Log[c*(d + e*Sqrt[x])^n])^3,x]","\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{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{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{\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{9 b^3 d^2 n^3 \left(d+e \sqrt{x}\right)^2}{4 e^4}+\frac{12 b^3 d^3 n^3 \sqrt{x}}{e^3}-\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}","\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{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{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{\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{9 b^3 d^2 n^3 \left(d+e \sqrt{x}\right)^2}{4 e^4}+\frac{12 b^3 d^3 n^3 \sqrt{x}}{e^3}-\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,"(-9*b^3*d^2*n^3*(d + e*Sqrt[x])^2)/(4*e^4) + (4*b^3*d*n^3*(d + e*Sqrt[x])^3)/(9*e^4) - (3*b^3*n^3*(d + e*Sqrt[x])^4)/(64*e^4) - (12*a*b^2*d^3*n^2*Sqrt[x])/e^3 + (12*b^3*d^3*n^3*Sqrt[x])/e^3 - (12*b^3*d^3*n^2*(d + e*Sqrt[x])*Log[c*(d + e*Sqrt[x])^n])/e^4 + (9*b^2*d^2*n^2*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(2*e^4) - (4*b^2*d*n^2*(d + e*Sqrt[x])^3*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(3*e^4) + (3*b^2*n^2*(d + e*Sqrt[x])^4*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(16*e^4) + (6*b*d^3*n*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/e^4 - (9*b*d^2*n*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(2*e^4) + (2*b*d*n*(d + e*Sqrt[x])^3*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/e^4 - (3*b*n*(d + e*Sqrt[x])^4*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(8*e^4) - (2*d^3*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/e^4 + (3*d^2*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/e^4 - (2*d*(d + e*Sqrt[x])^3*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/e^4 + ((d + e*Sqrt[x])^4*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/(2*e^4)","A",20,8,22,0.3636,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
417,1,284,0,0.2511274,"\int \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3 \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])^3,x]","\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}","\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,"(-3*b^3*n^3*(d + e*Sqrt[x])^2)/(4*e^2) - (12*a*b^2*d*n^2*Sqrt[x])/e + (12*b^3*d*n^3*Sqrt[x])/e - (12*b^3*d*n^2*(d + e*Sqrt[x])*Log[c*(d + e*Sqrt[x])^n])/e^2 + (3*b^2*n^2*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(2*e^2) + (6*b*d*n*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/e^2 - (3*b*n*(d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(2*e^2) - (2*d*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/e^2 + ((d + e*Sqrt[x])^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/e^2","A",12,8,20,0.4000,1,"{2451, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
418,1,135,0,0.1964248,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{x} \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])^3/x,x]","-12 b^2 n^2 \text{PolyLog}\left(3,\frac{e \sqrt{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+6 b n \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2+12 b^3 n^3 \text{PolyLog}\left(4,\frac{e \sqrt{x}}{d}+1\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)^3","-12 b^2 n^2 \text{PolyLog}\left(3,\frac{e \sqrt{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)+6 b n \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2+12 b^3 n^3 \text{PolyLog}\left(4,\frac{e \sqrt{x}}{d}+1\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)^3",1,"2*(a + b*Log[c*(d + e*Sqrt[x])^n])^3*Log[-((e*Sqrt[x])/d)] + 6*b*n*(a + b*Log[c*(d + e*Sqrt[x])^n])^2*PolyLog[2, 1 + (e*Sqrt[x])/d] - 12*b^2*n^2*(a + b*Log[c*(d + e*Sqrt[x])^n])*PolyLog[3, 1 + (e*Sqrt[x])/d] + 12*b^3*n^3*PolyLog[4, 1 + (e*Sqrt[x])/d]","A",6,6,24,0.2500,1,"{2454, 2396, 2433, 2374, 2383, 6589}"
419,1,283,0,0.5947437,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{x^2} \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])^3/x^2,x]","-\frac{6 b^2 e^2 n^2 \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{d^2}+\frac{6 b^3 e^2 n^3 \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right)}{d^2}+\frac{6 b^3 e^2 n^3 \text{PolyLog}\left(3,\frac{e \sqrt{x}}{d}+1\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(-\frac{e \sqrt{x}}{d}\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{d^2}+\frac{e^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{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^2 e^2 n^2 \text{PolyLog}\left(2,\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^3 e^2 n^3 \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right)}{d^2}+\frac{6 b^3 e^2 n^3 \text{PolyLog}\left(3,\frac{d}{d+e \sqrt{x}}\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}",1,"(-3*b*e*n*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(d^2*Sqrt[x]) + (e^2*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/d^2 - (a + b*Log[c*(d + e*Sqrt[x])^n])^3/x + (6*b^2*e^2*n^2*(a + b*Log[c*(d + e*Sqrt[x])^n])*Log[-((e*Sqrt[x])/d)])/d^2 - (3*b*e^2*n*(a + b*Log[c*(d + e*Sqrt[x])^n])^2*Log[-((e*Sqrt[x])/d)])/d^2 + (6*b^3*e^2*n^3*PolyLog[2, 1 + (e*Sqrt[x])/d])/d^2 - (6*b^2*e^2*n^2*(a + b*Log[c*(d + e*Sqrt[x])^n])*PolyLog[2, 1 + (e*Sqrt[x])/d])/d^2 + (6*b^3*e^2*n^3*PolyLog[3, 1 + (e*Sqrt[x])/d])/d^2","A",13,12,24,0.5000,1,"{2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391}"
420,1,550,0,1.4969474,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{x^3} \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^n])^3/x^3,x]","-\frac{3 b^2 e^4 n^2 \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)}{d^4}+\frac{11 b^3 e^4 n^3 \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right)}{2 d^4}+\frac{3 b^3 e^4 n^3 \text{PolyLog}\left(3,\frac{e \sqrt{x}}{d}+1\right)}{d^4}+\frac{11 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)}{2 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{e^4 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^3}{2 d^4}-\frac{5 b e^4 n \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^n\right)\right)^2}{4 d^4}-\frac{3 b e^4 n \log \left(-\frac{e \sqrt{x}}{d}\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{b^3 e^3 n^3}{2 d^3 \sqrt{x}}+\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{3 b^2 e^4 n^2 \text{PolyLog}\left(2,\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^3 e^4 n^3 \text{PolyLog}\left(2,\frac{d}{d+e \sqrt{x}}\right)}{2 d^4}+\frac{3 b^3 e^4 n^3 \text{PolyLog}\left(2,\frac{e \sqrt{x}}{d}+1\right)}{d^4}+\frac{3 b^3 e^4 n^3 \text{PolyLog}\left(3,\frac{d}{d+e \sqrt{x}}\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{b^3 e^3 n^3}{2 d^3 \sqrt{x}}+\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}",1,"-(b^3*e^3*n^3)/(2*d^3*Sqrt[x]) + (b^3*e^4*n^3*Log[d + e*Sqrt[x]])/(2*d^4) - (b^2*e^2*n^2*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(2*d^2*x) + (5*b^2*e^3*n^2*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n]))/(2*d^4*Sqrt[x]) - (5*b*e^4*n*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(4*d^4) - (b*e*n*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(2*d*x^(3/2)) + (3*b*e^2*n*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(4*d^2*x) - (3*b*e^3*n*(d + e*Sqrt[x])*(a + b*Log[c*(d + e*Sqrt[x])^n])^2)/(2*d^4*Sqrt[x]) + (e^4*(a + b*Log[c*(d + e*Sqrt[x])^n])^3)/(2*d^4) - (a + b*Log[c*(d + e*Sqrt[x])^n])^3/(2*x^2) + (11*b^2*e^4*n^2*(a + b*Log[c*(d + e*Sqrt[x])^n])*Log[-((e*Sqrt[x])/d)])/(2*d^4) - (3*b*e^4*n*(a + b*Log[c*(d + e*Sqrt[x])^n])^2*Log[-((e*Sqrt[x])/d)])/(2*d^4) - (3*b^3*e^4*n^3*Log[x])/(2*d^4) + (11*b^3*e^4*n^3*PolyLog[2, 1 + (e*Sqrt[x])/d])/(2*d^4) - (3*b^2*e^4*n^2*(a + b*Log[c*(d + e*Sqrt[x])^n])*PolyLog[2, 1 + (e*Sqrt[x])/d])/d^4 + (3*b^3*e^4*n^3*PolyLog[3, 1 + (e*Sqrt[x])/d])/d^4","A",35,17,24,0.7083,1,"{2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31, 44}"
421,1,171,0,0.1315679,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \, dx","Int[x^3*(a + b*Log[c*(d + e/Sqrt[x])^n]),x]","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)+\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^7 n \sqrt{x}}{4 d^7}-\frac{b e^6 n x}{8 d^6}-\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 n x^{7/2}}{28 d}","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)+\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^7 n \sqrt{x}}{4 d^7}-\frac{b e^6 n x}{8 d^6}-\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 n x^{7/2}}{28 d}",1,"(b*e^7*n*Sqrt[x])/(4*d^7) - (b*e^6*n*x)/(8*d^6) + (b*e^5*n*x^(3/2))/(12*d^5) - (b*e^4*n*x^2)/(16*d^4) + (b*e^3*n*x^(5/2))/(20*d^3) - (b*e^2*n*x^3)/(24*d^2) + (b*e*n*x^(7/2))/(28*d) - (b*e^8*n*Log[d + e/Sqrt[x]])/(4*d^8) + (x^4*(a + b*Log[c*(d + e/Sqrt[x])^n]))/4 - (b*e^8*n*Log[x])/(8*d^8)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
422,1,139,0,0.0962967,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \, dx","Int[x^2*(a + b*Log[c*(d + e/Sqrt[x])^n]),x]","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)+\frac{b e^3 n x^{3/2}}{9 d^3}-\frac{b e^2 n x^2}{12 d^2}+\frac{b e^5 n \sqrt{x}}{3 d^5}-\frac{b e^4 n x}{6 d^4}-\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 n x^{5/2}}{15 d}","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)+\frac{b e^3 n x^{3/2}}{9 d^3}-\frac{b e^2 n x^2}{12 d^2}+\frac{b e^5 n \sqrt{x}}{3 d^5}-\frac{b e^4 n x}{6 d^4}-\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 n x^{5/2}}{15 d}",1,"(b*e^5*n*Sqrt[x])/(3*d^5) - (b*e^4*n*x)/(6*d^4) + (b*e^3*n*x^(3/2))/(9*d^3) - (b*e^2*n*x^2)/(12*d^2) + (b*e*n*x^(5/2))/(15*d) - (b*e^6*n*Log[d + e/Sqrt[x]])/(3*d^6) + (x^3*(a + b*Log[c*(d + e/Sqrt[x])^n]))/3 - (b*e^6*n*Log[x])/(6*d^6)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
423,1,107,0,0.0727471,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \, dx","Int[x*(a + b*Log[c*(d + e/Sqrt[x])^n]),x]","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)+\frac{b e^3 n \sqrt{x}}{2 d^3}-\frac{b e^2 n x}{4 d^2}-\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 n x^{3/2}}{6 d}","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)+\frac{b e^3 n \sqrt{x}}{2 d^3}-\frac{b e^2 n x}{4 d^2}-\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 n x^{3/2}}{6 d}",1,"(b*e^3*n*Sqrt[x])/(2*d^3) - (b*e^2*n*x)/(4*d^2) + (b*e*n*x^(3/2))/(6*d) - (b*e^4*n*Log[d + e/Sqrt[x]])/(2*d^4) + (x^2*(a + b*Log[c*(d + e/Sqrt[x])^n]))/2 - (b*e^4*n*Log[x])/(4*d^4)","A",4,3,20,0.1500,1,"{2454, 2395, 44}"
424,1,53,0,0.0343658,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right) \, dx","Int[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)-\frac{b e^2 n \log \left(d \sqrt{x}+e\right)}{d^2}+\frac{b e n \sqrt{x}}{d}","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,"(b*e*n*Sqrt[x])/d + a*x + b*x*Log[c*(d + e/Sqrt[x])^n] - (b*e^2*n*Log[e + d*Sqrt[x]])/d^2","A",6,4,18,0.2222,1,"{2448, 263, 190, 43}"
425,1,51,0,0.0502189,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{x} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])/x,x]","-2 b n \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\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{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\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)",1,"-2*(a + b*Log[c*(d + e/Sqrt[x])^n])*Log[-(e/(d*Sqrt[x]))] - 2*b*n*PolyLog[2, 1 + e/(d*Sqrt[x])]","A",3,3,22,0.1364,1,"{2454, 2394, 2315}"
426,1,65,0,0.051102,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{x^2} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])/x^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}","-\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,"(b*n)/(2*x) - (b*d*n)/(e*Sqrt[x]) + (b*d^2*n*Log[d + e/Sqrt[x]])/e^2 - (a + b*Log[c*(d + e/Sqrt[x])^n])/x","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
427,1,104,0,0.0757875,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{x^3} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])/x^3,x]","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{2 x^2}-\frac{b d^3 n}{2 e^3 \sqrt{x}}+\frac{b d^2 n}{4 e^2 x}+\frac{b d^4 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{2 e^4}-\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^3 n}{2 e^3 \sqrt{x}}+\frac{b d^2 n}{4 e^2 x}+\frac{b d^4 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{2 e^4}-\frac{b d n}{6 e x^{3/2}}+\frac{b n}{8 x^2}",1,"(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) - (a + b*Log[c*(d + e/Sqrt[x])^n])/(2*x^2)","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
428,1,136,0,0.0970842,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{x^4} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])/x^4,x]","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{3 x^3}-\frac{b d^3 n}{9 e^3 x^{3/2}}+\frac{b d^2 n}{12 e^2 x^2}-\frac{b d^5 n}{3 e^5 \sqrt{x}}+\frac{b d^4 n}{6 e^4 x}+\frac{b d^6 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{3 e^6}-\frac{b d n}{15 e x^{5/2}}+\frac{b n}{18 x^3}","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)}{3 x^3}-\frac{b d^3 n}{9 e^3 x^{3/2}}+\frac{b d^2 n}{12 e^2 x^2}-\frac{b d^5 n}{3 e^5 \sqrt{x}}+\frac{b d^4 n}{6 e^4 x}+\frac{b d^6 n \log \left(d+\frac{e}{\sqrt{x}}\right)}{3 e^6}-\frac{b d n}{15 e x^{5/2}}+\frac{b n}{18 x^3}",1,"(b*n)/(18*x^3) - (b*d*n)/(15*e*x^(5/2)) + (b*d^2*n)/(12*e^2*x^2) - (b*d^3*n)/(9*e^3*x^(3/2)) + (b*d^4*n)/(6*e^4*x) - (b*d^5*n)/(3*e^5*Sqrt[x]) + (b*d^6*n*Log[d + e/Sqrt[x]])/(3*e^6) - (a + b*Log[c*(d + e/Sqrt[x])^n])/(3*x^3)","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
429,1,428,0,1.0071948,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \, dx","Int[x^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^2,x]","\frac{2 b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right)}{3 d^6}+\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{e^6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{3 d^6}+\frac{2 b e^6 n \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 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 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{b^2 e^3 n^2 x^{3/2}}{10 d^3}+\frac{b^2 e^2 n^2 x^2}{30 d^2}-\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{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{2 b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{\sqrt{x}}}\right)}{3 d^6}+\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^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 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{b^2 e^3 n^2 x^{3/2}}{10 d^3}+\frac{b^2 e^2 n^2 x^2}{30 d^2}-\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{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}",1,"(-77*b^2*e^5*n^2*Sqrt[x])/(90*d^5) + (47*b^2*e^4*n^2*x)/(180*d^4) - (b^2*e^3*n^2*x^(3/2))/(10*d^3) + (b^2*e^2*n^2*x^2)/(30*d^2) + (77*b^2*e^6*n^2*Log[d + e/Sqrt[x]])/(90*d^6) + (2*b*e^5*n*(d + e/Sqrt[x])*Sqrt[x]*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(3*d^6) - (b*e^4*n*x*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(3*d^4) + (2*b*e^3*n*x^(3/2)*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(9*d^3) - (b*e^2*n*x^2*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(6*d^2) + (2*b*e*n*x^(5/2)*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(15*d) - (e^6*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(3*d^6) + (x^3*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/3 + (2*b*e^6*n*(a + b*Log[c*(d + e/Sqrt[x])^n])*Log[-(e/(d*Sqrt[x]))])/(3*d^6) + (137*b^2*e^6*n^2*Log[x])/(180*d^6) + (2*b^2*e^6*n^2*PolyLog[2, 1 + e/(d*Sqrt[x])])/(3*d^6)","A",26,12,24,0.5000,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
430,1,311,0,0.6372957,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \, dx","Int[x*(a + b*Log[c*(d + e/Sqrt[x])^n])^2,x]","\frac{b^2 e^4 n^2 \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right)}{d^4}-\frac{e^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{2 d^4}+\frac{b e^4 n \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{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{5 b^2 e^3 n^2 \sqrt{x}}{6 d^3}+\frac{b^2 e^2 n^2 x}{6 d^2}+\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{b^2 e^4 n^2 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{\sqrt{x}}}\right)}{d^4}+\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{5 b^2 e^3 n^2 \sqrt{x}}{6 d^3}+\frac{b^2 e^2 n^2 x}{6 d^2}+\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}",1,"(-5*b^2*e^3*n^2*Sqrt[x])/(6*d^3) + (b^2*e^2*n^2*x)/(6*d^2) + (5*b^2*e^4*n^2*Log[d + e/Sqrt[x]])/(6*d^4) + (b*e^3*n*(d + e/Sqrt[x])*Sqrt[x]*(a + b*Log[c*(d + e/Sqrt[x])^n]))/d^4 - (b*e^2*n*x*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(2*d^2) + (b*e*n*x^(3/2)*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(3*d) - (e^4*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(2*d^4) + (x^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/2 + (b*e^4*n*(a + b*Log[c*(d + e/Sqrt[x])^n])*Log[-(e/(d*Sqrt[x]))])/d^4 + (11*b^2*e^4*n^2*Log[x])/(12*d^4) + (b^2*e^4*n^2*PolyLog[2, 1 + e/(d*Sqrt[x])])/d^4","A",18,12,22,0.5455,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
431,1,174,0,0.3544662,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2 \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])^2,x]","\frac{2 b^2 e^2 n^2 \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right)}{d^2}-\frac{e^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{d^2}+\frac{2 b e^2 n \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{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{b^2 e^2 n^2 \log (x)}{d^2}","-\frac{2 b^2 e^2 n^2 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{\sqrt{x}}}\right)}{d^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{b^2 e^2 n^2 \log (x)}{d^2}",1,"(2*b*e*n*(d + e/Sqrt[x])*Sqrt[x]*(a + b*Log[c*(d + e/Sqrt[x])^n]))/d^2 - (e^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/d^2 + x*(a + b*Log[c*(d + e/Sqrt[x])^n])^2 + (2*b*e^2*n*(a + b*Log[c*(d + e/Sqrt[x])^n])*Log[-(e/(d*Sqrt[x]))])/d^2 + (b^2*e^2*n^2*Log[x])/d^2 + (2*b^2*e^2*n^2*PolyLog[2, 1 + e/(d*Sqrt[x])])/d^2","A",11,11,20,0.5500,1,"{2451, 2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31}"
432,1,93,0,0.1311655,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{x} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])^2/x,x]","-4 b n \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)+4 b^2 n^2 \text{PolyLog}\left(3,\frac{e}{d \sqrt{x}}+1\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 n \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)+4 b^2 n^2 \text{PolyLog}\left(3,\frac{e}{d \sqrt{x}}+1\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",1,"-2*(a + b*Log[c*(d + e/Sqrt[x])^n])^2*Log[-(e/(d*Sqrt[x]))] - 4*b*n*(a + b*Log[c*(d + e/Sqrt[x])^n])*PolyLog[2, 1 + e/(d*Sqrt[x])] + 4*b^2*n^2*PolyLog[3, 1 + e/(d*Sqrt[x])]","A",5,5,24,0.2083,1,"{2454, 2396, 2433, 2374, 6589}"
433,1,195,0,0.1976996,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{x^2} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])^2/x^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}}","\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,"-(b^2*n^2*(d + e/Sqrt[x])^2)/(2*e^2) - (4*a*b*d*n)/(e*Sqrt[x]) + (4*b^2*d*n^2)/(e*Sqrt[x]) - (4*b^2*d*n*(d + e/Sqrt[x])*Log[c*(d + e/Sqrt[x])^n])/e^2 + (b*n*(d + e/Sqrt[x])^2*(a + b*Log[c*(d + e/Sqrt[x])^n]))/e^2 + (2*d*(d + e/Sqrt[x])*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/e^2 - ((d + e/Sqrt[x])^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/e^2","A",10,8,24,0.3333,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
434,1,263,0,0.366075,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{x^3} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])^2/x^3,x]","-\frac{1}{12} b n \left(\frac{48 d^3 \left(d+\frac{e}{\sqrt{x}}\right)}{e^4}-\frac{36 d^2 \left(d+\frac{e}{\sqrt{x}}\right)^2}{e^4}-\frac{12 d^4 \log \left(d+\frac{e}{\sqrt{x}}\right)}{e^4}+\frac{16 d \left(d+\frac{e}{\sqrt{x}}\right)^3}{e^4}-\frac{3 \left(d+\frac{e}{\sqrt{x}}\right)^4}{e^4}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)-\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{2 x^2}+\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{b^2 d^4 n^2 \log ^2\left(d+\frac{e}{\sqrt{x}}\right)}{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}","\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{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{b^2 d^4 n^2 \log ^2\left(d+\frac{e}{\sqrt{x}}\right)}{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,"(-3*b^2*d^2*n^2*(d + e/Sqrt[x])^2)/(2*e^4) + (4*b^2*d*n^2*(d + e/Sqrt[x])^3)/(9*e^4) - (b^2*n^2*(d + e/Sqrt[x])^4)/(16*e^4) + (4*b^2*d^3*n^2)/(e^3*Sqrt[x]) - (b^2*d^4*n^2*Log[d + e/Sqrt[x]]^2)/(2*e^4) - (b*n*((48*d^3*(d + e/Sqrt[x]))/e^4 - (36*d^2*(d + e/Sqrt[x])^2)/e^4 + (16*d*(d + e/Sqrt[x])^3)/e^4 - (3*(d + e/Sqrt[x])^4)/e^4 - (12*d^4*Log[d + e/Sqrt[x]])/e^4)*(a + b*Log[c*(d + e/Sqrt[x])^n]))/12 - (a + b*Log[c*(d + e/Sqrt[x])^n])^2/(2*x^2)","A",8,8,24,0.3333,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
435,1,355,0,0.4707049,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{x^4} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])^2/x^4,x]","-\frac{1}{90} b n \left(\frac{360 d^5 \left(d+\frac{e}{\sqrt{x}}\right)}{e^6}-\frac{450 d^4 \left(d+\frac{e}{\sqrt{x}}\right)^2}{e^6}+\frac{400 d^3 \left(d+\frac{e}{\sqrt{x}}\right)^3}{e^6}-\frac{225 d^2 \left(d+\frac{e}{\sqrt{x}}\right)^4}{e^6}-\frac{60 d^6 \log \left(d+\frac{e}{\sqrt{x}}\right)}{e^6}+\frac{72 d \left(d+\frac{e}{\sqrt{x}}\right)^5}{e^6}-\frac{10 \left(d+\frac{e}{\sqrt{x}}\right)^6}{e^6}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)-\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{3 x^3}+\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{b^2 d^6 n^2 \log ^2\left(d+\frac{e}{\sqrt{x}}\right)}{3 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}","\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{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{b^2 d^6 n^2 \log ^2\left(d+\frac{e}{\sqrt{x}}\right)}{3 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,"(-5*b^2*d^4*n^2*(d + e/Sqrt[x])^2)/(2*e^6) + (40*b^2*d^3*n^2*(d + e/Sqrt[x])^3)/(27*e^6) - (5*b^2*d^2*n^2*(d + e/Sqrt[x])^4)/(8*e^6) + (4*b^2*d*n^2*(d + e/Sqrt[x])^5)/(25*e^6) - (b^2*n^2*(d + e/Sqrt[x])^6)/(54*e^6) + (4*b^2*d^5*n^2)/(e^5*Sqrt[x]) - (b^2*d^6*n^2*Log[d + e/Sqrt[x]]^2)/(3*e^6) - (b*n*((360*d^5*(d + e/Sqrt[x]))/e^6 - (450*d^4*(d + e/Sqrt[x])^2)/e^6 + (400*d^3*(d + e/Sqrt[x])^3)/e^6 - (225*d^2*(d + e/Sqrt[x])^4)/e^6 + (72*d*(d + e/Sqrt[x])^5)/e^6 - (10*(d + e/Sqrt[x])^6)/e^6 - (60*d^6*Log[d + e/Sqrt[x]])/e^6)*(a + b*Log[c*(d + e/Sqrt[x])^n]))/90 - (a + b*Log[c*(d + e/Sqrt[x])^n])^2/(3*x^3)","A",8,8,24,0.3333,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
436,1,546,0,1.4915439,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3 \, dx","Int[x*(a + b*Log[c*(d + e/Sqrt[x])^n])^3,x]","\frac{3 b^2 e^4 n^2 \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{d^4}-\frac{11 b^3 e^4 n^3 \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right)}{2 d^4}-\frac{3 b^3 e^4 n^3 \text{PolyLog}\left(3,\frac{e}{d \sqrt{x}}+1\right)}{d^4}-\frac{11 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)}{2 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{e^4 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{2 d^4}+\frac{5 b e^4 n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{4 d^4}+\frac{3 b e^4 n \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}{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{b^3 e^3 n^3 \sqrt{x}}{2 d^3}-\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{3 b^2 e^4 n^2 \text{PolyLog}\left(2,\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^3 e^4 n^3 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{\sqrt{x}}}\right)}{2 d^4}-\frac{3 b^3 e^4 n^3 \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right)}{d^4}-\frac{3 b^3 e^4 n^3 \text{PolyLog}\left(3,\frac{d}{d+\frac{e}{\sqrt{x}}}\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{b^3 e^3 n^3 \sqrt{x}}{2 d^3}-\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}",1,"(b^3*e^3*n^3*Sqrt[x])/(2*d^3) - (b^3*e^4*n^3*Log[d + e/Sqrt[x]])/(2*d^4) - (5*b^2*e^3*n^2*(d + e/Sqrt[x])*Sqrt[x]*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(2*d^4) + (b^2*e^2*n^2*x*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(2*d^2) + (5*b*e^4*n*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(4*d^4) + (3*b*e^3*n*(d + e/Sqrt[x])*Sqrt[x]*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(2*d^4) - (3*b*e^2*n*x*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(4*d^2) + (b*e*n*x^(3/2)*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(2*d) - (e^4*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/(2*d^4) + (x^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/2 - (11*b^2*e^4*n^2*(a + b*Log[c*(d + e/Sqrt[x])^n])*Log[-(e/(d*Sqrt[x]))])/(2*d^4) + (3*b*e^4*n*(a + b*Log[c*(d + e/Sqrt[x])^n])^2*Log[-(e/(d*Sqrt[x]))])/(2*d^4) - (3*b^3*e^4*n^3*Log[x])/(2*d^4) - (11*b^3*e^4*n^3*PolyLog[2, 1 + e/(d*Sqrt[x])])/(2*d^4) + (3*b^2*e^4*n^2*(a + b*Log[c*(d + e/Sqrt[x])^n])*PolyLog[2, 1 + e/(d*Sqrt[x])])/d^4 - (3*b^3*e^4*n^3*PolyLog[3, 1 + e/(d*Sqrt[x])])/d^4","A",35,17,22,0.7727,1,"{2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31, 44}"
437,1,281,0,0.6161065,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3 \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])^3,x]","\frac{6 b^2 e^2 n^2 \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)}{d^2}-\frac{6 b^3 e^2 n^3 \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right)}{d^2}-\frac{6 b^3 e^2 n^3 \text{PolyLog}\left(3,\frac{e}{d \sqrt{x}}+1\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(-\frac{e}{d \sqrt{x}}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2}{d^2}-\frac{e^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{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^2 e^2 n^2 \text{PolyLog}\left(2,\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^3 e^2 n^3 \text{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right)}{d^2}-\frac{6 b^3 e^2 n^3 \text{PolyLog}\left(3,\frac{d}{d+\frac{e}{\sqrt{x}}}\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",1,"(3*b*e*n*(d + e/Sqrt[x])*Sqrt[x]*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/d^2 - (e^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/d^2 + x*(a + b*Log[c*(d + e/Sqrt[x])^n])^3 - (6*b^2*e^2*n^2*(a + b*Log[c*(d + e/Sqrt[x])^n])*Log[-(e/(d*Sqrt[x]))])/d^2 + (3*b*e^2*n*(a + b*Log[c*(d + e/Sqrt[x])^n])^2*Log[-(e/(d*Sqrt[x]))])/d^2 - (6*b^3*e^2*n^3*PolyLog[2, 1 + e/(d*Sqrt[x])])/d^2 + (6*b^2*e^2*n^2*(a + b*Log[c*(d + e/Sqrt[x])^n])*PolyLog[2, 1 + e/(d*Sqrt[x])])/d^2 - (6*b^3*e^2*n^3*PolyLog[3, 1 + e/(d*Sqrt[x])])/d^2","A",14,13,20,0.6500,1,"{2451, 2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391}"
438,1,135,0,0.1975348,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{x} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])^3/x,x]","12 b^2 n^2 \text{PolyLog}\left(3,\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{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2-12 b^3 n^3 \text{PolyLog}\left(4,\frac{e}{d \sqrt{x}}+1\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)^3","12 b^2 n^2 \text{PolyLog}\left(3,\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{PolyLog}\left(2,\frac{e}{d \sqrt{x}}+1\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^2-12 b^3 n^3 \text{PolyLog}\left(4,\frac{e}{d \sqrt{x}}+1\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)^3",1,"-2*(a + b*Log[c*(d + e/Sqrt[x])^n])^3*Log[-(e/(d*Sqrt[x]))] - 6*b*n*(a + b*Log[c*(d + e/Sqrt[x])^n])^2*PolyLog[2, 1 + e/(d*Sqrt[x])] + 12*b^2*n^2*(a + b*Log[c*(d + e/Sqrt[x])^n])*PolyLog[3, 1 + e/(d*Sqrt[x])] - 12*b^3*n^3*PolyLog[4, 1 + e/(d*Sqrt[x])]","A",6,6,24,0.2500,1,"{2454, 2396, 2433, 2374, 2383, 6589}"
439,1,285,0,0.2723808,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{x^2} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])^3/x^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}}","-\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,"(3*b^3*n^3*(d + e/Sqrt[x])^2)/(4*e^2) + (12*a*b^2*d*n^2)/(e*Sqrt[x]) - (12*b^3*d*n^3)/(e*Sqrt[x]) + (12*b^3*d*n^2*(d + e/Sqrt[x])*Log[c*(d + e/Sqrt[x])^n])/e^2 - (3*b^2*n^2*(d + e/Sqrt[x])^2*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(2*e^2) - (6*b*d*n*(d + e/Sqrt[x])*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/e^2 + (3*b*n*(d + e/Sqrt[x])^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(2*e^2) + (2*d*(d + e/Sqrt[x])*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/e^2 - ((d + e/Sqrt[x])^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/e^2","A",12,8,24,0.3333,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
440,1,595,0,0.6416989,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{x^3} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])^3/x^3,x]","-\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{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{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{\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{9 b^3 d^2 n^3 \left(d+\frac{e}{\sqrt{x}}\right)^2}{4 e^4}-\frac{12 b^3 d^3 n^3}{e^3 \sqrt{x}}+\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}","-\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{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{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{\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{9 b^3 d^2 n^3 \left(d+\frac{e}{\sqrt{x}}\right)^2}{4 e^4}-\frac{12 b^3 d^3 n^3}{e^3 \sqrt{x}}+\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,"(9*b^3*d^2*n^3*(d + e/Sqrt[x])^2)/(4*e^4) - (4*b^3*d*n^3*(d + e/Sqrt[x])^3)/(9*e^4) + (3*b^3*n^3*(d + e/Sqrt[x])^4)/(64*e^4) + (12*a*b^2*d^3*n^2)/(e^3*Sqrt[x]) - (12*b^3*d^3*n^3)/(e^3*Sqrt[x]) + (12*b^3*d^3*n^2*(d + e/Sqrt[x])*Log[c*(d + e/Sqrt[x])^n])/e^4 - (9*b^2*d^2*n^2*(d + e/Sqrt[x])^2*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(2*e^4) + (4*b^2*d*n^2*(d + e/Sqrt[x])^3*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(3*e^4) - (3*b^2*n^2*(d + e/Sqrt[x])^4*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(16*e^4) - (6*b*d^3*n*(d + e/Sqrt[x])*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/e^4 + (9*b*d^2*n*(d + e/Sqrt[x])^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(2*e^4) - (2*b*d*n*(d + e/Sqrt[x])^3*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/e^4 + (3*b*n*(d + e/Sqrt[x])^4*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(8*e^4) + (2*d^3*(d + e/Sqrt[x])*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/e^4 - (3*d^2*(d + e/Sqrt[x])^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/e^4 + (2*d*(d + e/Sqrt[x])^3*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/e^4 - ((d + e/Sqrt[x])^4*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/(2*e^4)","A",20,8,24,0.3333,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
441,1,907,0,1.01085,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^n\right)\right)^3}{x^4} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^n])^3/x^4,x]","\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}}","\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,"(15*b^3*d^4*n^3*(d + e/Sqrt[x])^2)/(4*e^6) - (40*b^3*d^3*n^3*(d + e/Sqrt[x])^3)/(27*e^6) + (15*b^3*d^2*n^3*(d + e/Sqrt[x])^4)/(32*e^6) - (12*b^3*d*n^3*(d + e/Sqrt[x])^5)/(125*e^6) + (b^3*n^3*(d + e/Sqrt[x])^6)/(108*e^6) + (12*a*b^2*d^5*n^2)/(e^5*Sqrt[x]) - (12*b^3*d^5*n^3)/(e^5*Sqrt[x]) + (12*b^3*d^5*n^2*(d + e/Sqrt[x])*Log[c*(d + e/Sqrt[x])^n])/e^6 - (15*b^2*d^4*n^2*(d + e/Sqrt[x])^2*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(2*e^6) + (40*b^2*d^3*n^2*(d + e/Sqrt[x])^3*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(9*e^6) - (15*b^2*d^2*n^2*(d + e/Sqrt[x])^4*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(8*e^6) + (12*b^2*d*n^2*(d + e/Sqrt[x])^5*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(25*e^6) - (b^2*n^2*(d + e/Sqrt[x])^6*(a + b*Log[c*(d + e/Sqrt[x])^n]))/(18*e^6) - (6*b*d^5*n*(d + e/Sqrt[x])*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/e^6 + (15*b*d^4*n*(d + e/Sqrt[x])^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(2*e^6) - (20*b*d^3*n*(d + e/Sqrt[x])^3*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(3*e^6) + (15*b*d^2*n*(d + e/Sqrt[x])^4*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(4*e^6) - (6*b*d*n*(d + e/Sqrt[x])^5*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(5*e^6) + (b*n*(d + e/Sqrt[x])^6*(a + b*Log[c*(d + e/Sqrt[x])^n])^2)/(6*e^6) + (2*d^5*(d + e/Sqrt[x])*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/e^6 - (5*d^4*(d + e/Sqrt[x])^2*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/e^6 + (20*d^3*(d + e/Sqrt[x])^3*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/(3*e^6) - (5*d^2*(d + e/Sqrt[x])^4*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/e^6 + (2*d*(d + e/Sqrt[x])^5*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/e^6 - ((d + e/Sqrt[x])^6*(a + b*Log[c*(d + e/Sqrt[x])^n])^3)/(3*e^6)","A",28,8,24,0.3333,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
442,1,234,0,0.1879926,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \, dx","Int[x^3*(a + b*Log[c*(d + e*x^(1/3))^n]),x]","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)-\frac{b d^{10} n x^{2/3}}{8 e^{10}}-\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^{11} n \sqrt[3]{x}}{4 e^{11}}+\frac{b d^9 n x}{12 e^9}-\frac{b d^{12} n \log \left(d+e \sqrt[3]{x}\right)}{4 e^{12}}+\frac{b d n x^{11/3}}{44 e}-\frac{1}{48} b n x^4","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)-\frac{b d^{10} n x^{2/3}}{8 e^{10}}-\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^{11} n \sqrt[3]{x}}{4 e^{11}}+\frac{b d^9 n x}{12 e^9}-\frac{b d^{12} n \log \left(d+e \sqrt[3]{x}\right)}{4 e^{12}}+\frac{b d n x^{11/3}}{44 e}-\frac{1}{48} b n x^4",1,"(b*d^11*n*x^(1/3))/(4*e^11) - (b*d^10*n*x^(2/3))/(8*e^10) + (b*d^9*n*x)/(12*e^9) - (b*d^8*n*x^(4/3))/(16*e^8) + (b*d^7*n*x^(5/3))/(20*e^7) - (b*d^6*n*x^2)/(24*e^6) + (b*d^5*n*x^(7/3))/(28*e^5) - (b*d^4*n*x^(8/3))/(32*e^4) + (b*d^3*n*x^3)/(36*e^3) - (b*d^2*n*x^(10/3))/(40*e^2) + (b*d*n*x^(11/3))/(44*e) - (b*n*x^4)/48 - (b*d^12*n*Log[d + e*x^(1/3)])/(4*e^12) + (x^4*(a + b*Log[c*(d + e*x^(1/3))^n]))/4","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
443,1,185,0,0.134155,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \, dx","Int[x^2*(a + b*Log[c*(d + e*x^(1/3))^n]),x]","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)+\frac{b d^7 n x^{2/3}}{6 e^7}+\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^8 n \sqrt[3]{x}}{3 e^8}-\frac{b d^6 n x}{9 e^6}+\frac{b d^9 n \log \left(d+e \sqrt[3]{x}\right)}{3 e^9}+\frac{b d n x^{8/3}}{24 e}-\frac{1}{27} b n x^3","\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)+\frac{b d^7 n x^{2/3}}{6 e^7}+\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^8 n \sqrt[3]{x}}{3 e^8}-\frac{b d^6 n x}{9 e^6}+\frac{b d^9 n \log \left(d+e \sqrt[3]{x}\right)}{3 e^9}+\frac{b d n x^{8/3}}{24 e}-\frac{1}{27} b n x^3",1,"-(b*d^8*n*x^(1/3))/(3*e^8) + (b*d^7*n*x^(2/3))/(6*e^7) - (b*d^6*n*x)/(9*e^6) + (b*d^5*n*x^(4/3))/(12*e^5) - (b*d^4*n*x^(5/3))/(15*e^4) + (b*d^3*n*x^2)/(18*e^3) - (b*d^2*n*x^(7/3))/(21*e^2) + (b*d*n*x^(8/3))/(24*e) - (b*n*x^3)/27 + (b*d^9*n*Log[d + e*x^(1/3)])/(3*e^9) + (x^3*(a + b*Log[c*(d + e*x^(1/3))^n]))/3","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
444,1,136,0,0.0949436,"\int x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \, dx","Int[x*(a + b*Log[c*(d + e*x^(1/3))^n]),x]","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)-\frac{b d^4 n x^{2/3}}{4 e^4}-\frac{b d^2 n x^{4/3}}{8 e^2}+\frac{b d^5 n \sqrt[3]{x}}{2 e^5}+\frac{b d^3 n x}{6 e^3}-\frac{b d^6 n \log \left(d+e \sqrt[3]{x}\right)}{2 e^6}+\frac{b d n x^{5/3}}{10 e}-\frac{1}{12} b n x^2","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)-\frac{b d^4 n x^{2/3}}{4 e^4}-\frac{b d^2 n x^{4/3}}{8 e^2}+\frac{b d^5 n \sqrt[3]{x}}{2 e^5}+\frac{b d^3 n x}{6 e^3}-\frac{b d^6 n \log \left(d+e \sqrt[3]{x}\right)}{2 e^6}+\frac{b d n x^{5/3}}{10 e}-\frac{1}{12} b n x^2",1,"(b*d^5*n*x^(1/3))/(2*e^5) - (b*d^4*n*x^(2/3))/(4*e^4) + (b*d^3*n*x)/(6*e^3) - (b*d^2*n*x^(4/3))/(8*e^2) + (b*d*n*x^(5/3))/(10*e) - (b*n*x^2)/12 - (b*d^6*n*Log[d + e*x^(1/3)])/(2*e^6) + (x^2*(a + b*Log[c*(d + e*x^(1/3))^n]))/2","A",4,3,20,0.1500,1,"{2454, 2395, 43}"
445,1,77,0,0.0531322,"\int \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right) \, dx","Int[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^2 n \sqrt[3]{x}}{e^2}+\frac{b d^3 n \log \left(d+e \sqrt[3]{x}\right)}{e^3}+\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^2 n \sqrt[3]{x}}{e^2}+\frac{b d^3 n \log \left(d+e \sqrt[3]{x}\right)}{e^3}+\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",5,3,18,0.1667,1,"{2448, 266, 43}"
446,1,51,0,0.0505669,"\int \frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x} \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])/x,x]","3 b n \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\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{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\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)",1,"3*(a + b*Log[c*(d + e*x^(1/3))^n])*Log[-((e*x^(1/3))/d)] + 3*b*n*PolyLog[2, 1 + (e*x^(1/3))/d]","A",3,3,22,0.1364,1,"{2454, 2394, 2315}"
447,1,87,0,0.0679198,"\int \frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x^2} \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])/x^2,x]","-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x}+\frac{b e^2 n}{d^2 \sqrt[3]{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 n}{2 d x^{2/3}}","-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x}+\frac{b e^2 n}{d^2 \sqrt[3]{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 n}{2 d x^{2/3}}",1,"-(b*e*n)/(2*d*x^(2/3)) + (b*e^2*n)/(d^2*x^(1/3)) - (b*e^3*n*Log[d + e*x^(1/3)])/d^3 - (a + b*Log[c*(d + e*x^(1/3))^n])/x + (b*e^3*n*Log[x])/(3*d^3)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
448,1,143,0,0.0927983,"\int \frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x^3} \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])/x^3,x]","-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{2 x^2}+\frac{b e^4 n}{4 d^4 x^{2/3}}+\frac{b e^2 n}{8 d^2 x^{4/3}}-\frac{b e^5 n}{2 d^5 \sqrt[3]{x}}-\frac{b e^3 n}{6 d^3 x}+\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 n}{10 d x^{5/3}}","-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{2 x^2}+\frac{b e^4 n}{4 d^4 x^{2/3}}+\frac{b e^2 n}{8 d^2 x^{4/3}}-\frac{b e^5 n}{2 d^5 \sqrt[3]{x}}-\frac{b e^3 n}{6 d^3 x}+\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 n}{10 d x^{5/3}}",1,"-(b*e*n)/(10*d*x^(5/3)) + (b*e^2*n)/(8*d^2*x^(4/3)) - (b*e^3*n)/(6*d^3*x) + (b*e^4*n)/(4*d^4*x^(2/3)) - (b*e^5*n)/(2*d^5*x^(1/3)) + (b*e^6*n*Log[d + e*x^(1/3)])/(2*d^6) - (a + b*Log[c*(d + e*x^(1/3))^n])/(2*x^2) - (b*e^6*n*Log[x])/(6*d^6)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
449,1,192,0,0.1254049,"\int \frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{x^4} \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])/x^4,x]","-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{3 x^3}-\frac{b e^7 n}{6 d^7 x^{2/3}}-\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^8 n}{3 d^8 \sqrt[3]{x}}+\frac{b e^6 n}{9 d^6 x}-\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 n}{24 d x^{8/3}}","-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)}{3 x^3}-\frac{b e^7 n}{6 d^7 x^{2/3}}-\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^8 n}{3 d^8 \sqrt[3]{x}}+\frac{b e^6 n}{9 d^6 x}-\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 n}{24 d x^{8/3}}",1,"-(b*e*n)/(24*d*x^(8/3)) + (b*e^2*n)/(21*d^2*x^(7/3)) - (b*e^3*n)/(18*d^3*x^2) + (b*e^4*n)/(15*d^4*x^(5/3)) - (b*e^5*n)/(12*d^5*x^(4/3)) + (b*e^6*n)/(9*d^6*x) - (b*e^7*n)/(6*d^7*x^(2/3)) + (b*e^8*n)/(3*d^8*x^(1/3)) - (b*e^9*n*Log[d + e*x^(1/3)])/(3*d^9) - (a + b*Log[c*(d + e*x^(1/3))^n])/(3*x^3) + (b*e^9*n*Log[x])/(9*d^9)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
450,1,491,0,0.6973827,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \, dx","Int[x^2*(a + b*Log[c*(d + e*x^(1/3))^n])^2,x]","-\frac{b n \left(\frac{22680 d^8 \left(d+e \sqrt[3]{x}\right)}{e^9}-\frac{45360 d^7 \left(d+e \sqrt[3]{x}\right)^2}{e^9}+\frac{70560 d^6 \left(d+e \sqrt[3]{x}\right)^3}{e^9}-\frac{79380 d^5 \left(d+e \sqrt[3]{x}\right)^4}{e^9}+\frac{63504 d^4 \left(d+e \sqrt[3]{x}\right)^5}{e^9}-\frac{35280 d^3 \left(d+e \sqrt[3]{x}\right)^6}{e^9}+\frac{12960 d^2 \left(d+e \sqrt[3]{x}\right)^7}{e^9}-\frac{2520 d^9 \log \left(d+e \sqrt[3]{x}\right)}{e^9}-\frac{2835 d \left(d+e \sqrt[3]{x}\right)^8}{e^9}+\frac{280 \left(d+e \sqrt[3]{x}\right)^9}{e^9}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{3780}+\frac{1}{3} x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2+\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{b^2 d^9 n^2 \log ^2\left(d+e \sqrt[3]{x}\right)}{3 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}","\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{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{b^2 d^9 n^2 \log ^2\left(d+e \sqrt[3]{x}\right)}{3 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,"(-6*b^2*d^7*n^2*(d + e*x^(1/3))^2)/e^9 + (56*b^2*d^6*n^2*(d + e*x^(1/3))^3)/(9*e^9) - (21*b^2*d^5*n^2*(d + e*x^(1/3))^4)/(4*e^9) + (84*b^2*d^4*n^2*(d + e*x^(1/3))^5)/(25*e^9) - (14*b^2*d^3*n^2*(d + e*x^(1/3))^6)/(9*e^9) + (24*b^2*d^2*n^2*(d + e*x^(1/3))^7)/(49*e^9) - (3*b^2*d*n^2*(d + e*x^(1/3))^8)/(32*e^9) + (2*b^2*n^2*(d + e*x^(1/3))^9)/(243*e^9) + (6*b^2*d^8*n^2*x^(1/3))/e^8 - (b^2*d^9*n^2*Log[d + e*x^(1/3)]^2)/(3*e^9) - (b*n*((22680*d^8*(d + e*x^(1/3)))/e^9 - (45360*d^7*(d + e*x^(1/3))^2)/e^9 + (70560*d^6*(d + e*x^(1/3))^3)/e^9 - (79380*d^5*(d + e*x^(1/3))^4)/e^9 + (63504*d^4*(d + e*x^(1/3))^5)/e^9 - (35280*d^3*(d + e*x^(1/3))^6)/e^9 + (12960*d^2*(d + e*x^(1/3))^7)/e^9 - (2835*d*(d + e*x^(1/3))^8)/e^9 + (280*(d + e*x^(1/3))^9)/e^9 - (2520*d^9*Log[d + e*x^(1/3)])/e^9)*(a + b*Log[c*(d + e*x^(1/3))^n]))/3780 + (x^3*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/3","A",8,8,24,0.3333,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
451,1,355,0,0.4619512,"\int x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \, dx","Int[x*(a + b*Log[c*(d + e*x^(1/3))^n])^2,x]","\frac{1}{60} b n \left(\frac{360 d^5 \left(d+e \sqrt[3]{x}\right)}{e^6}-\frac{450 d^4 \left(d+e \sqrt[3]{x}\right)^2}{e^6}+\frac{400 d^3 \left(d+e \sqrt[3]{x}\right)^3}{e^6}-\frac{225 d^2 \left(d+e \sqrt[3]{x}\right)^4}{e^6}-\frac{60 d^6 \log \left(d+e \sqrt[3]{x}\right)}{e^6}+\frac{72 d \left(d+e \sqrt[3]{x}\right)^5}{e^6}-\frac{10 \left(d+e \sqrt[3]{x}\right)^6}{e^6}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2-\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{b^2 d^6 n^2 \log ^2\left(d+e \sqrt[3]{x}\right)}{2 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}","-\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{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{b^2 d^6 n^2 \log ^2\left(d+e \sqrt[3]{x}\right)}{2 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,"(15*b^2*d^4*n^2*(d + e*x^(1/3))^2)/(4*e^6) - (20*b^2*d^3*n^2*(d + e*x^(1/3))^3)/(9*e^6) + (15*b^2*d^2*n^2*(d + e*x^(1/3))^4)/(16*e^6) - (6*b^2*d*n^2*(d + e*x^(1/3))^5)/(25*e^6) + (b^2*n^2*(d + e*x^(1/3))^6)/(36*e^6) - (6*b^2*d^5*n^2*x^(1/3))/e^5 + (b^2*d^6*n^2*Log[d + e*x^(1/3)]^2)/(2*e^6) + (b*n*((360*d^5*(d + e*x^(1/3)))/e^6 - (450*d^4*(d + e*x^(1/3))^2)/e^6 + (400*d^3*(d + e*x^(1/3))^3)/e^6 - (225*d^2*(d + e*x^(1/3))^4)/e^6 + (72*d*(d + e*x^(1/3))^5)/e^6 - (10*(d + e*x^(1/3))^6)/e^6 - (60*d^6*Log[d + e*x^(1/3)])/e^6)*(a + b*Log[c*(d + e*x^(1/3))^n]))/60 + (x^2*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/2","A",8,8,22,0.3636,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
452,1,210,0,0.2897833,"\int \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2 \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])^2,x]","-\frac{1}{3} b n \left(\frac{18 d^2 \left(d+e \sqrt[3]{x}\right)}{e^3}-\frac{6 d^3 \log \left(d+e \sqrt[3]{x}\right)}{e^3}-\frac{9 d \left(d+e \sqrt[3]{x}\right)^2}{e^3}+\frac{2 \left(d+e \sqrt[3]{x}\right)^3}{e^3}\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)+x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2+\frac{6 b^2 d^2 n^2 \sqrt[3]{x}}{e^2}-\frac{b^2 d^3 n^2 \log ^2\left(d+e \sqrt[3]{x}\right)}{e^3}-\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}","\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{6 b^2 d^2 n^2 \sqrt[3]{x}}{e^2}-\frac{b^2 d^3 n^2 \log ^2\left(d+e \sqrt[3]{x}\right)}{e^3}-\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,"(-3*b^2*d*n^2*(d + e*x^(1/3))^2)/(2*e^3) + (2*b^2*n^2*(d + e*x^(1/3))^3)/(9*e^3) + (6*b^2*d^2*n^2*x^(1/3))/e^2 - (b^2*d^3*n^2*Log[d + e*x^(1/3)]^2)/e^3 - (b*n*((18*d^2*(d + e*x^(1/3)))/e^3 - (9*d*(d + e*x^(1/3))^2)/e^3 + (2*(d + e*x^(1/3))^3)/e^3 - (6*d^3*Log[d + e*x^(1/3)])/e^3)*(a + b*Log[c*(d + e*x^(1/3))^n]))/3 + x*(a + b*Log[c*(d + e*x^(1/3))^n])^2","A",8,8,20,0.4000,1,"{2451, 2398, 2411, 43, 2334, 12, 14, 2301}"
453,1,93,0,0.1314299,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{x} \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])^2/x,x]","6 b n \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)-6 b^2 n^2 \text{PolyLog}\left(3,\frac{e \sqrt[3]{x}}{d}+1\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 n \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)-6 b^2 n^2 \text{PolyLog}\left(3,\frac{e \sqrt[3]{x}}{d}+1\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",1,"3*(a + b*Log[c*(d + e*x^(1/3))^n])^2*Log[-((e*x^(1/3))/d)] + 6*b*n*(a + b*Log[c*(d + e*x^(1/3))^n])*PolyLog[2, 1 + (e*x^(1/3))/d] - 6*b^2*n^2*PolyLog[3, 1 + (e*x^(1/3))/d]","A",5,5,24,0.2083,1,"{2454, 2396, 2433, 2374, 6589}"
454,1,253,0,0.5012073,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{x^2} \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])^2/x^2,x]","\frac{2 b^2 e^3 n^2 \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right)}{d^3}-\frac{e^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{d^3}+\frac{2 b e^3 n \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{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{b^2 e^2 n^2}{d^2 \sqrt[3]{x}}+\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{2 b^2 e^3 n^2 \text{PolyLog}\left(2,\frac{d}{d+e \sqrt[3]{x}}\right)}{d^3}+\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{b^2 e^2 n^2}{d^2 \sqrt[3]{x}}+\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}",1,"-((b^2*e^2*n^2)/(d^2*x^(1/3))) + (b^2*e^3*n^2*Log[d + e*x^(1/3)])/d^3 - (b*e*n*(a + b*Log[c*(d + e*x^(1/3))^n]))/(d*x^(2/3)) + (2*b*e^2*n*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n]))/(d^3*x^(1/3)) - (e^3*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/d^3 - (a + b*Log[c*(d + e*x^(1/3))^n])^2/x + (2*b*e^3*n*(a + b*Log[c*(d + e*x^(1/3))^n])*Log[-((e*x^(1/3))/d)])/d^3 - (b^2*e^3*n^2*Log[x])/d^3 + (2*b^2*e^3*n^2*PolyLog[2, 1 + (e*x^(1/3))/d])/d^3","A",14,12,24,0.5000,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
455,1,430,0,1.0125518,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{x^3} \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])^2/x^3,x]","-\frac{b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right)}{d^6}+\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^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{e^6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{2 d^6}-\frac{b e^6 n \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{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^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 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{47 b^2 e^4 n^2}{120 d^4 x^{2/3}}-\frac{b^2 e^2 n^2}{20 d^2 x^{4/3}}+\frac{77 b^2 e^5 n^2}{60 d^5 \sqrt[3]{x}}+\frac{3 b^2 e^3 n^2}{20 d^3 x}-\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{b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{d}{d+e \sqrt[3]{x}}\right)}{d^6}+\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^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^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^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 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{47 b^2 e^4 n^2}{120 d^4 x^{2/3}}-\frac{b^2 e^2 n^2}{20 d^2 x^{4/3}}+\frac{77 b^2 e^5 n^2}{60 d^5 \sqrt[3]{x}}+\frac{3 b^2 e^3 n^2}{20 d^3 x}-\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}",1,"-(b^2*e^2*n^2)/(20*d^2*x^(4/3)) + (3*b^2*e^3*n^2)/(20*d^3*x) - (47*b^2*e^4*n^2)/(120*d^4*x^(2/3)) + (77*b^2*e^5*n^2)/(60*d^5*x^(1/3)) - (77*b^2*e^6*n^2*Log[d + e*x^(1/3)])/(60*d^6) - (b*e*n*(a + b*Log[c*(d + e*x^(1/3))^n]))/(5*d*x^(5/3)) + (b*e^2*n*(a + b*Log[c*(d + e*x^(1/3))^n]))/(4*d^2*x^(4/3)) - (b*e^3*n*(a + b*Log[c*(d + e*x^(1/3))^n]))/(3*d^3*x) + (b*e^4*n*(a + b*Log[c*(d + e*x^(1/3))^n]))/(2*d^4*x^(2/3)) - (b*e^5*n*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n]))/(d^6*x^(1/3)) + (e^6*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(2*d^6) - (a + b*Log[c*(d + e*x^(1/3))^n])^2/(2*x^2) - (b*e^6*n*(a + b*Log[c*(d + e*x^(1/3))^n])*Log[-((e*x^(1/3))/d)])/d^6 + (137*b^2*e^6*n^2*Log[x])/(180*d^6) - (b^2*e^6*n^2*PolyLog[2, 1 + (e*x^(1/3))/d])/d^6","A",26,12,24,0.5000,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
456,1,1835,0,2.2667579,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \, dx","Int[x^3*(a + b*Log[c*(d + e*x^(1/3))^n])^3,x]","-\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}}","-\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,"(-99*b^3*d^10*n^3*(d + e*x^(1/3))^2)/(8*e^12) + (110*b^3*d^9*n^3*(d + e*x^(1/3))^3)/(9*e^12) - (1485*b^3*d^8*n^3*(d + e*x^(1/3))^4)/(128*e^12) + (1188*b^3*d^7*n^3*(d + e*x^(1/3))^5)/(125*e^12) - (77*b^3*d^6*n^3*(d + e*x^(1/3))^6)/(12*e^12) + (1188*b^3*d^5*n^3*(d + e*x^(1/3))^7)/(343*e^12) - (1485*b^3*d^4*n^3*(d + e*x^(1/3))^8)/(1024*e^12) + (110*b^3*d^3*n^3*(d + e*x^(1/3))^9)/(243*e^12) - (99*b^3*d^2*n^3*(d + e*x^(1/3))^10)/(1000*e^12) + (18*b^3*d*n^3*(d + e*x^(1/3))^11)/(1331*e^12) - (b^3*n^3*(d + e*x^(1/3))^12)/(1152*e^12) - (18*a*b^2*d^11*n^2*x^(1/3))/e^11 + (18*b^3*d^11*n^3*x^(1/3))/e^11 - (18*b^3*d^11*n^2*(d + e*x^(1/3))*Log[c*(d + e*x^(1/3))^n])/e^12 + (99*b^2*d^10*n^2*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n]))/(4*e^12) - (110*b^2*d^9*n^2*(d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n]))/(3*e^12) + (1485*b^2*d^8*n^2*(d + e*x^(1/3))^4*(a + b*Log[c*(d + e*x^(1/3))^n]))/(32*e^12) - (1188*b^2*d^7*n^2*(d + e*x^(1/3))^5*(a + b*Log[c*(d + e*x^(1/3))^n]))/(25*e^12) + (77*b^2*d^6*n^2*(d + e*x^(1/3))^6*(a + b*Log[c*(d + e*x^(1/3))^n]))/(2*e^12) - (1188*b^2*d^5*n^2*(d + e*x^(1/3))^7*(a + b*Log[c*(d + e*x^(1/3))^n]))/(49*e^12) + (1485*b^2*d^4*n^2*(d + e*x^(1/3))^8*(a + b*Log[c*(d + e*x^(1/3))^n]))/(128*e^12) - (110*b^2*d^3*n^2*(d + e*x^(1/3))^9*(a + b*Log[c*(d + e*x^(1/3))^n]))/(27*e^12) + (99*b^2*d^2*n^2*(d + e*x^(1/3))^10*(a + b*Log[c*(d + e*x^(1/3))^n]))/(100*e^12) - (18*b^2*d*n^2*(d + e*x^(1/3))^11*(a + b*Log[c*(d + e*x^(1/3))^n]))/(121*e^12) + (b^2*n^2*(d + e*x^(1/3))^12*(a + b*Log[c*(d + e*x^(1/3))^n]))/(96*e^12) + (9*b*d^11*n*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/e^12 - (99*b*d^10*n*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(4*e^12) + (55*b*d^9*n*(d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/e^12 - (1485*b*d^8*n*(d + e*x^(1/3))^4*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(16*e^12) + (594*b*d^7*n*(d + e*x^(1/3))^5*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(5*e^12) - (231*b*d^6*n*(d + e*x^(1/3))^6*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(2*e^12) + (594*b*d^5*n*(d + e*x^(1/3))^7*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(7*e^12) - (1485*b*d^4*n*(d + e*x^(1/3))^8*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(32*e^12) + (55*b*d^3*n*(d + e*x^(1/3))^9*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(3*e^12) - (99*b*d^2*n*(d + e*x^(1/3))^10*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(20*e^12) + (9*b*d*n*(d + e*x^(1/3))^11*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(11*e^12) - (b*n*(d + e*x^(1/3))^12*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(16*e^12) - (3*d^11*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^12 + (33*d^10*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/(2*e^12) - (55*d^9*(d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^12 + (495*d^8*(d + e*x^(1/3))^4*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/(4*e^12) - (198*d^7*(d + e*x^(1/3))^5*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^12 + (231*d^6*(d + e*x^(1/3))^6*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^12 - (198*d^5*(d + e*x^(1/3))^7*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^12 + (495*d^4*(d + e*x^(1/3))^8*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/(4*e^12) - (55*d^3*(d + e*x^(1/3))^9*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^12 + (33*d^2*(d + e*x^(1/3))^10*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/(2*e^12) - (3*d*(d + e*x^(1/3))^11*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^12 + ((d + e*x^(1/3))^12*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/(4*e^12)","A",52,8,24,0.3333,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
457,1,1357,0,1.5732997,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \, dx","Int[x^2*(a + b*Log[c*(d + e*x^(1/3))^n])^3,x]","-\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}","-\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,"(9*b^3*d^7*n^3*(d + e*x^(1/3))^2)/e^9 - (56*b^3*d^6*n^3*(d + e*x^(1/3))^3)/(9*e^9) + (63*b^3*d^5*n^3*(d + e*x^(1/3))^4)/(16*e^9) - (252*b^3*d^4*n^3*(d + e*x^(1/3))^5)/(125*e^9) + (7*b^3*d^3*n^3*(d + e*x^(1/3))^6)/(9*e^9) - (72*b^3*d^2*n^3*(d + e*x^(1/3))^7)/(343*e^9) + (9*b^3*d*n^3*(d + e*x^(1/3))^8)/(256*e^9) - (2*b^3*n^3*(d + e*x^(1/3))^9)/(729*e^9) + (18*a*b^2*d^8*n^2*x^(1/3))/e^8 - (18*b^3*d^8*n^3*x^(1/3))/e^8 + (18*b^3*d^8*n^2*(d + e*x^(1/3))*Log[c*(d + e*x^(1/3))^n])/e^9 - (18*b^2*d^7*n^2*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n]))/e^9 + (56*b^2*d^6*n^2*(d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n]))/(3*e^9) - (63*b^2*d^5*n^2*(d + e*x^(1/3))^4*(a + b*Log[c*(d + e*x^(1/3))^n]))/(4*e^9) + (252*b^2*d^4*n^2*(d + e*x^(1/3))^5*(a + b*Log[c*(d + e*x^(1/3))^n]))/(25*e^9) - (14*b^2*d^3*n^2*(d + e*x^(1/3))^6*(a + b*Log[c*(d + e*x^(1/3))^n]))/(3*e^9) + (72*b^2*d^2*n^2*(d + e*x^(1/3))^7*(a + b*Log[c*(d + e*x^(1/3))^n]))/(49*e^9) - (9*b^2*d*n^2*(d + e*x^(1/3))^8*(a + b*Log[c*(d + e*x^(1/3))^n]))/(32*e^9) + (2*b^2*n^2*(d + e*x^(1/3))^9*(a + b*Log[c*(d + e*x^(1/3))^n]))/(81*e^9) - (9*b*d^8*n*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/e^9 + (18*b*d^7*n*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/e^9 - (28*b*d^6*n*(d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/e^9 + (63*b*d^5*n*(d + e*x^(1/3))^4*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(2*e^9) - (126*b*d^4*n*(d + e*x^(1/3))^5*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(5*e^9) + (14*b*d^3*n*(d + e*x^(1/3))^6*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/e^9 - (36*b*d^2*n*(d + e*x^(1/3))^7*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(7*e^9) + (9*b*d*n*(d + e*x^(1/3))^8*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(8*e^9) - (b*n*(d + e*x^(1/3))^9*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(9*e^9) + (3*d^8*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^9 - (12*d^7*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^9 + (28*d^6*(d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^9 - (42*d^5*(d + e*x^(1/3))^4*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^9 + (42*d^4*(d + e*x^(1/3))^5*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^9 - (28*d^3*(d + e*x^(1/3))^6*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^9 + (12*d^2*(d + e*x^(1/3))^7*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^9 - (3*d*(d + e*x^(1/3))^8*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^9 + ((d + e*x^(1/3))^9*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/(3*e^9)","A",40,8,24,0.3333,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
458,1,907,0,0.9792173,"\int x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \, dx","Int[x*(a + b*Log[c*(d + e*x^(1/3))^n])^3,x]","-\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}","-\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,"(-45*b^3*d^4*n^3*(d + e*x^(1/3))^2)/(8*e^6) + (20*b^3*d^3*n^3*(d + e*x^(1/3))^3)/(9*e^6) - (45*b^3*d^2*n^3*(d + e*x^(1/3))^4)/(64*e^6) + (18*b^3*d*n^3*(d + e*x^(1/3))^5)/(125*e^6) - (b^3*n^3*(d + e*x^(1/3))^6)/(72*e^6) - (18*a*b^2*d^5*n^2*x^(1/3))/e^5 + (18*b^3*d^5*n^3*x^(1/3))/e^5 - (18*b^3*d^5*n^2*(d + e*x^(1/3))*Log[c*(d + e*x^(1/3))^n])/e^6 + (45*b^2*d^4*n^2*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n]))/(4*e^6) - (20*b^2*d^3*n^2*(d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n]))/(3*e^6) + (45*b^2*d^2*n^2*(d + e*x^(1/3))^4*(a + b*Log[c*(d + e*x^(1/3))^n]))/(16*e^6) - (18*b^2*d*n^2*(d + e*x^(1/3))^5*(a + b*Log[c*(d + e*x^(1/3))^n]))/(25*e^6) + (b^2*n^2*(d + e*x^(1/3))^6*(a + b*Log[c*(d + e*x^(1/3))^n]))/(12*e^6) + (9*b*d^5*n*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/e^6 - (45*b*d^4*n*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(4*e^6) + (10*b*d^3*n*(d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/e^6 - (45*b*d^2*n*(d + e*x^(1/3))^4*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(8*e^6) + (9*b*d*n*(d + e*x^(1/3))^5*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(5*e^6) - (b*n*(d + e*x^(1/3))^6*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(4*e^6) - (3*d^5*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^6 + (15*d^4*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/(2*e^6) - (10*d^3*(d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^6 + (15*d^2*(d + e*x^(1/3))^4*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/(2*e^6) - (3*d*(d + e*x^(1/3))^5*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^6 + ((d + e*x^(1/3))^6*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/(2*e^6)","A",28,8,22,0.3636,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
459,1,438,0,0.4439277,"\int \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3 \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])^3,x]","\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}","\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,"(9*b^3*d*n^3*(d + e*x^(1/3))^2)/(4*e^3) - (2*b^3*n^3*(d + e*x^(1/3))^3)/(9*e^3) + (18*a*b^2*d^2*n^2*x^(1/3))/e^2 - (18*b^3*d^2*n^3*x^(1/3))/e^2 + (18*b^3*d^2*n^2*(d + e*x^(1/3))*Log[c*(d + e*x^(1/3))^n])/e^3 - (9*b^2*d*n^2*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n]))/(2*e^3) + (2*b^2*n^2*(d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n]))/(3*e^3) - (9*b*d^2*n*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/e^3 + (9*b*d*n*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(2*e^3) - (b*n*(d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/e^3 + (3*d^2*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^3 - (3*d*(d + e*x^(1/3))^2*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^3 + ((d + e*x^(1/3))^3*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/e^3","A",16,8,20,0.4000,1,"{2451, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
460,1,135,0,0.1945498,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{x} \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])^3/x,x]","-18 b^2 n^2 \text{PolyLog}\left(3,\frac{e \sqrt[3]{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)+9 b n \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2+18 b^3 n^3 \text{PolyLog}\left(4,\frac{e \sqrt[3]{x}}{d}+1\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","-18 b^2 n^2 \text{PolyLog}\left(3,\frac{e \sqrt[3]{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)+9 b n \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2+18 b^3 n^3 \text{PolyLog}\left(4,\frac{e \sqrt[3]{x}}{d}+1\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",1,"3*(a + b*Log[c*(d + e*x^(1/3))^n])^3*Log[-((e*x^(1/3))/d)] + 9*b*n*(a + b*Log[c*(d + e*x^(1/3))^n])^2*PolyLog[2, 1 + (e*x^(1/3))/d] - 18*b^2*n^2*(a + b*Log[c*(d + e*x^(1/3))^n])*PolyLog[3, 1 + (e*x^(1/3))/d] + 18*b^3*n^3*PolyLog[4, 1 + (e*x^(1/3))/d]","A",6,6,24,0.2500,1,"{2454, 2396, 2433, 2374, 2383, 6589}"
461,1,414,0,1.005938,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{x^2} \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])^3/x^2,x]","\frac{6 b^2 e^3 n^2 \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^3}-\frac{9 b^3 e^3 n^3 \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right)}{d^3}-\frac{6 b^3 e^3 n^3 \text{PolyLog}\left(3,\frac{e \sqrt[3]{x}}{d}+1\right)}{d^3}-\frac{9 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{e^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{d^3}+\frac{3 b e^3 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{2 d^3}+\frac{3 b e^3 n \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}{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{b^3 e^3 n^3 \log (x)}{d^3}","-\frac{6 b^2 e^3 n^2 \text{PolyLog}\left(2,\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^3 e^3 n^3 \text{PolyLog}\left(2,\frac{d}{d+e \sqrt[3]{x}}\right)}{d^3}-\frac{6 b^3 e^3 n^3 \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right)}{d^3}-\frac{6 b^3 e^3 n^3 \text{PolyLog}\left(3,\frac{d}{d+e \sqrt[3]{x}}\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{b^3 e^3 n^3 \log (x)}{d^3}",1,"(-3*b^2*e^2*n^2*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n]))/(d^3*x^(1/3)) + (3*b*e^3*n*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(2*d^3) - (3*b*e*n*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(2*d*x^(2/3)) + (3*b*e^2*n*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(d^3*x^(1/3)) - (e^3*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/d^3 - (a + b*Log[c*(d + e*x^(1/3))^n])^3/x - (9*b^2*e^3*n^2*(a + b*Log[c*(d + e*x^(1/3))^n])*Log[-((e*x^(1/3))/d)])/d^3 + (3*b*e^3*n*(a + b*Log[c*(d + e*x^(1/3))^n])^2*Log[-((e*x^(1/3))/d)])/d^3 + (b^3*e^3*n^3*Log[x])/d^3 - (9*b^3*e^3*n^3*PolyLog[2, 1 + (e*x^(1/3))/d])/d^3 + (6*b^2*e^3*n^2*(a + b*Log[c*(d + e*x^(1/3))^n])*PolyLog[2, 1 + (e*x^(1/3))/d])/d^3 - (6*b^3*e^3*n^3*PolyLog[3, 1 + (e*x^(1/3))/d])/d^3","A",22,16,24,0.6667,1,"{2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31}"
462,1,742,0,3.0525472,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{x^3} \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^n])^3/x^3,x]","-\frac{3 b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right) \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)}{d^6}+\frac{137 b^3 e^6 n^3 \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right)}{20 d^6}+\frac{3 b^3 e^6 n^3 \text{PolyLog}\left(3,\frac{e \sqrt[3]{x}}{d}+1\right)}{d^6}-\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{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{137 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)}{20 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{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 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{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{e^6 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^3}{2 d^6}-\frac{77 b e^6 n \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^n\right)\right)^2}{40 d^6}-\frac{3 b e^6 n \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}{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{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 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{3 b^3 e^4 n^3}{10 d^4 x^{2/3}}-\frac{71 b^3 e^5 n^3}{40 d^5 \sqrt[3]{x}}-\frac{b^3 e^3 n^3}{20 d^3 x}+\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{3 b^2 e^6 n^2 \text{PolyLog}\left(2,\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^3 e^6 n^3 \text{PolyLog}\left(2,\frac{d}{d+e \sqrt[3]{x}}\right)}{20 d^6}+\frac{3 b^3 e^6 n^3 \text{PolyLog}\left(2,\frac{e \sqrt[3]{x}}{d}+1\right)}{d^6}+\frac{3 b^3 e^6 n^3 \text{PolyLog}\left(3,\frac{d}{d+e \sqrt[3]{x}}\right)}{d^6}-\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{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{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{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 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{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^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{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 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{3 b^3 e^4 n^3}{10 d^4 x^{2/3}}-\frac{71 b^3 e^5 n^3}{40 d^5 \sqrt[3]{x}}-\frac{b^3 e^3 n^3}{20 d^3 x}+\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}",1,"-(b^3*e^3*n^3)/(20*d^3*x) + (3*b^3*e^4*n^3)/(10*d^4*x^(2/3)) - (71*b^3*e^5*n^3)/(40*d^5*x^(1/3)) + (71*b^3*e^6*n^3*Log[d + e*x^(1/3)])/(40*d^6) - (3*b^2*e^2*n^2*(a + b*Log[c*(d + e*x^(1/3))^n]))/(20*d^2*x^(4/3)) + (9*b^2*e^3*n^2*(a + b*Log[c*(d + e*x^(1/3))^n]))/(20*d^3*x) - (47*b^2*e^4*n^2*(a + b*Log[c*(d + e*x^(1/3))^n]))/(40*d^4*x^(2/3)) + (77*b^2*e^5*n^2*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n]))/(20*d^6*x^(1/3)) - (77*b*e^6*n*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(40*d^6) - (3*b*e*n*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(10*d*x^(5/3)) + (3*b*e^2*n*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(8*d^2*x^(4/3)) - (b*e^3*n*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(2*d^3*x) + (3*b*e^4*n*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(4*d^4*x^(2/3)) - (3*b*e^5*n*(d + e*x^(1/3))*(a + b*Log[c*(d + e*x^(1/3))^n])^2)/(2*d^6*x^(1/3)) + (e^6*(a + b*Log[c*(d + e*x^(1/3))^n])^3)/(2*d^6) - (a + b*Log[c*(d + e*x^(1/3))^n])^3/(2*x^2) + (137*b^2*e^6*n^2*(a + b*Log[c*(d + e*x^(1/3))^n])*Log[-((e*x^(1/3))/d)])/(20*d^6) - (3*b*e^6*n*(a + b*Log[c*(d + e*x^(1/3))^n])^2*Log[-((e*x^(1/3))/d)])/(2*d^6) - (15*b^3*e^6*n^3*Log[x])/(8*d^6) + (137*b^3*e^6*n^3*PolyLog[2, 1 + (e*x^(1/3))/d])/(20*d^6) - (3*b^2*e^6*n^2*(a + b*Log[c*(d + e*x^(1/3))^n])*PolyLog[2, 1 + (e*x^(1/3))/d])/d^6 + (3*b^3*e^6*n^3*PolyLog[3, 1 + (e*x^(1/3))/d])/d^6","A",73,17,24,0.7083,1,"{2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31, 44}"
463,1,138,0,0.1068754,"\int x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \, dx","Int[x^3*(a + b*Log[c*(d + e*x^(2/3))^n]),x]","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+\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^6 n \log \left(d+e x^{2/3}\right)}{4 e^6}+\frac{b d n x^{10/3}}{20 e}-\frac{1}{24} b n x^4","\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+\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^6 n \log \left(d+e x^{2/3}\right)}{4 e^6}+\frac{b d n x^{10/3}}{20 e}-\frac{1}{24} b n x^4",1,"(b*d^5*n*x^(2/3))/(4*e^5) - (b*d^4*n*x^(4/3))/(8*e^4) + (b*d^3*n*x^2)/(12*e^3) - (b*d^2*n*x^(8/3))/(16*e^2) + (b*d*n*x^(10/3))/(20*e) - (b*n*x^4)/24 - (b*d^6*n*Log[d + e*x^(2/3)])/(4*e^6) + (x^4*(a + b*Log[c*(d + e*x^(2/3))^n]))/4","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
464,1,130,0,0.0780661,"\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \, dx","Int[x^2*(a + b*Log[c*(d + e*x^(2/3))^n]),x]","\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^2 n x^{5/3}}{15 e^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^{9/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{3 e^{9/2}}+\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^2 n x^{5/3}}{15 e^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^{9/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{3 e^{9/2}}+\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) - (2*b*n*x^3)/27 + (2*b*d^(9/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/(3*e^(9/2)) + (x^3*(a + b*Log[c*(d + e*x^(2/3))^n]))/3","A",5,4,22,0.1818,1,"{2455, 341, 302, 205}"
465,1,89,0,0.065433,"\int x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \, dx","Int[x*(a + b*Log[c*(d + e*x^(2/3))^n]),x]","\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)-\frac{b d^2 n x^{2/3}}{2 e^2}+\frac{b d^3 n \log \left(d+e x^{2/3}\right)}{2 e^3}+\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^2 n x^{2/3}}{2 e^2}+\frac{b d^3 n \log \left(d+e x^{2/3}\right)}{2 e^3}+\frac{b d n x^{4/3}}{4 e}-\frac{1}{6} b n x^2",1,"-(b*d^2*n*x^(2/3))/(2*e^2) + (b*d*n*x^(4/3))/(4*e) - (b*n*x^2)/6 + (b*d^3*n*Log[d + e*x^(2/3)])/(2*e^3) + (x^2*(a + b*Log[c*(d + e*x^(2/3))^n]))/2","A",4,3,20,0.1500,1,"{2454, 2395, 43}"
466,1,72,0,0.0530306,"\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right) \, dx","Int[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",6,4,18,0.2222,1,"{2448, 341, 302, 205}"
467,1,55,0,0.0507591,"\int \frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{x} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])/x,x]","\frac{3}{2} b n \text{PolyLog}\left(2,\frac{e x^{2/3}}{d}+1\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{PolyLog}\left(2,\frac{e x^{2/3}}{d}+1\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)",1,"(3*(a + b*Log[c*(d + e*x^(2/3))^n])*Log[-((e*x^(2/3))/d)])/2 + (3*b*n*PolyLog[2, 1 + (e*x^(2/3))/d])/2","A",3,3,22,0.1364,1,"{2454, 2394, 2315}"
468,1,68,0,0.0401322,"\int \frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{x^2} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])/x^2,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}}","-\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,"(-2*b*e*n)/(d*x^(1/3)) - (2*b*e^(3/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/d^(3/2) - (a + b*Log[c*(d + e*x^(2/3))^n])/x","A",4,4,22,0.1818,1,"{2455, 341, 325, 205}"
469,1,94,0,0.0704927,"\int \frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{x^3} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])/x^3,x]","-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{2 x^2}+\frac{b e^2 n}{2 d^2 x^{2/3}}-\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 n}{4 d x^{4/3}}","-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{2 x^2}+\frac{b e^2 n}{2 d^2 x^{2/3}}-\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 n}{4 d x^{4/3}}",1,"-(b*e*n)/(4*d*x^(4/3)) + (b*e^2*n)/(2*d^2*x^(2/3)) - (b*e^3*n*Log[d + e*x^(2/3)])/(2*d^3) - (a + b*Log[c*(d + e*x^(2/3))^n])/(2*x^2) + (b*e^3*n*Log[x])/(3*d^3)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
470,1,123,0,0.0768091,"\int \frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{x^4} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])/x^4,x]","-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)}{3 x^3}+\frac{2 b e^2 n}{15 d^2 x^{5/3}}+\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^{9/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{3 d^{9/2}}-\frac{2 b e n}{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^2 n}{15 d^2 x^{5/3}}+\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^{9/2} n \tan ^{-1}\left(\frac{\sqrt{e} \sqrt[3]{x}}{\sqrt{d}}\right)}{3 d^{9/2}}-\frac{2 b e n}{21 d x^{7/3}}",1,"(-2*b*e*n)/(21*d*x^(7/3)) + (2*b*e^2*n)/(15*d^2*x^(5/3)) - (2*b*e^3*n)/(9*d^3*x) + (2*b*e^4*n)/(3*d^4*x^(1/3)) + (2*b*e^(9/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/(3*d^(9/2)) - (a + b*Log[c*(d + e*x^(2/3))^n])/(3*x^3)","A",7,4,22,0.1818,1,"{2455, 341, 325, 205}"
471,1,355,0,0.4879997,"\int x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \, dx","Int[x^3*(a + b*Log[c*(d + e*x^(2/3))^n])^2,x]","\frac{1}{120} b n \left(\frac{360 d^5 \left(d+e x^{2/3}\right)}{e^6}-\frac{450 d^4 \left(d+e x^{2/3}\right)^2}{e^6}+\frac{400 d^3 \left(d+e x^{2/3}\right)^3}{e^6}-\frac{225 d^2 \left(d+e x^{2/3}\right)^4}{e^6}-\frac{60 d^6 \log \left(d+e x^{2/3}\right)}{e^6}+\frac{72 d \left(d+e x^{2/3}\right)^5}{e^6}-\frac{10 \left(d+e x^{2/3}\right)^6}{e^6}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+\frac{1}{4} x^4 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2-\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{b^2 d^6 n^2 \log ^2\left(d+e x^{2/3}\right)}{4 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}","-\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{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{b^2 d^6 n^2 \log ^2\left(d+e x^{2/3}\right)}{4 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,"(15*b^2*d^4*n^2*(d + e*x^(2/3))^2)/(8*e^6) - (10*b^2*d^3*n^2*(d + e*x^(2/3))^3)/(9*e^6) + (15*b^2*d^2*n^2*(d + e*x^(2/3))^4)/(32*e^6) - (3*b^2*d*n^2*(d + e*x^(2/3))^5)/(25*e^6) + (b^2*n^2*(d + e*x^(2/3))^6)/(72*e^6) - (3*b^2*d^5*n^2*x^(2/3))/e^5 + (b^2*d^6*n^2*Log[d + e*x^(2/3)]^2)/(4*e^6) + (b*n*((360*d^5*(d + e*x^(2/3)))/e^6 - (450*d^4*(d + e*x^(2/3))^2)/e^6 + (400*d^3*(d + e*x^(2/3))^3)/e^6 - (225*d^2*(d + e*x^(2/3))^4)/e^6 + (72*d*(d + e*x^(2/3))^5)/e^6 - (10*(d + e*x^(2/3))^6)/e^6 - (60*d^6*Log[d + e*x^(2/3)])/e^6)*(a + b*Log[c*(d + e*x^(2/3))^n]))/120 + (x^4*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/4","A",8,8,24,0.3333,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
472,1,217,0,0.3050879,"\int x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \, dx","Int[x*(a + b*Log[c*(d + e*x^(2/3))^n])^2,x]","-\frac{1}{6} b n \left(\frac{18 d^2 \left(d+e x^{2/3}\right)}{e^3}-\frac{6 d^3 \log \left(d+e x^{2/3}\right)}{e^3}-\frac{9 d \left(d+e x^{2/3}\right)^2}{e^3}+\frac{2 \left(d+e x^{2/3}\right)^3}{e^3}\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)+\frac{1}{2} x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2+\frac{3 b^2 d^2 n^2 x^{2/3}}{e^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 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}","\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{3 b^2 d^2 n^2 x^{2/3}}{e^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 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,"(-3*b^2*d*n^2*(d + e*x^(2/3))^2)/(4*e^3) + (b^2*n^2*(d + e*x^(2/3))^3)/(9*e^3) + (3*b^2*d^2*n^2*x^(2/3))/e^2 - (b^2*d^3*n^2*Log[d + e*x^(2/3)]^2)/(2*e^3) - (b*n*((18*d^2*(d + e*x^(2/3)))/e^3 - (9*d*(d + e*x^(2/3))^2)/e^3 + (2*(d + e*x^(2/3))^3)/e^3 - (6*d^3*Log[d + e*x^(2/3)])/e^3)*(a + b*Log[c*(d + e*x^(2/3))^n]))/6 + (x^2*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/2","A",8,8,22,0.3636,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
473,1,95,0,0.1310044,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x,x]","3 b n \text{PolyLog}\left(2,\frac{e x^{2/3}}{d}+1\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)-3 b^2 n^2 \text{PolyLog}\left(3,\frac{e x^{2/3}}{d}+1\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 n \text{PolyLog}\left(2,\frac{e x^{2/3}}{d}+1\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)-3 b^2 n^2 \text{PolyLog}\left(3,\frac{e x^{2/3}}{d}+1\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",1,"(3*(a + b*Log[c*(d + e*x^(2/3))^n])^2*Log[-((e*x^(2/3))/d)])/2 + 3*b*n*(a + b*Log[c*(d + e*x^(2/3))^n])*PolyLog[2, 1 + (e*x^(2/3))/d] - 3*b^2*n^2*PolyLog[3, 1 + (e*x^(2/3))/d]","A",5,5,24,0.2083,1,"{2454, 2396, 2433, 2374, 6589}"
474,1,261,0,0.5000073,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^3} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^3,x]","\frac{b^2 e^3 n^2 \text{PolyLog}\left(2,\frac{e x^{2/3}}{d}+1\right)}{d^3}-\frac{e^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{2 d^3}+\frac{b e^3 n \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{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^2 n^2}{2 d^2 x^{2/3}}+\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^3 n^2 \text{PolyLog}\left(2,\frac{d}{d+e x^{2/3}}\right)}{d^3}+\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^2 n^2}{2 d^2 x^{2/3}}+\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}",1,"-(b^2*e^2*n^2)/(2*d^2*x^(2/3)) + (b^2*e^3*n^2*Log[d + e*x^(2/3)])/(2*d^3) - (b*e*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(2*d*x^(4/3)) + (b*e^2*n*(d + e*x^(2/3))*(a + b*Log[c*(d + e*x^(2/3))^n]))/(d^3*x^(2/3)) - (e^3*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(2*d^3) - (a + b*Log[c*(d + e*x^(2/3))^n])^2/(2*x^2) + (b*e^3*n*(a + b*Log[c*(d + e*x^(2/3))^n])*Log[-((e*x^(2/3))/d)])/d^3 - (b^2*e^3*n^2*Log[x])/d^3 + (b^2*e^3*n^2*PolyLog[2, 1 + (e*x^(2/3))/d])/d^3","A",14,12,24,0.5000,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
475,1,436,0,1.0157769,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^5} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^5,x]","-\frac{b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{e x^{2/3}}{d}+1\right)}{2 d^6}+\frac{e^6 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{4 d^6}-\frac{b e^6 n \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 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{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}}-\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{b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{d}{d+e x^{2/3}}\right)}{2 d^6}-\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{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}}-\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}",1,"-(b^2*e^2*n^2)/(40*d^2*x^(8/3)) + (3*b^2*e^3*n^2)/(40*d^3*x^2) - (47*b^2*e^4*n^2)/(240*d^4*x^(4/3)) + (77*b^2*e^5*n^2)/(120*d^5*x^(2/3)) - (77*b^2*e^6*n^2*Log[d + e*x^(2/3)])/(120*d^6) - (b*e*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(10*d*x^(10/3)) + (b*e^2*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(8*d^2*x^(8/3)) - (b*e^3*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(6*d^3*x^2) + (b*e^4*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(4*d^4*x^(4/3)) - (b*e^5*n*(d + e*x^(2/3))*(a + b*Log[c*(d + e*x^(2/3))^n]))/(2*d^6*x^(2/3)) + (e^6*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(4*d^6) - (a + b*Log[c*(d + e*x^(2/3))^n])^2/(4*x^4) - (b*e^6*n*(a + b*Log[c*(d + e*x^(2/3))^n])*Log[-((e*x^(2/3))/d)])/(2*d^6) + (137*b^2*e^6*n^2*Log[x])/(180*d^6) - (b^2*e^6*n^2*PolyLog[2, 1 + (e*x^(2/3))/d])/(2*d^6)","A",26,12,24,0.5000,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
476,1,547,0,0.7690747,"\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \, dx","Int[x^2*(a + b*Log[c*(d + e*x^(2/3))^n])^2,x]","\frac{4 i b^2 d^{9/2} n^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\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^{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 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{1144 b^2 d^2 n^2 x^{5/3}}{4725 e^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{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{128 b^2 d n^2 x^{7/3}}{1323 e}+\frac{8}{243} b^2 n^2 x^3","\frac{4 i b^2 d^{9/2} n^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\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^{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 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{1144 b^2 d^2 n^2 x^{5/3}}{4725 e^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{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{128 b^2 d n^2 x^{7/3}}{1323 e}+\frac{8}{243} b^2 n^2 x^3",1,"(-4*a*b*d^4*n*x^(1/3))/(3*e^4) + (4504*b^2*d^4*n^2*x^(1/3))/(945*e^4) - (1984*b^2*d^3*n^2*x)/(2835*e^3) + (1144*b^2*d^2*n^2*x^(5/3))/(4725*e^2) - (128*b^2*d*n^2*x^(7/3))/(1323*e) + (8*b^2*n^2*x^3)/243 - (4504*b^2*d^(9/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/(945*e^(9/2)) + (((4*I)/3)*b^2*d^(9/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2)/e^(9/2) + (8*b^2*d^(9/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/(3*e^(9/2)) - (4*b^2*d^4*n*x^(1/3)*Log[c*(d + e*x^(2/3))^n])/(3*e^4) + (4*b*d^3*n*x*(a + b*Log[c*(d + e*x^(2/3))^n]))/(9*e^3) - (4*b*d^2*n*x^(5/3)*(a + b*Log[c*(d + e*x^(2/3))^n]))/(15*e^2) + (4*b*d*n*x^(7/3)*(a + b*Log[c*(d + e*x^(2/3))^n]))/(21*e) - (4*b*n*x^3*(a + b*Log[c*(d + e*x^(2/3))^n]))/27 + (4*b*d^(9/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*Log[c*(d + e*x^(2/3))^n]))/(3*e^(9/2)) + (x^3*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/3 + (((4*I)/3)*b^2*d^(9/2)*n^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/e^(9/2)","A",30,14,24,0.5833,1,"{2458, 2457, 2476, 2448, 321, 205, 2455, 302, 2470, 12, 4920, 4854, 2402, 2315}"
477,1,364,0,0.4467776,"\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2 \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^2,x]","-\frac{4 i b^2 d^{3/2} n^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{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 \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","-\frac{4 i b^2 d^{3/2} n^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{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 \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,"(4*a*b*d*n*x^(1/3))/e - (32*b^2*d*n^2*x^(1/3))/(3*e) + (8*b^2*n^2*x)/9 + (32*b^2*d^(3/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/(3*e^(3/2)) - ((4*I)*b^2*d^(3/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2)/e^(3/2) - (8*b^2*d^(3/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/e^(3/2) + (4*b^2*d*n*x^(1/3)*Log[c*(d + e*x^(2/3))^n])/e - (4*b*n*x*(a + b*Log[c*(d + e*x^(2/3))^n]))/3 - (4*b*d^(3/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*Log[c*(d + e*x^(2/3))^n]))/e^(3/2) + x*(a + b*Log[c*(d + e*x^(2/3))^n])^2 - ((4*I)*b^2*d^(3/2)*n^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/e^(3/2)","A",18,14,20,0.7000,1,"{2451, 2457, 2476, 2448, 321, 205, 2455, 302, 2470, 12, 4920, 4854, 2402, 2315}"
478,1,298,0,0.4059292,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^2} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^2,x]","-\frac{4 i b^2 e^{3/2} n^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{d^{3/2}}-\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 \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}}","-\frac{4 i b^2 e^{3/2} n^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{d^{3/2}}-\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 \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,"(8*b^2*e^(3/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/d^(3/2) - ((4*I)*b^2*e^(3/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2)/d^(3/2) - (8*b^2*e^(3/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/d^(3/2) - (4*b*e*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(d*x^(1/3)) - (4*b*e^(3/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*Log[c*(d + e*x^(2/3))^n]))/d^(3/2) - (a + b*Log[c*(d + e*x^(2/3))^n])^2/x - ((4*I)*b^2*e^(3/2)*n^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/d^(3/2)","A",12,11,24,0.4583,1,"{2458, 2457, 2476, 2455, 205, 2470, 12, 4920, 4854, 2402, 2315}"
479,1,476,0,0.6200843,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^4} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^4,x]","\frac{4 i b^2 e^{9/2} n^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\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^{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 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{8 b^2 e^2 n^2}{105 d^2 x^{5/3}}-\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{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{4 i b^2 e^{9/2} n^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\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^{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 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{8 b^2 e^2 n^2}{105 d^2 x^{5/3}}-\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{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}}",1,"(-8*b^2*e^2*n^2)/(105*d^2*x^(5/3)) + (32*b^2*e^3*n^2)/(105*d^3*x) - (568*b^2*e^4*n^2)/(315*d^4*x^(1/3)) - (1408*b^2*e^(9/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/(315*d^(9/2)) + (((4*I)/3)*b^2*e^(9/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2)/d^(9/2) + (8*b^2*e^(9/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/(3*d^(9/2)) - (4*b*e*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(21*d*x^(7/3)) + (4*b*e^2*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(15*d^2*x^(5/3)) - (4*b*e^3*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(9*d^3*x) + (4*b*e^4*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(3*d^4*x^(1/3)) + (4*b*e^(9/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*Log[c*(d + e*x^(2/3))^n]))/(3*d^(9/2)) - (a + b*Log[c*(d + e*x^(2/3))^n])^2/(3*x^3) + (((4*I)/3)*b^2*e^(9/2)*n^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/d^(9/2)","A",24,12,24,0.5000,1,"{2458, 2457, 2476, 2455, 325, 205, 2470, 12, 4920, 4854, 2402, 2315}"
480,1,640,0,0.9440011,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{x^6} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^2/x^6,x]","-\frac{4 i b^2 e^{15/2} n^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\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^{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 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{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}}+\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{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{4 i b^2 e^{15/2} n^2 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\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^{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 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{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}}+\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{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}}",1,"(-8*b^2*e^2*n^2)/(715*d^2*x^(11/3)) + (64*b^2*e^3*n^2)/(2145*d^3*x^3) - (2872*b^2*e^4*n^2)/(45045*d^4*x^(7/3)) + (1216*b^2*e^5*n^2)/(9009*d^5*x^(5/3)) - (224072*b^2*e^6*n^2)/(675675*d^6*x) + (344192*b^2*e^7*n^2)/(225225*d^7*x^(1/3)) + (704552*b^2*e^(15/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/(225225*d^(15/2)) - (((4*I)/5)*b^2*e^(15/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2)/d^(15/2) - (8*b^2*e^(15/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/(5*d^(15/2)) - (4*b*e*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(65*d*x^(13/3)) + (4*b*e^2*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(55*d^2*x^(11/3)) - (4*b*e^3*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(45*d^3*x^3) + (4*b*e^4*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(35*d^4*x^(7/3)) - (4*b*e^5*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(25*d^5*x^(5/3)) + (4*b*e^6*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(15*d^6*x) - (4*b*e^7*n*(a + b*Log[c*(d + e*x^(2/3))^n]))/(5*d^7*x^(1/3)) - (4*b*e^(15/2)*n*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*Log[c*(d + e*x^(2/3))^n]))/(5*d^(15/2)) - (a + b*Log[c*(d + e*x^(2/3))^n])^2/(5*x^5) - (((4*I)/5)*b^2*e^(15/2)*n^2*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/d^(15/2)","A",45,12,24,0.5000,1,"{2458, 2457, 2476, 2455, 325, 205, 2470, 12, 4920, 4854, 2402, 2315}"
481,1,913,0,1.0323816,"\int x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \, dx","Int[x^3*(a + b*Log[c*(d + e*x^(2/3))^n])^3,x]","-\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}","-\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,"(-45*b^3*d^4*n^3*(d + e*x^(2/3))^2)/(16*e^6) + (10*b^3*d^3*n^3*(d + e*x^(2/3))^3)/(9*e^6) - (45*b^3*d^2*n^3*(d + e*x^(2/3))^4)/(128*e^6) + (9*b^3*d*n^3*(d + e*x^(2/3))^5)/(125*e^6) - (b^3*n^3*(d + e*x^(2/3))^6)/(144*e^6) - (9*a*b^2*d^5*n^2*x^(2/3))/e^5 + (9*b^3*d^5*n^3*x^(2/3))/e^5 - (9*b^3*d^5*n^2*(d + e*x^(2/3))*Log[c*(d + e*x^(2/3))^n])/e^6 + (45*b^2*d^4*n^2*(d + e*x^(2/3))^2*(a + b*Log[c*(d + e*x^(2/3))^n]))/(8*e^6) - (10*b^2*d^3*n^2*(d + e*x^(2/3))^3*(a + b*Log[c*(d + e*x^(2/3))^n]))/(3*e^6) + (45*b^2*d^2*n^2*(d + e*x^(2/3))^4*(a + b*Log[c*(d + e*x^(2/3))^n]))/(32*e^6) - (9*b^2*d*n^2*(d + e*x^(2/3))^5*(a + b*Log[c*(d + e*x^(2/3))^n]))/(25*e^6) + (b^2*n^2*(d + e*x^(2/3))^6*(a + b*Log[c*(d + e*x^(2/3))^n]))/(24*e^6) + (9*b*d^5*n*(d + e*x^(2/3))*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(2*e^6) - (45*b*d^4*n*(d + e*x^(2/3))^2*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(8*e^6) + (5*b*d^3*n*(d + e*x^(2/3))^3*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/e^6 - (45*b*d^2*n*(d + e*x^(2/3))^4*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(16*e^6) + (9*b*d*n*(d + e*x^(2/3))^5*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(10*e^6) - (b*n*(d + e*x^(2/3))^6*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(8*e^6) - (3*d^5*(d + e*x^(2/3))*(a + b*Log[c*(d + e*x^(2/3))^n])^3)/(2*e^6) + (15*d^4*(d + e*x^(2/3))^2*(a + b*Log[c*(d + e*x^(2/3))^n])^3)/(4*e^6) - (5*d^3*(d + e*x^(2/3))^3*(a + b*Log[c*(d + e*x^(2/3))^n])^3)/e^6 + (15*d^2*(d + e*x^(2/3))^4*(a + b*Log[c*(d + e*x^(2/3))^n])^3)/(4*e^6) - (3*d*(d + e*x^(2/3))^5*(a + b*Log[c*(d + e*x^(2/3))^n])^3)/(2*e^6) + ((d + e*x^(2/3))^6*(a + b*Log[c*(d + e*x^(2/3))^n])^3)/(4*e^6)","A",28,8,24,0.3333,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
482,1,449,0,0.4588708,"\int x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \, dx","Int[x*(a + b*Log[c*(d + e*x^(2/3))^n])^3,x]","\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}","\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,"(9*b^3*d*n^3*(d + e*x^(2/3))^2)/(8*e^3) - (b^3*n^3*(d + e*x^(2/3))^3)/(9*e^3) + (9*a*b^2*d^2*n^2*x^(2/3))/e^2 - (9*b^3*d^2*n^3*x^(2/3))/e^2 + (9*b^3*d^2*n^2*(d + e*x^(2/3))*Log[c*(d + e*x^(2/3))^n])/e^3 - (9*b^2*d*n^2*(d + e*x^(2/3))^2*(a + b*Log[c*(d + e*x^(2/3))^n]))/(4*e^3) + (b^2*n^2*(d + e*x^(2/3))^3*(a + b*Log[c*(d + e*x^(2/3))^n]))/(3*e^3) - (9*b*d^2*n*(d + e*x^(2/3))*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(2*e^3) + (9*b*d*n*(d + e*x^(2/3))^2*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(4*e^3) - (b*n*(d + e*x^(2/3))^3*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(2*e^3) + (3*d^2*(d + e*x^(2/3))*(a + b*Log[c*(d + e*x^(2/3))^n])^3)/(2*e^3) - (3*d*(d + e*x^(2/3))^2*(a + b*Log[c*(d + e*x^(2/3))^n])^3)/(2*e^3) + ((d + e*x^(2/3))^3*(a + b*Log[c*(d + e*x^(2/3))^n])^3)/(2*e^3)","A",16,8,22,0.3636,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
483,1,139,0,0.2014166,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{x} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^3/x,x]","-9 b^2 n^2 \text{PolyLog}\left(3,\frac{e x^{2/3}}{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{PolyLog}\left(2,\frac{e x^{2/3}}{d}+1\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2+9 b^3 n^3 \text{PolyLog}\left(4,\frac{e x^{2/3}}{d}+1\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)^3","-9 b^2 n^2 \text{PolyLog}\left(3,\frac{e x^{2/3}}{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{PolyLog}\left(2,\frac{e x^{2/3}}{d}+1\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2+9 b^3 n^3 \text{PolyLog}\left(4,\frac{e x^{2/3}}{d}+1\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)^3",1,"(3*(a + b*Log[c*(d + e*x^(2/3))^n])^3*Log[-((e*x^(2/3))/d)])/2 + (9*b*n*(a + b*Log[c*(d + e*x^(2/3))^n])^2*PolyLog[2, 1 + (e*x^(2/3))/d])/2 - 9*b^2*n^2*(a + b*Log[c*(d + e*x^(2/3))^n])*PolyLog[3, 1 + (e*x^(2/3))/d] + 9*b^3*n^3*PolyLog[4, 1 + (e*x^(2/3))/d]","A",6,6,24,0.2500,1,"{2454, 2396, 2433, 2374, 2383, 6589}"
484,1,428,0,1.0076308,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{x^3} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^3/x^3,x]","\frac{3 b^2 e^3 n^2 \text{PolyLog}\left(2,\frac{e x^{2/3}}{d}+1\right) \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)}{d^3}-\frac{9 b^3 e^3 n^3 \text{PolyLog}\left(2,\frac{e x^{2/3}}{d}+1\right)}{2 d^3}-\frac{3 b^3 e^3 n^3 \text{PolyLog}\left(3,\frac{e x^{2/3}}{d}+1\right)}{d^3}-\frac{9 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)}{2 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{e^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{2 d^3}+\frac{3 b e^3 n \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^2}{4 d^3}+\frac{3 b e^3 n \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}{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{b^3 e^3 n^3 \log (x)}{d^3}","-\frac{3 b^2 e^3 n^2 \text{PolyLog}\left(2,\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^3 e^3 n^3 \text{PolyLog}\left(2,\frac{d}{d+e x^{2/3}}\right)}{2 d^3}-\frac{3 b^3 e^3 n^3 \text{PolyLog}\left(2,\frac{e x^{2/3}}{d}+1\right)}{d^3}-\frac{3 b^3 e^3 n^3 \text{PolyLog}\left(3,\frac{d}{d+e x^{2/3}}\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{b^3 e^3 n^3 \log (x)}{d^3}",1,"(-3*b^2*e^2*n^2*(d + e*x^(2/3))*(a + b*Log[c*(d + e*x^(2/3))^n]))/(2*d^3*x^(2/3)) + (3*b*e^3*n*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(4*d^3) - (3*b*e*n*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(4*d*x^(4/3)) + (3*b*e^2*n*(d + e*x^(2/3))*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(2*d^3*x^(2/3)) - (e^3*(a + b*Log[c*(d + e*x^(2/3))^n])^3)/(2*d^3) - (a + b*Log[c*(d + e*x^(2/3))^n])^3/(2*x^2) - (9*b^2*e^3*n^2*(a + b*Log[c*(d + e*x^(2/3))^n])*Log[-((e*x^(2/3))/d)])/(2*d^3) + (3*b*e^3*n*(a + b*Log[c*(d + e*x^(2/3))^n])^2*Log[-((e*x^(2/3))/d)])/(2*d^3) + (b^3*e^3*n^3*Log[x])/d^3 - (9*b^3*e^3*n^3*PolyLog[2, 1 + (e*x^(2/3))/d])/(2*d^3) + (3*b^2*e^3*n^2*(a + b*Log[c*(d + e*x^(2/3))^n])*PolyLog[2, 1 + (e*x^(2/3))/d])/d^3 - (3*b^3*e^3*n^3*PolyLog[3, 1 + (e*x^(2/3))/d])/d^3","A",22,16,24,0.6667,1,"{2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31}"
485,0,0,0,3.0063895,"\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \, dx","Int[x^2*(a + b*Log[c*(d + e*x^(2/3))^n])^3,x]","\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \, dx","\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 i b^3 d^{9/2} n^3 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\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{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{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{221344 b^3 d^2 n^3 x^{5/3}}{496125 e^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{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{3088 b^3 d n^3 x^{7/3}}{27783 e}-\frac{16}{729} b^3 n^3 x^3",0,"(4504*a*b^2*d^4*n^2*x^(1/3))/(315*e^4) - (3475504*b^3*d^4*n^3*x^(1/3))/(99225*e^4) + (637984*b^3*d^3*n^3*x)/(297675*e^3) - (221344*b^3*d^2*n^3*x^(5/3))/(496125*e^2) + (3088*b^3*d*n^3*x^(7/3))/(27783*e) - (16*b^3*n^3*x^3)/729 + (3475504*b^3*d^(9/2)*n^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/(99225*e^(9/2)) - (((4504*I)/315)*b^3*d^(9/2)*n^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2)/e^(9/2) - (9008*b^3*d^(9/2)*n^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/(315*e^(9/2)) + (4504*b^3*d^4*n^2*x^(1/3)*Log[c*(d + e*x^(2/3))^n])/(315*e^4) - (1984*b^2*d^3*n^2*x*(a + b*Log[c*(d + e*x^(2/3))^n]))/(945*e^3) + (1144*b^2*d^2*n^2*x^(5/3)*(a + b*Log[c*(d + e*x^(2/3))^n]))/(1575*e^2) - (128*b^2*d*n^2*x^(7/3)*(a + b*Log[c*(d + e*x^(2/3))^n]))/(441*e) + (8*b^2*n^2*x^3*(a + b*Log[c*(d + e*x^(2/3))^n]))/81 - (4504*b^2*d^(9/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*Log[c*(d + e*x^(2/3))^n]))/(315*e^(9/2)) - (2*b*d^4*n*x^(1/3)*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/e^4 + (2*b*d^3*n*x*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(3*e^3) - (2*b*d^2*n*x^(5/3)*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(5*e^2) + (2*b*d*n*x^(7/3)*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(7*e) - (2*b*n*x^3*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/9 + (x^3*(a + b*Log[c*(d + e*x^(2/3))^n])^3)/3 - (((4504*I)/315)*b^3*d^(9/2)*n^3*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/e^(9/2) + (2*b*d^5*n*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x^2)^n])^2/(d + e*x^2), x], x, x^(1/3)])/e^4","A",0,0,0,0,-1,"{}"
486,0,0,0,1.0792195,"\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^3,x]","\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3 \, dx","-\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 i b^3 d^{3/2} n^3 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{e^{3/2}}+\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 \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,"(-32*a*b^2*d*n^2*x^(1/3))/e + (208*b^3*d*n^3*x^(1/3))/(3*e) - (16*b^3*n^3*x)/9 - (208*b^3*d^(3/2)*n^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/(3*e^(3/2)) + ((32*I)*b^3*d^(3/2)*n^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2)/e^(3/2) + (64*b^3*d^(3/2)*n^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/e^(3/2) - (32*b^3*d*n^2*x^(1/3)*Log[c*(d + e*x^(2/3))^n])/e + (8*b^2*n^2*x*(a + b*Log[c*(d + e*x^(2/3))^n]))/3 + (32*b^2*d^(3/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*Log[c*(d + e*x^(2/3))^n]))/e^(3/2) + (6*b*d*n*x^(1/3)*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/e - 2*b*n*x*(a + b*Log[c*(d + e*x^(2/3))^n])^2 + x*(a + b*Log[c*(d + e*x^(2/3))^n])^3 + ((32*I)*b^3*d^(3/2)*n^3*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/e^(3/2) - (6*b*d^2*n*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x^2)^n])^2/(d + e*x^2), x], x, x^(1/3)])/e","A",0,0,0,0,-1,"{}"
487,0,0,0,0.4869845,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{x^2} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^3/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{x^2} \, dx","-\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 i b^3 e^{3/2} n^3 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\right)}{d^{3/2}}+\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 \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,"((24*I)*b^3*e^(3/2)*n^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2)/d^(3/2) + (48*b^3*e^(3/2)*n^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/d^(3/2) + (24*b^2*e^(3/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*Log[c*(d + e*x^(2/3))^n]))/d^(3/2) - (6*b*e*n*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(d*x^(1/3)) - (a + b*Log[c*(d + e*x^(2/3))^n])^3/x + ((24*I)*b^3*e^(3/2)*n^3*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/d^(3/2) - (6*b*e^2*n*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x^2)^n])^2/(d + e*x^2), x], x, x^(1/3)])/d","A",0,0,0,0,-1,"{}"
488,0,0,0,1.8702789,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{x^4} \, dx","Int[(a + b*Log[c*(d + e*x^(2/3))^n])^3/x^4,x]","\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^n\right)\right)^3}{x^4} \, dx","\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 i b^3 e^{9/2} n^3 \text{PolyLog}\left(2,1-\frac{2 \sqrt{d}}{\sqrt{d}+i \sqrt{e} \sqrt[3]{x}}\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{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{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{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}-\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}}",0,"(-16*b^3*e^3*n^3)/(105*d^3*x) + (16*b^3*e^4*n^3)/(7*d^4*x^(1/3)) + (1376*b^3*e^(9/2)*n^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]])/(105*d^(9/2)) - (((1408*I)/105)*b^3*e^(9/2)*n^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]^2)/d^(9/2) - (2816*b^3*e^(9/2)*n^3*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*Log[(2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/(105*d^(9/2)) - (8*b^2*e^2*n^2*(a + b*Log[c*(d + e*x^(2/3))^n]))/(35*d^2*x^(5/3)) + (32*b^2*e^3*n^2*(a + b*Log[c*(d + e*x^(2/3))^n]))/(35*d^3*x) - (568*b^2*e^4*n^2*(a + b*Log[c*(d + e*x^(2/3))^n]))/(105*d^4*x^(1/3)) - (1408*b^2*e^(9/2)*n^2*ArcTan[(Sqrt[e]*x^(1/3))/Sqrt[d]]*(a + b*Log[c*(d + e*x^(2/3))^n]))/(105*d^(9/2)) - (2*b*e*n*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(7*d*x^(7/3)) + (2*b*e^2*n*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(5*d^2*x^(5/3)) - (2*b*e^3*n*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(3*d^3*x) + (2*b*e^4*n*(a + b*Log[c*(d + e*x^(2/3))^n])^2)/(d^4*x^(1/3)) - (a + b*Log[c*(d + e*x^(2/3))^n])^3/(3*x^3) - (((1408*I)/105)*b^3*e^(9/2)*n^3*PolyLog[2, 1 - (2*Sqrt[d])/(Sqrt[d] + I*Sqrt[e]*x^(1/3))])/d^(9/2) + (2*b*e^5*n*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x^2)^n])^2/(d + e*x^2), x], x, x^(1/3)])/d^4","A",0,0,0,0,-1,"{}"
489,1,239,0,0.1708414,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \, dx","Int[x^3*(a + b*Log[c*(d + e/x^(1/3))^n]),x]","\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^{10} n x^{2/3}}{8 d^{10}}-\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^{11} n \sqrt[3]{x}}{4 d^{11}}+\frac{b e^9 n x}{12 d^9}-\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 n x^{11/3}}{44 d}","\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^{10} n x^{2/3}}{8 d^{10}}-\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^{11} n \sqrt[3]{x}}{4 d^{11}}+\frac{b e^9 n x}{12 d^9}-\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 n x^{11/3}}{44 d}",1,"(b*e^11*n*x^(1/3))/(4*d^11) - (b*e^10*n*x^(2/3))/(8*d^10) + (b*e^9*n*x)/(12*d^9) - (b*e^8*n*x^(4/3))/(16*d^8) + (b*e^7*n*x^(5/3))/(20*d^7) - (b*e^6*n*x^2)/(24*d^6) + (b*e^5*n*x^(7/3))/(28*d^5) - (b*e^4*n*x^(8/3))/(32*d^4) + (b*e^3*n*x^3)/(36*d^3) - (b*e^2*n*x^(10/3))/(40*d^2) + (b*e*n*x^(11/3))/(44*d) - (b*e^12*n*Log[d + e/x^(1/3)])/(4*d^12) + (x^4*(a + b*Log[c*(d + e/x^(1/3))^n]))/4 - (b*e^12*n*Log[x])/(12*d^12)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
490,1,190,0,0.1301312,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \, dx","Int[x^2*(a + b*Log[c*(d + e/x^(1/3))^n]),x]","\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^7 n x^{2/3}}{6 d^7}+\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^8 n \sqrt[3]{x}}{3 d^8}-\frac{b e^6 n x}{9 d^6}+\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 n x^{8/3}}{24 d}","\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^7 n x^{2/3}}{6 d^7}+\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^8 n \sqrt[3]{x}}{3 d^8}-\frac{b e^6 n x}{9 d^6}+\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 n x^{8/3}}{24 d}",1,"-(b*e^8*n*x^(1/3))/(3*d^8) + (b*e^7*n*x^(2/3))/(6*d^7) - (b*e^6*n*x)/(9*d^6) + (b*e^5*n*x^(4/3))/(12*d^5) - (b*e^4*n*x^(5/3))/(15*d^4) + (b*e^3*n*x^2)/(18*d^3) - (b*e^2*n*x^(7/3))/(21*d^2) + (b*e*n*x^(8/3))/(24*d) + (b*e^9*n*Log[d + e/x^(1/3)])/(3*d^9) + (x^3*(a + b*Log[c*(d + e/x^(1/3))^n]))/3 + (b*e^9*n*Log[x])/(9*d^9)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
491,1,141,0,0.0916034,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \, dx","Int[x*(a + b*Log[c*(d + e/x^(1/3))^n]),x]","\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^4 n x^{2/3}}{4 d^4}-\frac{b e^2 n x^{4/3}}{8 d^2}+\frac{b e^5 n \sqrt[3]{x}}{2 d^5}+\frac{b e^3 n x}{6 d^3}-\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 n x^{5/3}}{10 d}","\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^4 n x^{2/3}}{4 d^4}-\frac{b e^2 n x^{4/3}}{8 d^2}+\frac{b e^5 n \sqrt[3]{x}}{2 d^5}+\frac{b e^3 n x}{6 d^3}-\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 n x^{5/3}}{10 d}",1,"(b*e^5*n*x^(1/3))/(2*d^5) - (b*e^4*n*x^(2/3))/(4*d^4) + (b*e^3*n*x)/(6*d^3) - (b*e^2*n*x^(4/3))/(8*d^2) + (b*e*n*x^(5/3))/(10*d) - (b*e^6*n*Log[d + e/x^(1/3)])/(2*d^6) + (x^2*(a + b*Log[c*(d + e/x^(1/3))^n]))/2 - (b*e^6*n*Log[x])/(6*d^6)","A",4,3,20,0.1500,1,"{2454, 2395, 44}"
492,1,70,0,0.0501666,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right) \, dx","Int[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)-\frac{b e^2 n \sqrt[3]{x}}{d^2}+\frac{b e^3 n \log \left(d \sqrt[3]{x}+e\right)}{d^3}+\frac{b e n x^{2/3}}{2 d}","a x+b x \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)-\frac{b e^2 n \sqrt[3]{x}}{d^2}+\frac{b e^3 n \log \left(d \sqrt[3]{x}+e\right)}{d^3}+\frac{b e n x^{2/3}}{2 d}",1,"-((b*e^2*n*x^(1/3))/d^2) + (b*e*n*x^(2/3))/(2*d) + a*x + b*x*Log[c*(d + e/x^(1/3))^n] + (b*e^3*n*Log[e + d*x^(1/3)])/d^3","A",6,4,18,0.2222,1,"{2448, 263, 190, 43}"
493,1,51,0,0.0499843,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{x} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])/x,x]","-3 b n \text{PolyLog}\left(2,\frac{e}{d \sqrt[3]{x}}+1\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{PolyLog}\left(2,\frac{e}{d \sqrt[3]{x}}+1\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)",1,"-3*(a + b*Log[c*(d + e/x^(1/3))^n])*Log[-(e/(d*x^(1/3)))] - 3*b*n*PolyLog[2, 1 + e/(d*x^(1/3))]","A",3,3,22,0.1364,1,"{2454, 2394, 2315}"
494,1,82,0,0.0682031,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{x^2} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])/x^2,x]","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{x}+\frac{b d^2 n}{e^2 \sqrt[3]{x}}-\frac{b d^3 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^3}-\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^2 n}{e^2 \sqrt[3]{x}}-\frac{b d^3 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^3}-\frac{b d n}{2 e x^{2/3}}+\frac{b n}{3 x}",1,"(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 - (a + b*Log[c*(d + e/x^(1/3))^n])/x","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
495,1,138,0,0.097263,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{x^3} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])/x^3,x]","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{2 x^2}+\frac{b d^4 n}{4 e^4 x^{2/3}}+\frac{b d^2 n}{8 e^2 x^{4/3}}-\frac{b d^5 n}{2 e^5 \sqrt[3]{x}}-\frac{b d^3 n}{6 e^3 x}+\frac{b d^6 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{2 e^6}-\frac{b d n}{10 e x^{5/3}}+\frac{b n}{12 x^2}","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{2 x^2}+\frac{b d^4 n}{4 e^4 x^{2/3}}+\frac{b d^2 n}{8 e^2 x^{4/3}}-\frac{b d^5 n}{2 e^5 \sqrt[3]{x}}-\frac{b d^3 n}{6 e^3 x}+\frac{b d^6 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{2 e^6}-\frac{b d n}{10 e x^{5/3}}+\frac{b n}{12 x^2}",1,"(b*n)/(12*x^2) - (b*d*n)/(10*e*x^(5/3)) + (b*d^2*n)/(8*e^2*x^(4/3)) - (b*d^3*n)/(6*e^3*x) + (b*d^4*n)/(4*e^4*x^(2/3)) - (b*d^5*n)/(2*e^5*x^(1/3)) + (b*d^6*n*Log[d + e/x^(1/3)])/(2*e^6) - (a + b*Log[c*(d + e/x^(1/3))^n])/(2*x^2)","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
496,1,187,0,0.1334263,"\int \frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{x^4} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])/x^4,x]","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{3 x^3}-\frac{b d^7 n}{6 e^7 x^{2/3}}-\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^8 n}{3 e^8 \sqrt[3]{x}}+\frac{b d^6 n}{9 e^6 x}-\frac{b d^9 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{3 e^9}-\frac{b d n}{24 e x^{8/3}}+\frac{b n}{27 x^3}","-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)}{3 x^3}-\frac{b d^7 n}{6 e^7 x^{2/3}}-\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^8 n}{3 e^8 \sqrt[3]{x}}+\frac{b d^6 n}{9 e^6 x}-\frac{b d^9 n \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{3 e^9}-\frac{b d n}{24 e x^{8/3}}+\frac{b n}{27 x^3}",1,"(b*n)/(27*x^3) - (b*d*n)/(24*e*x^(8/3)) + (b*d^2*n)/(21*e^2*x^(7/3)) - (b*d^3*n)/(18*e^3*x^2) + (b*d^4*n)/(15*e^4*x^(5/3)) - (b*d^5*n)/(12*e^5*x^(4/3)) + (b*d^6*n)/(9*e^6*x) - (b*d^7*n)/(6*e^7*x^(2/3)) + (b*d^8*n)/(3*e^8*x^(1/3)) - (b*d^9*n*Log[d + e/x^(1/3)])/(3*e^9) - (a + b*Log[c*(d + e/x^(1/3))^n])/(3*x^3)","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
497,1,596,0,1.7150858,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \, dx","Int[x^2*(a + b*Log[c*(d + e/x^(1/3))^n])^2,x]","-\frac{2 b^2 e^9 n^2 \text{PolyLog}\left(2,\frac{e}{d \sqrt[3]{x}}+1\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{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{e^9 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{3 d^9}-\frac{2 b e^9 n \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 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{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 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{341 b^2 e^7 n^2 x^{2/3}}{840 d^7}-\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}+\frac{481 b^2 e^8 n^2 \sqrt[3]{x}}{420 d^8}+\frac{743 b^2 e^6 n^2 x}{3780 d^6}-\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{2 b^2 e^9 n^2 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\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{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{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{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 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{341 b^2 e^7 n^2 x^{2/3}}{840 d^7}-\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}+\frac{481 b^2 e^8 n^2 \sqrt[3]{x}}{420 d^8}+\frac{743 b^2 e^6 n^2 x}{3780 d^6}-\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}",1,"(481*b^2*e^8*n^2*x^(1/3))/(420*d^8) - (341*b^2*e^7*n^2*x^(2/3))/(840*d^7) + (743*b^2*e^6*n^2*x)/(3780*d^6) - (533*b^2*e^5*n^2*x^(4/3))/(5040*d^5) + (73*b^2*e^4*n^2*x^(5/3))/(1260*d^4) - (5*b^2*e^3*n^2*x^2)/(168*d^3) + (b^2*e^2*n^2*x^(7/3))/(84*d^2) - (481*b^2*e^9*n^2*Log[d + e/x^(1/3)])/(420*d^9) - (2*b*e^8*n*(d + e/x^(1/3))*x^(1/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(3*d^9) + (b*e^7*n*x^(2/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(3*d^7) - (2*b*e^6*n*x*(a + b*Log[c*(d + e/x^(1/3))^n]))/(9*d^6) + (b*e^5*n*x^(4/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(6*d^5) - (2*b*e^4*n*x^(5/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(15*d^4) + (b*e^3*n*x^2*(a + b*Log[c*(d + e/x^(1/3))^n]))/(9*d^3) - (2*b*e^2*n*x^(7/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(21*d^2) + (b*e*n*x^(8/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(12*d) + (e^9*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(3*d^9) + (x^3*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/3 - (2*b*e^9*n*(a + b*Log[c*(d + e/x^(1/3))^n])*Log[-(e/(d*x^(1/3)))])/(3*d^9) - (761*b^2*e^9*n^2*Log[x])/(1260*d^9) - (2*b^2*e^9*n^2*PolyLog[2, 1 + e/(d*x^(1/3))])/(3*d^9)","A",38,12,24,0.5000,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
498,1,423,0,1.0241227,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \, dx","Int[x*(a + b*Log[c*(d + e/x^(1/3))^n])^2,x]","\frac{b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{e}{d \sqrt[3]{x}}+1\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^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{e^6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{2 d^6}+\frac{b e^6 n \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{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^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 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{47 b^2 e^4 n^2 x^{2/3}}{120 d^4}+\frac{b^2 e^2 n^2 x^{4/3}}{20 d^2}-\frac{77 b^2 e^5 n^2 \sqrt[3]{x}}{60 d^5}-\frac{3 b^2 e^3 n^2 x}{20 d^3}+\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{b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\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^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^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^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 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{47 b^2 e^4 n^2 x^{2/3}}{120 d^4}+\frac{b^2 e^2 n^2 x^{4/3}}{20 d^2}-\frac{77 b^2 e^5 n^2 \sqrt[3]{x}}{60 d^5}-\frac{3 b^2 e^3 n^2 x}{20 d^3}+\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}",1,"(-77*b^2*e^5*n^2*x^(1/3))/(60*d^5) + (47*b^2*e^4*n^2*x^(2/3))/(120*d^4) - (3*b^2*e^3*n^2*x)/(20*d^3) + (b^2*e^2*n^2*x^(4/3))/(20*d^2) + (77*b^2*e^6*n^2*Log[d + e/x^(1/3)])/(60*d^6) + (b*e^5*n*(d + e/x^(1/3))*x^(1/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/d^6 - (b*e^4*n*x^(2/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(2*d^4) + (b*e^3*n*x*(a + b*Log[c*(d + e/x^(1/3))^n]))/(3*d^3) - (b*e^2*n*x^(4/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(4*d^2) + (b*e*n*x^(5/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(5*d) - (e^6*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(2*d^6) + (x^2*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/2 + (b*e^6*n*(a + b*Log[c*(d + e/x^(1/3))^n])*Log[-(e/(d*x^(1/3)))])/d^6 + (137*b^2*e^6*n^2*Log[x])/(180*d^6) + (b^2*e^6*n^2*PolyLog[2, 1 + e/(d*x^(1/3))])/d^6","A",26,12,22,0.5455,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
499,1,248,0,0.5331604,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2 \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])^2,x]","-\frac{2 b^2 e^3 n^2 \text{PolyLog}\left(2,\frac{e}{d \sqrt[3]{x}}+1\right)}{d^3}+\frac{e^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{d^3}-\frac{2 b e^3 n \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{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{b^2 e^2 n^2 \sqrt[3]{x}}{d^2}-\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{2 b^2 e^3 n^2 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right)}{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{b^2 e^2 n^2 \sqrt[3]{x}}{d^2}-\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}",1,"(b^2*e^2*n^2*x^(1/3))/d^2 - (b^2*e^3*n^2*Log[d + e/x^(1/3)])/d^3 - (2*b*e^2*n*(d + e/x^(1/3))*x^(1/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/d^3 + (b*e*n*x^(2/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/d + (e^3*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/d^3 + x*(a + b*Log[c*(d + e/x^(1/3))^n])^2 - (2*b*e^3*n*(a + b*Log[c*(d + e/x^(1/3))^n])*Log[-(e/(d*x^(1/3)))])/d^3 - (b^2*e^3*n^2*Log[x])/d^3 - (2*b^2*e^3*n^2*PolyLog[2, 1 + e/(d*x^(1/3))])/d^3","A",15,13,20,0.6500,1,"{2451, 2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
500,1,93,0,0.1308826,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{x} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])^2/x,x]","-6 b n \text{PolyLog}\left(2,\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)+6 b^2 n^2 \text{PolyLog}\left(3,\frac{e}{d \sqrt[3]{x}}+1\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 n \text{PolyLog}\left(2,\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)+6 b^2 n^2 \text{PolyLog}\left(3,\frac{e}{d \sqrt[3]{x}}+1\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",1,"-3*(a + b*Log[c*(d + e/x^(1/3))^n])^2*Log[-(e/(d*x^(1/3)))] - 6*b*n*(a + b*Log[c*(d + e/x^(1/3))^n])*PolyLog[2, 1 + e/(d*x^(1/3))] + 6*b^2*n^2*PolyLog[3, 1 + e/(d*x^(1/3))]","A",5,5,24,0.2083,1,"{2454, 2396, 2433, 2374, 6589}"
501,1,212,0,0.3110757,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{x^2} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])^2/x^2,x]","\frac{1}{3} b n \left(\frac{18 d^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^3}-\frac{6 d^3 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^3}-\frac{9 d \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}{e^3}+\frac{2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^3}{e^3}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)-\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{x}-\frac{6 b^2 d^2 n^2}{e^2 \sqrt[3]{x}}+\frac{b^2 d^3 n^2 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^3}+\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}","-\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{6 b^2 d^2 n^2}{e^2 \sqrt[3]{x}}+\frac{b^2 d^3 n^2 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^3}+\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,"(3*b^2*d*n^2*(d + e/x^(1/3))^2)/(2*e^3) - (2*b^2*n^2*(d + e/x^(1/3))^3)/(9*e^3) - (6*b^2*d^2*n^2)/(e^2*x^(1/3)) + (b^2*d^3*n^2*Log[d + e/x^(1/3)]^2)/e^3 + (b*n*((18*d^2*(d + e/x^(1/3)))/e^3 - (9*d*(d + e/x^(1/3))^2)/e^3 + (2*(d + e/x^(1/3))^3)/e^3 - (6*d^3*Log[d + e/x^(1/3)])/e^3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/3 - (a + b*Log[c*(d + e/x^(1/3))^n])^2/x","A",8,8,24,0.3333,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
502,1,355,0,0.4796691,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{x^3} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])^2/x^3,x]","-\frac{1}{60} b n \left(\frac{360 d^5 \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^6}-\frac{450 d^4 \left(d+\frac{e}{\sqrt[3]{x}}\right)^2}{e^6}+\frac{400 d^3 \left(d+\frac{e}{\sqrt[3]{x}}\right)^3}{e^6}-\frac{225 d^2 \left(d+\frac{e}{\sqrt[3]{x}}\right)^4}{e^6}-\frac{60 d^6 \log \left(d+\frac{e}{\sqrt[3]{x}}\right)}{e^6}+\frac{72 d \left(d+\frac{e}{\sqrt[3]{x}}\right)^5}{e^6}-\frac{10 \left(d+\frac{e}{\sqrt[3]{x}}\right)^6}{e^6}\right) \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)-\frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{2 x^2}+\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{b^2 d^6 n^2 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)}{2 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}","\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{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{b^2 d^6 n^2 \log ^2\left(d+\frac{e}{\sqrt[3]{x}}\right)}{2 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,"(-15*b^2*d^4*n^2*(d + e/x^(1/3))^2)/(4*e^6) + (20*b^2*d^3*n^2*(d + e/x^(1/3))^3)/(9*e^6) - (15*b^2*d^2*n^2*(d + e/x^(1/3))^4)/(16*e^6) + (6*b^2*d*n^2*(d + e/x^(1/3))^5)/(25*e^6) - (b^2*n^2*(d + e/x^(1/3))^6)/(36*e^6) + (6*b^2*d^5*n^2)/(e^5*x^(1/3)) - (b^2*d^6*n^2*Log[d + e/x^(1/3)]^2)/(2*e^6) - (b*n*((360*d^5*(d + e/x^(1/3)))/e^6 - (450*d^4*(d + e/x^(1/3))^2)/e^6 + (400*d^3*(d + e/x^(1/3))^3)/e^6 - (225*d^2*(d + e/x^(1/3))^4)/e^6 + (72*d*(d + e/x^(1/3))^5)/e^6 - (10*(d + e/x^(1/3))^6)/e^6 - (60*d^6*Log[d + e/x^(1/3)])/e^6)*(a + b*Log[c*(d + e/x^(1/3))^n]))/60 - (a + b*Log[c*(d + e/x^(1/3))^n])^2/(2*x^2)","A",8,8,24,0.3333,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
503,1,736,0,2.9745489,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3 \, dx","Int[x*(a + b*Log[c*(d + e/x^(1/3))^n])^3,x]","\frac{3 b^2 e^6 n^2 \text{PolyLog}\left(2,\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)}{d^6}-\frac{137 b^3 e^6 n^3 \text{PolyLog}\left(2,\frac{e}{d \sqrt[3]{x}}+1\right)}{20 d^6}-\frac{3 b^3 e^6 n^3 \text{PolyLog}\left(3,\frac{e}{d \sqrt[3]{x}}+1\right)}{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{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{137 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)}{20 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{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 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{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{e^6 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3}{2 d^6}+\frac{77 b e^6 n \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^2}{40 d^6}+\frac{3 b e^6 n \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}{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{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 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{3 b^3 e^4 n^3 x^{2/3}}{10 d^4}+\frac{71 b^3 e^5 n^3 \sqrt[3]{x}}{40 d^5}+\frac{b^3 e^3 n^3 x}{20 d^3}-\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{3 b^2 e^6 n^2 \text{PolyLog}\left(2,\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^3 e^6 n^3 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right)}{20 d^6}-\frac{3 b^3 e^6 n^3 \text{PolyLog}\left(2,\frac{e}{d \sqrt[3]{x}}+1\right)}{d^6}-\frac{3 b^3 e^6 n^3 \text{PolyLog}\left(3,\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right)}{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{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{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{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 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{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^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{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 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{3 b^3 e^4 n^3 x^{2/3}}{10 d^4}+\frac{71 b^3 e^5 n^3 \sqrt[3]{x}}{40 d^5}+\frac{b^3 e^3 n^3 x}{20 d^3}-\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}",1,"(71*b^3*e^5*n^3*x^(1/3))/(40*d^5) - (3*b^3*e^4*n^3*x^(2/3))/(10*d^4) + (b^3*e^3*n^3*x)/(20*d^3) - (71*b^3*e^6*n^3*Log[d + e/x^(1/3)])/(40*d^6) - (77*b^2*e^5*n^2*(d + e/x^(1/3))*x^(1/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(20*d^6) + (47*b^2*e^4*n^2*x^(2/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(40*d^4) - (9*b^2*e^3*n^2*x*(a + b*Log[c*(d + e/x^(1/3))^n]))/(20*d^3) + (3*b^2*e^2*n^2*x^(4/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/(20*d^2) + (77*b*e^6*n*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(40*d^6) + (3*b*e^5*n*(d + e/x^(1/3))*x^(1/3)*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(2*d^6) - (3*b*e^4*n*x^(2/3)*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(4*d^4) + (b*e^3*n*x*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(2*d^3) - (3*b*e^2*n*x^(4/3)*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(8*d^2) + (3*b*e*n*x^(5/3)*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(10*d) - (e^6*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/(2*d^6) + (x^2*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/2 - (137*b^2*e^6*n^2*(a + b*Log[c*(d + e/x^(1/3))^n])*Log[-(e/(d*x^(1/3)))])/(20*d^6) + (3*b*e^6*n*(a + b*Log[c*(d + e/x^(1/3))^n])^2*Log[-(e/(d*x^(1/3)))])/(2*d^6) - (15*b^3*e^6*n^3*Log[x])/(8*d^6) - (137*b^3*e^6*n^3*PolyLog[2, 1 + e/(d*x^(1/3))])/(20*d^6) + (3*b^2*e^6*n^2*(a + b*Log[c*(d + e/x^(1/3))^n])*PolyLog[2, 1 + e/(d*x^(1/3))])/d^6 - (3*b^3*e^6*n^3*PolyLog[3, 1 + e/(d*x^(1/3))])/d^6","A",73,17,22,0.7727,1,"{2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31, 44}"
504,1,410,0,1.0421513,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3 \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])^3,x]","-\frac{6 b^2 e^3 n^2 \text{PolyLog}\left(2,\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)}{d^3}+\frac{9 b^3 e^3 n^3 \text{PolyLog}\left(2,\frac{e}{d \sqrt[3]{x}}+1\right)}{d^3}+\frac{6 b^3 e^3 n^3 \text{PolyLog}\left(3,\frac{e}{d \sqrt[3]{x}}+1\right)}{d^3}+\frac{9 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{e^3 \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3}{d^3}-\frac{3 b e^3 n \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^3 n \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}{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{b^3 e^3 n^3 \log (x)}{d^3}","\frac{6 b^2 e^3 n^2 \text{PolyLog}\left(2,\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^3 e^3 n^3 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\right)}{d^3}+\frac{6 b^3 e^3 n^3 \text{PolyLog}\left(2,\frac{e}{d \sqrt[3]{x}}+1\right)}{d^3}+\frac{6 b^3 e^3 n^3 \text{PolyLog}\left(3,\frac{d}{d+\frac{e}{\sqrt[3]{x}}}\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{b^3 e^3 n^3 \log (x)}{d^3}",1,"(3*b^2*e^2*n^2*(d + e/x^(1/3))*x^(1/3)*(a + b*Log[c*(d + e/x^(1/3))^n]))/d^3 - (3*b*e^3*n*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(2*d^3) - (3*b*e^2*n*(d + e/x^(1/3))*x^(1/3)*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/d^3 + (3*b*e*n*x^(2/3)*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(2*d) + (e^3*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/d^3 + x*(a + b*Log[c*(d + e/x^(1/3))^n])^3 + (9*b^2*e^3*n^2*(a + b*Log[c*(d + e/x^(1/3))^n])*Log[-(e/(d*x^(1/3)))])/d^3 - (3*b*e^3*n*(a + b*Log[c*(d + e/x^(1/3))^n])^2*Log[-(e/(d*x^(1/3)))])/d^3 + (b^3*e^3*n^3*Log[x])/d^3 + (9*b^3*e^3*n^3*PolyLog[2, 1 + e/(d*x^(1/3))])/d^3 - (6*b^2*e^3*n^2*(a + b*Log[c*(d + e/x^(1/3))^n])*PolyLog[2, 1 + e/(d*x^(1/3))])/d^3 + (6*b^3*e^3*n^3*PolyLog[3, 1 + e/(d*x^(1/3))])/d^3","A",23,17,20,0.8500,1,"{2451, 2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31}"
505,1,135,0,0.1965746,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3}{x} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])^3/x,x]","18 b^2 n^2 \text{PolyLog}\left(3,\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{PolyLog}\left(2,\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)^2-18 b^3 n^3 \text{PolyLog}\left(4,\frac{e}{d \sqrt[3]{x}}+1\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","18 b^2 n^2 \text{PolyLog}\left(3,\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{PolyLog}\left(2,\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)^2-18 b^3 n^3 \text{PolyLog}\left(4,\frac{e}{d \sqrt[3]{x}}+1\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",1,"-3*(a + b*Log[c*(d + e/x^(1/3))^n])^3*Log[-(e/(d*x^(1/3)))] - 9*b*n*(a + b*Log[c*(d + e/x^(1/3))^n])^2*PolyLog[2, 1 + e/(d*x^(1/3))] + 18*b^2*n^2*(a + b*Log[c*(d + e/x^(1/3))^n])*PolyLog[3, 1 + e/(d*x^(1/3))] - 18*b^3*n^3*PolyLog[4, 1 + e/(d*x^(1/3))]","A",6,6,24,0.2500,1,"{2454, 2396, 2433, 2374, 2383, 6589}"
506,1,438,0,0.4522477,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3}{x^2} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])^3/x^2,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}","-\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,"(-9*b^3*d*n^3*(d + e/x^(1/3))^2)/(4*e^3) + (2*b^3*n^3*(d + e/x^(1/3))^3)/(9*e^3) - (18*a*b^2*d^2*n^2)/(e^2*x^(1/3)) + (18*b^3*d^2*n^3)/(e^2*x^(1/3)) - (18*b^3*d^2*n^2*(d + e/x^(1/3))*Log[c*(d + e/x^(1/3))^n])/e^3 + (9*b^2*d*n^2*(d + e/x^(1/3))^2*(a + b*Log[c*(d + e/x^(1/3))^n]))/(2*e^3) - (2*b^2*n^2*(d + e/x^(1/3))^3*(a + b*Log[c*(d + e/x^(1/3))^n]))/(3*e^3) + (9*b*d^2*n*(d + e/x^(1/3))*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/e^3 - (9*b*d*n*(d + e/x^(1/3))^2*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(2*e^3) + (b*n*(d + e/x^(1/3))^3*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/e^3 - (3*d^2*(d + e/x^(1/3))*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/e^3 + (3*d*(d + e/x^(1/3))^2*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/e^3 - ((d + e/x^(1/3))^3*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/e^3","A",16,8,24,0.3333,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
507,1,907,0,1.0012973,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^n\right)\right)^3}{x^3} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^n])^3/x^3,x]","\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}}","\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,"(45*b^3*d^4*n^3*(d + e/x^(1/3))^2)/(8*e^6) - (20*b^3*d^3*n^3*(d + e/x^(1/3))^3)/(9*e^6) + (45*b^3*d^2*n^3*(d + e/x^(1/3))^4)/(64*e^6) - (18*b^3*d*n^3*(d + e/x^(1/3))^5)/(125*e^6) + (b^3*n^3*(d + e/x^(1/3))^6)/(72*e^6) + (18*a*b^2*d^5*n^2)/(e^5*x^(1/3)) - (18*b^3*d^5*n^3)/(e^5*x^(1/3)) + (18*b^3*d^5*n^2*(d + e/x^(1/3))*Log[c*(d + e/x^(1/3))^n])/e^6 - (45*b^2*d^4*n^2*(d + e/x^(1/3))^2*(a + b*Log[c*(d + e/x^(1/3))^n]))/(4*e^6) + (20*b^2*d^3*n^2*(d + e/x^(1/3))^3*(a + b*Log[c*(d + e/x^(1/3))^n]))/(3*e^6) - (45*b^2*d^2*n^2*(d + e/x^(1/3))^4*(a + b*Log[c*(d + e/x^(1/3))^n]))/(16*e^6) + (18*b^2*d*n^2*(d + e/x^(1/3))^5*(a + b*Log[c*(d + e/x^(1/3))^n]))/(25*e^6) - (b^2*n^2*(d + e/x^(1/3))^6*(a + b*Log[c*(d + e/x^(1/3))^n]))/(12*e^6) - (9*b*d^5*n*(d + e/x^(1/3))*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/e^6 + (45*b*d^4*n*(d + e/x^(1/3))^2*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(4*e^6) - (10*b*d^3*n*(d + e/x^(1/3))^3*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/e^6 + (45*b*d^2*n*(d + e/x^(1/3))^4*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(8*e^6) - (9*b*d*n*(d + e/x^(1/3))^5*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(5*e^6) + (b*n*(d + e/x^(1/3))^6*(a + b*Log[c*(d + e/x^(1/3))^n])^2)/(4*e^6) + (3*d^5*(d + e/x^(1/3))*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/e^6 - (15*d^4*(d + e/x^(1/3))^2*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/(2*e^6) + (10*d^3*(d + e/x^(1/3))^3*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/e^6 - (15*d^2*(d + e/x^(1/3))^4*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/(2*e^6) + (3*d*(d + e/x^(1/3))^5*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/e^6 - ((d + e/x^(1/3))^6*(a + b*Log[c*(d + e/x^(1/3))^n])^3)/(2*e^6)","A",28,8,24,0.3333,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
508,1,143,0,0.1053979,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \, dx","Int[x^3*(a + b*Log[c*(d + e/x^(2/3))^n]),x]","\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^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^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 n x^{10/3}}{20 d}","\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^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^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 n x^{10/3}}{20 d}",1,"(b*e^5*n*x^(2/3))/(4*d^5) - (b*e^4*n*x^(4/3))/(8*d^4) + (b*e^3*n*x^2)/(12*d^3) - (b*e^2*n*x^(8/3))/(16*d^2) + (b*e*n*x^(10/3))/(20*d) - (b*e^6*n*Log[d + e/x^(2/3)])/(4*d^6) + (x^4*(a + b*Log[c*(d + e/x^(2/3))^n]))/4 - (b*e^6*n*Log[x])/(6*d^6)","A",4,3,22,0.1364,1,"{2454, 2395, 44}"
509,1,121,0,0.0718126,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \, dx","Int[x^2*(a + b*Log[c*(d + e/x^(2/3))^n]),x]","\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^2 n x^{5/3}}{15 d^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^{9/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{3 d^{9/2}}+\frac{2 b e n x^{7/3}}{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^2 n x^{5/3}}{15 d^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^{9/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{3 d^{9/2}}+\frac{2 b e n x^{7/3}}{21 d}",1,"(-2*b*e^4*n*x^(1/3))/(3*d^4) + (2*b*e^3*n*x)/(9*d^3) - (2*b*e^2*n*x^(5/3))/(15*d^2) + (2*b*e*n*x^(7/3))/(21*d) + (2*b*e^(9/2)*n*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]])/(3*d^(9/2)) + (x^3*(a + b*Log[c*(d + e/x^(2/3))^n]))/3","A",6,5,22,0.2273,1,"{2455, 263, 341, 302, 205}"
510,1,94,0,0.0624697,"\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \, dx","Int[x*(a + b*Log[c*(d + e/x^(2/3))^n]),x]","\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^2 n x^{2/3}}{2 d^2}+\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 n x^{4/3}}{4 d}","\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^2 n x^{2/3}}{2 d^2}+\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 n x^{4/3}}{4 d}",1,"-(b*e^2*n*x^(2/3))/(2*d^2) + (b*e*n*x^(4/3))/(4*d) + (b*e^3*n*Log[d + e/x^(2/3)])/(2*d^3) + (x^2*(a + b*Log[c*(d + e/x^(2/3))^n]))/2 + (b*e^3*n*Log[x])/(3*d^3)","A",4,3,20,0.1500,1,"{2454, 2395, 44}"
511,1,65,0,0.0417612,"\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right) \, dx","Int[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^{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}","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,"(2*b*e*n*x^(1/3))/d + a*x - (2*b*e^(3/2)*n*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]])/d^(3/2) + b*x*Log[c*(d + e/x^(2/3))^n]","A",6,5,18,0.2778,1,"{2448, 263, 243, 321, 205}"
512,1,55,0,0.0514524,"\int \frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{x} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])/x,x]","-\frac{3}{2} b n \text{PolyLog}\left(2,\frac{e}{d x^{2/3}}+1\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{PolyLog}\left(2,\frac{e}{d x^{2/3}}+1\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)",1,"(-3*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[-(e/(d*x^(2/3)))])/2 - (3*b*n*PolyLog[2, 1 + e/(d*x^(2/3))])/2","A",3,3,22,0.1364,1,"{2454, 2394, 2315}"
513,1,77,0,0.0509336,"\int \frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{x^2} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])/x^2,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}","-\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,"(2*b*n)/(3*x) - (2*b*d*n)/(e*x^(1/3)) - (2*b*d^(3/2)*n*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]])/e^(3/2) - (a + b*Log[c*(d + e/x^(2/3))^n])/x","A",6,5,22,0.2273,1,"{2455, 263, 341, 325, 205}"
514,1,89,0,0.0680862,"\int \frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{x^3} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])/x^3,x]","-\frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{2 x^2}+\frac{b d^2 n}{2 e^2 x^{2/3}}-\frac{b d^3 n \log \left(d+\frac{e}{x^{2/3}}\right)}{2 e^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^2 n}{2 e^2 x^{2/3}}-\frac{b d^3 n \log \left(d+\frac{e}{x^{2/3}}\right)}{2 e^3}-\frac{b d n}{4 e x^{4/3}}+\frac{b n}{6 x^2}",1,"(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) - (a + b*Log[c*(d + e/x^(2/3))^n])/(2*x^2)","A",4,3,22,0.1364,1,"{2454, 2395, 43}"
515,1,132,0,0.088075,"\int \frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{x^4} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])/x^4,x]","-\frac{a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)}{3 x^3}+\frac{2 b d^2 n}{15 e^2 x^{5/3}}+\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^{9/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{3 e^{9/2}}-\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^2 n}{15 e^2 x^{5/3}}+\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^{9/2} n \tan ^{-1}\left(\frac{\sqrt{d} \sqrt[3]{x}}{\sqrt{e}}\right)}{3 e^{9/2}}-\frac{2 b d n}{21 e x^{7/3}}+\frac{2 b n}{27 x^3}",1,"(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[d]*x^(1/3))/Sqrt[e]])/(3*e^(9/2)) - (a + b*Log[c*(d + e/x^(2/3))^n])/(3*x^3)","A",9,5,22,0.2273,1,"{2455, 263, 341, 325, 205}"
516,1,436,0,1.0166741,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 \, dx","Int[x^3*(a + b*Log[c*(d + e/x^(2/3))^n])^2,x]","\frac{b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{e}{d x^{2/3}}+1\right)}{2 d^6}-\frac{e^6 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{4 d^6}+\frac{b e^6 n \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{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{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}+\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{b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{x^{2/3}}}\right)}{2 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{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}+\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}",1,"(-77*b^2*e^5*n^2*x^(2/3))/(120*d^5) + (47*b^2*e^4*n^2*x^(4/3))/(240*d^4) - (3*b^2*e^3*n^2*x^2)/(40*d^3) + (b^2*e^2*n^2*x^(8/3))/(40*d^2) + (77*b^2*e^6*n^2*Log[d + e/x^(2/3)])/(120*d^6) + (b*e^5*n*(d + e/x^(2/3))*x^(2/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(2*d^6) - (b*e^4*n*x^(4/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(4*d^4) + (b*e^3*n*x^2*(a + b*Log[c*(d + e/x^(2/3))^n]))/(6*d^3) - (b*e^2*n*x^(8/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(8*d^2) + (b*e*n*x^(10/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(10*d) - (e^6*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(4*d^6) + (x^4*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/4 + (b*e^6*n*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[-(e/(d*x^(2/3)))])/(2*d^6) + (137*b^2*e^6*n^2*Log[x])/(180*d^6) + (b^2*e^6*n^2*PolyLog[2, 1 + e/(d*x^(2/3))])/(2*d^6)","A",26,12,24,0.5000,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
517,1,264,0,0.4842851,"\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 \, dx","Int[x*(a + b*Log[c*(d + e/x^(2/3))^n])^2,x]","-\frac{b^2 e^3 n^2 \text{PolyLog}\left(2,\frac{e}{d x^{2/3}}+1\right)}{d^3}+\frac{e^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{2 d^3}-\frac{b e^3 n \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{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^2 n^2 x^{2/3}}{2 d^2}-\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^3 n^2 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{x^{2/3}}}\right)}{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^2 n^2 x^{2/3}}{2 d^2}-\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}",1,"(b^2*e^2*n^2*x^(2/3))/(2*d^2) - (b^2*e^3*n^2*Log[d + e/x^(2/3)])/(2*d^3) - (b*e^2*n*(d + e/x^(2/3))*x^(2/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/d^3 + (b*e*n*x^(4/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(2*d) + (e^3*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(2*d^3) + (x^2*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/2 - (b*e^3*n*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[-(e/(d*x^(2/3)))])/d^3 - (b^2*e^3*n^2*Log[x])/d^3 - (b^2*e^3*n^2*PolyLog[2, 1 + e/(d*x^(2/3))])/d^3","A",14,12,22,0.5455,1,"{2454, 2398, 2411, 2347, 2344, 2301, 2317, 2391, 2314, 31, 2319, 44}"
518,1,95,0,0.1310489,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])^2/x,x]","-3 b n \text{PolyLog}\left(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)+3 b^2 n^2 \text{PolyLog}\left(3,\frac{e}{d x^{2/3}}+1\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 n \text{PolyLog}\left(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)+3 b^2 n^2 \text{PolyLog}\left(3,\frac{e}{d x^{2/3}}+1\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",1,"(-3*(a + b*Log[c*(d + e/x^(2/3))^n])^2*Log[-(e/(d*x^(2/3)))])/2 - 3*b*n*(a + b*Log[c*(d + e/x^(2/3))^n])*PolyLog[2, 1 + e/(d*x^(2/3))] + 3*b^2*n^2*PolyLog[3, 1 + e/(d*x^(2/3))]","A",5,5,24,0.2083,1,"{2454, 2396, 2433, 2374, 6589}"
519,1,217,0,0.3009811,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x^3} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])^2/x^3,x]","\frac{1}{6} b n \left(\frac{18 d^2 \left(d+\frac{e}{x^{2/3}}\right)}{e^3}-\frac{6 d^3 \log \left(d+\frac{e}{x^{2/3}}\right)}{e^3}-\frac{9 d \left(d+\frac{e}{x^{2/3}}\right)^2}{e^3}+\frac{2 \left(d+\frac{e}{x^{2/3}}\right)^3}{e^3}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{2 x^2}-\frac{3 b^2 d^2 n^2}{e^2 x^{2/3}}+\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 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}","-\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{3 b^2 d^2 n^2}{e^2 x^{2/3}}+\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 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,"(3*b^2*d*n^2*(d + e/x^(2/3))^2)/(4*e^3) - (b^2*n^2*(d + e/x^(2/3))^3)/(9*e^3) - (3*b^2*d^2*n^2)/(e^2*x^(2/3)) + (b^2*d^3*n^2*Log[d + e/x^(2/3)]^2)/(2*e^3) + (b*n*((18*d^2*(d + e/x^(2/3)))/e^3 - (9*d*(d + e/x^(2/3))^2)/e^3 + (2*(d + e/x^(2/3))^3)/e^3 - (6*d^3*Log[d + e/x^(2/3)])/e^3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/6 - (a + b*Log[c*(d + e/x^(2/3))^n])^2/(2*x^2)","A",8,8,24,0.3333,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
520,1,355,0,0.4762943,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x^5} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])^2/x^5,x]","-\frac{1}{120} b n \left(\frac{360 d^5 \left(d+\frac{e}{x^{2/3}}\right)}{e^6}-\frac{450 d^4 \left(d+\frac{e}{x^{2/3}}\right)^2}{e^6}+\frac{400 d^3 \left(d+\frac{e}{x^{2/3}}\right)^3}{e^6}-\frac{225 d^2 \left(d+\frac{e}{x^{2/3}}\right)^4}{e^6}-\frac{60 d^6 \log \left(d+\frac{e}{x^{2/3}}\right)}{e^6}+\frac{72 d \left(d+\frac{e}{x^{2/3}}\right)^5}{e^6}-\frac{10 \left(d+\frac{e}{x^{2/3}}\right)^6}{e^6}\right) \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)-\frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{4 x^4}+\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{b^2 d^6 n^2 \log ^2\left(d+\frac{e}{x^{2/3}}\right)}{4 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}","\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{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{b^2 d^6 n^2 \log ^2\left(d+\frac{e}{x^{2/3}}\right)}{4 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,"(-15*b^2*d^4*n^2*(d + e/x^(2/3))^2)/(8*e^6) + (10*b^2*d^3*n^2*(d + e/x^(2/3))^3)/(9*e^6) - (15*b^2*d^2*n^2*(d + e/x^(2/3))^4)/(32*e^6) + (3*b^2*d*n^2*(d + e/x^(2/3))^5)/(25*e^6) - (b^2*n^2*(d + e/x^(2/3))^6)/(72*e^6) + (3*b^2*d^5*n^2)/(e^5*x^(2/3)) - (b^2*d^6*n^2*Log[d + e/x^(2/3)]^2)/(4*e^6) - (b*n*((360*d^5*(d + e/x^(2/3)))/e^6 - (450*d^4*(d + e/x^(2/3))^2)/e^6 + (400*d^3*(d + e/x^(2/3))^3)/e^6 - (225*d^2*(d + e/x^(2/3))^4)/e^6 + (72*d*(d + e/x^(2/3))^5)/e^6 - (10*(d + e/x^(2/3))^6)/e^6 - (60*d^6*Log[d + e/x^(2/3)])/e^6)*(a + b*Log[c*(d + e/x^(2/3))^n]))/120 - (a + b*Log[c*(d + e/x^(2/3))^n])^2/(4*x^4)","A",8,8,24,0.3333,1,"{2454, 2398, 2411, 43, 2334, 12, 14, 2301}"
521,1,490,0,0.8069121,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 \, dx","Int[x^2*(a + b*Log[c*(d + e/x^(2/3))^n])^2,x]","-\frac{4 i b^2 e^{9/2} n^2 \text{PolyLog}\left(2,-1+\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\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^{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 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{8 b^2 e^2 n^2 x^{5/3}}{105 d^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{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{4 i b^2 e^{9/2} n^2 \text{PolyLog}\left(2,-1+\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\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^{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 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{8 b^2 e^2 n^2 x^{5/3}}{105 d^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{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}}",1,"(-4*a*b*e^4*n*x^(1/3))/(3*d^4) + (568*b^2*e^4*n^2*x^(1/3))/(315*d^4) - (32*b^2*e^3*n^2*x)/(105*d^3) + (8*b^2*e^2*n^2*x^(5/3))/(105*d^2) - (1408*b^2*e^(9/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]])/(315*d^(9/2)) - (((4*I)/3)*b^2*e^(9/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]^2)/d^(9/2) + (8*b^2*e^(9/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*Log[2 - (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/(3*d^(9/2)) - (4*b^2*e^4*n*x^(1/3)*Log[c*(d + e/x^(2/3))^n])/(3*d^4) + (4*b*e^3*n*x*(a + b*Log[c*(d + e/x^(2/3))^n]))/(9*d^3) - (4*b*e^2*n*x^(5/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(15*d^2) + (4*b*e*n*x^(7/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(21*d) + (4*b*e^(9/2)*n*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*(a + b*Log[c*(d + e/x^(2/3))^n]))/(3*d^(9/2)) + (x^3*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/3 - (((4*I)/3)*b^2*e^(9/2)*n^2*PolyLog[2, -1 + (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/d^(9/2)","A",28,17,24,0.7083,1,"{2458, 2457, 2476, 2448, 263, 205, 2455, 193, 321, 302, 2470, 12, 260, 6688, 4924, 4868, 2447}"
522,1,309,0,0.4445659,"\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2 \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])^2,x]","\frac{4 i b^2 e^{3/2} n^2 \text{PolyLog}\left(2,-1+\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\right)}{d^{3/2}}-\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 \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}}","\frac{4 i b^2 e^{3/2} n^2 \text{PolyLog}\left(2,-1+\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\right)}{d^{3/2}}-\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 \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,"(4*a*b*e*n*x^(1/3))/d + (8*b^2*e^(3/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]])/d^(3/2) + ((4*I)*b^2*e^(3/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]^2)/d^(3/2) - (8*b^2*e^(3/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*Log[2 - (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/d^(3/2) + (4*b^2*e*n*x^(1/3)*Log[c*(d + e/x^(2/3))^n])/d - (4*b*e^(3/2)*n*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*(a + b*Log[c*(d + e/x^(2/3))^n]))/d^(3/2) + x*(a + b*Log[c*(d + e/x^(2/3))^n])^2 + ((4*I)*b^2*e^(3/2)*n^2*PolyLog[2, -1 + (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/d^(3/2)","A",14,13,20,0.6500,1,"{2451, 2457, 2471, 2448, 263, 205, 2470, 12, 260, 6688, 4924, 4868, 2447}"
523,1,361,0,0.5940363,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{x^2} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])^2/x^2,x]","\frac{4 i b^2 d^{3/2} n^2 \text{PolyLog}\left(2,-1+\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\right)}{e^{3/2}}-\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 \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}","\frac{4 i b^2 d^{3/2} n^2 \text{PolyLog}\left(2,-1+\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\right)}{e^{3/2}}-\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 \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,"(-8*b^2*n^2)/(9*x) + (32*b^2*d*n^2)/(3*e*x^(1/3)) + (32*b^2*d^(3/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]])/(3*e^(3/2)) + ((4*I)*b^2*d^(3/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]^2)/e^(3/2) - (8*b^2*d^(3/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*Log[2 - (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/e^(3/2) + (4*b*n*(a + b*Log[c*(d + e/x^(2/3))^n]))/(3*x) - (4*b*d*n*(a + b*Log[c*(d + e/x^(2/3))^n]))/(e*x^(1/3)) - (4*b*d^(3/2)*n*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*(a + b*Log[c*(d + e/x^(2/3))^n]))/e^(3/2) - (a + b*Log[c*(d + e/x^(2/3))^n])^2/x + ((4*I)*b^2*d^(3/2)*n^2*PolyLog[2, -1 + (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/e^(3/2)","A",19,14,24,0.5833,1,"{2458, 2457, 2476, 2455, 263, 325, 205, 2470, 12, 260, 6688, 4924, 4868, 2447}"
524,1,746,0,3.0194699,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3 \, dx","Int[x^3*(a + b*Log[c*(d + e/x^(2/3))^n])^3,x]","\frac{3 b^2 e^6 n^2 \text{PolyLog}\left(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)}{2 d^6}-\frac{137 b^3 e^6 n^3 \text{PolyLog}\left(2,\frac{e}{d x^{2/3}}+1\right)}{40 d^6}-\frac{3 b^3 e^6 n^3 \text{PolyLog}\left(3,\frac{e}{d x^{2/3}}+1\right)}{2 d^6}-\frac{137 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)}{40 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{e^6 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{4 d^6}+\frac{77 b e^6 n \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^2}{80 d^6}+\frac{3 b e^6 n \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}{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{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}-\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{3 b^2 e^6 n^2 \text{PolyLog}\left(2,\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^3 e^6 n^3 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{x^{2/3}}}\right)}{40 d^6}-\frac{3 b^3 e^6 n^3 \text{PolyLog}\left(2,\frac{e}{d x^{2/3}}+1\right)}{2 d^6}-\frac{3 b^3 e^6 n^3 \text{PolyLog}\left(3,\frac{d}{d+\frac{e}{x^{2/3}}}\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{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}-\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}",1,"(71*b^3*e^5*n^3*x^(2/3))/(80*d^5) - (3*b^3*e^4*n^3*x^(4/3))/(20*d^4) + (b^3*e^3*n^3*x^2)/(40*d^3) - (71*b^3*e^6*n^3*Log[d + e/x^(2/3)])/(80*d^6) - (77*b^2*e^5*n^2*(d + e/x^(2/3))*x^(2/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(40*d^6) + (47*b^2*e^4*n^2*x^(4/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(80*d^4) - (9*b^2*e^3*n^2*x^2*(a + b*Log[c*(d + e/x^(2/3))^n]))/(40*d^3) + (3*b^2*e^2*n^2*x^(8/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(40*d^2) + (77*b*e^6*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(80*d^6) + (3*b*e^5*n*(d + e/x^(2/3))*x^(2/3)*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(4*d^6) - (3*b*e^4*n*x^(4/3)*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(8*d^4) + (b*e^3*n*x^2*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(4*d^3) - (3*b*e^2*n*x^(8/3)*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(16*d^2) + (3*b*e*n*x^(10/3)*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(20*d) - (e^6*(a + b*Log[c*(d + e/x^(2/3))^n])^3)/(4*d^6) + (x^4*(a + b*Log[c*(d + e/x^(2/3))^n])^3)/4 - (137*b^2*e^6*n^2*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[-(e/(d*x^(2/3)))])/(40*d^6) + (3*b*e^6*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2*Log[-(e/(d*x^(2/3)))])/(4*d^6) - (15*b^3*e^6*n^3*Log[x])/(8*d^6) - (137*b^3*e^6*n^3*PolyLog[2, 1 + e/(d*x^(2/3))])/(40*d^6) + (3*b^2*e^6*n^2*(a + b*Log[c*(d + e/x^(2/3))^n])*PolyLog[2, 1 + e/(d*x^(2/3))])/(2*d^6) - (3*b^3*e^6*n^3*PolyLog[3, 1 + e/(d*x^(2/3))])/(2*d^6)","A",73,17,24,0.7083,1,"{2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31, 44}"
525,1,428,0,1.0032195,"\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3 \, dx","Int[x*(a + b*Log[c*(d + e/x^(2/3))^n])^3,x]","-\frac{3 b^2 e^3 n^2 \text{PolyLog}\left(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)}{d^3}+\frac{9 b^3 e^3 n^3 \text{PolyLog}\left(2,\frac{e}{d x^{2/3}}+1\right)}{2 d^3}+\frac{3 b^3 e^3 n^3 \text{PolyLog}\left(3,\frac{e}{d x^{2/3}}+1\right)}{d^3}+\frac{9 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)}{2 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{e^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{2 d^3}-\frac{3 b e^3 n \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^3 n \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}{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{b^3 e^3 n^3 \log (x)}{d^3}","\frac{3 b^2 e^3 n^2 \text{PolyLog}\left(2,\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^3 e^3 n^3 \text{PolyLog}\left(2,\frac{d}{d+\frac{e}{x^{2/3}}}\right)}{2 d^3}+\frac{3 b^3 e^3 n^3 \text{PolyLog}\left(2,\frac{e}{d x^{2/3}}+1\right)}{d^3}+\frac{3 b^3 e^3 n^3 \text{PolyLog}\left(3,\frac{d}{d+\frac{e}{x^{2/3}}}\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{b^3 e^3 n^3 \log (x)}{d^3}",1,"(3*b^2*e^2*n^2*(d + e/x^(2/3))*x^(2/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(2*d^3) - (3*b*e^3*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(4*d^3) - (3*b*e^2*n*(d + e/x^(2/3))*x^(2/3)*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(2*d^3) + (3*b*e*n*x^(4/3)*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(4*d) + (e^3*(a + b*Log[c*(d + e/x^(2/3))^n])^3)/(2*d^3) + (x^2*(a + b*Log[c*(d + e/x^(2/3))^n])^3)/2 + (9*b^2*e^3*n^2*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[-(e/(d*x^(2/3)))])/(2*d^3) - (3*b*e^3*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2*Log[-(e/(d*x^(2/3)))])/(2*d^3) + (b^3*e^3*n^3*Log[x])/d^3 + (9*b^3*e^3*n^3*PolyLog[2, 1 + e/(d*x^(2/3))])/(2*d^3) - (3*b^2*e^3*n^2*(a + b*Log[c*(d + e/x^(2/3))^n])*PolyLog[2, 1 + e/(d*x^(2/3))])/d^3 + (3*b^3*e^3*n^3*PolyLog[3, 1 + e/(d*x^(2/3))])/d^3","A",22,16,22,0.7273,1,"{2454, 2398, 2411, 2347, 2344, 2302, 30, 2317, 2374, 6589, 2318, 2391, 2319, 2301, 2314, 31}"
526,1,139,0,0.2015334,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{x} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])^3/x,x]","9 b^2 n^2 \text{PolyLog}\left(3,\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{PolyLog}\left(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)^2-9 b^3 n^3 \text{PolyLog}\left(4,\frac{e}{d x^{2/3}}+1\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)^3","9 b^2 n^2 \text{PolyLog}\left(3,\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{PolyLog}\left(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)^2-9 b^3 n^3 \text{PolyLog}\left(4,\frac{e}{d x^{2/3}}+1\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)^3",1,"(-3*(a + b*Log[c*(d + e/x^(2/3))^n])^3*Log[-(e/(d*x^(2/3)))])/2 - (9*b*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2*PolyLog[2, 1 + e/(d*x^(2/3))])/2 + 9*b^2*n^2*(a + b*Log[c*(d + e/x^(2/3))^n])*PolyLog[3, 1 + e/(d*x^(2/3))] - 9*b^3*n^3*PolyLog[4, 1 + e/(d*x^(2/3))]","A",6,6,24,0.2500,1,"{2454, 2396, 2433, 2374, 2383, 6589}"
527,1,449,0,0.4628111,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{x^3} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])^3/x^3,x]","-\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}","-\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,"(-9*b^3*d*n^3*(d + e/x^(2/3))^2)/(8*e^3) + (b^3*n^3*(d + e/x^(2/3))^3)/(9*e^3) - (9*a*b^2*d^2*n^2)/(e^2*x^(2/3)) + (9*b^3*d^2*n^3)/(e^2*x^(2/3)) - (9*b^3*d^2*n^2*(d + e/x^(2/3))*Log[c*(d + e/x^(2/3))^n])/e^3 + (9*b^2*d*n^2*(d + e/x^(2/3))^2*(a + b*Log[c*(d + e/x^(2/3))^n]))/(4*e^3) - (b^2*n^2*(d + e/x^(2/3))^3*(a + b*Log[c*(d + e/x^(2/3))^n]))/(3*e^3) + (9*b*d^2*n*(d + e/x^(2/3))*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(2*e^3) - (9*b*d*n*(d + e/x^(2/3))^2*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(4*e^3) + (b*n*(d + e/x^(2/3))^3*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(2*e^3) - (3*d^2*(d + e/x^(2/3))*(a + b*Log[c*(d + e/x^(2/3))^n])^3)/(2*e^3) + (3*d*(d + e/x^(2/3))^2*(a + b*Log[c*(d + e/x^(2/3))^n])^3)/(2*e^3) - ((d + e/x^(2/3))^3*(a + b*Log[c*(d + e/x^(2/3))^n])^3)/(2*e^3)","A",16,8,24,0.3333,1,"{2454, 2401, 2389, 2296, 2295, 2390, 2305, 2304}"
528,0,0,0,3.1686933,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3 \, dx","Int[x^2*(a + b*Log[c*(d + e/x^(2/3))^n])^3,x]","\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3 \, dx","\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{PolyLog}\left(2,\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{PolyLog}\left(2,1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right) e^{9/2}}{(-d)^{9/2}}-\frac{4 b^3 n^3 \text{PolyLog}\left(2,\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{PolyLog}\left(2,\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{PolyLog}\left(2,\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,"(568*a*b^2*e^4*n^2*x^(1/3))/(105*d^4) - (16*b^3*e^4*n^3*x^(1/3))/(7*d^4) + (16*b^3*e^3*n^3*x)/(105*d^3) + (1376*b^3*e^(9/2)*n^3*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]])/(105*d^(9/2)) + (((568*I)/105)*b^3*e^(9/2)*n^3*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]^2)/d^(9/2) - (1136*b^3*e^(9/2)*n^3*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*Log[2 - (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/(105*d^(9/2)) + (568*b^3*e^4*n^2*x^(1/3)*Log[c*(d + e/x^(2/3))^n])/(105*d^4) - (32*b^2*e^3*n^2*x*(a + b*Log[c*(d + e/x^(2/3))^n]))/(35*d^3) + (8*b^2*e^2*n^2*x^(5/3)*(a + b*Log[c*(d + e/x^(2/3))^n]))/(35*d^2) - (568*b^2*e^(9/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*(a + b*Log[c*(d + e/x^(2/3))^n]))/(105*d^(9/2)) - (2*b*e^4*n*x^(1/3)*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/d^4 + (2*b*e^3*n*x*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(3*d^3) - (2*b*e^2*n*x^(5/3)*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(5*d^2) + (2*b*e*n*x^(7/3)*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(7*d) + (x^3*(a + b*Log[c*(d + e/x^(2/3))^n])^3)/3 + (4*b^2*e^(9/2)*n^2*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)])/(-d)^(9/2) - (2*b^3*e^(9/2)*n^3*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]^2)/(-d)^(9/2) - (4*b^2*e^(9/2)*n^2*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)])/(-d)^(9/2) + (2*b^3*e^(9/2)*n^3*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]^2)/(-d)^(9/2) + (4*b^3*e^(9/2)*n^3*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])])/(-d)^(9/2) - (4*b^3*e^(9/2)*n^3*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2])/(-d)^(9/2) - (8*b^3*e^(9/2)*n^3*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[-((Sqrt[-d]*x^(1/3))/Sqrt[e])])/(-d)^(9/2) + (8*b^3*e^(9/2)*n^3*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(Sqrt[-d]*x^(1/3))/Sqrt[e]])/(-d)^(9/2) + (((568*I)/105)*b^3*e^(9/2)*n^3*PolyLog[2, -1 + (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/d^(9/2) + (8*b^3*e^(9/2)*n^3*PolyLog[2, 1 - (Sqrt[-d]*x^(1/3))/Sqrt[e]])/(-d)^(9/2) - (4*b^3*e^(9/2)*n^3*PolyLog[2, 1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])])/(-d)^(9/2) + (4*b^3*e^(9/2)*n^3*PolyLog[2, (1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2])/(-d)^(9/2) - (8*b^3*e^(9/2)*n^3*PolyLog[2, 1 + (Sqrt[-d]*x^(1/3))/Sqrt[e]])/(-d)^(9/2) + (2*b*e^5*n*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x^2)^n])^2/(e + d*x^2), x], x, x^(1/3)])/d^4","A",0,0,0,0,-1,"{}"
529,0,0,0,1.2971426,"\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3 \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])^3,x]","\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3 \, dx","-\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{24 b^3 e^{3/2} n^3 \text{PolyLog}\left(2,1-\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}\right)}{(-d)^{3/2}}-\frac{12 b^3 e^{3/2} n^3 \text{PolyLog}\left(2,\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{PolyLog}\left(2,\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 \text{PolyLog}\left(2,\frac{\sqrt{-d} \sqrt[3]{x}}{\sqrt{e}}+1\right)}{(-d)^{3/2}}+\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{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,"(6*b*e*n*x^(1/3)*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/d + x*(a + b*Log[c*(d + e/x^(2/3))^n])^3 + (12*b^2*e^(3/2)*n^2*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)])/(-d)^(3/2) - (6*b^3*e^(3/2)*n^3*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]^2)/(-d)^(3/2) - (12*b^2*e^(3/2)*n^2*(a + b*Log[c*(d + e/x^(2/3))^n])*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)])/(-d)^(3/2) + (6*b^3*e^(3/2)*n^3*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]^2)/(-d)^(3/2) + (12*b^3*e^(3/2)*n^3*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])])/(-d)^(3/2) - (12*b^3*e^(3/2)*n^3*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2])/(-d)^(3/2) - (24*b^3*e^(3/2)*n^3*Log[Sqrt[e] + Sqrt[-d]*x^(1/3)]*Log[-((Sqrt[-d]*x^(1/3))/Sqrt[e])])/(-d)^(3/2) + (24*b^3*e^(3/2)*n^3*Log[Sqrt[e] - Sqrt[-d]*x^(1/3)]*Log[(Sqrt[-d]*x^(1/3))/Sqrt[e]])/(-d)^(3/2) + (24*b^3*e^(3/2)*n^3*PolyLog[2, 1 - (Sqrt[-d]*x^(1/3))/Sqrt[e]])/(-d)^(3/2) - (12*b^3*e^(3/2)*n^3*PolyLog[2, 1/2 - (Sqrt[-d]*x^(1/3))/(2*Sqrt[e])])/(-d)^(3/2) + (12*b^3*e^(3/2)*n^3*PolyLog[2, (1 + (Sqrt[-d]*x^(1/3))/Sqrt[e])/2])/(-d)^(3/2) - (24*b^3*e^(3/2)*n^3*PolyLog[2, 1 + (Sqrt[-d]*x^(1/3))/Sqrt[e]])/(-d)^(3/2) - (6*b*e^2*n*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x^2)^n])^2/(e + d*x^2), x], x, x^(1/3)])/d","A",0,0,0,0,-1,"{}"
530,0,0,0,1.3832499,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{x^2} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])^3/x^2,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{x^2} \, dx","-\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 i b^3 d^{3/2} n^3 \text{PolyLog}\left(2,-1+\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\right)}{e^{3/2}}+\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 \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,"(16*b^3*n^3)/(9*x) - (208*b^3*d*n^3)/(3*e*x^(1/3)) - (208*b^3*d^(3/2)*n^3*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]])/(3*e^(3/2)) - ((32*I)*b^3*d^(3/2)*n^3*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]^2)/e^(3/2) + (64*b^3*d^(3/2)*n^3*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*Log[2 - (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/e^(3/2) - (8*b^2*n^2*(a + b*Log[c*(d + e/x^(2/3))^n]))/(3*x) + (32*b^2*d*n^2*(a + b*Log[c*(d + e/x^(2/3))^n]))/(e*x^(1/3)) + (32*b^2*d^(3/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*(a + b*Log[c*(d + e/x^(2/3))^n]))/e^(3/2) + (2*b*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/x - (6*b*d*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(e*x^(1/3)) - (a + b*Log[c*(d + e/x^(2/3))^n])^3/x - ((32*I)*b^3*d^(3/2)*n^3*PolyLog[2, -1 + (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/e^(3/2) - (6*b*d^2*n*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x^2)^n])^2/(e + d*x^2), x], x, x^(1/3)])/e","A",0,0,0,0,-1,"{}"
531,0,0,0,3.6248874,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{x^4} \, dx","Int[(a + b*Log[c*(d + e/x^(2/3))^n])^3/x^4,x]","\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^n\right)\right)^3}{x^4} \, dx","\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 i b^3 d^{9/2} n^3 \text{PolyLog}\left(2,-1+\frac{2 \sqrt{e}}{\sqrt{e}-i \sqrt{d} \sqrt[3]{x}}\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{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{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{221344 b^3 d^2 n^3}{496125 e^2 x^{5/3}}+\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{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{3088 b^3 d n^3}{27783 e x^{7/3}}+\frac{16 b^3 n^3}{729 x^3}",0,"(16*b^3*n^3)/(729*x^3) - (3088*b^3*d*n^3)/(27783*e*x^(7/3)) + (221344*b^3*d^2*n^3)/(496125*e^2*x^(5/3)) - (637984*b^3*d^3*n^3)/(297675*e^3*x) + (3475504*b^3*d^4*n^3)/(99225*e^4*x^(1/3)) + (3475504*b^3*d^(9/2)*n^3*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]])/(99225*e^(9/2)) + (((4504*I)/315)*b^3*d^(9/2)*n^3*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]^2)/e^(9/2) - (9008*b^3*d^(9/2)*n^3*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*Log[2 - (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/(315*e^(9/2)) - (8*b^2*n^2*(a + b*Log[c*(d + e/x^(2/3))^n]))/(81*x^3) + (128*b^2*d*n^2*(a + b*Log[c*(d + e/x^(2/3))^n]))/(441*e*x^(7/3)) - (1144*b^2*d^2*n^2*(a + b*Log[c*(d + e/x^(2/3))^n]))/(1575*e^2*x^(5/3)) + (1984*b^2*d^3*n^2*(a + b*Log[c*(d + e/x^(2/3))^n]))/(945*e^3*x) - (4504*b^2*d^4*n^2*(a + b*Log[c*(d + e/x^(2/3))^n]))/(315*e^4*x^(1/3)) - (4504*b^2*d^(9/2)*n^2*ArcTan[(Sqrt[d]*x^(1/3))/Sqrt[e]]*(a + b*Log[c*(d + e/x^(2/3))^n]))/(315*e^(9/2)) + (2*b*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(9*x^3) - (2*b*d*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(7*e*x^(7/3)) + (2*b*d^2*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(5*e^2*x^(5/3)) - (2*b*d^3*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(3*e^3*x) + (2*b*d^4*n*(a + b*Log[c*(d + e/x^(2/3))^n])^2)/(e^4*x^(1/3)) - (a + b*Log[c*(d + e/x^(2/3))^n])^3/(3*x^3) + (((4504*I)/315)*b^3*d^(9/2)*n^3*PolyLog[2, -1 + (2*Sqrt[e])/(Sqrt[e] - I*Sqrt[d]*x^(1/3))])/e^(9/2) + (2*b*d^5*n*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x^2)^n])^2/(e + d*x^2), x], x, x^(1/3)])/e^4","A",0,0,0,0,-1,"{}"
532,1,730,0,1.3364044,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \, dx","Int[x^3*(a + b*Log[c*(d + e*Sqrt[x])])^p,x]","\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} \text{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} \text{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} \text{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} \text{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} \text{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^{-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} \text{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} \text{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{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)}{c 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} \text{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} \text{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} \text{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} \text{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} \text{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^{-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} \text{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} \text{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{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} \text{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)*Gamma[1 + p, (-8*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(c^8*e^8*E^((8*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) - (2*d*Gamma[1 + p, (-7*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(7^p*c^7*e^8*E^((7*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) + (7*d^2*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(6^p*c^6*e^8*E^((6*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) - (14*d^3*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(5^p*c^5*e^8*E^((5*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) + (35*2^(-1 - 2*p)*d^4*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(c^4*e^8*E^((4*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) - (14*d^5*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(3^p*c^3*e^8*E^((3*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) + (7*d^6*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(2^p*c^2*e^8*E^((2*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) - (2*d^7*Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])])/b)]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(c*e^8*E^(a/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p)","A",27,7,22,0.3182,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
533,1,551,0,0.8639015,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \, dx","Int[x^2*(a + b*Log[c*(d + e*Sqrt[x])])^p,x]","\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} \text{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} \text{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} \text{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^{-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} \text{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} \text{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{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)}{c 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} \text{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} \text{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} \text{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^{-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} \text{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} \text{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{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} \text{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)*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(2^p*c^6*e^6*E^((6*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) - (2*d*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(5^p*c^5*e^6*E^((5*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) + (5*d^2*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(4^p*c^4*e^6*E^((4*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) - (20*3^(-1 - p)*d^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(c^3*e^6*E^((3*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) + (5*d^4*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(2^p*c^2*e^6*E^((2*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) - (2*d^5*Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])])/b)]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(c*e^6*E^(a/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p)","A",21,7,22,0.3182,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
534,1,360,0,0.5434315,"\int x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \, dx","Int[x*(a + b*Log[c*(d + e*Sqrt[x])])^p,x]","\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} \text{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^{-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} \text{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} \text{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{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)}{c 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} \text{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^{-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} \text{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} \text{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{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} \text{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)*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(c^4*e^4*E^((4*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) - (2*d*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(3^p*c^3*e^4*E^((3*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) + (3*d^2*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*Sqrt[x])]))/b]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(2^p*c^2*e^4*E^((2*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p) - (2*d^3*Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])])/b)]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(c*e^4*E^(a/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p)","A",15,7,20,0.3500,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
535,1,174,0,0.2219953,"\int \left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p \, dx","Int[(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} \text{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+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+e \sqrt{x}\right)\right)\right)^p \left(-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)\right)}{b}\right)^{-p} \text{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} \text{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]*(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) - (2*d*Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])])/b)]*(a + b*Log[c*(d + e*Sqrt[x])])^p)/(c*e^2*E^(a/b)*(-((a + b*Log[c*(d + e*Sqrt[x])])/b))^p)","A",9,7,18,0.3889,1,"{2451, 2401, 2389, 2299, 2181, 2390, 2309}"
536,0,0,0,0.0528729,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p}{x} \, dx","Int[(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,"2*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x)])^p/x, x], x, Sqrt[x]]","A",0,0,0,0,-1,"{}"
537,0,0,0,0.0533969,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)\right)\right)^p}{x^2} \, dx","Int[(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,"2*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x)])^p/x^3, x], x, Sqrt[x]]","A",0,0,0,0,-1,"{}"
538,1,907,0,1.4044242,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","Int[x^3*(a + b*Log[c*(d + e*Sqrt[x])^2])^p,x]","\frac{2^{-2 (p+1)} e^{-\frac{4 a}{b}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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) \text{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}}","\frac{2^{-2 (p+1)} e^{-\frac{4 a}{b}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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) \text{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,"(Gamma[1 + p, (-4*(a + b*Log[c*(d + e*Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(2^(2*(1 + p))*c^4*e^8*E^((4*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) - (2^(1 + p)*d*(d + e*Sqrt[x])^7*Gamma[1 + p, (-7*(a + b*Log[c*(d + e*Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(7^p*e^8*E^((7*a)/(2*b))*(c*(d + e*Sqrt[x])^2)^(7/2)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) + (7*d^2*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(3^p*c^3*e^8*E^((3*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) - (7*2^(1 + p)*d^3*(d + e*Sqrt[x])^5*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(5^p*e^8*E^((5*a)/(2*b))*(c*(d + e*Sqrt[x])^2)^(5/2)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) + (35*2^(-1 - p)*d^4*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(c^2*e^8*E^((2*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) - (7*2^(1 + p)*d^5*(d + e*Sqrt[x])^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(3^p*e^8*E^((3*a)/(2*b))*(c*(d + e*Sqrt[x])^2)^(3/2)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) + (7*d^6*Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])^2])/b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(c*e^8*E^(a/b)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) - (2^(1 + p)*d^7*(d + e*Sqrt[x])*Gamma[1 + p, -(a + b*Log[c*(d + e*Sqrt[x])^2])/(2*b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(e^8*E^(a/(2*b))*Sqrt[c*(d + e*Sqrt[x])^2]*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p)","A",27,7,24,0.2917,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
539,1,677,0,0.9819969,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","Int[x^2*(a + b*Log[c*(d + e*Sqrt[x])^2])^p,x]","\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} \text{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{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} \text{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^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} \text{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{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)}{c 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} \text{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{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} \text{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}}","\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} \text{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{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} \text{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^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} \text{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{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)}{b}\right)}{c 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} \text{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{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} \text{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,"(3^(-1 - p)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(c^3*e^6*E^((3*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) - (2^(1 + p)*d*(d + e*Sqrt[x])^5*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(5^p*e^6*E^((5*a)/(2*b))*(c*(d + e*Sqrt[x])^2)^(5/2)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) + (5*d^2*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(2^p*c^2*e^6*E^((2*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) - (5*2^(2 + p)*3^(-1 - p)*d^3*(d + e*Sqrt[x])^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(e^6*E^((3*a)/(2*b))*(c*(d + e*Sqrt[x])^2)^(3/2)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) + (5*d^4*Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])^2])/b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(c*e^6*E^(a/b)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) - (2^(1 + p)*d^5*(d + e*Sqrt[x])*Gamma[1 + p, -(a + b*Log[c*(d + e*Sqrt[x])^2])/(2*b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(e^6*E^(a/(2*b))*Sqrt[c*(d + e*Sqrt[x])^2]*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p)","A",21,7,24,0.2917,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
540,1,445,0,0.6268892,"\int x \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","Int[x*(a + b*Log[c*(d + e*Sqrt[x])^2])^p,x]","\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} \text{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{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} \text{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^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} \text{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{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} \text{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}}","\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} \text{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{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} \text{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^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} \text{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{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} \text{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,"(2^(-1 - p)*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(c^2*e^4*E^((2*a)/b)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) - (2^(1 + p)*d*(d + e*Sqrt[x])^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(3^p*e^4*E^((3*a)/(2*b))*(c*(d + e*Sqrt[x])^2)^(3/2)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) + (3*d^2*Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])^2])/b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(c*e^4*E^(a/b)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) - (2^(1 + p)*d^3*(d + e*Sqrt[x])*Gamma[1 + p, -(a + b*Log[c*(d + e*Sqrt[x])^2])/(2*b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(e^4*E^(a/(2*b))*Sqrt[c*(d + e*Sqrt[x])^2]*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p)","A",15,7,22,0.3182,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
541,1,213,0,0.2611621,"\int \left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p \, dx","Int[(a + b*Log[c*(d + e*Sqrt[x])^2])^p,x]","\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} \text{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} \text{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}}","\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} \text{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} \text{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,"(Gamma[1 + p, -((a + b*Log[c*(d + e*Sqrt[x])^2])/b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(c*e^2*E^(a/b)*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p) - (2^(1 + p)*d*(d + e*Sqrt[x])*Gamma[1 + p, -(a + b*Log[c*(d + e*Sqrt[x])^2])/(2*b)]*(a + b*Log[c*(d + e*Sqrt[x])^2])^p)/(e^2*E^(a/(2*b))*Sqrt[c*(d + e*Sqrt[x])^2]*(-((a + b*Log[c*(d + e*Sqrt[x])^2])/b))^p)","A",9,7,20,0.3500,1,"{2451, 2401, 2389, 2300, 2181, 2390, 2310}"
542,0,0,0,0.0540136,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p}{x} \, dx","Int[(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,"2*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x)^2])^p/x, x], x, Sqrt[x]]","A",0,0,0,0,-1,"{}"
543,0,0,0,0.0526444,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt{x}\right)^2\right)\right)^p}{x^2} \, dx","Int[(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,"2*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x)^2])^p/x^3, x], x, Sqrt[x]]","A",0,0,0,0,-1,"{}"
544,0,0,0,0.0449333,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \, dx","Int[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,"2*Defer[Subst][Defer[Int][x^3*(a + b*Log[c*(d + e/x)])^p, x], x, Sqrt[x]]","A",0,0,0,0,-1,"{}"
545,0,0,0,0.021141,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p \, dx","Int[(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,"2*Defer[Subst][Defer[Int][x*(a + b*Log[c*(d + e/x)])^p, x], x, Sqrt[x]]","A",0,0,0,0,-1,"{}"
546,0,0,0,0.0548585,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p}{x} \, dx","Int[(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,"2*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x)])^p/x, x], x, Sqrt[x]]","A",0,0,0,0,-1,"{}"
547,1,175,0,0.2469245,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p}{x^2} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])])^p/x^2,x]","\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} \text{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} \text{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}","\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} \text{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} \text{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]*(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)) + (2*d*Gamma[1 + p, -((a + b*Log[c*(d + e/Sqrt[x])])/b)]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(c*e^2*E^(a/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p)","A",9,7,22,0.3182,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
548,1,552,0,0.8484731,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p}{x^4} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])])^p/x^4,x]","-\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} \text{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} \text{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} \text{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^{-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} \text{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} \text{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{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)}{b}\right)}{c 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} \text{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} \text{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} \text{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^{-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} \text{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} \text{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{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} \text{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)*Gamma[1 + p, (-6*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(2^p*c^6*e^6*E^((6*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p)) + (2*d*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(5^p*c^5*e^6*E^((5*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) - (5*d^2*Gamma[1 + p, (-4*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(4^p*c^4*e^6*E^((4*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) + (20*3^(-1 - p)*d^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(c^3*e^6*E^((3*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) - (5*d^4*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(2^p*c^2*e^6*E^((2*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) + (2*d^5*Gamma[1 + p, -((a + b*Log[c*(d + e/Sqrt[x])])/b)]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(c*e^6*E^(a/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p)","A",21,7,22,0.3182,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
549,1,926,0,1.5565978,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)\right)\right)^p}{x^6} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])])^p/x^6,x]","-\frac{2^{-p} 5^{-p-1} e^{-\frac{10 a}{b}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}}","-\frac{2^{-p} 5^{-p-1} e^{-\frac{10 a}{b}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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)*Gamma[1 + p, (-10*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(2^p*c^10*e^10*E^((10*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p)) + (2*d*Gamma[1 + p, (-9*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(9^p*c^9*e^10*E^((9*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) - (9*d^2*Gamma[1 + p, (-8*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(8^p*c^8*e^10*E^((8*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) + (24*d^3*Gamma[1 + p, (-7*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(7^p*c^7*e^10*E^((7*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) - (7*6^(1 - p)*d^4*Gamma[1 + p, (-6*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(c^6*e^10*E^((6*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) + (252*5^(-1 - p)*d^5*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(c^5*e^10*E^((5*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) - (21*2^(1 - 2*p)*d^6*Gamma[1 + p, (-4*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(c^4*e^10*E^((4*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) + (8*3^(1 - p)*d^7*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(c^3*e^10*E^((3*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) - (9*d^8*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/Sqrt[x])]))/b]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(2^p*c^2*e^10*E^((2*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p) + (2*d^9*Gamma[1 + p, -((a + b*Log[c*(d + e/Sqrt[x])])/b)]*(a + b*Log[c*(d + e/Sqrt[x])])^p)/(c*e^10*E^(a/b)*(-((a + b*Log[c*(d + e/Sqrt[x])])/b))^p)","A",33,7,22,0.3182,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
550,0,0,0,0.0468434,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \, dx","Int[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,"2*Defer[Subst][Defer[Int][x^3*(a + b*Log[c*(d + e/x)^2])^p, x], x, Sqrt[x]]","A",0,0,0,0,-1,"{}"
551,0,0,0,0.0225073,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p \, dx","Int[(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,"2*Defer[Subst][Defer[Int][x*(a + b*Log[c*(d + e/x)^2])^p, x], x, Sqrt[x]]","A",0,0,0,0,-1,"{}"
552,0,0,0,0.0598604,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x} \, dx","Int[(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,"2*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x)^2])^p/x, x], x, Sqrt[x]]","A",0,0,0,0,-1,"{}"
553,1,213,0,0.2878758,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x^2} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^2])^p/x^2,x]","\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} \text{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)}{b}\right)}{c e^2}","\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} \text{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} \text{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,"-((Gamma[1 + p, -((a + b*Log[c*(d + e/Sqrt[x])^2])/b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(c*e^2*E^(a/b)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p)) + (2^(1 + p)*d*(d + e/Sqrt[x])*Gamma[1 + p, -(a + b*Log[c*(d + e/Sqrt[x])^2])/(2*b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(e^2*E^(a/(2*b))*Sqrt[c*(d + e/Sqrt[x])^2]*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p)","A",9,7,24,0.2917,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
554,1,676,0,0.9950545,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x^4} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^2])^p/x^4,x]","-\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} \text{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{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} \text{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^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} \text{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{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} \text{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{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} \text{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{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} \text{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}}","-\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} \text{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{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} \text{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^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} \text{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{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} \text{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{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} \text{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{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} \text{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,"-((3^(-1 - p)*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(c^3*e^6*E^((3*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p)) + (2^(1 + p)*d*(d + e/Sqrt[x])^5*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(5^p*e^6*E^((5*a)/(2*b))*(c*(d + e/Sqrt[x])^2)^(5/2)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) - (5*d^2*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(2^p*c^2*e^6*E^((2*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) + (5*2^(2 + p)*3^(-1 - p)*d^3*(d + e/Sqrt[x])^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(e^6*E^((3*a)/(2*b))*(c*(d + e/Sqrt[x])^2)^(3/2)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) - (5*d^4*Gamma[1 + p, -((a + b*Log[c*(d + e/Sqrt[x])^2])/b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(c*e^6*E^(a/b)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) + (2^(1 + p)*d^5*(d + e/Sqrt[x])*Gamma[1 + p, -(a + b*Log[c*(d + e/Sqrt[x])^2])/(2*b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(e^6*E^(a/(2*b))*Sqrt[c*(d + e/Sqrt[x])^2]*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p)","A",21,7,24,0.2917,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
555,1,1141,0,1.7384306,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt{x}}\right)^2\right)\right)^p}{x^6} \, dx","Int[(a + b*Log[c*(d + e/Sqrt[x])^2])^p/x^6,x]","-\frac{5^{-p-1} e^{-\frac{5 a}{b}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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) \text{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}}","-\frac{5^{-p-1} e^{-\frac{5 a}{b}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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) \text{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,"-((5^(-1 - p)*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(c^5*e^10*E^((5*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p)) + (2^(1 + p)*d*(d + e/Sqrt[x])^9*Gamma[1 + p, (-9*(a + b*Log[c*(d + e/Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(9^p*e^10*E^((9*a)/(2*b))*(c*(d + e/Sqrt[x])^2)^(9/2)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) - (9*d^2*Gamma[1 + p, (-4*(a + b*Log[c*(d + e/Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(4^p*c^4*e^10*E^((4*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) + (3*2^(3 + p)*d^3*(d + e/Sqrt[x])^7*Gamma[1 + p, (-7*(a + b*Log[c*(d + e/Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(7^p*e^10*E^((7*a)/(2*b))*(c*(d + e/Sqrt[x])^2)^(7/2)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) - (14*3^(1 - p)*d^4*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(c^3*e^10*E^((3*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) + (63*2^(2 + p)*5^(-1 - p)*d^5*(d + e/Sqrt[x])^5*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(e^10*E^((5*a)/(2*b))*(c*(d + e/Sqrt[x])^2)^(5/2)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) - (21*2^(1 - p)*d^6*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/Sqrt[x])^2]))/b]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(c^2*e^10*E^((2*a)/b)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) + (2^(3 + p)*3^(1 - p)*d^7*(d + e/Sqrt[x])^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/Sqrt[x])^2]))/(2*b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(e^10*E^((3*a)/(2*b))*(c*(d + e/Sqrt[x])^2)^(3/2)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) - (9*d^8*Gamma[1 + p, -((a + b*Log[c*(d + e/Sqrt[x])^2])/b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(c*e^10*E^(a/b)*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p) + (2^(1 + p)*d^9*(d + e/Sqrt[x])*Gamma[1 + p, -(a + b*Log[c*(d + e/Sqrt[x])^2])/(2*b)]*(a + b*Log[c*(d + e/Sqrt[x])^2])^p)/(e^10*E^(a/(2*b))*Sqrt[c*(d + e/Sqrt[x])^2]*(-((a + b*Log[c*(d + e/Sqrt[x])^2])/b))^p)","A",33,7,24,0.2917,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
556,1,1121,0,1.8676887,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \, dx","Int[x^3*(a + b*Log[c*(d + e*x^(1/3))])^p,x]","\frac{3^{-p} 4^{-p-1} e^{-\frac{12 a}{b}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}}","\frac{3^{-p} 4^{-p-1} e^{-\frac{12 a}{b}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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,"(4^(-1 - p)*Gamma[1 + p, (-12*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(3^p*c^12*e^12*E^((12*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (3*d*Gamma[1 + p, (-11*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(11^p*c^11*e^12*E^((11*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (33*2^(-1 - p)*d^2*Gamma[1 + p, (-10*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(5^p*c^10*e^12*E^((10*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (55*d^3*Gamma[1 + p, (-9*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(9^p*c^9*e^12*E^((9*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (495*2^(-2 - 3*p)*d^4*Gamma[1 + p, (-8*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c^8*e^12*E^((8*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (198*d^5*Gamma[1 + p, (-7*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(7^p*c^7*e^12*E^((7*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (77*3^(1 - p)*d^6*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(2^p*c^6*e^12*E^((6*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (198*d^7*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(5^p*c^5*e^12*E^((5*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (495*4^(-1 - p)*d^8*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c^4*e^12*E^((4*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (55*d^9*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(3^p*c^3*e^12*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (33*2^(-1 - p)*d^10*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c^2*e^12*E^((2*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (3*d^11*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))])/b)]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c*e^12*E^(a/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p)","A",39,7,22,0.3182,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
557,1,831,0,1.3521702,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \, dx","Int[x^2*(a + b*Log[c*(d + e*x^(1/3))])^p,x]","\frac{3^{-2 p-1} e^{-\frac{9 a}{b}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}","\frac{3^{-2 p-1} e^{-\frac{9 a}{b}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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)*Gamma[1 + p, (-9*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c^9*e^9*E^((9*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (3*d*Gamma[1 + p, (-8*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(8^p*c^8*e^9*E^((8*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (12*d^2*Gamma[1 + p, (-7*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(7^p*c^7*e^9*E^((7*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (7*2^(2 - p)*d^3*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(3^p*c^6*e^9*E^((6*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (42*d^4*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(5^p*c^5*e^9*E^((5*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (21*2^(1 - 2*p)*d^5*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c^4*e^9*E^((4*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (28*d^6*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(3^p*c^3*e^9*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (3*2^(2 - p)*d^7*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c^2*e^9*E^((2*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (3*d^8*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))])/b)]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c*e^9*E^(a/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p)","A",30,7,22,0.3182,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
558,1,553,0,0.8456616,"\int x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \, dx","Int[x*(a + b*Log[c*(d + e*x^(1/3))])^p,x]","\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} \text{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} \text{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} \text{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{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} \text{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} \text{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{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)}{c 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} \text{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} \text{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} \text{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{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} \text{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} \text{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{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} \text{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 - p)*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(3^p*c^6*e^6*E^((6*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (3*d*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(5^p*c^5*e^6*E^((5*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (15*2^(-1 - 2*p)*d^2*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c^4*e^6*E^((4*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (10*d^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(3^p*c^3*e^6*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (15*2^(-1 - p)*d^4*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c^2*e^6*E^((2*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (3*d^5*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))])/b)]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c*e^6*E^(a/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p)","A",21,7,20,0.3500,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
559,1,266,0,0.3933573,"\int \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))])^p,x]","\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} \text{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} \text{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)}{c 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} \text{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} \text{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)}{b}\right)}{c e^3}",1,"(Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(3^p*c^3*e^3*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) - (3*d*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(1/3))]))/b]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(2^p*c^2*e^3*E^((2*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p) + (3*d^2*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))])/b)]*(a + b*Log[c*(d + e*x^(1/3))])^p)/(c*e^3*E^(a/b)*(-((a + b*Log[c*(d + e*x^(1/3))])/b))^p)","A",12,7,18,0.3889,1,"{2451, 2401, 2389, 2299, 2181, 2390, 2309}"
560,0,0,0,0.0520717,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p}{x} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x)])^p/x, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
561,0,0,0,0.0520194,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)\right)\right)^p}{x^2} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x)])^p/x^4, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
562,1,1363,0,2.1327676,"\int x^3 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","Int[x^3*(a + b*Log[c*(d + e*x^(1/3))^2])^p,x]","\frac{2^{-p-2} 3^{-p} e^{-\frac{6 a}{b}} \text{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} \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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) \text{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}}","\frac{2^{-p-2} 3^{-p} e^{-\frac{6 a}{b}} \text{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} \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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) \text{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,"(2^(-2 - p)*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*x^(1/3))^2]))/b]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(3^p*c^6*e^12*E^((6*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (3*(2/11)^p*d*(d + e*x^(1/3))^11*Gamma[1 + p, (-11*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(e^12*E^((11*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(11/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (33*d^2*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(1/3))^2]))/b]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(2*5^p*c^5*e^12*E^((5*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (55*(2/9)^p*d^3*(d + e*x^(1/3))^9*Gamma[1 + p, (-9*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(e^12*E^((9*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(9/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (495*d^4*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*x^(1/3))^2]))/b]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(2^(2*(1 + p))*c^4*e^12*E^((4*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (99*2^(1 + p)*d^5*(d + e*x^(1/3))^7*Gamma[1 + p, (-7*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(7^p*e^12*E^((7*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(7/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (77*3^(1 - p)*d^6*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))^2]))/b]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(c^3*e^12*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (99*2^(1 + p)*d^7*(d + e*x^(1/3))^5*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(5^p*e^12*E^((5*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(5/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (495*2^(-2 - p)*d^8*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(1/3))^2]))/b]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(c^2*e^12*E^((2*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (55*(2/3)^p*d^9*(d + e*x^(1/3))^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(e^12*E^((3*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(3/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (33*d^10*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))^2])/b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(2*c*e^12*E^(a/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (3*2^p*d^11*(d + e*x^(1/3))*Gamma[1 + p, -(a + b*Log[c*(d + e*x^(1/3))^2])/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(e^12*E^(a/(2*b))*Sqrt[c*(d + e*x^(1/3))^2]*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p)","A",39,7,24,0.2917,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
563,1,1035,0,1.5656424,"\int x^2 \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","Int[x^2*(a + b*Log[c*(d + e*x^(1/3))^2])^p,x]","\frac{2^p 3^{-2 p-1} e^{-\frac{9 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^9 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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) \text{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}}","\frac{2^p 3^{-2 p-1} e^{-\frac{9 a}{2 b}} \left(d+e \sqrt[3]{x}\right)^9 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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) \text{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,"(2^p*3^(-1 - 2*p)*(d + e*x^(1/3))^9*Gamma[1 + p, (-9*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(e^9*E^((9*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(9/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (3*d*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*x^(1/3))^2]))/b]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(4^p*c^4*e^9*E^((4*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (3*2^(2 + p)*d^2*(d + e*x^(1/3))^7*Gamma[1 + p, (-7*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(7^p*e^9*E^((7*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(7/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (28*d^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))^2]))/b]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(3^p*c^3*e^9*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (21*2^(1 + p)*d^4*(d + e*x^(1/3))^5*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(5^p*e^9*E^((5*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(5/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (21*2^(1 - p)*d^5*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(1/3))^2]))/b]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(c^2*e^9*E^((2*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (7*2^(2 + p)*d^6*(d + e*x^(1/3))^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(3^p*e^9*E^((3*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(3/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (12*d^7*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))^2])/b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(c*e^9*E^(a/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (3*2^p*d^8*(d + e*x^(1/3))*Gamma[1 + p, -(a + b*Log[c*(d + e*x^(1/3))^2])/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(e^9*E^(a/(2*b))*Sqrt[c*(d + e*x^(1/3))^2]*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p)","A",30,7,24,0.2917,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
564,1,673,0,0.9713747,"\int x \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","Int[x*(a + b*Log[c*(d + e*x^(1/3))^2])^p,x]","\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} \text{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^{-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} \text{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{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} \text{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{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} \text{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{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} \text{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{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} \text{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}}","\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} \text{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^{-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} \text{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{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} \text{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{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} \text{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{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} \text{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{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} \text{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,"(Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))^2]))/b]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(2*3^p*c^3*e^6*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (3*(2/5)^p*d*(d + e*x^(1/3))^5*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(e^6*E^((5*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(5/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (15*2^(-1 - p)*d^2*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(1/3))^2]))/b]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(c^2*e^6*E^((2*a)/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (5*2^(1 + p)*d^3*(d + e*x^(1/3))^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(3^p*e^6*E^((3*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(3/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (15*d^4*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))^2])/b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(2*c*e^6*E^(a/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (3*2^p*d^5*(d + e*x^(1/3))*Gamma[1 + p, -(a + b*Log[c*(d + e*x^(1/3))^2])/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(e^6*E^(a/(2*b))*Sqrt[c*(d + e*x^(1/3))^2]*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p)","A",21,7,22,0.3182,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
565,1,338,0,0.4596091,"\int \left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p \, dx","Int[(a + b*Log[c*(d + e*x^(1/3))^2])^p,x]","\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} \text{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} \text{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)}{b}\right)}{c e^3}","\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} \text{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} \text{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} \text{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,"((2/3)^p*(d + e*x^(1/3))^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(e^3*E^((3*a)/(2*b))*(c*(d + e*x^(1/3))^2)^(3/2)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) - (3*d*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(1/3))^2])/b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(c*e^3*E^(a/b)*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p) + (3*2^p*d^2*(d + e*x^(1/3))*Gamma[1 + p, -(a + b*Log[c*(d + e*x^(1/3))^2])/(2*b)]*(a + b*Log[c*(d + e*x^(1/3))^2])^p)/(e^3*E^(a/(2*b))*Sqrt[c*(d + e*x^(1/3))^2]*(-((a + b*Log[c*(d + e*x^(1/3))^2])/b))^p)","A",12,7,20,0.3500,1,"{2451, 2401, 2389, 2300, 2181, 2390, 2310}"
566,0,0,0,0.0540624,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p}{x} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x)^2])^p/x, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
567,0,0,0,0.0537709,"\int \frac{\left(a+b \log \left(c \left(d+e \sqrt[3]{x}\right)^2\right)\right)^p}{x^2} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x)^2])^p/x^4, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
568,1,557,0,0.8687334,"\int x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \, dx","Int[x^3*(a + b*Log[c*(d + e*x^(2/3))])^p,x]","\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} \text{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} \text{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} \text{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{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} \text{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} \text{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{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)}{2 c 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} \text{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} \text{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} \text{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{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} \text{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} \text{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{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} \text{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,"(2^(-2 - p)*Gamma[1 + p, (-6*(a + b*Log[c*(d + e*x^(2/3))]))/b]*(a + b*Log[c*(d + e*x^(2/3))])^p)/(3^p*c^6*e^6*E^((6*a)/b)*(-((a + b*Log[c*(d + e*x^(2/3))])/b))^p) - (3*d*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(2/3))]))/b]*(a + b*Log[c*(d + e*x^(2/3))])^p)/(2*5^p*c^5*e^6*E^((5*a)/b)*(-((a + b*Log[c*(d + e*x^(2/3))])/b))^p) + (15*d^2*Gamma[1 + p, (-4*(a + b*Log[c*(d + e*x^(2/3))]))/b]*(a + b*Log[c*(d + e*x^(2/3))])^p)/(2^(2*(1 + p))*c^4*e^6*E^((4*a)/b)*(-((a + b*Log[c*(d + e*x^(2/3))])/b))^p) - (5*d^3*Gamma[1 + p, (-3*(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^6*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(2/3))])/b))^p) + (15*2^(-2 - p)*d^4*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(2/3))]))/b]*(a + b*Log[c*(d + e*x^(2/3))])^p)/(c^2*e^6*E^((2*a)/b)*(-((a + b*Log[c*(d + e*x^(2/3))])/b))^p) - (3*d^5*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(2/3))])/b)]*(a + b*Log[c*(d + e*x^(2/3))])^p)/(2*c*e^6*E^(a/b)*(-((a + b*Log[c*(d + e*x^(2/3))])/b))^p)","A",21,7,22,0.3182,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
569,1,273,0,0.3807797,"\int x \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \, dx","Int[x*(a + b*Log[c*(d + e*x^(2/3))])^p,x]","\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} \text{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} \text{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+e x^{2/3}\right)\right)}{b}\right)}{2 c 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} \text{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} \text{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} \text{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,"(Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(2/3))]))/b]*(a + b*Log[c*(d + e*x^(2/3))])^p)/(2*3^p*c^3*e^3*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(2/3))])/b))^p) - (3*2^(-1 - p)*d*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(2/3))]))/b]*(a + b*Log[c*(d + e*x^(2/3))])^p)/(c^2*e^3*E^((2*a)/b)*(-((a + b*Log[c*(d + e*x^(2/3))])/b))^p) + (3*d^2*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(2/3))])/b)]*(a + b*Log[c*(d + e*x^(2/3))])^p)/(2*c*e^3*E^(a/b)*(-((a + b*Log[c*(d + e*x^(2/3))])/b))^p)","A",12,7,20,0.3500,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
570,0,0,0,0.0527489,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x^2)])^p/x, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
571,0,0,0,0.0530978,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x^3} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x^2)])^p/x^7, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
572,0,0,0,0.0547608,"\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \, dx","Int[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,"3*Defer[Subst][Defer[Int][x^8*(a + b*Log[c*(d + e*x^2)])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
573,0,0,0,0.0319482,"\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p \, dx","Int[(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,"3*Defer[Subst][Defer[Int][x^2*(a + b*Log[c*(d + e*x^2)])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
574,0,0,0,0.0533673,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)\right)\right)^p}{x^2} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x^2)])^p/x^4, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
575,1,675,0,0.9705609,"\int x^3 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","Int[x^3*(a + b*Log[c*(d + e*x^(2/3))^2])^p,x]","\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} \text{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^{-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} \text{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{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} \text{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{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} \text{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{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} \text{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{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} \text{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}}","\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} \text{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^{-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} \text{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{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} \text{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{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} \text{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{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} \text{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{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} \text{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,"(Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(2/3))^2]))/b]*(a + b*Log[c*(d + e*x^(2/3))^2])^p)/(4*3^p*c^3*e^6*E^((3*a)/b)*(-((a + b*Log[c*(d + e*x^(2/3))^2])/b))^p) - (3*2^(-1 + p)*d*(d + e*x^(2/3))^5*Gamma[1 + p, (-5*(a + b*Log[c*(d + e*x^(2/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(2/3))^2])^p)/(5^p*e^6*E^((5*a)/(2*b))*(c*(d + e*x^(2/3))^2)^(5/2)*(-((a + b*Log[c*(d + e*x^(2/3))^2])/b))^p) + (15*2^(-2 - p)*d^2*Gamma[1 + p, (-2*(a + b*Log[c*(d + e*x^(2/3))^2]))/b]*(a + b*Log[c*(d + e*x^(2/3))^2])^p)/(c^2*e^6*E^((2*a)/b)*(-((a + b*Log[c*(d + e*x^(2/3))^2])/b))^p) - (5*(2/3)^p*d^3*(d + e*x^(2/3))^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(2/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(2/3))^2])^p)/(e^6*E^((3*a)/(2*b))*(c*(d + e*x^(2/3))^2)^(3/2)*(-((a + b*Log[c*(d + e*x^(2/3))^2])/b))^p) + (15*d^4*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(2/3))^2])/b)]*(a + b*Log[c*(d + e*x^(2/3))^2])^p)/(4*c*e^6*E^(a/b)*(-((a + b*Log[c*(d + e*x^(2/3))^2])/b))^p) - (3*2^(-1 + p)*d^5*(d + e*x^(2/3))*Gamma[1 + p, -(a + b*Log[c*(d + e*x^(2/3))^2])/(2*b)]*(a + b*Log[c*(d + e*x^(2/3))^2])^p)/(e^6*E^(a/(2*b))*Sqrt[c*(d + e*x^(2/3))^2]*(-((a + b*Log[c*(d + e*x^(2/3))^2])/b))^p)","A",21,7,24,0.2917,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
576,1,347,0,0.4532417,"\int x \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","Int[x*(a + b*Log[c*(d + e*x^(2/3))^2])^p,x]","\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} \text{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} \text{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} \text{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}","\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} \text{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} \text{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} \text{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,"(2^(-1 + p)*(d + e*x^(2/3))^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e*x^(2/3))^2]))/(2*b)]*(a + b*Log[c*(d + e*x^(2/3))^2])^p)/(3^p*e^3*E^((3*a)/(2*b))*(c*(d + e*x^(2/3))^2)^(3/2)*(-((a + b*Log[c*(d + e*x^(2/3))^2])/b))^p) - (3*d*Gamma[1 + p, -((a + b*Log[c*(d + e*x^(2/3))^2])/b)]*(a + b*Log[c*(d + e*x^(2/3))^2])^p)/(2*c*e^3*E^(a/b)*(-((a + b*Log[c*(d + e*x^(2/3))^2])/b))^p) + (3*2^(-1 + p)*d^2*(d + e*x^(2/3))*Gamma[1 + p, -(a + b*Log[c*(d + e*x^(2/3))^2])/(2*b)]*(a + b*Log[c*(d + e*x^(2/3))^2])^p)/(e^3*E^(a/(2*b))*Sqrt[c*(d + e*x^(2/3))^2]*(-((a + b*Log[c*(d + e*x^(2/3))^2])/b))^p)","A",12,7,22,0.3182,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
577,0,0,0,0.0552981,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x^2)^2])^p/x, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
578,0,0,0,0.0551799,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x^3} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x^2)^2])^p/x^7, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
579,0,0,0,0.0581975,"\int x^2 \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","Int[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,"3*Defer[Subst][Defer[Int][x^8*(a + b*Log[c*(d + e*x^2)^2])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
580,0,0,0,0.033729,"\int \left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p \, dx","Int[(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,"3*Defer[Subst][Defer[Int][x^2*(a + b*Log[c*(d + e*x^2)^2])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
581,0,0,0,0.0561046,"\int \frac{\left(a+b \log \left(c \left(d+e x^{2/3}\right)^2\right)\right)^p}{x^2} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e*x^2)^2])^p/x^4, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
582,0,0,0,0.0471712,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \, dx","Int[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,"3*Defer[Subst][Defer[Int][x^5*(a + b*Log[c*(d + e/x)])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
583,0,0,0,0.0333854,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p \, dx","Int[(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,"3*Defer[Subst][Defer[Int][x^2*(a + b*Log[c*(d + e/x)])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
584,0,0,0,0.0545988,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p}{x} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x)])^p/x, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
585,1,267,0,0.3923883,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p}{x^2} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))])^p/x^2,x]","-\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} \text{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} \text{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)}{c 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} \text{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} \text{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} \text{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,"-((Gamma[1 + p, (-3*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(3^p*c^3*e^3*E^((3*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p)) + (3*d*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(2^p*c^2*e^3*E^((2*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) - (3*d^2*Gamma[1 + p, -((a + b*Log[c*(d + e/x^(1/3))])/b)]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(c*e^3*E^(a/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p)","A",12,7,22,0.3182,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
586,1,554,0,0.8332111,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p}{x^3} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))])^p/x^3,x]","-\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} \text{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} \text{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} \text{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{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} \text{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} \text{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{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} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)}{b}\right)}{c 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} \text{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} \text{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} \text{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{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} \text{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} \text{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{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} \text{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 - p)*Gamma[1 + p, (-6*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(3^p*c^6*e^6*E^((6*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p)) + (3*d*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(5^p*c^5*e^6*E^((5*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) - (15*2^(-1 - 2*p)*d^2*Gamma[1 + p, (-4*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(c^4*e^6*E^((4*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) + (10*d^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(3^p*c^3*e^6*E^((3*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) - (15*2^(-1 - p)*d^4*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(c^2*e^6*E^((2*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) + (3*d^5*Gamma[1 + p, -((a + b*Log[c*(d + e/x^(1/3))])/b)]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(c*e^6*E^(a/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p)","A",21,7,22,0.3182,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
587,1,832,0,1.302597,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)\right)\right)^p}{x^4} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))])^p/x^4,x]","-\frac{3^{-2 p-1} e^{-\frac{9 a}{b}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}","-\frac{3^{-2 p-1} e^{-\frac{9 a}{b}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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}} \text{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)*Gamma[1 + p, (-9*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(c^9*e^9*E^((9*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p)) + (3*d*Gamma[1 + p, (-8*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(8^p*c^8*e^9*E^((8*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) - (12*d^2*Gamma[1 + p, (-7*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(7^p*c^7*e^9*E^((7*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) + (7*2^(2 - p)*d^3*Gamma[1 + p, (-6*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(3^p*c^6*e^9*E^((6*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) - (42*d^4*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(5^p*c^5*e^9*E^((5*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) + (21*2^(1 - 2*p)*d^5*Gamma[1 + p, (-4*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(c^4*e^9*E^((4*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) - (28*d^6*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(3^p*c^3*e^9*E^((3*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) + (3*2^(2 - p)*d^7*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/x^(1/3))]))/b]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(c^2*e^9*E^((2*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p) - (3*d^8*Gamma[1 + p, -((a + b*Log[c*(d + e/x^(1/3))])/b)]*(a + b*Log[c*(d + e/x^(1/3))])^p)/(c*e^9*E^(a/b)*(-((a + b*Log[c*(d + e/x^(1/3))])/b))^p)","A",30,7,22,0.3182,1,"{2454, 2401, 2389, 2299, 2181, 2390, 2309}"
588,0,0,0,0.0469373,"\int x \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \, dx","Int[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,"3*Defer[Subst][Defer[Int][x^5*(a + b*Log[c*(d + e/x)^2])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
589,0,0,0,0.0350846,"\int \left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p \, dx","Int[(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,"3*Defer[Subst][Defer[Int][x^2*(a + b*Log[c*(d + e/x)^2])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
590,0,0,0,0.0569865,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x)^2])^p/x, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
591,1,339,0,0.4780854,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x^2} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^2])^p/x^2,x]","-\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} \text{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} \text{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} \text{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}","-\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} \text{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} \text{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} \text{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,"-(((2/3)^p*(d + e/x^(1/3))^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(e^3*E^((3*a)/(2*b))*(c*(d + e/x^(1/3))^2)^(3/2)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p)) + (3*d*Gamma[1 + p, -((a + b*Log[c*(d + e/x^(1/3))^2])/b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(c*e^3*E^(a/b)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) - (3*2^p*d^2*(d + e/x^(1/3))*Gamma[1 + p, -(a + b*Log[c*(d + e/x^(1/3))^2])/(2*b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(e^3*E^(a/(2*b))*Sqrt[c*(d + e/x^(1/3))^2]*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p)","A",12,7,24,0.2917,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
592,1,673,0,0.9723841,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x^3} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^2])^p/x^3,x]","-\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} \text{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^{-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} \text{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{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} \text{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{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} \text{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{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} \text{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{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} \text{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}}","-\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} \text{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^{-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} \text{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{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} \text{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{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} \text{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{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} \text{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{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} \text{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,"-(Gamma[1 + p, (-3*(a + b*Log[c*(d + e/x^(1/3))^2]))/b]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(2*3^p*c^3*e^6*E^((3*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) + (3*(2/5)^p*d*(d + e/x^(1/3))^5*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(e^6*E^((5*a)/(2*b))*(c*(d + e/x^(1/3))^2)^(5/2)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) - (15*2^(-1 - p)*d^2*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/x^(1/3))^2]))/b]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(c^2*e^6*E^((2*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) + (5*2^(1 + p)*d^3*(d + e/x^(1/3))^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(3^p*e^6*E^((3*a)/(2*b))*(c*(d + e/x^(1/3))^2)^(3/2)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) - (15*d^4*Gamma[1 + p, -((a + b*Log[c*(d + e/x^(1/3))^2])/b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(2*c*e^6*E^(a/b)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) + (3*2^p*d^5*(d + e/x^(1/3))*Gamma[1 + p, -(a + b*Log[c*(d + e/x^(1/3))^2])/(2*b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(e^6*E^(a/(2*b))*Sqrt[c*(d + e/x^(1/3))^2]*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p)","A",21,7,24,0.2917,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
593,1,1036,0,1.5190153,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{\sqrt[3]{x}}\right)^2\right)\right)^p}{x^4} \, dx","Int[(a + b*Log[c*(d + e/x^(1/3))^2])^p/x^4,x]","-\frac{2^p 3^{-2 p-1} e^{-\frac{9 a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right)^9 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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) \text{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}}","-\frac{2^p 3^{-2 p-1} e^{-\frac{9 a}{2 b}} \left(d+\frac{e}{\sqrt[3]{x}}\right)^9 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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 \text{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}} \text{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) \text{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,"-((2^p*3^(-1 - 2*p)*(d + e/x^(1/3))^9*Gamma[1 + p, (-9*(a + b*Log[c*(d + e/x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(e^9*E^((9*a)/(2*b))*(c*(d + e/x^(1/3))^2)^(9/2)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p)) + (3*d*Gamma[1 + p, (-4*(a + b*Log[c*(d + e/x^(1/3))^2]))/b]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(4^p*c^4*e^9*E^((4*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) - (3*2^(2 + p)*d^2*(d + e/x^(1/3))^7*Gamma[1 + p, (-7*(a + b*Log[c*(d + e/x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(7^p*e^9*E^((7*a)/(2*b))*(c*(d + e/x^(1/3))^2)^(7/2)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) + (28*d^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/x^(1/3))^2]))/b]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(3^p*c^3*e^9*E^((3*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) - (21*2^(1 + p)*d^4*(d + e/x^(1/3))^5*Gamma[1 + p, (-5*(a + b*Log[c*(d + e/x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(5^p*e^9*E^((5*a)/(2*b))*(c*(d + e/x^(1/3))^2)^(5/2)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) + (21*2^(1 - p)*d^5*Gamma[1 + p, (-2*(a + b*Log[c*(d + e/x^(1/3))^2]))/b]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(c^2*e^9*E^((2*a)/b)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) - (7*2^(2 + p)*d^6*(d + e/x^(1/3))^3*Gamma[1 + p, (-3*(a + b*Log[c*(d + e/x^(1/3))^2]))/(2*b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(3^p*e^9*E^((3*a)/(2*b))*(c*(d + e/x^(1/3))^2)^(3/2)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) + (12*d^7*Gamma[1 + p, -((a + b*Log[c*(d + e/x^(1/3))^2])/b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(c*e^9*E^(a/b)*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p) - (3*2^p*d^8*(d + e/x^(1/3))*Gamma[1 + p, -(a + b*Log[c*(d + e/x^(1/3))^2])/(2*b)]*(a + b*Log[c*(d + e/x^(1/3))^2])^p)/(e^9*E^(a/(2*b))*Sqrt[c*(d + e/x^(1/3))^2]*(-((a + b*Log[c*(d + e/x^(1/3))^2])/b))^p)","A",30,7,24,0.2917,1,"{2454, 2401, 2389, 2300, 2181, 2390, 2310}"
594,0,0,0,0.0561933,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","Int[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,"3*Defer[Subst][Defer[Int][x^11*(a + b*Log[c*(d + e/x^2)])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
595,0,0,0,0.0563921,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","Int[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,"3*Defer[Subst][Defer[Int][x^8*(a + b*Log[c*(d + e/x^2)])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
596,0,0,0,0.0446302,"\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","Int[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,"3*Defer[Subst][Defer[Int][x^5*(a + b*Log[c*(d + e/x^2)])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
597,0,0,0,0.0332621,"\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p \, dx","Int[(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,"3*Defer[Subst][Defer[Int][x^2*(a + b*Log[c*(d + e/x^2)])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
598,0,0,0,0.0543736,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p}{x} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x^2)])^p/x, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
599,0,0,0,0.0538691,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)\right)\right)^p}{x^2} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x^2)])^p/x^4, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
600,0,0,0,0.0606486,"\int x^3 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","Int[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,"3*Defer[Subst][Defer[Int][x^11*(a + b*Log[c*(d + e/x^2)^2])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
601,0,0,0,0.0590958,"\int x^2 \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","Int[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,"3*Defer[Subst][Defer[Int][x^8*(a + b*Log[c*(d + e/x^2)^2])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
602,0,0,0,0.0458282,"\int x \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","Int[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,"3*Defer[Subst][Defer[Int][x^5*(a + b*Log[c*(d + e/x^2)^2])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
603,0,0,0,0.0344933,"\int \left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p \, dx","Int[(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,"3*Defer[Subst][Defer[Int][x^2*(a + b*Log[c*(d + e/x^2)^2])^p, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
604,0,0,0,0.0569371,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p}{x} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x^2)^2])^p/x, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
605,0,0,0,0.0553495,"\int \frac{\left(a+b \log \left(c \left(d+\frac{e}{x^{2/3}}\right)^2\right)\right)^p}{x^2} \, dx","Int[(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,"3*Defer[Subst][Defer[Int][(a + b*Log[c*(d + e/x^2)^2])^p/x^4, x], x, x^(1/3)]","A",0,0,0,0,-1,"{}"
606,1,631,0,0.8952283,"\int \frac{(f+g x) \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{\sqrt{h x}} \, dx","Int[((f + g*x)*(a + b*Log[c*(d + e*x^2)^p]))/Sqrt[h*x],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}","\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*a*f*Sqrt[h*x])/h - (8*b*f*p*Sqrt[h*x])/h - (8*b*g*p*(h*x)^(3/2))/(9*h^2) - (2*Sqrt[2]*b*d^(1/4)*f*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*Sqrt[h]) - (2*Sqrt[2]*b*d^(3/4)*g*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*e^(3/4)*Sqrt[h]) + (2*Sqrt[2]*b*d^(1/4)*f*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*Sqrt[h]) + (2*Sqrt[2]*b*d^(3/4)*g*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*e^(3/4)*Sqrt[h]) + (2*b*f*Sqrt[h*x]*Log[c*(d + e*x^2)^p])/h + (2*g*(h*x)^(3/2)*(a + b*Log[c*(d + e*x^2)^p]))/(3*h^2) - (Sqrt[2]*b*d^(1/4)*f*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*Sqrt[h]) + (Sqrt[2]*b*d^(3/4)*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*e^(3/4)*Sqrt[h]) + (Sqrt[2]*b*d^(1/4)*f*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*Sqrt[h]) - (Sqrt[2]*b*d^(3/4)*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*e^(3/4)*Sqrt[h])","A",26,12,29,0.4138,1,"{2467, 2471, 2448, 321, 211, 1165, 628, 1162, 617, 204, 2455, 297}"
607,1,603,0,0.7948422,"\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","Int[((f + g*x)*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(3/2),x]","-\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}","-\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*a*g*Sqrt[h*x])/h^2 - (8*b*g*p*Sqrt[h*x])/h^2 - (2*Sqrt[2]*b*e^(1/4)*f*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*h^(3/2)) - (2*Sqrt[2]*b*d^(1/4)*g*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*h^(3/2)) + (2*Sqrt[2]*b*e^(1/4)*f*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*h^(3/2)) + (2*Sqrt[2]*b*d^(1/4)*g*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*h^(3/2)) + (2*b*g*Sqrt[h*x]*Log[c*(d + e*x^2)^p])/h^2 - (2*f*(a + b*Log[c*(d + e*x^2)^p]))/(h*Sqrt[h*x]) + (Sqrt[2]*b*e^(1/4)*f*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*h^(3/2)) - (Sqrt[2]*b*d^(1/4)*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*h^(3/2)) - (Sqrt[2]*b*e^(1/4)*f*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*h^(3/2)) + (Sqrt[2]*b*d^(1/4)*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*h^(3/2))","A",25,12,29,0.4138,1,"{2467, 2476, 2448, 321, 211, 1165, 628, 1162, 617, 204, 2455, 297}"
608,1,588,0,0.7408697,"\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","Int[((f + g*x)*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(5/2),x]","-\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}}","-\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*Sqrt[2]*b*e^(3/4)*f*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*d^(3/4)*h^(5/2)) - (2*Sqrt[2]*b*e^(1/4)*g*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*h^(5/2)) + (2*Sqrt[2]*b*e^(3/4)*f*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*d^(3/4)*h^(5/2)) + (2*Sqrt[2]*b*e^(1/4)*g*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*h^(5/2)) - (2*f*(a + b*Log[c*(d + e*x^2)^p]))/(3*h*(h*x)^(3/2)) - (2*g*(a + b*Log[c*(d + e*x^2)^p]))/(h^2*Sqrt[h*x]) - (Sqrt[2]*b*e^(3/4)*f*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*d^(3/4)*h^(5/2)) + (Sqrt[2]*b*e^(1/4)*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*h^(5/2)) + (Sqrt[2]*b*e^(3/4)*f*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*d^(3/4)*h^(5/2)) - (Sqrt[2]*b*e^(1/4)*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*h^(5/2))","A",23,10,29,0.3448,1,"{2467, 2476, 2455, 211, 1165, 628, 1162, 617, 204, 297}"
609,1,620,0,0.7990254,"\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","Int[((f + g*x)*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(7/2),x]","-\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}}","-\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,"(-8*b*e*f*p)/(5*d*h^3*Sqrt[h*x]) + (2*Sqrt[2]*b*e^(5/4)*f*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(5*d^(5/4)*h^(7/2)) - (2*Sqrt[2]*b*e^(3/4)*g*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*d^(3/4)*h^(7/2)) - (2*Sqrt[2]*b*e^(5/4)*f*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(5*d^(5/4)*h^(7/2)) + (2*Sqrt[2]*b*e^(3/4)*g*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*d^(3/4)*h^(7/2)) - (2*f*(a + b*Log[c*(d + e*x^2)^p]))/(5*h*(h*x)^(5/2)) - (2*g*(a + b*Log[c*(d + e*x^2)^p]))/(3*h^2*(h*x)^(3/2)) - (Sqrt[2]*b*e^(5/4)*f*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(5*d^(5/4)*h^(7/2)) - (Sqrt[2]*b*e^(3/4)*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*d^(3/4)*h^(7/2)) + (Sqrt[2]*b*e^(5/4)*f*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(5*d^(5/4)*h^(7/2)) + (Sqrt[2]*b*e^(3/4)*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*d^(3/4)*h^(7/2))","A",24,11,29,0.3793,1,"{2467, 2476, 2455, 325, 297, 1162, 617, 204, 1165, 628, 211}"
610,1,641,0,0.8269267,"\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","Int[((f + g*x)*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(9/2),x]","-\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}}","-\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,"(-8*b*e*f*p)/(21*d*h^3*(h*x)^(3/2)) - (8*b*e*g*p)/(5*d*h^4*Sqrt[h*x]) + (2*Sqrt[2]*b*e^(7/4)*f*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(7*d^(7/4)*h^(9/2)) + (2*Sqrt[2]*b*e^(5/4)*g*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(5*d^(5/4)*h^(9/2)) - (2*Sqrt[2]*b*e^(7/4)*f*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(7*d^(7/4)*h^(9/2)) - (2*Sqrt[2]*b*e^(5/4)*g*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(5*d^(5/4)*h^(9/2)) - (2*f*(a + b*Log[c*(d + e*x^2)^p]))/(7*h*(h*x)^(7/2)) - (2*g*(a + b*Log[c*(d + e*x^2)^p]))/(5*h^2*(h*x)^(5/2)) + (Sqrt[2]*b*e^(7/4)*f*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(7*d^(7/4)*h^(9/2)) - (Sqrt[2]*b*e^(5/4)*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(5*d^(5/4)*h^(9/2)) - (Sqrt[2]*b*e^(7/4)*f*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(7*d^(7/4)*h^(9/2)) + (Sqrt[2]*b*e^(5/4)*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(5*d^(5/4)*h^(9/2))","A",25,11,29,0.3793,1,"{2467, 2476, 2455, 325, 211, 1165, 628, 1162, 617, 204, 297}"
611,1,1002,0,1.3094299,"\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","Int[((f + g*x)^2*(a + b*Log[c*(d + e*x^2)^p]))/Sqrt[h*x],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}}","-\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*a*f^2*Sqrt[h*x])/h - (8*b*f^2*p*Sqrt[h*x])/h + (8*b*d*g^2*p*Sqrt[h*x])/(5*e*h) - (16*b*f*g*p*(h*x)^(3/2))/(9*h^2) - (8*b*g^2*p*(h*x)^(5/2))/(25*h^3) - (2*Sqrt[2]*b*d^(1/4)*f^2*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*Sqrt[h]) - (4*Sqrt[2]*b*d^(3/4)*f*g*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*e^(3/4)*Sqrt[h]) + (2*Sqrt[2]*b*d^(5/4)*g^2*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(5*e^(5/4)*Sqrt[h]) + (2*Sqrt[2]*b*d^(1/4)*f^2*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*Sqrt[h]) + (4*Sqrt[2]*b*d^(3/4)*f*g*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*e^(3/4)*Sqrt[h]) - (2*Sqrt[2]*b*d^(5/4)*g^2*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(5*e^(5/4)*Sqrt[h]) + (2*b*f^2*Sqrt[h*x]*Log[c*(d + e*x^2)^p])/h + (4*f*g*(h*x)^(3/2)*(a + b*Log[c*(d + e*x^2)^p]))/(3*h^2) + (2*g^2*(h*x)^(5/2)*(a + b*Log[c*(d + e*x^2)^p]))/(5*h^3) - (Sqrt[2]*b*d^(1/4)*f^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*Sqrt[h]) + (2*Sqrt[2]*b*d^(3/4)*f*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*e^(3/4)*Sqrt[h]) + (Sqrt[2]*b*d^(5/4)*g^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(5*e^(5/4)*Sqrt[h]) + (Sqrt[2]*b*d^(1/4)*f^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*Sqrt[h]) - (2*Sqrt[2]*b*d^(3/4)*f*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*e^(3/4)*Sqrt[h]) - (Sqrt[2]*b*d^(5/4)*g^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(5*e^(5/4)*Sqrt[h])","A",38,13,31,0.4194,1,"{2467, 2471, 2448, 321, 211, 1165, 628, 1162, 617, 204, 2455, 297, 302}"
612,1,949,0,1.2613162,"\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","Int[((f + g*x)^2*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(3/2),x]","-\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}}","-\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,"(4*a*f*g*Sqrt[h*x])/h^2 - (16*b*f*g*p*Sqrt[h*x])/h^2 - (8*b*g^2*p*(h*x)^(3/2))/(9*h^3) - (2*Sqrt[2]*b*e^(1/4)*f^2*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*h^(3/2)) - (4*Sqrt[2]*b*d^(1/4)*f*g*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*h^(3/2)) - (2*Sqrt[2]*b*d^(3/4)*g^2*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*e^(3/4)*h^(3/2)) + (2*Sqrt[2]*b*e^(1/4)*f^2*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*h^(3/2)) + (4*Sqrt[2]*b*d^(1/4)*f*g*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*h^(3/2)) + (2*Sqrt[2]*b*d^(3/4)*g^2*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*e^(3/4)*h^(3/2)) + (4*b*f*g*Sqrt[h*x]*Log[c*(d + e*x^2)^p])/h^2 - (2*f^2*(a + b*Log[c*(d + e*x^2)^p]))/(h*Sqrt[h*x]) + (2*g^2*(h*x)^(3/2)*(a + b*Log[c*(d + e*x^2)^p]))/(3*h^3) + (Sqrt[2]*b*e^(1/4)*f^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*h^(3/2)) - (2*Sqrt[2]*b*d^(1/4)*f*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*h^(3/2)) + (Sqrt[2]*b*d^(3/4)*g^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*e^(3/4)*h^(3/2)) - (Sqrt[2]*b*e^(1/4)*f^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*h^(3/2)) + (2*Sqrt[2]*b*d^(1/4)*f*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*h^(3/2)) - (Sqrt[2]*b*d^(3/4)*g^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*e^(3/4)*h^(3/2))","A",36,12,31,0.3871,1,"{2467, 2476, 2448, 321, 211, 1165, 628, 1162, 617, 204, 2455, 297}"
613,1,932,0,1.2150461,"\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","Int[((f + g*x)^2*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(5/2),x]","-\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}","-\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*a*g^2*Sqrt[h*x])/h^3 - (8*b*g^2*p*Sqrt[h*x])/h^3 - (2*Sqrt[2]*b*e^(3/4)*f^2*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*d^(3/4)*h^(5/2)) - (4*Sqrt[2]*b*e^(1/4)*f*g*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*h^(5/2)) - (2*Sqrt[2]*b*d^(1/4)*g^2*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*h^(5/2)) + (2*Sqrt[2]*b*e^(3/4)*f^2*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*d^(3/4)*h^(5/2)) + (4*Sqrt[2]*b*e^(1/4)*f*g*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*h^(5/2)) + (2*Sqrt[2]*b*d^(1/4)*g^2*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*h^(5/2)) + (2*b*g^2*Sqrt[h*x]*Log[c*(d + e*x^2)^p])/h^3 - (2*f^2*(a + b*Log[c*(d + e*x^2)^p]))/(3*h*(h*x)^(3/2)) - (4*f*g*(a + b*Log[c*(d + e*x^2)^p]))/(h^2*Sqrt[h*x]) - (Sqrt[2]*b*e^(3/4)*f^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*d^(3/4)*h^(5/2)) + (2*Sqrt[2]*b*e^(1/4)*f*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*h^(5/2)) - (Sqrt[2]*b*d^(1/4)*g^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*h^(5/2)) + (Sqrt[2]*b*e^(3/4)*f^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*d^(3/4)*h^(5/2)) - (2*Sqrt[2]*b*e^(1/4)*f*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*h^(5/2)) + (Sqrt[2]*b*d^(1/4)*g^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*h^(5/2))","A",35,12,31,0.3871,1,"{2467, 2476, 2448, 321, 211, 1165, 628, 1162, 617, 204, 2455, 297}"
614,1,935,0,1.1826465,"\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","Int[((f + g*x)^2*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(7/2),x]","\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}}","\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,"(-8*b*e*f^2*p)/(5*d*h^3*Sqrt[h*x]) + (2*Sqrt[2]*b*e^(5/4)*f^2*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(5*d^(5/4)*h^(7/2)) - (4*Sqrt[2]*b*e^(3/4)*f*g*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*d^(3/4)*h^(7/2)) - (2*Sqrt[2]*b*e^(1/4)*g^2*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*h^(7/2)) - (2*Sqrt[2]*b*e^(5/4)*f^2*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(5*d^(5/4)*h^(7/2)) + (4*Sqrt[2]*b*e^(3/4)*f*g*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*d^(3/4)*h^(7/2)) + (2*Sqrt[2]*b*e^(1/4)*g^2*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*h^(7/2)) - (2*f^2*(a + b*Log[c*(d + e*x^2)^p]))/(5*h*(h*x)^(5/2)) - (4*f*g*(a + b*Log[c*(d + e*x^2)^p]))/(3*h^2*(h*x)^(3/2)) - (2*g^2*(a + b*Log[c*(d + e*x^2)^p]))/(h^3*Sqrt[h*x]) - (Sqrt[2]*b*e^(5/4)*f^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(5*d^(5/4)*h^(7/2)) - (2*Sqrt[2]*b*e^(3/4)*f*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*d^(3/4)*h^(7/2)) + (Sqrt[2]*b*e^(1/4)*g^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*h^(7/2)) + (Sqrt[2]*b*e^(5/4)*f^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(5*d^(5/4)*h^(7/2)) + (2*Sqrt[2]*b*e^(3/4)*f*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*d^(3/4)*h^(7/2)) - (Sqrt[2]*b*e^(1/4)*g^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*h^(7/2))","A",34,11,31,0.3548,1,"{2467, 2476, 2455, 325, 297, 1162, 617, 204, 1165, 628, 211}"
615,1,968,0,1.2318635,"\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","Int[((f + g*x)^2*(a + b*Log[c*(d + e*x^2)^p]))/(h*x)^(9/2),x]","\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}}","\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,"(-8*b*e*f^2*p)/(21*d*h^3*(h*x)^(3/2)) - (16*b*e*f*g*p)/(5*d*h^4*Sqrt[h*x]) + (2*Sqrt[2]*b*e^(7/4)*f^2*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(7*d^(7/4)*h^(9/2)) + (4*Sqrt[2]*b*e^(5/4)*f*g*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(5*d^(5/4)*h^(9/2)) - (2*Sqrt[2]*b*e^(3/4)*g^2*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*d^(3/4)*h^(9/2)) - (2*Sqrt[2]*b*e^(7/4)*f^2*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(7*d^(7/4)*h^(9/2)) - (4*Sqrt[2]*b*e^(5/4)*f*g*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(5*d^(5/4)*h^(9/2)) + (2*Sqrt[2]*b*e^(3/4)*g^2*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(3*d^(3/4)*h^(9/2)) - (2*f^2*(a + b*Log[c*(d + e*x^2)^p]))/(7*h*(h*x)^(7/2)) - (4*f*g*(a + b*Log[c*(d + e*x^2)^p]))/(5*h^2*(h*x)^(5/2)) - (2*g^2*(a + b*Log[c*(d + e*x^2)^p]))/(3*h^3*(h*x)^(3/2)) + (Sqrt[2]*b*e^(7/4)*f^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(7*d^(7/4)*h^(9/2)) - (2*Sqrt[2]*b*e^(5/4)*f*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(5*d^(5/4)*h^(9/2)) - (Sqrt[2]*b*e^(3/4)*g^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*d^(3/4)*h^(9/2)) - (Sqrt[2]*b*e^(7/4)*f^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(7*d^(7/4)*h^(9/2)) + (2*Sqrt[2]*b*e^(5/4)*f*g*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(5*d^(5/4)*h^(9/2)) + (Sqrt[2]*b*e^(3/4)*g^2*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(3*d^(3/4)*h^(9/2))","A",35,11,31,0.3548,1,"{2467, 2476, 2455, 325, 211, 1165, 628, 1162, 617, 204, 297}"
616,1,1680,0,3.0846148,"\int \frac{\sqrt{h x} \left(a+b \log \left(c \left(d+e x^2\right)^p\right)\right)}{f+g x} \, dx","Int[(Sqrt[h*x]*(a + b*Log[c*(d + e*x^2)^p]))/(f + g*x),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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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}","\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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,"(2*a*Sqrt[h*x])/g - (8*b*p*Sqrt[h*x])/g - (2*Sqrt[2]*b*d^(1/4)*Sqrt[h]*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*g) + (2*Sqrt[2]*b*d^(1/4)*Sqrt[h]*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(e^(1/4)*g) + (2*b*Sqrt[h*x]*Log[c*(d + e*x^2)^p])/g - (2*Sqrt[f]*Sqrt[h]*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*(a + b*Log[c*(d + e*x^2)^p]))/g^(3/2) - (Sqrt[2]*b*d^(1/4)*Sqrt[h]*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*g) + (Sqrt[2]*b*d^(1/4)*Sqrt[h]*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(e^(1/4)*g) - (8*b*Sqrt[f]*Sqrt[h]*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[h])/(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x])])/g^(3/2) + (2*b*Sqrt[f]*Sqrt[h]*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] - e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] - I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/g^(3/2) + (2*b*Sqrt[f]*Sqrt[h]*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(-2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] - e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] - (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/g^(3/2) + (2*b*Sqrt[f]*Sqrt[h]*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] + e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] + I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/g^(3/2) + (2*b*Sqrt[f]*Sqrt[h]*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] + e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] + (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/g^(3/2) + ((4*I)*b*Sqrt[f]*Sqrt[h]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[h])/(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x])])/g^(3/2) - (I*b*Sqrt[f]*Sqrt[h]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] - e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] - I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/g^(3/2) - (I*b*Sqrt[f]*Sqrt[h]*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] - e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] - (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/g^(3/2) - (I*b*Sqrt[f]*Sqrt[h]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] + e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] + I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/g^(3/2) - (I*b*Sqrt[f]*Sqrt[h]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] + e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] + (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/g^(3/2)","A",39,20,31,0.6452,1,"{2467, 2476, 2448, 321, 211, 1165, 628, 1162, 617, 204, 205, 2470, 12, 260, 6725, 4928, 4856, 2402, 2315, 2447}"
617,1,1361,0,1.8305806,"\int \frac{a+b \log \left(c \left(d+e x^2\right)^p\right)}{\sqrt{h x} (f+g x)} \, dx","Int[(a + b*Log[c*(d + e*x^2)^p])/(Sqrt[h*x]*(f + g*x)),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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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}}","\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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,"(2*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*(a + b*Log[c*(d + e*x^2)^p]))/(Sqrt[f]*Sqrt[g]*Sqrt[h]) + (8*b*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[h])/(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x])])/(Sqrt[f]*Sqrt[g]*Sqrt[h]) - (2*b*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] - e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] - I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(Sqrt[f]*Sqrt[g]*Sqrt[h]) - (2*b*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(-2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] - e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] - (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(Sqrt[f]*Sqrt[g]*Sqrt[h]) - (2*b*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] + e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] + I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(Sqrt[f]*Sqrt[g]*Sqrt[h]) - (2*b*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] + e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] + (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(Sqrt[f]*Sqrt[g]*Sqrt[h]) - ((4*I)*b*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[h])/(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x])])/(Sqrt[f]*Sqrt[g]*Sqrt[h]) + (I*b*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] - e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] - I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(Sqrt[f]*Sqrt[g]*Sqrt[h]) + (I*b*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] - e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] - (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(Sqrt[f]*Sqrt[g]*Sqrt[h]) + (I*b*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] + e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] + I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(Sqrt[f]*Sqrt[g]*Sqrt[h]) + (I*b*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] + e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] + (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(Sqrt[f]*Sqrt[g]*Sqrt[h])","A",25,11,31,0.3548,1,"{2467, 205, 2470, 12, 260, 6725, 4928, 4856, 2402, 2315, 2447}"
618,1,1659,0,2.5285385,"\int \frac{a+b \log \left(c \left(d+e x^2\right)^p\right)}{(h x)^{3/2} (f+g x)} \, dx","Int[(a + b*Log[c*(d + e*x^2)^p])/((h*x)^(3/2)*(f + g*x)),x]","-\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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}}","-\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,\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{PolyLog}\left(2,1-\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{PolyLog}\left(2,1-\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,"(-2*Sqrt[2]*b*e^(1/4)*p*ArcTan[1 - (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*f*h^(3/2)) + (2*Sqrt[2]*b*e^(1/4)*p*ArcTan[1 + (Sqrt[2]*e^(1/4)*Sqrt[h*x])/(d^(1/4)*Sqrt[h])])/(d^(1/4)*f*h^(3/2)) - (2*(a + b*Log[c*(d + e*x^2)^p]))/(f*h*Sqrt[h*x]) - (2*Sqrt[g]*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*(a + b*Log[c*(d + e*x^2)^p]))/(f^(3/2)*h^(3/2)) + (Sqrt[2]*b*e^(1/4)*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x - Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*f*h^(3/2)) - (Sqrt[2]*b*e^(1/4)*p*Log[Sqrt[d]*Sqrt[h] + Sqrt[e]*Sqrt[h]*x + Sqrt[2]*d^(1/4)*e^(1/4)*Sqrt[h*x]])/(d^(1/4)*f*h^(3/2)) - (8*b*Sqrt[g]*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[h])/(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x])])/(f^(3/2)*h^(3/2)) + (2*b*Sqrt[g]*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] - e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] - I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(f^(3/2)*h^(3/2)) + (2*b*Sqrt[g]*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(-2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] - e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] - (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(f^(3/2)*h^(3/2)) + (2*b*Sqrt[g]*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] + e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] + I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(f^(3/2)*h^(3/2)) + (2*b*Sqrt[g]*p*ArcTan[(Sqrt[g]*Sqrt[h*x])/(Sqrt[f]*Sqrt[h])]*Log[(2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] + e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] + (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(f^(3/2)*h^(3/2)) + ((4*I)*b*Sqrt[g]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[h])/(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x])])/(f^(3/2)*h^(3/2)) - (I*b*Sqrt[g]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] - e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] - I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(f^(3/2)*h^(3/2)) - (I*b*Sqrt[g]*p*PolyLog[2, 1 + (2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] - e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] - (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(f^(3/2)*h^(3/2)) - (I*b*Sqrt[g]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*Sqrt[h]*((-d)^(1/4)*Sqrt[-h] + e^(1/4)*Sqrt[h*x]))/(((-d)^(1/4)*Sqrt[g]*Sqrt[-h] + I*e^(1/4)*Sqrt[f]*Sqrt[h])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(f^(3/2)*h^(3/2)) - (I*b*Sqrt[g]*p*PolyLog[2, 1 - (2*Sqrt[f]*Sqrt[g]*((-d)^(1/4)*Sqrt[h] + e^(1/4)*Sqrt[h*x]))/((I*e^(1/4)*Sqrt[f] + (-d)^(1/4)*Sqrt[g])*(Sqrt[f]*Sqrt[h] - I*Sqrt[g]*Sqrt[h*x]))])/(f^(3/2)*h^(3/2))","A",37,19,31,0.6129,1,"{2467, 2476, 2455, 297, 1162, 617, 204, 1165, 628, 205, 2470, 12, 260, 6725, 4928, 4856, 2402, 2315, 2447}"
619,1,33,0,0.0260934,"\int \frac{\log \left(f x^p\right) \log \left(1+e x^m\right)}{x} \, dx","Int[(Log[f*x^p]*Log[1 + e*x^m])/x,x]","\frac{p \text{PolyLog}\left(3,-e x^m\right)}{m^2}-\frac{\log \left(f x^p\right) \text{PolyLog}\left(2,-e x^m\right)}{m}","\frac{p \text{PolyLog}\left(3,-e x^m\right)}{m^2}-\frac{\log \left(f x^p\right) \text{PolyLog}\left(2,-e x^m\right)}{m}",1,"-((Log[f*x^p]*PolyLog[2, -(e*x^m)])/m) + (p*PolyLog[3, -(e*x^m)])/m^2","A",2,2,18,0.1111,1,"{2374, 6589}"
620,1,75,0,0.1200385,"\int \frac{x^{-1+m} \log ^2\left(f x^p\right)}{d+e x^m} \, dx","Int[(x^(-1 + m)*Log[f*x^p]^2)/(d + e*x^m),x]","\frac{2 p \log \left(f x^p\right) \text{PolyLog}\left(2,-\frac{e x^m}{d}\right)}{e m^2}-\frac{2 p^2 \text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{e m^3}+\frac{\log ^2\left(f x^p\right) \log \left(\frac{e x^m}{d}+1\right)}{e m}","\frac{2 p \log \left(f x^p\right) \text{PolyLog}\left(2,-\frac{e x^m}{d}\right)}{e m^2}-\frac{2 p^2 \text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{e m^3}+\frac{\log ^2\left(f x^p\right) \log \left(\frac{e x^m}{d}+1\right)}{e m}",1,"(Log[f*x^p]^2*Log[1 + (e*x^m)/d])/(e*m) + (2*p*Log[f*x^p]*PolyLog[2, -((e*x^m)/d)])/(e*m^2) - (2*p^2*PolyLog[3, -((e*x^m)/d)])/(e*m^3)","A",3,3,23,0.1304,1,"{2337, 2374, 6589}"
621,1,161,0,0.2244292,"\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","Int[(Log[f*x^p]^3*(a + b*Log[c*(d + e*x^m)^n]))/x,x]","-\frac{6 b n p^2 \log \left(f x^p\right) \text{PolyLog}\left(4,-\frac{e x^m}{d}\right)}{m^3}+\frac{3 b n p \log ^2\left(f x^p\right) \text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{m^2}-\frac{b n \log ^3\left(f x^p\right) \text{PolyLog}\left(2,-\frac{e x^m}{d}\right)}{m}+\frac{6 b n p^3 \text{PolyLog}\left(5,-\frac{e x^m}{d}\right)}{m^4}+\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{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^2 \log \left(f x^p\right) \text{PolyLog}\left(4,-\frac{e x^m}{d}\right)}{m^3}+\frac{3 b n p \log ^2\left(f x^p\right) \text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{m^2}-\frac{b n \log ^3\left(f x^p\right) \text{PolyLog}\left(2,-\frac{e x^m}{d}\right)}{m}+\frac{6 b n p^3 \text{PolyLog}\left(5,-\frac{e x^m}{d}\right)}{m^4}+\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{b n \log ^4\left(f x^p\right) \log \left(\frac{e x^m}{d}+1\right)}{4 p}",1,"(Log[f*x^p]^4*(a + b*Log[c*(d + e*x^m)^n]))/(4*p) - (b*n*Log[f*x^p]^4*Log[1 + (e*x^m)/d])/(4*p) - (b*n*Log[f*x^p]^3*PolyLog[2, -((e*x^m)/d)])/m + (3*b*n*p*Log[f*x^p]^2*PolyLog[3, -((e*x^m)/d)])/m^2 - (6*b*n*p^2*Log[f*x^p]*PolyLog[4, -((e*x^m)/d)])/m^3 + (6*b*n*p^3*PolyLog[5, -((e*x^m)/d)])/m^4","A",6,5,28,0.1786,1,"{2481, 2337, 2374, 2383, 6589}"
622,1,132,0,0.1876956,"\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","Int[(Log[f*x^p]^2*(a + b*Log[c*(d + e*x^m)^n]))/x,x]","\frac{2 b n p \log \left(f x^p\right) \text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{m^2}-\frac{b n \log ^2\left(f x^p\right) \text{PolyLog}\left(2,-\frac{e x^m}{d}\right)}{m}-\frac{2 b n p^2 \text{PolyLog}\left(4,-\frac{e x^m}{d}\right)}{m^3}+\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{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 \log \left(f x^p\right) \text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{m^2}-\frac{b n \log ^2\left(f x^p\right) \text{PolyLog}\left(2,-\frac{e x^m}{d}\right)}{m}-\frac{2 b n p^2 \text{PolyLog}\left(4,-\frac{e x^m}{d}\right)}{m^3}+\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{b n \log ^3\left(f x^p\right) \log \left(\frac{e x^m}{d}+1\right)}{3 p}",1,"(Log[f*x^p]^3*(a + b*Log[c*(d + e*x^m)^n]))/(3*p) - (b*n*Log[f*x^p]^3*Log[1 + (e*x^m)/d])/(3*p) - (b*n*Log[f*x^p]^2*PolyLog[2, -((e*x^m)/d)])/m + (2*b*n*p*Log[f*x^p]*PolyLog[3, -((e*x^m)/d)])/m^2 - (2*b*n*p^2*PolyLog[4, -((e*x^m)/d)])/m^3","A",5,5,28,0.1786,1,"{2481, 2337, 2374, 2383, 6589}"
623,1,102,0,0.1448928,"\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","Int[(Log[f*x^p]*(a + b*Log[c*(d + e*x^m)^n]))/x,x]","-\frac{b n \log \left(f x^p\right) \text{PolyLog}\left(2,-\frac{e x^m}{d}\right)}{m}+\frac{b n p \text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{m^2}+\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 ^2\left(f x^p\right) \log \left(\frac{e x^m}{d}+1\right)}{2 p}","-\frac{b n \log \left(f x^p\right) \text{PolyLog}\left(2,-\frac{e x^m}{d}\right)}{m}+\frac{b n p \text{PolyLog}\left(3,-\frac{e x^m}{d}\right)}{m^2}+\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 ^2\left(f x^p\right) \log \left(\frac{e x^m}{d}+1\right)}{2 p}",1,"(Log[f*x^p]^2*(a + b*Log[c*(d + e*x^m)^n]))/(2*p) - (b*n*Log[f*x^p]^2*Log[1 + (e*x^m)/d])/(2*p) - (b*n*Log[f*x^p]*PolyLog[2, -((e*x^m)/d)])/m + (b*n*p*PolyLog[3, -((e*x^m)/d)])/m^2","A",4,4,26,0.1538,1,"{2481, 2337, 2374, 6589}"
624,1,49,0,0.0528,"\int \frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{x} \, dx","Int[(a + b*Log[c*(d + e*x^m)^n])/x,x]","\frac{b n \text{PolyLog}\left(2,\frac{e x^m}{d}+1\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{PolyLog}\left(2,\frac{e x^m}{d}+1\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}",1,"(Log[-((e*x^m)/d)]*(a + b*Log[c*(d + e*x^m)^n]))/m + (b*n*PolyLog[2, 1 + (e*x^m)/d])/m","A",3,3,20,0.1500,1,"{2454, 2394, 2315}"
625,0,0,0,0.2923617,"\int \frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{x \log \left(f x^p\right)} \, dx","Int[(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,"(a*Log[Log[f*x^p]])/p + b*Defer[Int][Log[c*(d + e*x^m)^n]/(x*Log[f*x^p]), x]","A",0,0,0,0,-1,"{}"
626,0,0,0,0.1195125,"\int \frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{x \log ^2\left(f x^p\right)} \, dx","Int[(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,"-((a + b*Log[c*(d + e*x^m)^n])/(p*Log[f*x^p])) + (b*e*m*n*Defer[Int][x^(-1 + m)/((d + e*x^m)*Log[f*x^p]), x])/p","A",0,0,0,0,-1,"{}"
627,0,0,0,0.1167144,"\int \frac{a+b \log \left(c \left(d+e x^m\right)^n\right)}{x \log ^3\left(f x^p\right)} \, dx","Int[(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,"-(a + b*Log[c*(d + e*x^m)^n])/(2*p*Log[f*x^p]^2) + (b*e*m*n*Defer[Int][x^(-1 + m)/((d + e*x^m)*Log[f*x^p]^2), x])/(2*p)","A",0,0,0,0,-1,"{}"
628,1,76,0,0.0443628,"\int \log \left(c \left(d+e (f+g x)^p\right)^q\right) \, dx","Int[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{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)}","\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,"-((e*p*q*(f + g*x)^(1 + p)*Hypergeometric2F1[1, 1 + p^(-1), 2 + p^(-1), -((e*(f + g*x)^p)/d)])/(d*g*(1 + p))) + ((f + g*x)*Log[c*(d + e*(f + g*x)^p)^q])/g","A",3,3,16,0.1875,1,"{2483, 2448, 364}"
629,1,169,0,0.2057362,"\int \log \left(c \left(d+e (f+g x)^3\right)^q\right) \, dx","Int[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 \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","\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 - (Sqrt[3]*d^(1/3)*q*ArcTan[(d^(1/3) - 2*e^(1/3)*(f + g*x))/(Sqrt[3]*d^(1/3))])/(e^(1/3)*g) + (d^(1/3)*q*Log[d^(1/3) + e^(1/3)*(f + g*x)])/(e^(1/3)*g) - (d^(1/3)*q*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",9,9,16,0.5625,1,"{2483, 2448, 321, 200, 31, 634, 617, 204, 628}"
630,1,63,0,0.047829,"\int \log \left(c \left(d+e (f+g x)^2\right)^q\right) \, dx","Int[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",4,4,16,0.2500,1,"{2483, 2448, 321, 205}"
631,1,35,0,0.0160286,"\int \log \left(c (d+e (f+g x))^q\right) \, dx","Int[Log[c*(d + e*(f + g*x))^q],x]","\frac{(d+e f+e g x) \log \left(c (d+e (f+g x))^q\right)}{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 + e*f + e*g*x)*Log[c*(d + e*(f + g*x))^q])/(e*g)","A",3,3,14,0.2143,1,"{2444, 2389, 2295}"
632,1,45,0,0.0267869,"\int \log \left(c \left(d+\frac{e}{f+g x}\right)^q\right) \, dx","Int[Log[c*(d + e/(f + g*x))^q],x]","\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}","\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,"((f + g*x)*Log[c*(d + e/(f + g*x))^q])/g + (e*q*Log[e + d*(f + g*x)])/(d*g)","A",4,4,16,0.2500,1,"{2483, 2448, 263, 31}"
633,1,59,0,0.0356361,"\int \log \left(c \left(d+\frac{e}{(f+g x)^2}\right)^q\right) \, dx","Int[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{d} (f+g x)}{\sqrt{e}}\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[d]*(f + g*x))/Sqrt[e]])/(Sqrt[d]*g) + ((f + g*x)*Log[c*(d + e/(f + g*x)^2)^q])/g","A",4,4,16,0.2500,1,"{2483, 2448, 263, 205}"
634,1,165,0,0.1729575,"\int \log \left(c \left(d+\frac{e}{(f+g x)^3}\right)^q\right) \, dx","Int[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{\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}","\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,"-((Sqrt[3]*e^(1/3)*q*ArcTan[(e^(1/3) - 2*d^(1/3)*(f + g*x))/(Sqrt[3]*e^(1/3))])/(d^(1/3)*g)) + ((f + g*x)*Log[c*(d + e/(f + g*x)^3)^q])/g + (e^(1/3)*q*Log[e^(1/3) + d^(1/3)*(f + g*x)])/(d^(1/3)*g) - (e^(1/3)*q*Log[e^(2/3) - d^(1/3)*e^(1/3)*(f + g*x) + d^(2/3)*(f + g*x)^2])/(2*d^(1/3)*g)","A",9,9,16,0.5625,1,"{2483, 2448, 263, 200, 31, 634, 617, 204, 628}"
635,0,0,0,0.0059268,"\int \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^n \, dx","Int[(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,"Defer[Int][(a + b*Log[c*(d + e/(f + g*x))^p])^n, x]","A",0,0,0,0,-1,"{}"
636,1,221,0,0.2777804,"\int \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^4 \, dx","Int[(a + b*Log[c*(d + e/(f + g*x))^p])^4,x]","\frac{24 b^3 e p^3 \text{PolyLog}\left(3,\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{PolyLog}\left(2,\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{24 b^4 e p^4 \text{PolyLog}\left(4,\frac{e}{d (f+g x)}+1\right)}{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^3 e p^3 \text{PolyLog}\left(3,\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{PolyLog}\left(2,\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{24 b^4 e p^4 \text{PolyLog}\left(4,\frac{e}{d (f+g x)}+1\right)}{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}",1,"(-4*b*e*p*Log[-(e/(d*(f + g*x)))]*(a + b*Log[c*(d + e/(f + g*x))^p])^3)/(d*g) + ((e + d*(f + g*x))*(a + b*Log[c*(d + e/(f + g*x))^p])^4)/(d*g) - (12*b^2*e*p^2*(a + b*Log[c*(d + e/(f + g*x))^p])^2*PolyLog[2, 1 + e/(d*(f + g*x))])/(d*g) + (24*b^3*e*p^3*(a + b*Log[c*(d + e/(f + g*x))^p])*PolyLog[3, 1 + e/(d*(f + g*x))])/(d*g) - (24*b^4*e*p^4*PolyLog[4, 1 + e/(d*(f + g*x))])/(d*g)","A",8,8,22,0.3636,1,"{2483, 2449, 2454, 2396, 2433, 2374, 2383, 6589}"
637,1,168,0,0.1841005,"\int \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^3 \, dx","Int[(a + b*Log[c*(d + e/(f + g*x))^p])^3,x]","-\frac{6 b^2 e p^2 \text{PolyLog}\left(2,\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{6 b^3 e p^3 \text{PolyLog}\left(3,\frac{e}{d (f+g x)}+1\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^2 e p^2 \text{PolyLog}\left(2,\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{6 b^3 e p^3 \text{PolyLog}\left(3,\frac{e}{d (f+g x)}+1\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}",1,"(-3*b*e*p*Log[-(e/(d*(f + g*x)))]*(a + b*Log[c*(d + e/(f + g*x))^p])^2)/(d*g) + ((e + d*(f + g*x))*(a + b*Log[c*(d + e/(f + g*x))^p])^3)/(d*g) - (6*b^2*e*p^2*(a + b*Log[c*(d + e/(f + g*x))^p])*PolyLog[2, 1 + e/(d*(f + g*x))])/(d*g) + (6*b^3*e*p^3*PolyLog[3, 1 + e/(d*(f + g*x))])/(d*g)","A",7,7,22,0.3182,1,"{2483, 2449, 2454, 2396, 2433, 2374, 6589}"
638,1,115,0,0.0900471,"\int \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^2 \, dx","Int[(a + b*Log[c*(d + e/(f + g*x))^p])^2,x]","-\frac{2 b^2 e p^2 \text{PolyLog}\left(2,\frac{e}{d (f+g x)}+1\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{PolyLog}\left(2,\frac{e}{d (f+g x)}+1\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}",1,"(-2*b*e*p*Log[-(e/(d*(f + g*x)))]*(a + b*Log[c*(d + e/(f + g*x))^p]))/(d*g) + ((e + d*(f + g*x))*(a + b*Log[c*(d + e/(f + g*x))^p])^2)/(d*g) - (2*b^2*e*p^2*PolyLog[2, 1 + e/(d*(f + g*x))])/(d*g)","A",5,5,22,0.2273,1,"{2483, 2449, 2454, 2394, 2315}"
639,1,50,0,0.0376744,"\int \left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right) \, dx","Int[a + b*Log[c*(d + e/(f + g*x))^p],x]","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}","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*(f + g*x)*Log[c*(d + e/(f + g*x))^p])/g + (b*e*p*Log[e + d*(f + g*x)])/(d*g)","A",5,4,20,0.2000,1,"{2483, 2448, 263, 31}"
640,0,0,0,0.0059505,"\int \frac{1}{a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)} \, dx","Int[(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,"Defer[Int][(a + b*Log[c*(d + e/(f + g*x))^p])^(-1), x]","A",0,0,0,0,-1,"{}"
641,0,0,0,0.0057474,"\int \frac{1}{\left(a+b \log \left(c \left(d+\frac{e}{f+g x}\right)^p\right)\right)^2} \, dx","Int[(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,"Defer[Int][(a + b*Log[c*(d + e/(f + g*x))^p])^(-2), x]","A",0,0,0,0,-1,"{}"