1,1,73,86,0.0444105,"\int x^4 \text{Li}_2(a x) \, dx","Integrate[x^4*PolyLog[2, a*x],x]","\frac{300 a^5 x^5 \text{Li}_2(a x)+60 \left(a^5 x^5-1\right) \log (1-a x)-a x \left(12 a^4 x^4+15 a^3 x^3+20 a^2 x^2+30 a x+60\right)}{1500 a^5}","-\frac{\log (1-a x)}{25 a^5}-\frac{x}{25 a^4}-\frac{x^2}{50 a^3}-\frac{x^3}{75 a^2}+\frac{1}{5} x^5 \text{Li}_2(a x)+\frac{1}{25} x^5 \log (1-a x)-\frac{x^4}{100 a}-\frac{x^5}{125}",1,"(-(a*x*(60 + 30*a*x + 20*a^2*x^2 + 15*a^3*x^3 + 12*a^4*x^4)) + 60*(-1 + a^5*x^5)*Log[1 - a*x] + 300*a^5*x^5*PolyLog[2, a*x])/(1500*a^5)","A",1
2,1,65,76,0.0313884,"\int x^3 \text{Li}_2(a x) \, dx","Integrate[x^3*PolyLog[2, a*x],x]","\frac{48 a^4 x^4 \text{Li}_2(a x)+12 \left(a^4 x^4-1\right) \log (1-a x)-a x \left(3 a^3 x^3+4 a^2 x^2+6 a x+12\right)}{192 a^4}","-\frac{\log (1-a x)}{16 a^4}-\frac{x}{16 a^3}-\frac{x^2}{32 a^2}+\frac{1}{4} x^4 \text{Li}_2(a x)+\frac{1}{16} x^4 \log (1-a x)-\frac{x^3}{48 a}-\frac{x^4}{64}",1,"(-(a*x*(12 + 6*a*x + 4*a^2*x^2 + 3*a^3*x^3)) + 12*(-1 + a^4*x^4)*Log[1 - a*x] + 48*a^4*x^4*PolyLog[2, a*x])/(192*a^4)","A",1
3,1,57,66,0.0284889,"\int x^2 \text{Li}_2(a x) \, dx","Integrate[x^2*PolyLog[2, a*x],x]","\frac{18 a^3 x^3 \text{Li}_2(a x)+6 \left(a^3 x^3-1\right) \log (1-a x)-a x \left(2 a^2 x^2+3 a x+6\right)}{54 a^3}","-\frac{\log (1-a x)}{9 a^3}-\frac{x}{9 a^2}+\frac{1}{3} x^3 \text{Li}_2(a x)+\frac{1}{9} x^3 \log (1-a x)-\frac{x^2}{18 a}-\frac{x^3}{27}",1,"(-(a*x*(6 + 3*a*x + 2*a^2*x^2)) + 6*(-1 + a^3*x^3)*Log[1 - a*x] + 18*a^3*x^3*PolyLog[2, a*x])/(54*a^3)","A",1
4,1,48,56,0.0237466,"\int x \text{Li}_2(a x) \, dx","Integrate[x*PolyLog[2, a*x],x]","\frac{4 a^2 x^2 \text{Li}_2(a x)+2 \left(a^2 x^2-1\right) \log (1-a x)-a x (a x+2)}{8 a^2}","-\frac{\log (1-a x)}{4 a^2}+\frac{1}{2} x^2 \text{Li}_2(a x)+\frac{1}{4} x^2 \log (1-a x)-\frac{x}{4 a}-\frac{x^2}{8}",1,"(-(a*x*(2 + a*x)) + 2*(-1 + a^2*x^2)*Log[1 - a*x] + 4*a^2*x^2*PolyLog[2, a*x])/(8*a^2)","A",1
5,1,26,29,0.0127108,"\int \text{Li}_2(a x) \, dx","Integrate[PolyLog[2, a*x],x]","x \text{Li}_2(a x)+\left(x-\frac{1}{a}\right) \log (1-a x)-x","x \text{Li}_2(a x)-\frac{(1-a x) \log (1-a x)}{a}-x",1,"-x + (-a^(-1) + x)*Log[1 - a*x] + x*PolyLog[2, a*x]","A",1
6,1,5,5,0.0014171,"\int \frac{\text{Li}_2(a x)}{x} \, dx","Integrate[PolyLog[2, a*x]/x,x]","\text{Li}_3(a x)","\text{Li}_3(a x)",1,"PolyLog[3, a*x]","A",1
7,1,36,36,0.0104108,"\int \frac{\text{Li}_2(a x)}{x^2} \, dx","Integrate[PolyLog[2, a*x]/x^2,x]","-\frac{\text{Li}_2(a x)}{x}+a \log (x)-a \log (1-a x)+\frac{\log (1-a x)}{x}","-\frac{\text{Li}_2(a x)}{x}+a \log (x)-a \log (1-a x)+\frac{\log (1-a x)}{x}",1,"a*Log[x] - a*Log[1 - a*x] + Log[1 - a*x]/x - PolyLog[2, a*x]/x","A",1
8,1,50,58,0.0227579,"\int \frac{\text{Li}_2(a x)}{x^3} \, dx","Integrate[PolyLog[2, a*x]/x^3,x]","\frac{a^2 x^2 \log (x)-a^2 x^2 \log (1-a x)-2 \text{Li}_2(a x)-a x+\log (1-a x)}{4 x^2}","\frac{1}{4} a^2 \log (x)-\frac{1}{4} a^2 \log (1-a x)-\frac{\text{Li}_2(a x)}{2 x^2}+\frac{\log (1-a x)}{4 x^2}-\frac{a}{4 x}",1,"(-(a*x) + a^2*x^2*Log[x] + Log[1 - a*x] - a^2*x^2*Log[1 - a*x] - 2*PolyLog[2, a*x])/(4*x^2)","A",1
9,1,52,68,0.0308813,"\int \frac{\text{Li}_2(a x)}{x^4} \, dx","Integrate[PolyLog[2, a*x]/x^4,x]","-\frac{-2 a^3 x^3 \log (x)+2 \left(a^3 x^3-1\right) \log (1-a x)+6 \text{Li}_2(a x)+a x (2 a x+1)}{18 x^3}","\frac{1}{9} a^3 \log (x)-\frac{1}{9} a^3 \log (1-a x)-\frac{a^2}{9 x}-\frac{\text{Li}_2(a x)}{3 x^3}+\frac{\log (1-a x)}{9 x^3}-\frac{a}{18 x^2}",1,"-1/18*(a*x*(1 + 2*a*x) - 2*a^3*x^3*Log[x] + 2*(-1 + a^3*x^3)*Log[1 - a*x] + 6*PolyLog[2, a*x])/x^3","A",1
10,1,60,78,0.0338723,"\int \frac{\text{Li}_2(a x)}{x^5} \, dx","Integrate[PolyLog[2, a*x]/x^5,x]","-\frac{-6 a^4 x^4 \log (x)+6 \left(a^4 x^4-1\right) \log (1-a x)+a x \left(6 a^2 x^2+3 a x+2\right)+24 \text{Li}_2(a x)}{96 x^4}","\frac{1}{16} a^4 \log (x)-\frac{1}{16} a^4 \log (1-a x)-\frac{a^3}{16 x}-\frac{a^2}{32 x^2}-\frac{\text{Li}_2(a x)}{4 x^4}+\frac{\log (1-a x)}{16 x^4}-\frac{a}{48 x^3}",1,"-1/96*(a*x*(2 + 3*a*x + 6*a^2*x^2) - 6*a^4*x^4*Log[x] + 6*(-1 + a^4*x^4)*Log[1 - a*x] + 24*PolyLog[2, a*x])/x^4","A",1
11,1,86,88,0.0116432,"\int x^3 \text{Li}_3(a x) \, dx","Integrate[x^3*PolyLog[3, a*x],x]","\frac{-48 a^4 x^4 \text{Li}_2(a x)+192 a^4 x^4 \text{Li}_3(a x)+3 a^4 x^4-12 a^4 x^4 \log (1-a x)+4 a^3 x^3+6 a^2 x^2+12 a x+12 \log (1-a x)}{768 a^4}","\frac{\log (1-a x)}{64 a^4}+\frac{x}{64 a^3}+\frac{x^2}{128 a^2}-\frac{1}{16} x^4 \text{Li}_2(a x)+\frac{1}{4} x^4 \text{Li}_3(a x)-\frac{1}{64} x^4 \log (1-a x)+\frac{x^3}{192 a}+\frac{x^4}{256}",1,"(12*a*x + 6*a^2*x^2 + 4*a^3*x^3 + 3*a^4*x^4 + 12*Log[1 - a*x] - 12*a^4*x^4*Log[1 - a*x] - 48*a^4*x^4*PolyLog[2, a*x] + 192*a^4*x^4*PolyLog[3, a*x])/(768*a^4)","A",1
12,1,78,78,0.0108296,"\int x^2 \text{Li}_3(a x) \, dx","Integrate[x^2*PolyLog[3, a*x],x]","\frac{-18 a^3 x^3 \text{Li}_2(a x)+54 a^3 x^3 \text{Li}_3(a x)+2 a^3 x^3-6 a^3 x^3 \log (1-a x)+3 a^2 x^2+6 a x+6 \log (1-a x)}{162 a^3}","\frac{\log (1-a x)}{27 a^3}+\frac{x}{27 a^2}-\frac{1}{9} x^3 \text{Li}_2(a x)+\frac{1}{3} x^3 \text{Li}_3(a x)-\frac{1}{27} x^3 \log (1-a x)+\frac{x^2}{54 a}+\frac{x^3}{81}",1,"(6*a*x + 3*a^2*x^2 + 2*a^3*x^3 + 6*Log[1 - a*x] - 6*a^3*x^3*Log[1 - a*x] - 18*a^3*x^3*PolyLog[2, a*x] + 54*a^3*x^3*PolyLog[3, a*x])/(162*a^3)","A",1
13,1,69,68,0.0091717,"\int x \text{Li}_3(a x) \, dx","Integrate[x*PolyLog[3, a*x],x]","\frac{-4 a^2 x^2 \text{Li}_2(a x)+8 a^2 x^2 \text{Li}_3(a x)+a^2 x^2-2 a^2 x^2 \log (1-a x)+2 a x+2 \log (1-a x)}{16 a^2}","\frac{\log (1-a x)}{8 a^2}-\frac{1}{4} x^2 \text{Li}_2(a x)+\frac{1}{2} x^2 \text{Li}_3(a x)-\frac{1}{8} x^2 \log (1-a x)+\frac{x}{8 a}+\frac{x^2}{16}",1,"(2*a*x + a^2*x^2 + 2*Log[1 - a*x] - 2*a^2*x^2*Log[1 - a*x] - 4*a^2*x^2*PolyLog[2, a*x] + 8*a^2*x^2*PolyLog[3, a*x])/(16*a^2)","A",1
14,1,39,34,0.0121507,"\int \text{Li}_3(a x) \, dx","Integrate[PolyLog[3, a*x],x]","x \left(-\text{Li}_2(a x)+\text{Li}_3(a x)+\frac{\log (1-a x)}{a x}-\log (1-a x)+1\right)","x (-\text{Li}_2(a x))+x \text{Li}_3(a x)+\frac{(1-a x) \log (1-a x)}{a}+x",1,"x*(1 - Log[1 - a*x] + Log[1 - a*x]/(a*x) - PolyLog[2, a*x] + PolyLog[3, a*x])","A",1
15,1,5,5,0.0012435,"\int \frac{\text{Li}_3(a x)}{x} \, dx","Integrate[PolyLog[3, a*x]/x,x]","\text{Li}_4(a x)","\text{Li}_4(a x)",1,"PolyLog[4, a*x]","A",1
16,1,44,46,0.103642,"\int \frac{\text{Li}_3(a x)}{x^2} \, dx","Integrate[PolyLog[3, a*x]/x^2,x]","-\frac{\text{Li}_2(a x)+\text{Li}_3(a x)-a x \log (-a x)+a x \log (1-a x)-\log (1-a x)}{x}","-\frac{\text{Li}_2(a x)}{x}-\frac{\text{Li}_3(a x)}{x}+a \log (x)-a \log (1-a x)+\frac{\log (1-a x)}{x}",1,"-((-(a*x*Log[-(a*x)]) - Log[1 - a*x] + a*x*Log[1 - a*x] + PolyLog[2, a*x] + PolyLog[3, a*x])/x)","A",1
17,1,25,70,0.008424,"\int \frac{\text{Li}_3(a x)}{x^3} \, dx","Integrate[PolyLog[3, a*x]/x^3,x]","\frac{G_{5,5}^{2,4}\left(-a x\left|\begin{array}{c} 1,1,1,1,3 \\ 1,2,0,0,0 \\\end{array}\right.\right)}{x^2}","\frac{1}{8} a^2 \log (x)-\frac{1}{8} a^2 \log (1-a x)-\frac{\text{Li}_2(a x)}{4 x^2}-\frac{\text{Li}_3(a x)}{2 x^2}+\frac{\log (1-a x)}{8 x^2}-\frac{a}{8 x}",1,"MeijerG[{{1, 1, 1, 1}, {3}}, {{1, 2}, {0, 0, 0}}, -(a*x)]/x^2","C",0
18,1,25,80,0.009447,"\int \frac{\text{Li}_3(a x)}{x^4} \, dx","Integrate[PolyLog[3, a*x]/x^4,x]","\frac{G_{5,5}^{2,4}\left(-a x\left|\begin{array}{c} 1,1,1,1,4 \\ 1,3,0,0,0 \\\end{array}\right.\right)}{x^3}","\frac{1}{27} a^3 \log (x)-\frac{1}{27} a^3 \log (1-a x)-\frac{a^2}{27 x}-\frac{\text{Li}_2(a x)}{9 x^3}-\frac{\text{Li}_3(a x)}{3 x^3}+\frac{\log (1-a x)}{27 x^3}-\frac{a}{54 x^2}",1,"MeijerG[{{1, 1, 1, 1}, {4}}, {{1, 3}, {0, 0, 0}}, -(a*x)]/x^3","C",0
19,1,65,74,0.0224186,"\int x^5 \text{Li}_2\left(a x^2\right) \, dx","Integrate[x^5*PolyLog[2, a*x^2],x]","\frac{18 a^3 x^6 \text{Li}_2\left(a x^2\right)+6 \left(a^3 x^6-1\right) \log \left(1-a x^2\right)-a x^2 \left(2 a^2 x^4+3 a x^2+6\right)}{108 a^3}","-\frac{\log \left(1-a x^2\right)}{18 a^3}-\frac{x^2}{18 a^2}+\frac{1}{6} x^6 \text{Li}_2\left(a x^2\right)-\frac{x^4}{36 a}+\frac{1}{18} x^6 \log \left(1-a x^2\right)-\frac{x^6}{54}",1,"(-(a*x^2*(6 + 3*a*x^2 + 2*a^2*x^4)) + 6*(-1 + a^3*x^6)*Log[1 - a*x^2] + 18*a^3*x^6*PolyLog[2, a*x^2])/(108*a^3)","A",1
20,1,56,64,0.0176597,"\int x^3 \text{Li}_2\left(a x^2\right) \, dx","Integrate[x^3*PolyLog[2, a*x^2],x]","\frac{4 a^2 x^4 \text{Li}_2\left(a x^2\right)+2 \left(a^2 x^4-1\right) \log \left(1-a x^2\right)-a x^2 \left(a x^2+2\right)}{16 a^2}","-\frac{\log \left(1-a x^2\right)}{8 a^2}+\frac{1}{4} x^4 \text{Li}_2\left(a x^2\right)-\frac{x^2}{8 a}+\frac{1}{8} x^4 \log \left(1-a x^2\right)-\frac{x^4}{16}",1,"(-(a*x^2*(2 + a*x^2)) + 2*(-1 + a^2*x^4)*Log[1 - a*x^2] + 4*a^2*x^4*PolyLog[2, a*x^2])/(16*a^2)","A",1
21,1,43,46,0.0085223,"\int x \text{Li}_2\left(a x^2\right) \, dx","Integrate[x*PolyLog[2, a*x^2],x]","\frac{a x^2 \text{Li}_2\left(a x^2\right)-a x^2+\left(a x^2-1\right) \log \left(1-a x^2\right)}{2 a}","\frac{1}{2} x^2 \text{Li}_2\left(a x^2\right)-\frac{\left(1-a x^2\right) \log \left(1-a x^2\right)}{2 a}-\frac{x^2}{2}",1,"(-(a*x^2) + (-1 + a*x^2)*Log[1 - a*x^2] + a*x^2*PolyLog[2, a*x^2])/(2*a)","A",1
22,1,11,11,0.0013014,"\int \frac{\text{Li}_2\left(a x^2\right)}{x} \, dx","Integrate[PolyLog[2, a*x^2]/x,x]","\frac{\text{Li}_3\left(a x^2\right)}{2}","\frac{\text{Li}_3\left(a x^2\right)}{2}",1,"PolyLog[3, a*x^2]/2","A",1
23,1,49,49,0.0128127,"\int \frac{\text{Li}_2\left(a x^2\right)}{x^3} \, dx","Integrate[PolyLog[2, a*x^2]/x^3,x]","-\frac{\text{Li}_2\left(a x^2\right)}{2 x^2}-\frac{1}{2} a \log \left(1-a x^2\right)+\frac{\log \left(1-a x^2\right)}{2 x^2}+a \log (x)","-\frac{\text{Li}_2\left(a x^2\right)}{2 x^2}-\frac{1}{2} a \log \left(1-a x^2\right)+\frac{\log \left(1-a x^2\right)}{2 x^2}+a \log (x)",1,"a*Log[x] - (a*Log[1 - a*x^2])/2 + Log[1 - a*x^2]/(2*x^2) - PolyLog[2, a*x^2]/(2*x^2)","A",1
24,1,51,64,0.0272379,"\int \frac{\text{Li}_2\left(a x^2\right)}{x^5} \, dx","Integrate[PolyLog[2, a*x^2]/x^5,x]","-\frac{-2 a^2 x^4 \log (x)+\left(a^2 x^4-1\right) \log \left(1-a x^2\right)+2 \text{Li}_2\left(a x^2\right)+a x^2}{8 x^4}","-\frac{1}{8} a^2 \log \left(1-a x^2\right)+\frac{1}{4} a^2 \log (x)-\frac{\text{Li}_2\left(a x^2\right)}{4 x^4}-\frac{a}{8 x^2}+\frac{\log \left(1-a x^2\right)}{8 x^4}",1,"-1/8*(a*x^2 - 2*a^2*x^4*Log[x] + (-1 + a^2*x^4)*Log[1 - a*x^2] + 2*PolyLog[2, a*x^2])/x^4","A",1
25,1,60,74,0.0305616,"\int \frac{\text{Li}_2\left(a x^2\right)}{x^7} \, dx","Integrate[PolyLog[2, a*x^2]/x^7,x]","-\frac{-4 a^3 x^6 \log (x)+2 \left(a^3 x^6-1\right) \log \left(1-a x^2\right)+6 \text{Li}_2\left(a x^2\right)+a x^2 \left(2 a x^2+1\right)}{36 x^6}","-\frac{1}{18} a^3 \log \left(1-a x^2\right)+\frac{1}{9} a^3 \log (x)-\frac{a^2}{18 x^2}-\frac{\text{Li}_2\left(a x^2\right)}{6 x^6}-\frac{a}{36 x^4}+\frac{\log \left(1-a x^2\right)}{18 x^6}",1,"-1/36*(a*x^2*(1 + 2*a*x^2) - 4*a^3*x^6*Log[x] + 2*(-1 + a^3*x^6)*Log[1 - a*x^2] + 6*PolyLog[2, a*x^2])/x^6","A",1
26,1,65,73,0.0692539,"\int x^4 \text{Li}_2\left(a x^2\right) \, dx","Integrate[x^4*PolyLog[2, a*x^2],x]","\frac{1}{375} \left(\frac{60 \tanh ^{-1}\left(\sqrt{a} x\right)}{a^{5/2}}-\frac{60 x}{a^2}+75 x^5 \text{Li}_2\left(a x^2\right)-\frac{20 x^3}{a}+30 x^5 \log \left(1-a x^2\right)-12 x^5\right)","\frac{4 \tanh ^{-1}\left(\sqrt{a} x\right)}{25 a^{5/2}}-\frac{4 x}{25 a^2}+\frac{1}{5} x^5 \text{Li}_2\left(a x^2\right)-\frac{4 x^3}{75 a}+\frac{2}{25} x^5 \log \left(1-a x^2\right)-\frac{4 x^5}{125}",1,"((-60*x)/a^2 - (20*x^3)/a - 12*x^5 + (60*ArcTanh[Sqrt[a]*x])/a^(5/2) + 30*x^5*Log[1 - a*x^2] + 75*x^5*PolyLog[2, a*x^2])/375","A",1
27,1,57,63,0.0515576,"\int x^2 \text{Li}_2\left(a x^2\right) \, dx","Integrate[x^2*PolyLog[2, a*x^2],x]","\frac{1}{27} \left(\frac{12 \tanh ^{-1}\left(\sqrt{a} x\right)}{a^{3/2}}+9 x^3 \text{Li}_2\left(a x^2\right)+6 x^3 \log \left(1-a x^2\right)-\frac{12 x}{a}-4 x^3\right)","\frac{4 \tanh ^{-1}\left(\sqrt{a} x\right)}{9 a^{3/2}}+\frac{1}{3} x^3 \text{Li}_2\left(a x^2\right)+\frac{2}{9} x^3 \log \left(1-a x^2\right)-\frac{4 x}{9 a}-\frac{4 x^3}{27}",1,"((-12*x)/a - 4*x^3 + (12*ArcTanh[Sqrt[a]*x])/a^(3/2) + 6*x^3*Log[1 - a*x^2] + 9*x^3*PolyLog[2, a*x^2])/27","A",1
28,1,39,40,0.0272489,"\int \text{Li}_2\left(a x^2\right) \, dx","Integrate[PolyLog[2, a*x^2],x]","x \text{Li}_2\left(a x^2\right)+2 x \left(\log \left(1-a x^2\right)-2\right)+\frac{4 \tanh ^{-1}\left(\sqrt{a} x\right)}{\sqrt{a}}","x \text{Li}_2\left(a x^2\right)+2 x \log \left(1-a x^2\right)+\frac{4 \tanh ^{-1}\left(\sqrt{a} x\right)}{\sqrt{a}}-4 x",1,"(4*ArcTanh[Sqrt[a]*x])/Sqrt[a] + 2*x*(-2 + Log[1 - a*x^2]) + x*PolyLog[2, a*x^2]","A",1
29,1,41,42,0.0167099,"\int \frac{\text{Li}_2\left(a x^2\right)}{x^2} \, dx","Integrate[PolyLog[2, a*x^2]/x^2,x]","\frac{-\text{Li}_2\left(a x^2\right)+2 \log \left(1-a x^2\right)+4 \sqrt{a} x \tanh ^{-1}\left(\sqrt{a} x\right)}{x}","-\frac{\text{Li}_2\left(a x^2\right)}{x}+\frac{2 \log \left(1-a x^2\right)}{x}+4 \sqrt{a} \tanh ^{-1}\left(\sqrt{a} x\right)",1,"(4*Sqrt[a]*x*ArcTanh[Sqrt[a]*x] + 2*Log[1 - a*x^2] - PolyLog[2, a*x^2])/x","A",1
30,1,47,56,0.0138488,"\int \frac{\text{Li}_2\left(a x^2\right)}{x^4} \, dx","Integrate[PolyLog[2, a*x^2]/x^4,x]","-\frac{4 a x^2 \, _2F_1\left(-\frac{1}{2},1;\frac{1}{2};a x^2\right)+3 \text{Li}_2\left(a x^2\right)-2 \log \left(1-a x^2\right)}{9 x^3}","\frac{4}{9} a^{3/2} \tanh ^{-1}\left(\sqrt{a} x\right)-\frac{\text{Li}_2\left(a x^2\right)}{3 x^3}+\frac{2 \log \left(1-a x^2\right)}{9 x^3}-\frac{4 a}{9 x}",1,"-1/9*(4*a*x^2*Hypergeometric2F1[-1/2, 1, 1/2, a*x^2] - 2*Log[1 - a*x^2] + 3*PolyLog[2, a*x^2])/x^3","C",1
31,1,47,66,0.0143899,"\int \frac{\text{Li}_2\left(a x^2\right)}{x^6} \, dx","Integrate[PolyLog[2, a*x^2]/x^6,x]","-\frac{4 a x^2 \, _2F_1\left(-\frac{3}{2},1;-\frac{1}{2};a x^2\right)+15 \text{Li}_2\left(a x^2\right)-6 \log \left(1-a x^2\right)}{75 x^5}","\frac{4}{25} a^{5/2} \tanh ^{-1}\left(\sqrt{a} x\right)-\frac{4 a^2}{25 x}-\frac{\text{Li}_2\left(a x^2\right)}{5 x^5}-\frac{4 a}{75 x^3}+\frac{2 \log \left(1-a x^2\right)}{25 x^5}",1,"-1/75*(4*a*x^2*Hypergeometric2F1[-3/2, 1, -1/2, a*x^2] - 6*Log[1 - a*x^2] + 15*PolyLog[2, a*x^2])/x^5","C",1
32,1,88,88,0.016891,"\int x^5 \text{Li}_3\left(a x^2\right) \, dx","Integrate[x^5*PolyLog[3, a*x^2],x]","\frac{-18 a^3 x^6 \text{Li}_2\left(a x^2\right)+54 a^3 x^6 \text{Li}_3\left(a x^2\right)+2 a^3 x^6-6 a^3 x^6 \log \left(1-a x^2\right)+3 a^2 x^4+6 a x^2+6 \log \left(1-a x^2\right)}{324 a^3}","\frac{\log \left(1-a x^2\right)}{54 a^3}+\frac{x^2}{54 a^2}-\frac{1}{18} x^6 \text{Li}_2\left(a x^2\right)+\frac{1}{6} x^6 \text{Li}_3\left(a x^2\right)+\frac{x^4}{108 a}-\frac{1}{54} x^6 \log \left(1-a x^2\right)+\frac{x^6}{162}",1,"(6*a*x^2 + 3*a^2*x^4 + 2*a^3*x^6 + 6*Log[1 - a*x^2] - 6*a^3*x^6*Log[1 - a*x^2] - 18*a^3*x^6*PolyLog[2, a*x^2] + 54*a^3*x^6*PolyLog[3, a*x^2])/(324*a^3)","A",1
33,1,79,78,0.0152387,"\int x^3 \text{Li}_3\left(a x^2\right) \, dx","Integrate[x^3*PolyLog[3, a*x^2],x]","\frac{-4 a^2 x^4 \text{Li}_2\left(a x^2\right)+8 a^2 x^4 \text{Li}_3\left(a x^2\right)+a^2 x^4-2 a^2 x^4 \log \left(1-a x^2\right)+2 a x^2+2 \log \left(1-a x^2\right)}{32 a^2}","\frac{\log \left(1-a x^2\right)}{16 a^2}-\frac{1}{8} x^4 \text{Li}_2\left(a x^2\right)+\frac{1}{4} x^4 \text{Li}_3\left(a x^2\right)+\frac{x^2}{16 a}-\frac{1}{16} x^4 \log \left(1-a x^2\right)+\frac{x^4}{32}",1,"(2*a*x^2 + a^2*x^4 + 2*Log[1 - a*x^2] - 2*a^2*x^4*Log[1 - a*x^2] - 4*a^2*x^4*PolyLog[2, a*x^2] + 8*a^2*x^4*PolyLog[3, a*x^2])/(32*a^2)","A",1
34,1,52,60,0.0110509,"\int x \text{Li}_3\left(a x^2\right) \, dx","Integrate[x*PolyLog[3, a*x^2],x]","\frac{1}{2} x^2 \left(-\text{Li}_2\left(a x^2\right)+\text{Li}_3\left(a x^2\right)+\frac{\log \left(1-a x^2\right)}{a x^2}-\log \left(1-a x^2\right)+1\right)","-\frac{1}{2} x^2 \text{Li}_2\left(a x^2\right)+\frac{1}{2} x^2 \text{Li}_3\left(a x^2\right)+\frac{\left(1-a x^2\right) \log \left(1-a x^2\right)}{2 a}+\frac{x^2}{2}",1,"(x^2*(1 - Log[1 - a*x^2] + Log[1 - a*x^2]/(a*x^2) - PolyLog[2, a*x^2] + PolyLog[3, a*x^2]))/2","A",1
35,1,11,11,0.0013696,"\int \frac{\text{Li}_3\left(a x^2\right)}{x} \, dx","Integrate[PolyLog[3, a*x^2]/x,x]","\frac{\text{Li}_4\left(a x^2\right)}{2}","\frac{\text{Li}_4\left(a x^2\right)}{2}",1,"PolyLog[4, a*x^2]/2","A",1
36,1,60,63,0.0276436,"\int \frac{\text{Li}_3\left(a x^2\right)}{x^3} \, dx","Integrate[PolyLog[3, a*x^2]/x^3,x]","-\frac{\text{Li}_2\left(a x^2\right)+\text{Li}_3\left(a x^2\right)-a x^2 \log \left(-a x^2\right)+a x^2 \log \left(1-a x^2\right)-\log \left(1-a x^2\right)}{2 x^2}","-\frac{\text{Li}_2\left(a x^2\right)}{2 x^2}-\frac{\text{Li}_3\left(a x^2\right)}{2 x^2}-\frac{1}{2} a \log \left(1-a x^2\right)+\frac{\log \left(1-a x^2\right)}{2 x^2}+a \log (x)",1,"-1/2*(-(a*x^2*Log[-(a*x^2)]) - Log[1 - a*x^2] + a*x^2*Log[1 - a*x^2] + PolyLog[2, a*x^2] + PolyLog[3, a*x^2])/x^2","A",1
37,1,30,78,0.011838,"\int \frac{\text{Li}_3\left(a x^2\right)}{x^5} \, dx","Integrate[PolyLog[3, a*x^2]/x^5,x]","\frac{G_{5,5}^{2,4}\left(-a x^2|\begin{array}{c} 1,1,1,1,3 \\ 1,2,0,0,0 \\\end{array}\right)}{2 x^4}","-\frac{1}{16} a^2 \log \left(1-a x^2\right)+\frac{1}{8} a^2 \log (x)-\frac{\text{Li}_2\left(a x^2\right)}{8 x^4}-\frac{\text{Li}_3\left(a x^2\right)}{4 x^4}-\frac{a}{16 x^2}+\frac{\log \left(1-a x^2\right)}{16 x^4}",1,"MeijerG[{{1, 1, 1, 1}, {3}}, {{1, 2}, {0, 0, 0}}, -(a*x^2)]/(2*x^4)","C",0
38,1,30,88,0.0117438,"\int \frac{\text{Li}_3\left(a x^2\right)}{x^7} \, dx","Integrate[PolyLog[3, a*x^2]/x^7,x]","\frac{G_{5,5}^{2,4}\left(-a x^2|\begin{array}{c} 1,1,1,1,4 \\ 1,3,0,0,0 \\\end{array}\right)}{2 x^6}","-\frac{1}{54} a^3 \log \left(1-a x^2\right)+\frac{1}{27} a^3 \log (x)-\frac{a^2}{54 x^2}-\frac{\text{Li}_2\left(a x^2\right)}{18 x^6}-\frac{\text{Li}_3\left(a x^2\right)}{6 x^6}-\frac{a}{108 x^4}+\frac{\log \left(1-a x^2\right)}{54 x^6}",1,"MeijerG[{{1, 1, 1, 1}, {4}}, {{1, 3}, {0, 0, 0}}, -(a*x^2)]/(2*x^6)","C",0
39,1,77,87,0.1549847,"\int x^4 \text{Li}_3\left(a x^2\right) \, dx","Integrate[x^4*PolyLog[3, a*x^2],x]","\frac{-\frac{120 \tanh ^{-1}\left(\sqrt{a} x\right)}{a^{5/2}}+\frac{120 x}{a^2}-150 x^5 \text{Li}_2\left(a x^2\right)+375 x^5 \text{Li}_3\left(a x^2\right)+\frac{40 x^3}{a}-60 x^5 \log \left(1-a x^2\right)+24 x^5}{1875}","-\frac{8 \tanh ^{-1}\left(\sqrt{a} x\right)}{125 a^{5/2}}+\frac{8 x}{125 a^2}-\frac{2}{25} x^5 \text{Li}_2\left(a x^2\right)+\frac{1}{5} x^5 \text{Li}_3\left(a x^2\right)+\frac{8 x^3}{375 a}-\frac{4}{125} x^5 \log \left(1-a x^2\right)+\frac{8 x^5}{625}",1,"((120*x)/a^2 + (40*x^3)/a + 24*x^5 - (120*ArcTanh[Sqrt[a]*x])/a^(5/2) - 60*x^5*Log[1 - a*x^2] - 150*x^5*PolyLog[2, a*x^2] + 375*x^5*PolyLog[3, a*x^2])/1875","A",1
40,1,69,77,0.1302058,"\int x^2 \text{Li}_3\left(a x^2\right) \, dx","Integrate[x^2*PolyLog[3, a*x^2],x]","\frac{1}{81} \left(-\frac{24 \tanh ^{-1}\left(\sqrt{a} x\right)}{a^{3/2}}-18 x^3 \text{Li}_2\left(a x^2\right)+27 x^3 \text{Li}_3\left(a x^2\right)-12 x^3 \log \left(1-a x^2\right)+\frac{24 x}{a}+8 x^3\right)","-\frac{8 \tanh ^{-1}\left(\sqrt{a} x\right)}{27 a^{3/2}}-\frac{2}{9} x^3 \text{Li}_2\left(a x^2\right)+\frac{1}{3} x^3 \text{Li}_3\left(a x^2\right)-\frac{4}{27} x^3 \log \left(1-a x^2\right)+\frac{8 x}{27 a}+\frac{8 x^3}{81}",1,"((24*x)/a + 8*x^3 - (24*ArcTanh[Sqrt[a]*x])/a^(3/2) - 12*x^3*Log[1 - a*x^2] - 18*x^3*PolyLog[2, a*x^2] + 27*x^3*PolyLog[3, a*x^2])/81","A",1
41,1,50,50,0.0833828,"\int \text{Li}_3\left(a x^2\right) \, dx","Integrate[PolyLog[3, a*x^2],x]","-2 x \text{Li}_2\left(a x^2\right)+x \text{Li}_3\left(a x^2\right)-4 x \log \left(1-a x^2\right)-\frac{8 \tanh ^{-1}\left(\sqrt{a} x\right)}{\sqrt{a}}+8 x","-2 x \text{Li}_2\left(a x^2\right)+x \text{Li}_3\left(a x^2\right)-4 x \log \left(1-a x^2\right)-\frac{8 \tanh ^{-1}\left(\sqrt{a} x\right)}{\sqrt{a}}+8 x",1,"8*x - (8*ArcTanh[Sqrt[a]*x])/Sqrt[a] - 4*x*Log[1 - a*x^2] - 2*x*PolyLog[2, a*x^2] + x*PolyLog[3, a*x^2]","A",1
42,1,50,54,0.0774248,"\int \frac{\text{Li}_3\left(a x^2\right)}{x^2} \, dx","Integrate[PolyLog[3, a*x^2]/x^2,x]","\frac{-2 \text{Li}_2\left(a x^2\right)-\text{Li}_3\left(a x^2\right)+4 \log \left(1-a x^2\right)+8 \sqrt{a} x \tanh ^{-1}\left(\sqrt{a} x\right)}{x}","-\frac{2 \text{Li}_2\left(a x^2\right)}{x}-\frac{\text{Li}_3\left(a x^2\right)}{x}+\frac{4 \log \left(1-a x^2\right)}{x}+8 \sqrt{a} \tanh ^{-1}\left(\sqrt{a} x\right)",1,"(8*Sqrt[a]*x*ArcTanh[Sqrt[a]*x] + 4*Log[1 - a*x^2] - 2*PolyLog[2, a*x^2] - PolyLog[3, a*x^2])/x","A",1
43,1,61,70,0.0830897,"\int \frac{\text{Li}_3\left(a x^2\right)}{x^4} \, dx","Integrate[PolyLog[3, a*x^2]/x^4,x]","-\frac{-8 a^{3/2} x^3 \tanh ^{-1}\left(\sqrt{a} x\right)+6 \text{Li}_2\left(a x^2\right)+9 \text{Li}_3\left(a x^2\right)+8 a x^2-4 \log \left(1-a x^2\right)}{27 x^3}","\frac{8}{27} a^{3/2} \tanh ^{-1}\left(\sqrt{a} x\right)-\frac{2 \text{Li}_2\left(a x^2\right)}{9 x^3}-\frac{\text{Li}_3\left(a x^2\right)}{3 x^3}+\frac{4 \log \left(1-a x^2\right)}{27 x^3}-\frac{8 a}{27 x}",1,"-1/27*(8*a*x^2 - 8*a^(3/2)*x^3*ArcTanh[Sqrt[a]*x] - 4*Log[1 - a*x^2] + 6*PolyLog[2, a*x^2] + 9*PolyLog[3, a*x^2])/x^3","A",1
44,1,69,80,0.0952461,"\int \frac{\text{Li}_3\left(a x^2\right)}{x^6} \, dx","Integrate[PolyLog[3, a*x^2]/x^6,x]","-\frac{-24 a^{5/2} x^5 \tanh ^{-1}\left(\sqrt{a} x\right)+24 a^2 x^4+30 \text{Li}_2\left(a x^2\right)+75 \text{Li}_3\left(a x^2\right)+8 a x^2-12 \log \left(1-a x^2\right)}{375 x^5}","\frac{8}{125} a^{5/2} \tanh ^{-1}\left(\sqrt{a} x\right)-\frac{8 a^2}{125 x}-\frac{2 \text{Li}_2\left(a x^2\right)}{25 x^5}-\frac{\text{Li}_3\left(a x^2\right)}{5 x^5}-\frac{8 a}{375 x^3}+\frac{4 \log \left(1-a x^2\right)}{125 x^5}",1,"-1/375*(8*a*x^2 + 24*a^2*x^4 - 24*a^(5/2)*x^5*ArcTanh[Sqrt[a]*x] - 12*Log[1 - a*x^2] + 30*PolyLog[2, a*x^2] + 75*PolyLog[3, a*x^2])/x^5","A",1
45,1,69,71,0.0430711,"\int x^2 \text{Li}_2\left(a x^q\right) \, dx","Integrate[x^2*PolyLog[2, a*x^q],x]","\frac{q x^3 \left(a q x^q \, _2F_1\left(1,\frac{q+3}{q};2+\frac{3}{q};a x^q\right)+(q+3) \log \left(1-a x^q\right)\right)}{9 (q+3)}+\frac{1}{3} x^3 \text{Li}_2\left(a x^q\right)","\frac{a q^2 x^{q+3} \, _2F_1\left(1,\frac{q+3}{q};2+\frac{3}{q};a x^q\right)}{9 (q+3)}+\frac{1}{3} x^3 \text{Li}_2\left(a x^q\right)+\frac{1}{9} q x^3 \log \left(1-a x^q\right)",1,"(q*x^3*(a*q*x^q*Hypergeometric2F1[1, (3 + q)/q, 2 + 3/q, a*x^q] + (3 + q)*Log[1 - a*x^q]))/(9*(3 + q)) + (x^3*PolyLog[2, a*x^q])/3","A",1
46,1,69,71,0.03745,"\int x \text{Li}_2\left(a x^q\right) \, dx","Integrate[x*PolyLog[2, a*x^q],x]","\frac{q x^2 \left(a q x^q \, _2F_1\left(1,\frac{q+2}{q};2+\frac{2}{q};a x^q\right)+(q+2) \log \left(1-a x^q\right)\right)}{4 (q+2)}+\frac{1}{2} x^2 \text{Li}_2\left(a x^q\right)","\frac{a q^2 x^{q+2} \, _2F_1\left(1,\frac{q+2}{q};2 \left(1+\frac{1}{q}\right);a x^q\right)}{4 (q+2)}+\frac{1}{2} x^2 \text{Li}_2\left(a x^q\right)+\frac{1}{4} q x^2 \log \left(1-a x^q\right)",1,"(q*x^2*(a*q*x^q*Hypergeometric2F1[1, (2 + q)/q, 2 + 2/q, a*x^q] + (2 + q)*Log[1 - a*x^q]))/(4*(2 + q)) + (x^2*PolyLog[2, a*x^q])/2","A",1
47,1,51,54,0.0444794,"\int \text{Li}_2\left(a x^q\right) \, dx","Integrate[PolyLog[2, a*x^q],x]","q x \left(\frac{a q x^q \, _2F_1\left(1,1+\frac{1}{q};2+\frac{1}{q};a x^q\right)}{q+1}+\log \left(1-a x^q\right)\right)+x \text{Li}_2\left(a x^q\right)","\frac{a q^2 x^{q+1} \, _2F_1\left(1,1+\frac{1}{q};2+\frac{1}{q};a x^q\right)}{q+1}+x \text{Li}_2\left(a x^q\right)+q x \log \left(1-a x^q\right)",1,"q*x*((a*q*x^q*Hypergeometric2F1[1, 1 + q^(-1), 2 + q^(-1), a*x^q])/(1 + q) + Log[1 - a*x^q]) + x*PolyLog[2, a*x^q]","A",1
48,1,11,11,0.0013647,"\int \frac{\text{Li}_2\left(a x^q\right)}{x} \, dx","Integrate[PolyLog[2, a*x^q]/x,x]","\frac{\text{Li}_3\left(a x^q\right)}{q}","\frac{\text{Li}_3\left(a x^q\right)}{q}",1,"PolyLog[3, a*x^q]/q","A",1
49,1,60,69,0.054303,"\int \frac{\text{Li}_2\left(a x^q\right)}{x^2} \, dx","Integrate[PolyLog[2, a*x^q]/x^2,x]","\frac{q \left(\frac{a q x^q \, _2F_1\left(1,\frac{q-1}{q};2-\frac{1}{q};a x^q\right)}{q-1}+\log \left(1-a x^q\right)\right)}{x}-\frac{\text{Li}_2\left(a x^q\right)}{x}","-\frac{a q^2 x^{q-1} \, _2F_1\left(1,-\frac{1-q}{q};2-\frac{1}{q};a x^q\right)}{1-q}-\frac{\text{Li}_2\left(a x^q\right)}{x}+\frac{q \log \left(1-a x^q\right)}{x}",1,"(q*((a*q*x^q*Hypergeometric2F1[1, (-1 + q)/q, 2 - q^(-1), a*x^q])/(-1 + q) + Log[1 - a*x^q]))/x - PolyLog[2, a*x^q]/x","A",1
50,1,61,78,0.050185,"\int \frac{\text{Li}_2\left(a x^q\right)}{x^3} \, dx","Integrate[PolyLog[2, a*x^q]/x^3,x]","\frac{q \left(\frac{a q x^q \, _2F_1\left(1,\frac{q-2}{q};2-\frac{2}{q};a x^q\right)}{q-2}+\log \left(1-a x^q\right)\right)-2 \text{Li}_2\left(a x^q\right)}{4 x^2}","-\frac{a q^2 x^{q-2} \, _2F_1\left(1,-\frac{2-q}{q};2 \left(1-\frac{1}{q}\right);a x^q\right)}{4 (2-q)}-\frac{\text{Li}_2\left(a x^q\right)}{2 x^2}+\frac{q \log \left(1-a x^q\right)}{4 x^2}",1,"(q*((a*q*x^q*Hypergeometric2F1[1, (-2 + q)/q, 2 - 2/q, a*x^q])/(-2 + q) + Log[1 - a*x^q]) - 2*PolyLog[2, a*x^q])/(4*x^2)","A",1
51,1,61,76,0.0516831,"\int \frac{\text{Li}_2\left(a x^q\right)}{x^4} \, dx","Integrate[PolyLog[2, a*x^q]/x^4,x]","\frac{q \left(\frac{a q x^q \, _2F_1\left(1,\frac{q-3}{q};2-\frac{3}{q};a x^q\right)}{q-3}+\log \left(1-a x^q\right)\right)-3 \text{Li}_2\left(a x^q\right)}{9 x^3}","-\frac{a q^2 x^{q-3} \, _2F_1\left(1,-\frac{3-q}{q};2-\frac{3}{q};a x^q\right)}{9 (3-q)}-\frac{\text{Li}_2\left(a x^q\right)}{3 x^3}+\frac{q \log \left(1-a x^q\right)}{9 x^3}",1,"(q*((a*q*x^q*Hypergeometric2F1[1, (-3 + q)/q, 2 - 3/q, a*x^q])/(-3 + q) + Log[1 - a*x^q]) - 3*PolyLog[2, a*x^q])/(9*x^3)","A",1
52,1,41,88,0.008888,"\int x^2 \text{Li}_3\left(a x^q\right) \, dx","Integrate[x^2*PolyLog[3, a*x^q],x]","-\frac{x^3 G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,\frac{q-3}{q} \\ 1,0,0,0,-\frac{3}{q} \\\end{array}\right)}{q}","-\frac{a q^3 x^{q+3} \, _2F_1\left(1,\frac{q+3}{q};2+\frac{3}{q};a x^q\right)}{27 (q+3)}-\frac{1}{9} q x^3 \text{Li}_2\left(a x^q\right)+\frac{1}{3} x^3 \text{Li}_3\left(a x^q\right)-\frac{1}{27} q^2 x^3 \log \left(1-a x^q\right)",1,"-((x^3*MeijerG[{{1, 1, 1, 1, (-3 + q)/q}, {}}, {{1}, {0, 0, 0, -3/q}}, -(a*x^q)])/q)","C",0
53,1,41,88,0.0072881,"\int x \text{Li}_3\left(a x^q\right) \, dx","Integrate[x*PolyLog[3, a*x^q],x]","-\frac{x^2 G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,\frac{q-2}{q} \\ 1,0,0,0,-\frac{2}{q} \\\end{array}\right)}{q}","-\frac{a q^3 x^{q+2} \, _2F_1\left(1,\frac{q+2}{q};2 \left(1+\frac{1}{q}\right);a x^q\right)}{8 (q+2)}-\frac{1}{4} q x^2 \text{Li}_2\left(a x^q\right)+\frac{1}{2} x^2 \text{Li}_3\left(a x^q\right)-\frac{1}{8} q^2 x^2 \log \left(1-a x^q\right)",1,"-((x^2*MeijerG[{{1, 1, 1, 1, (-2 + q)/q}, {}}, {{1}, {0, 0, 0, -2/q}}, -(a*x^q)])/q)","C",0
54,1,39,69,0.0056708,"\int \text{Li}_3\left(a x^q\right) \, dx","Integrate[PolyLog[3, a*x^q],x]","-\frac{x G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,\frac{q-1}{q} \\ 1,0,0,0,-\frac{1}{q} \\\end{array}\right)}{q}","-\frac{a q^3 x^{q+1} \, _2F_1\left(1,1+\frac{1}{q};2+\frac{1}{q};a x^q\right)}{q+1}-q x \text{Li}_2\left(a x^q\right)+x \text{Li}_3\left(a x^q\right)-q^2 x \log \left(1-a x^q\right)",1,"-((x*MeijerG[{{1, 1, 1, 1, (-1 + q)/q}, {}}, {{1}, {0, 0, 0, -q^(-1)}}, -(a*x^q)])/q)","C",0
55,1,11,11,0.0013045,"\int \frac{\text{Li}_3\left(a x^q\right)}{x} \, dx","Integrate[PolyLog[3, a*x^q]/x,x]","\frac{\text{Li}_4\left(a x^q\right)}{q}","\frac{\text{Li}_4\left(a x^q\right)}{q}",1,"PolyLog[4, a*x^q]/q","A",1
56,1,37,84,0.0085727,"\int \frac{\text{Li}_3\left(a x^q\right)}{x^2} \, dx","Integrate[PolyLog[3, a*x^q]/x^2,x]","-\frac{G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,1+\frac{1}{q} \\ 1,0,0,0,\frac{1}{q} \\\end{array}\right)}{q x}","-\frac{a q^3 x^{q-1} \, _2F_1\left(1,-\frac{1-q}{q};2-\frac{1}{q};a x^q\right)}{1-q}-\frac{q \text{Li}_2\left(a x^q\right)}{x}-\frac{\text{Li}_3\left(a x^q\right)}{x}+\frac{q^2 \log \left(1-a x^q\right)}{x}",1,"-(MeijerG[{{1, 1, 1, 1, 1 + q^(-1)}, {}}, {{1}, {0, 0, 0, q^(-1)}}, -(a*x^q)]/(q*x))","C",0
57,1,41,95,0.0087039,"\int \frac{\text{Li}_3\left(a x^q\right)}{x^3} \, dx","Integrate[PolyLog[3, a*x^q]/x^3,x]","-\frac{G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,\frac{q+2}{q} \\ 1,0,0,0,\frac{2}{q} \\\end{array}\right)}{q x^2}","-\frac{a q^3 x^{q-2} \, _2F_1\left(1,-\frac{2-q}{q};2 \left(1-\frac{1}{q}\right);a x^q\right)}{8 (2-q)}-\frac{q \text{Li}_2\left(a x^q\right)}{4 x^2}-\frac{\text{Li}_3\left(a x^q\right)}{2 x^2}+\frac{q^2 \log \left(1-a x^q\right)}{8 x^2}",1,"-(MeijerG[{{1, 1, 1, 1, (2 + q)/q}, {}}, {{1}, {0, 0, 0, 2/q}}, -(a*x^q)]/(q*x^2))","C",0
58,1,41,93,0.0088699,"\int \frac{\text{Li}_3\left(a x^q\right)}{x^4} \, dx","Integrate[PolyLog[3, a*x^q]/x^4,x]","-\frac{G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,\frac{q+3}{q} \\ 1,0,0,0,\frac{3}{q} \\\end{array}\right)}{q x^3}","-\frac{a q^3 x^{q-3} \, _2F_1\left(1,-\frac{3-q}{q};2-\frac{3}{q};a x^q\right)}{27 (3-q)}-\frac{q \text{Li}_2\left(a x^q\right)}{9 x^3}-\frac{\text{Li}_3\left(a x^q\right)}{3 x^3}+\frac{q^2 \log \left(1-a x^q\right)}{27 x^3}",1,"-(MeijerG[{{1, 1, 1, 1, (3 + q)/q}, {}}, {{1}, {0, 0, 0, 3/q}}, -(a*x^q)]/(q*x^3))","C",0
59,1,90,117,0.1019524,"\int (d x)^{3/2} \text{Li}_2(a x) \, dx","Integrate[(d*x)^(3/2)*PolyLog[2, a*x],x]","\frac{2 (d x)^{3/2} \left(\frac{4 \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{5 a^{5/2}}+\frac{2}{75} \sqrt{x} \left(15 x^2 \log (1-a x)-\frac{2 \left(3 a^2 x^2+5 a x+15\right)}{a^2}\right)+x^{5/2} \text{Li}_2(a x)\right)}{5 x^{3/2}}","\frac{8 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{25 a^{5/2}}-\frac{8 d \sqrt{d x}}{25 a^2}+\frac{2 (d x)^{5/2} \text{Li}_2(a x)}{5 d}-\frac{8 (d x)^{3/2}}{75 a}+\frac{4 (d x)^{5/2} \log (1-a x)}{25 d}-\frac{8 (d x)^{5/2}}{125 d}",1,"(2*(d*x)^(3/2)*((4*ArcTanh[Sqrt[a]*Sqrt[x]])/(5*a^(5/2)) + (2*Sqrt[x]*((-2*(15 + 5*a*x + 3*a^2*x^2))/a^2 + 15*x^2*Log[1 - a*x]))/75 + x^(5/2)*PolyLog[2, a*x]))/(5*x^(3/2))","A",1
60,1,75,102,0.0797329,"\int \sqrt{d x} \text{Li}_2(a x) \, dx","Integrate[Sqrt[d*x]*PolyLog[2, a*x],x]","\frac{2 \sqrt{d x} \left(\frac{12 \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{3/2}}+9 x^{3/2} \text{Li}_2(a x)+\frac{2 \sqrt{x} (-2 a x+3 a x \log (1-a x)-6)}{a}\right)}{27 \sqrt{x}}","\frac{8 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{9 a^{3/2}}+\frac{2 (d x)^{3/2} \text{Li}_2(a x)}{3 d}-\frac{8 \sqrt{d x}}{9 a}+\frac{4 (d x)^{3/2} \log (1-a x)}{9 d}-\frac{8 (d x)^{3/2}}{27 d}",1,"(2*Sqrt[d*x]*((12*ArcTanh[Sqrt[a]*Sqrt[x]])/a^(3/2) + (2*Sqrt[x]*(-6 - 2*a*x + 3*a*x*Log[1 - a*x]))/a + 9*x^(3/2)*PolyLog[2, a*x]))/(27*Sqrt[x])","A",1
61,1,63,80,0.0749481,"\int \frac{\text{Li}_2(a x)}{\sqrt{d x}} \, dx","Integrate[PolyLog[2, a*x]/Sqrt[d*x],x]","\frac{2 \sqrt{a} x \text{Li}_2(a x)+4 \sqrt{a} x (\log (1-a x)-2)+8 \sqrt{x} \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a} \sqrt{d x}}","\frac{2 \sqrt{d x} \text{Li}_2(a x)}{d}+\frac{4 \sqrt{d x} \log (1-a x)}{d}+\frac{8 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt{a} \sqrt{d}}-\frac{8 \sqrt{d x}}{d}",1,"(8*Sqrt[x]*ArcTanh[Sqrt[a]*Sqrt[x]] + 4*Sqrt[a]*x*(-2 + Log[1 - a*x]) + 2*Sqrt[a]*x*PolyLog[2, a*x])/(Sqrt[a]*Sqrt[d*x])","A",1
62,1,51,68,0.0668332,"\int \frac{\text{Li}_2(a x)}{(d x)^{3/2}} \, dx","Integrate[PolyLog[2, a*x]/(d*x)^(3/2),x]","\frac{2 x \left(-\text{Li}_2(a x)+2 \log (1-a x)+4 \sqrt{a} \sqrt{x} \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{(d x)^{3/2}}","\frac{8 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \text{Li}_2(a x)}{d \sqrt{d x}}+\frac{4 \log (1-a x)}{d \sqrt{d x}}",1,"(2*x*(4*Sqrt[a]*Sqrt[x]*ArcTanh[Sqrt[a]*Sqrt[x]] + 2*Log[1 - a*x] - PolyLog[2, a*x]))/(d*x)^(3/2)","A",1
63,1,57,89,0.0723564,"\int \frac{\text{Li}_2(a x)}{(d x)^{5/2}} \, dx","Integrate[PolyLog[2, a*x]/(d*x)^(5/2),x]","-\frac{2 x \left(-4 a^{3/2} x^{3/2} \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+3 \text{Li}_2(a x)+4 a x-2 \log (1-a x)\right)}{9 (d x)^{5/2}}","\frac{8 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{9 d^{5/2}}-\frac{8 a}{9 d^2 \sqrt{d x}}-\frac{2 \text{Li}_2(a x)}{3 d (d x)^{3/2}}+\frac{4 \log (1-a x)}{9 d (d x)^{3/2}}",1,"(-2*x*(4*a*x - 4*a^(3/2)*x^(3/2)*ArcTanh[Sqrt[a]*Sqrt[x]] - 2*Log[1 - a*x] + 3*PolyLog[2, a*x]))/(9*(d*x)^(5/2))","A",1
64,1,65,106,0.089451,"\int \frac{\text{Li}_2(a x)}{(d x)^{7/2}} \, dx","Integrate[PolyLog[2, a*x]/(d*x)^(7/2),x]","-\frac{2 x \left(-12 a^{5/2} x^{5/2} \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+12 a^2 x^2+15 \text{Li}_2(a x)+4 a x-6 \log (1-a x)\right)}{75 (d x)^{7/2}}","\frac{8 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{25 d^{7/2}}-\frac{8 a^2}{25 d^3 \sqrt{d x}}-\frac{8 a}{75 d^2 (d x)^{3/2}}-\frac{2 \text{Li}_2(a x)}{5 d (d x)^{5/2}}+\frac{4 \log (1-a x)}{25 d (d x)^{5/2}}",1,"(-2*x*(4*a*x + 12*a^2*x^2 - 12*a^(5/2)*x^(5/2)*ArcTanh[Sqrt[a]*Sqrt[x]] - 6*Log[1 - a*x] + 15*PolyLog[2, a*x]))/(75*(d*x)^(7/2))","A",1
65,1,98,153,0.2543264,"\int (d x)^{5/2} \text{Li}_3(a x) \, dx","Integrate[(d*x)^(5/2)*PolyLog[3, a*x],x]","\frac{2 (d x)^{5/2} \left(-\frac{840 \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{7/2} \sqrt{x}}+\frac{8 \left(15 a^3 x^3+21 a^2 x^2+35 a x+105\right)}{a^3}-1470 x^3 \text{Li}_2(a x)+5145 x^3 \text{Li}_3(a x)-420 x^3 \log (1-a x)\right)}{36015 x^2}","-\frac{16 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{343 a^{7/2}}+\frac{16 d^2 \sqrt{d x}}{343 a^3}+\frac{16 d (d x)^{3/2}}{1029 a^2}-\frac{4 (d x)^{7/2} \text{Li}_2(a x)}{49 d}+\frac{2 (d x)^{7/2} \text{Li}_3(a x)}{7 d}+\frac{16 (d x)^{5/2}}{1715 a}-\frac{8 (d x)^{7/2} \log (1-a x)}{343 d}+\frac{16 (d x)^{7/2}}{2401 d}",1,"(2*(d*x)^(5/2)*((8*(105 + 35*a*x + 21*a^2*x^2 + 15*a^3*x^3))/a^3 - (840*ArcTanh[Sqrt[a]*Sqrt[x]])/(a^(7/2)*Sqrt[x]) - 420*x^3*Log[1 - a*x] - 1470*x^3*PolyLog[2, a*x] + 5145*x^3*PolyLog[3, a*x]))/(36015*x^2)","A",1
66,1,88,136,0.2083479,"\int (d x)^{3/2} \text{Li}_3(a x) \, dx","Integrate[(d*x)^(3/2)*PolyLog[3, a*x],x]","\frac{2 d \sqrt{d x} \left(4 \left(-\frac{30 \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{5/2} \sqrt{x}}+\frac{30}{a^2}-15 x^2 \log (1-a x)+\frac{10 x}{a}+6 x^2\right)-150 x^2 \text{Li}_2(a x)+375 x^2 \text{Li}_3(a x)\right)}{1875}","-\frac{16 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{125 a^{5/2}}+\frac{16 d \sqrt{d x}}{125 a^2}-\frac{4 (d x)^{5/2} \text{Li}_2(a x)}{25 d}+\frac{2 (d x)^{5/2} \text{Li}_3(a x)}{5 d}+\frac{16 (d x)^{3/2}}{375 a}-\frac{8 (d x)^{5/2} \log (1-a x)}{125 d}+\frac{16 (d x)^{5/2}}{625 d}",1,"(2*d*Sqrt[d*x]*(4*(30/a^2 + (10*x)/a + 6*x^2 - (30*ArcTanh[Sqrt[a]*Sqrt[x]])/(a^(5/2)*Sqrt[x]) - 15*x^2*Log[1 - a*x]) - 150*x^2*PolyLog[2, a*x] + 375*x^2*PolyLog[3, a*x]))/1875","A",1
67,1,73,121,0.1810159,"\int \sqrt{d x} \text{Li}_3(a x) \, dx","Integrate[Sqrt[d*x]*PolyLog[3, a*x],x]","\frac{2}{81} \sqrt{d x} \left(4 \left(-\frac{6 \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{a^{3/2} \sqrt{x}}-3 x \log (1-a x)+\frac{6}{a}+2 x\right)-18 x \text{Li}_2(a x)+27 x \text{Li}_3(a x)\right)","-\frac{16 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{27 a^{3/2}}-\frac{4 (d x)^{3/2} \text{Li}_2(a x)}{9 d}+\frac{2 (d x)^{3/2} \text{Li}_3(a x)}{3 d}+\frac{16 \sqrt{d x}}{27 a}-\frac{8 (d x)^{3/2} \log (1-a x)}{27 d}+\frac{16 (d x)^{3/2}}{81 d}",1,"(2*Sqrt[d*x]*(4*(6/a + 2*x - (6*ArcTanh[Sqrt[a]*Sqrt[x]])/(a^(3/2)*Sqrt[x]) - 3*x*Log[1 - a*x]) - 18*x*PolyLog[2, a*x] + 27*x*PolyLog[3, a*x]))/81","A",1
68,1,57,97,0.1331336,"\int \frac{\text{Li}_3(a x)}{\sqrt{d x}} \, dx","Integrate[PolyLog[3, a*x]/Sqrt[d*x],x]","\frac{2 x \left(-2 \text{Li}_2(a x)+\text{Li}_3(a x)-4 \log (1-a x)-\frac{8 \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)}{\sqrt{a} \sqrt{x}}+8\right)}{\sqrt{d x}}","-\frac{4 \sqrt{d x} \text{Li}_2(a x)}{d}+\frac{2 \sqrt{d x} \text{Li}_3(a x)}{d}-\frac{8 \sqrt{d x} \log (1-a x)}{d}-\frac{16 \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt{a} \sqrt{d}}+\frac{16 \sqrt{d x}}{d}",1,"(2*x*(8 - (8*ArcTanh[Sqrt[a]*Sqrt[x]])/(Sqrt[a]*Sqrt[x]) - 4*Log[1 - a*x] - 2*PolyLog[2, a*x] + PolyLog[3, a*x]))/Sqrt[d*x]","A",1
69,1,58,85,0.0959492,"\int \frac{\text{Li}_3(a x)}{(d x)^{3/2}} \, dx","Integrate[PolyLog[3, a*x]/(d*x)^(3/2),x]","\frac{2 x \left(-2 \text{Li}_2(a x)-\text{Li}_3(a x)+4 \log (1-a x)+8 \sqrt{a} \sqrt{x} \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)\right)}{(d x)^{3/2}}","\frac{16 \sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{4 \text{Li}_2(a x)}{d \sqrt{d x}}-\frac{2 \text{Li}_3(a x)}{d \sqrt{d x}}+\frac{8 \log (1-a x)}{d \sqrt{d x}}",1,"(2*x*(8*Sqrt[a]*Sqrt[x]*ArcTanh[Sqrt[a]*Sqrt[x]] + 4*Log[1 - a*x] - 2*PolyLog[2, a*x] - PolyLog[3, a*x]))/(d*x)^(3/2)","A",1
70,1,64,108,0.0912277,"\int \frac{\text{Li}_3(a x)}{(d x)^{5/2}} \, dx","Integrate[PolyLog[3, a*x]/(d*x)^(5/2),x]","-\frac{2 x \left(-8 a^{3/2} x^{3/2} \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+6 \text{Li}_2(a x)+9 \text{Li}_3(a x)+8 a x-4 \log (1-a x)\right)}{27 (d x)^{5/2}}","\frac{16 a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{27 d^{5/2}}-\frac{16 a}{27 d^2 \sqrt{d x}}-\frac{4 \text{Li}_2(a x)}{9 d (d x)^{3/2}}-\frac{2 \text{Li}_3(a x)}{3 d (d x)^{3/2}}+\frac{8 \log (1-a x)}{27 d (d x)^{3/2}}",1,"(-2*x*(8*a*x - 8*a^(3/2)*x^(3/2)*ArcTanh[Sqrt[a]*Sqrt[x]] - 4*Log[1 - a*x] + 6*PolyLog[2, a*x] + 9*PolyLog[3, a*x]))/(27*(d*x)^(5/2))","A",1
71,1,72,125,0.1265087,"\int \frac{\text{Li}_3(a x)}{(d x)^{7/2}} \, dx","Integrate[PolyLog[3, a*x]/(d*x)^(7/2),x]","-\frac{2 x \left(-24 a^{5/2} x^{5/2} \tanh ^{-1}\left(\sqrt{a} \sqrt{x}\right)+24 a^2 x^2+30 \text{Li}_2(a x)+75 \text{Li}_3(a x)+8 a x-12 \log (1-a x)\right)}{375 (d x)^{7/2}}","\frac{16 a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{a} \sqrt{d x}}{\sqrt{d}}\right)}{125 d^{7/2}}-\frac{16 a^2}{125 d^3 \sqrt{d x}}-\frac{16 a}{375 d^2 (d x)^{3/2}}-\frac{4 \text{Li}_2(a x)}{25 d (d x)^{5/2}}-\frac{2 \text{Li}_3(a x)}{5 d (d x)^{5/2}}+\frac{8 \log (1-a x)}{125 d (d x)^{5/2}}",1,"(-2*x*(8*a*x + 24*a^2*x^2 - 24*a^(5/2)*x^(5/2)*ArcTanh[Sqrt[a]*Sqrt[x]] - 12*Log[1 - a*x] + 30*PolyLog[2, a*x] + 75*PolyLog[3, a*x]))/(375*(d*x)^(7/2))","A",1
72,1,101,140,0.102093,"\int (d x)^{3/2} \text{Li}_2\left(a x^2\right) \, dx","Integrate[(d*x)^(3/2)*PolyLog[2, a*x^2],x]","\frac{2 (d x)^{3/2} \left(\frac{4 \sqrt[4]{a} \sqrt{x} \left(-4 a x^2+5 a x^2 \log \left(1-a x^2\right)-20\right)+40 \tan ^{-1}\left(\sqrt[4]{a} \sqrt{x}\right)+40 \tanh ^{-1}\left(\sqrt[4]{a} \sqrt{x}\right)}{a^{5/4}}+25 x^{5/2} \text{Li}_2\left(a x^2\right)\right)}{125 x^{3/2}}","\frac{16 d^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{25 a^{5/4}}+\frac{16 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{25 a^{5/4}}+\frac{2 (d x)^{5/2} \text{Li}_2\left(a x^2\right)}{5 d}+\frac{8 (d x)^{5/2} \log \left(1-a x^2\right)}{25 d}-\frac{32 d \sqrt{d x}}{25 a}-\frac{32 (d x)^{5/2}}{125 d}",1,"(2*(d*x)^(3/2)*((40*ArcTan[a^(1/4)*Sqrt[x]] + 40*ArcTanh[a^(1/4)*Sqrt[x]] + 4*a^(1/4)*Sqrt[x]*(-20 - 4*a*x^2 + 5*a*x^2*Log[1 - a*x^2]))/a^(5/4) + 25*x^(5/2)*PolyLog[2, a*x^2]))/(125*x^(3/2))","A",1
73,1,91,125,0.0685405,"\int \sqrt{d x} \text{Li}_2\left(a x^2\right) \, dx","Integrate[Sqrt[d*x]*PolyLog[2, a*x^2],x]","\frac{2 \sqrt{d x} \left(\frac{4 \left(a^{3/4} x^{3/2} \left(3 \log \left(1-a x^2\right)-4\right)-6 \tan ^{-1}\left(\sqrt[4]{a} \sqrt{x}\right)+6 \tanh ^{-1}\left(\sqrt[4]{a} \sqrt{x}\right)\right)}{a^{3/4}}+9 x^{3/2} \text{Li}_2\left(a x^2\right)\right)}{27 \sqrt{x}}","-\frac{16 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{9 a^{3/4}}+\frac{16 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{9 a^{3/4}}+\frac{2 (d x)^{3/2} \text{Li}_2\left(a x^2\right)}{3 d}+\frac{8 (d x)^{3/2} \log \left(1-a x^2\right)}{9 d}-\frac{32 (d x)^{3/2}}{27 d}",1,"(2*Sqrt[d*x]*((4*(-6*ArcTan[a^(1/4)*Sqrt[x]] + 6*ArcTanh[a^(1/4)*Sqrt[x]] + a^(3/4)*x^(3/2)*(-4 + 3*Log[1 - a*x^2])))/a^(3/4) + 9*x^(3/2)*PolyLog[2, a*x^2]))/(27*Sqrt[x])","A",1
74,1,57,115,0.0662404,"\int \frac{\text{Li}_2\left(a x^2\right)}{\sqrt{d x}} \, dx","Integrate[PolyLog[2, a*x^2]/Sqrt[d*x],x]","\frac{5 x \Gamma \left(\frac{5}{4}\right) \left(16 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};a x^2\right)+\text{Li}_2\left(a x^2\right)+4 \log \left(1-a x^2\right)-16\right)}{2 \Gamma \left(\frac{9}{4}\right) \sqrt{d x}}","\frac{2 \sqrt{d x} \text{Li}_2\left(a x^2\right)}{d}+\frac{8 \sqrt{d x} \log \left(1-a x^2\right)}{d}+\frac{16 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt[4]{a} \sqrt{d}}+\frac{16 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt[4]{a} \sqrt{d}}-\frac{32 \sqrt{d x}}{d}",1,"(5*x*Gamma[5/4]*(-16 + 16*Hypergeometric2F1[1/4, 1, 5/4, a*x^2] + 4*Log[1 - a*x^2] + PolyLog[2, a*x^2]))/(2*Sqrt[d*x]*Gamma[9/4])","C",0
75,1,62,103,0.0666647,"\int \frac{\text{Li}_2\left(a x^2\right)}{(d x)^{3/2}} \, dx","Integrate[PolyLog[2, a*x^2]/(d*x)^(3/2),x]","\frac{x \Gamma \left(\frac{3}{4}\right) \left(16 a x^2 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};a x^2\right)-3 \text{Li}_2\left(a x^2\right)+12 \log \left(1-a x^2\right)\right)}{2 \Gamma \left(\frac{7}{4}\right) (d x)^{3/2}}","-\frac{16 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{16 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{2 \text{Li}_2\left(a x^2\right)}{d \sqrt{d x}}+\frac{8 \log \left(1-a x^2\right)}{d \sqrt{d x}}",1,"(x*Gamma[3/4]*(16*a*x^2*Hypergeometric2F1[3/4, 1, 7/4, a*x^2] + 12*Log[1 - a*x^2] - 3*PolyLog[2, a*x^2]))/(2*(d*x)^(3/2)*Gamma[7/4])","C",0
76,1,62,111,0.0636253,"\int \frac{\text{Li}_2\left(a x^2\right)}{(d x)^{5/2}} \, dx","Integrate[PolyLog[2, a*x^2]/(d*x)^(5/2),x]","\frac{x \Gamma \left(\frac{1}{4}\right) \left(16 a x^2 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};a x^2\right)-3 \text{Li}_2\left(a x^2\right)+4 \log \left(1-a x^2\right)\right)}{18 \Gamma \left(\frac{5}{4}\right) (d x)^{5/2}}","\frac{16 a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{9 d^{5/2}}+\frac{16 a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{9 d^{5/2}}-\frac{2 \text{Li}_2\left(a x^2\right)}{3 d (d x)^{3/2}}+\frac{8 \log \left(1-a x^2\right)}{9 d (d x)^{3/2}}",1,"(x*Gamma[1/4]*(16*a*x^2*Hypergeometric2F1[1/4, 1, 5/4, a*x^2] + 4*Log[1 - a*x^2] - 3*PolyLog[2, a*x^2]))/(18*(d*x)^(5/2)*Gamma[5/4])","C",0
77,1,70,126,0.073757,"\int \frac{\text{Li}_2\left(a x^2\right)}{(d x)^{7/2}} \, dx","Integrate[PolyLog[2, a*x^2]/(d*x)^(7/2),x]","-\frac{x \Gamma \left(-\frac{1}{4}\right) \left(16 a^2 x^4 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};a x^2\right)-15 \text{Li}_2\left(a x^2\right)-48 a x^2+12 \log \left(1-a x^2\right)\right)}{150 \Gamma \left(\frac{3}{4}\right) (d x)^{7/2}}","-\frac{16 a^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{25 d^{7/2}}+\frac{16 a^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{25 d^{7/2}}-\frac{32 a}{25 d^3 \sqrt{d x}}-\frac{2 \text{Li}_2\left(a x^2\right)}{5 d (d x)^{5/2}}+\frac{8 \log \left(1-a x^2\right)}{25 d (d x)^{5/2}}",1,"-1/150*(x*Gamma[-1/4]*(-48*a*x^2 + 16*a^2*x^4*Hypergeometric2F1[3/4, 1, 7/4, a*x^2] + 12*Log[1 - a*x^2] - 15*PolyLog[2, a*x^2]))/((d*x)^(7/2)*Gamma[3/4])","C",0
78,1,89,161,0.0963172,"\int (d x)^{5/2} \text{Li}_3\left(a x^2\right) \, dx","Integrate[(d*x)^(5/2)*PolyLog[3, a*x^2],x]","-\frac{11 d \Gamma \left(\frac{11}{4}\right) (d x)^{3/2} \left(448 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};a x^2\right)+588 a x^2 \text{Li}_2\left(a x^2\right)-1029 a x^2 \text{Li}_3\left(a x^2\right)-192 a x^2+336 a x^2 \log \left(1-a x^2\right)-448\right)}{14406 a \Gamma \left(\frac{15}{4}\right)}","\frac{64 d^{5/2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{343 a^{7/4}}-\frac{64 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{343 a^{7/4}}-\frac{8 (d x)^{7/2} \text{Li}_2\left(a x^2\right)}{49 d}+\frac{2 (d x)^{7/2} \text{Li}_3\left(a x^2\right)}{7 d}-\frac{32 (d x)^{7/2} \log \left(1-a x^2\right)}{343 d}+\frac{128 d (d x)^{3/2}}{1029 a}+\frac{128 (d x)^{7/2}}{2401 d}",1,"(-11*d*(d*x)^(3/2)*Gamma[11/4]*(-448 - 192*a*x^2 + 448*Hypergeometric2F1[3/4, 1, 7/4, a*x^2] + 336*a*x^2*Log[1 - a*x^2] + 588*a*x^2*PolyLog[2, a*x^2] - 1029*a*x^2*PolyLog[3, a*x^2]))/(14406*a*Gamma[15/4])","C",0
79,1,89,161,0.0942889,"\int (d x)^{3/2} \text{Li}_3\left(a x^2\right) \, dx","Integrate[(d*x)^(3/2)*PolyLog[3, a*x^2],x]","-\frac{9 d \Gamma \left(\frac{9}{4}\right) \sqrt{d x} \left(320 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};a x^2\right)+100 a x^2 \text{Li}_2\left(a x^2\right)-125 a x^2 \text{Li}_3\left(a x^2\right)-64 a x^2+80 a x^2 \log \left(1-a x^2\right)-320\right)}{1250 a \Gamma \left(\frac{13}{4}\right)}","-\frac{64 d^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{125 a^{5/4}}-\frac{64 d^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{125 a^{5/4}}-\frac{8 (d x)^{5/2} \text{Li}_2\left(a x^2\right)}{25 d}+\frac{2 (d x)^{5/2} \text{Li}_3\left(a x^2\right)}{5 d}-\frac{32 (d x)^{5/2} \log \left(1-a x^2\right)}{125 d}+\frac{128 d \sqrt{d x}}{125 a}+\frac{128 (d x)^{5/2}}{625 d}",1,"(-9*d*Sqrt[d*x]*Gamma[9/4]*(-320 - 64*a*x^2 + 320*Hypergeometric2F1[1/4, 1, 5/4, a*x^2] + 80*a*x^2*Log[1 - a*x^2] + 100*a*x^2*PolyLog[2, a*x^2] - 125*a*x^2*PolyLog[3, a*x^2]))/(1250*a*Gamma[13/4])","C",0
80,1,68,146,0.0856873,"\int \sqrt{d x} \text{Li}_3\left(a x^2\right) \, dx","Integrate[Sqrt[d*x]*PolyLog[3, a*x^2],x]","-\frac{7 x \Gamma \left(\frac{7}{4}\right) \sqrt{d x} \left(64 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};a x^2\right)+36 \text{Li}_2\left(a x^2\right)-27 \text{Li}_3\left(a x^2\right)+48 \log \left(1-a x^2\right)-64\right)}{162 \Gamma \left(\frac{11}{4}\right)}","\frac{64 \sqrt{d} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{27 a^{3/4}}-\frac{64 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{27 a^{3/4}}-\frac{8 (d x)^{3/2} \text{Li}_2\left(a x^2\right)}{9 d}+\frac{2 (d x)^{3/2} \text{Li}_3\left(a x^2\right)}{3 d}-\frac{32 (d x)^{3/2} \log \left(1-a x^2\right)}{27 d}+\frac{128 (d x)^{3/2}}{81 d}",1,"(-7*x*Sqrt[d*x]*Gamma[7/4]*(-64 + 64*Hypergeometric2F1[3/4, 1, 7/4, a*x^2] + 48*Log[1 - a*x^2] + 36*PolyLog[2, a*x^2] - 27*PolyLog[3, a*x^2]))/(162*Gamma[11/4])","C",0
81,1,68,134,0.0814214,"\int \frac{\text{Li}_3\left(a x^2\right)}{\sqrt{d x}} \, dx","Integrate[PolyLog[3, a*x^2]/Sqrt[d*x],x]","-\frac{5 x \Gamma \left(\frac{5}{4}\right) \left(64 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};a x^2\right)+4 \text{Li}_2\left(a x^2\right)-\text{Li}_3\left(a x^2\right)+16 \log \left(1-a x^2\right)-64\right)}{2 \Gamma \left(\frac{9}{4}\right) \sqrt{d x}}","-\frac{8 \sqrt{d x} \text{Li}_2\left(a x^2\right)}{d}+\frac{2 \sqrt{d x} \text{Li}_3\left(a x^2\right)}{d}-\frac{32 \sqrt{d x} \log \left(1-a x^2\right)}{d}-\frac{64 \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt[4]{a} \sqrt{d}}-\frac{64 \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{\sqrt[4]{a} \sqrt{d}}+\frac{128 \sqrt{d x}}{d}",1,"(-5*x*Gamma[5/4]*(-64 + 64*Hypergeometric2F1[1/4, 1, 5/4, a*x^2] + 16*Log[1 - a*x^2] + 4*PolyLog[2, a*x^2] - PolyLog[3, a*x^2]))/(2*Sqrt[d*x]*Gamma[9/4])","C",0
82,1,71,122,0.0841594,"\int \frac{\text{Li}_3\left(a x^2\right)}{(d x)^{3/2}} \, dx","Integrate[PolyLog[3, a*x^2]/(d*x)^(3/2),x]","\frac{x \Gamma \left(\frac{3}{4}\right) \left(64 a x^2 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};a x^2\right)-12 \text{Li}_2\left(a x^2\right)-3 \text{Li}_3\left(a x^2\right)+48 \log \left(1-a x^2\right)\right)}{2 \Gamma \left(\frac{7}{4}\right) (d x)^{3/2}}","-\frac{64 \sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}+\frac{64 \sqrt[4]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{d^{3/2}}-\frac{8 \text{Li}_2\left(a x^2\right)}{d \sqrt{d x}}-\frac{2 \text{Li}_3\left(a x^2\right)}{d \sqrt{d x}}+\frac{32 \log \left(1-a x^2\right)}{d \sqrt{d x}}",1,"(x*Gamma[3/4]*(64*a*x^2*Hypergeometric2F1[3/4, 1, 7/4, a*x^2] + 48*Log[1 - a*x^2] - 12*PolyLog[2, a*x^2] - 3*PolyLog[3, a*x^2]))/(2*(d*x)^(3/2)*Gamma[7/4])","C",0
83,1,71,132,0.0900508,"\int \frac{\text{Li}_3\left(a x^2\right)}{(d x)^{5/2}} \, dx","Integrate[PolyLog[3, a*x^2]/(d*x)^(5/2),x]","\frac{x \Gamma \left(\frac{1}{4}\right) \left(64 a x^2 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};a x^2\right)-12 \text{Li}_2\left(a x^2\right)-9 \text{Li}_3\left(a x^2\right)+16 \log \left(1-a x^2\right)\right)}{54 \Gamma \left(\frac{5}{4}\right) (d x)^{5/2}}","\frac{64 a^{3/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{27 d^{5/2}}+\frac{64 a^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{27 d^{5/2}}-\frac{8 \text{Li}_2\left(a x^2\right)}{9 d (d x)^{3/2}}-\frac{2 \text{Li}_3\left(a x^2\right)}{3 d (d x)^{3/2}}+\frac{32 \log \left(1-a x^2\right)}{27 d (d x)^{3/2}}",1,"(x*Gamma[1/4]*(64*a*x^2*Hypergeometric2F1[1/4, 1, 5/4, a*x^2] + 16*Log[1 - a*x^2] - 12*PolyLog[2, a*x^2] - 9*PolyLog[3, a*x^2]))/(54*(d*x)^(5/2)*Gamma[5/4])","C",0
84,1,79,147,0.0900821,"\int \frac{\text{Li}_3\left(a x^2\right)}{(d x)^{7/2}} \, dx","Integrate[PolyLog[3, a*x^2]/(d*x)^(7/2),x]","-\frac{x \Gamma \left(-\frac{1}{4}\right) \left(64 a^2 x^4 \, _2F_1\left(\frac{3}{4},1;\frac{7}{4};a x^2\right)-60 \text{Li}_2\left(a x^2\right)-75 \text{Li}_3\left(a x^2\right)-192 a x^2+48 \log \left(1-a x^2\right)\right)}{750 \Gamma \left(\frac{3}{4}\right) (d x)^{7/2}}","-\frac{64 a^{5/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{125 d^{7/2}}+\frac{64 a^{5/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{125 d^{7/2}}-\frac{128 a}{125 d^3 \sqrt{d x}}-\frac{8 \text{Li}_2\left(a x^2\right)}{25 d (d x)^{5/2}}-\frac{2 \text{Li}_3\left(a x^2\right)}{5 d (d x)^{5/2}}+\frac{32 \log \left(1-a x^2\right)}{125 d (d x)^{5/2}}",1,"-1/750*(x*Gamma[-1/4]*(-192*a*x^2 + 64*a^2*x^4*Hypergeometric2F1[3/4, 1, 7/4, a*x^2] + 48*Log[1 - a*x^2] - 60*PolyLog[2, a*x^2] - 75*PolyLog[3, a*x^2]))/((d*x)^(7/2)*Gamma[3/4])","C",0
85,1,84,147,0.093135,"\int \frac{\text{Li}_3\left(a x^2\right)}{(d x)^{9/2}} \, dx","Integrate[PolyLog[3, a*x^2]/(d*x)^(9/2),x]","-\frac{\Gamma \left(-\frac{3}{4}\right) \sqrt{d x} \left(192 a^2 x^4 \, _2F_1\left(\frac{1}{4},1;\frac{5}{4};a x^2\right)-84 \text{Li}_2\left(a x^2\right)-147 \text{Li}_3\left(a x^2\right)-64 a x^2+48 \log \left(1-a x^2\right)\right)}{686 d^5 x^4 \Gamma \left(\frac{1}{4}\right)}","\frac{64 a^{7/4} \tan ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{343 d^{9/2}}+\frac{64 a^{7/4} \tanh ^{-1}\left(\frac{\sqrt[4]{a} \sqrt{d x}}{\sqrt{d}}\right)}{343 d^{9/2}}-\frac{128 a}{1029 d^3 (d x)^{3/2}}-\frac{8 \text{Li}_2\left(a x^2\right)}{49 d (d x)^{7/2}}-\frac{2 \text{Li}_3\left(a x^2\right)}{7 d (d x)^{7/2}}+\frac{32 \log \left(1-a x^2\right)}{343 d (d x)^{7/2}}",1,"-1/686*(Sqrt[d*x]*Gamma[-3/4]*(-64*a*x^2 + 192*a^2*x^4*Hypergeometric2F1[1/4, 1, 5/4, a*x^2] + 48*Log[1 - a*x^2] - 84*PolyLog[2, a*x^2] - 147*PolyLog[3, a*x^2]))/(d^5*x^4*Gamma[1/4])","C",0
86,1,82,101,0.1198938,"\int (d x)^{3/2} \text{Li}_2\left(a x^q\right) \, dx","Integrate[(d*x)^(3/2)*PolyLog[2, a*x^q],x]","\frac{2 x (d x)^{3/2} \left(4 a q^2 x^q \, _2F_1\left(1,\frac{q+\frac{5}{2}}{q};2+\frac{5}{2 q};a x^q\right)+(2 q+5) \left(5 \text{Li}_2\left(a x^q\right)+2 q \log \left(1-a x^q\right)\right)\right)}{25 (2 q+5)}","\frac{8 a d q^2 \sqrt{d x} x^{q+2} \, _2F_1\left(1,\frac{q+\frac{5}{2}}{q};\frac{1}{2} \left(4+\frac{5}{q}\right);a x^q\right)}{25 (2 q+5)}+\frac{2 (d x)^{5/2} \text{Li}_2\left(a x^q\right)}{5 d}+\frac{4 q (d x)^{5/2} \log \left(1-a x^q\right)}{25 d}",1,"(2*x*(d*x)^(3/2)*(4*a*q^2*x^q*Hypergeometric2F1[1, (5/2 + q)/q, 2 + 5/(2*q), a*x^q] + (5 + 2*q)*(2*q*Log[1 - a*x^q] + 5*PolyLog[2, a*x^q])))/(25*(5 + 2*q))","A",1
87,1,82,100,0.1038292,"\int \sqrt{d x} \text{Li}_2\left(a x^q\right) \, dx","Integrate[Sqrt[d*x]*PolyLog[2, a*x^q],x]","\frac{2 x \sqrt{d x} \left(4 a q^2 x^q \, _2F_1\left(1,\frac{q+\frac{3}{2}}{q};2+\frac{3}{2 q};a x^q\right)+(2 q+3) \left(3 \text{Li}_2\left(a x^q\right)+2 q \log \left(1-a x^q\right)\right)\right)}{9 (2 q+3)}","\frac{8 a q^2 \sqrt{d x} x^{q+1} \, _2F_1\left(1,\frac{q+\frac{3}{2}}{q};\frac{1}{2} \left(4+\frac{3}{q}\right);a x^q\right)}{9 (2 q+3)}+\frac{2 (d x)^{3/2} \text{Li}_2\left(a x^q\right)}{3 d}+\frac{4 q (d x)^{3/2} \log \left(1-a x^q\right)}{9 d}",1,"(2*x*Sqrt[d*x]*(4*a*q^2*x^q*Hypergeometric2F1[1, (3/2 + q)/q, 2 + 3/(2*q), a*x^q] + (3 + 2*q)*(2*q*Log[1 - a*x^q] + 3*PolyLog[2, a*x^q])))/(9*(3 + 2*q))","A",1
88,1,48,93,0.0214943,"\int \frac{\text{Li}_2\left(a x^q\right)}{\sqrt{d x}} \, dx","Integrate[PolyLog[2, a*x^q]/Sqrt[d*x],x]","-\frac{x G_{4,4}^{1,4}\left(-a x^q|\begin{array}{c} 1,1,1,1-\frac{1}{2 q} \\ 1,0,0,-\frac{1}{2 q} \\\end{array}\right)}{q \sqrt{d x}}","\frac{8 a q^2 \sqrt{d x} x^q \, _2F_1\left(1,\frac{q+\frac{1}{2}}{q};\frac{1}{2} \left(4+\frac{1}{q}\right);a x^q\right)}{d (2 q+1)}+\frac{2 \sqrt{d x} \text{Li}_2\left(a x^q\right)}{d}+\frac{4 q \sqrt{d x} \log \left(1-a x^q\right)}{d}",1,"-((x*MeijerG[{{1, 1, 1, 1 - 1/(2*q)}, {}}, {{1}, {0, 0, -1/2*1/q}}, -(a*x^q)])/(q*Sqrt[d*x]))","C",0
89,1,48,97,0.0262003,"\int \frac{\text{Li}_2\left(a x^q\right)}{(d x)^{3/2}} \, dx","Integrate[PolyLog[2, a*x^q]/(d*x)^(3/2),x]","-\frac{x G_{4,4}^{1,4}\left(-a x^q|\begin{array}{c} 1,1,1,1+\frac{1}{2 q} \\ 1,0,0,\frac{1}{2 q} \\\end{array}\right)}{q (d x)^{3/2}}","-\frac{8 a q^2 x^q \, _2F_1\left(1,\frac{1}{2} \left(2-\frac{1}{q}\right);\frac{1}{2} \left(4-\frac{1}{q}\right);a x^q\right)}{d (1-2 q) \sqrt{d x}}-\frac{2 \text{Li}_2\left(a x^q\right)}{d \sqrt{d x}}+\frac{4 q \log \left(1-a x^q\right)}{d \sqrt{d x}}",1,"-((x*MeijerG[{{1, 1, 1, 1 + 1/(2*q)}, {}}, {{1}, {0, 0, 1/(2*q)}}, -(a*x^q)])/(q*(d*x)^(3/2)))","C",0
90,1,48,105,0.0272478,"\int \frac{\text{Li}_2\left(a x^q\right)}{(d x)^{5/2}} \, dx","Integrate[PolyLog[2, a*x^q]/(d*x)^(5/2),x]","-\frac{x G_{4,4}^{1,4}\left(-a x^q|\begin{array}{c} 1,1,1,1+\frac{3}{2 q} \\ 1,0,0,\frac{3}{2 q} \\\end{array}\right)}{q (d x)^{5/2}}","-\frac{8 a q^2 x^{q-1} \, _2F_1\left(1,\frac{1}{2} \left(2-\frac{3}{q}\right);\frac{1}{2} \left(4-\frac{3}{q}\right);a x^q\right)}{9 d^2 (3-2 q) \sqrt{d x}}-\frac{2 \text{Li}_2\left(a x^q\right)}{3 d (d x)^{3/2}}+\frac{4 q \log \left(1-a x^q\right)}{9 d (d x)^{3/2}}",1,"-((x*MeijerG[{{1, 1, 1, 1 + 3/(2*q)}, {}}, {{1}, {0, 0, 3/(2*q)}}, -(a*x^q)])/(q*(d*x)^(5/2)))","C",0
91,1,50,125,0.0295597,"\int (d x)^{3/2} \text{Li}_3\left(a x^q\right) \, dx","Integrate[(d*x)^(3/2)*PolyLog[3, a*x^q],x]","-\frac{x (d x)^{3/2} G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,1-\frac{5}{2 q} \\ 1,0,0,0,-\frac{5}{2 q} \\\end{array}\right)}{q}","-\frac{16 a d q^3 \sqrt{d x} x^{q+2} \, _2F_1\left(1,\frac{q+\frac{5}{2}}{q};\frac{1}{2} \left(4+\frac{5}{q}\right);a x^q\right)}{125 (2 q+5)}-\frac{4 q (d x)^{5/2} \text{Li}_2\left(a x^q\right)}{25 d}+\frac{2 (d x)^{5/2} \text{Li}_3\left(a x^q\right)}{5 d}-\frac{8 q^2 (d x)^{5/2} \log \left(1-a x^q\right)}{125 d}",1,"-((x*(d*x)^(3/2)*MeijerG[{{1, 1, 1, 1, 1 - 5/(2*q)}, {}}, {{1}, {0, 0, 0, -5/(2*q)}}, -(a*x^q)])/q)","C",0
92,1,50,124,0.0246662,"\int \sqrt{d x} \text{Li}_3\left(a x^q\right) \, dx","Integrate[Sqrt[d*x]*PolyLog[3, a*x^q],x]","-\frac{x \sqrt{d x} G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,1-\frac{3}{2 q} \\ 1,0,0,0,-\frac{3}{2 q} \\\end{array}\right)}{q}","-\frac{16 a q^3 \sqrt{d x} x^{q+1} \, _2F_1\left(1,\frac{q+\frac{3}{2}}{q};\frac{1}{2} \left(4+\frac{3}{q}\right);a x^q\right)}{27 (2 q+3)}-\frac{4 q (d x)^{3/2} \text{Li}_2\left(a x^q\right)}{9 d}+\frac{2 (d x)^{3/2} \text{Li}_3\left(a x^q\right)}{3 d}-\frac{8 q^2 (d x)^{3/2} \log \left(1-a x^q\right)}{27 d}",1,"-((x*Sqrt[d*x]*MeijerG[{{1, 1, 1, 1, 1 - 3/(2*q)}, {}}, {{1}, {0, 0, 0, -3/(2*q)}}, -(a*x^q)])/q)","C",0
93,1,50,115,0.0197551,"\int \frac{\text{Li}_3\left(a x^q\right)}{\sqrt{d x}} \, dx","Integrate[PolyLog[3, a*x^q]/Sqrt[d*x],x]","-\frac{x G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,1-\frac{1}{2 q} \\ 1,0,0,0,-\frac{1}{2 q} \\\end{array}\right)}{q \sqrt{d x}}","-\frac{16 a q^3 \sqrt{d x} x^q \, _2F_1\left(1,\frac{q+\frac{1}{2}}{q};\frac{1}{2} \left(4+\frac{1}{q}\right);a x^q\right)}{d (2 q+1)}-\frac{4 q \sqrt{d x} \text{Li}_2\left(a x^q\right)}{d}+\frac{2 \sqrt{d x} \text{Li}_3\left(a x^q\right)}{d}-\frac{8 q^2 \sqrt{d x} \log \left(1-a x^q\right)}{d}",1,"-((x*MeijerG[{{1, 1, 1, 1, 1 - 1/(2*q)}, {}}, {{1}, {0, 0, 0, -1/2*1/q}}, -(a*x^q)])/(q*Sqrt[d*x]))","C",0
94,1,50,119,0.0234079,"\int \frac{\text{Li}_3\left(a x^q\right)}{(d x)^{3/2}} \, dx","Integrate[PolyLog[3, a*x^q]/(d*x)^(3/2),x]","-\frac{x G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,1+\frac{1}{2 q} \\ 1,0,0,0,\frac{1}{2 q} \\\end{array}\right)}{q (d x)^{3/2}}","-\frac{16 a q^3 x^q \, _2F_1\left(1,\frac{1}{2} \left(2-\frac{1}{q}\right);\frac{1}{2} \left(4-\frac{1}{q}\right);a x^q\right)}{d (1-2 q) \sqrt{d x}}-\frac{4 q \text{Li}_2\left(a x^q\right)}{d \sqrt{d x}}-\frac{2 \text{Li}_3\left(a x^q\right)}{d \sqrt{d x}}+\frac{8 q^2 \log \left(1-a x^q\right)}{d \sqrt{d x}}",1,"-((x*MeijerG[{{1, 1, 1, 1, 1 + 1/(2*q)}, {}}, {{1}, {0, 0, 0, 1/(2*q)}}, -(a*x^q)])/(q*(d*x)^(3/2)))","C",0
95,1,50,129,0.0232844,"\int \frac{\text{Li}_3\left(a x^q\right)}{(d x)^{5/2}} \, dx","Integrate[PolyLog[3, a*x^q]/(d*x)^(5/2),x]","-\frac{x G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,1+\frac{3}{2 q} \\ 1,0,0,0,\frac{3}{2 q} \\\end{array}\right)}{q (d x)^{5/2}}","-\frac{16 a q^3 x^{q-1} \, _2F_1\left(1,\frac{1}{2} \left(2-\frac{3}{q}\right);\frac{1}{2} \left(4-\frac{3}{q}\right);a x^q\right)}{27 d^2 (3-2 q) \sqrt{d x}}-\frac{4 q \text{Li}_2\left(a x^q\right)}{9 d (d x)^{3/2}}-\frac{2 \text{Li}_3\left(a x^q\right)}{3 d (d x)^{3/2}}+\frac{8 q^2 \log \left(1-a x^q\right)}{27 d (d x)^{3/2}}",1,"-((x*MeijerG[{{1, 1, 1, 1, 1 + 3/(2*q)}, {}}, {{1}, {0, 0, 0, 3/(2*q)}}, -(a*x^q)])/(q*(d*x)^(5/2)))","C",0
96,0,0,30,0.0062431,"\int \text{Li}_{\frac{3}{2}}(a x) \, dx","Integrate[PolyLog[3/2, a*x],x]","\int \text{Li}_{\frac{3}{2}}(a x) \, dx","\text{Int}\left(\text{Li}_{-\frac{1}{2}}(a x),x\right)-x \text{Li}_{\frac{1}{2}}(a x)+x \text{Li}_{\frac{3}{2}}(a x)",0,"Integrate[PolyLog[3/2, a*x], x]","A",-1
97,0,0,22,0.0061387,"\int \text{Li}_{\frac{1}{2}}(a x) \, dx","Integrate[PolyLog[1/2, a*x],x]","\int \text{Li}_{\frac{1}{2}}(a x) \, dx","x \text{Li}_{\frac{1}{2}}(a x)-\text{Int}\left(\text{Li}_{-\frac{1}{2}}(a x),x\right)",0,"Integrate[PolyLog[1/2, a*x], x]","A",-1
98,0,0,10,0.006166,"\int \text{Li}_{-\frac{1}{2}}(a x) \, dx","Integrate[PolyLog[-1/2, a*x],x]","\int \text{Li}_{-\frac{1}{2}}(a x) \, dx","\text{Int}\left(\text{Li}_{-\frac{1}{2}}(a x),x\right)",0,"Integrate[PolyLog[-1/2, a*x], x]","A",-1
99,0,0,22,0.0067119,"\int \text{Li}_{-\frac{3}{2}}(a x) \, dx","Integrate[PolyLog[-3/2, a*x],x]","\int \text{Li}_{-\frac{3}{2}}(a x) \, dx","x \text{Li}_{-\frac{1}{2}}(a x)-\text{Int}\left(\text{Li}_{-\frac{1}{2}}(a x),x\right)",0,"Integrate[PolyLog[-3/2, a*x], x]","A",-1
100,0,0,30,0.0076984,"\int \text{Li}_{-\frac{5}{2}}(a x) \, dx","Integrate[PolyLog[-5/2, a*x],x]","\int \text{Li}_{-\frac{5}{2}}(a x) \, dx","\text{Int}\left(\text{Li}_{-\frac{1}{2}}(a x),x\right)+x \text{Li}_{-\frac{3}{2}}(a x)-x \text{Li}_{-\frac{1}{2}}(a x)",0,"Integrate[PolyLog[-5/2, a*x], x]","A",-1
101,0,0,9,0.0072645,"\int \left(\text{Li}_{-\frac{3}{2}}(a x)+\text{Li}_{-\frac{1}{2}}(a x)\right) \, dx","Integrate[PolyLog[-3/2, a*x] + PolyLog[-1/2, a*x],x]","\int \left(\text{Li}_{-\frac{3}{2}}(a x)+\text{Li}_{-\frac{1}{2}}(a x)\right) \, dx","x \text{Li}_{-\frac{1}{2}}(a x)",1,"Integrate[PolyLog[-3/2, a*x] + PolyLog[-1/2, a*x], x]","F",-1
102,1,53,78,0.0408181,"\int (d x)^m \text{Li}_2(a x) \, dx","Integrate[(d*x)^m*PolyLog[2, a*x],x]","\frac{x (d x)^m (a x \, _2F_1(1,m+2;m+3;a x)+(m+2) ((m+1) \text{Li}_2(a x)+\log (1-a x)))}{(m+1)^2 (m+2)}","\frac{a (d x)^{m+2} \, _2F_1(1,m+2;m+3;a x)}{d^2 (m+1)^2 (m+2)}+\frac{\text{Li}_2(a x) (d x)^{m+1}}{d (m+1)}+\frac{\log (1-a x) (d x)^{m+1}}{d (m+1)^2}",1,"(x*(d*x)^m*(a*x*Hypergeometric2F1[1, 2 + m, 3 + m, a*x] + (2 + m)*(Log[1 - a*x] + (1 + m)*PolyLog[2, a*x])))/((1 + m)^2*(2 + m))","A",1
103,1,88,102,0.0585666,"\int (d x)^m \text{Li}_3(a x) \, dx","Integrate[(d*x)^m*PolyLog[3, a*x],x]","-\frac{x \Gamma (m+2) (d x)^m \left(a (m+1) x \Gamma (m+1) \, _2\tilde{F}_1(1,m+2;m+3;a x)+m^2 (-\text{Li}_3(a x))-2 m \text{Li}_3(a x)+(m+1) \text{Li}_2(a x)-\text{Li}_3(a x)+\log (1-a x)\right)}{(m+1)^4 \Gamma (m+1)}","-\frac{a (d x)^{m+2} \, _2F_1(1,m+2;m+3;a x)}{d^2 (m+1)^3 (m+2)}-\frac{\text{Li}_2(a x) (d x)^{m+1}}{d (m+1)^2}+\frac{\text{Li}_3(a x) (d x)^{m+1}}{d (m+1)}-\frac{\log (1-a x) (d x)^{m+1}}{d (m+1)^3}",1,"-((x*(d*x)^m*Gamma[2 + m]*(a*(1 + m)*x*Gamma[1 + m]*HypergeometricPFQRegularized[{1, 2 + m}, {3 + m}, a*x] + Log[1 - a*x] + (1 + m)*PolyLog[2, a*x] - PolyLog[3, a*x] - 2*m*PolyLog[3, a*x] - m^2*PolyLog[3, a*x]))/((1 + m)^4*Gamma[1 + m]))","C",0
104,1,119,121,0.0719022,"\int (d x)^m \text{Li}_4(a x) \, dx","Integrate[(d*x)^m*PolyLog[4, a*x],x]","\frac{x \Gamma (m+2) (d x)^m \left(a (m+1) x \Gamma (m+1) \, _2\tilde{F}_1(1,m+2;m+3;a x)+m^3 \text{Li}_4(a x)-m^2 \text{Li}_3(a x)+3 m^2 \text{Li}_4(a x)-2 m \text{Li}_3(a x)+3 m \text{Li}_4(a x)+(m+1) \text{Li}_2(a x)-\text{Li}_3(a x)+\text{Li}_4(a x)+\log (1-a x)\right)}{(m+1)^5 \Gamma (m+1)}","\frac{a (d x)^{m+2} \, _2F_1(1,m+2;m+3;a x)}{d^2 (m+1)^4 (m+2)}+\frac{\text{Li}_2(a x) (d x)^{m+1}}{d (m+1)^3}-\frac{\text{Li}_3(a x) (d x)^{m+1}}{d (m+1)^2}+\frac{\text{Li}_4(a x) (d x)^{m+1}}{d (m+1)}+\frac{\log (1-a x) (d x)^{m+1}}{d (m+1)^4}",1,"(x*(d*x)^m*Gamma[2 + m]*(a*(1 + m)*x*Gamma[1 + m]*HypergeometricPFQRegularized[{1, 2 + m}, {3 + m}, a*x] + Log[1 - a*x] + (1 + m)*PolyLog[2, a*x] - PolyLog[3, a*x] - 2*m*PolyLog[3, a*x] - m^2*PolyLog[3, a*x] + PolyLog[4, a*x] + 3*m*PolyLog[4, a*x] + 3*m^2*PolyLog[4, a*x] + m^3*PolyLog[4, a*x]))/((1 + m)^5*Gamma[1 + m])","C",0
105,1,72,94,0.0442404,"\int (d x)^m \text{Li}_2\left(a x^2\right) \, dx","Integrate[(d*x)^m*PolyLog[2, a*x^2],x]","\frac{x (d x)^m \left(4 a x^2 \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};a x^2\right)+(m+3) \left((m+1) \text{Li}_2\left(a x^2\right)+2 \log \left(1-a x^2\right)\right)\right)}{(m+1)^2 (m+3)}","\frac{4 a (d x)^{m+3} \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};a x^2\right)}{d^3 (m+1)^2 (m+3)}+\frac{\text{Li}_2\left(a x^2\right) (d x)^{m+1}}{d (m+1)}+\frac{2 \log \left(1-a x^2\right) (d x)^{m+1}}{d (m+1)^2}",1,"(x*(d*x)^m*(4*a*x^2*Hypergeometric2F1[1, (3 + m)/2, (5 + m)/2, a*x^2] + (3 + m)*(2*Log[1 - a*x^2] + (1 + m)*PolyLog[2, a*x^2])))/((1 + m)^2*(3 + m))","A",1
106,1,126,118,0.0773006,"\int (d x)^m \text{Li}_3\left(a x^2\right) \, dx","Integrate[(d*x)^m*PolyLog[3, a*x^2],x]","-\frac{2 x \Gamma \left(\frac{m+3}{2}\right) (d x)^m \left(2 a (m+1) x^2 \Gamma \left(\frac{m+1}{2}\right) \, _2\tilde{F}_1\left(1,\frac{m+3}{2};\frac{m+5}{2};a x^2\right)+m^2 \left(-\text{Li}_3\left(a x^2\right)\right)-2 m \text{Li}_3\left(a x^2\right)+2 (m+1) \text{Li}_2\left(a x^2\right)-\text{Li}_3\left(a x^2\right)+4 \log \left(1-a x^2\right)\right)}{(m+1)^4 \Gamma \left(\frac{m+1}{2}\right)}","-\frac{8 a (d x)^{m+3} \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};a x^2\right)}{d^3 (m+1)^3 (m+3)}-\frac{2 \text{Li}_2\left(a x^2\right) (d x)^{m+1}}{d (m+1)^2}+\frac{\text{Li}_3\left(a x^2\right) (d x)^{m+1}}{d (m+1)}-\frac{4 \log \left(1-a x^2\right) (d x)^{m+1}}{d (m+1)^3}",1,"(-2*x*(d*x)^m*Gamma[(3 + m)/2]*(2*a*(1 + m)*x^2*Gamma[(1 + m)/2]*HypergeometricPFQRegularized[{1, (3 + m)/2}, {(5 + m)/2}, a*x^2] + 4*Log[1 - a*x^2] + 2*(1 + m)*PolyLog[2, a*x^2] - PolyLog[3, a*x^2] - 2*m*PolyLog[3, a*x^2] - m^2*PolyLog[3, a*x^2]))/((1 + m)^4*Gamma[(1 + m)/2])","C",0
107,1,166,142,0.0928258,"\int (d x)^m \text{Li}_4\left(a x^2\right) \, dx","Integrate[(d*x)^m*PolyLog[4, a*x^2],x]","\frac{2 x \Gamma \left(\frac{m+3}{2}\right) (d x)^m \left(4 a (m+1) x^2 \Gamma \left(\frac{m+1}{2}\right) \, _2\tilde{F}_1\left(1,\frac{m+3}{2};\frac{m+5}{2};a x^2\right)+m^3 \text{Li}_4\left(a x^2\right)-2 m^2 \text{Li}_3\left(a x^2\right)+3 m^2 \text{Li}_4\left(a x^2\right)-4 m \text{Li}_3\left(a x^2\right)+3 m \text{Li}_4\left(a x^2\right)+4 (m+1) \text{Li}_2\left(a x^2\right)-2 \text{Li}_3\left(a x^2\right)+\text{Li}_4\left(a x^2\right)+8 \log \left(1-a x^2\right)\right)}{(m+1)^5 \Gamma \left(\frac{m+1}{2}\right)}","\frac{16 a (d x)^{m+3} \, _2F_1\left(1,\frac{m+3}{2};\frac{m+5}{2};a x^2\right)}{d^3 (m+1)^4 (m+3)}+\frac{4 \text{Li}_2\left(a x^2\right) (d x)^{m+1}}{d (m+1)^3}-\frac{2 \text{Li}_3\left(a x^2\right) (d x)^{m+1}}{d (m+1)^2}+\frac{\text{Li}_4\left(a x^2\right) (d x)^{m+1}}{d (m+1)}+\frac{8 \log \left(1-a x^2\right) (d x)^{m+1}}{d (m+1)^4}",1,"(2*x*(d*x)^m*Gamma[(3 + m)/2]*(4*a*(1 + m)*x^2*Gamma[(1 + m)/2]*HypergeometricPFQRegularized[{1, (3 + m)/2}, {(5 + m)/2}, a*x^2] + 8*Log[1 - a*x^2] + 4*(1 + m)*PolyLog[2, a*x^2] - 2*PolyLog[3, a*x^2] - 4*m*PolyLog[3, a*x^2] - 2*m^2*PolyLog[3, a*x^2] + PolyLog[4, a*x^2] + 3*m*PolyLog[4, a*x^2] + 3*m^2*PolyLog[4, a*x^2] + m^3*PolyLog[4, a*x^2]))/((1 + m)^5*Gamma[(1 + m)/2])","C",0
108,1,72,94,0.0456059,"\int (d x)^m \text{Li}_2\left(a x^3\right) \, dx","Integrate[(d*x)^m*PolyLog[2, a*x^3],x]","\frac{x (d x)^m \left(9 a x^3 \, _2F_1\left(1,\frac{m+4}{3};\frac{m+7}{3};a x^3\right)+(m+4) \left((m+1) \text{Li}_2\left(a x^3\right)+3 \log \left(1-a x^3\right)\right)\right)}{(m+1)^2 (m+4)}","\frac{9 a (d x)^{m+4} \, _2F_1\left(1,\frac{m+4}{3};\frac{m+7}{3};a x^3\right)}{d^4 (m+1)^2 (m+4)}+\frac{\text{Li}_2\left(a x^3\right) (d x)^{m+1}}{d (m+1)}+\frac{3 \log \left(1-a x^3\right) (d x)^{m+1}}{d (m+1)^2}",1,"(x*(d*x)^m*(9*a*x^3*Hypergeometric2F1[1, (4 + m)/3, (7 + m)/3, a*x^3] + (4 + m)*(3*Log[1 - a*x^3] + (1 + m)*PolyLog[2, a*x^3])))/((1 + m)^2*(4 + m))","A",1
109,1,126,118,0.0787977,"\int (d x)^m \text{Li}_3\left(a x^3\right) \, dx","Integrate[(d*x)^m*PolyLog[3, a*x^3],x]","-\frac{3 x \Gamma \left(\frac{m+4}{3}\right) (d x)^m \left(3 a (m+1) x^3 \Gamma \left(\frac{m+1}{3}\right) \, _2\tilde{F}_1\left(1,\frac{m+4}{3};\frac{m+7}{3};a x^3\right)-m^2 \text{Li}_3\left(a x^3\right)+3 (m+1) \text{Li}_2\left(a x^3\right)-2 m \text{Li}_3\left(a x^3\right)-\text{Li}_3\left(a x^3\right)+9 \log \left(1-a x^3\right)\right)}{(m+1)^4 \Gamma \left(\frac{m+1}{3}\right)}","-\frac{27 a (d x)^{m+4} \, _2F_1\left(1,\frac{m+4}{3};\frac{m+7}{3};a x^3\right)}{d^4 (m+1)^3 (m+4)}-\frac{3 \text{Li}_2\left(a x^3\right) (d x)^{m+1}}{d (m+1)^2}+\frac{\text{Li}_3\left(a x^3\right) (d x)^{m+1}}{d (m+1)}-\frac{9 \log \left(1-a x^3\right) (d x)^{m+1}}{d (m+1)^3}",1,"(-3*x*(d*x)^m*Gamma[(4 + m)/3]*(3*a*(1 + m)*x^3*Gamma[(1 + m)/3]*HypergeometricPFQRegularized[{1, (4 + m)/3}, {(7 + m)/3}, a*x^3] + 9*Log[1 - a*x^3] + 3*(1 + m)*PolyLog[2, a*x^3] - PolyLog[3, a*x^3] - 2*m*PolyLog[3, a*x^3] - m^2*PolyLog[3, a*x^3]))/((1 + m)^4*Gamma[(1 + m)/3])","C",0
110,1,166,142,0.0923256,"\int (d x)^m \text{Li}_4\left(a x^3\right) \, dx","Integrate[(d*x)^m*PolyLog[4, a*x^3],x]","\frac{3 x \Gamma \left(\frac{m+4}{3}\right) (d x)^m \left(9 a (m+1) x^3 \Gamma \left(\frac{m+1}{3}\right) \, _2\tilde{F}_1\left(1,\frac{m+4}{3};\frac{m+7}{3};a x^3\right)+m^3 \text{Li}_4\left(a x^3\right)-3 m^2 \text{Li}_3\left(a x^3\right)+3 m^2 \text{Li}_4\left(a x^3\right)-6 m \text{Li}_3\left(a x^3\right)+3 m \text{Li}_4\left(a x^3\right)+9 (m+1) \text{Li}_2\left(a x^3\right)-3 \text{Li}_3\left(a x^3\right)+\text{Li}_4\left(a x^3\right)+27 \log \left(1-a x^3\right)\right)}{(m+1)^5 \Gamma \left(\frac{m+1}{3}\right)}","\frac{81 a (d x)^{m+4} \, _2F_1\left(1,\frac{m+4}{3};\frac{m+7}{3};a x^3\right)}{d^4 (m+1)^4 (m+4)}+\frac{9 \text{Li}_2\left(a x^3\right) (d x)^{m+1}}{d (m+1)^3}-\frac{3 \text{Li}_3\left(a x^3\right) (d x)^{m+1}}{d (m+1)^2}+\frac{\text{Li}_4\left(a x^3\right) (d x)^{m+1}}{d (m+1)}+\frac{27 \log \left(1-a x^3\right) (d x)^{m+1}}{d (m+1)^4}",1,"(3*x*(d*x)^m*Gamma[(4 + m)/3]*(9*a*(1 + m)*x^3*Gamma[(1 + m)/3]*HypergeometricPFQRegularized[{1, (4 + m)/3}, {(7 + m)/3}, a*x^3] + 27*Log[1 - a*x^3] + 9*(1 + m)*PolyLog[2, a*x^3] - 3*PolyLog[3, a*x^3] - 6*m*PolyLog[3, a*x^3] - 3*m^2*PolyLog[3, a*x^3] + PolyLog[4, a*x^3] + 3*m*PolyLog[4, a*x^3] + 3*m^2*PolyLog[4, a*x^3] + m^3*PolyLog[4, a*x^3]))/((1 + m)^5*Gamma[(1 + m)/3])","C",0
111,1,80,101,0.0652516,"\int (d x)^m \text{Li}_2\left(a x^q\right) \, dx","Integrate[(d*x)^m*PolyLog[2, a*x^q],x]","\frac{x (d x)^m \left(a q^2 x^q \, _2F_1\left(1,\frac{m+q+1}{q};\frac{m+2 q+1}{q};a x^q\right)+(m+q+1) \left((m+1) \text{Li}_2\left(a x^q\right)+q \log \left(1-a x^q\right)\right)\right)}{(m+1)^2 (m+q+1)}","\frac{a q^2 x^{q+1} (d x)^m \, _2F_1\left(1,\frac{m+q+1}{q};\frac{m+2 q+1}{q};a x^q\right)}{(m+1)^2 (m+q+1)}+\frac{(d x)^{m+1} \text{Li}_2\left(a x^q\right)}{d (m+1)}+\frac{q (d x)^{m+1} \log \left(1-a x^q\right)}{d (m+1)^2}",1,"(x*(d*x)^m*(a*q^2*x^q*Hypergeometric2F1[1, (1 + m + q)/q, (1 + m + 2*q)/q, a*x^q] + (1 + m + q)*(q*Log[1 - a*x^q] + (1 + m)*PolyLog[2, a*x^q])))/((1 + m)^2*(1 + m + q))","A",1
112,1,50,130,0.0231,"\int (d x)^m \text{Li}_3\left(a x^q\right) \, dx","Integrate[(d*x)^m*PolyLog[3, a*x^q],x]","-\frac{x (d x)^m G_{5,5}^{1,5}\left(-a x^q|\begin{array}{c} 1,1,1,1,1-\frac{m+1}{q} \\ 1,0,0,0,-\frac{m+1}{q} \\\end{array}\right)}{q}","-\frac{a q^3 x^{q+1} (d x)^m \, _2F_1\left(1,\frac{m+q+1}{q};\frac{m+2 q+1}{q};a x^q\right)}{(m+1)^3 (m+q+1)}-\frac{q (d x)^{m+1} \text{Li}_2\left(a x^q\right)}{d (m+1)^2}+\frac{(d x)^{m+1} \text{Li}_3\left(a x^q\right)}{d (m+1)}-\frac{q^2 (d x)^{m+1} \log \left(1-a x^q\right)}{d (m+1)^3}",1,"-((x*(d*x)^m*MeijerG[{{1, 1, 1, 1, 1 - (1 + m)/q}, {}}, {{1}, {0, 0, 0, -((1 + m)/q)}}, -(a*x^q)])/q)","C",0
113,1,52,154,0.0198879,"\int (d x)^m \text{Li}_4\left(a x^q\right) \, dx","Integrate[(d*x)^m*PolyLog[4, a*x^q],x]","-\frac{x (d x)^m G_{6,6}^{1,6}\left(-a x^q|\begin{array}{c} 1,1,1,1,1,1-\frac{m+1}{q} \\ 1,0,0,0,0,-\frac{m+1}{q} \\\end{array}\right)}{q}","\frac{a q^4 x^{q+1} (d x)^m \, _2F_1\left(1,\frac{m+q+1}{q};\frac{m+2 q+1}{q};a x^q\right)}{(m+1)^4 (m+q+1)}+\frac{q^2 (d x)^{m+1} \text{Li}_2\left(a x^q\right)}{d (m+1)^3}-\frac{q (d x)^{m+1} \text{Li}_3\left(a x^q\right)}{d (m+1)^2}+\frac{(d x)^{m+1} \text{Li}_4\left(a x^q\right)}{d (m+1)}+\frac{q^3 (d x)^{m+1} \log \left(1-a x^q\right)}{d (m+1)^4}",1,"-((x*(d*x)^m*MeijerG[{{1, 1, 1, 1, 1, 1 - (1 + m)/q}, {}}, {{1}, {0, 0, 0, 0, -((1 + m)/q)}}, -(a*x^q)])/q)","C",0
114,0,0,10,0.0224954,"\int x \text{Li}_n(a x) \, dx","Integrate[x*PolyLog[n, a*x],x]","\int x \text{Li}_n(a x) \, dx","\text{Int}(x \text{Li}_n(a x),x)",0,"Integrate[x*PolyLog[n, a*x], x]","A",-1
115,0,0,8,0.0009945,"\int \text{Li}_n(a x) \, dx","Integrate[PolyLog[n, a*x],x]","\int \text{Li}_n(a x) \, dx","\text{Int}(\text{Li}_n(a x),x)",0,"Integrate[PolyLog[n, a*x], x]","A",-1
116,1,7,7,0.0014071,"\int \frac{\text{Li}_n(a x)}{x} \, dx","Integrate[PolyLog[n, a*x]/x,x]","\text{Li}_{n+1}(a x)","\text{Li}_{n+1}(a x)",1,"PolyLog[1 + n, a*x]","A",1
117,0,0,12,0.0197806,"\int \frac{\text{Li}_n(a x)}{x^2} \, dx","Integrate[PolyLog[n, a*x]/x^2,x]","\int \frac{\text{Li}_n(a x)}{x^2} \, dx","\text{Int}\left(\frac{\text{Li}_n(a x)}{x^2},x\right)",0,"Integrate[PolyLog[n, a*x]/x^2, x]","A",-1
118,0,0,12,0.0198584,"\int \frac{\text{Li}_n(a x)}{x^3} \, dx","Integrate[PolyLog[n, a*x]/x^3,x]","\int \frac{\text{Li}_n(a x)}{x^3} \, dx","\text{Int}\left(\frac{\text{Li}_n(a x)}{x^3},x\right)",0,"Integrate[PolyLog[n, a*x]/x^3, x]","A",-1
119,0,0,12,0.0240039,"\int x \text{Li}_n\left(a x^q\right) \, dx","Integrate[x*PolyLog[n, a*x^q],x]","\int x \text{Li}_n\left(a x^q\right) \, dx","\text{Int}\left(x \text{Li}_n\left(a x^q\right),x\right)",0,"Integrate[x*PolyLog[n, a*x^q], x]","A",-1
120,0,0,10,0.0040528,"\int \text{Li}_n\left(a x^q\right) \, dx","Integrate[PolyLog[n, a*x^q],x]","\int \text{Li}_n\left(a x^q\right) \, dx","\text{Int}\left(\text{Li}_n\left(a x^q\right),x\right)",0,"Integrate[PolyLog[n, a*x^q], x]","A",-1
121,1,13,13,0.0014856,"\int \frac{\text{Li}_n\left(a x^q\right)}{x} \, dx","Integrate[PolyLog[n, a*x^q]/x,x]","\frac{\text{Li}_{n+1}\left(a x^q\right)}{q}","\frac{\text{Li}_{n+1}\left(a x^q\right)}{q}",1,"PolyLog[1 + n, a*x^q]/q","A",1
122,0,0,14,0.0219382,"\int \frac{\text{Li}_n\left(a x^q\right)}{x^2} \, dx","Integrate[PolyLog[n, a*x^q]/x^2,x]","\int \frac{\text{Li}_n\left(a x^q\right)}{x^2} \, dx","\text{Int}\left(\frac{\text{Li}_n\left(a x^q\right)}{x^2},x\right)",0,"Integrate[PolyLog[n, a*x^q]/x^2, x]","A",-1
123,0,0,14,0.0217251,"\int \frac{\text{Li}_n\left(a x^q\right)}{x^3} \, dx","Integrate[PolyLog[n, a*x^q]/x^3,x]","\int \frac{\text{Li}_n\left(a x^q\right)}{x^3} \, dx","\text{Int}\left(\frac{\text{Li}_n\left(a x^q\right)}{x^3},x\right)",0,"Integrate[PolyLog[n, a*x^q]/x^3, x]","A",-1
124,1,144,260,0.1953778,"\int x^2 \text{Li}_2(c (a+b x)) \, dx","Integrate[x^2*PolyLog[2, c*(a + b*x)],x]","\frac{36 c^3 \left(a^3+b^3 x^3\right) \text{Li}_2(c (a+b x))-b c x \left(66 a^2 c^2-3 a c (5 b c x+14)+4 b^2 c^2 x^2+6 b c x+12\right)+6 \left(11 a^3 c^3+6 a^2 c^2 (b c x-3)+a \left(9 c-3 b^2 c^3 x^2\right)+2 b^3 c^3 x^3-2\right) \log (-a c-b c x+1)}{108 b^3 c^3}","\frac{a^3 \text{Li}_2(c (a+b x))}{3 b^3}-\frac{a^2 (-a c-b c x+1) \log (-a c-b c x+1)}{3 b^3 c}-\frac{a^2 x}{3 b^2}-\frac{(1-a c)^3 \log (-a c-b c x+1)}{9 b^3 c^3}+\frac{a (1-a c)^2 \log (-a c-b c x+1)}{6 b^3 c^2}-\frac{x (1-a c)^2}{9 b^2 c^2}+\frac{a x (1-a c)}{6 b^2 c}+\frac{1}{3} x^3 \text{Li}_2(c (a+b x))+\frac{1}{9} x^3 \log (-a c-b c x+1)-\frac{x^2 (1-a c)}{18 b c}-\frac{a x^2 \log (-a c-b c x+1)}{6 b}+\frac{a x^2}{12 b}-\frac{x^3}{27}",1,"(-(b*c*x*(12 + 66*a^2*c^2 + 6*b*c*x + 4*b^2*c^2*x^2 - 3*a*c*(14 + 5*b*c*x))) + 6*(-2 + 11*a^3*c^3 + 2*b^3*c^3*x^3 + 6*a^2*c^2*(-3 + b*c*x) + a*(9*c - 3*b^2*c^3*x^2))*Log[1 - a*c - b*c*x] + 36*c^3*(a^3 + b^3*x^3)*PolyLog[2, c*(a + b*x)])/(108*b^3*c^3)","A",1
125,1,96,152,0.0926835,"\int x \text{Li}_2(c (a+b x)) \, dx","Integrate[x*PolyLog[2, c*(a + b*x)],x]","\frac{-4 c^2 \left(a^2-b^2 x^2\right) \text{Li}_2(c (a+b x))+\left(-6 a^2 c^2-4 a c (b c x-2)+2 b^2 c^2 x^2-2\right) \log (-a c-b c x+1)-b c x (-6 a c+b c x+2)}{8 b^2 c^2}","-\frac{a^2 \text{Li}_2(c (a+b x))}{2 b^2}-\frac{(1-a c)^2 \log (-a c-b c x+1)}{4 b^2 c^2}+\frac{a (-a c-b c x+1) \log (-a c-b c x+1)}{2 b^2 c}+\frac{1}{2} x^2 \text{Li}_2(c (a+b x))+\frac{1}{4} x^2 \log (-a c-b c x+1)-\frac{x (1-a c)}{4 b c}+\frac{a x}{2 b}-\frac{x^2}{8}",1,"(-(b*c*x*(2 - 6*a*c + b*c*x)) + (-2 - 6*a^2*c^2 + 2*b^2*c^2*x^2 - 4*a*c*(-2 + b*c*x))*Log[1 - a*c - b*c*x] - 4*c^2*(a^2 - b^2*x^2)*PolyLog[2, c*(a + b*x)])/(8*b^2*c^2)","A",1
126,1,53,60,0.0172503,"\int \text{Li}_2(c (a+b x)) \, dx","Integrate[PolyLog[2, c*(a + b*x)],x]","\frac{c (a+b x) \text{Li}_2(c (a+b x))-c (a+b x)+(c (a+b x)-1) \log (1-c (a+b x))}{b c}","x \text{Li}_2(c (a+b x))+\frac{a \text{Li}_2(c (a+b x))}{b}-\frac{(-a c-b c x+1) \log (-a c-b c x+1)}{b c}-x",1,"(-(c*(a + b*x)) + (-1 + c*(a + b*x))*Log[1 - c*(a + b*x)] + c*(a + b*x)*PolyLog[2, c*(a + b*x)])/(b*c)","A",1
127,1,422,401,0.1311408,"\int \frac{\text{Li}_2(c (a+b x))}{x} \, dx","Integrate[PolyLog[2, c*(a + b*x)]/x,x]","-\text{Li}_3(-a c-b x c+1)+\text{Li}_3\left(\frac{a (a c+b x c-1)}{b x}\right)-\text{Li}_3\left(\frac{a c+b x c-1}{b c x}\right)+\left(\text{Li}_2\left(\frac{a c+b x c-1}{b c x}\right)-\text{Li}_2\left(\frac{a (a c+b x c-1)}{b x}\right)\right) \log \left(\frac{a (a c+b c x-1)}{b x}\right)+\text{Li}_2\left(-\frac{b x}{a}\right) \left(\log (-a c-b c x+1)-\log \left(\frac{a (a c+b c x-1)}{b x}\right)\right)+\text{Li}_2(-a c-b x c+1) \left(\log \left(\frac{a (a c+b c x-1)}{b x}\right)+\log (x)\right)+\log (x) \text{Li}_2(a c+b x c)+\frac{1}{2} \left(\log \left(\frac{1-a c}{b c x}\right)-\log \left(\frac{(1-a c) (a+b x)}{b x}\right)+\log \left(\frac{b x}{a}+1\right)\right) \log ^2\left(\frac{a (a c+b c x-1)}{b x}\right)+\left(\log (c (a+b x))-\log \left(\frac{b x}{a}+1\right)\right) \log (-a c-b c x+1) \log \left(\frac{a (a c+b c x-1)}{b x}\right)+\log (x) \log \left(\frac{b x}{a}+1\right) \log (-a c-b c x+1)+\frac{1}{2} \left(\log \left(\frac{b x}{a}+1\right)-\log (c (a+b x))\right) \log (-a c-b c x+1) (\log (-a c-b c x+1)-2 \log (x))-\text{Li}_3\left(-\frac{b x}{a}\right)","\text{Li}_3\left(-\frac{b x}{a (1-c (a+b x))}\right)-\text{Li}_3\left(-\frac{b c x}{1-c (a+b x)}\right)-\text{Li}_3(1-c (a+b x))+\text{Li}_2\left(-\frac{b x}{a (1-c (a+b x))}\right) \log \left(-\frac{a (1-c (a+b x))}{b x}\right)-\text{Li}_2\left(-\frac{b c x}{1-c (a+b x)}\right) \log \left(-\frac{a (1-c (a+b x))}{b x}\right)+\text{Li}_2\left(-\frac{b x}{a}\right) \left(\log (1-c (a+b x))-\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right)+\log (x) \text{Li}_2(c (a+b x))+\text{Li}_2(1-c (a+b x)) \left(\log \left(-\frac{a (1-c (a+b x))}{b x}\right)+\log (x)\right)+\frac{1}{2} \left(\log \left(\frac{1-a c}{1-c (a+b x)}\right)-\log \left(\frac{(1-a c) (a+b x)}{a (1-c (a+b x))}\right)+\log \left(\frac{b x}{a}+1\right)\right) \log ^2\left(-\frac{a (1-c (a+b x))}{b x}\right)+\frac{1}{2} \left(\log (c (a+b x))-\log \left(\frac{b x}{a}+1\right)\right) \left(\log \left(-\frac{a (1-c (a+b x))}{b x}\right)+\log (x)\right)^2+\log (x) \log \left(\frac{b x}{a}+1\right) \log (1-c (a+b x))-\text{Li}_3\left(-\frac{b x}{a}\right)",1,"Log[x]*Log[1 + (b*x)/a]*Log[1 - a*c - b*c*x] + ((-Log[c*(a + b*x)] + Log[1 + (b*x)/a])*Log[1 - a*c - b*c*x]*(-2*Log[x] + Log[1 - a*c - b*c*x]))/2 + (Log[c*(a + b*x)] - Log[1 + (b*x)/a])*Log[1 - a*c - b*c*x]*Log[(a*(-1 + a*c + b*c*x))/(b*x)] + ((Log[(1 - a*c)/(b*c*x)] - Log[((1 - a*c)*(a + b*x))/(b*x)] + Log[1 + (b*x)/a])*Log[(a*(-1 + a*c + b*c*x))/(b*x)]^2)/2 + (Log[1 - a*c - b*c*x] - Log[(a*(-1 + a*c + b*c*x))/(b*x)])*PolyLog[2, -((b*x)/a)] + (Log[x] + Log[(a*(-1 + a*c + b*c*x))/(b*x)])*PolyLog[2, 1 - a*c - b*c*x] + Log[(a*(-1 + a*c + b*c*x))/(b*x)]*(-PolyLog[2, (a*(-1 + a*c + b*c*x))/(b*x)] + PolyLog[2, (-1 + a*c + b*c*x)/(b*c*x)]) + Log[x]*PolyLog[2, a*c + b*c*x] - PolyLog[3, -((b*x)/a)] - PolyLog[3, 1 - a*c - b*c*x] + PolyLog[3, (a*(-1 + a*c + b*c*x))/(b*x)] - PolyLog[3, (-1 + a*c + b*c*x)/(b*c*x)]","A",1
128,1,73,84,0.0509049,"\int \frac{\text{Li}_2(c (a+b x))}{x^2} \, dx","Integrate[PolyLog[2, c*(a + b*x)]/x^2,x]","-\frac{(a+b x) \text{Li}_2(c (a+b x))+b x \left(\text{Li}_2\left(\frac{a c+b x c-1}{a c-1}\right)+\log \left(\frac{b c x}{1-a c}\right) \log (-a c-b c x+1)\right)}{a x}","-\frac{b \text{Li}_2(c (a+b x))}{a}-\frac{\text{Li}_2(c (a+b x))}{x}-\frac{b \text{Li}_2\left(1-\frac{b c x}{1-a c}\right)}{a}-\frac{b \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b c x+1)}{a}",1,"-(((a + b*x)*PolyLog[2, c*(a + b*x)] + b*x*(Log[(b*c*x)/(1 - a*c)]*Log[1 - a*c - b*c*x] + PolyLog[2, (-1 + a*c + b*c*x)/(-1 + a*c)]))/(a*x))","A",1
129,1,131,173,0.157919,"\int \frac{\text{Li}_2(c (a+b x))}{x^3} \, dx","Integrate[PolyLog[2, c*(a + b*x)]/x^3,x]","\frac{b x \left(b x (a c-1) \text{Li}_2\left(\frac{a c+b x c-1}{a c-1}\right)-a b c x \log (x)+\left(a (a c+b c x-1)+b x (a c-1) \log \left(\frac{b c x}{1-a c}\right)\right) \log (-a c-b c x+1)\right)-(a c-1) \left(a^2-b^2 x^2\right) \text{Li}_2(c (a+b x))}{2 a^2 x^2 (a c-1)}","\frac{b^2 \text{Li}_2(c (a+b x))}{2 a^2}+\frac{b^2 \text{Li}_2\left(1-\frac{b c x}{1-a c}\right)}{2 a^2}+\frac{b^2 \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b c x+1)}{2 a^2}+\frac{b^2 c \log (x)}{2 a (1-a c)}-\frac{b^2 c \log (-a c-b c x+1)}{2 a (1-a c)}-\frac{\text{Li}_2(c (a+b x))}{2 x^2}+\frac{b \log (-a c-b c x+1)}{2 a x}",1,"(-((-1 + a*c)*(a^2 - b^2*x^2)*PolyLog[2, c*(a + b*x)]) + b*x*(-(a*b*c*x*Log[x]) + (a*(-1 + a*c + b*c*x) + b*(-1 + a*c)*x*Log[(b*c*x)/(1 - a*c)])*Log[1 - a*c - b*c*x] + b*(-1 + a*c)*x*PolyLog[2, (-1 + a*c + b*c*x)/(-1 + a*c)]))/(2*a^2*(-1 + a*c)*x^2)","A",1
130,1,210,276,0.2859272,"\int \frac{\text{Li}_2(c (a+b x))}{x^4} \, dx","Integrate[PolyLog[2, c*(a + b*x)]/x^4,x]","-\frac{b \left(-\frac{a^2 \log (-a c-b c x+1)}{x^2}-\frac{a^2 b c (-b c x \log (-a c-b c x+1)+a c+b c x \log (x)-1)}{x (a c-1)^2}+2 b^2 \text{Li}_2(c (a+b x))+2 b^2 \text{Li}_2\left(\frac{a c+b x c-1}{a c-1}\right)-\frac{2 a b^2 c (\log (x)-\log (-a c-b c x+1))}{a c-1}+2 b^2 \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b c x+1)+\frac{2 a b \log (-a c-b c x+1)}{x}\right)}{6 a^3}-\frac{\text{Li}_2(a c+b x c)}{3 x^3}","-\frac{b^3 \text{Li}_2(c (a+b x))}{3 a^3}-\frac{b^3 \text{Li}_2\left(1-\frac{b c x}{1-a c}\right)}{3 a^3}-\frac{b^3 \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b c x+1)}{3 a^3}-\frac{b^3 c \log (x)}{3 a^2 (1-a c)}+\frac{b^3 c \log (-a c-b c x+1)}{3 a^2 (1-a c)}-\frac{b^2 \log (-a c-b c x+1)}{3 a^2 x}+\frac{b^3 c^2 \log (x)}{6 a (1-a c)^2}-\frac{b^3 c^2 \log (-a c-b c x+1)}{6 a (1-a c)^2}-\frac{b^2 c}{6 a x (1-a c)}-\frac{\text{Li}_2(c (a+b x))}{3 x^3}+\frac{b \log (-a c-b c x+1)}{6 a x^2}",1,"-1/6*(b*((-2*a*b^2*c*(Log[x] - Log[1 - a*c - b*c*x]))/(-1 + a*c) - (a^2*Log[1 - a*c - b*c*x])/x^2 + (2*a*b*Log[1 - a*c - b*c*x])/x + 2*b^2*Log[(b*c*x)/(1 - a*c)]*Log[1 - a*c - b*c*x] - (a^2*b*c*(-1 + a*c + b*c*x*Log[x] - b*c*x*Log[1 - a*c - b*c*x]))/((-1 + a*c)^2*x) + 2*b^2*PolyLog[2, c*(a + b*x)] + 2*b^2*PolyLog[2, (-1 + a*c + b*c*x)/(-1 + a*c)]))/a^3 - PolyLog[2, a*c + b*c*x]/(3*x^3)","A",1
131,1,296,347,0.0642357,"\int x^2 \text{Li}_3(c (a+b x)) \, dx","Integrate[x^2*PolyLog[3, c*(a + b*x)],x]","\frac{216 c^3 \left(a^3+b^3 x^3\right) \text{Li}_3(c (a+b x))-510 a^3 c^3 \log (-a c-b c x+1)+575 a^3 c^3+510 a^2 b c^3 x-396 a^2 b c^3 x \log (-a c-b c x+1)+648 a^2 c^2 \log (-a c-b c x+1)-150 a^2 c^2-36 c^3 \left(11 a^3+6 a^2 b x-3 a b^2 x^2+2 b^3 x^3\right) \text{Li}_2(c (a+b x))-24 b^3 c^3 x^3 \log (-a c-b c x+1)-57 a b^2 c^3 x^2+90 a b^2 c^3 x^2 \log (-a c-b c x+1)-138 a b c^2 x-162 a c \log (-a c-b c x+1)+24 \log (-a c-b c x+1)+24 a c+8 b^3 c^3 x^3+12 b^2 c^2 x^2+24 b c x}{648 b^3 c^3}","-\frac{\left(a^3-b^3 x^3\right) \text{Li}_3(c (a+b x))}{3 b^3}-\frac{11 a^3 \text{Li}_2(c (a+b x))}{18 b^3}+\frac{2 a^3 \text{Li}_3(c (a+b x))}{3 b^3}+\frac{11 a^2 (-a c-b c x+1) \log (-a c-b c x+1)}{18 b^3 c}-\frac{a^2 x \text{Li}_2(c (a+b x))}{3 b^2}+\frac{11 a^2 x}{18 b^2}+\frac{(1-a c)^3 \log (-a c-b c x+1)}{27 b^3 c^3}-\frac{5 a (1-a c)^2 \log (-a c-b c x+1)}{36 b^3 c^2}+\frac{x (1-a c)^2}{27 b^2 c^2}-\frac{5 a x (1-a c)}{36 b^2 c}-\frac{1}{9} x^3 \text{Li}_2(c (a+b x))+\frac{a x^2 \text{Li}_2(c (a+b x))}{6 b}-\frac{1}{27} x^3 \log (-a c-b c x+1)+\frac{x^2 (1-a c)}{54 b c}+\frac{5 a x^2 \log (-a c-b c x+1)}{36 b}-\frac{5 a x^2}{72 b}+\frac{x^3}{81}",1,"(24*a*c - 150*a^2*c^2 + 575*a^3*c^3 + 24*b*c*x - 138*a*b*c^2*x + 510*a^2*b*c^3*x + 12*b^2*c^2*x^2 - 57*a*b^2*c^3*x^2 + 8*b^3*c^3*x^3 + 24*Log[1 - a*c - b*c*x] - 162*a*c*Log[1 - a*c - b*c*x] + 648*a^2*c^2*Log[1 - a*c - b*c*x] - 510*a^3*c^3*Log[1 - a*c - b*c*x] - 396*a^2*b*c^3*x*Log[1 - a*c - b*c*x] + 90*a*b^2*c^3*x^2*Log[1 - a*c - b*c*x] - 24*b^3*c^3*x^3*Log[1 - a*c - b*c*x] - 36*c^3*(11*a^3 + 6*a^2*b*x - 3*a*b^2*x^2 + 2*b^3*x^3)*PolyLog[2, c*(a + b*x)] + 216*c^3*(a^3 + b^3*x^3)*PolyLog[3, c*(a + b*x)])/(648*b^3*c^3)","A",1
132,1,198,198,0.0454533,"\int x \text{Li}_3(c (a+b x)) \, dx","Integrate[x*PolyLog[3, c*(a + b*x)],x]","\frac{4 c^2 \left(3 a^2+2 a b x-b^2 x^2\right) \text{Li}_2(c (a+b x))-8 c^2 \left(a^2-b^2 x^2\right) \text{Li}_3(c (a+b x))+14 a^2 c^2 \log (-a c-b c x+1)-15 a^2 c^2-2 b^2 c^2 x^2 \log (-a c-b c x+1)-14 a b c^2 x+12 a b c^2 x \log (-a c-b c x+1)-16 a c \log (-a c-b c x+1)+2 \log (-a c-b c x+1)+2 a c+b^2 c^2 x^2+2 b c x}{16 b^2 c^2}","-\frac{\left(a^2-b^2 x^2\right) \text{Li}_3(c (a+b x))}{2 b^2}+\frac{3 a^2 \text{Li}_2(c (a+b x))}{4 b^2}+\frac{(1-a c)^2 \log (-a c-b c x+1)}{8 b^2 c^2}-\frac{3 a (-a c-b c x+1) \log (-a c-b c x+1)}{4 b^2 c}-\frac{1}{4} x^2 \text{Li}_2(c (a+b x))+\frac{a x \text{Li}_2(c (a+b x))}{2 b}-\frac{1}{8} x^2 \log (-a c-b c x+1)+\frac{x (1-a c)}{8 b c}-\frac{3 a x}{4 b}+\frac{x^2}{16}",1,"(2*a*c - 15*a^2*c^2 + 2*b*c*x - 14*a*b*c^2*x + b^2*c^2*x^2 + 2*Log[1 - a*c - b*c*x] - 16*a*c*Log[1 - a*c - b*c*x] + 14*a^2*c^2*Log[1 - a*c - b*c*x] + 12*a*b*c^2*x*Log[1 - a*c - b*c*x] - 2*b^2*c^2*x^2*Log[1 - a*c - b*c*x] + 4*c^2*(3*a^2 + 2*a*b*x - b^2*x^2)*PolyLog[2, c*(a + b*x)] - 8*c^2*(a^2 - b^2*x^2)*PolyLog[3, c*(a + b*x)])/(16*b^2*c^2)","A",1
133,1,66,84,0.0239561,"\int \text{Li}_3(c (a+b x)) \, dx","Integrate[PolyLog[3, c*(a + b*x)],x]","\frac{(a+b x) \left(-\text{Li}_2(c (a+b x))+\text{Li}_3(c (a+b x))+\frac{\log (1-c (a+b x))}{c (a+b x)}-\log (1-c (a+b x))+1\right)}{b}","x (-\text{Li}_2(c (a+b x)))+x \text{Li}_3(c (a+b x))-\frac{a \text{Li}_2(c (a+b x))}{b}+\frac{a \text{Li}_3(c (a+b x))}{b}+\frac{(-a c-b c x+1) \log (-a c-b c x+1)}{b c}+x",1,"((a + b*x)*(1 - Log[1 - c*(a + b*x)] + Log[1 - c*(a + b*x)]/(c*(a + b*x)) - PolyLog[2, c*(a + b*x)] + PolyLog[3, c*(a + b*x)]))/b","A",1
134,0,0,17,0.0358084,"\int \frac{\text{Li}_3(c (a+b x))}{x} \, dx","Integrate[PolyLog[3, c*(a + b*x)]/x,x]","\int \frac{\text{Li}_3(c (a+b x))}{x} \, dx","\text{Int}\left(\frac{\text{Li}_3(a c+b x c)}{x},x\right)",0,"Integrate[PolyLog[3, c*(a + b*x)]/x, x]","A",-1
135,1,477,486,0.697275,"\int \frac{\text{Li}_3(c (a+b x))}{x^2} \, dx","Integrate[PolyLog[3, c*(a + b*x)]/x^2,x]","\frac{b \left(-\text{Li}_3(c (a+b x))-\text{Li}_3(-a c-b x c+1)+\text{Li}_3\left(\frac{a (a c+b x c-1)}{b x}\right)-\text{Li}_3\left(\frac{a c+b x c-1}{b c x}\right)+\left(\text{Li}_2\left(\frac{a c+b x c-1}{b c x}\right)-\text{Li}_2\left(\frac{a (a c+b x c-1)}{b x}\right)\right) \log \left(\frac{a (a c+b c x-1)}{b x}\right)+\text{Li}_2\left(-\frac{b x}{a}\right) \left(\log (-a c-b c x+1)-\log \left(\frac{a (a c+b c x-1)}{b x}\right)\right)+(\log (x)-\log (a+b x)) \text{Li}_2(c (a+b x))+\log (a+b x) \text{Li}_2(c (a+b x))+\text{Li}_2(-a c-b x c+1) \left(\log \left(\frac{a (a c+b c x-1)}{b x}\right)+\log (x)\right)+\frac{1}{2} \left(\log \left(\frac{1-a c}{b c x}\right)-\log \left(\frac{(1-a c) (a+b x)}{b x}\right)+\log \left(\frac{b x}{a}+1\right)\right) \log ^2\left(\frac{a (a c+b c x-1)}{b x}\right)+\left(\log (c (a+b x))-\log \left(\frac{b x}{a}+1\right)\right) \log (-a c-b c x+1) \log \left(\frac{a (a c+b c x-1)}{b x}\right)+\log (x) \log \left(\frac{b x}{a}+1\right) \log (-a c-b c x+1)+\frac{1}{2} \left(\log \left(\frac{b x}{a}+1\right)-\log (c (a+b x))\right) \log (-a c-b c x+1) (\log (-a c-b c x+1)-2 \log (x))-\text{Li}_3\left(-\frac{b x}{a}\right)\right)}{a}-\frac{\text{Li}_3(c (a+b x))}{x}","-\frac{2 b \text{Li}_3(c (a+b x))}{a}+\frac{\left(b-\frac{a}{x}\right) \text{Li}_3(c (a+b x))}{a}+\frac{b \text{Li}_3\left(-\frac{b x}{a (1-c (a+b x))}\right)}{a}-\frac{b \text{Li}_3\left(-\frac{b c x}{1-c (a+b x)}\right)}{a}-\frac{b \text{Li}_3(1-c (a+b x))}{a}+\frac{b \text{Li}_2\left(-\frac{b x}{a (1-c (a+b x))}\right) \log \left(-\frac{a (1-c (a+b x))}{b x}\right)}{a}-\frac{b \text{Li}_2\left(-\frac{b c x}{1-c (a+b x)}\right) \log \left(-\frac{a (1-c (a+b x))}{b x}\right)}{a}+\frac{b \text{Li}_2\left(-\frac{b x}{a}\right) \left(\log (1-c (a+b x))-\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right)}{a}+\frac{b \log (x) \text{Li}_2(c (a+b x))}{a}+\frac{b \text{Li}_2(1-c (a+b x)) \left(\log \left(-\frac{a (1-c (a+b x))}{b x}\right)+\log (x)\right)}{a}+\frac{b \left(\log \left(\frac{1-a c}{1-c (a+b x)}\right)-\log \left(\frac{(1-a c) (a+b x)}{a (1-c (a+b x))}\right)+\log \left(\frac{b x}{a}+1\right)\right) \log ^2\left(-\frac{a (1-c (a+b x))}{b x}\right)}{2 a}+\frac{b \left(\log (c (a+b x))-\log \left(\frac{b x}{a}+1\right)\right) \left(\log \left(-\frac{a (1-c (a+b x))}{b x}\right)+\log (x)\right)^2}{2 a}+\frac{b \log (x) \log \left(\frac{b x}{a}+1\right) \log (1-c (a+b x))}{a}-\frac{b \text{Li}_3\left(-\frac{b x}{a}\right)}{a}",1,"-(PolyLog[3, c*(a + b*x)]/x) + (b*(Log[x]*Log[1 + (b*x)/a]*Log[1 - a*c - b*c*x] + ((-Log[c*(a + b*x)] + Log[1 + (b*x)/a])*Log[1 - a*c - b*c*x]*(-2*Log[x] + Log[1 - a*c - b*c*x]))/2 + (Log[c*(a + b*x)] - Log[1 + (b*x)/a])*Log[1 - a*c - b*c*x]*Log[(a*(-1 + a*c + b*c*x))/(b*x)] + ((Log[(1 - a*c)/(b*c*x)] - Log[((1 - a*c)*(a + b*x))/(b*x)] + Log[1 + (b*x)/a])*Log[(a*(-1 + a*c + b*c*x))/(b*x)]^2)/2 + (Log[1 - a*c - b*c*x] - Log[(a*(-1 + a*c + b*c*x))/(b*x)])*PolyLog[2, -((b*x)/a)] + (Log[x] - Log[a + b*x])*PolyLog[2, c*(a + b*x)] + Log[a + b*x]*PolyLog[2, c*(a + b*x)] + (Log[x] + Log[(a*(-1 + a*c + b*c*x))/(b*x)])*PolyLog[2, 1 - a*c - b*c*x] + Log[(a*(-1 + a*c + b*c*x))/(b*x)]*(-PolyLog[2, (a*(-1 + a*c + b*c*x))/(b*x)] + PolyLog[2, (-1 + a*c + b*c*x)/(b*c*x)]) - PolyLog[3, -((b*x)/a)] - PolyLog[3, c*(a + b*x)] - PolyLog[3, 1 - a*c - b*c*x] + PolyLog[3, (a*(-1 + a*c + b*c*x))/(b*x)] - PolyLog[3, (-1 + a*c + b*c*x)/(b*c*x)]))/a","A",1
136,1,573,629,1.7344213,"\int \frac{\text{Li}_3(c (a+b x))}{x^3} \, dx","Integrate[PolyLog[3, c*(a + b*x)]/x^3,x]","\frac{\frac{b x \left(b x \left(\text{Li}_2\left(\frac{b c x}{1-a c}\right)+\text{Li}_2(-a c-b x c+1)+\text{Li}_3(c (a+b x))+\text{Li}_3(-a c-b x c+1)-\text{Li}_3\left(\frac{a (a c+b x c-1)}{b x}\right)+\text{Li}_3\left(\frac{a c+b x c-1}{b c x}\right)+\left(\text{Li}_2\left(\frac{a (a c+b x c-1)}{b x}\right)-\text{Li}_2\left(\frac{a c+b x c-1}{b c x}\right)\right) \log \left(\frac{a (a c+b c x-1)}{b x}\right)-\text{Li}_2\left(-\frac{b x}{a}\right) \left(\log (-a c-b c x+1)-\log \left(\frac{a (a c+b c x-1)}{b x}\right)\right)-\log (a+b x) \text{Li}_2(c (a+b x))-\text{Li}_2(-a c-b x c+1) \left(\log \left(\frac{a (a c+b c x-1)}{b x}\right)+\log (x)\right)-\frac{1}{2} \left(\log \left(\frac{1-a c}{b c x}\right)-\log \left(\frac{(1-a c) (a+b x)}{b x}\right)+\log \left(\frac{b x}{a}+1\right)\right) \log ^2\left(\frac{a (a c+b c x-1)}{b x}\right)-\left(\log (c (a+b x))-\log \left(\frac{b x}{a}+1\right)\right) \log (-a c-b c x+1) \log \left(\frac{a (a c+b c x-1)}{b x}\right)+\log (c (a+b x)) \log (-a c-b c x+1)-\log (x) \log \left(\frac{b x}{a}+1\right) \log (-a c-b c x+1)+\frac{1}{2} \left(\log (c (a+b x))-\log \left(\frac{b x}{a}+1\right)\right) \log (-a c-b c x+1) (\log (-a c-b c x+1)-2 \log (x))-\log (x) \left(\log (-a c-b c x+1)-\log \left(\frac{b c x}{a c-1}+1\right)\right)+\text{Li}_3\left(-\frac{b x}{a}\right)\right)-(-b x \log (a+b x)+a+b x \log (x)) \text{Li}_2(c (a+b x))\right)}{a^2}-\text{Li}_3(c (a+b x))}{2 x^2}","\frac{\left(b^2-\frac{a^2}{x^2}\right) \text{Li}_3(c (a+b x))}{2 a^2}-\frac{b^2 \text{Li}_2(c (a+b x))}{2 a^2}-\frac{b^2 \text{Li}_2\left(1-\frac{b c x}{1-a c}\right)}{2 a^2}-\frac{b^2 \text{Li}_3\left(-\frac{b x}{a (1-c (a+b x))}\right)}{2 a^2}+\frac{b^2 \text{Li}_3\left(-\frac{b c x}{1-c (a+b x)}\right)}{2 a^2}+\frac{b^2 \text{Li}_3(1-c (a+b x))}{2 a^2}-\frac{b^2 \text{Li}_2\left(-\frac{b x}{a}\right) \left(\log (1-c (a+b x))-\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right)}{2 a^2}-\frac{b^2 \log (x) \text{Li}_2(c (a+b x))}{2 a^2}-\frac{b^2 \text{Li}_2\left(-\frac{b x}{a (1-c (a+b x))}\right) \log \left(-\frac{a (1-c (a+b x))}{b x}\right)}{2 a^2}+\frac{b^2 \text{Li}_2\left(-\frac{b c x}{1-c (a+b x)}\right) \log \left(-\frac{a (1-c (a+b x))}{b x}\right)}{2 a^2}-\frac{b^2 \text{Li}_2(1-c (a+b x)) \left(\log \left(-\frac{a (1-c (a+b x))}{b x}\right)+\log (x)\right)}{2 a^2}-\frac{b^2 \left(\log \left(\frac{1-a c}{1-c (a+b x)}\right)-\log \left(\frac{(1-a c) (a+b x)}{a (1-c (a+b x))}\right)+\log \left(\frac{b x}{a}+1\right)\right) \log ^2\left(-\frac{a (1-c (a+b x))}{b x}\right)}{4 a^2}-\frac{b^2 \left(\log (c (a+b x))-\log \left(\frac{b x}{a}+1\right)\right) \left(\log \left(-\frac{a (1-c (a+b x))}{b x}\right)+\log (x)\right)^2}{4 a^2}-\frac{b^2 \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b c x+1)}{2 a^2}-\frac{b^2 \log (x) \log \left(\frac{b x}{a}+1\right) \log (1-c (a+b x))}{2 a^2}+\frac{b^2 \text{Li}_3\left(-\frac{b x}{a}\right)}{2 a^2}-\frac{b \text{Li}_2(c (a+b x))}{2 a x}",1,"(-PolyLog[3, c*(a + b*x)] + (b*x*(-((a + b*x*Log[x] - b*x*Log[a + b*x])*PolyLog[2, c*(a + b*x)]) + b*x*(Log[c*(a + b*x)]*Log[1 - a*c - b*c*x] - Log[x]*Log[1 + (b*x)/a]*Log[1 - a*c - b*c*x] + ((Log[c*(a + b*x)] - Log[1 + (b*x)/a])*Log[1 - a*c - b*c*x]*(-2*Log[x] + Log[1 - a*c - b*c*x]))/2 - (Log[c*(a + b*x)] - Log[1 + (b*x)/a])*Log[1 - a*c - b*c*x]*Log[(a*(-1 + a*c + b*c*x))/(b*x)] - ((Log[(1 - a*c)/(b*c*x)] - Log[((1 - a*c)*(a + b*x))/(b*x)] + Log[1 + (b*x)/a])*Log[(a*(-1 + a*c + b*c*x))/(b*x)]^2)/2 - Log[x]*(Log[1 - a*c - b*c*x] - Log[1 + (b*c*x)/(-1 + a*c)]) - (Log[1 - a*c - b*c*x] - Log[(a*(-1 + a*c + b*c*x))/(b*x)])*PolyLog[2, -((b*x)/a)] + PolyLog[2, (b*c*x)/(1 - a*c)] - Log[a + b*x]*PolyLog[2, c*(a + b*x)] + PolyLog[2, 1 - a*c - b*c*x] - (Log[x] + Log[(a*(-1 + a*c + b*c*x))/(b*x)])*PolyLog[2, 1 - a*c - b*c*x] + Log[(a*(-1 + a*c + b*c*x))/(b*x)]*(PolyLog[2, (a*(-1 + a*c + b*c*x))/(b*x)] - PolyLog[2, (-1 + a*c + b*c*x)/(b*c*x)]) + PolyLog[3, -((b*x)/a)] + PolyLog[3, c*(a + b*x)] + PolyLog[3, 1 - a*c - b*c*x] - PolyLog[3, (a*(-1 + a*c + b*c*x))/(b*x)] + PolyLog[3, (-1 + a*c + b*c*x)/(b*c*x)])))/a^2)/(2*x^2)","A",1
137,1,485,605,0.5327589,"\int (d+e x)^3 \text{Li}_2(c (a+b x)) \, dx","Integrate[(d + e*x)^3*PolyLog[2, c*(a + b*x)],x]","\frac{12 e (a c+b c x-1) \log (-a c-b c x+1) \left(b c e \left(8 d \left(11 a^2 c^2-7 a c+2\right)+e x \left(13 a^2 c^2-10 a c+3\right)\right)+e^2 \left(-25 a^3 c^3+23 a^2 c^2-13 a c+3\right)+b^2 c^2 \left(-36 d^2 (3 a c-1)-8 d e x (5 a c-2)+e^2 x^2 (3-7 a c)\right)+b^3 c^3 x \left(36 d^2+16 d e x+3 e^2 x^2\right)\right)+b c \left(300 a^3 c^3 e^3 x-6 a^2 c^2 e^2 x (b c (176 d+13 e x)+46 e)+576 b^2 c^2 d^3 (a c+b c x-1) \log (1-c (a+b x))+4 a c \left(b^2 c^2 \left(-144 d^3+324 d^2 e x+60 d e^2 x^2+7 e^3 x^3\right)+3 b c e^2 x (56 d+5 e x)+39 e^3 x\right)-x \left(b^3 c^3 \left(576 d^3+216 d^2 e x+64 d e^2 x^2+9 e^3 x^3\right)+12 b^2 c^2 e \left(36 d^2+8 d e x+e^2 x^2\right)+6 b c e^2 (32 d+3 e x)+36 e^3\right)\right)-144 c^4 \text{Li}_2(c (a+b x)) \left(a^4 e^3-4 a^3 b d e^2+6 a^2 b^2 d^2 e-4 a b^3 d^3-b^4 x \left(4 d^3+6 d^2 e x+4 d e^2 x^2+e^3 x^3\right)\right)}{576 b^4 c^4}","-\frac{(-a c e+b c d+e)^4 \log (-a c-b c x+1)}{16 b^4 c^4 e}-\frac{(b d-a e) (-a c e+b c d+e)^3 \log (-a c-b c x+1)}{12 b^4 c^3 e}-\frac{(b d-a e)^2 (-a c e+b c d+e)^2 \log (-a c-b c x+1)}{8 b^4 c^2 e}-\frac{(b d-a e)^4 \text{Li}_2(c (a+b x))}{4 b^4 e}-\frac{(-a c-b c x+1) (b d-a e)^3 \log (-a c-b c x+1)}{4 b^4 c}-\frac{x (-a c e+b c d+e)^3}{16 b^3 c^3}-\frac{x (b d-a e) (-a c e+b c d+e)^2}{12 b^3 c^2}-\frac{x (b d-a e)^2 (-a c e+b c d+e)}{8 b^3 c}-\frac{x (b d-a e)^3}{4 b^3}-\frac{(d+e x)^2 (-a c e+b c d+e)^2}{32 b^2 c^2 e}-\frac{(d+e x)^2 (b d-a e) (-a c e+b c d+e)}{24 b^2 c e}+\frac{(d+e x)^2 (b d-a e)^2 \log (-a c-b c x+1)}{8 b^2 e}-\frac{(d+e x)^2 (b d-a e)^2}{16 b^2 e}+\frac{(d+e x)^4 \text{Li}_2(c (a+b x))}{4 e}-\frac{(d+e x)^3 (-a c e+b c d+e)}{48 b c e}+\frac{(d+e x)^3 (b d-a e) \log (-a c-b c x+1)}{12 b e}+\frac{(d+e x)^4 \log (-a c-b c x+1)}{16 e}-\frac{(d+e x)^3 (b d-a e)}{36 b e}-\frac{(d+e x)^4}{64 e}",1,"(12*e*(-1 + a*c + b*c*x)*((3 - 13*a*c + 23*a^2*c^2 - 25*a^3*c^3)*e^2 + b*c*e*(8*(2 - 7*a*c + 11*a^2*c^2)*d + (3 - 10*a*c + 13*a^2*c^2)*e*x) + b^3*c^3*x*(36*d^2 + 16*d*e*x + 3*e^2*x^2) + b^2*c^2*(-36*(-1 + 3*a*c)*d^2 - 8*(-2 + 5*a*c)*d*e*x + (3 - 7*a*c)*e^2*x^2))*Log[1 - a*c - b*c*x] + b*c*(300*a^3*c^3*e^3*x - 6*a^2*c^2*e^2*x*(46*e + b*c*(176*d + 13*e*x)) + 4*a*c*(39*e^3*x + 3*b*c*e^2*x*(56*d + 5*e*x) + b^2*c^2*(-144*d^3 + 324*d^2*e*x + 60*d*e^2*x^2 + 7*e^3*x^3)) - x*(36*e^3 + 6*b*c*e^2*(32*d + 3*e*x) + 12*b^2*c^2*e*(36*d^2 + 8*d*e*x + e^2*x^2) + b^3*c^3*(576*d^3 + 216*d^2*e*x + 64*d*e^2*x^2 + 9*e^3*x^3)) + 576*b^2*c^2*d^3*(-1 + a*c + b*c*x)*Log[1 - c*(a + b*x)]) - 144*c^4*(-4*a*b^3*d^3 + 6*a^2*b^2*d^2*e - 4*a^3*b*d*e^2 + a^4*e^3 - b^4*x*(4*d^3 + 6*d^2*e*x + 4*d*e^2*x^2 + e^3*x^3))*PolyLog[2, c*(a + b*x)])/(576*b^4*c^4)","A",1
138,1,274,385,0.1790909,"\int (d+e x)^2 \text{Li}_2(c (a+b x)) \, dx","Integrate[(d + e*x)^2*PolyLog[2, c*(a + b*x)],x]","\frac{b c \left(-66 a^2 c^2 e^2 x+3 a c \left(b c \left(-36 d^2+54 d e x+5 e^2 x^2\right)+14 e^2 x\right)+108 b c d^2 (a c+b c x-1) \log (1-c (a+b x))-x \left(b^2 c^2 \left(108 d^2+27 d e x+4 e^2 x^2\right)+6 b c e (9 d+e x)+12 e^2\right)\right)+6 e (a c+b c x-1) \log (-a c-b c x+1) \left(e \left(11 a^2 c^2-7 a c+2\right)+b c (d (9-27 a c)+e x (2-5 a c))+b^2 c^2 x (9 d+2 e x)\right)+36 c^3 \text{Li}_2(c (a+b x)) \left(a^3 e^2-3 a^2 b d e+3 a b^2 d^2+b^3 x \left(3 d^2+3 d e x+e^2 x^2\right)\right)}{108 b^3 c^3}","-\frac{(-a c e+b c d+e)^3 \log (-a c-b c x+1)}{9 b^3 c^3 e}-\frac{(b d-a e) (-a c e+b c d+e)^2 \log (-a c-b c x+1)}{6 b^3 c^2 e}-\frac{(b d-a e)^3 \text{Li}_2(c (a+b x))}{3 b^3 e}-\frac{(-a c-b c x+1) (b d-a e)^2 \log (-a c-b c x+1)}{3 b^3 c}-\frac{x (-a c e+b c d+e)^2}{9 b^2 c^2}-\frac{x (b d-a e) (-a c e+b c d+e)}{6 b^2 c}-\frac{x (b d-a e)^2}{3 b^2}+\frac{(d+e x)^3 \text{Li}_2(c (a+b x))}{3 e}-\frac{(d+e x)^2 (-a c e+b c d+e)}{18 b c e}+\frac{(d+e x)^2 (b d-a e) \log (-a c-b c x+1)}{6 b e}+\frac{(d+e x)^3 \log (-a c-b c x+1)}{9 e}-\frac{(d+e x)^2 (b d-a e)}{12 b e}-\frac{(d+e x)^3}{27 e}",1,"(6*e*(-1 + a*c + b*c*x)*((2 - 7*a*c + 11*a^2*c^2)*e + b^2*c^2*x*(9*d + 2*e*x) + b*c*((9 - 27*a*c)*d + (2 - 5*a*c)*e*x))*Log[1 - a*c - b*c*x] + b*c*(-66*a^2*c^2*e^2*x - x*(12*e^2 + 6*b*c*e*(9*d + e*x) + b^2*c^2*(108*d^2 + 27*d*e*x + 4*e^2*x^2)) + 3*a*c*(14*e^2*x + b*c*(-36*d^2 + 54*d*e*x + 5*e^2*x^2)) + 108*b*c*d^2*(-1 + a*c + b*c*x)*Log[1 - c*(a + b*x)]) + 36*c^3*(3*a*b^2*d^2 - 3*a^2*b*d*e + a^3*e^2 + b^3*x*(3*d^2 + 3*d*e*x + e^2*x^2))*PolyLog[2, c*(a + b*x)])/(108*b^3*c^3)","A",1
139,1,161,210,0.0821486,"\int (d+e x) \text{Li}_2(c (a+b x)) \, dx","Integrate[(d + e*x)*PolyLog[2, c*(a + b*x)],x]","\frac{e \left(\left(-6 a^2 c^2-4 a c (b c x-2)+2 b^2 c^2 x^2-2\right) \log (-a c-b c x+1)-4 a^2 c^2 \text{Li}_2(c (a+b x))-b c x (-6 a c+b c x+2)\right)}{8 b^2 c^2}+\frac{d (c (a+b x) \text{Li}_2(c (a+b x))-c (a+b x)+(c (a+b x)-1) \log (1-c (a+b x)))}{b c}+\frac{1}{2} e x^2 \text{Li}_2(a c+b x c)","-\frac{(-a c e+b c d+e)^2 \log (-a c-b c x+1)}{4 b^2 c^2 e}-\frac{(b d-a e)^2 \text{Li}_2(c (a+b x))}{2 b^2 e}-\frac{(-a c-b c x+1) (b d-a e) \log (-a c-b c x+1)}{2 b^2 c}+\frac{(d+e x)^2 \text{Li}_2(c (a+b x))}{2 e}-\frac{x (-a c e+b c d+e)}{4 b c}+\frac{(d+e x)^2 \log (-a c-b c x+1)}{4 e}-\frac{x (b d-a e)}{2 b}-\frac{(d+e x)^2}{8 e}",1,"(e*(-(b*c*x*(2 - 6*a*c + b*c*x)) + (-2 - 6*a^2*c^2 + 2*b^2*c^2*x^2 - 4*a*c*(-2 + b*c*x))*Log[1 - a*c - b*c*x] - 4*a^2*c^2*PolyLog[2, c*(a + b*x)]))/(8*b^2*c^2) + (d*(-(c*(a + b*x)) + (-1 + c*(a + b*x))*Log[1 - c*(a + b*x)] + c*(a + b*x)*PolyLog[2, c*(a + b*x)]))/(b*c) + (e*x^2*PolyLog[2, a*c + b*c*x])/2","A",1
140,1,53,60,0.0149051,"\int \text{Li}_2(c (a+b x)) \, dx","Integrate[PolyLog[2, c*(a + b*x)],x]","\frac{c (a+b x) \text{Li}_2(c (a+b x))-c (a+b x)+(c (a+b x)-1) \log (1-c (a+b x))}{b c}","x \text{Li}_2(c (a+b x))+\frac{a \text{Li}_2(c (a+b x))}{b}-\frac{(-a c-b c x+1) \log (-a c-b c x+1)}{b c}-x",1,"(-(c*(a + b*x)) + (-1 + c*(a + b*x))*Log[1 - c*(a + b*x)] + c*(a + b*x)*PolyLog[2, c*(a + b*x)])/(b*c)","A",1
141,1,622,591,0.2265114,"\int \frac{\text{Li}_2(c (a+b x))}{d+e x} \, dx","Integrate[PolyLog[2, c*(a + b*x)]/(d + e*x),x]","\frac{-\text{Li}_3\left(\frac{b c (d+e x)}{e (a c+b x c-1)}\right)+\text{Li}_3\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\left(\text{Li}_2\left(\frac{b c (d+e x)}{e (a c+b x c-1)}\right)-\text{Li}_2\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \log \left(-\frac{b (d+e x)}{(a c+b c x-1) (b d-a e)}\right)+\log (d+e x) \text{Li}_2(c (a+b x))+\text{Li}_2(-a c-b x c+1) \left(\log (d+e x)-\log \left(-\frac{b (d+e x)}{(a c+b c x-1) (b d-a e)}\right)\right)+\text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right) \left(\log \left(-\frac{b (d+e x)}{(a c+b c x-1) (b d-a e)}\right)+\log (-a c-b c x+1)\right)+\frac{1}{2} \left(-\log \left(\frac{(a+b x) (-a c e+b c d+e)}{(a c+b c x-1) (b d-a e)}\right)+\log \left(\frac{-a c e+b c d+e}{-a c e-b c e x+e}\right)+\log (c (a+b x))\right) \log ^2\left(-\frac{b (d+e x)}{(a c+b c x-1) (b d-a e)}\right)+\log \left(\frac{b (d+e x)}{b d-a e}\right) \left(\log \left(\frac{e (a+b x)}{a e-b d}\right)-\log (c (a+b x))\right) \log \left(-\frac{b (d+e x)}{(a c+b c x-1) (b d-a e)}\right)+\log (d+e x) \log (c (a+b x)) \log (-a c-b c x+1)+\frac{1}{2} \log \left(\frac{b (d+e x)}{b d-a e}\right) \left(\log (c (a+b x))-\log \left(\frac{e (a+b x)}{a e-b d}\right)\right) \left(\log \left(\frac{b (d+e x)}{b d-a e}\right)-2 \log (-a c-b c x+1)\right)-\text{Li}_3(-a c-b x c+1)-\text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)}{e}","-\frac{\text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{e}+\frac{\text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{e}-\frac{\text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right) \log \left(\frac{b (d+e x)}{(1-c (a+b x)) (b d-a e)}\right)}{e}+\frac{\text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right) \log \left(\frac{b (d+e x)}{(1-c (a+b x)) (b d-a e)}\right)}{e}+\frac{\log (d+e x) \text{Li}_2(c (a+b x))}{e}+\frac{\text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right) \left(\log \left(\frac{b (d+e x)}{(1-c (a+b x)) (b d-a e)}\right)+\log (1-c (a+b x))\right)}{e}+\frac{\text{Li}_2(1-c (a+b x)) \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(1-c (a+b x)) (b d-a e)}\right)\right)}{e}+\frac{\left(\log \left(\frac{-a c e+b c d+e}{b c (d+e x)}\right)-\log \left(\frac{(a+b x) (-a c e+b c d+e)}{b (d+e x)}\right)+\log (c (a+b x))\right) \log ^2\left(\frac{b (d+e x)}{(1-c (a+b x)) (b d-a e)}\right)}{2 e}-\frac{\left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(1-c (a+b x)) (b d-a e)}\right)+\log (1-c (a+b x))\right)^2}{2 e}+\frac{\log (d+e x) \log (c (a+b x)) \log (1-c (a+b x))}{e}-\frac{\text{Li}_3(1-c (a+b x))}{e}-\frac{\text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)}{e}",1,"(Log[c*(a + b*x)]*Log[1 - a*c - b*c*x]*Log[d + e*x] + ((Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*(-2*Log[1 - a*c - b*c*x] + Log[(b*(d + e*x))/(b*d - a*e)]))/2 + (-Log[c*(a + b*x)] + Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] + (Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]^2*(Log[c*(a + b*x)] - Log[((b*c*d + e - a*c*e)*(a + b*x))/((b*d - a*e)*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + Log[d + e*x]*PolyLog[2, c*(a + b*x)] + (Log[d + e*x] - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, 1 - a*c - b*c*x] + (Log[1 - a*c - b*c*x] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, (b*(d + e*x))/(b*d - a*e)] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]*(PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] - PolyLog[2, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - PolyLog[3, 1 - a*c - b*c*x] - PolyLog[3, (b*(d + e*x))/(b*d - a*e)] - PolyLog[3, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] + PolyLog[3, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])/e","A",1
142,1,108,138,0.1314749,"\int \frac{\text{Li}_2(c (a+b x))}{(d+e x)^2} \, dx","Integrate[PolyLog[2, c*(a + b*x)]/(d + e*x)^2,x]","\frac{\frac{b \left(\text{Li}_2\left(\frac{e (a c+b x c-1)}{-b c d+a c e-e}\right)+\log (-a c-b c x+1) \log \left(\frac{b c (d+e x)}{-a c e+b c d+e}\right)+\text{Li}_2(c (a+b x))\right)}{b d-a e}-\frac{\text{Li}_2(c (a+b x))}{d+e x}}{e}","\frac{b \text{Li}_2(c (a+b x))}{e (b d-a e)}-\frac{\text{Li}_2(c (a+b x))}{e (d+e x)}+\frac{b \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right)}{e (b d-a e)}+\frac{b \log (-a c-b c x+1) \log \left(\frac{b c (d+e x)}{-a c e+b c d+e}\right)}{e (b d-a e)}",1,"(-(PolyLog[2, c*(a + b*x)]/(d + e*x)) + (b*(Log[1 - a*c - b*c*x]*Log[(b*c*(d + e*x))/(b*c*d + e - a*c*e)] + PolyLog[2, c*(a + b*x)] + PolyLog[2, (e*(-1 + a*c + b*c*x))/(-(b*c*d) - e + a*c*e)]))/(b*d - a*e))/e","A",1
143,1,190,278,0.3107194,"\int \frac{\text{Li}_2(c (a+b x))}{(d+e x)^3} \, dx","Integrate[PolyLog[2, c*(a + b*x)]/(d + e*x)^3,x]","\frac{\frac{b \left(b \text{Li}_2\left(\frac{e (a c+b x c-1)}{(a c-1) e-b c d}\right)+b \log (-a c-b c x+1) \log \left(\frac{b c (d+e x)}{-a c e+b c d+e}\right)-\frac{(b d-a e) \log (-a c-b c x+1)}{d+e x}+\frac{b c (b d-a e) (\log (-a c-b c x+1)-\log (d+e x))}{-a c e+b c d+e}+b \text{Li}_2(c (a+b x))\right)}{(b d-a e)^2}-\frac{\text{Li}_2(c (a+b x))}{(d+e x)^2}}{2 e}","\frac{b^2 \text{Li}_2(c (a+b x))}{2 e (b d-a e)^2}+\frac{b^2 \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right)}{2 e (b d-a e)^2}+\frac{b^2 c \log (-a c-b c x+1)}{2 e (b d-a e) (-a c e+b c d+e)}-\frac{b^2 c \log (d+e x)}{2 e (b d-a e) (-a c e+b c d+e)}+\frac{b^2 \log (-a c-b c x+1) \log \left(\frac{b c (d+e x)}{-a c e+b c d+e}\right)}{2 e (b d-a e)^2}-\frac{\text{Li}_2(c (a+b x))}{2 e (d+e x)^2}-\frac{b \log (-a c-b c x+1)}{2 e (d+e x) (b d-a e)}",1,"(-(PolyLog[2, c*(a + b*x)]/(d + e*x)^2) + (b*(-(((b*d - a*e)*Log[1 - a*c - b*c*x])/(d + e*x)) + (b*c*(b*d - a*e)*(Log[1 - a*c - b*c*x] - Log[d + e*x]))/(b*c*d + e - a*c*e) + b*Log[1 - a*c - b*c*x]*Log[(b*c*(d + e*x))/(b*c*d + e - a*c*e)] + b*PolyLog[2, c*(a + b*x)] + b*PolyLog[2, (e*(-1 + a*c + b*c*x))/(-(b*c*d) + (-1 + a*c)*e)]))/(b*d - a*e)^2)/(2*e)","A",1
144,1,313,448,0.5302078,"\int \frac{\text{Li}_2(c (a+b x))}{(d+e x)^4} \, dx","Integrate[PolyLog[2, c*(a + b*x)]/(d + e*x)^4,x]","\frac{\frac{b \left(2 b^2 \text{Li}_2\left(\frac{e (a c+b x c-1)}{(a c-1) e-b c d}\right)+\frac{2 b^2 c (b d-a e) (\log (-a c-b c x+1)-\log (d+e x))}{-a c e+b c d+e}+2 b^2 \log (-a c-b c x+1) \log \left(\frac{b c (d+e x)}{-a c e+b c d+e}\right)+2 b^2 \text{Li}_2(c (a+b x))-\frac{2 b (b d-a e) \log (-a c-b c x+1)}{d+e x}+\frac{b c (b d-a e)^2 (b c (d+e x) \log (-a c-b c x+1)-a c e-b c (d+e x) \log (d+e x)+b c d+e)}{(d+e x) (-a c e+b c d+e)^2}-\frac{(b d-a e)^2 \log (-a c-b c x+1)}{(d+e x)^2}\right)}{(b d-a e)^3}-\frac{2 \text{Li}_2(c (a+b x))}{(d+e x)^3}}{6 e}","\frac{b^3 c^2 \log (-a c-b c x+1)}{6 e (b d-a e) (-a c e+b c d+e)^2}-\frac{b^3 c^2 \log (d+e x)}{6 e (b d-a e) (-a c e+b c d+e)^2}+\frac{b^3 \text{Li}_2(c (a+b x))}{3 e (b d-a e)^3}+\frac{b^3 \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right)}{3 e (b d-a e)^3}+\frac{b^3 c \log (-a c-b c x+1)}{3 e (b d-a e)^2 (-a c e+b c d+e)}-\frac{b^3 c \log (d+e x)}{3 e (b d-a e)^2 (-a c e+b c d+e)}+\frac{b^3 \log (-a c-b c x+1) \log \left(\frac{b c (d+e x)}{-a c e+b c d+e}\right)}{3 e (b d-a e)^3}+\frac{b^2 c}{6 e (d+e x) (b d-a e) (-a c e+b c d+e)}-\frac{b^2 \log (-a c-b c x+1)}{3 e (d+e x) (b d-a e)^2}-\frac{\text{Li}_2(c (a+b x))}{3 e (d+e x)^3}-\frac{b \log (-a c-b c x+1)}{6 e (d+e x)^2 (b d-a e)}",1,"((-2*PolyLog[2, c*(a + b*x)])/(d + e*x)^3 + (b*(-(((b*d - a*e)^2*Log[1 - a*c - b*c*x])/(d + e*x)^2) - (2*b*(b*d - a*e)*Log[1 - a*c - b*c*x])/(d + e*x) + (2*b^2*c*(b*d - a*e)*(Log[1 - a*c - b*c*x] - Log[d + e*x]))/(b*c*d + e - a*c*e) + (b*c*(b*d - a*e)^2*(b*c*d + e - a*c*e + b*c*(d + e*x)*Log[1 - a*c - b*c*x] - b*c*(d + e*x)*Log[d + e*x]))/((b*c*d + e - a*c*e)^2*(d + e*x)) + 2*b^2*Log[1 - a*c - b*c*x]*Log[(b*c*(d + e*x))/(b*c*d + e - a*c*e)] + 2*b^2*PolyLog[2, c*(a + b*x)] + 2*b^2*PolyLog[2, (e*(-1 + a*c + b*c*x))/(-(b*c*d) + (-1 + a*c)*e)]))/(b*d - a*e)^3)/(6*e)","A",1
145,1,46,46,0.0406464,"\int \frac{\text{Li}_2(x)}{-1+x} \, dx","Integrate[PolyLog[2, x]/(-1 + x),x]","-2 \text{Li}_3(1-x)+2 \text{Li}_2(1-x) \log (1-x)+\text{Li}_2(x) \log (1-x)+\log (x) \log ^2(1-x)","-2 \text{Li}_3(1-x)+2 \text{Li}_2(1-x) \log (1-x)+\text{Li}_2(x) \log (1-x)+\log (x) \log ^2(1-x)",1,"Log[1 - x]^2*Log[x] + 2*Log[1 - x]*PolyLog[2, 1 - x] + Log[1 - x]*PolyLog[2, x] - 2*PolyLog[3, 1 - x]","A",1
146,1,46,46,0.0068254,"\int -\frac{\text{Li}_2(x)}{1-x} \, dx","Integrate[-(PolyLog[2, x]/(1 - x)),x]","-2 \text{Li}_3(1-x)+2 \text{Li}_2(1-x) \log (1-x)+\text{Li}_2(x) \log (1-x)+\log (x) \log ^2(1-x)","-2 \text{Li}_3(1-x)+2 \text{Li}_2(1-x) \log (1-x)+\text{Li}_2(x) \log (1-x)+\log (x) \log ^2(1-x)",1,"Log[1 - x]^2*Log[x] + 2*Log[1 - x]*PolyLog[2, 1 - x] + Log[1 - x]*PolyLog[2, x] - 2*PolyLog[3, 1 - x]","A",1
147,1,51,51,0.0382535,"\int \frac{\text{Li}_2(x)}{(-1+x) x} \, dx","Integrate[PolyLog[2, x]/((-1 + x)*x),x]","-2 \text{Li}_3(1-x)-\text{Li}_3(x)+2 \text{Li}_2(1-x) \log (1-x)+\text{Li}_2(x) \log (1-x)+\log (x) \log ^2(1-x)","-2 \text{Li}_3(1-x)-\text{Li}_3(x)+2 \text{Li}_2(1-x) \log (1-x)+\text{Li}_2(x) \log (1-x)+\log (x) \log ^2(1-x)",1,"Log[1 - x]^2*Log[x] + 2*Log[1 - x]*PolyLog[2, 1 - x] + Log[1 - x]*PolyLog[2, x] - 2*PolyLog[3, 1 - x] - PolyLog[3, x]","A",1
148,1,51,51,0.0143328,"\int -\frac{\text{Li}_2(x)}{(1-x) x} \, dx","Integrate[-(PolyLog[2, x]/((1 - x)*x)),x]","-2 \text{Li}_3(1-x)-\text{Li}_3(x)+2 \text{Li}_2(1-x) \log (1-x)+\text{Li}_2(x) \log (1-x)+\log (x) \log ^2(1-x)","-2 \text{Li}_3(1-x)-\text{Li}_3(x)+2 \text{Li}_2(1-x) \log (1-x)+\text{Li}_2(x) \log (1-x)+\log (x) \log ^2(1-x)",1,"Log[1 - x]^2*Log[x] + 2*Log[1 - x]*PolyLog[2, 1 - x] + Log[1 - x]*PolyLog[2, x] - 2*PolyLog[3, 1 - x] - PolyLog[3, x]","A",1
149,1,34,35,0.0191351,"\int \frac{\text{Li}_n\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a+b x) (c+d x)} \, dx","Integrate[PolyLog[n, e*((a + b*x)/(c + d*x))^n]/((a + b*x)*(c + d*x)),x]","\frac{\text{Li}_{n+1}\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c n-a d n}","\frac{\text{Li}_{n+1}\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n (b c-a d)}",1,"PolyLog[1 + n, e*((a + b*x)/(c + d*x))^n]/(b*c*n - a*d*n)","A",1
150,1,32,33,0.0068883,"\int \frac{\text{Li}_3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a+b x) (c+d x)} \, dx","Integrate[PolyLog[3, e*((a + b*x)/(c + d*x))^n]/((a + b*x)*(c + d*x)),x]","\frac{\text{Li}_4\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c n-a d n}","\frac{\text{Li}_4\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n (b c-a d)}",1,"PolyLog[4, e*((a + b*x)/(c + d*x))^n]/(b*c*n - a*d*n)","A",1
151,1,32,33,0.0066276,"\int \frac{\text{Li}_2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a+b x) (c+d x)} \, dx","Integrate[PolyLog[2, e*((a + b*x)/(c + d*x))^n]/((a + b*x)*(c + d*x)),x]","\frac{\text{Li}_3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c n-a d n}","\frac{\text{Li}_3\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n (b c-a d)}",1,"PolyLog[3, e*((a + b*x)/(c + d*x))^n]/(b*c*n - a*d*n)","A",1
152,1,40,33,1.7723629,"\int -\frac{\log \left(1-e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a+b x) (c+d x)} \, dx","Integrate[-(Log[1 - e*((a + b*x)/(c + d*x))^n]/((a + b*x)*(c + d*x))),x]","-\int \frac{\log \left(1-e \left(\frac{a+b x}{c+d x}\right)^n\right)}{(a+b x) (c+d x)} \, dx","\frac{\text{Li}_2\left(e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n (b c-a d)}",1,"-Integrate[Log[1 - e*((a + b*x)/(c + d*x))^n]/((a + b*x)*(c + d*x)), x]","F",1
153,1,38,36,0.087401,"\int \frac{e \left(\frac{a+b x}{c+d x}\right)^n}{(a+b x) (c+d x) \left(1-e \left(\frac{a+b x}{c+d x}\right)^n\right)} \, dx","Integrate[(e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)*(1 - e*((a + b*x)/(c + d*x))^n)),x]","-\frac{e \log \left(1-e \left(\frac{a+b x}{c+d x}\right)^n\right)}{b c e n-a d e n}","-\frac{\log \left(1-e \left(\frac{a+b x}{c+d x}\right)^n\right)}{n (b c-a d)}",1,"-((e*Log[1 - e*((a + b*x)/(c + d*x))^n])/(b*c*e*n - a*d*e*n))","A",1
154,1,35,36,0.1014695,"\int \frac{e \left(\frac{a+b x}{c+d x}\right)^n}{(a+b x) (c+d x) \left(1-e \left(\frac{a+b x}{c+d x}\right)^n\right)^2} \, dx","Integrate[(e*((a + b*x)/(c + d*x))^n)/((a + b*x)*(c + d*x)*(1 - e*((a + b*x)/(c + d*x))^n)^2),x]","\frac{1}{n (a d-b c) \left(e \left(\frac{a+b x}{c+d x}\right)^n-1\right)}","\frac{1}{n (b c-a d) \left(1-e \left(\frac{a+b x}{c+d x}\right)^n\right)}",1,"1/((-(b*c) + a*d)*n*(-1 + e*((a + b*x)/(c + d*x))^n))","A",1
155,1,52,52,0.2488066,"\int \frac{e \left(\frac{a+b x}{c+d x}\right)^n+e^2 \left(\frac{a+b x}{c+d x}\right)^{2 n}}{(a+b x) (c+d x) \left(1-e \left(\frac{a+b x}{c+d x}\right)^n\right)^3} \, dx","Integrate[(e*((a + b*x)/(c + d*x))^n + e^2*((a + b*x)/(c + d*x))^(2*n))/((a + b*x)*(c + d*x)*(1 - e*((a + b*x)/(c + d*x))^n)^3),x]","-\frac{e \left(\frac{a+b x}{c+d x}\right)^n}{n (a d-b c) \left(e \left(\frac{a+b x}{c+d x}\right)^n-1\right)^2}","\frac{e \left(\frac{a+b x}{c+d x}\right)^n}{n (b c-a d) \left(1-e \left(\frac{a+b x}{c+d x}\right)^n\right)^2}",1,"-((e*((a + b*x)/(c + d*x))^n)/((-(b*c) + a*d)*n*(-1 + e*((a + b*x)/(c + d*x))^n)^2))","A",1
156,1,135,135,0.0111225,"\int x^3 \text{Li}_n\left(d \left(F^{c (a+b x)}\right)^p\right) \, dx","Integrate[x^3*PolyLog[n, d*(F^(c*(a + b*x)))^p],x]","-\frac{6 \text{Li}_{n+4}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^4 c^4 p^4 \log ^4(F)}+\frac{6 x \text{Li}_{n+3}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^3 c^3 p^3 \log ^3(F)}-\frac{3 x^2 \text{Li}_{n+2}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^2 c^2 p^2 \log ^2(F)}+\frac{x^3 \text{Li}_{n+1}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b c p \log (F)}","-\frac{6 \text{Li}_{n+4}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^4 c^4 p^4 \log ^4(F)}+\frac{6 x \text{Li}_{n+3}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^3 c^3 p^3 \log ^3(F)}-\frac{3 x^2 \text{Li}_{n+2}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^2 c^2 p^2 \log ^2(F)}+\frac{x^3 \text{Li}_{n+1}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b c p \log (F)}",1,"(x^3*PolyLog[1 + n, d*(F^(c*(a + b*x)))^p])/(b*c*p*Log[F]) - (3*x^2*PolyLog[2 + n, d*(F^(c*(a + b*x)))^p])/(b^2*c^2*p^2*Log[F]^2) + (6*x*PolyLog[3 + n, d*(F^(c*(a + b*x)))^p])/(b^3*c^3*p^3*Log[F]^3) - (6*PolyLog[4 + n, d*(F^(c*(a + b*x)))^p])/(b^4*c^4*p^4*Log[F]^4)","A",1
157,1,100,100,0.005993,"\int x^2 \text{Li}_n\left(d \left(F^{c (a+b x)}\right)^p\right) \, dx","Integrate[x^2*PolyLog[n, d*(F^(c*(a + b*x)))^p],x]","\frac{2 \text{Li}_{n+3}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^3 c^3 p^3 \log ^3(F)}-\frac{2 x \text{Li}_{n+2}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^2 c^2 p^2 \log ^2(F)}+\frac{x^2 \text{Li}_{n+1}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b c p \log (F)}","\frac{2 \text{Li}_{n+3}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^3 c^3 p^3 \log ^3(F)}-\frac{2 x \text{Li}_{n+2}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^2 c^2 p^2 \log ^2(F)}+\frac{x^2 \text{Li}_{n+1}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b c p \log (F)}",1,"(x^2*PolyLog[1 + n, d*(F^(c*(a + b*x)))^p])/(b*c*p*Log[F]) - (2*x*PolyLog[2 + n, d*(F^(c*(a + b*x)))^p])/(b^2*c^2*p^2*Log[F]^2) + (2*PolyLog[3 + n, d*(F^(c*(a + b*x)))^p])/(b^3*c^3*p^3*Log[F]^3)","A",1
158,1,65,65,0.0050009,"\int x \text{Li}_n\left(d \left(F^{c (a+b x)}\right)^p\right) \, dx","Integrate[x*PolyLog[n, d*(F^(c*(a + b*x)))^p],x]","\frac{x \text{Li}_{n+1}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b c p \log (F)}-\frac{\text{Li}_{n+2}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^2 c^2 p^2 \log ^2(F)}","\frac{x \text{Li}_{n+1}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b c p \log (F)}-\frac{\text{Li}_{n+2}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b^2 c^2 p^2 \log ^2(F)}",1,"(x*PolyLog[1 + n, d*(F^(c*(a + b*x)))^p])/(b*c*p*Log[F]) - PolyLog[2 + n, d*(F^(c*(a + b*x)))^p]/(b^2*c^2*p^2*Log[F]^2)","A",1
159,1,31,31,0.0038426,"\int \text{Li}_n\left(d \left(F^{c (a+b x)}\right)^p\right) \, dx","Integrate[PolyLog[n, d*(F^(c*(a + b*x)))^p],x]","\frac{\text{Li}_{n+1}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b c p \log (F)}","\frac{\text{Li}_{n+1}\left(d \left(F^{c (a+b x)}\right)^p\right)}{b c p \log (F)}",1,"PolyLog[1 + n, d*(F^(c*(a + b*x)))^p]/(b*c*p*Log[F])","A",1
160,0,0,23,0.0532084,"\int \frac{\text{Li}_n\left(d \left(F^{c (a+b x)}\right)^p\right)}{x} \, dx","Integrate[PolyLog[n, d*(F^(c*(a + b*x)))^p]/x,x]","\int \frac{\text{Li}_n\left(d \left(F^{c (a+b x)}\right)^p\right)}{x} \, dx","\text{Int}\left(\frac{\text{Li}_n\left(d \left(F^{a c+b x c}\right)^p\right)}{x},x\right)",0,"Integrate[PolyLog[n, d*(F^(c*(a + b*x)))^p]/x, x]","A",-1
161,1,223,300,0.5613253,"\int x^3 \log (1-c x) \text{Li}_2(c x) \, dx","Integrate[x^3*Log[1 - c*x]*PolyLog[2, c*x],x]","\frac{81 c^4 x^4+432 c^4 x^4 \log ^2(1-c x)-324 c^4 x^4 \log (1-c x)+268 c^3 x^3-480 c^3 x^3 \log (1-c x)+834 c^2 x^2-864 c^2 x^2 \log (1-c x)+144 \text{Li}_2(c x) \left(12 \left(c^4 x^4-1\right) \log (1-c x)-c x \left(3 c^3 x^3+4 c^2 x^2+6 c x+12\right)\right)+3456 \text{Li}_3(1-c x)-3456 \text{Li}_2(1-c x) \log (1-c x)+4260 c x-1728 \log (c x) \log ^2(1-c x)-432 \log ^2(1-c x)-2592 c x \log (1-c x)+4260 \log (1-c x)}{6912 c^4}","\frac{\text{Li}_3(1-c x)}{2 c^4}-\frac{\text{Li}_2(c x) \log (1-c x)}{4 c^4}-\frac{\text{Li}_2(1-c x) \log (1-c x)}{2 c^4}-\frac{\log (c x) \log ^2(1-c x)}{4 c^4}-\frac{\log ^2(1-c x)}{16 c^4}+\frac{3 (1-c x) \log (1-c x)}{8 c^4}+\frac{139 \log (1-c x)}{576 c^4}-\frac{x \text{Li}_2(c x)}{4 c^3}+\frac{355 x}{576 c^3}-\frac{x^2 \text{Li}_2(c x)}{8 c^2}+\frac{139 x^2}{1152 c^2}-\frac{x^2 \log (1-c x)}{8 c^2}-\frac{1}{16} x^4 \text{Li}_2(c x)+\frac{1}{4} x^4 \text{Li}_2(c x) \log (1-c x)-\frac{x^3 \text{Li}_2(c x)}{12 c}+\frac{1}{16} x^4 \log ^2(1-c x)-\frac{3}{64} x^4 \log (1-c x)+\frac{67 x^3}{1728 c}-\frac{5 x^3 \log (1-c x)}{72 c}+\frac{3 x^4}{256}",1,"(4260*c*x + 834*c^2*x^2 + 268*c^3*x^3 + 81*c^4*x^4 + 4260*Log[1 - c*x] - 2592*c*x*Log[1 - c*x] - 864*c^2*x^2*Log[1 - c*x] - 480*c^3*x^3*Log[1 - c*x] - 324*c^4*x^4*Log[1 - c*x] - 432*Log[1 - c*x]^2 + 432*c^4*x^4*Log[1 - c*x]^2 - 1728*Log[c*x]*Log[1 - c*x]^2 + 144*(-(c*x*(12 + 6*c*x + 4*c^2*x^2 + 3*c^3*x^3)) + 12*(-1 + c^4*x^4)*Log[1 - c*x])*PolyLog[2, c*x] - 3456*Log[1 - c*x]*PolyLog[2, 1 - c*x] + 3456*PolyLog[3, 1 - c*x])/(6912*c^4)","A",1
162,1,192,258,0.3226632,"\int x^2 \log (1-c x) \text{Li}_2(c x) \, dx","Integrate[x^2*Log[1 - c*x]*PolyLog[2, c*x],x]","\frac{8 c^3 x^3+24 c^3 x^3 \log ^2(1-c x)-24 c^3 x^3 \log (1-c x)+33 c^2 x^2-42 c^2 x^2 \log (1-c x)+12 \text{Li}_2(c x) \left(6 \left(c^3 x^3-1\right) \log (1-c x)-c x \left(2 c^2 x^2+3 c x+6\right)\right)+144 \text{Li}_3(1-c x)-144 \text{Li}_2(1-c x) \log (1-c x)+186 c x-72 \log (c x) \log ^2(1-c x)-24 \log ^2(1-c x)-120 c x \log (1-c x)+186 \log (1-c x)}{216 c^3}","\frac{2 \text{Li}_3(1-c x)}{3 c^3}-\frac{\text{Li}_2(c x) \log (1-c x)}{3 c^3}-\frac{2 \text{Li}_2(1-c x) \log (1-c x)}{3 c^3}-\frac{\log (c x) \log ^2(1-c x)}{3 c^3}-\frac{\log ^2(1-c x)}{9 c^3}+\frac{5 (1-c x) \log (1-c x)}{9 c^3}+\frac{11 \log (1-c x)}{36 c^3}-\frac{x \text{Li}_2(c x)}{3 c^2}+\frac{31 x}{36 c^2}-\frac{1}{9} x^3 \text{Li}_2(c x)+\frac{1}{3} x^3 \text{Li}_2(c x) \log (1-c x)-\frac{x^2 \text{Li}_2(c x)}{6 c}+\frac{1}{9} x^3 \log ^2(1-c x)-\frac{1}{9} x^3 \log (1-c x)+\frac{11 x^2}{72 c}-\frac{7 x^2 \log (1-c x)}{36 c}+\frac{x^3}{27}",1,"(186*c*x + 33*c^2*x^2 + 8*c^3*x^3 + 186*Log[1 - c*x] - 120*c*x*Log[1 - c*x] - 42*c^2*x^2*Log[1 - c*x] - 24*c^3*x^3*Log[1 - c*x] - 24*Log[1 - c*x]^2 + 24*c^3*x^3*Log[1 - c*x]^2 - 72*Log[c*x]*Log[1 - c*x]^2 + 12*(-(c*x*(6 + 3*c*x + 2*c^2*x^2)) + 6*(-1 + c^3*x^3)*Log[1 - c*x])*PolyLog[2, c*x] - 144*Log[1 - c*x]*PolyLog[2, 1 - c*x] + 144*PolyLog[3, 1 - c*x])/(216*c^3)","A",1
163,1,160,262,0.2846065,"\int x \log (1-c x) \text{Li}_2(c x) \, dx","Integrate[x*Log[1 - c*x]*PolyLog[2, c*x],x]","\frac{\text{Li}_2(c x) \left(8 \left(c^2 x^2-1\right) \log (1-c x)-4 c x (c x+2)\right)+3 c^2 x^2+4 c^2 x^2 \log ^2(1-c x)-6 c^2 x^2 \log (1-c x)+16 \text{Li}_3(1-c x)-16 \text{Li}_2(1-c x) \log (1-c x)+22 c x-8 \log (c x) \log ^2(1-c x)-4 \log ^2(1-c x)-16 c x \log (1-c x)+22 \log (1-c x)-14}{16 c^2}","\frac{\text{Li}_3(1-c x)}{c^2}-\frac{\text{Li}_2(c x) \log (1-c x)}{2 c^2}-\frac{\text{Li}_2(1-c x) \log (1-c x)}{c^2}+\frac{(1-c x)^2}{8 c^2}+\frac{(1-c x)^2 \log ^2(1-c x)}{4 c^2}-\frac{(1-c x) \log ^2(1-c x)}{2 c^2}-\frac{\log (c x) \log ^2(1-c x)}{2 c^2}-\frac{(1-c x)^2 \log (1-c x)}{4 c^2}+\frac{3 (1-c x) \log (1-c x)}{2 c^2}+\frac{\log (1-c x)}{8 c^2}-\frac{1}{4} x^2 \text{Li}_2(c x)+\frac{1}{2} x^2 \text{Li}_2(c x) \log (1-c x)-\frac{x \text{Li}_2(c x)}{2 c}-\frac{1}{8} x^2 \log (1-c x)+\frac{13 x}{8 c}+\frac{x^2}{16}",1,"(-14 + 22*c*x + 3*c^2*x^2 + 22*Log[1 - c*x] - 16*c*x*Log[1 - c*x] - 6*c^2*x^2*Log[1 - c*x] - 4*Log[1 - c*x]^2 + 4*c^2*x^2*Log[1 - c*x]^2 - 8*Log[c*x]*Log[1 - c*x]^2 + (-4*c*x*(2 + c*x) + 8*(-1 + c^2*x^2)*Log[1 - c*x])*PolyLog[2, c*x] - 16*Log[1 - c*x]*PolyLog[2, 1 - c*x] + 16*PolyLog[3, 1 - c*x])/(16*c^2)","A",1
164,1,119,132,0.0237811,"\int \log (1-c x) \text{Li}_2(c x) \, dx","Integrate[Log[1 - c*x]*PolyLog[2, c*x],x]","\frac{2 \text{Li}_3(1-c x)-2 \text{Li}_2(1-c x) \log (1-c x)+\text{Li}_2(c x) ((c x-1) \log (1-c x)-c x)+3 c x+c x \log ^2(1-c x)-\log (c x) \log ^2(1-c x)-\log ^2(1-c x)-3 c x \log (1-c x)+3 \log (1-c x)-2}{c}","-x \text{Li}_2(c x)+\frac{2 \text{Li}_3(1-c x)}{c}+x \text{Li}_2(c x) \log (1-c x)-\frac{\text{Li}_2(c x) \log (1-c x)}{c}-\frac{2 \text{Li}_2(1-c x) \log (1-c x)}{c}-\frac{(1-c x) \log ^2(1-c x)}{c}-\frac{\log (c x) \log ^2(1-c x)}{c}+\frac{3 (1-c x) \log (1-c x)}{c}+3 x",1,"(-2 + 3*c*x + 3*Log[1 - c*x] - 3*c*x*Log[1 - c*x] - Log[1 - c*x]^2 + c*x*Log[1 - c*x]^2 - Log[c*x]*Log[1 - c*x]^2 + (-(c*x) + (-1 + c*x)*Log[1 - c*x])*PolyLog[2, c*x] - 2*Log[1 - c*x]*PolyLog[2, 1 - c*x] + 2*PolyLog[3, 1 - c*x])/c","A",1
165,1,11,11,0.0102341,"\int \frac{\log (1-c x) \text{Li}_2(c x)}{x} \, dx","Integrate[(Log[1 - c*x]*PolyLog[2, c*x])/x,x]","-\frac{1}{2} \text{Li}_2(c x){}^2","-\frac{1}{2} \text{Li}_2(c x){}^2",1,"-1/2*PolyLog[2, c*x]^2","A",1
166,1,115,111,0.1313089,"\int \frac{\log (1-c x) \text{Li}_2(c x)}{x^2} \, dx","Integrate[(Log[1 - c*x]*PolyLog[2, c*x])/x^2,x]","-c \text{Li}_3(c x)-2 c \text{Li}_3(1-c x)+\frac{(c x-1) \text{Li}_2(c x) \log (1-c x)}{x}+2 c \text{Li}_2(1-c x) (\log (1-c x)+1)-c \log ^2(1-c x)+c \log (c x) \log ^2(1-c x)+\frac{\log ^2(1-c x)}{x}+2 c \log (c x) \log (1-c x)","-2 c \text{Li}_2(c x)-c \text{Li}_3(c x)-2 c \text{Li}_3(1-c x)+c \text{Li}_2(c x) \log (1-c x)-\frac{\text{Li}_2(c x) \log (1-c x)}{x}+2 c \text{Li}_2(1-c x) \log (1-c x)+\frac{(1-c x) \log ^2(1-c x)}{x}+c \log (c x) \log ^2(1-c x)",1,"2*c*Log[c*x]*Log[1 - c*x] - c*Log[1 - c*x]^2 + Log[1 - c*x]^2/x + c*Log[c*x]*Log[1 - c*x]^2 + ((-1 + c*x)*Log[1 - c*x]*PolyLog[2, c*x])/x + 2*c*(1 + Log[1 - c*x])*PolyLog[2, 1 - c*x] - c*PolyLog[3, c*x] - 2*c*PolyLog[3, 1 - c*x]","A",1
167,1,185,191,0.2636198,"\int \frac{\log (1-c x) \text{Li}_2(c x)}{x^3} \, dx","Integrate[(Log[1 - c*x]*PolyLog[2, c*x])/x^3,x]","\frac{1}{4} \left(\frac{2 \text{Li}_2(c x) \left(\left(c^2 x^2-1\right) \log (1-c x)+c x\right)}{x^2}-2 c^2 \text{Li}_3(c x)-4 c^2 \text{Li}_3(1-c x)+2 c^2 \text{Li}_2(1-c x) (2 \log (1-c x)+1)+2 c^2 \log (c x) \log ^2(1-c x)-c^2 \log ^2(1-c x)-2 c^2 \log (x)-2 c^2 \log (c x)+2 c^2 \log (c x) \log (1-c x)+4 c^2 \log (1-c x)+\frac{\log ^2(1-c x)}{x^2}-\frac{4 c \log (1-c x)}{x}\right)","-\frac{1}{2} c^2 \text{Li}_2(c x)-\frac{1}{2} c^2 \text{Li}_3(c x)-c^2 \text{Li}_3(1-c x)+\frac{1}{2} c^2 \text{Li}_2(c x) \log (1-c x)+c^2 \text{Li}_2(1-c x) \log (1-c x)+\frac{1}{2} c^2 \log (c x) \log ^2(1-c x)-\frac{1}{4} c^2 \log ^2(1-c x)-c^2 \log (x)+c^2 \log (1-c x)-\frac{\text{Li}_2(c x) \log (1-c x)}{2 x^2}+\frac{c \text{Li}_2(c x)}{2 x}+\frac{\log ^2(1-c x)}{4 x^2}-\frac{c \log (1-c x)}{x}",1,"(-2*c^2*Log[x] - 2*c^2*Log[c*x] + 4*c^2*Log[1 - c*x] - (4*c*Log[1 - c*x])/x + 2*c^2*Log[c*x]*Log[1 - c*x] - c^2*Log[1 - c*x]^2 + Log[1 - c*x]^2/x^2 + 2*c^2*Log[c*x]*Log[1 - c*x]^2 + (2*(c*x + (-1 + c^2*x^2)*Log[1 - c*x])*PolyLog[2, c*x])/x^2 + 2*c^2*(1 + 2*Log[1 - c*x])*PolyLog[2, 1 - c*x] - 2*c^2*PolyLog[3, c*x] - 4*c^2*PolyLog[3, 1 - c*x])/4","A",1
168,1,246,245,0.2262437,"\int \frac{\log (1-c x) \text{Li}_2(c x)}{x^4} \, dx","Integrate[(Log[1 - c*x]*PolyLog[2, c*x])/x^4,x]","\frac{-12 c^3 x^3 \text{Li}_3(c x)-24 c^3 x^3 \text{Li}_3(1-c x)+8 c^3 x^3 \text{Li}_2(1-c x) (3 \log (1-c x)+1)+6 \text{Li}_2(c x) \left(2 \left(c^3 x^3-1\right) \log (1-c x)+c x (2 c x+1)\right)-4 c^3 x^3-4 c^3 x^3 \log ^2(1-c x)+12 c^3 x^3 \log (c x) \log ^2(1-c x)-15 c^3 x^3 \log (x)-12 c^3 x^3 \log (c x)+27 c^3 x^3 \log (1-c x)+8 c^3 x^3 \log (c x) \log (1-c x)+7 c^2 x^2-20 c^2 x^2 \log (1-c x)+4 \log ^2(1-c x)-7 c x \log (1-c x)}{36 x^3}","-\frac{2}{9} c^3 \text{Li}_2(c x)-\frac{1}{3} c^3 \text{Li}_3(c x)-\frac{2}{3} c^3 \text{Li}_3(1-c x)+\frac{1}{3} c^3 \text{Li}_2(c x) \log (1-c x)+\frac{2}{3} c^3 \text{Li}_2(1-c x) \log (1-c x)+\frac{1}{3} c^3 \log (c x) \log ^2(1-c x)-\frac{1}{9} c^3 \log ^2(1-c x)-\frac{3}{4} c^3 \log (x)+\frac{3}{4} c^3 \log (1-c x)+\frac{c^2 \text{Li}_2(c x)}{3 x}+\frac{7 c^2}{36 x}-\frac{5 c^2 \log (1-c x)}{9 x}-\frac{\text{Li}_2(c x) \log (1-c x)}{3 x^3}+\frac{c \text{Li}_2(c x)}{6 x^2}+\frac{\log ^2(1-c x)}{9 x^3}-\frac{7 c \log (1-c x)}{36 x^2}",1,"(7*c^2*x^2 - 4*c^3*x^3 - 15*c^3*x^3*Log[x] - 12*c^3*x^3*Log[c*x] - 7*c*x*Log[1 - c*x] - 20*c^2*x^2*Log[1 - c*x] + 27*c^3*x^3*Log[1 - c*x] + 8*c^3*x^3*Log[c*x]*Log[1 - c*x] + 4*Log[1 - c*x]^2 - 4*c^3*x^3*Log[1 - c*x]^2 + 12*c^3*x^3*Log[c*x]*Log[1 - c*x]^2 + 6*(c*x*(1 + 2*c*x) + 2*(-1 + c^3*x^3)*Log[1 - c*x])*PolyLog[2, c*x] + 8*c^3*x^3*(1 + 3*Log[1 - c*x])*PolyLog[2, 1 - c*x] - 12*c^3*x^3*PolyLog[3, c*x] - 24*c^3*x^3*PolyLog[3, 1 - c*x])/(36*x^3)","A",1
169,1,277,287,0.2285928,"\int \frac{\log (1-c x) \text{Li}_2(c x)}{x^5} \, dx","Integrate[(Log[1 - c*x]*PolyLog[2, c*x])/x^5,x]","\frac{-36 c^4 x^4 \text{Li}_3(c x)-72 c^4 x^4 \text{Li}_3(1-c x)+18 c^4 x^4 \text{Li}_2(1-c x) (4 \log (1-c x)+1)-18 c^4 x^4-9 c^4 x^4 \log ^2(1-c x)+36 c^4 x^4 \log (c x) \log ^2(1-c x)-49 c^4 x^4 \log (x)-33 c^4 x^4 \log (c x)+82 c^4 x^4 \log (1-c x)+18 c^4 x^4 \log (c x) \log (1-c x)+28 c^3 x^3-54 c^3 x^3 \log (1-c x)+5 c^2 x^2-18 c^2 x^2 \log (1-c x)+6 \text{Li}_2(c x) \left(6 \left(c^4 x^4-1\right) \log (1-c x)+c x \left(6 c^2 x^2+3 c x+2\right)\right)+9 \log ^2(1-c x)-10 c x \log (1-c x)}{144 x^4}","-\frac{1}{8} c^4 \text{Li}_2(c x)-\frac{1}{4} c^4 \text{Li}_3(c x)-\frac{1}{2} c^4 \text{Li}_3(1-c x)+\frac{1}{4} c^4 \text{Li}_2(c x) \log (1-c x)+\frac{1}{2} c^4 \text{Li}_2(1-c x) \log (1-c x)+\frac{1}{4} c^4 \log (c x) \log ^2(1-c x)-\frac{1}{16} c^4 \log ^2(1-c x)-\frac{41}{72} c^4 \log (x)+\frac{41}{72} c^4 \log (1-c x)+\frac{c^3 \text{Li}_2(c x)}{4 x}+\frac{7 c^3}{36 x}-\frac{3 c^3 \log (1-c x)}{8 x}+\frac{c^2 \text{Li}_2(c x)}{8 x^2}+\frac{5 c^2}{144 x^2}-\frac{c^2 \log (1-c x)}{8 x^2}-\frac{\text{Li}_2(c x) \log (1-c x)}{4 x^4}+\frac{c \text{Li}_2(c x)}{12 x^3}+\frac{\log ^2(1-c x)}{16 x^4}-\frac{5 c \log (1-c x)}{72 x^3}",1,"(5*c^2*x^2 + 28*c^3*x^3 - 18*c^4*x^4 - 49*c^4*x^4*Log[x] - 33*c^4*x^4*Log[c*x] - 10*c*x*Log[1 - c*x] - 18*c^2*x^2*Log[1 - c*x] - 54*c^3*x^3*Log[1 - c*x] + 82*c^4*x^4*Log[1 - c*x] + 18*c^4*x^4*Log[c*x]*Log[1 - c*x] + 9*Log[1 - c*x]^2 - 9*c^4*x^4*Log[1 - c*x]^2 + 36*c^4*x^4*Log[c*x]*Log[1 - c*x]^2 + 6*(c*x*(2 + 3*c*x + 6*c^2*x^2) + 6*(-1 + c^4*x^4)*Log[1 - c*x])*PolyLog[2, c*x] + 18*c^4*x^4*(1 + 4*Log[1 - c*x])*PolyLog[2, 1 - c*x] - 36*c^4*x^4*PolyLog[3, c*x] - 72*c^4*x^4*PolyLog[3, 1 - c*x])/(144*x^4)","A",1
170,1,252,423,0.406075,"\int x^2 (g+h \log (1-c x)) \text{Li}_2(c x) \, dx","Integrate[x^2*(g + h*Log[1 - c*x])*PolyLog[2, c*x],x]","\frac{g \left(18 c^3 x^3 \text{Li}_2(c x)+6 \left(c^3 x^3-1\right) \log (1-c x)-c x \left(2 c^2 x^2+3 c x+6\right)\right)}{54 c^3}+\frac{h \left(8 c^3 x^3+24 c^3 x^3 \log ^2(1-c x)-24 c^3 x^3 \log (1-c x)+33 c^2 x^2-42 c^2 x^2 \log (1-c x)+12 \text{Li}_2(c x) \left(6 \left(c^3 x^3-1\right) \log (1-c x)-c x \left(2 c^2 x^2+3 c x+6\right)\right)+144 \text{Li}_3(1-c x)-144 \text{Li}_2(1-c x) \log (1-c x)+186 c x-72 \log (c x) \log ^2(1-c x)-24 \log ^2(1-c x)-120 c x \log (1-c x)+186 \log (1-c x)\right)}{216 c^3}","\frac{(1-c x)^3 (2 h \log (1-c x)+g)}{27 c^3}-\frac{(1-c x)^2 (2 h \log (1-c x)+g)}{6 c^3}+\frac{(1-c x) (2 h \log (1-c x)+g)}{3 c^3}-\frac{\log (1-c x) (2 h \log (1-c x)+g)}{9 c^3}+\frac{2 h \text{Li}_3(1-c x)}{3 c^3}-\frac{h \text{Li}_2(c x) \log (1-c x)}{3 c^3}-\frac{2 h \text{Li}_2(1-c x) \log (1-c x)}{3 c^3}-\frac{2 h (1-c x)^3}{81 c^3}+\frac{h (1-c x)^2}{6 c^3}+\frac{h \log ^2(1-c x)}{9 c^3}-\frac{h \log (c x) \log ^2(1-c x)}{3 c^3}+\frac{13 h \log (1-c x)}{108 c^3}+\frac{h (1-c x) \log (1-c x)}{3 c^3}-\frac{h x \text{Li}_2(c x)}{3 c^2}+\frac{121 h x}{108 c^2}+\frac{1}{3} x^3 \text{Li}_2(c x) (h \log (1-c x)+g)+\frac{1}{9} x^3 \log (1-c x) (h \log (1-c x)+g)-\frac{1}{9} h x^3 \text{Li}_2(c x)-\frac{h x^2 \text{Li}_2(c x)}{6 c}-\frac{1}{27} h x^3 \log (1-c x)+\frac{13 h x^2}{216 c}-\frac{h x^2 \log (1-c x)}{12 c}+\frac{h x^3}{81}",1,"(g*(-(c*x*(6 + 3*c*x + 2*c^2*x^2)) + 6*(-1 + c^3*x^3)*Log[1 - c*x] + 18*c^3*x^3*PolyLog[2, c*x]))/(54*c^3) + (h*(186*c*x + 33*c^2*x^2 + 8*c^3*x^3 + 186*Log[1 - c*x] - 120*c*x*Log[1 - c*x] - 42*c^2*x^2*Log[1 - c*x] - 24*c^3*x^3*Log[1 - c*x] - 24*Log[1 - c*x]^2 + 24*c^3*x^3*Log[1 - c*x]^2 - 72*Log[c*x]*Log[1 - c*x]^2 + 12*(-(c*x*(6 + 3*c*x + 2*c^2*x^2)) + 6*(-1 + c^3*x^3)*Log[1 - c*x])*PolyLog[2, c*x] - 144*Log[1 - c*x]*PolyLog[2, 1 - c*x] + 144*PolyLog[3, 1 - c*x]))/(216*c^3)","A",1
171,1,211,330,0.3129043,"\int x (g+h \log (1-c x)) \text{Li}_2(c x) \, dx","Integrate[x*(g + h*Log[1 - c*x])*PolyLog[2, c*x],x]","\frac{g \left(4 c^2 x^2 \text{Li}_2(c x)+2 \left(c^2 x^2-1\right) \log (1-c x)-c x (c x+2)\right)}{8 c^2}+\frac{h \left(\text{Li}_2(c x) \left(8 \left(c^2 x^2-1\right) \log (1-c x)-4 c x (c x+2)\right)+3 c^2 x^2+4 c^2 x^2 \log ^2(1-c x)-6 c^2 x^2 \log (1-c x)+16 \text{Li}_3(1-c x)-16 \text{Li}_2(1-c x) \log (1-c x)+22 c x-8 \log (c x) \log ^2(1-c x)-4 \log ^2(1-c x)-16 c x \log (1-c x)+22 \log (1-c x)-14\right)}{16 c^2}","-\frac{(1-c x)^2 (2 h \log (1-c x)+g)}{8 c^2}+\frac{(1-c x) (2 h \log (1-c x)+g)}{2 c^2}-\frac{\log (1-c x) (2 h \log (1-c x)+g)}{4 c^2}+\frac{h \text{Li}_3(1-c x)}{c^2}-\frac{h \text{Li}_2(c x) \log (1-c x)}{2 c^2}-\frac{h \text{Li}_2(1-c x) \log (1-c x)}{c^2}+\frac{h (1-c x)^2}{8 c^2}+\frac{h \log ^2(1-c x)}{4 c^2}-\frac{h \log (c x) \log ^2(1-c x)}{2 c^2}+\frac{h \log (1-c x)}{8 c^2}+\frac{h (1-c x) \log (1-c x)}{2 c^2}+\frac{1}{2} x^2 \text{Li}_2(c x) (h \log (1-c x)+g)+\frac{1}{4} x^2 \log (1-c x) (h \log (1-c x)+g)-\frac{1}{4} h x^2 \text{Li}_2(c x)-\frac{h x \text{Li}_2(c x)}{2 c}-\frac{1}{8} h x^2 \log (1-c x)+\frac{13 h x}{8 c}+\frac{h x^2}{16}",1,"(g*(-(c*x*(2 + c*x)) + 2*(-1 + c^2*x^2)*Log[1 - c*x] + 4*c^2*x^2*PolyLog[2, c*x]))/(8*c^2) + (h*(-14 + 22*c*x + 3*c^2*x^2 + 22*Log[1 - c*x] - 16*c*x*Log[1 - c*x] - 6*c^2*x^2*Log[1 - c*x] - 4*Log[1 - c*x]^2 + 4*c^2*x^2*Log[1 - c*x]^2 - 8*Log[c*x]*Log[1 - c*x]^2 + (-4*c*x*(2 + c*x) + 8*(-1 + c^2*x^2)*Log[1 - c*x])*PolyLog[2, c*x] - 16*Log[1 - c*x]*PolyLog[2, 1 - c*x] + 16*PolyLog[3, 1 - c*x]))/(16*c^2)","A",1
172,1,149,167,0.0684103,"\int (g+h \log (1-c x)) \text{Li}_2(c x) \, dx","Integrate[(g + h*Log[1 - c*x])*PolyLog[2, c*x],x]","g \left(x \text{Li}_2(c x)+\left(x-\frac{1}{c}\right) \log (1-c x)-x\right)+\frac{h \left(2 \text{Li}_3(1-c x)-2 \text{Li}_2(1-c x) \log (1-c x)+\text{Li}_2(c x) ((c x-1) \log (1-c x)-c x)+3 c x+c x \log ^2(1-c x)-\log (c x) \log ^2(1-c x)-\log ^2(1-c x)-3 c x \log (1-c x)+3 \log (1-c x)-2\right)}{c}","x \text{Li}_2(c x) (h \log (1-c x)+g)-\frac{g (1-c x) \log (1-c x)}{c}-h x \text{Li}_2(c x)+\frac{2 h \text{Li}_3(1-c x)}{c}-\frac{h \text{Li}_2(c x) \log (1-c x)}{c}-\frac{2 h \text{Li}_2(1-c x) \log (1-c x)}{c}-\frac{h (1-c x) \log ^2(1-c x)}{c}-\frac{h \log (c x) \log ^2(1-c x)}{c}+\frac{3 h (1-c x) \log (1-c x)}{c}-g x+3 h x",1,"g*(-x + (-c^(-1) + x)*Log[1 - c*x] + x*PolyLog[2, c*x]) + (h*(-2 + 3*c*x + 3*Log[1 - c*x] - 3*c*x*Log[1 - c*x] - Log[1 - c*x]^2 + c*x*Log[1 - c*x]^2 - Log[c*x]*Log[1 - c*x]^2 + (-(c*x) + (-1 + c*x)*Log[1 - c*x])*PolyLog[2, c*x] - 2*Log[1 - c*x]*PolyLog[2, 1 - c*x] + 2*PolyLog[3, 1 - c*x]))/c","A",1
173,1,20,20,0.0103741,"\int \frac{(g+h \log (1-c x)) \text{Li}_2(c x)}{x} \, dx","Integrate[((g + h*Log[1 - c*x])*PolyLog[2, c*x])/x,x]","g \text{Li}_3(c x)-\frac{1}{2} h \text{Li}_2(c x){}^2","g \text{Li}_3(c x)-\frac{1}{2} h \text{Li}_2(c x){}^2",1,"-1/2*(h*PolyLog[2, c*x]^2) + g*PolyLog[3, c*x]","A",1
174,1,150,156,0.1512647,"\int \frac{(g+h \log (1-c x)) \text{Li}_2(c x)}{x^2} \, dx","Integrate[((g + h*Log[1 - c*x])*PolyLog[2, c*x])/x^2,x]","\frac{g (-\text{Li}_2(c x)+c x \log (x)+(1-c x) \log (1-c x))}{x}+h \left(-c \text{Li}_3(c x)-2 c \text{Li}_3(1-c x)+\frac{(c x-1) \text{Li}_2(c x) \log (1-c x)}{x}+2 c \text{Li}_2(1-c x) (\log (1-c x)+1)-c \log ^2(1-c x)+c \log (c x) \log ^2(1-c x)+\frac{\log ^2(1-c x)}{x}+2 c \log (c x) \log (1-c x)\right)","-\frac{\text{Li}_2(c x) (h \log (1-c x)+g)}{x}+\frac{\log (1-c x) (h \log (1-c x)+g)}{x}+c \log \left(1-\frac{1}{1-c x}\right) (2 h \log (1-c x)+g)-2 c h \text{Li}_2\left(\frac{1}{1-c x}\right)-c h \text{Li}_3(c x)-2 c h \text{Li}_3(1-c x)+c h \text{Li}_2(c x) \log (1-c x)+2 c h \text{Li}_2(1-c x) \log (1-c x)+c h \log (c x) \log ^2(1-c x)",1,"(g*(c*x*Log[x] + (1 - c*x)*Log[1 - c*x] - PolyLog[2, c*x]))/x + h*(2*c*Log[c*x]*Log[1 - c*x] - c*Log[1 - c*x]^2 + Log[1 - c*x]^2/x + c*Log[c*x]*Log[1 - c*x]^2 + ((-1 + c*x)*Log[1 - c*x]*PolyLog[2, c*x])/x + 2*c*(1 + Log[1 - c*x])*PolyLog[2, 1 - c*x] - c*PolyLog[3, c*x] - 2*c*PolyLog[3, 1 - c*x])","A",1
175,1,238,266,0.1177439,"\int \frac{(g+h \log (1-c x)) \text{Li}_2(c x)}{x^3} \, dx","Integrate[((g + h*Log[1 - c*x])*PolyLog[2, c*x])/x^3,x]","\frac{g \left(c^2 x^2 \log (x)-c^2 x^2 \log (1-c x)-2 \text{Li}_2(c x)-c x+\log (1-c x)\right)}{4 x^2}+\frac{1}{4} h \left(\frac{2 \text{Li}_2(c x) \left(\left(c^2 x^2-1\right) \log (1-c x)+c x\right)}{x^2}-2 c^2 \text{Li}_3(c x)-4 c^2 \text{Li}_3(1-c x)+2 c^2 \text{Li}_2(1-c x) (2 \log (1-c x)+1)+2 c^2 \log (c x) \log ^2(1-c x)-c^2 \log ^2(1-c x)-2 c^2 \log (x)-2 c^2 \log (c x)+2 c^2 \log (c x) \log (1-c x)+4 c^2 \log (1-c x)+\frac{\log ^2(1-c x)}{x^2}-\frac{4 c \log (1-c x)}{x}\right)","\frac{1}{4} c^2 \log \left(1-\frac{1}{1-c x}\right) (2 h \log (1-c x)+g)-\frac{1}{2} c^2 h \text{Li}_2\left(\frac{1}{1-c x}\right)-\frac{1}{2} c^2 h \text{Li}_3(c x)-c^2 h \text{Li}_3(1-c x)+\frac{1}{2} c^2 h \text{Li}_2(c x) \log (1-c x)+c^2 h \text{Li}_2(1-c x) \log (1-c x)+\frac{1}{2} c^2 h \log (c x) \log ^2(1-c x)-c^2 h \log (x)+\frac{1}{2} c^2 h \log (1-c x)-\frac{\text{Li}_2(c x) (h \log (1-c x)+g)}{2 x^2}+\frac{\log (1-c x) (h \log (1-c x)+g)}{4 x^2}-\frac{c (1-c x) (2 h \log (1-c x)+g)}{4 x}+\frac{c h \text{Li}_2(c x)}{2 x}-\frac{c h \log (1-c x)}{2 x}",1,"(g*(-(c*x) + c^2*x^2*Log[x] + Log[1 - c*x] - c^2*x^2*Log[1 - c*x] - 2*PolyLog[2, c*x]))/(4*x^2) + (h*(-2*c^2*Log[x] - 2*c^2*Log[c*x] + 4*c^2*Log[1 - c*x] - (4*c*Log[1 - c*x])/x + 2*c^2*Log[c*x]*Log[1 - c*x] - c^2*Log[1 - c*x]^2 + Log[1 - c*x]^2/x^2 + 2*c^2*Log[c*x]*Log[1 - c*x]^2 + (2*(c*x + (-1 + c^2*x^2)*Log[1 - c*x])*PolyLog[2, c*x])/x^2 + 2*c^2*(1 + 2*Log[1 - c*x])*PolyLog[2, 1 - c*x] - 2*c^2*PolyLog[3, c*x] - 4*c^2*PolyLog[3, 1 - c*x]))/4","A",1
176,1,301,340,0.2675999,"\int \frac{(g+h \log (1-c x)) \text{Li}_2(c x)}{x^4} \, dx","Integrate[((g + h*Log[1 - c*x])*PolyLog[2, c*x])/x^4,x]","\frac{h \left(-12 c^3 x^3 \text{Li}_3(c x)-24 c^3 x^3 \text{Li}_3(1-c x)+8 c^3 x^3 \text{Li}_2(1-c x) (3 \log (1-c x)+1)+6 \text{Li}_2(c x) \left(2 \left(c^3 x^3-1\right) \log (1-c x)+c x (2 c x+1)\right)-4 c^3 x^3-4 c^3 x^3 \log ^2(1-c x)+12 c^3 x^3 \log (c x) \log ^2(1-c x)-15 c^3 x^3 \log (x)-12 c^3 x^3 \log (c x)+27 c^3 x^3 \log (1-c x)+8 c^3 x^3 \log (c x) \log (1-c x)+7 c^2 x^2-20 c^2 x^2 \log (1-c x)+4 \log ^2(1-c x)-7 c x \log (1-c x)\right)}{36 x^3}-\frac{g \left(-2 c^3 x^3 \log (x)+2 \left(c^3 x^3-1\right) \log (1-c x)+6 \text{Li}_2(c x)+c x (2 c x+1)\right)}{18 x^3}","\frac{1}{9} c^3 \log \left(1-\frac{1}{1-c x}\right) (2 h \log (1-c x)+g)-\frac{2}{9} c^3 h \text{Li}_2\left(\frac{1}{1-c x}\right)-\frac{1}{3} c^3 h \text{Li}_3(c x)-\frac{2}{3} c^3 h \text{Li}_3(1-c x)+\frac{1}{3} c^3 h \text{Li}_2(c x) \log (1-c x)+\frac{2}{3} c^3 h \text{Li}_2(1-c x) \log (1-c x)+\frac{1}{3} c^3 h \log (c x) \log ^2(1-c x)-\frac{3}{4} c^3 h \log (x)+\frac{19}{36} c^3 h \log (1-c x)-\frac{c^2 (1-c x) (2 h \log (1-c x)+g)}{9 x}+\frac{c^2 h \text{Li}_2(c x)}{3 x}+\frac{7 c^2 h}{36 x}-\frac{c^2 h \log (1-c x)}{3 x}-\frac{\text{Li}_2(c x) (h \log (1-c x)+g)}{3 x^3}+\frac{\log (1-c x) (h \log (1-c x)+g)}{9 x^3}-\frac{c (2 h \log (1-c x)+g)}{18 x^2}+\frac{c h \text{Li}_2(c x)}{6 x^2}-\frac{c h \log (1-c x)}{12 x^2}",1,"-1/18*(g*(c*x*(1 + 2*c*x) - 2*c^3*x^3*Log[x] + 2*(-1 + c^3*x^3)*Log[1 - c*x] + 6*PolyLog[2, c*x]))/x^3 + (h*(7*c^2*x^2 - 4*c^3*x^3 - 15*c^3*x^3*Log[x] - 12*c^3*x^3*Log[c*x] - 7*c*x*Log[1 - c*x] - 20*c^2*x^2*Log[1 - c*x] + 27*c^3*x^3*Log[1 - c*x] + 8*c^3*x^3*Log[c*x]*Log[1 - c*x] + 4*Log[1 - c*x]^2 - 4*c^3*x^3*Log[1 - c*x]^2 + 12*c^3*x^3*Log[c*x]*Log[1 - c*x]^2 + 6*(c*x*(1 + 2*c*x) + 2*(-1 + c^3*x^3)*Log[1 - c*x])*PolyLog[2, c*x] + 8*c^3*x^3*(1 + 3*Log[1 - c*x])*PolyLog[2, 1 - c*x] - 12*c^3*x^3*PolyLog[3, c*x] - 24*c^3*x^3*PolyLog[3, 1 - c*x]))/(36*x^3)","A",1
177,1,2610,2995,10.1674797,"\int x^2 \left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x)) \, dx","Integrate[x^2*(g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)],x]","\text{Result too large to show}","-\frac{h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) a^3}{6 b^3}+\frac{h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right)^2 a^3}{6 b^3}-\frac{h n \log (c (a+b x)) \log (d+e x) \log (1-c (a+b x)) a^3}{3 b^3}+\frac{g \text{Li}_2(c (a+b x)) a^3}{3 b^3}-\frac{h n \text{Li}_2(c (a+b x)) a^3}{9 b^3}-\frac{h \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x)) a^3}{3 b^3}-\frac{h n \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right) a^3}{3 b^3}-\frac{h n \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)\right) \text{Li}_2(1-c (a+b x)) a^3}{3 b^3}+\frac{h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right) a^3}{3 b^3}-\frac{h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right) a^3}{3 b^3}+\frac{h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right) a^3}{3 b^3}+\frac{h n \text{Li}_3(1-c (a+b x)) a^3}{3 b^3}+\frac{h n \text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right) a^3}{3 b^3}-\frac{h n \text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right) a^3}{3 b^3}-\frac{g x a^2}{3 b^2}+\frac{7 h n x a^2}{9 b^2}+\frac{4 h n (-a c-b x c+1) \log (-a c-b x c+1) a^2}{9 b^3 c}+\frac{d h n \log (-a c-b x c+1) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right) a^2}{3 b^2 e}-\frac{h (d+e x) \log \left(f (d+e x)^n\right) a^2}{3 b^2 e}+\frac{x \log (-a c-b x c+1) \left(g+h \log \left(f (d+e x)^n\right)\right) a^2}{3 b^2}-\frac{(1-a c) \log \left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) \left(g+h \log \left(f (d+e x)^n\right)\right) a^2}{3 b^3 c}-\frac{d h n \text{Li}_2(c (a+b x)) a^2}{6 b^2 e}+\frac{d h n \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) a^2}{3 b^2 e}-\frac{(1-a c) h n \text{Li}_2\left(\frac{b c (d+e x)}{b c d-a c e+e}\right) a^2}{3 b^3 c}-\frac{h n x^2 a}{9 b}+\frac{(1-a c) g x a}{6 b^2 c}-\frac{11 (1-a c) h n x a}{36 b^2 c}+\frac{5 d h n x a}{12 b e}+\frac{5 h n x^2 \log (-a c-b x c+1) a}{36 b}-\frac{5 (1-a c)^2 h n \log (-a c-b x c+1) a}{36 b^3 c^2}+\frac{d h n (-a c-b x c+1) \log (-a c-b x c+1) a}{3 b^2 c e}-\frac{d^2 h n \log (d+e x) a}{12 b e^2}+\frac{d^2 h n \log (-a c-b x c+1) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right) a}{6 b e^2}+\frac{(1-a c) h (d+e x) \log \left(f (d+e x)^n\right) a}{6 b^2 c e}+\frac{x^2 \left(g+h \log \left(f (d+e x)^n\right)\right) a}{12 b}-\frac{x^2 \log (-a c-b x c+1) \left(g+h \log \left(f (d+e x)^n\right)\right) a}{6 b}+\frac{(1-a c)^2 \log \left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) \left(g+h \log \left(f (d+e x)^n\right)\right) a}{6 b^3 c^2}-\frac{d^2 h n \text{Li}_2(c (a+b x)) a}{3 b e^2}+\frac{d^2 h n \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) a}{6 b e^2}+\frac{(1-a c)^2 h n \text{Li}_2\left(\frac{b c (d+e x)}{b c d-a c e+e}\right) a}{6 b^3 c^2}+\frac{1}{27} h n x^3+\frac{7 (1-a c) h n x^2}{108 b c}-\frac{19 d h n x^2}{216 e}+\frac{d^3 h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)}{6 e^3}-\frac{d^3 h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right)^2}{6 e^3}-\frac{(1-a c)^2 g x}{9 b^2 c^2}+\frac{5 (1-a c)^2 h n x}{27 b^2 c^2}-\frac{7 (1-a c) d h n x}{36 b c e}+\frac{13 d^2 h n x}{27 e^2}-\frac{2}{27} h n x^3 \log (-a c-b x c+1)+\frac{5 d h n x^2 \log (-a c-b x c+1)}{36 e}+\frac{2 (1-a c)^3 h n \log (-a c-b x c+1)}{27 b^3 c^3}-\frac{5 (1-a c)^2 d h n \log (-a c-b x c+1)}{36 b^2 c^2 e}+\frac{4 d^2 h n (-a c-b x c+1) \log (-a c-b x c+1)}{9 b c e^2}+\frac{(1-a c) d^2 h n \log (d+e x)}{18 b c e^2}-\frac{d^3 h n \log (d+e x)}{27 e^3}+\frac{d^3 h n \log (-a c-b x c+1) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right)}{9 e^3}-\frac{(1-a c)^2 h (d+e x) \log \left(f (d+e x)^n\right)}{9 b^2 c^2 e}-\frac{1}{27} x^3 \left(g+h \log \left(f (d+e x)^n\right)\right)-\frac{(1-a c) x^2 \left(g+h \log \left(f (d+e x)^n\right)\right)}{18 b c}+\frac{1}{9} x^3 \log (-a c-b x c+1) \left(g+h \log \left(f (d+e x)^n\right)\right)-\frac{(1-a c)^3 \log \left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) \left(g+h \log \left(f (d+e x)^n\right)\right)}{9 b^3 c^3}+\frac{d^3 h n \log (c (a+b x)) \log (d+e x) \log (1-c (a+b x))}{3 e^3}-\frac{1}{9} h n x^3 \text{Li}_2(c (a+b x))+\frac{d h n x^2 \text{Li}_2(c (a+b x))}{6 e}-\frac{d^2 h n x \text{Li}_2(c (a+b x))}{3 e^2}+\frac{d^3 h n \log (d+e x) \text{Li}_2(c (a+b x))}{3 e^3}+\frac{1}{3} x^3 \left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))+\frac{d^3 h n \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right)}{9 e^3}+\frac{d^3 h n \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)}{3 e^3}-\frac{(1-a c)^3 h n \text{Li}_2\left(\frac{b c (d+e x)}{b c d-a c e+e}\right)}{9 b^3 c^3}+\frac{d^3 h n \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)\right) \text{Li}_2(1-c (a+b x))}{3 e^3}-\frac{d^3 h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{3 e^3}+\frac{d^3 h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{3 e^3}-\frac{d^3 h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)}{3 e^3}-\frac{d^3 h n \text{Li}_3(1-c (a+b x))}{3 e^3}-\frac{d^3 h n \text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{3 e^3}+\frac{d^3 h n \text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{3 e^3}",1,"((g - h*n*Log[d + e*x] + h*Log[f*(d + e*x)^n])*(-(b*c*x*(12 + 66*a^2*c^2 + 6*b*c*x + 4*b^2*c^2*x^2 - 3*a*c*(14 + 5*b*c*x))) + 6*(-2 + 11*a^3*c^3 + 2*b^3*c^3*x^3 + 6*a^2*c^2*(-3 + b*c*x) + a*(9*c - 3*b^2*c^3*x^2))*Log[1 - a*c - b*c*x] + 36*c^3*(a^3 + b^3*x^3)*PolyLog[2, c*(a + b*x)]))/(108*b^3*c^3) + (h*n*(36*b^3*c^3*(e*x*(-6*d^2 + 3*d*e*x - 2*e^2*x^2) + 6*(d^3 + e^3*x^3)*Log[d + e*x])*PolyLog[2, c*(a + b*x)] - 216*b^2*c^2*d^2*e*(1 - a*c - b*c*x + (-1 + a*c + b*c*x - a*c*Log[c*(a + b*x)])*Log[1 - a*c - b*c*x] - a*c*PolyLog[2, 1 - a*c - b*c*x]) - 27*b*c*d*e^2*(c*(-4*a^2*c + a*(4 - 6*b*c*x) + b*x*(2 + b*c*x)) + (2 + 6*a^2*c^2 - 2*b^2*c^2*x^2 + 4*a*c*(-2 + b*c*x) - 4*a^2*c^2*Log[c*(a + b*x)])*Log[1 - a*c - b*c*x] - 4*a^2*c^2*PolyLog[2, 1 - a*c - b*c*x]) - 2*e^3*(-(c*(36*a^3*c^2 - 3*a*b*c*x*(14 + 5*b*c*x) + 6*a^2*c*(-6 + 11*b*c*x) + 2*b*x*(6 + 3*b*c*x + 2*b^2*c^2*x^2))) - 6*(2 - 11*a^3*c^3 - 2*b^3*c^3*x^3 - 6*a^2*c^2*(-3 + b*c*x) + 3*a*c*(-3 + b^2*c^2*x^2) + 6*a^3*c^3*Log[c*(a + b*x)])*Log[1 - a*c - b*c*x] - 36*a^3*c^3*PolyLog[2, 1 - a*c - b*c*x]) + 216*b^3*c^3*d^3*(Log[c*(a + b*x)]*Log[1 - a*c - b*c*x]*Log[d + e*x] + ((Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*(-2*Log[1 - a*c - b*c*x] + Log[(b*(d + e*x))/(b*d - a*e)]))/2 + (-Log[c*(a + b*x)] + Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] + (Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]^2*(Log[c*(a + b*x)] - Log[((b*c*d + e - a*c*e)*(a + b*x))/((b*d - a*e)*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + (Log[d + e*x] - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, 1 - a*c - b*c*x] + (Log[1 - a*c - b*c*x] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, (b*(d + e*x))/(b*d - a*e)] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]*(PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] - PolyLog[2, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - PolyLog[3, 1 - a*c - b*c*x] - PolyLog[3, (b*(d + e*x))/(b*d - a*e)] - PolyLog[3, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] + PolyLog[3, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) + 2*(b*c*(e*(48*(-1 + a*c)^2*e^2*x + 3*b*c*(-1 + a*c)*(12*d^2 + 12*d*e*x - 5*e^2*x^2) + b^2*c^2*x*(48*d^2 - 15*d*e*x + 8*e^2*x^2)) - 6*(d + e*x)*(6*(-1 + a*c)^2*e^2 + 3*b*c*(-1 + a*c)*e*(d - e*x) + 2*b^2*c^2*(d^2 - d*e*x + e^2*x^2))*Log[d + e*x]) + 6*Log[1 - a*c - b*c*x]*(-(e*(-1 + a*c + b*c*x)*(2*(-1 + a*c)^2*e^2 + b*c*(-1 + a*c)*e*(3*d - 2*e*x) + b^2*c^2*(6*d^2 - 3*d*e*x + 2*e^2*x^2))) + 6*e^3*(-1 + 3*a*c - 3*a^2*c^2 + a^3*c^3 + b^3*c^3*x^3)*Log[d + e*x] + 6*(b^3*c^3*d^3 - (-1 + a*c)^3*e^3)*Log[(b*c*(d + e*x))/(b*c*d + e - a*c*e)]) + 36*(b^3*c^3*d^3 - (-1 + a*c)^3*e^3)*PolyLog[2, (e*(-1 + a*c + b*c*x))/(-(b*c*d) + (-1 + a*c)*e)] - 108*a^2*c^2*e^2*(e - a*c*e - 2*b*c*e*x + b*c*d*Log[d + e*x] + b*c*e*x*Log[d + e*x] - Log[1 - a*c - b*c*x]*(-(e*(-1 + a*c + b*c*x)) + e*(-1 + a*c + b*c*x)*Log[d + e*x] + (b*c*d + e - a*c*e)*Log[(b*c*(d + e*x))/(b*c*d + e - a*c*e)]) - (b*c*d + e - a*c*e)*PolyLog[2, (e*(-1 + a*c + b*c*x))/(-(b*c*d) + (-1 + a*c)*e)]) - 27*a*c*e*(b*c*(e*(d*(2 - 2*a*c - 3*b*c*x) + e*x*(3 - 3*a*c + b*c*x)) + (d + e*x)*(2*(-1 + a*c)*e + b*c*(d - e*x))*Log[d + e*x]) + Log[1 - a*c - b*c*x]*(e*(-1 + a*c + b*c*x)*((-1 + a*c)*e + b*c*(2*d - e*x)) - 2*e^2*(1 - 2*a*c + a^2*c^2 - b^2*c^2*x^2)*Log[d + e*x] + 2*(-(b^2*c^2*d^2) + (-1 + a*c)^2*e^2)*Log[(b*c*(d + e*x))/(b*c*d + e - a*c*e)]) + 2*(-(b^2*c^2*d^2) + (-1 + a*c)^2*e^2)*PolyLog[2, (e*(-1 + a*c + b*c*x))/(-(b*c*d) + (-1 + a*c)*e)]) - 108*a^3*c^3*e^3*(Log[c*(a + b*x)]*Log[1 - a*c - b*c*x]*Log[d + e*x] + ((Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*(-2*Log[1 - a*c - b*c*x] + Log[(b*(d + e*x))/(b*d - a*e)]))/2 + (-Log[c*(a + b*x)] + Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] + (Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]^2*(Log[c*(a + b*x)] - Log[((b*c*d + e - a*c*e)*(a + b*x))/((b*d - a*e)*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + (Log[d + e*x] - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, 1 - a*c - b*c*x] + (Log[1 - a*c - b*c*x] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, (b*(d + e*x))/(b*d - a*e)] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]*(PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] - PolyLog[2, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - PolyLog[3, 1 - a*c - b*c*x] - PolyLog[3, (b*(d + e*x))/(b*d - a*e)] - PolyLog[3, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] + PolyLog[3, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]))))/(648*b^3*c^3*e^3)","A",1
178,1,1996,2252,6.1567823,"\int x \left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x)) \, dx","Integrate[x*(g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)],x]","\frac{\left(g-h n \log (d+e x)+h \log \left(f (d+e x)^n\right)\right) \left(-4 \left(a^2-b^2 x^2\right) \text{Li}_2(c (a+b x)) c^2-b x (-6 a c+b x c+2) c+\left(-6 a^2 c^2+2 b^2 x^2 c^2-4 a (b c x-2) c-2\right) \log (-a c-b x c+1)\right)}{8 b^2 c^2}+\frac{h n \left(4 b^2 \left(e x (2 d-e x)-2 \left(d^2-e^2 x^2\right) \log (d+e x)\right) \text{Li}_2(c (a+b x)) c^2-8 b^2 d^2 \left(\frac{1}{2} \left(\log (c (a+b x))-\log \left(\frac{(b c d-a c e+e) (a+b x)}{(b d-a e) (a c+b x c-1)}\right)+\log \left(\frac{b c d-a c e+e}{-a c e-b c x e+e}\right)\right) \log ^2\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\left(\log \left(\frac{e (a+b x)}{a e-b d}\right)-\log (c (a+b x))\right) \log \left(\frac{b (d+e x)}{b d-a e}\right) \log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\left(\text{Li}_2\left(\frac{b c (d+e x)}{e (a c+b x c-1)}\right)-\text{Li}_2\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\log (c (a+b x)) \log (-a c-b x c+1) \log (d+e x)+\frac{1}{2} \left(\log (c (a+b x))-\log \left(\frac{e (a+b x)}{a e-b d}\right)\right) \log \left(\frac{b (d+e x)}{b d-a e}\right) \left(\log \left(\frac{b (d+e x)}{b d-a e}\right)-2 \log (-a c-b x c+1)\right)+\left(\log (d+e x)-\log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \text{Li}_2(-a c-b x c+1)+\left(\log (-a c-b x c+1)+\log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)-\text{Li}_3(-a c-b x c+1)-\text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)-\text{Li}_3\left(\frac{b c (d+e x)}{e (a c+b x c-1)}\right)+\text{Li}_3\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) c^2+8 b d e (-a c-b x c-a \text{Li}_2(-a c-b x c+1) c+(a c+b x c-a \log (c (a+b x)) c-1) \log (-a c-b x c+1)+1) c+e^2 \left(-4 a^2 \text{Li}_2(-a c-b x c+1) c^2+\left(-4 c a^2+(4-6 b c x) a+b x (b c x+2)\right) c+\left(6 a^2 c^2-2 b^2 x^2 c^2-4 a^2 \log (c (a+b x)) c^2+4 a (b c x-2) c+2\right) \log (-a c-b x c+1)\right)+2 \left(4 a^2 c^2 \left(\frac{1}{2} \left(\log (c (a+b x))-\log \left(\frac{(b c d-a c e+e) (a+b x)}{(b d-a e) (a c+b x c-1)}\right)+\log \left(\frac{b c d-a c e+e}{-a c e-b c x e+e}\right)\right) \log ^2\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\left(\log \left(\frac{e (a+b x)}{a e-b d}\right)-\log (c (a+b x))\right) \log \left(\frac{b (d+e x)}{b d-a e}\right) \log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\left(\text{Li}_2\left(\frac{b c (d+e x)}{e (a c+b x c-1)}\right)-\text{Li}_2\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\log (c (a+b x)) \log (-a c-b x c+1) \log (d+e x)+\frac{1}{2} \left(\log (c (a+b x))-\log \left(\frac{e (a+b x)}{a e-b d}\right)\right) \log \left(\frac{b (d+e x)}{b d-a e}\right) \left(\log \left(\frac{b (d+e x)}{b d-a e}\right)-2 \log (-a c-b x c+1)\right)+\left(\log (d+e x)-\log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \text{Li}_2(-a c-b x c+1)+\left(\log (-a c-b x c+1)+\log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)-\text{Li}_3(-a c-b x c+1)-\text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)-\text{Li}_3\left(\frac{b c (d+e x)}{e (a c+b x c-1)}\right)+\text{Li}_3\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) e^2+4 a c \left(-a c e-2 b c x e+b c x \log (d+e x) e+e+b c d \log (d+e x)-\log (-a c-b x c+1) \left(-e (a c+b x c-1)+e \log (d+e x) (a c+b x c-1)+(b c d-a c e+e) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right)\right)-(b c d-a c e+e) \text{Li}_2\left(\frac{e (a c+b x c-1)}{(a c-1) e-b c d}\right)\right) e+b c (e (d (-2 a c-3 b x c+2)+e x (-3 a c+b x c+3))+(d+e x) (2 (a c-1) e+b c (d-e x)) \log (d+e x))+\log (-a c-b x c+1) \left(-2 \left(a^2 c^2-b^2 x^2 c^2-2 a c+1\right) \log (d+e x) e^2+(a c+b x c-1) ((a c-1) e+b c (2 d-e x)) e+2 \left((a c-1)^2 e^2-b^2 c^2 d^2\right) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right)\right)+2 \left((a c-1)^2 e^2-b^2 c^2 d^2\right) \text{Li}_2\left(\frac{e (a c+b x c-1)}{(a c-1) e-b c d}\right)\right)\right)}{16 b^2 c^2 e^2}","\frac{h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) a^2}{4 b^2}-\frac{h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right)^2 a^2}{4 b^2}+\frac{h n \log (c (a+b x)) \log (d+e x) \log (1-c (a+b x)) a^2}{2 b^2}-\frac{g \text{Li}_2(c (a+b x)) a^2}{2 b^2}+\frac{h n \text{Li}_2(c (a+b x)) a^2}{4 b^2}+\frac{h \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x)) a^2}{2 b^2}+\frac{h n \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right) a^2}{2 b^2}+\frac{h n \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)\right) \text{Li}_2(1-c (a+b x)) a^2}{2 b^2}-\frac{h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right) a^2}{2 b^2}+\frac{h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right) a^2}{2 b^2}-\frac{h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right) a^2}{2 b^2}-\frac{h n \text{Li}_3(1-c (a+b x)) a^2}{2 b^2}-\frac{h n \text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right) a^2}{2 b^2}+\frac{h n \text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right) a^2}{2 b^2}+\frac{g x a}{2 b}-\frac{5 h n x a}{4 b}-\frac{3 h n (-a c-b x c+1) \log (-a c-b x c+1) a}{4 b^2 c}-\frac{d h n \log (-a c-b x c+1) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right) a}{2 b e}+\frac{h (d+e x) \log \left(f (d+e x)^n\right) a}{2 b e}-\frac{x \log (-a c-b x c+1) \left(g+h \log \left(f (d+e x)^n\right)\right) a}{2 b}+\frac{(1-a c) \log \left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) \left(g+h \log \left(f (d+e x)^n\right)\right) a}{2 b^2 c}+\frac{d h n \text{Li}_2(c (a+b x)) a}{2 b e}-\frac{d h n \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) a}{2 b e}+\frac{(1-a c) h n \text{Li}_2\left(\frac{b c (d+e x)}{b c d-a c e+e}\right) a}{2 b^2 c}+\frac{3}{16} h n x^2-\frac{d^2 h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)}{4 e^2}+\frac{d^2 h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right)^2}{4 e^2}-\frac{(1-a c) g x}{4 b c}+\frac{(1-a c) h n x}{2 b c}-\frac{7 d h n x}{8 e}-\frac{1}{4} h n x^2 \log (-a c-b x c+1)+\frac{(1-a c)^2 h n \log (-a c-b x c+1)}{4 b^2 c^2}-\frac{3 d h n (-a c-b x c+1) \log (-a c-b x c+1)}{4 b c e}+\frac{d^2 h n \log (d+e x)}{8 e^2}-\frac{d^2 h n \log (-a c-b x c+1) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right)}{4 e^2}-\frac{(1-a c) h (d+e x) \log \left(f (d+e x)^n\right)}{4 b c e}-\frac{1}{8} x^2 \left(g+h \log \left(f (d+e x)^n\right)\right)+\frac{1}{4} x^2 \log (-a c-b x c+1) \left(g+h \log \left(f (d+e x)^n\right)\right)-\frac{(1-a c)^2 \log \left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) \left(g+h \log \left(f (d+e x)^n\right)\right)}{4 b^2 c^2}-\frac{d^2 h n \log (c (a+b x)) \log (d+e x) \log (1-c (a+b x))}{2 e^2}-\frac{1}{4} h n x^2 \text{Li}_2(c (a+b x))+\frac{d h n x \text{Li}_2(c (a+b x))}{2 e}-\frac{d^2 h n \log (d+e x) \text{Li}_2(c (a+b x))}{2 e^2}+\frac{1}{2} x^2 \left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))-\frac{d^2 h n \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right)}{4 e^2}-\frac{d^2 h n \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)}{2 e^2}-\frac{(1-a c)^2 h n \text{Li}_2\left(\frac{b c (d+e x)}{b c d-a c e+e}\right)}{4 b^2 c^2}-\frac{d^2 h n \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)\right) \text{Li}_2(1-c (a+b x))}{2 e^2}+\frac{d^2 h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{2 e^2}-\frac{d^2 h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{2 e^2}+\frac{d^2 h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)}{2 e^2}+\frac{d^2 h n \text{Li}_3(1-c (a+b x))}{2 e^2}+\frac{d^2 h n \text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{2 e^2}-\frac{d^2 h n \text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{2 e^2}",1,"((g - h*n*Log[d + e*x] + h*Log[f*(d + e*x)^n])*(-(b*c*x*(2 - 6*a*c + b*c*x)) + (-2 - 6*a^2*c^2 + 2*b^2*c^2*x^2 - 4*a*c*(-2 + b*c*x))*Log[1 - a*c - b*c*x] - 4*c^2*(a^2 - b^2*x^2)*PolyLog[2, c*(a + b*x)]))/(8*b^2*c^2) + (h*n*(4*b^2*c^2*(e*x*(2*d - e*x) - 2*(d^2 - e^2*x^2)*Log[d + e*x])*PolyLog[2, c*(a + b*x)] + 8*b*c*d*e*(1 - a*c - b*c*x + (-1 + a*c + b*c*x - a*c*Log[c*(a + b*x)])*Log[1 - a*c - b*c*x] - a*c*PolyLog[2, 1 - a*c - b*c*x]) + e^2*(c*(-4*a^2*c + a*(4 - 6*b*c*x) + b*x*(2 + b*c*x)) + (2 + 6*a^2*c^2 - 2*b^2*c^2*x^2 + 4*a*c*(-2 + b*c*x) - 4*a^2*c^2*Log[c*(a + b*x)])*Log[1 - a*c - b*c*x] - 4*a^2*c^2*PolyLog[2, 1 - a*c - b*c*x]) - 8*b^2*c^2*d^2*(Log[c*(a + b*x)]*Log[1 - a*c - b*c*x]*Log[d + e*x] + ((Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*(-2*Log[1 - a*c - b*c*x] + Log[(b*(d + e*x))/(b*d - a*e)]))/2 + (-Log[c*(a + b*x)] + Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] + (Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]^2*(Log[c*(a + b*x)] - Log[((b*c*d + e - a*c*e)*(a + b*x))/((b*d - a*e)*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + (Log[d + e*x] - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, 1 - a*c - b*c*x] + (Log[1 - a*c - b*c*x] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, (b*(d + e*x))/(b*d - a*e)] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]*(PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] - PolyLog[2, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - PolyLog[3, 1 - a*c - b*c*x] - PolyLog[3, (b*(d + e*x))/(b*d - a*e)] - PolyLog[3, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] + PolyLog[3, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) + 2*(b*c*(e*(d*(2 - 2*a*c - 3*b*c*x) + e*x*(3 - 3*a*c + b*c*x)) + (d + e*x)*(2*(-1 + a*c)*e + b*c*(d - e*x))*Log[d + e*x]) + Log[1 - a*c - b*c*x]*(e*(-1 + a*c + b*c*x)*((-1 + a*c)*e + b*c*(2*d - e*x)) - 2*e^2*(1 - 2*a*c + a^2*c^2 - b^2*c^2*x^2)*Log[d + e*x] + 2*(-(b^2*c^2*d^2) + (-1 + a*c)^2*e^2)*Log[(b*c*(d + e*x))/(b*c*d + e - a*c*e)]) + 2*(-(b^2*c^2*d^2) + (-1 + a*c)^2*e^2)*PolyLog[2, (e*(-1 + a*c + b*c*x))/(-(b*c*d) + (-1 + a*c)*e)] + 4*a*c*e*(e - a*c*e - 2*b*c*e*x + b*c*d*Log[d + e*x] + b*c*e*x*Log[d + e*x] - Log[1 - a*c - b*c*x]*(-(e*(-1 + a*c + b*c*x)) + e*(-1 + a*c + b*c*x)*Log[d + e*x] + (b*c*d + e - a*c*e)*Log[(b*c*(d + e*x))/(b*c*d + e - a*c*e)]) - (b*c*d + e - a*c*e)*PolyLog[2, (e*(-1 + a*c + b*c*x))/(-(b*c*d) + (-1 + a*c)*e)]) + 4*a^2*c^2*e^2*(Log[c*(a + b*x)]*Log[1 - a*c - b*c*x]*Log[d + e*x] + ((Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*(-2*Log[1 - a*c - b*c*x] + Log[(b*(d + e*x))/(b*d - a*e)]))/2 + (-Log[c*(a + b*x)] + Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] + (Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]^2*(Log[c*(a + b*x)] - Log[((b*c*d + e - a*c*e)*(a + b*x))/((b*d - a*e)*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + (Log[d + e*x] - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, 1 - a*c - b*c*x] + (Log[1 - a*c - b*c*x] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, (b*(d + e*x))/(b*d - a*e)] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]*(PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] - PolyLog[2, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - PolyLog[3, 1 - a*c - b*c*x] - PolyLog[3, (b*(d + e*x))/(b*d - a*e)] - PolyLog[3, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] + PolyLog[3, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]))))/(16*b^2*c^2*e^2)","A",1
179,1,1546,1653,2.4656101,"\int \left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x)) \, dx","Integrate[(g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)],x]","\frac{\left(g-h n \log (d+e x)+h \log \left(f (d+e x)^n\right)\right) (-b c x+(a c+b x c-1) \log (-a c-b x c+1)+c (a+b x) \text{Li}_2(c (a+b x)))}{b c}+\frac{h n \left(((d+e x) \log (d+e x)-e x) \text{Li}_2(c (a+b x))+\frac{a c e+2 b c x e-b c x \log (d+e x) e+(a c+b x c+a \text{Li}_2(-a c-b x c+1) c+(-a c-b x c+a \log (c (a+b x)) c+1) \log (-a c-b x c+1)-1) e-a c \left(\frac{1}{2} \left(\log (c (a+b x))-\log \left(\frac{(b c d-a c e+e) (a+b x)}{(b d-a e) (a c+b x c-1)}\right)+\log \left(\frac{b c d-a c e+e}{-a c e-b c x e+e}\right)\right) \log ^2\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\left(\log \left(\frac{e (a+b x)}{a e-b d}\right)-\log (c (a+b x))\right) \log \left(\frac{b (d+e x)}{b d-a e}\right) \log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\left(\text{Li}_2\left(\frac{b c (d+e x)}{e (a c+b x c-1)}\right)-\text{Li}_2\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\log (c (a+b x)) \log (-a c-b x c+1) \log (d+e x)+\frac{1}{2} \left(\log (c (a+b x))-\log \left(\frac{e (a+b x)}{a e-b d}\right)\right) \log \left(\frac{b (d+e x)}{b d-a e}\right) \left(\log \left(\frac{b (d+e x)}{b d-a e}\right)-2 \log (-a c-b x c+1)\right)+\left(\log (d+e x)-\log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \text{Li}_2(-a c-b x c+1)+\left(\log (-a c-b x c+1)+\log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)-\text{Li}_3(-a c-b x c+1)-\text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)-\text{Li}_3\left(\frac{b c (d+e x)}{e (a c+b x c-1)}\right)+\text{Li}_3\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) e-e-b c d \log (d+e x)+\log (-a c-b x c+1) \left(-e (a c+b x c-1)+e \log (d+e x) (a c+b x c-1)+(b c d-a c e+e) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right)\right)+(b c d-a c e+e) \text{Li}_2\left(\frac{e (a c+b x c-1)}{(a c-1) e-b c d}\right)+b c d \left(\frac{1}{2} \left(\log (c (a+b x))-\log \left(\frac{(b c d-a c e+e) (a+b x)}{(b d-a e) (a c+b x c-1)}\right)+\log \left(\frac{b c d-a c e+e}{-a c e-b c x e+e}\right)\right) \log ^2\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\left(\log \left(\frac{e (a+b x)}{a e-b d}\right)-\log (c (a+b x))\right) \log \left(\frac{b (d+e x)}{b d-a e}\right) \log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\left(\text{Li}_2\left(\frac{b c (d+e x)}{e (a c+b x c-1)}\right)-\text{Li}_2\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)+\log (c (a+b x)) \log (-a c-b x c+1) \log (d+e x)+\frac{1}{2} \left(\log (c (a+b x))-\log \left(\frac{e (a+b x)}{a e-b d}\right)\right) \log \left(\frac{b (d+e x)}{b d-a e}\right) \left(\log \left(\frac{b (d+e x)}{b d-a e}\right)-2 \log (-a c-b x c+1)\right)+\left(\log (d+e x)-\log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \text{Li}_2(-a c-b x c+1)+\left(\log (-a c-b x c+1)+\log \left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)-\text{Li}_3(-a c-b x c+1)-\text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)-\text{Li}_3\left(\frac{b c (d+e x)}{e (a c+b x c-1)}\right)+\text{Li}_3\left(-\frac{b (d+e x)}{(b d-a e) (a c+b x c-1)}\right)\right)}{b c}\right)}{e}","\frac{d h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (-a c-b x c+1)}\right)}{2 e}-\frac{d h n \text{Li}_2\left(-\frac{e (-a c-b x c+1)}{b c (d+e x)}\right) \log \left(\frac{b (d+e x)}{(b d-a e) (-a c-b x c+1)}\right)}{e}+\frac{d h n \text{Li}_2\left(\frac{(b d-a e) (-a c-b x c+1)}{b (d+e x)}\right) \log \left(\frac{b (d+e x)}{(b d-a e) (-a c-b x c+1)}\right)}{e}-\frac{d h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log (-a c-b x c+1)+\log \left(\frac{b (d+e x)}{(b d-a e) (-a c-b x c+1)}\right)\right)^2}{2 e}-\frac{a h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)}{2 b}+\frac{a h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right)^2}{2 b}-g x+3 h n x-\frac{g (-a c-b x c+1) \log (-a c-b x c+1)}{b c}+\frac{2 h n (-a c-b x c+1) \log (-a c-b x c+1)}{b c}+\frac{d h n \log (c (a+b x)) \log (-a c-b x c+1) \log (-d-e x)}{e}+\frac{d h n \log (-a c-b x c+1) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right)}{e}-\frac{h (d+e x) \log \left(f (d+e x)^n\right)}{e}+h x \log (-a c-b x c+1) \log \left(f (d+e x)^n\right)-\frac{(1-a c) h \log \left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) \log \left(f (d+e x)^n\right)}{b c}-\frac{a h n \log (c (a+b x)) \log (d+e x) \log (1-c (a+b x))}{b}+\frac{a g \text{Li}_2(c (a+b x))}{b}-\frac{a h n \text{Li}_2(c (a+b x))}{b}-\frac{a h \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))}{b}+x \left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))+\frac{d h n \left(\log (-d-e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (-a c-b x c+1)}\right)\right) \text{Li}_2(-a c-b x c+1)}{e}+\frac{d h n \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right)}{e}-h n x \text{Li}_2(a c+b x c)+\frac{d h n \log (-d-e x) \text{Li}_2(a c+b x c)}{e}+\frac{d h n \left(\log (-a c-b x c+1)+\log \left(\frac{b (d+e x)}{(b d-a e) (-a c-b x c+1)}\right)\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)}{e}-\frac{a h n \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)}{b}-\frac{(1-a c) h n \text{Li}_2\left(\frac{b c (d+e x)}{b c d-a c e+e}\right)}{b c}-\frac{a h n \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)\right) \text{Li}_2(1-c (a+b x))}{b}+\frac{a h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{b}-\frac{a h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{b}-\frac{d h n \text{Li}_3(-a c-b x c+1)}{e}-\frac{d h n \text{Li}_3\left(-\frac{e (-a c-b x c+1)}{b c (d+e x)}\right)}{e}+\frac{d h n \text{Li}_3\left(\frac{(b d-a e) (-a c-b x c+1)}{b (d+e x)}\right)}{e}+\frac{a h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)}{b}-\frac{d h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)}{e}+\frac{a h n \text{Li}_3(1-c (a+b x))}{b}+\frac{a h n \text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{b}-\frac{a h n \text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{b}",1,"((g - h*n*Log[d + e*x] + h*Log[f*(d + e*x)^n])*(-(b*c*x) + (-1 + a*c + b*c*x)*Log[1 - a*c - b*c*x] + c*(a + b*x)*PolyLog[2, c*(a + b*x)]))/(b*c) + (h*n*((-(e*x) + (d + e*x)*Log[d + e*x])*PolyLog[2, c*(a + b*x)] + (-e + a*c*e + 2*b*c*e*x - b*c*d*Log[d + e*x] - b*c*e*x*Log[d + e*x] + Log[1 - a*c - b*c*x]*(-(e*(-1 + a*c + b*c*x)) + e*(-1 + a*c + b*c*x)*Log[d + e*x] + (b*c*d + e - a*c*e)*Log[(b*c*(d + e*x))/(b*c*d + e - a*c*e)]) + e*(-1 + a*c + b*c*x + (1 - a*c - b*c*x + a*c*Log[c*(a + b*x)])*Log[1 - a*c - b*c*x] + a*c*PolyLog[2, 1 - a*c - b*c*x]) + (b*c*d + e - a*c*e)*PolyLog[2, (e*(-1 + a*c + b*c*x))/(-(b*c*d) + (-1 + a*c)*e)] + b*c*d*(Log[c*(a + b*x)]*Log[1 - a*c - b*c*x]*Log[d + e*x] + ((Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*(-2*Log[1 - a*c - b*c*x] + Log[(b*(d + e*x))/(b*d - a*e)]))/2 + (-Log[c*(a + b*x)] + Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] + (Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]^2*(Log[c*(a + b*x)] - Log[((b*c*d + e - a*c*e)*(a + b*x))/((b*d - a*e)*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + (Log[d + e*x] - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, 1 - a*c - b*c*x] + (Log[1 - a*c - b*c*x] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, (b*(d + e*x))/(b*d - a*e)] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]*(PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] - PolyLog[2, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - PolyLog[3, 1 - a*c - b*c*x] - PolyLog[3, (b*(d + e*x))/(b*d - a*e)] - PolyLog[3, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] + PolyLog[3, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - a*c*e*(Log[c*(a + b*x)]*Log[1 - a*c - b*c*x]*Log[d + e*x] + ((Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*(-2*Log[1 - a*c - b*c*x] + Log[(b*(d + e*x))/(b*d - a*e)]))/2 + (-Log[c*(a + b*x)] + Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] + (Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]^2*(Log[c*(a + b*x)] - Log[((b*c*d + e - a*c*e)*(a + b*x))/((b*d - a*e)*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + (Log[d + e*x] - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, 1 - a*c - b*c*x] + (Log[1 - a*c - b*c*x] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, (b*(d + e*x))/(b*d - a*e)] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]*(PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] - PolyLog[2, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - PolyLog[3, 1 - a*c - b*c*x] - PolyLog[3, (b*(d + e*x))/(b*d - a*e)] - PolyLog[3, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] + PolyLog[3, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]))/(b*c)))/e","A",1
180,0,0,30,2.4321994,"\int \frac{\left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))}{x} \, dx","Integrate[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x,x]","\int \frac{\left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))}{x} \, dx","\text{Int}\left(\frac{\text{Li}_2(c (a+b x)) \left(h \log \left(f (d+e x)^n\right)+g\right)}{x},x\right)",0,"Integrate[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x, x]","A",-1
181,1,2247,2498,7.3927993,"\int \frac{\left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))}{x^2} \, dx","Integrate[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x^2,x]","\text{Result too large to show}","-\frac{b h n \left(\log \left(\frac{b c x}{1-a c}\right)+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) x}{(1-a c) (d+e x)}\right)\right) \log ^2\left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)}{2 a}-\frac{b h n \text{Li}_2\left(\frac{d (-a c-b x c+1)}{(1-a c) (d+e x)}\right) \log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)}{a}+\frac{b h n \text{Li}_2\left(-\frac{e (-a c-b x c+1)}{b c (d+e x)}\right) \log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)}{a}+\frac{b h n \left(\log \left(\frac{b c x}{1-a c}\right)-\log \left(-\frac{e x}{d}\right)\right) \left(\log (-a c-b x c+1)+\log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)\right)^2}{2 a}+\frac{b h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)}{2 a}-\frac{e h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)}{2 d}-\frac{b h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right)^2}{2 a}+\frac{e h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right)^2}{2 d}+\frac{e h n \left(\log \left(\frac{b x}{a}+1\right)+\log \left(\frac{1-a c}{1-c (a+b x)}\right)-\log \left(\frac{(1-a c) (a+b x)}{a (1-c (a+b x))}\right)\right) \log ^2\left(-\frac{a (1-c (a+b x))}{b x}\right)}{2 d}+\frac{e h n \left(\log (c (a+b x))-\log \left(\frac{b x}{a}+1\right)\right) \left(\log (x)+\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right)^2}{2 d}-\frac{b g \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1)}{a}-\frac{b h n \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1) \log (d+e x)}{a}+\frac{b h \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1) \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right)}{a}+\frac{e h n \log (x) \log \left(\frac{b x}{a}+1\right) \log (1-c (a+b x))}{d}+\frac{b h n \log (c (a+b x)) \log (d+e x) \log (1-c (a+b x))}{a}-\frac{e h n \log (c (a+b x)) \log (d+e x) \log (1-c (a+b x))}{d}+\frac{e h n \left(\log (1-c (a+b x))-\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right) \text{Li}_2\left(-\frac{b x}{a}\right)}{d}-\frac{b g \text{Li}_2(c (a+b x))}{a}+\frac{e h n \log (x) \text{Li}_2(c (a+b x))}{d}-\frac{e h n \log (d+e x) \text{Li}_2(c (a+b x))}{d}+\frac{b h \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))}{a}-\frac{\left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))}{x}-\frac{b g \text{Li}_2\left(1-\frac{b c x}{1-a c}\right)}{a}-\frac{b h n \left(\log (d+e x)-\log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)\right) \text{Li}_2\left(1-\frac{b c x}{1-a c}\right)}{a}+\frac{b h \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right) \text{Li}_2\left(1-\frac{b c x}{1-a c}\right)}{a}+\frac{b h n \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)}{a}-\frac{e h n \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)}{d}-\frac{b h n \left(\log (-a c-b x c+1)+\log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)\right) \text{Li}_2\left(\frac{e x}{d}+1\right)}{a}+\frac{e h n \log \left(-\frac{a (1-c (a+b x))}{b x}\right) \text{Li}_2\left(-\frac{b x}{a (1-c (a+b x))}\right)}{d}-\frac{e h n \log \left(-\frac{a (1-c (a+b x))}{b x}\right) \text{Li}_2\left(-\frac{b c x}{1-c (a+b x)}\right)}{d}+\frac{b h n \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)\right) \text{Li}_2(1-c (a+b x))}{a}-\frac{e h n \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)\right) \text{Li}_2(1-c (a+b x))}{d}+\frac{e h n \left(\log (x)+\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right) \text{Li}_2(1-c (a+b x))}{d}-\frac{b h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{a}+\frac{e h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{d}+\frac{b h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{a}-\frac{e h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{d}-\frac{e h n \text{Li}_3\left(-\frac{b x}{a}\right)}{d}+\frac{b h n \text{Li}_3\left(1-\frac{b c x}{1-a c}\right)}{a}-\frac{b h n \text{Li}_3\left(\frac{d (-a c-b x c+1)}{(1-a c) (d+e x)}\right)}{a}+\frac{b h n \text{Li}_3\left(-\frac{e (-a c-b x c+1)}{b c (d+e x)}\right)}{a}-\frac{b h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)}{a}+\frac{e h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)}{d}+\frac{b h n \text{Li}_3\left(\frac{e x}{d}+1\right)}{a}+\frac{e h n \text{Li}_3\left(-\frac{b x}{a (1-c (a+b x))}\right)}{d}-\frac{e h n \text{Li}_3\left(-\frac{b c x}{1-c (a+b x)}\right)}{d}-\frac{b h n \text{Li}_3(1-c (a+b x))}{a}-\frac{b h n \text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{a}+\frac{e h n \text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{d}+\frac{b h n \text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{a}-\frac{e h n \text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{d}",1,"-(((g - h*n*Log[d + e*x] + h*Log[f*(d + e*x)^n])*((a + b*x)*PolyLog[2, c*(a + b*x)] + b*x*(Log[(b*c*x)/(1 - a*c)]*Log[1 - a*c - b*c*x] + PolyLog[2, (-1 + a*c + b*c*x)/(-1 + a*c)])))/(a*x)) + (h*n*(a*(e*x*Log[x] - (d + e*x)*Log[d + e*x])*PolyLog[2, c*(a + b*x)] + x*(a*e*(Log[x]*Log[1 + (b*x)/a]*Log[1 - a*c - b*c*x] + ((-Log[c*(a + b*x)] + Log[1 + (b*x)/a])*Log[1 - a*c - b*c*x]*(-2*Log[x] + Log[1 - a*c - b*c*x]))/2 + (Log[c*(a + b*x)] - Log[1 + (b*x)/a])*Log[1 - a*c - b*c*x]*Log[(a*(-1 + a*c + b*c*x))/(b*x)] + ((Log[(1 - a*c)/(b*c*x)] - Log[((1 - a*c)*(a + b*x))/(b*x)] + Log[1 + (b*x)/a])*Log[(a*(-1 + a*c + b*c*x))/(b*x)]^2)/2 + (Log[1 - a*c - b*c*x] - Log[(a*(-1 + a*c + b*c*x))/(b*x)])*PolyLog[2, -((b*x)/a)] + (Log[x] + Log[(a*(-1 + a*c + b*c*x))/(b*x)])*PolyLog[2, 1 - a*c - b*c*x] + Log[(a*(-1 + a*c + b*c*x))/(b*x)]*(-PolyLog[2, (a*(-1 + a*c + b*c*x))/(b*x)] + PolyLog[2, (-1 + a*c + b*c*x)/(b*c*x)]) - PolyLog[3, -((b*x)/a)] - PolyLog[3, 1 - a*c - b*c*x] + PolyLog[3, (a*(-1 + a*c + b*c*x))/(b*x)] - PolyLog[3, (-1 + a*c + b*c*x)/(b*c*x)]) - a*e*(Log[c*(a + b*x)]*Log[1 - a*c - b*c*x]*Log[d + e*x] + ((Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*(-2*Log[1 - a*c - b*c*x] + Log[(b*(d + e*x))/(b*d - a*e)]))/2 + (-Log[c*(a + b*x)] + Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] + (Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]^2*(Log[c*(a + b*x)] - Log[((b*c*d + e - a*c*e)*(a + b*x))/((b*d - a*e)*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + (Log[d + e*x] - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, 1 - a*c - b*c*x] + (Log[1 - a*c - b*c*x] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, (b*(d + e*x))/(b*d - a*e)] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]*(PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] - PolyLog[2, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - PolyLog[3, 1 - a*c - b*c*x] - PolyLog[3, (b*(d + e*x))/(b*d - a*e)] - PolyLog[3, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] + PolyLog[3, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - b*d*(Log[(b*c*x)/(1 - a*c)]*Log[1 - a*c - b*c*x]*Log[d + e*x] - Log[c*(a + b*x)]*Log[1 - a*c - b*c*x]*Log[d + e*x] - ((Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*(-2*Log[1 - a*c - b*c*x] + Log[(b*(d + e*x))/(b*d - a*e)]))/2 + (Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] + (Log[((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))]^2*(Log[(b*c*x)/(1 - a*c)] - Log[((b*c*d + e - a*c*e)*x)/(d*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 - (Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]^2*(Log[c*(a + b*x)] - Log[((b*c*d + e - a*c*e)*(a + b*x))/((b*d - a*e)*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + (-Log[(b*c*x)/(1 - a*c)] + Log[-((e*x)/d)])*Log[((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))]*Log[1 + (e*x)/d] + ((Log[(b*c*x)/(1 - a*c)] - Log[-((e*x)/d)])*Log[1 + (e*x)/d]*(-2*Log[1 - a*c - b*c*x] + Log[1 + (e*x)/d]))/2 - (Log[d + e*x] - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, 1 - a*c - b*c*x] + (Log[d + e*x] - Log[((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))])*PolyLog[2, (-1 + a*c + b*c*x)/(-1 + a*c)] - (Log[1 - a*c - b*c*x] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, (b*(d + e*x))/(b*d - a*e)] + Log[((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))]*(-PolyLog[2, ((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))] + PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))]) - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]*(PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] - PolyLog[2, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) + (Log[1 - a*c - b*c*x] + Log[((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))])*PolyLog[2, 1 + (e*x)/d] + PolyLog[3, 1 - a*c - b*c*x] - PolyLog[3, (-1 + a*c + b*c*x)/(-1 + a*c)] + PolyLog[3, (b*(d + e*x))/(b*d - a*e)] + PolyLog[3, ((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))] - PolyLog[3, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] - PolyLog[3, 1 + (e*x)/d]))))/(a*d*x)","A",1
182,1,2673,3119,14.5982472,"\int \frac{\left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))}{x^3} \, dx","Integrate[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x^3,x]","\text{Result too large to show}","\frac{h n \left(\log \left(\frac{b c x}{1-a c}\right)+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) x}{(1-a c) (d+e x)}\right)\right) \log ^2\left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right) b^2}{4 a^2}-\frac{h n \left(\log \left(\frac{b c x}{1-a c}\right)-\log \left(-\frac{e x}{d}\right)\right) \left(\log (-a c-b x c+1)+\log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)\right)^2 b^2}{4 a^2}-\frac{h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) b^2}{4 a^2}+\frac{h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right)^2 b^2}{4 a^2}+\frac{g \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1) b^2}{2 a^2}+\frac{h n \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1) \log (d+e x) b^2}{2 a^2}-\frac{h \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1) \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right) b^2}{2 a^2}+\frac{c \log \left(-\frac{e x}{d}\right) \left(g+h \log \left(f (d+e x)^n\right)\right) b^2}{2 a (1-a c)}-\frac{c \log \left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) \left(g+h \log \left(f (d+e x)^n\right)\right) b^2}{2 a (1-a c)}-\frac{h n \log (c (a+b x)) \log (d+e x) \log (1-c (a+b x)) b^2}{2 a^2}+\frac{g \text{Li}_2(c (a+b x)) b^2}{2 a^2}-\frac{h \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x)) b^2}{2 a^2}+\frac{g \text{Li}_2\left(1-\frac{b c x}{1-a c}\right) b^2}{2 a^2}+\frac{h n \left(\log (d+e x)-\log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)\right) \text{Li}_2\left(1-\frac{b c x}{1-a c}\right) b^2}{2 a^2}-\frac{h \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right) \text{Li}_2\left(1-\frac{b c x}{1-a c}\right) b^2}{2 a^2}+\frac{h n \log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right) \text{Li}_2\left(\frac{d (-a c-b x c+1)}{(1-a c) (d+e x)}\right) b^2}{2 a^2}-\frac{h n \log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right) \text{Li}_2\left(-\frac{e (-a c-b x c+1)}{b c (d+e x)}\right) b^2}{2 a^2}-\frac{h n \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right) b^2}{2 a^2}-\frac{c h n \text{Li}_2\left(\frac{b c (d+e x)}{b c d-a c e+e}\right) b^2}{2 a (1-a c)}+\frac{c h n \text{Li}_2\left(\frac{e x}{d}+1\right) b^2}{2 a (1-a c)}+\frac{h n \left(\log (-a c-b x c+1)+\log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)\right) \text{Li}_2\left(\frac{e x}{d}+1\right) b^2}{2 a^2}-\frac{h n \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)\right) \text{Li}_2(1-c (a+b x)) b^2}{2 a^2}+\frac{h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right) b^2}{2 a^2}-\frac{h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right) b^2}{2 a^2}-\frac{h n \text{Li}_3\left(1-\frac{b c x}{1-a c}\right) b^2}{2 a^2}+\frac{h n \text{Li}_3\left(\frac{d (-a c-b x c+1)}{(1-a c) (d+e x)}\right) b^2}{2 a^2}-\frac{h n \text{Li}_3\left(-\frac{e (-a c-b x c+1)}{b c (d+e x)}\right) b^2}{2 a^2}+\frac{h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right) b^2}{2 a^2}-\frac{h n \text{Li}_3\left(\frac{e x}{d}+1\right) b^2}{2 a^2}+\frac{h n \text{Li}_3(1-c (a+b x)) b^2}{2 a^2}+\frac{h n \text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right) b^2}{2 a^2}-\frac{h n \text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right) b^2}{2 a^2}-\frac{e h n \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1) b}{a d}+\frac{e h n \log (-a c-b x c+1) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right) b}{2 a d}+\frac{\log (-a c-b x c+1) \left(g+h \log \left(f (d+e x)^n\right)\right) b}{2 a x}-\frac{e h n \text{Li}_2(c (a+b x)) b}{2 a d}+\frac{e h n \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) b}{2 a d}-\frac{e h n \text{Li}_2\left(1-\frac{b c x}{1-a c}\right) b}{a d}+\frac{e^2 h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)}{4 d^2}-\frac{e^2 h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right)^2}{4 d^2}-\frac{e^2 h n \left(\log \left(\frac{b x}{a}+1\right)+\log \left(\frac{1-a c}{1-c (a+b x)}\right)-\log \left(\frac{(1-a c) (a+b x)}{a (1-c (a+b x))}\right)\right) \log ^2\left(-\frac{a (1-c (a+b x))}{b x}\right)}{4 d^2}-\frac{e^2 h n \left(\log (c (a+b x))-\log \left(\frac{b x}{a}+1\right)\right) \left(\log (x)+\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right)^2}{4 d^2}-\frac{e^2 h n \log (x) \log \left(\frac{b x}{a}+1\right) \log (1-c (a+b x))}{2 d^2}+\frac{e^2 h n \log (c (a+b x)) \log (d+e x) \log (1-c (a+b x))}{2 d^2}-\frac{e^2 h n \left(\log (1-c (a+b x))-\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right) \text{Li}_2\left(-\frac{b x}{a}\right)}{2 d^2}-\frac{e^2 h n \log (x) \text{Li}_2(c (a+b x))}{2 d^2}+\frac{e^2 h n \log (d+e x) \text{Li}_2(c (a+b x))}{2 d^2}-\frac{\left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))}{2 x^2}-\frac{e h n \text{Li}_2(c (a+b x))}{2 d x}+\frac{e^2 h n \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)}{2 d^2}-\frac{e^2 h n \log \left(-\frac{a (1-c (a+b x))}{b x}\right) \text{Li}_2\left(-\frac{b x}{a (1-c (a+b x))}\right)}{2 d^2}+\frac{e^2 h n \log \left(-\frac{a (1-c (a+b x))}{b x}\right) \text{Li}_2\left(-\frac{b c x}{1-c (a+b x)}\right)}{2 d^2}+\frac{e^2 h n \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)\right) \text{Li}_2(1-c (a+b x))}{2 d^2}-\frac{e^2 h n \left(\log (x)+\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right) \text{Li}_2(1-c (a+b x))}{2 d^2}-\frac{e^2 h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{2 d^2}+\frac{e^2 h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{2 d^2}+\frac{e^2 h n \text{Li}_3\left(-\frac{b x}{a}\right)}{2 d^2}-\frac{e^2 h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)}{2 d^2}-\frac{e^2 h n \text{Li}_3\left(-\frac{b x}{a (1-c (a+b x))}\right)}{2 d^2}+\frac{e^2 h n \text{Li}_3\left(-\frac{b c x}{1-c (a+b x)}\right)}{2 d^2}-\frac{e^2 h n \text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{2 d^2}+\frac{e^2 h n \text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{2 d^2}",1,"((g - h*n*Log[d + e*x] + h*Log[f*(d + e*x)^n])*(-((-1 + a*c)*(a^2 - b^2*x^2)*PolyLog[2, c*(a + b*x)]) + b*x*(-(a*b*c*x*Log[x]) + (a*(-1 + a*c + b*c*x) + b*(-1 + a*c)*x*Log[(b*c*x)/(1 - a*c)])*Log[1 - a*c - b*c*x] + b*(-1 + a*c)*x*PolyLog[2, (-1 + a*c + b*c*x)/(-1 + a*c)])))/(2*a^2*(-1 + a*c)*x^2) - (h*n*(((d*e*x + e^2*x^2*Log[x] + (d^2 - e^2*x^2)*Log[d + e*x])*PolyLog[2, c*(a + b*x)])/x^2 + (b*d*e*(Log[x]*Log[1 - a*c - b*c*x] - Log[c*(a + b*x)]*Log[1 - a*c - b*c*x] - Log[x]*Log[1 + (b*c*x)/(-1 + a*c)] - PolyLog[2, (b*c*x)/(1 - a*c)] - PolyLog[2, 1 - a*c - b*c*x]))/a + e^2*(Log[x]*Log[1 + (b*x)/a]*Log[1 - a*c - b*c*x] + ((-Log[c*(a + b*x)] + Log[1 + (b*x)/a])*Log[1 - a*c - b*c*x]*(-2*Log[x] + Log[1 - a*c - b*c*x]))/2 + (Log[c*(a + b*x)] - Log[1 + (b*x)/a])*Log[1 - a*c - b*c*x]*Log[(a*(-1 + a*c + b*c*x))/(b*x)] + ((Log[(1 - a*c)/(b*c*x)] - Log[((1 - a*c)*(a + b*x))/(b*x)] + Log[1 + (b*x)/a])*Log[(a*(-1 + a*c + b*c*x))/(b*x)]^2)/2 + (Log[1 - a*c - b*c*x] - Log[(a*(-1 + a*c + b*c*x))/(b*x)])*PolyLog[2, -((b*x)/a)] + (Log[x] + Log[(a*(-1 + a*c + b*c*x))/(b*x)])*PolyLog[2, 1 - a*c - b*c*x] + Log[(a*(-1 + a*c + b*c*x))/(b*x)]*(-PolyLog[2, (a*(-1 + a*c + b*c*x))/(b*x)] + PolyLog[2, (-1 + a*c + b*c*x)/(b*c*x)]) - PolyLog[3, -((b*x)/a)] - PolyLog[3, 1 - a*c - b*c*x] + PolyLog[3, (a*(-1 + a*c + b*c*x))/(b*x)] - PolyLog[3, (-1 + a*c + b*c*x)/(b*c*x)]) - e^2*(Log[c*(a + b*x)]*Log[1 - a*c - b*c*x]*Log[d + e*x] + ((Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*(-2*Log[1 - a*c - b*c*x] + Log[(b*(d + e*x))/(b*d - a*e)]))/2 + (-Log[c*(a + b*x)] + Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] + (Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]^2*(Log[c*(a + b*x)] - Log[((b*c*d + e - a*c*e)*(a + b*x))/((b*d - a*e)*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + (Log[d + e*x] - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, 1 - a*c - b*c*x] + (Log[1 - a*c - b*c*x] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, (b*(d + e*x))/(b*d - a*e)] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]*(PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] - PolyLog[2, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - PolyLog[3, 1 - a*c - b*c*x] - PolyLog[3, (b*(d + e*x))/(b*d - a*e)] - PolyLog[3, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] + PolyLog[3, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) + (b*d^2*(-((a*Log[1 - a*c - b*c*x]*Log[d + e*x])/x) - b*Log[(b*c*x)/(1 - a*c)]*Log[1 - a*c - b*c*x]*Log[d + e*x] + b*Log[c*(a + b*x)]*Log[1 - a*c - b*c*x]*Log[d + e*x] + (b*(Log[c*(a + b*x)] - Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*(-2*Log[1 - a*c - b*c*x] + Log[(b*(d + e*x))/(b*d - a*e)]))/2 + b*(-Log[c*(a + b*x)] + Log[(e*(a + b*x))/(-(b*d) + a*e)])*Log[(b*(d + e*x))/(b*d - a*e)]*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] - (b*Log[((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))]^2*(Log[(b*c*x)/(1 - a*c)] - Log[((b*c*d + e - a*c*e)*x)/(d*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + (b*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]^2*(Log[c*(a + b*x)] - Log[((b*c*d + e - a*c*e)*(a + b*x))/((b*d - a*e)*(-1 + a*c + b*c*x))] + Log[(b*c*d + e - a*c*e)/(e - a*c*e - b*c*e*x)]))/2 + b*(Log[(b*c*x)/(1 - a*c)] - Log[-((e*x)/d)])*Log[((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))]*Log[1 + (e*x)/d] - (b*(Log[(b*c*x)/(1 - a*c)] - Log[-((e*x)/d)])*Log[1 + (e*x)/d]*(-2*Log[1 - a*c - b*c*x] + Log[1 + (e*x)/d]))/2 + b*(Log[d + e*x] - Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, 1 - a*c - b*c*x] - b*(Log[d + e*x] - Log[((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))])*PolyLog[2, (-1 + a*c + b*c*x)/(-1 + a*c)] + (a*e*(Log[x]*Log[1 - a*c - b*c*x] - Log[x]*Log[1 + (b*c*x)/(-1 + a*c)] - Log[1 - a*c - b*c*x]*Log[(b*c*(d + e*x))/(b*c*d + e - a*c*e)] - PolyLog[2, (b*c*x)/(1 - a*c)] - PolyLog[2, (e*(-1 + a*c + b*c*x))/(-(b*c*d) - e + a*c*e)]))/d + b*(Log[1 - a*c - b*c*x] + Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))])*PolyLog[2, (b*(d + e*x))/(b*d - a*e)] + b*Log[((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))]*(PolyLog[2, ((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))] - PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))]) + b*Log[-((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]*(PolyLog[2, (b*c*(d + e*x))/(e*(-1 + a*c + b*c*x))] - PolyLog[2, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))]) - b*(Log[1 - a*c - b*c*x] + Log[((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))])*PolyLog[2, 1 + (e*x)/d] + (a*b*c*(Log[d + e*x]*(Log[-((e*x)/d)] - Log[1 - (b*c*(d + e*x))/(b*c*d + e - a*c*e)]) - PolyLog[2, (b*c*(d + e*x))/(b*c*d + e - a*c*e)] + PolyLog[2, 1 + (e*x)/d]))/(-1 + a*c) - b*PolyLog[3, 1 - a*c - b*c*x] + b*PolyLog[3, (-1 + a*c + b*c*x)/(-1 + a*c)] - b*PolyLog[3, (b*(d + e*x))/(b*d - a*e)] - b*PolyLog[3, ((-1 + a*c)*(d + e*x))/(d*(-1 + a*c + b*c*x))] + b*PolyLog[3, -((b*(d + e*x))/((b*d - a*e)*(-1 + a*c + b*c*x)))] + b*PolyLog[3, 1 + (e*x)/d]))/a^2))/(2*d^2)","A",1
183,0,0,3733,10.4711484,"\int \frac{\left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))}{x^4} \, dx","Integrate[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x^4,x]","\int \frac{\left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))}{x^4} \, dx","-\frac{h n \left(\log \left(\frac{b c x}{1-a c}\right)+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) x}{(1-a c) (d+e x)}\right)\right) \log ^2\left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right) b^3}{6 a^3}+\frac{h n \left(\log \left(\frac{b c x}{1-a c}\right)-\log \left(-\frac{e x}{d}\right)\right) \left(\log (-a c-b x c+1)+\log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)\right)^2 b^3}{6 a^3}+\frac{h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) b^3}{6 a^3}-\frac{h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right)^2 b^3}{6 a^3}-\frac{g \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1) b^3}{3 a^3}-\frac{h n \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1) \log (d+e x) b^3}{3 a^3}+\frac{h \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1) \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right) b^3}{3 a^3}-\frac{c \log \left(-\frac{e x}{d}\right) \left(g+h \log \left(f (d+e x)^n\right)\right) b^3}{3 a^2 (1-a c)}+\frac{c^2 \log \left(-\frac{e x}{d}\right) \left(g+h \log \left(f (d+e x)^n\right)\right) b^3}{6 a (1-a c)^2}+\frac{c \log \left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) \left(g+h \log \left(f (d+e x)^n\right)\right) b^3}{3 a^2 (1-a c)}-\frac{c^2 \log \left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) \left(g+h \log \left(f (d+e x)^n\right)\right) b^3}{6 a (1-a c)^2}+\frac{h n \log (c (a+b x)) \log (d+e x) \log (1-c (a+b x)) b^3}{3 a^3}-\frac{g \text{Li}_2(c (a+b x)) b^3}{3 a^3}+\frac{h \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x)) b^3}{3 a^3}-\frac{g \text{Li}_2\left(1-\frac{b c x}{1-a c}\right) b^3}{3 a^3}-\frac{h n \left(\log (d+e x)-\log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)\right) \text{Li}_2\left(1-\frac{b c x}{1-a c}\right) b^3}{3 a^3}+\frac{h \left(n \log (d+e x)-\log \left(f (d+e x)^n\right)\right) \text{Li}_2\left(1-\frac{b c x}{1-a c}\right) b^3}{3 a^3}-\frac{h n \log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right) \text{Li}_2\left(\frac{d (-a c-b x c+1)}{(1-a c) (d+e x)}\right) b^3}{3 a^3}+\frac{h n \log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right) \text{Li}_2\left(-\frac{e (-a c-b x c+1)}{b c (d+e x)}\right) b^3}{3 a^3}+\frac{h n \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right) b^3}{3 a^3}+\frac{c h n \text{Li}_2\left(\frac{b c (d+e x)}{b c d-a c e+e}\right) b^3}{3 a^2 (1-a c)}-\frac{c^2 h n \text{Li}_2\left(\frac{b c (d+e x)}{b c d-a c e+e}\right) b^3}{6 a (1-a c)^2}-\frac{c h n \text{Li}_2\left(\frac{e x}{d}+1\right) b^3}{3 a^2 (1-a c)}+\frac{c^2 h n \text{Li}_2\left(\frac{e x}{d}+1\right) b^3}{6 a (1-a c)^2}-\frac{h n \left(\log (-a c-b x c+1)+\log \left(\frac{(1-a c) (d+e x)}{d (-a c-b x c+1)}\right)\right) \text{Li}_2\left(\frac{e x}{d}+1\right) b^3}{3 a^3}+\frac{h n \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)\right) \text{Li}_2(1-c (a+b x)) b^3}{3 a^3}-\frac{h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right) b^3}{3 a^3}+\frac{h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right) b^3}{3 a^3}+\frac{h n \text{Li}_3\left(1-\frac{b c x}{1-a c}\right) b^3}{3 a^3}-\frac{h n \text{Li}_3\left(\frac{d (-a c-b x c+1)}{(1-a c) (d+e x)}\right) b^3}{3 a^3}+\frac{h n \text{Li}_3\left(-\frac{e (-a c-b x c+1)}{b c (d+e x)}\right) b^3}{3 a^3}-\frac{h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right) b^3}{3 a^3}+\frac{h n \text{Li}_3\left(\frac{e x}{d}+1\right) b^3}{3 a^3}-\frac{h n \text{Li}_3(1-c (a+b x)) b^3}{3 a^3}-\frac{h n \text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right) b^3}{3 a^3}+\frac{h n \text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right) b^3}{3 a^3}+\frac{c e h n \log (x) b^2}{2 a (1-a c) d}-\frac{c e h n \log (-a c-b x c+1) b^2}{3 a (1-a c) d}+\frac{e h n \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1) b^2}{2 a^2 d}-\frac{c e h n \log (d+e x) b^2}{6 a (1-a c) d}-\frac{e h n \log (-a c-b x c+1) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right) b^2}{3 a^2 d}-\frac{\log (-a c-b x c+1) \left(g+h \log \left(f (d+e x)^n\right)\right) b^2}{3 a^2 x}-\frac{c \left(g+h \log \left(f (d+e x)^n\right)\right) b^2}{6 a (1-a c) x}+\frac{e h n \text{Li}_2(c (a+b x)) b^2}{6 a^2 d}-\frac{e h n \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) b^2}{3 a^2 d}+\frac{e h n \text{Li}_2\left(1-\frac{b c x}{1-a c}\right) b^2}{2 a^2 d}+\frac{e^2 h n \log \left(\frac{b c x}{1-a c}\right) \log (-a c-b x c+1) b}{2 a d^2}+\frac{e h n \log (-a c-b x c+1) b}{3 a d x}-\frac{e^2 h n \log (-a c-b x c+1) \log \left(\frac{b c (d+e x)}{b c d-a c e+e}\right) b}{6 a d^2}+\frac{\log (-a c-b x c+1) \left(g+h \log \left(f (d+e x)^n\right)\right) b}{6 a x^2}+\frac{e^2 h n \text{Li}_2(c (a+b x)) b}{3 a d^2}-\frac{e^2 h n \text{Li}_2\left(\frac{e (-a c-b x c+1)}{b c d-a c e+e}\right) b}{6 a d^2}+\frac{e^2 h n \text{Li}_2\left(1-\frac{b c x}{1-a c}\right) b}{2 a d^2}-\frac{e^3 h n \left(\log (c (a+b x))+\log \left(\frac{b c d-a c e+e}{b c (d+e x)}\right)-\log \left(\frac{(b c d-a c e+e) (a+b x)}{b (d+e x)}\right)\right) \log ^2\left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)}{6 d^3}+\frac{e^3 h n \left(\log (c (a+b x))-\log \left(-\frac{e (a+b x)}{b d-a e}\right)\right) \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right)^2}{6 d^3}+\frac{e^3 h n \left(\log \left(\frac{b x}{a}+1\right)+\log \left(\frac{1-a c}{1-c (a+b x)}\right)-\log \left(\frac{(1-a c) (a+b x)}{a (1-c (a+b x))}\right)\right) \log ^2\left(-\frac{a (1-c (a+b x))}{b x}\right)}{6 d^3}+\frac{e^3 h n \left(\log (c (a+b x))-\log \left(\frac{b x}{a}+1\right)\right) \left(\log (x)+\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right)^2}{6 d^3}+\frac{e^3 h n \log (x) \log \left(\frac{b x}{a}+1\right) \log (1-c (a+b x))}{3 d^3}-\frac{e^3 h n \log (c (a+b x)) \log (d+e x) \log (1-c (a+b x))}{3 d^3}+\frac{e^3 h n \left(\log (1-c (a+b x))-\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right) \text{Li}_2\left(-\frac{b x}{a}\right)}{3 d^3}+\frac{e^3 h n \log (x) \text{Li}_2(c (a+b x))}{3 d^3}-\frac{e^3 h n \log (d+e x) \text{Li}_2(c (a+b x))}{3 d^3}-\frac{\left(g+h \log \left(f (d+e x)^n\right)\right) \text{Li}_2(c (a+b x))}{3 x^3}+\frac{e^2 h n \text{Li}_2(c (a+b x))}{3 d^2 x}-\frac{e h n \text{Li}_2(c (a+b x))}{6 d x^2}-\frac{e^3 h n \left(\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)+\log (1-c (a+b x))\right) \text{Li}_2\left(\frac{b (d+e x)}{b d-a e}\right)}{3 d^3}+\frac{e^3 h n \log \left(-\frac{a (1-c (a+b x))}{b x}\right) \text{Li}_2\left(-\frac{b x}{a (1-c (a+b x))}\right)}{3 d^3}-\frac{e^3 h n \log \left(-\frac{a (1-c (a+b x))}{b x}\right) \text{Li}_2\left(-\frac{b c x}{1-c (a+b x)}\right)}{3 d^3}-\frac{e^3 h n \left(\log (d+e x)-\log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right)\right) \text{Li}_2(1-c (a+b x))}{3 d^3}+\frac{e^3 h n \left(\log (x)+\log \left(-\frac{a (1-c (a+b x))}{b x}\right)\right) \text{Li}_2(1-c (a+b x))}{3 d^3}+\frac{e^3 h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{3 d^3}-\frac{e^3 h n \log \left(\frac{b (d+e x)}{(b d-a e) (1-c (a+b x))}\right) \text{Li}_2\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{3 d^3}-\frac{e^3 h n \text{Li}_3\left(-\frac{b x}{a}\right)}{3 d^3}+\frac{e^3 h n \text{Li}_3\left(\frac{b (d+e x)}{b d-a e}\right)}{3 d^3}+\frac{e^3 h n \text{Li}_3\left(-\frac{b x}{a (1-c (a+b x))}\right)}{3 d^3}-\frac{e^3 h n \text{Li}_3\left(-\frac{b c x}{1-c (a+b x)}\right)}{3 d^3}+\frac{e^3 h n \text{Li}_3\left(-\frac{e (1-c (a+b x))}{b c (d+e x)}\right)}{3 d^3}-\frac{e^3 h n \text{Li}_3\left(\frac{(b d-a e) (1-c (a+b x))}{b (d+e x)}\right)}{3 d^3}",1,"Integrate[((g + h*Log[f*(d + e*x)^n])*PolyLog[2, c*(a + b*x)])/x^4, x]","F",-1
184,1,425,661,0.7145612,"\int x^2 (a+b x) \log (1-c x) \text{Li}_2(c x) \, dx","Integrate[x^2*(a + b*x)*Log[1 - c*x]*PolyLog[2, c*x],x]","\frac{48 \text{Li}_2(c x) \left(12 \log (1-c x) \left(4 a c \left(c^3 x^3-1\right)+3 b \left(c^4 x^4-1\right)\right)-c x \left(8 a c \left(2 c^2 x^2+3 c x+6\right)+3 b \left(3 c^3 x^3+4 c^2 x^2+6 c x+12\right)\right)\right)-1152 (4 a c+3 b) \text{Li}_2(1-c x) \log (1-c x)+256 a c^4 x^3+768 a c^4 x^3 \log ^2(1-c x)-768 a c^4 x^3 \log (1-c x)+1056 a c^3 x^2-1344 a c^3 x^2 \log (1-c x)+5952 a c^2 x-3840 a c^2 x \log (1-c x)+4608 a c \text{Li}_3(1-c x)-768 a c \log ^2(1-c x)-2304 a c \log (c x) \log ^2(1-c x)+5952 a c \log (1-c x)+81 b c^4 x^4+432 b c^4 x^4 \log ^2(1-c x)-324 b c^4 x^4 \log (1-c x)+268 b c^3 x^3-480 b c^3 x^3 \log (1-c x)+834 b c^2 x^2-864 b c^2 x^2 \log (1-c x)+3456 b \text{Li}_3(1-c x)+4260 b c x-432 b \log ^2(1-c x)-1728 b \log (c x) \log ^2(1-c x)-2592 b c x \log (1-c x)+4260 b \log (1-c x)}{6912 c^4}","\frac{(4 a c+3 b) \text{Li}_3(1-c x)}{6 c^4}-\frac{(4 a c+3 b) \text{Li}_2(c x) \log (1-c x)}{12 c^4}-\frac{(4 a c+3 b) \text{Li}_2(1-c x) \log (1-c x)}{6 c^4}-\frac{(4 a c+3 b) \log (c x) \log ^2(1-c x)}{12 c^4}+\frac{13 (4 a c+3 b) \log (1-c x)}{432 c^4}+\frac{(1-c x) (4 a c+3 b) \log (1-c x)}{12 c^4}-\frac{x (4 a c+3 b) \text{Li}_2(c x)}{12 c^3}+\frac{49 x (4 a c+3 b)}{432 c^3}-\frac{x^2 (4 a c+3 b) \text{Li}_2(c x)}{24 c^2}+\frac{13 x^2 (4 a c+3 b)}{864 c^2}-\frac{x^2 (4 a c+3 b) \log (1-c x)}{48 c^2}-\frac{x^3 (4 a c+3 b) \text{Li}_2(c x)}{36 c}+\frac{1}{12} \left(4 a x^3+3 b x^4\right) \text{Li}_2(c x) \log (1-c x)+\frac{x^3 (4 a c+3 b)}{324 c}-\frac{x^3 (4 a c+3 b) \log (1-c x)}{108 c}-\frac{a \log ^2(1-c x)}{9 c^3}+\frac{2 a (1-c x) \log (1-c x)}{9 c^3}+\frac{5 a \log (1-c x)}{27 c^3}+\frac{11 a x}{27 c^2}+\frac{1}{9} a x^3 \log ^2(1-c x)-\frac{2}{27} a x^3 \log (1-c x)+\frac{5 a x^2}{54 c}-\frac{a x^2 \log (1-c x)}{9 c}+\frac{2 a x^3}{81}-\frac{b \log ^2(1-c x)}{16 c^4}+\frac{b (1-c x) \log (1-c x)}{8 c^4}+\frac{29 b \log (1-c x)}{192 c^4}+\frac{53 b x}{192 c^3}+\frac{29 b x^2}{384 c^2}-\frac{b x^2 \log (1-c x)}{16 c^2}-\frac{1}{16} b x^4 \text{Li}_2(c x)+\frac{1}{16} b x^4 \log ^2(1-c x)-\frac{3}{64} b x^4 \log (1-c x)+\frac{17 b x^3}{576 c}-\frac{b x^3 \log (1-c x)}{24 c}+\frac{3 b x^4}{256}",1,"(4260*b*c*x + 5952*a*c^2*x + 834*b*c^2*x^2 + 1056*a*c^3*x^2 + 268*b*c^3*x^3 + 256*a*c^4*x^3 + 81*b*c^4*x^4 + 4260*b*Log[1 - c*x] + 5952*a*c*Log[1 - c*x] - 2592*b*c*x*Log[1 - c*x] - 3840*a*c^2*x*Log[1 - c*x] - 864*b*c^2*x^2*Log[1 - c*x] - 1344*a*c^3*x^2*Log[1 - c*x] - 480*b*c^3*x^3*Log[1 - c*x] - 768*a*c^4*x^3*Log[1 - c*x] - 324*b*c^4*x^4*Log[1 - c*x] - 432*b*Log[1 - c*x]^2 - 768*a*c*Log[1 - c*x]^2 + 768*a*c^4*x^3*Log[1 - c*x]^2 + 432*b*c^4*x^4*Log[1 - c*x]^2 - 1728*b*Log[c*x]*Log[1 - c*x]^2 - 2304*a*c*Log[c*x]*Log[1 - c*x]^2 + 48*(-(c*x*(8*a*c*(6 + 3*c*x + 2*c^2*x^2) + 3*b*(12 + 6*c*x + 4*c^2*x^2 + 3*c^3*x^3))) + 12*(4*a*c*(-1 + c^3*x^3) + 3*b*(-1 + c^4*x^4))*Log[1 - c*x])*PolyLog[2, c*x] - 1152*(3*b + 4*a*c)*Log[1 - c*x]*PolyLog[2, 1 - c*x] + 3456*b*PolyLog[3, 1 - c*x] + 4608*a*c*PolyLog[3, 1 - c*x])/(6912*c^4)","A",1
185,1,362,546,0.5681398,"\int x (a+b x) \log (1-c x) \text{Li}_2(c x) \, dx","Integrate[x*(a + b*x)*Log[1 - c*x]*PolyLog[2, c*x],x]","\frac{12 \text{Li}_2(c x) \left(6 \log (1-c x) \left(3 a c \left(c^2 x^2-1\right)+2 b \left(c^3 x^3-1\right)\right)-c x \left(9 a c (c x+2)+2 b \left(2 c^2 x^2+3 c x+6\right)\right)\right)-144 (3 a c+2 b) \text{Li}_2(1-c x) \log (1-c x)+81 a c^3 x^2+108 a c^3 x^2 \log ^2(1-c x)-162 a c^3 x^2 \log (1-c x)+594 a c^2 x-432 a c^2 x \log (1-c x)+432 a c \text{Li}_3(1-c x)-108 a c \log ^2(1-c x)-216 a c \log (c x) \log ^2(1-c x)+594 a c \log (1-c x)-378 a c+16 b c^3 x^3+48 b c^3 x^3 \log ^2(1-c x)-48 b c^3 x^3 \log (1-c x)+66 b c^2 x^2-84 b c^2 x^2 \log (1-c x)+288 b \text{Li}_3(1-c x)+372 b c x-48 b \log ^2(1-c x)-144 b \log (c x) \log ^2(1-c x)-240 b c x \log (1-c x)+372 b \log (1-c x)}{432 c^3}","\frac{(3 a c+2 b) \text{Li}_3(1-c x)}{3 c^3}-\frac{(3 a c+2 b) \text{Li}_2(c x) \log (1-c x)}{6 c^3}-\frac{(3 a c+2 b) \text{Li}_2(1-c x) \log (1-c x)}{3 c^3}-\frac{(3 a c+2 b) \log (c x) \log ^2(1-c x)}{6 c^3}+\frac{(3 a c+2 b) \log (1-c x)}{24 c^3}+\frac{(1-c x) (3 a c+2 b) \log (1-c x)}{6 c^3}-\frac{x (3 a c+2 b) \text{Li}_2(c x)}{6 c^2}+\frac{5 x (3 a c+2 b)}{24 c^2}-\frac{x^2 (3 a c+2 b) \text{Li}_2(c x)}{12 c}+\frac{1}{6} \left(3 a x^2+2 b x^3\right) \text{Li}_2(c x) \log (1-c x)+\frac{x^2 (3 a c+2 b)}{48 c}-\frac{x^2 (3 a c+2 b) \log (1-c x)}{24 c}+\frac{a (1-c x)^2}{8 c^2}+\frac{a (1-c x)^2 \log ^2(1-c x)}{4 c^2}-\frac{a (1-c x) \log ^2(1-c x)}{2 c^2}-\frac{a (1-c x)^2 \log (1-c x)}{4 c^2}+\frac{a (1-c x) \log (1-c x)}{c^2}+\frac{a x}{c}-\frac{b \log ^2(1-c x)}{9 c^3}+\frac{2 b (1-c x) \log (1-c x)}{9 c^3}+\frac{2 b \log (1-c x)}{9 c^3}+\frac{4 b x}{9 c^2}-\frac{1}{9} b x^3 \text{Li}_2(c x)+\frac{1}{9} b x^3 \log ^2(1-c x)-\frac{1}{9} b x^3 \log (1-c x)+\frac{b x^2}{9 c}-\frac{b x^2 \log (1-c x)}{9 c}+\frac{b x^3}{27}",1,"(-378*a*c + 372*b*c*x + 594*a*c^2*x + 66*b*c^2*x^2 + 81*a*c^3*x^2 + 16*b*c^3*x^3 + 372*b*Log[1 - c*x] + 594*a*c*Log[1 - c*x] - 240*b*c*x*Log[1 - c*x] - 432*a*c^2*x*Log[1 - c*x] - 84*b*c^2*x^2*Log[1 - c*x] - 162*a*c^3*x^2*Log[1 - c*x] - 48*b*c^3*x^3*Log[1 - c*x] - 48*b*Log[1 - c*x]^2 - 108*a*c*Log[1 - c*x]^2 + 108*a*c^3*x^2*Log[1 - c*x]^2 + 48*b*c^3*x^3*Log[1 - c*x]^2 - 144*b*Log[c*x]*Log[1 - c*x]^2 - 216*a*c*Log[c*x]*Log[1 - c*x]^2 + 12*(-(c*x*(9*a*c*(2 + c*x) + 2*b*(6 + 3*c*x + 2*c^2*x^2))) + 6*(3*a*c*(-1 + c^2*x^2) + 2*b*(-1 + c^3*x^3))*Log[1 - c*x])*PolyLog[2, c*x] - 144*(2*b + 3*a*c)*Log[1 - c*x]*PolyLog[2, 1 - c*x] + 288*b*PolyLog[3, 1 - c*x] + 432*a*c*PolyLog[3, 1 - c*x])/(432*c^3)","A",1
186,1,285,390,0.4514995,"\int (a+b x) \log (1-c x) \text{Li}_2(c x) \, dx","Integrate[(a + b*x)*Log[1 - c*x]*PolyLog[2, c*x],x]","\frac{4 \text{Li}_2(c x) (2 (c x-1) \log (1-c x) (2 a c+b c x+b)-c x (4 a c+b c x+2 b))-16 (2 a c+b) \text{Li}_2(1-c x) \log (1-c x)+48 a c^2 x+16 a c^2 x \log ^2(1-c x)-48 a c^2 x \log (1-c x)+32 a c \text{Li}_3(1-c x)-16 a c \log ^2(1-c x)-16 a c \log (c x) \log ^2(1-c x)+48 a c \log (1-c x)-32 a c+3 b c^2 x^2+4 b c^2 x^2 \log ^2(1-c x)-6 b c^2 x^2 \log (1-c x)+16 b \text{Li}_3(1-c x)+22 b c x-4 b \log ^2(1-c x)-8 b \log (c x) \log ^2(1-c x)-16 b c x \log (1-c x)+22 b \log (1-c x)-14 b}{16 c^2}","\frac{(2 a c+b) \text{Li}_3(1-c x)}{c^2}-\frac{(2 a c+b) \text{Li}_2(c x) \log (1-c x)}{2 c^2}-\frac{(2 a c+b) \text{Li}_2(1-c x) \log (1-c x)}{c^2}-\frac{(2 a c+b) \log (c x) \log ^2(1-c x)}{2 c^2}+\frac{(1-c x) (2 a c+b) \log (1-c x)}{2 c^2}+\frac{1}{2} \left(2 a x+b x^2\right) \text{Li}_2(c x) \log (1-c x)-\frac{x (2 a c+b) \text{Li}_2(c x)}{2 c}+\frac{x (2 a c+b)}{2 c}-\frac{a (1-c x) \log ^2(1-c x)}{c}+\frac{2 a (1-c x) \log (1-c x)}{c}+2 a x+\frac{b (1-c x)^2}{8 c^2}+\frac{b (1-c x)^2 \log ^2(1-c x)}{4 c^2}-\frac{b (1-c x) \log ^2(1-c x)}{2 c^2}-\frac{b (1-c x)^2 \log (1-c x)}{4 c^2}+\frac{b (1-c x) \log (1-c x)}{c^2}+\frac{b \log (1-c x)}{8 c^2}-\frac{1}{4} b x^2 \text{Li}_2(c x)-\frac{1}{8} b x^2 \log (1-c x)+\frac{9 b x}{8 c}+\frac{b x^2}{16}",1,"(-14*b - 32*a*c + 22*b*c*x + 48*a*c^2*x + 3*b*c^2*x^2 + 22*b*Log[1 - c*x] + 48*a*c*Log[1 - c*x] - 16*b*c*x*Log[1 - c*x] - 48*a*c^2*x*Log[1 - c*x] - 6*b*c^2*x^2*Log[1 - c*x] - 4*b*Log[1 - c*x]^2 - 16*a*c*Log[1 - c*x]^2 + 16*a*c^2*x*Log[1 - c*x]^2 + 4*b*c^2*x^2*Log[1 - c*x]^2 - 8*b*Log[c*x]*Log[1 - c*x]^2 - 16*a*c*Log[c*x]*Log[1 - c*x]^2 + 4*(-(c*x*(2*b + 4*a*c + b*c*x)) + 2*(-1 + c*x)*(b + 2*a*c + b*c*x)*Log[1 - c*x])*PolyLog[2, c*x] - 16*(b + 2*a*c)*Log[1 - c*x]*PolyLog[2, 1 - c*x] + 16*b*PolyLog[3, 1 - c*x] + 32*a*c*PolyLog[3, 1 - c*x])/(16*c^2)","A",1
187,1,137,153,0.2272872,"\int \frac{(a+b x) \log (1-c x) \text{Li}_2(c x)}{x} \, dx","Integrate[((a + b*x)*Log[1 - c*x]*PolyLog[2, c*x])/x,x]","-\frac{1}{2} a \text{Li}_2(c x){}^2+\frac{b \left(2 \text{Li}_3(1-c x)-2 \text{Li}_2(1-c x) \log (1-c x)+3 c x+c x \log ^2(1-c x)-\log (c x) \log ^2(1-c x)-\log ^2(1-c x)-3 c x \log (1-c x)+3 \log (1-c x)-2\right)}{c}+\frac{b \text{Li}_2(c x) ((c x-1) \log (1-c x)-c x)}{c}","-\frac{1}{2} a \text{Li}_2(c x){}^2-b x \text{Li}_2(c x)+\frac{2 b \text{Li}_3(1-c x)}{c}+b x \text{Li}_2(c x) \log (1-c x)-\frac{b \text{Li}_2(c x) \log (1-c x)}{c}-\frac{2 b \text{Li}_2(1-c x) \log (1-c x)}{c}-\frac{b (1-c x) \log ^2(1-c x)}{c}-\frac{b \log (c x) \log ^2(1-c x)}{c}+\frac{3 b (1-c x) \log (1-c x)}{c}+3 b x",1,"(b*(-(c*x) + (-1 + c*x)*Log[1 - c*x])*PolyLog[2, c*x])/c - (a*PolyLog[2, c*x]^2)/2 + (b*(-2 + 3*c*x + 3*Log[1 - c*x] - 3*c*x*Log[1 - c*x] - Log[1 - c*x]^2 + c*x*Log[1 - c*x]^2 - Log[c*x]*Log[1 - c*x]^2 - 2*Log[1 - c*x]*PolyLog[2, 1 - c*x] + 2*PolyLog[3, 1 - c*x]))/c","A",1
188,1,135,131,0.6825177,"\int \frac{(a+b x) \log (1-c x) \text{Li}_2(c x)}{x^2} \, dx","Integrate[((a + b*x)*Log[1 - c*x]*PolyLog[2, c*x])/x^2,x]","-a c \text{Li}_3(c x)-2 a c \text{Li}_3(1-c x)+\frac{a (c x-1) \text{Li}_2(c x) \log (1-c x)}{x}+2 a c \text{Li}_2(1-c x) (\log (1-c x)+1)-a c \log ^2(1-c x)+a c \log (c x) \log ^2(1-c x)+\frac{a \log ^2(1-c x)}{x}+2 a c \log (c x) \log (1-c x)-\frac{1}{2} b \text{Li}_2(c x){}^2","-2 a c \text{Li}_2(c x)-a c \text{Li}_3(c x)-2 a c \text{Li}_3(1-c x)+a c \text{Li}_2(c x) \log (1-c x)-\frac{a \text{Li}_2(c x) \log (1-c x)}{x}+2 a c \text{Li}_2(1-c x) \log (1-c x)+\frac{a (1-c x) \log ^2(1-c x)}{x}+a c \log (c x) \log ^2(1-c x)-\frac{1}{2} b \text{Li}_2(c x){}^2",1,"2*a*c*Log[c*x]*Log[1 - c*x] - a*c*Log[1 - c*x]^2 + (a*Log[1 - c*x]^2)/x + a*c*Log[c*x]*Log[1 - c*x]^2 + (a*(-1 + c*x)*Log[1 - c*x]*PolyLog[2, c*x])/x - (b*PolyLog[2, c*x]^2)/2 + 2*a*c*(1 + Log[1 - c*x])*PolyLog[2, 1 - c*x] - a*c*PolyLog[3, c*x] - 2*a*c*PolyLog[3, 1 - c*x]","A",1
189,1,285,331,1.1345477,"\int \frac{(a+b x) \log (1-c x) \text{Li}_2(c x)}{x^3} \, dx","Integrate[((a + b*x)*Log[1 - c*x]*PolyLog[2, c*x])/x^3,x]","\frac{1}{4} \left(\frac{2 \text{Li}_2(c x) ((c x-1) \log (1-c x) (a c x+a+2 b x)+a c x)}{x^2}+2 c \text{Li}_2(1-c x) (2 (a c+2 b) \log (1-c x)+a c+4 b)-2 a c^2 \text{Li}_3(c x)-4 a c^2 \text{Li}_3(1-c x)-a c^2 \log ^2(1-c x)+2 a c^2 \log (c x) \log ^2(1-c x)-4 a c^2 \log (c x)+4 a c^2 \log (1-c x)+2 a c^2 \log (c x) \log (1-c x)+\frac{a \log ^2(1-c x)}{x^2}-\frac{4 a c \log (1-c x)}{x}-4 b c \text{Li}_3(c x)-8 b c \text{Li}_3(1-c x)-4 b c \log ^2(1-c x)+4 b c \log (c x) \log ^2(1-c x)+\frac{4 b \log ^2(1-c x)}{x}+8 b c \log (c x) \log (1-c x)\right)","\frac{b^2 \text{Li}_3(1-c x)}{a}-\frac{b^2 \text{Li}_2(1-c x) \log (1-c x)}{a}-\frac{b^2 \log (c x) \log ^2(1-c x)}{2 a}-\frac{(a+b x)^2 \text{Li}_2(c x) \log (1-c x)}{2 a x^2}-\frac{1}{2} c (a c+2 b) \text{Li}_3(c x)-\frac{(a c+b)^2 \text{Li}_3(1-c x)}{a}+\frac{(a c+b)^2 \text{Li}_2(c x) \log (1-c x)}{2 a}+\frac{(a c+b)^2 \text{Li}_2(1-c x) \log (1-c x)}{a}+\frac{(a c+b)^2 \log (c x) \log ^2(1-c x)}{2 a}-\frac{1}{2} a c^2 \text{Li}_2(c x)-\frac{1}{4} a c^2 \log ^2(1-c x)-a c^2 \log (x)+a c^2 \log (1-c x)+\frac{a c \text{Li}_2(c x)}{2 x}+\frac{a \log ^2(1-c x)}{4 x^2}-\frac{a c \log (1-c x)}{x}-2 b c \text{Li}_2(c x)+\frac{b (1-c x) \log ^2(1-c x)}{x}",1,"(-4*a*c^2*Log[c*x] + 4*a*c^2*Log[1 - c*x] - (4*a*c*Log[1 - c*x])/x + 8*b*c*Log[c*x]*Log[1 - c*x] + 2*a*c^2*Log[c*x]*Log[1 - c*x] - 4*b*c*Log[1 - c*x]^2 - a*c^2*Log[1 - c*x]^2 + (a*Log[1 - c*x]^2)/x^2 + (4*b*Log[1 - c*x]^2)/x + 4*b*c*Log[c*x]*Log[1 - c*x]^2 + 2*a*c^2*Log[c*x]*Log[1 - c*x]^2 + (2*(a*c*x + (-1 + c*x)*(a + 2*b*x + a*c*x)*Log[1 - c*x])*PolyLog[2, c*x])/x^2 + 2*c*(4*b + a*c + 2*(2*b + a*c)*Log[1 - c*x])*PolyLog[2, 1 - c*x] - 4*b*c*PolyLog[3, c*x] - 2*a*c^2*PolyLog[3, c*x] - 8*b*c*PolyLog[3, 1 - c*x] - 4*a*c^2*PolyLog[3, 1 - c*x])/4","A",1
190,1,389,460,1.3589229,"\int \frac{(a+b x) \log (1-c x) \text{Li}_2(c x)}{x^4} \, dx","Integrate[((a + b*x)*Log[1 - c*x]*PolyLog[2, c*x])/x^4,x]","\frac{1}{36} \left(2 c^2 \text{Li}_2(1-c x) (6 (2 a c+3 b) \log (1-c x)+4 a c+9 b)+\frac{6 \text{Li}_2(c x) \left(\log (1-c x) \left(2 a c^3 x^3-2 a+3 b c^2 x^3-3 b x\right)+c x (2 a c x+a+3 b x)\right)}{x^3}-12 a c^3 \text{Li}_3(c x)-24 a c^3 \text{Li}_3(1-c x)-4 a c^3 \log ^2(1-c x)+12 a c^3 \log (c x) \log ^2(1-c x)-27 a c^3 \log (c x)+27 a c^3 \log (1-c x)+8 a c^3 \log (c x) \log (1-c x)-7 a c^3+\frac{7 a c^2}{x}-\frac{20 a c^2 \log (1-c x)}{x}+\frac{4 a \log ^2(1-c x)}{x^3}-\frac{7 a c \log (1-c x)}{x^2}-18 b c^2 \text{Li}_3(c x)-36 b c^2 \text{Li}_3(1-c x)-9 b c^2 \log ^2(1-c x)+18 b c^2 \log (c x) \log ^2(1-c x)-36 b c^2 \log (c x)+36 b c^2 \log (1-c x)+18 b c^2 \log (c x) \log (1-c x)+\frac{9 b \log ^2(1-c x)}{x^2}-\frac{36 b c \log (1-c x)}{x}\right)","-\frac{1}{6} c^2 (2 a c+3 b) \text{Li}_3(c x)-\frac{1}{3} c^2 (2 a c+3 b) \text{Li}_3(1-c x)+\frac{1}{6} c^2 (2 a c+3 b) \text{Li}_2(c x) \log (1-c x)+\frac{1}{3} c^2 (2 a c+3 b) \text{Li}_2(1-c x) \log (1-c x)+\frac{1}{6} c^2 (2 a c+3 b) \log (c x) \log ^2(1-c x)-\frac{1}{6} c^2 \log (x) (2 a c+3 b)+\frac{1}{6} c^2 (2 a c+3 b) \log (1-c x)-\frac{1}{6} \left(\frac{2 a}{x^3}+\frac{3 b}{x^2}\right) \text{Li}_2(c x) \log (1-c x)+\frac{c (2 a c+3 b) \text{Li}_2(c x)}{6 x}-\frac{c (2 a c+3 b) \log (1-c x)}{6 x}-\frac{2}{9} a c^3 \text{Li}_2(c x)-\frac{1}{9} a c^3 \log ^2(1-c x)-\frac{5}{12} a c^3 \log (x)+\frac{5}{12} a c^3 \log (1-c x)+\frac{7 a c^2}{36 x}-\frac{2 a c^2 \log (1-c x)}{9 x}+\frac{a c \text{Li}_2(c x)}{6 x^2}+\frac{a \log ^2(1-c x)}{9 x^3}-\frac{7 a c \log (1-c x)}{36 x^2}-\frac{1}{2} b c^2 \text{Li}_2(c x)-\frac{1}{4} b c^2 \log ^2(1-c x)-\frac{1}{2} b c^2 \log (x)+\frac{1}{2} b c^2 \log (1-c x)+\frac{b \log ^2(1-c x)}{4 x^2}-\frac{b c \log (1-c x)}{2 x}",1,"(-7*a*c^3 + (7*a*c^2)/x - 36*b*c^2*Log[c*x] - 27*a*c^3*Log[c*x] + 36*b*c^2*Log[1 - c*x] + 27*a*c^3*Log[1 - c*x] - (7*a*c*Log[1 - c*x])/x^2 - (36*b*c*Log[1 - c*x])/x - (20*a*c^2*Log[1 - c*x])/x + 18*b*c^2*Log[c*x]*Log[1 - c*x] + 8*a*c^3*Log[c*x]*Log[1 - c*x] - 9*b*c^2*Log[1 - c*x]^2 - 4*a*c^3*Log[1 - c*x]^2 + (4*a*Log[1 - c*x]^2)/x^3 + (9*b*Log[1 - c*x]^2)/x^2 + 18*b*c^2*Log[c*x]*Log[1 - c*x]^2 + 12*a*c^3*Log[c*x]*Log[1 - c*x]^2 + (6*(c*x*(a + 3*b*x + 2*a*c*x) + (-2*a - 3*b*x + 3*b*c^2*x^3 + 2*a*c^3*x^3)*Log[1 - c*x])*PolyLog[2, c*x])/x^3 + 2*c^2*(9*b + 4*a*c + 6*(3*b + 2*a*c)*Log[1 - c*x])*PolyLog[2, 1 - c*x] - 18*b*c^2*PolyLog[3, c*x] - 12*a*c^3*PolyLog[3, c*x] - 36*b*c^2*PolyLog[3, 1 - c*x] - 24*a*c^3*PolyLog[3, 1 - c*x])/36","A",1
191,1,505,584,1.4680581,"\int \frac{(a+b x) \log (1-c x) \text{Li}_2(c x)}{x^5} \, dx","Integrate[((a + b*x)*Log[1 - c*x]*PolyLog[2, c*x])/x^5,x]","-\frac{-2 c^3 x^4 \text{Li}_2(1-c x) (12 (3 a c+4 b) \log (1-c x)+9 a c+16 b)-6 \text{Li}_2(c x) \left(c x \left(a \left(6 c^2 x^2+3 c x+2\right)+4 b x (2 c x+1)\right)+\log (1-c x) \left(6 a \left(c^4 x^4-1\right)+8 b x \left(c^3 x^3-1\right)\right)\right)+36 a c^4 x^4 \text{Li}_3(c x)+72 a c^4 x^4 \text{Li}_3(1-c x)+33 a c^4 x^4+9 a c^4 x^4 \log ^2(1-c x)-36 a c^4 x^4 \log (c x) \log ^2(1-c x)+82 a c^4 x^4 \log (c x)-82 a c^4 x^4 \log (1-c x)-18 a c^4 x^4 \log (c x) \log (1-c x)-28 a c^3 x^3+54 a c^3 x^3 \log (1-c x)-5 a c^2 x^2+18 a c^2 x^2 \log (1-c x)-9 a \log ^2(1-c x)+10 a c x \log (1-c x)+48 b c^3 x^4 \text{Li}_3(c x)+96 b c^3 x^4 \text{Li}_3(1-c x)+28 b c^3 x^4+16 b c^3 x^4 \log ^2(1-c x)-48 b c^3 x^4 \log (c x) \log ^2(1-c x)+108 b c^3 x^4 \log (c x)-108 b c^3 x^4 \log (1-c x)-32 b c^3 x^4 \log (c x) \log (1-c x)-28 b c^2 x^3+80 b c^2 x^3 \log (1-c x)+28 b c x^2 \log (1-c x)-16 b x \log ^2(1-c x)}{144 x^4}","-\frac{1}{12} c^3 (3 a c+4 b) \text{Li}_3(c x)-\frac{1}{6} c^3 (3 a c+4 b) \text{Li}_3(1-c x)+\frac{1}{12} c^3 (3 a c+4 b) \text{Li}_2(c x) \log (1-c x)+\frac{1}{6} c^3 (3 a c+4 b) \text{Li}_2(1-c x) \log (1-c x)+\frac{1}{12} c^3 (3 a c+4 b) \log (c x) \log ^2(1-c x)-\frac{5}{48} c^3 \log (x) (3 a c+4 b)+\frac{5}{48} c^3 (3 a c+4 b) \log (1-c x)+\frac{c^2 (3 a c+4 b) \text{Li}_2(c x)}{12 x}+\frac{c^2 (3 a c+4 b)}{48 x}-\frac{c^2 (3 a c+4 b) \log (1-c x)}{12 x}+\frac{c (3 a c+4 b) \text{Li}_2(c x)}{24 x^2}-\frac{1}{12} \left(\frac{3 a}{x^4}+\frac{4 b}{x^3}\right) \text{Li}_2(c x) \log (1-c x)-\frac{c (3 a c+4 b) \log (1-c x)}{48 x^2}-\frac{1}{8} a c^4 \text{Li}_2(c x)-\frac{1}{16} a c^4 \log ^2(1-c x)-\frac{37}{144} a c^4 \log (x)+\frac{37}{144} a c^4 \log (1-c x)+\frac{19 a c^3}{144 x}-\frac{a c^3 \log (1-c x)}{8 x}+\frac{5 a c^2}{144 x^2}-\frac{a c^2 \log (1-c x)}{16 x^2}+\frac{a c \text{Li}_2(c x)}{12 x^3}+\frac{a \log ^2(1-c x)}{16 x^4}-\frac{5 a c \log (1-c x)}{72 x^3}-\frac{2}{9} b c^3 \text{Li}_2(c x)-\frac{1}{9} b c^3 \log ^2(1-c x)-\frac{1}{3} b c^3 \log (x)+\frac{1}{3} b c^3 \log (1-c x)+\frac{b c^2}{9 x}-\frac{2 b c^2 \log (1-c x)}{9 x}+\frac{b \log ^2(1-c x)}{9 x^3}-\frac{b c \log (1-c x)}{9 x^2}",1,"-1/144*(-5*a*c^2*x^2 - 28*b*c^2*x^3 - 28*a*c^3*x^3 + 28*b*c^3*x^4 + 33*a*c^4*x^4 + 108*b*c^3*x^4*Log[c*x] + 82*a*c^4*x^4*Log[c*x] + 10*a*c*x*Log[1 - c*x] + 28*b*c*x^2*Log[1 - c*x] + 18*a*c^2*x^2*Log[1 - c*x] + 80*b*c^2*x^3*Log[1 - c*x] + 54*a*c^3*x^3*Log[1 - c*x] - 108*b*c^3*x^4*Log[1 - c*x] - 82*a*c^4*x^4*Log[1 - c*x] - 32*b*c^3*x^4*Log[c*x]*Log[1 - c*x] - 18*a*c^4*x^4*Log[c*x]*Log[1 - c*x] - 9*a*Log[1 - c*x]^2 - 16*b*x*Log[1 - c*x]^2 + 16*b*c^3*x^4*Log[1 - c*x]^2 + 9*a*c^4*x^4*Log[1 - c*x]^2 - 48*b*c^3*x^4*Log[c*x]*Log[1 - c*x]^2 - 36*a*c^4*x^4*Log[c*x]*Log[1 - c*x]^2 - 6*(c*x*(4*b*x*(1 + 2*c*x) + a*(2 + 3*c*x + 6*c^2*x^2)) + (8*b*x*(-1 + c^3*x^3) + 6*a*(-1 + c^4*x^4))*Log[1 - c*x])*PolyLog[2, c*x] - 2*c^3*x^4*(16*b + 9*a*c + 12*(4*b + 3*a*c)*Log[1 - c*x])*PolyLog[2, 1 - c*x] + 48*b*c^3*x^4*PolyLog[3, c*x] + 36*a*c^4*x^4*PolyLog[3, c*x] + 96*b*c^3*x^4*PolyLog[3, 1 - c*x] + 72*a*c^4*x^4*PolyLog[3, 1 - c*x])/x^4","A",1
192,1,583,900,1.2075043,"\int x \left(a+b x+c x^2\right) \log (1-d x) \text{Li}_2(d x) \, dx","Integrate[x*(a + b*x + c*x^2)*Log[1 - d*x]*PolyLog[2, d*x],x]","\frac{24 \text{Li}_3(1-d x) \left(6 a d^2+4 b d+3 c\right)-24 \text{Li}_2(1-d x) \log (1-d x) \left(6 a d^2+4 b d+3 c\right)+\text{Li}_2(d x) \left(12 \log (1-d x) \left(6 a d^4 x^2-6 a d^2+4 b d^4 x^3-4 b d+3 c \left(d^4 x^4-1\right)\right)-d x \left(4 d \left(9 a d (d x+2)+2 b \left(2 d^2 x^2+3 d x+6\right)\right)+3 c \left(3 d^3 x^3+4 d^2 x^2+6 d x+12\right)\right)\right)+27 a d^4 x^2+36 a d^4 x^2 \log ^2(1-d x)-54 a d^4 x^2 \log (1-d x)+198 a d^3 x-144 a d^3 x \log (1-d x)-36 a d^2 \log ^2(1-d x)-72 a d^2 \log (d x) \log ^2(1-d x)+198 a d^2 \log (1-d x)+\frac{16}{3} b d^4 x^3+16 b d^4 x^3 \log ^2(1-d x)-16 b d^4 x^3 \log (1-d x)+22 b d^3 x^2-28 b d^3 x^2 \log (1-d x)+124 b d^2 x-80 b d^2 x \log (1-d x)-16 b d \log ^2(1-d x)-48 b d \log (d x) \log ^2(1-d x)+124 b d \log (1-d x)+\frac{27}{16} c d^4 x^4+9 c d^4 x^4 \log ^2(1-d x)-\frac{27}{4} c d^4 x^4 \log (1-d x)+\frac{67}{12} c d^3 x^3-10 c d^3 x^3 \log (1-d x)+\frac{139}{8} c d^2 x^2-18 c d^2 x^2 \log (1-d x)+\frac{355 c d x}{4}-9 c \log ^2(1-d x)-36 c \log (d x) \log ^2(1-d x)-54 c d x \log (1-d x)+\frac{355}{4} c \log (1-d x)}{144 d^4}","\frac{1}{16} c \log ^2(1-d x) x^4+\frac{3 c x^4}{256}-\frac{3}{64} c \log (1-d x) x^4-\frac{1}{16} c \text{Li}_2(d x) x^4+\frac{1}{9} b \log ^2(1-d x) x^3+\frac{2 b x^3}{81}+\frac{(3 c+4 b d) x^3}{324 d}-\frac{2}{27} b \log (1-d x) x^3-\frac{(3 c+4 b d) \log (1-d x) x^3}{108 d}-\frac{c \log (1-d x) x^3}{24 d}-\frac{(3 c+4 b d) \text{Li}_2(d x) x^3}{36 d}+\frac{17 c x^3}{576 d}+\frac{(3 c+4 b d) x^2}{216 d^2}+\frac{\left(6 a d^2+4 b d+3 c\right) x^2}{96 d^2}-\frac{\left(6 a d^2+4 b d+3 c\right) \log (1-d x) x^2}{48 d^2}-\frac{b \log (1-d x) x^2}{9 d}-\frac{c \log (1-d x) x^2}{16 d^2}-\frac{\left(6 a d^2+4 b d+3 c\right) \text{Li}_2(d x) x^2}{24 d^2}+\frac{5 b x^2}{54 d}+\frac{29 c x^2}{384 d^2}+\frac{(3 c+4 b d) x}{108 d^3}+\frac{5 \left(6 a d^2+4 b d+3 c\right) x}{48 d^3}-\frac{\left(6 a d^2+4 b d+3 c\right) \text{Li}_2(d x) x}{12 d^3}+\frac{a x}{d}+\frac{11 b x}{27 d^2}+\frac{53 c x}{192 d^3}+\frac{a (1-d x)^2}{8 d^2}+\frac{a (1-d x)^2 \log ^2(1-d x)}{4 d^2}-\frac{a (1-d x) \log ^2(1-d x)}{2 d^2}-\frac{\left(6 a d^2+4 b d+3 c\right) \log (d x) \log ^2(1-d x)}{12 d^4}-\frac{b \log ^2(1-d x)}{9 d^3}-\frac{c \log ^2(1-d x)}{16 d^4}-\frac{a (1-d x)^2 \log (1-d x)}{4 d^2}+\frac{(3 c+4 b d) \log (1-d x)}{108 d^4}+\frac{\left(6 a d^2+4 b d+3 c\right) \log (1-d x)}{48 d^4}+\frac{\left(6 a d^2+4 b d+3 c\right) (1-d x) \log (1-d x)}{12 d^4}+\frac{a (1-d x) \log (1-d x)}{d^2}+\frac{2 b (1-d x) \log (1-d x)}{9 d^3}+\frac{c (1-d x) \log (1-d x)}{8 d^4}+\frac{5 b \log (1-d x)}{27 d^3}+\frac{29 c \log (1-d x)}{192 d^4}-\frac{\left(6 a d^2+4 b d+3 c\right) \log (1-d x) \text{Li}_2(d x)}{12 d^4}+\frac{1}{12} \left(3 c x^4+4 b x^3+6 a x^2\right) \log (1-d x) \text{Li}_2(d x)-\frac{\left(6 a d^2+4 b d+3 c\right) \log (1-d x) \text{Li}_2(1-d x)}{6 d^4}+\frac{\left(6 a d^2+4 b d+3 c\right) \text{Li}_3(1-d x)}{6 d^4}",1,"((355*c*d*x)/4 + 124*b*d^2*x + 198*a*d^3*x + (139*c*d^2*x^2)/8 + 22*b*d^3*x^2 + 27*a*d^4*x^2 + (67*c*d^3*x^3)/12 + (16*b*d^4*x^3)/3 + (27*c*d^4*x^4)/16 + (355*c*Log[1 - d*x])/4 + 124*b*d*Log[1 - d*x] + 198*a*d^2*Log[1 - d*x] - 54*c*d*x*Log[1 - d*x] - 80*b*d^2*x*Log[1 - d*x] - 144*a*d^3*x*Log[1 - d*x] - 18*c*d^2*x^2*Log[1 - d*x] - 28*b*d^3*x^2*Log[1 - d*x] - 54*a*d^4*x^2*Log[1 - d*x] - 10*c*d^3*x^3*Log[1 - d*x] - 16*b*d^4*x^3*Log[1 - d*x] - (27*c*d^4*x^4*Log[1 - d*x])/4 - 9*c*Log[1 - d*x]^2 - 16*b*d*Log[1 - d*x]^2 - 36*a*d^2*Log[1 - d*x]^2 + 36*a*d^4*x^2*Log[1 - d*x]^2 + 16*b*d^4*x^3*Log[1 - d*x]^2 + 9*c*d^4*x^4*Log[1 - d*x]^2 - 36*c*Log[d*x]*Log[1 - d*x]^2 - 48*b*d*Log[d*x]*Log[1 - d*x]^2 - 72*a*d^2*Log[d*x]*Log[1 - d*x]^2 + (-(d*x*(3*c*(12 + 6*d*x + 4*d^2*x^2 + 3*d^3*x^3) + 4*d*(9*a*d*(2 + d*x) + 2*b*(6 + 3*d*x + 2*d^2*x^2)))) + 12*(-4*b*d - 6*a*d^2 + 6*a*d^4*x^2 + 4*b*d^4*x^3 + 3*c*(-1 + d^4*x^4))*Log[1 - d*x])*PolyLog[2, d*x] - 24*(3*c + 4*b*d + 6*a*d^2)*Log[1 - d*x]*PolyLog[2, 1 - d*x] + 24*(3*c + 4*b*d + 6*a*d^2)*PolyLog[3, 1 - d*x])/(144*d^4)","A",1
193,1,472,645,0.9799269,"\int \left(a+b x+c x^2\right) \log (1-d x) \text{Li}_2(d x) \, dx","Integrate[(a + b*x + c*x^2)*Log[1 - d*x]*PolyLog[2, d*x],x]","\frac{\text{Li}_2(d x) \left(6 (d x-1) \log (1-d x) \left(3 d (2 a d+b d x+b)+2 c \left(d^2 x^2+d x+1\right)\right)-d x \left(9 d (4 a d+b d x+2 b)+2 c \left(2 d^2 x^2+3 d x+6\right)\right)\right)+12 \text{Li}_3(1-d x) (3 d (2 a d+b)+2 c)-12 \text{Li}_2(1-d x) \log (1-d x) (3 d (2 a d+b)+2 c)+108 a d^3 x+36 a d^3 x \log ^2(1-d x)-108 a d^3 x \log (1-d x)-36 a d^2 \log ^2(1-d x)-36 a d^2 \log (d x) \log ^2(1-d x)+108 a d^2 \log (1-d x)+\frac{27}{4} b d^3 x^2+9 b d^3 x^2 \log ^2(1-d x)-\frac{27}{2} b d^3 x^2 \log (1-d x)+\frac{99}{2} b d^2 x-36 b d^2 x \log (1-d x)-9 b d \log ^2(1-d x)-18 b d \log (d x) \log ^2(1-d x)+\frac{99}{2} b d \log (1-d x)+\frac{4}{3} c d^3 x^3+4 c d^3 x^3 \log ^2(1-d x)-4 c d^3 x^3 \log (1-d x)+\frac{11}{2} c d^2 x^2-7 c d^2 x^2 \log (1-d x)+31 c d x-4 c \log ^2(1-d x)-12 c \log (d x) \log ^2(1-d x)-20 c d x \log (1-d x)+31 c \log (1-d x)}{36 d^3}","\frac{\text{Li}_3(1-d x) (3 d (2 a d+b)+2 c)}{3 d^3}-\frac{\text{Li}_2(d x) \log (1-d x) (3 d (2 a d+b)+2 c)}{6 d^3}-\frac{\text{Li}_2(1-d x) \log (1-d x) (3 d (2 a d+b)+2 c)}{3 d^3}-\frac{\log (d x) \log ^2(1-d x) (3 d (2 a d+b)+2 c)}{6 d^3}+\frac{(1-d x) \log (1-d x) (3 d (2 a d+b)+2 c)}{6 d^3}-\frac{x \text{Li}_2(d x) (3 d (2 a d+b)+2 c)}{6 d^2}+\frac{x (3 d (2 a d+b)+2 c)}{6 d^2}+\frac{1}{6} \text{Li}_2(d x) \log (1-d x) \left(6 a x+3 b x^2+2 c x^3\right)-\frac{a (1-d x) \log ^2(1-d x)}{d}+\frac{2 a (1-d x) \log (1-d x)}{d}+2 a x+\frac{(3 b d+2 c) \log (1-d x)}{24 d^3}+\frac{x (3 b d+2 c)}{24 d^2}-\frac{x^2 (3 b d+2 c) \text{Li}_2(d x)}{12 d}+\frac{x^2 (3 b d+2 c)}{48 d}-\frac{x^2 (3 b d+2 c) \log (1-d x)}{24 d}+\frac{b (1-d x)^2}{8 d^2}+\frac{b (1-d x)^2 \log ^2(1-d x)}{4 d^2}-\frac{b (1-d x) \log ^2(1-d x)}{2 d^2}-\frac{b (1-d x)^2 \log (1-d x)}{4 d^2}+\frac{b (1-d x) \log (1-d x)}{d^2}+\frac{b x}{d}-\frac{c \log ^2(1-d x)}{9 d^3}+\frac{2 c (1-d x) \log (1-d x)}{9 d^3}+\frac{2 c \log (1-d x)}{9 d^3}+\frac{4 c x}{9 d^2}-\frac{1}{9} c x^3 \text{Li}_2(d x)+\frac{1}{9} c x^3 \log ^2(1-d x)-\frac{1}{9} c x^3 \log (1-d x)+\frac{c x^2}{9 d}-\frac{c x^2 \log (1-d x)}{9 d}+\frac{c x^3}{27}",1,"(31*c*d*x + (99*b*d^2*x)/2 + 108*a*d^3*x + (11*c*d^2*x^2)/2 + (27*b*d^3*x^2)/4 + (4*c*d^3*x^3)/3 + 31*c*Log[1 - d*x] + (99*b*d*Log[1 - d*x])/2 + 108*a*d^2*Log[1 - d*x] - 20*c*d*x*Log[1 - d*x] - 36*b*d^2*x*Log[1 - d*x] - 108*a*d^3*x*Log[1 - d*x] - 7*c*d^2*x^2*Log[1 - d*x] - (27*b*d^3*x^2*Log[1 - d*x])/2 - 4*c*d^3*x^3*Log[1 - d*x] - 4*c*Log[1 - d*x]^2 - 9*b*d*Log[1 - d*x]^2 - 36*a*d^2*Log[1 - d*x]^2 + 36*a*d^3*x*Log[1 - d*x]^2 + 9*b*d^3*x^2*Log[1 - d*x]^2 + 4*c*d^3*x^3*Log[1 - d*x]^2 - 12*c*Log[d*x]*Log[1 - d*x]^2 - 18*b*d*Log[d*x]*Log[1 - d*x]^2 - 36*a*d^2*Log[d*x]*Log[1 - d*x]^2 + (-(d*x*(9*d*(2*b + 4*a*d + b*d*x) + 2*c*(6 + 3*d*x + 2*d^2*x^2))) + 6*(-1 + d*x)*(3*d*(b + 2*a*d + b*d*x) + 2*c*(1 + d*x + d^2*x^2))*Log[1 - d*x])*PolyLog[2, d*x] - 12*(2*c + 3*d*(b + 2*a*d))*Log[1 - d*x]*PolyLog[2, 1 - d*x] + 12*(2*c + 3*d*(b + 2*a*d))*PolyLog[3, 1 - d*x])/(36*d^3)","A",1
194,1,298,402,0.3558899,"\int \frac{\left(a+b x+c x^2\right) \log (1-d x) \text{Li}_2(d x)}{x} \, dx","Integrate[((a + b*x + c*x^2)*Log[1 - d*x]*PolyLog[2, d*x])/x,x]","\frac{-8 a d^2 \text{Li}_2(d x){}^2+4 \text{Li}_2(d x) (2 (d x-1) \log (1-d x) (2 b d+c d x+c)-d x (4 b d+c d x+2 c))-16 (2 b d+c) \text{Li}_2(1-d x) \log (1-d x)+48 b d^2 x+16 b d^2 x \log ^2(1-d x)-48 b d^2 x \log (1-d x)+32 b d \text{Li}_3(1-d x)-16 b d \log ^2(1-d x)-16 b d \log (d x) \log ^2(1-d x)+48 b d \log (1-d x)-32 b d+3 c d^2 x^2+4 c d^2 x^2 \log ^2(1-d x)-6 c d^2 x^2 \log (1-d x)+16 c \text{Li}_3(1-d x)+22 c d x-4 c \log ^2(1-d x)-8 c \log (d x) \log ^2(1-d x)-16 c d x \log (1-d x)+22 c \log (1-d x)-14 c}{16 d^2}","-\frac{1}{2} a \text{Li}_2(d x){}^2+\frac{(2 b d+c) \text{Li}_3(1-d x)}{d^2}-\frac{(2 b d+c) \text{Li}_2(d x) \log (1-d x)}{2 d^2}-\frac{(2 b d+c) \text{Li}_2(1-d x) \log (1-d x)}{d^2}-\frac{(2 b d+c) \log (d x) \log ^2(1-d x)}{2 d^2}+\frac{(1-d x) (2 b d+c) \log (1-d x)}{2 d^2}+\frac{1}{2} \left(2 b x+c x^2\right) \text{Li}_2(d x) \log (1-d x)-\frac{x (2 b d+c) \text{Li}_2(d x)}{2 d}+\frac{x (2 b d+c)}{2 d}-\frac{b (1-d x) \log ^2(1-d x)}{d}+\frac{2 b (1-d x) \log (1-d x)}{d}+2 b x+\frac{c (1-d x)^2}{8 d^2}+\frac{c (1-d x)^2 \log ^2(1-d x)}{4 d^2}-\frac{c (1-d x) \log ^2(1-d x)}{2 d^2}-\frac{c (1-d x)^2 \log (1-d x)}{4 d^2}+\frac{c (1-d x) \log (1-d x)}{d^2}+\frac{c \log (1-d x)}{8 d^2}-\frac{1}{4} c x^2 \text{Li}_2(d x)-\frac{1}{8} c x^2 \log (1-d x)+\frac{9 c x}{8 d}+\frac{c x^2}{16}",1,"(-14*c - 32*b*d + 22*c*d*x + 48*b*d^2*x + 3*c*d^2*x^2 + 22*c*Log[1 - d*x] + 48*b*d*Log[1 - d*x] - 16*c*d*x*Log[1 - d*x] - 48*b*d^2*x*Log[1 - d*x] - 6*c*d^2*x^2*Log[1 - d*x] - 4*c*Log[1 - d*x]^2 - 16*b*d*Log[1 - d*x]^2 + 16*b*d^2*x*Log[1 - d*x]^2 + 4*c*d^2*x^2*Log[1 - d*x]^2 - 8*c*Log[d*x]*Log[1 - d*x]^2 - 16*b*d*Log[d*x]*Log[1 - d*x]^2 + 4*(-(d*x*(2*c + 4*b*d + c*d*x)) + 2*(-1 + d*x)*(c + 2*b*d + c*d*x)*Log[1 - d*x])*PolyLog[2, d*x] - 8*a*d^2*PolyLog[2, d*x]^2 - 16*(c + 2*b*d)*Log[1 - d*x]*PolyLog[2, 1 - d*x] + 16*c*PolyLog[3, 1 - d*x] + 32*b*d*PolyLog[3, 1 - d*x])/(16*d^2)","A",1
195,1,280,218,0.7872181,"\int \frac{\left(a+b x+c x^2\right) \log (1-d x) \text{Li}_2(d x)}{x^2} \, dx","Integrate[((a + b*x + c*x^2)*Log[1 - d*x]*PolyLog[2, d*x])/x^2,x]","\frac{2 \left(2 x \text{Li}_2(1-d x) \left(\left(a d^2-c\right) \log (1-d x)+a d^2\right)-a d^2 x \text{Li}_3(d x)-2 a d^2 x \text{Li}_3(1-d x)-a d^2 x \log ^2(1-d x)+a d^2 x \log (d x) \log ^2(1-d x)+2 a d^2 x \log (d x) \log (1-d x)+a d \log ^2(1-d x)+2 c x \text{Li}_3(1-d x)+3 c d x^2+c d x^2 \log ^2(1-d x)-3 c d x^2 \log (1-d x)-c x \log ^2(1-d x)-c x \log (d x) \log ^2(1-d x)+3 c x \log (1-d x)-2 c x\right)+2 \text{Li}_2(d x) \left((d x-1) \log (1-d x) (a d+c x)-c d x^2\right)-b d x \text{Li}_2(d x){}^2}{2 d x}","-2 d \left(a-\frac{c}{d^2}\right) \text{Li}_3(1-d x)+d \left(a-\frac{c}{d^2}\right) \text{Li}_2(d x) \log (1-d x)+2 d \left(a-\frac{c}{d^2}\right) \text{Li}_2(1-d x) \log (1-d x)+d \left(a-\frac{c}{d^2}\right) \log (d x) \log ^2(1-d x)-\left(\frac{a}{x}-c x\right) \text{Li}_2(d x) \log (1-d x)-2 a d \text{Li}_2(d x)-a d \text{Li}_3(d x)+\frac{a (1-d x) \log ^2(1-d x)}{x}-\frac{1}{2} b \text{Li}_2(d x){}^2-c x \text{Li}_2(d x)-\frac{c (1-d x) \log ^2(1-d x)}{d}+\frac{3 c (1-d x) \log (1-d x)}{d}+3 c x",1,"(2*(-(c*d*x^2) + (a*d + c*x)*(-1 + d*x)*Log[1 - d*x])*PolyLog[2, d*x] - b*d*x*PolyLog[2, d*x]^2 + 2*(-2*c*x + 3*c*d*x^2 + 3*c*x*Log[1 - d*x] - 3*c*d*x^2*Log[1 - d*x] + 2*a*d^2*x*Log[d*x]*Log[1 - d*x] + a*d*Log[1 - d*x]^2 - c*x*Log[1 - d*x]^2 - a*d^2*x*Log[1 - d*x]^2 + c*d*x^2*Log[1 - d*x]^2 - c*x*Log[d*x]*Log[1 - d*x]^2 + a*d^2*x*Log[d*x]*Log[1 - d*x]^2 + 2*x*(a*d^2 + (-c + a*d^2)*Log[1 - d*x])*PolyLog[2, 1 - d*x] - a*d^2*x*PolyLog[3, d*x] + 2*c*x*PolyLog[3, 1 - d*x] - 2*a*d^2*x*PolyLog[3, 1 - d*x]))/(2*d*x)","A",1
196,0,0,343,1.6847894,"\int \frac{\left(a+b x+c x^2\right) \log (1-d x) \text{Li}_2(d x)}{x^3} \, dx","Integrate[((a + b*x + c*x^2)*Log[1 - d*x]*PolyLog[2, d*x])/x^3,x]","\int \frac{\left(a+b x+c x^2\right) \log (1-d x) \text{Li}_2(d x)}{x^3} \, dx","\frac{b^2 \text{Li}_3(1-d x)}{a}-\frac{b^2 \text{Li}_2(1-d x) \log (1-d x)}{a}-\frac{b^2 \log (d x) \log ^2(1-d x)}{2 a}-\frac{(a+b x)^2 \text{Li}_2(d x) \log (1-d x)}{2 a x^2}-\frac{1}{2} d (a d+2 b) \text{Li}_3(d x)-\frac{(a d+b)^2 \text{Li}_3(1-d x)}{a}+\frac{(a d+b)^2 \text{Li}_2(d x) \log (1-d x)}{2 a}+\frac{(a d+b)^2 \text{Li}_2(1-d x) \log (1-d x)}{a}+\frac{(a d+b)^2 \log (d x) \log ^2(1-d x)}{2 a}-\frac{1}{2} a d^2 \text{Li}_2(d x)-\frac{1}{4} a d^2 \log ^2(1-d x)-a d^2 \log (x)+a d^2 \log (1-d x)+\frac{a d \text{Li}_2(d x)}{2 x}+\frac{a \log ^2(1-d x)}{4 x^2}-\frac{a d \log (1-d x)}{x}-2 b d \text{Li}_2(d x)+\frac{b (1-d x) \log ^2(1-d x)}{x}-\frac{1}{2} c \text{Li}_2(d x){}^2",1,"Integrate[((a + b*x + c*x^2)*Log[1 - d*x]*PolyLog[2, d*x])/x^3, x]","F",-1
197,1,488,515,1.5892251,"\int \frac{\left(a+b x+c x^2\right) \log (1-d x) \text{Li}_2(d x)}{x^4} \, dx","Integrate[((a + b*x + c*x^2)*Log[1 - d*x]*PolyLog[2, d*x])/x^4,x]","\frac{1}{36} \left(\frac{6 \text{Li}_2(d x) \left((d x-1) \log (1-d x) \left(2 a \left(d^2 x^2+d x+1\right)+3 x (b d x+b+2 c x)\right)+d x (2 a d x+a+3 b x)\right)}{x^3}+2 d \text{Li}_2(1-d x) \left(6 \log (1-d x) \left(2 a d^2+3 b d+6 c\right)+4 a d^2+9 b d+36 c\right)-12 a d^3 \text{Li}_3(d x)-24 a d^3 \text{Li}_3(1-d x)-4 a d^3 \log ^2(1-d x)+12 a d^3 \log (d x) \log ^2(1-d x)-27 a d^3 \log (d x)+27 a d^3 \log (1-d x)+8 a d^3 \log (d x) \log (1-d x)-7 a d^3+\frac{7 a d^2}{x}-\frac{20 a d^2 \log (1-d x)}{x}+\frac{4 a \log ^2(1-d x)}{x^3}-\frac{7 a d \log (1-d x)}{x^2}-18 b d^2 \text{Li}_3(d x)-36 b d^2 \text{Li}_3(1-d x)-9 b d^2 \log ^2(1-d x)+18 b d^2 \log (d x) \log ^2(1-d x)-36 b d^2 \log (d x)+36 b d^2 \log (1-d x)+18 b d^2 \log (d x) \log (1-d x)+\frac{9 b \log ^2(1-d x)}{x^2}-\frac{36 b d \log (1-d x)}{x}-36 c d \text{Li}_3(d x)-72 c d \text{Li}_3(1-d x)-36 c d \log ^2(1-d x)+36 c d \log (d x) \log ^2(1-d x)+\frac{36 c \log ^2(1-d x)}{x}+72 c d \log (d x) \log (1-d x)\right)","-\frac{1}{6} \text{Li}_2(d x) \log (1-d x) \left(\frac{2 a}{x^3}+\frac{3 b}{x^2}+\frac{6 c}{x}\right)-\frac{1}{6} d \text{Li}_3(d x) (d (2 a d+3 b)+6 c)-\frac{1}{3} d \text{Li}_3(1-d x) (d (2 a d+3 b)+6 c)+\frac{1}{6} d \text{Li}_2(d x) \log (1-d x) (d (2 a d+3 b)+6 c)+\frac{1}{3} d \text{Li}_2(1-d x) \log (1-d x) (d (2 a d+3 b)+6 c)+\frac{1}{6} d \log (d x) \log ^2(1-d x) (d (2 a d+3 b)+6 c)-\frac{1}{6} d^2 \log (x) (2 a d+3 b)+\frac{1}{6} d^2 (2 a d+3 b) \log (1-d x)+\frac{d (2 a d+3 b) \text{Li}_2(d x)}{6 x}-\frac{d (2 a d+3 b) \log (1-d x)}{6 x}-\frac{2}{9} a d^3 \text{Li}_2(d x)-\frac{1}{9} a d^3 \log ^2(1-d x)-\frac{5}{12} a d^3 \log (x)+\frac{5}{12} a d^3 \log (1-d x)+\frac{7 a d^2}{36 x}-\frac{2 a d^2 \log (1-d x)}{9 x}+\frac{a d \text{Li}_2(d x)}{6 x^2}+\frac{a \log ^2(1-d x)}{9 x^3}-\frac{7 a d \log (1-d x)}{36 x^2}-\frac{1}{2} b d^2 \text{Li}_2(d x)-\frac{1}{4} b d^2 \log ^2(1-d x)-\frac{1}{2} b d^2 \log (x)+\frac{1}{2} b d^2 \log (1-d x)+\frac{b \log ^2(1-d x)}{4 x^2}-\frac{b d \log (1-d x)}{2 x}-2 c d \text{Li}_2(d x)+\frac{c (1-d x) \log ^2(1-d x)}{x}",1,"(-7*a*d^3 + (7*a*d^2)/x - 36*b*d^2*Log[d*x] - 27*a*d^3*Log[d*x] + 36*b*d^2*Log[1 - d*x] + 27*a*d^3*Log[1 - d*x] - (7*a*d*Log[1 - d*x])/x^2 - (36*b*d*Log[1 - d*x])/x - (20*a*d^2*Log[1 - d*x])/x + 72*c*d*Log[d*x]*Log[1 - d*x] + 18*b*d^2*Log[d*x]*Log[1 - d*x] + 8*a*d^3*Log[d*x]*Log[1 - d*x] - 36*c*d*Log[1 - d*x]^2 - 9*b*d^2*Log[1 - d*x]^2 - 4*a*d^3*Log[1 - d*x]^2 + (4*a*Log[1 - d*x]^2)/x^3 + (9*b*Log[1 - d*x]^2)/x^2 + (36*c*Log[1 - d*x]^2)/x + 36*c*d*Log[d*x]*Log[1 - d*x]^2 + 18*b*d^2*Log[d*x]*Log[1 - d*x]^2 + 12*a*d^3*Log[d*x]*Log[1 - d*x]^2 + (6*(d*x*(a + 3*b*x + 2*a*d*x) + (-1 + d*x)*(3*x*(b + 2*c*x + b*d*x) + 2*a*(1 + d*x + d^2*x^2))*Log[1 - d*x])*PolyLog[2, d*x])/x^3 + 2*d*(36*c + 9*b*d + 4*a*d^2 + 6*(6*c + 3*b*d + 2*a*d^2)*Log[1 - d*x])*PolyLog[2, 1 - d*x] - 36*c*d*PolyLog[3, d*x] - 18*b*d^2*PolyLog[3, d*x] - 12*a*d^3*PolyLog[3, d*x] - 72*c*d*PolyLog[3, 1 - d*x] - 36*b*d^2*PolyLog[3, 1 - d*x] - 24*a*d^3*PolyLog[3, 1 - d*x])/36","A",1
198,1,621,767,1.9121408,"\int \frac{\left(a+b x+c x^2\right) \log (1-d x) \text{Li}_2(d x)}{x^5} \, dx","Integrate[((a + b*x + c*x^2)*Log[1 - d*x]*PolyLog[2, d*x])/x^5,x]","\frac{1}{144} \left(2 d^2 \text{Li}_2(1-d x) \left(12 \log (1-d x) \left(3 a d^2+4 b d+6 c\right)+9 a d^2+16 b d+36 c\right)+\frac{6 \text{Li}_2(d x) \left(d x \left(a \left(6 d^2 x^2+3 d x+2\right)+4 x (2 b d x+b+3 c x)\right)+2 \log (1-d x) \left(3 a \left(d^4 x^4-1\right)+4 b d^3 x^4-4 b x+6 c d^2 x^4-6 c x^2\right)\right)}{x^4}-36 a d^4 \text{Li}_3(d x)-72 a d^4 \text{Li}_3(1-d x)-9 a d^4 \log ^2(1-d x)+36 a d^4 \log (d x) \log ^2(1-d x)-82 a d^4 \log (d x)+82 a d^4 \log (1-d x)+18 a d^4 \log (d x) \log (1-d x)-33 a d^4+\frac{28 a d^3}{x}-\frac{54 a d^3 \log (1-d x)}{x}+\frac{5 a d^2}{x^2}-\frac{18 a d^2 \log (1-d x)}{x^2}+\frac{9 a \log ^2(1-d x)}{x^4}-\frac{10 a d \log (1-d x)}{x^3}-48 b d^3 \text{Li}_3(d x)-96 b d^3 \text{Li}_3(1-d x)-16 b d^3 \log ^2(1-d x)+48 b d^3 \log (d x) \log ^2(1-d x)-108 b d^3 \log (d x)+108 b d^3 \log (1-d x)+32 b d^3 \log (d x) \log (1-d x)-28 b d^3+\frac{28 b d^2}{x}-\frac{80 b d^2 \log (1-d x)}{x}+\frac{16 b \log ^2(1-d x)}{x^3}-\frac{28 b d \log (1-d x)}{x^2}-72 c d^2 \text{Li}_3(d x)-144 c d^2 \text{Li}_3(1-d x)-36 c d^2 \log ^2(1-d x)+72 c d^2 \log (d x) \log ^2(1-d x)-144 c d^2 \log (d x)+144 c d^2 \log (1-d x)+72 c d^2 \log (d x) \log (1-d x)+\frac{36 c \log ^2(1-d x)}{x^2}-\frac{144 c d \log (1-d x)}{x}\right)","-\frac{1}{12} d^2 \text{Li}_3(d x) (d (3 a d+4 b)+6 c)-\frac{1}{6} d^2 \text{Li}_3(1-d x) (d (3 a d+4 b)+6 c)+\frac{1}{12} d^2 \text{Li}_2(d x) \log (1-d x) (d (3 a d+4 b)+6 c)+\frac{1}{6} d^2 \text{Li}_2(1-d x) \log (1-d x) (d (3 a d+4 b)+6 c)+\frac{1}{12} d^2 \log (d x) \log ^2(1-d x) (d (3 a d+4 b)+6 c)-\frac{1}{12} d^2 \log (x) (d (3 a d+4 b)+6 c)+\frac{1}{12} d^2 \log (1-d x) (d (3 a d+4 b)+6 c)-\frac{1}{12} \text{Li}_2(d x) \log (1-d x) \left(\frac{3 a}{x^4}+\frac{4 b}{x^3}+\frac{6 c}{x^2}\right)+\frac{d \text{Li}_2(d x) (d (3 a d+4 b)+6 c)}{12 x}-\frac{d \log (1-d x) (d (3 a d+4 b)+6 c)}{12 x}-\frac{1}{48} d^3 \log (x) (3 a d+4 b)+\frac{1}{48} d^3 (3 a d+4 b) \log (1-d x)+\frac{d^2 (3 a d+4 b)}{48 x}+\frac{d (3 a d+4 b) \text{Li}_2(d x)}{24 x^2}-\frac{d (3 a d+4 b) \log (1-d x)}{48 x^2}-\frac{1}{8} a d^4 \text{Li}_2(d x)-\frac{1}{16} a d^4 \log ^2(1-d x)-\frac{37}{144} a d^4 \log (x)+\frac{37}{144} a d^4 \log (1-d x)+\frac{19 a d^3}{144 x}-\frac{a d^3 \log (1-d x)}{8 x}+\frac{5 a d^2}{144 x^2}-\frac{a d^2 \log (1-d x)}{16 x^2}+\frac{a d \text{Li}_2(d x)}{12 x^3}+\frac{a \log ^2(1-d x)}{16 x^4}-\frac{5 a d \log (1-d x)}{72 x^3}-\frac{2}{9} b d^3 \text{Li}_2(d x)-\frac{1}{9} b d^3 \log ^2(1-d x)-\frac{1}{3} b d^3 \log (x)+\frac{1}{3} b d^3 \log (1-d x)+\frac{b d^2}{9 x}-\frac{2 b d^2 \log (1-d x)}{9 x}+\frac{b \log ^2(1-d x)}{9 x^3}-\frac{b d \log (1-d x)}{9 x^2}-\frac{1}{2} c d^2 \text{Li}_2(d x)-\frac{1}{4} c d^2 \log ^2(1-d x)-\frac{1}{2} c d^2 \log (x)+\frac{1}{2} c d^2 \log (1-d x)+\frac{c \log ^2(1-d x)}{4 x^2}-\frac{c d \log (1-d x)}{2 x}",1,"(-28*b*d^3 - 33*a*d^4 + (5*a*d^2)/x^2 + (28*b*d^2)/x + (28*a*d^3)/x - 144*c*d^2*Log[d*x] - 108*b*d^3*Log[d*x] - 82*a*d^4*Log[d*x] + 144*c*d^2*Log[1 - d*x] + 108*b*d^3*Log[1 - d*x] + 82*a*d^4*Log[1 - d*x] - (10*a*d*Log[1 - d*x])/x^3 - (28*b*d*Log[1 - d*x])/x^2 - (18*a*d^2*Log[1 - d*x])/x^2 - (144*c*d*Log[1 - d*x])/x - (80*b*d^2*Log[1 - d*x])/x - (54*a*d^3*Log[1 - d*x])/x + 72*c*d^2*Log[d*x]*Log[1 - d*x] + 32*b*d^3*Log[d*x]*Log[1 - d*x] + 18*a*d^4*Log[d*x]*Log[1 - d*x] - 36*c*d^2*Log[1 - d*x]^2 - 16*b*d^3*Log[1 - d*x]^2 - 9*a*d^4*Log[1 - d*x]^2 + (9*a*Log[1 - d*x]^2)/x^4 + (16*b*Log[1 - d*x]^2)/x^3 + (36*c*Log[1 - d*x]^2)/x^2 + 72*c*d^2*Log[d*x]*Log[1 - d*x]^2 + 48*b*d^3*Log[d*x]*Log[1 - d*x]^2 + 36*a*d^4*Log[d*x]*Log[1 - d*x]^2 + (6*(d*x*(4*x*(b + 3*c*x + 2*b*d*x) + a*(2 + 3*d*x + 6*d^2*x^2)) + 2*(-4*b*x - 6*c*x^2 + 6*c*d^2*x^4 + 4*b*d^3*x^4 + 3*a*(-1 + d^4*x^4))*Log[1 - d*x])*PolyLog[2, d*x])/x^4 + 2*d^2*(36*c + 16*b*d + 9*a*d^2 + 12*(6*c + 4*b*d + 3*a*d^2)*Log[1 - d*x])*PolyLog[2, 1 - d*x] - 72*c*d^2*PolyLog[3, d*x] - 48*b*d^3*PolyLog[3, d*x] - 36*a*d^4*PolyLog[3, d*x] - 144*c*d^2*PolyLog[3, 1 - d*x] - 96*b*d^3*PolyLog[3, 1 - d*x] - 72*a*d^4*PolyLog[3, 1 - d*x])/144","A",1