1,1,173,0,0.1798816,"\int \frac{a+b \log \left(c x^n\right)}{d+e x+f x^2} \, dx","Int[(a + b*Log[c*x^n])/(d + e*x + f*x^2),x]","\frac{b n \text{PolyLog}\left(2,-\frac{2 f x}{e-\sqrt{e^2-4 d f}}\right)}{\sqrt{e^2-4 d f}}-\frac{b n \text{PolyLog}\left(2,-\frac{2 f x}{\sqrt{e^2-4 d f}+e}\right)}{\sqrt{e^2-4 d f}}+\frac{\log \left(\frac{2 f x}{e-\sqrt{e^2-4 d f}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e^2-4 d f}}-\frac{\log \left(\frac{2 f x}{\sqrt{e^2-4 d f}+e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e^2-4 d f}}","\frac{b n \text{PolyLog}\left(2,-\frac{2 f x}{e-\sqrt{e^2-4 d f}}\right)}{\sqrt{e^2-4 d f}}-\frac{b n \text{PolyLog}\left(2,-\frac{2 f x}{\sqrt{e^2-4 d f}+e}\right)}{\sqrt{e^2-4 d f}}+\frac{\log \left(\frac{2 f x}{e-\sqrt{e^2-4 d f}}+1\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e^2-4 d f}}-\frac{\log \left(\frac{2 f x}{\sqrt{e^2-4 d f}+e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e^2-4 d f}}",1,"((a + b*Log[c*x^n])*Log[1 + (2*f*x)/(e - Sqrt[e^2 - 4*d*f])])/Sqrt[e^2 - 4*d*f] - ((a + b*Log[c*x^n])*Log[1 + (2*f*x)/(e + Sqrt[e^2 - 4*d*f])])/Sqrt[e^2 - 4*d*f] + (b*n*PolyLog[2, (-2*f*x)/(e - Sqrt[e^2 - 4*d*f])])/Sqrt[e^2 - 4*d*f] - (b*n*PolyLog[2, (-2*f*x)/(e + Sqrt[e^2 - 4*d*f])])/Sqrt[e^2 - 4*d*f]","A",6,3,23,0.1304,1,"{2357, 2317, 2391}"
2,1,210,0,0.1193994,"\int x^3 \left(a+b \log \left(c x^n\right)\right) \log (1+e x) \, dx","Int[x^3*(a + b*Log[c*x^n])*Log[1 + e*x],x]","-\frac{b n \text{PolyLog}(2,-e x)}{4 e^4}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{8 e^2}+\frac{x \left(a+b \log \left(c x^n\right)\right)}{4 e^3}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{4 e^4}+\frac{1}{4} x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{12 e}-\frac{1}{16} x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{3 b n x^2}{32 e^2}-\frac{5 b n x}{16 e^3}+\frac{b n \log (e x+1)}{16 e^4}-\frac{7 b n x^3}{144 e}-\frac{1}{16} b n x^4 \log (e x+1)+\frac{1}{32} b n x^4","-\frac{b n \text{PolyLog}(2,-e x)}{4 e^4}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{8 e^2}+\frac{x \left(a+b \log \left(c x^n\right)\right)}{4 e^3}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{4 e^4}+\frac{1}{4} x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)}{12 e}-\frac{1}{16} x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{3 b n x^2}{32 e^2}-\frac{5 b n x}{16 e^3}+\frac{b n \log (e x+1)}{16 e^4}-\frac{7 b n x^3}{144 e}-\frac{1}{16} b n x^4 \log (e x+1)+\frac{1}{32} b n x^4",1,"(-5*b*n*x)/(16*e^3) + (3*b*n*x^2)/(32*e^2) - (7*b*n*x^3)/(144*e) + (b*n*x^4)/32 + (x*(a + b*Log[c*x^n]))/(4*e^3) - (x^2*(a + b*Log[c*x^n]))/(8*e^2) + (x^3*(a + b*Log[c*x^n]))/(12*e) - (x^4*(a + b*Log[c*x^n]))/16 + (b*n*Log[1 + e*x])/(16*e^4) - (b*n*x^4*Log[1 + e*x])/16 - ((a + b*Log[c*x^n])*Log[1 + e*x])/(4*e^4) + (x^4*(a + b*Log[c*x^n])*Log[1 + e*x])/4 - (b*n*PolyLog[2, -(e*x)])/(4*e^4)","A",6,4,20,0.2000,1,"{2395, 43, 2376, 2391}"
3,1,178,0,0.1042926,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \log (1+e x) \, dx","Int[x^2*(a + b*Log[c*x^n])*Log[1 + e*x],x]","\frac{b n \text{PolyLog}(2,-e x)}{3 e^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{3 e^2}+\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{1}{3} x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{6 e}-\frac{1}{9} x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{4 b n x}{9 e^2}-\frac{b n \log (e x+1)}{9 e^3}-\frac{5 b n x^2}{36 e}-\frac{1}{9} b n x^3 \log (e x+1)+\frac{2}{27} b n x^3","\frac{b n \text{PolyLog}(2,-e x)}{3 e^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{3 e^2}+\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{1}{3} x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{6 e}-\frac{1}{9} x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{4 b n x}{9 e^2}-\frac{b n \log (e x+1)}{9 e^3}-\frac{5 b n x^2}{36 e}-\frac{1}{9} b n x^3 \log (e x+1)+\frac{2}{27} b n x^3",1,"(4*b*n*x)/(9*e^2) - (5*b*n*x^2)/(36*e) + (2*b*n*x^3)/27 - (x*(a + b*Log[c*x^n]))/(3*e^2) + (x^2*(a + b*Log[c*x^n]))/(6*e) - (x^3*(a + b*Log[c*x^n]))/9 - (b*n*Log[1 + e*x])/(9*e^3) - (b*n*x^3*Log[1 + e*x])/9 + ((a + b*Log[c*x^n])*Log[1 + e*x])/(3*e^3) + (x^3*(a + b*Log[c*x^n])*Log[1 + e*x])/3 + (b*n*PolyLog[2, -(e*x)])/(3*e^3)","A",6,4,20,0.2000,1,"{2395, 43, 2376, 2391}"
4,1,146,0,0.0756235,"\int x \left(a+b \log \left(c x^n\right)\right) \log (1+e x) \, dx","Int[x*(a + b*Log[c*x^n])*Log[1 + e*x],x]","-\frac{b n \text{PolyLog}(2,-e x)}{2 e^2}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{1}{2} x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{1}{4} x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{b n \log (e x+1)}{4 e^2}-\frac{1}{4} b n x^2 \log (e x+1)-\frac{3 b n x}{4 e}+\frac{1}{4} b n x^2","-\frac{b n \text{PolyLog}(2,-e x)}{2 e^2}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{1}{2} x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{1}{4} x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{b n \log (e x+1)}{4 e^2}-\frac{1}{4} b n x^2 \log (e x+1)-\frac{3 b n x}{4 e}+\frac{1}{4} b n x^2",1,"(-3*b*n*x)/(4*e) + (b*n*x^2)/4 + (x*(a + b*Log[c*x^n]))/(2*e) - (x^2*(a + b*Log[c*x^n]))/4 + (b*n*Log[1 + e*x])/(4*e^2) - (b*n*x^2*Log[1 + e*x])/4 - ((a + b*Log[c*x^n])*Log[1 + e*x])/(2*e^2) + (x^2*(a + b*Log[c*x^n])*Log[1 + e*x])/2 - (b*n*PolyLog[2, -(e*x)])/(2*e^2)","A",6,4,18,0.2222,1,"{2395, 43, 2376, 2391}"
5,1,74,0,0.0886038,"\int \left(a+b \log \left(c x^n\right)\right) \log (1+e x) \, dx","Int[(a + b*Log[c*x^n])*Log[1 + e*x],x]","\frac{b n \text{PolyLog}(2,-e x)}{e}+\frac{(e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{e}-x \left(a+b \log \left(c x^n\right)\right)-\frac{b n (e x+1) \log (e x+1)}{e}+2 b n x","\frac{b n \text{PolyLog}(2,-e x)}{e}+\frac{(e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{e}-x \left(a+b \log \left(c x^n\right)\right)-\frac{b n (e x+1) \log (e x+1)}{e}+2 b n x",1,"2*b*n*x - x*(a + b*Log[c*x^n]) - (b*n*(1 + e*x)*Log[1 + e*x])/e + ((1 + e*x)*(a + b*Log[c*x^n])*Log[1 + e*x])/e + (b*n*PolyLog[2, -(e*x)])/e","A",7,7,17,0.4118,1,"{2389, 2295, 2370, 2411, 43, 2351, 2315}"
6,1,28,0,0.0275801,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log (1+e x)}{x} \, dx","Int[((a + b*Log[c*x^n])*Log[1 + e*x])/x,x]","b n \text{PolyLog}(3,-e x)-\text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)","b n \text{PolyLog}(3,-e x)-\text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)",1,"-((a + b*Log[c*x^n])*PolyLog[2, -(e*x)]) + b*n*PolyLog[3, -(e*x)]","A",2,2,20,0.1000,1,"{2374, 6589}"
7,1,107,0,0.070474,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log (1+e x)}{x^2} \, dx","Int[((a + b*Log[c*x^n])*Log[1 + e*x])/x^2,x]","-b e n \text{PolyLog}(2,-e x)+e \log (x) \left(a+b \log \left(c x^n\right)\right)-e \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{1}{2} b e n \log ^2(x)+b e n \log (x)-b e n \log (e x+1)-\frac{b n \log (e x+1)}{x}","-b e n \text{PolyLog}(2,-e x)+e \log (x) \left(a+b \log \left(c x^n\right)\right)-e \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{1}{2} b e n \log ^2(x)+b e n \log (x)-b e n \log (e x+1)-\frac{b n \log (e x+1)}{x}",1,"b*e*n*Log[x] - (b*e*n*Log[x]^2)/2 + e*Log[x]*(a + b*Log[c*x^n]) - b*e*n*Log[1 + e*x] - (b*n*Log[1 + e*x])/x - e*(a + b*Log[c*x^n])*Log[1 + e*x] - ((a + b*Log[c*x^n])*Log[1 + e*x])/x - b*e*n*PolyLog[2, -(e*x)]","A",8,7,20,0.3500,1,"{2395, 36, 29, 31, 2376, 2301, 2391}"
8,1,163,0,0.0912584,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log (1+e x)}{x^3} \, dx","Int[((a + b*Log[c*x^n])*Log[1 + e*x])/x^3,x]","\frac{1}{2} b e^2 n \text{PolyLog}(2,-e x)-\frac{1}{2} e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} e^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{e \left(a+b \log \left(c x^n\right)\right)}{2 x}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+\frac{1}{4} b e^2 n \log ^2(x)-\frac{1}{4} b e^2 n \log (x)+\frac{1}{4} b e^2 n \log (e x+1)-\frac{b n \log (e x+1)}{4 x^2}-\frac{3 b e n}{4 x}","\frac{1}{2} b e^2 n \text{PolyLog}(2,-e x)-\frac{1}{2} e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} e^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{e \left(a+b \log \left(c x^n\right)\right)}{2 x}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}+\frac{1}{4} b e^2 n \log ^2(x)-\frac{1}{4} b e^2 n \log (x)+\frac{1}{4} b e^2 n \log (e x+1)-\frac{b n \log (e x+1)}{4 x^2}-\frac{3 b e n}{4 x}",1,"(-3*b*e*n)/(4*x) - (b*e^2*n*Log[x])/4 + (b*e^2*n*Log[x]^2)/4 - (e*(a + b*Log[c*x^n]))/(2*x) - (e^2*Log[x]*(a + b*Log[c*x^n]))/2 + (b*e^2*n*Log[1 + e*x])/4 - (b*n*Log[1 + e*x])/(4*x^2) + (e^2*(a + b*Log[c*x^n])*Log[1 + e*x])/2 - ((a + b*Log[c*x^n])*Log[1 + e*x])/(2*x^2) + (b*e^2*n*PolyLog[2, -(e*x)])/2","A",7,5,20,0.2500,1,"{2395, 44, 2376, 2301, 2391}"
9,1,195,0,0.106717,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log (1+e x)}{x^4} \, dx","Int[((a + b*Log[c*x^n])*Log[1 + e*x])/x^4,x]","-\frac{1}{3} b e^3 n \text{PolyLog}(2,-e x)+\frac{1}{3} e^3 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{3} e^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{3 x}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{6 x^2}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{3 x^3}+\frac{4 b e^2 n}{9 x}-\frac{1}{6} b e^3 n \log ^2(x)+\frac{1}{9} b e^3 n \log (x)-\frac{1}{9} b e^3 n \log (e x+1)-\frac{5 b e n}{36 x^2}-\frac{b n \log (e x+1)}{9 x^3}","-\frac{1}{3} b e^3 n \text{PolyLog}(2,-e x)+\frac{1}{3} e^3 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{3} e^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{e^2 \left(a+b \log \left(c x^n\right)\right)}{3 x}-\frac{e \left(a+b \log \left(c x^n\right)\right)}{6 x^2}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{3 x^3}+\frac{4 b e^2 n}{9 x}-\frac{1}{6} b e^3 n \log ^2(x)+\frac{1}{9} b e^3 n \log (x)-\frac{1}{9} b e^3 n \log (e x+1)-\frac{5 b e n}{36 x^2}-\frac{b n \log (e x+1)}{9 x^3}",1,"(-5*b*e*n)/(36*x^2) + (4*b*e^2*n)/(9*x) + (b*e^3*n*Log[x])/9 - (b*e^3*n*Log[x]^2)/6 - (e*(a + b*Log[c*x^n]))/(6*x^2) + (e^2*(a + b*Log[c*x^n]))/(3*x) + (e^3*Log[x]*(a + b*Log[c*x^n]))/3 - (b*e^3*n*Log[1 + e*x])/9 - (b*n*Log[1 + e*x])/(9*x^3) - (e^3*(a + b*Log[c*x^n])*Log[1 + e*x])/3 - ((a + b*Log[c*x^n])*Log[1 + e*x])/(3*x^3) - (b*e^3*n*PolyLog[2, -(e*x)])/3","A",7,5,20,0.2500,1,"{2395, 44, 2376, 2301, 2391}"
10,1,456,0,0.330808,"\int x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x) \, dx","Int[x^3*(a + b*Log[c*x^n])^2*Log[1 + e*x],x]","-\frac{b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}+\frac{b^2 n^2 \text{PolyLog}(2,-e x)}{8 e^4}+\frac{b^2 n^2 \text{PolyLog}(3,-e x)}{2 e^4}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{8 e^2}+\frac{3 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{16 e^2}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{4 e^3}-\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{8 e^3}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^4}+\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{8 e^4}+\frac{1}{4} x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{8} b n x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{12 e}-\frac{7 b n x^3 \left(a+b \log \left(c x^n\right)\right)}{72 e}-\frac{1}{16} x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{16} b n x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{a b n x}{2 e^3}-\frac{b^2 n x \log \left(c x^n\right)}{2 e^3}-\frac{7 b^2 n^2 x^2}{64 e^2}+\frac{21 b^2 n^2 x}{32 e^3}-\frac{b^2 n^2 \log (e x+1)}{32 e^4}+\frac{37 b^2 n^2 x^3}{864 e}+\frac{1}{32} b^2 n^2 x^4 \log (e x+1)-\frac{3}{128} b^2 n^2 x^4","-\frac{b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}+\frac{b^2 n^2 \text{PolyLog}(2,-e x)}{8 e^4}+\frac{b^2 n^2 \text{PolyLog}(3,-e x)}{2 e^4}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{8 e^2}+\frac{3 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{16 e^2}+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{4 e^3}-\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{8 e^3}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^4}+\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{8 e^4}+\frac{1}{4} x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{8} b n x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)^2}{12 e}-\frac{7 b n x^3 \left(a+b \log \left(c x^n\right)\right)}{72 e}-\frac{1}{16} x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{16} b n x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{a b n x}{2 e^3}-\frac{b^2 n x \log \left(c x^n\right)}{2 e^3}-\frac{7 b^2 n^2 x^2}{64 e^2}+\frac{21 b^2 n^2 x}{32 e^3}-\frac{b^2 n^2 \log (e x+1)}{32 e^4}+\frac{37 b^2 n^2 x^3}{864 e}+\frac{1}{32} b^2 n^2 x^4 \log (e x+1)-\frac{3}{128} b^2 n^2 x^4",1,"-(a*b*n*x)/(2*e^3) + (21*b^2*n^2*x)/(32*e^3) - (7*b^2*n^2*x^2)/(64*e^2) + (37*b^2*n^2*x^3)/(864*e) - (3*b^2*n^2*x^4)/128 - (b^2*n*x*Log[c*x^n])/(2*e^3) - (b*n*x*(a + b*Log[c*x^n]))/(8*e^3) + (3*b*n*x^2*(a + b*Log[c*x^n]))/(16*e^2) - (7*b*n*x^3*(a + b*Log[c*x^n]))/(72*e) + (b*n*x^4*(a + b*Log[c*x^n]))/16 + (x*(a + b*Log[c*x^n])^2)/(4*e^3) - (x^2*(a + b*Log[c*x^n])^2)/(8*e^2) + (x^3*(a + b*Log[c*x^n])^2)/(12*e) - (x^4*(a + b*Log[c*x^n])^2)/16 - (b^2*n^2*Log[1 + e*x])/(32*e^4) + (b^2*n^2*x^4*Log[1 + e*x])/32 + (b*n*(a + b*Log[c*x^n])*Log[1 + e*x])/(8*e^4) - (b*n*x^4*(a + b*Log[c*x^n])*Log[1 + e*x])/8 - ((a + b*Log[c*x^n])^2*Log[1 + e*x])/(4*e^4) + (x^4*(a + b*Log[c*x^n])^2*Log[1 + e*x])/4 + (b^2*n^2*PolyLog[2, -(e*x)])/(8*e^4) - (b*n*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)])/(2*e^4) + (b^2*n^2*PolyLog[3, -(e*x)])/(2*e^4)","A",15,9,22,0.4091,1,"{2395, 43, 2377, 2295, 2304, 2374, 6589, 2376, 2391}"
11,1,396,0,0.2877938,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x) \, dx","Int[x^2*(a + b*Log[c*x^n])^2*Log[1 + e*x],x]","\frac{2 b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{2 b^2 n^2 \text{PolyLog}(2,-e x)}{9 e^3}-\frac{2 b^2 n^2 \text{PolyLog}(3,-e x)}{3 e^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{3 e^2}+\frac{2 b n x \left(a+b \log \left(c x^n\right)\right)}{9 e^2}+\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{3 e^3}-\frac{2 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}+\frac{1}{3} x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{6 e}-\frac{5 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{18 e}-\frac{1}{9} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{4}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{2 a b n x}{3 e^2}+\frac{2 b^2 n x \log \left(c x^n\right)}{3 e^2}-\frac{26 b^2 n^2 x}{27 e^2}+\frac{2 b^2 n^2 \log (e x+1)}{27 e^3}+\frac{19 b^2 n^2 x^2}{108 e}+\frac{2}{27} b^2 n^2 x^3 \log (e x+1)-\frac{2}{27} b^2 n^2 x^3","\frac{2 b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{2 b^2 n^2 \text{PolyLog}(2,-e x)}{9 e^3}-\frac{2 b^2 n^2 \text{PolyLog}(3,-e x)}{3 e^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{3 e^2}+\frac{2 b n x \left(a+b \log \left(c x^n\right)\right)}{9 e^2}+\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{3 e^3}-\frac{2 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}+\frac{1}{3} x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{6 e}-\frac{5 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{18 e}-\frac{1}{9} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{4}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{2 a b n x}{3 e^2}+\frac{2 b^2 n x \log \left(c x^n\right)}{3 e^2}-\frac{26 b^2 n^2 x}{27 e^2}+\frac{2 b^2 n^2 \log (e x+1)}{27 e^3}+\frac{19 b^2 n^2 x^2}{108 e}+\frac{2}{27} b^2 n^2 x^3 \log (e x+1)-\frac{2}{27} b^2 n^2 x^3",1,"(2*a*b*n*x)/(3*e^2) - (26*b^2*n^2*x)/(27*e^2) + (19*b^2*n^2*x^2)/(108*e) - (2*b^2*n^2*x^3)/27 + (2*b^2*n*x*Log[c*x^n])/(3*e^2) + (2*b*n*x*(a + b*Log[c*x^n]))/(9*e^2) - (5*b*n*x^2*(a + b*Log[c*x^n]))/(18*e) + (4*b*n*x^3*(a + b*Log[c*x^n]))/27 - (x*(a + b*Log[c*x^n])^2)/(3*e^2) + (x^2*(a + b*Log[c*x^n])^2)/(6*e) - (x^3*(a + b*Log[c*x^n])^2)/9 + (2*b^2*n^2*Log[1 + e*x])/(27*e^3) + (2*b^2*n^2*x^3*Log[1 + e*x])/27 - (2*b*n*(a + b*Log[c*x^n])*Log[1 + e*x])/(9*e^3) - (2*b*n*x^3*(a + b*Log[c*x^n])*Log[1 + e*x])/9 + ((a + b*Log[c*x^n])^2*Log[1 + e*x])/(3*e^3) + (x^3*(a + b*Log[c*x^n])^2*Log[1 + e*x])/3 - (2*b^2*n^2*PolyLog[2, -(e*x)])/(9*e^3) + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)])/(3*e^3) - (2*b^2*n^2*PolyLog[3, -(e*x)])/(3*e^3)","A",14,9,22,0.4091,1,"{2395, 43, 2377, 2295, 2304, 2374, 6589, 2376, 2391}"
12,1,327,0,0.218963,"\int x \left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x) \, dx","Int[x*(a + b*Log[c*x^n])^2*Log[1 + e*x],x]","-\frac{b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{b^2 n^2 \text{PolyLog}(2,-e x)}{2 e^2}+\frac{b^2 n^2 \text{PolyLog}(3,-e x)}{e^2}+\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}-\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{1}{2} b n x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{2 e}+\frac{1}{2} x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{a b n x}{e}-\frac{b^2 n x \log \left(c x^n\right)}{e}-\frac{b^2 n^2 \log (e x+1)}{4 e^2}+\frac{1}{4} b^2 n^2 x^2 \log (e x+1)+\frac{7 b^2 n^2 x}{4 e}-\frac{3}{8} b^2 n^2 x^2","-\frac{b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{b^2 n^2 \text{PolyLog}(2,-e x)}{2 e^2}+\frac{b^2 n^2 \text{PolyLog}(3,-e x)}{e^2}+\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}-\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{1}{2} b n x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{2 e}+\frac{1}{2} x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{a b n x}{e}-\frac{b^2 n x \log \left(c x^n\right)}{e}-\frac{b^2 n^2 \log (e x+1)}{4 e^2}+\frac{1}{4} b^2 n^2 x^2 \log (e x+1)+\frac{7 b^2 n^2 x}{4 e}-\frac{3}{8} b^2 n^2 x^2",1,"-((a*b*n*x)/e) + (7*b^2*n^2*x)/(4*e) - (3*b^2*n^2*x^2)/8 - (b^2*n*x*Log[c*x^n])/e - (b*n*x*(a + b*Log[c*x^n]))/(2*e) + (b*n*x^2*(a + b*Log[c*x^n]))/2 + (x*(a + b*Log[c*x^n])^2)/(2*e) - (x^2*(a + b*Log[c*x^n])^2)/4 - (b^2*n^2*Log[1 + e*x])/(4*e^2) + (b^2*n^2*x^2*Log[1 + e*x])/4 + (b*n*(a + b*Log[c*x^n])*Log[1 + e*x])/(2*e^2) - (b*n*x^2*(a + b*Log[c*x^n])*Log[1 + e*x])/2 - ((a + b*Log[c*x^n])^2*Log[1 + e*x])/(2*e^2) + (x^2*(a + b*Log[c*x^n])^2*Log[1 + e*x])/2 + (b^2*n^2*PolyLog[2, -(e*x)])/(2*e^2) - (b*n*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)])/e^2 + (b^2*n^2*PolyLog[3, -(e*x)])/e^2","A",13,9,20,0.4500,1,"{2395, 43, 2377, 2295, 2304, 2374, 6589, 2376, 2391}"
13,1,193,0,0.3349745,"\int \left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x) \, dx","Int[(a + b*Log[c*x^n])^2*Log[1 + e*x],x]","\frac{2 b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{2 b^2 n^2 \text{PolyLog}(2,-e x)}{e}-\frac{2 b^2 n^2 \text{PolyLog}(3,-e x)}{e}-\frac{2 b n (e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{(e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{e}+2 b n x \left(a+b \log \left(c x^n\right)\right)-x \left(a+b \log \left(c x^n\right)\right)^2+2 a b n x+2 b^2 n x \log \left(c x^n\right)+\frac{2 b^2 n^2 (e x+1) \log (e x+1)}{e}-6 b^2 n^2 x","\frac{2 b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{2 b^2 n^2 \text{PolyLog}(2,-e x)}{e}-\frac{2 b^2 n^2 \text{PolyLog}(3,-e x)}{e}-\frac{2 b n (e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{(e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{e}+2 b n x \left(a+b \log \left(c x^n\right)\right)-x \left(a+b \log \left(c x^n\right)\right)^2+2 a b n x+2 b^2 n x \log \left(c x^n\right)+\frac{2 b^2 n^2 (e x+1) \log (e x+1)}{e}-6 b^2 n^2 x",1,"2*a*b*n*x - 6*b^2*n^2*x + 2*b^2*n*x*Log[c*x^n] + 2*b*n*x*(a + b*Log[c*x^n]) - x*(a + b*Log[c*x^n])^2 + (2*b^2*n^2*(1 + e*x)*Log[1 + e*x])/e - (2*b*n*(1 + e*x)*(a + b*Log[c*x^n])*Log[1 + e*x])/e + ((1 + e*x)*(a + b*Log[c*x^n])^2*Log[1 + e*x])/e - (2*b^2*n^2*PolyLog[2, -(e*x)])/e + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)])/e - (2*b^2*n^2*PolyLog[3, -(e*x)])/e","A",14,12,19,0.6316,1,"{2389, 2295, 2370, 2346, 2301, 6742, 2411, 43, 2351, 2315, 2374, 6589}"
14,1,55,0,0.060267,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x)}{x} \, dx","Int[((a + b*Log[c*x^n])^2*Log[1 + e*x])/x,x]","2 b n \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)-\text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2-2 b^2 n^2 \text{PolyLog}(4,-e x)","2 b n \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)-\text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2-2 b^2 n^2 \text{PolyLog}(4,-e x)",1,"-((a + b*Log[c*x^n])^2*PolyLog[2, -(e*x)]) + 2*b*n*(a + b*Log[c*x^n])*PolyLog[3, -(e*x)] - 2*b^2*n^2*PolyLog[4, -(e*x)]","A",3,3,22,0.1364,1,"{2374, 2383, 6589}"
15,1,220,0,0.3428431,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x)}{x^2} \, dx","Int[((a + b*Log[c*x^n])^2*Log[1 + e*x])/x^2,x]","-2 b e n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)-2 b^2 e n^2 \text{PolyLog}(2,-e x)+2 b^2 e n^2 \text{PolyLog}(3,-e x)+\frac{e \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}+e \left(a+b \log \left(c x^n\right)\right)^2-e \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{x}-2 b e n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{x}+2 b^2 e n^2 \log (x)-2 b^2 e n^2 \log (e x+1)-\frac{2 b^2 n^2 \log (e x+1)}{x}","2 b e n \text{PolyLog}\left(2,-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)+2 b^2 e n^2 \text{PolyLog}\left(2,-\frac{1}{e x}\right)+2 b^2 e n^2 \text{PolyLog}\left(3,-\frac{1}{e x}\right)-2 b e n \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{x}-e \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{x}+2 b^2 e n^2 \log (x)-2 b^2 e n^2 \log (e x+1)-\frac{2 b^2 n^2 \log (e x+1)}{x}",1,"2*b^2*e*n^2*Log[x] + e*(a + b*Log[c*x^n])^2 + (e*(a + b*Log[c*x^n])^3)/(3*b*n) - 2*b^2*e*n^2*Log[1 + e*x] - (2*b^2*n^2*Log[1 + e*x])/x - 2*b*e*n*(a + b*Log[c*x^n])*Log[1 + e*x] - (2*b*n*(a + b*Log[c*x^n])*Log[1 + e*x])/x - e*(a + b*Log[c*x^n])^2*Log[1 + e*x] - ((a + b*Log[c*x^n])^2*Log[1 + e*x])/x - 2*b^2*e*n^2*PolyLog[2, -(e*x)] - 2*b*e*n*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)] + 2*b^2*e*n^2*PolyLog[3, -(e*x)]","A",15,14,22,0.6364,1,"{2305, 2304, 2378, 36, 29, 31, 2344, 2301, 2317, 2391, 2302, 30, 2374, 6589}"
16,1,310,0,0.4835533,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log (1+e x)}{x^3} \, dx","Int[((a + b*Log[c*x^n])^2*Log[1 + e*x])/x^3,x]","b e^2 n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} b^2 e^2 n^2 \text{PolyLog}(2,-e x)-b^2 e^2 n^2 \text{PolyLog}(3,-e x)-\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^3}{6 b n}-\frac{1}{4} e^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} e^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b e^2 n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 x}-\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{3 b e n \left(a+b \log \left(c x^n\right)\right)}{2 x}-\frac{1}{4} b^2 e^2 n^2 \log (x)+\frac{1}{4} b^2 e^2 n^2 \log (e x+1)-\frac{b^2 n^2 \log (e x+1)}{4 x^2}-\frac{7 b^2 e n^2}{4 x}","-b e^2 n \text{PolyLog}\left(2,-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} b^2 e^2 n^2 \text{PolyLog}\left(2,-\frac{1}{e x}\right)-b^2 e^2 n^2 \text{PolyLog}\left(3,-\frac{1}{e x}\right)+\frac{1}{2} e^2 \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b e^2 n \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{e \left(a+b \log \left(c x^n\right)\right)^2}{2 x}-\frac{3 b e n \left(a+b \log \left(c x^n\right)\right)}{2 x}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{4} b^2 e^2 n^2 \log (x)+\frac{1}{4} b^2 e^2 n^2 \log (e x+1)-\frac{b^2 n^2 \log (e x+1)}{4 x^2}-\frac{7 b^2 e n^2}{4 x}",1,"(-7*b^2*e*n^2)/(4*x) - (b^2*e^2*n^2*Log[x])/4 - (3*b*e*n*(a + b*Log[c*x^n]))/(2*x) - (e^2*(a + b*Log[c*x^n])^2)/4 - (e*(a + b*Log[c*x^n])^2)/(2*x) - (e^2*(a + b*Log[c*x^n])^3)/(6*b*n) + (b^2*e^2*n^2*Log[1 + e*x])/4 - (b^2*n^2*Log[1 + e*x])/(4*x^2) + (b*e^2*n*(a + b*Log[c*x^n])*Log[1 + e*x])/2 - (b*n*(a + b*Log[c*x^n])*Log[1 + e*x])/(2*x^2) + (e^2*(a + b*Log[c*x^n])^2*Log[1 + e*x])/2 - ((a + b*Log[c*x^n])^2*Log[1 + e*x])/(2*x^2) + (b^2*e^2*n^2*PolyLog[2, -(e*x)])/2 + b*e^2*n*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)] - b^2*e^2*n^2*PolyLog[3, -(e*x)]","A",19,13,22,0.5909,1,"{2305, 2304, 2378, 44, 2351, 2301, 2317, 2391, 2353, 2302, 30, 2374, 6589}"
17,1,710,0,0.7773418,"\int x^3 \left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x) \, dx","Int[x^3*(a + b*Log[c*x^n])^3*Log[1 + e*x],x]","\frac{3 b^2 n^2 \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{8 e^4}+\frac{3 b^2 n^2 \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}-\frac{3 b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^4}-\frac{3 b^3 n^3 \text{PolyLog}(2,-e x)}{32 e^4}-\frac{3 b^3 n^3 \text{PolyLog}(3,-e x)}{8 e^4}-\frac{3 b^3 n^3 \text{PolyLog}(4,-e x)}{2 e^4}-\frac{21 b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{64 e^2}+\frac{3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)}{32 e^3}-\frac{3 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{32 e^4}+\frac{3}{32} b^2 n^2 x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{37 b^2 n^2 x^3 \left(a+b \log \left(c x^n\right)\right)}{288 e}-\frac{9}{128} b^2 n^2 x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{15 a b^2 n^2 x}{8 e^3}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^3}{8 e^2}+\frac{9 b n x^2 \left(a+b \log \left(c x^n\right)\right)^2}{32 e^2}+\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{4 e^3}-\frac{15 b n x \left(a+b \log \left(c x^n\right)\right)^2}{16 e^3}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{4 e^4}+\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{16 e^4}+\frac{1}{4} x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{16} b n x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)^3}{12 e}-\frac{7 b n x^3 \left(a+b \log \left(c x^n\right)\right)^2}{48 e}-\frac{1}{16} x^4 \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{32} b n x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{15 b^3 n^2 x \log \left(c x^n\right)}{8 e^3}+\frac{45 b^3 n^3 x^2}{256 e^2}-\frac{255 b^3 n^3 x}{128 e^3}+\frac{3 b^3 n^3 \log (e x+1)}{128 e^4}-\frac{175 b^3 n^3 x^3}{3456 e}-\frac{3}{128} b^3 n^3 x^4 \log (e x+1)+\frac{3}{128} b^3 n^3 x^4","\frac{3 b^2 n^2 \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{8 e^4}+\frac{3 b^2 n^2 \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}-\frac{3 b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^4}-\frac{3 b^3 n^3 \text{PolyLog}(2,-e x)}{32 e^4}-\frac{3 b^3 n^3 \text{PolyLog}(3,-e x)}{8 e^4}-\frac{3 b^3 n^3 \text{PolyLog}(4,-e x)}{2 e^4}-\frac{21 b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{64 e^2}+\frac{3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)}{32 e^3}-\frac{3 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{32 e^4}+\frac{3}{32} b^2 n^2 x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)+\frac{37 b^2 n^2 x^3 \left(a+b \log \left(c x^n\right)\right)}{288 e}-\frac{9}{128} b^2 n^2 x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{15 a b^2 n^2 x}{8 e^3}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^3}{8 e^2}+\frac{9 b n x^2 \left(a+b \log \left(c x^n\right)\right)^2}{32 e^2}+\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{4 e^3}-\frac{15 b n x \left(a+b \log \left(c x^n\right)\right)^2}{16 e^3}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{4 e^4}+\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{16 e^4}+\frac{1}{4} x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{16} b n x^4 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{x^3 \left(a+b \log \left(c x^n\right)\right)^3}{12 e}-\frac{7 b n x^3 \left(a+b \log \left(c x^n\right)\right)^2}{48 e}-\frac{1}{16} x^4 \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{32} b n x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{15 b^3 n^2 x \log \left(c x^n\right)}{8 e^3}+\frac{45 b^3 n^3 x^2}{256 e^2}-\frac{255 b^3 n^3 x}{128 e^3}+\frac{3 b^3 n^3 \log (e x+1)}{128 e^4}-\frac{175 b^3 n^3 x^3}{3456 e}-\frac{3}{128} b^3 n^3 x^4 \log (e x+1)+\frac{3}{128} b^3 n^3 x^4",1,"(15*a*b^2*n^2*x)/(8*e^3) - (255*b^3*n^3*x)/(128*e^3) + (45*b^3*n^3*x^2)/(256*e^2) - (175*b^3*n^3*x^3)/(3456*e) + (3*b^3*n^3*x^4)/128 + (15*b^3*n^2*x*Log[c*x^n])/(8*e^3) + (3*b^2*n^2*x*(a + b*Log[c*x^n]))/(32*e^3) - (21*b^2*n^2*x^2*(a + b*Log[c*x^n]))/(64*e^2) + (37*b^2*n^2*x^3*(a + b*Log[c*x^n]))/(288*e) - (9*b^2*n^2*x^4*(a + b*Log[c*x^n]))/128 - (15*b*n*x*(a + b*Log[c*x^n])^2)/(16*e^3) + (9*b*n*x^2*(a + b*Log[c*x^n])^2)/(32*e^2) - (7*b*n*x^3*(a + b*Log[c*x^n])^2)/(48*e) + (3*b*n*x^4*(a + b*Log[c*x^n])^2)/32 + (x*(a + b*Log[c*x^n])^3)/(4*e^3) - (x^2*(a + b*Log[c*x^n])^3)/(8*e^2) + (x^3*(a + b*Log[c*x^n])^3)/(12*e) - (x^4*(a + b*Log[c*x^n])^3)/16 + (3*b^3*n^3*Log[1 + e*x])/(128*e^4) - (3*b^3*n^3*x^4*Log[1 + e*x])/128 - (3*b^2*n^2*(a + b*Log[c*x^n])*Log[1 + e*x])/(32*e^4) + (3*b^2*n^2*x^4*(a + b*Log[c*x^n])*Log[1 + e*x])/32 + (3*b*n*(a + b*Log[c*x^n])^2*Log[1 + e*x])/(16*e^4) - (3*b*n*x^4*(a + b*Log[c*x^n])^2*Log[1 + e*x])/16 - ((a + b*Log[c*x^n])^3*Log[1 + e*x])/(4*e^4) + (x^4*(a + b*Log[c*x^n])^3*Log[1 + e*x])/4 - (3*b^3*n^3*PolyLog[2, -(e*x)])/(32*e^4) + (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)])/(8*e^4) - (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(e*x)])/(4*e^4) - (3*b^3*n^3*PolyLog[3, -(e*x)])/(8*e^4) + (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(e*x)])/(2*e^4) - (3*b^3*n^3*PolyLog[4, -(e*x)])/(2*e^4)","A",29,12,22,0.5455,1,"{2395, 43, 2377, 2296, 2295, 2305, 2304, 2374, 2383, 6589, 2376, 2391}"
18,1,615,0,0.637563,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x) \, dx","Int[x^2*(a + b*Log[c*x^n])^3*Log[1 + e*x],x]","-\frac{2 b^2 n^2 \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{2 b^2 n^2 \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2}{e^3}+\frac{2 b^3 n^3 \text{PolyLog}(2,-e x)}{9 e^3}+\frac{2 b^3 n^3 \text{PolyLog}(3,-e x)}{3 e^3}+\frac{2 b^3 n^3 \text{PolyLog}(4,-e x)}{e^3}-\frac{2 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)}{9 e^2}+\frac{2 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}+\frac{19 b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{36 e}+\frac{2}{9} b^2 n^2 x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{2}{9} b^2 n^2 x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{8 a b^2 n^2 x}{3 e^2}+\frac{4 b n x \left(a+b \log \left(c x^n\right)\right)^2}{3 e^2}-\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{3 e^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{3 e^2}+\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{3 e^3}-\frac{5 b n x^2 \left(a+b \log \left(c x^n\right)\right)^2}{12 e}-\frac{1}{3} b n x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^3}{6 e}+\frac{1}{3} x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3+\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{9} x^3 \left(a+b \log \left(c x^n\right)\right)^3-\frac{8 b^3 n^2 x \log \left(c x^n\right)}{3 e^2}+\frac{80 b^3 n^3 x}{27 e^2}-\frac{2 b^3 n^3 \log (e x+1)}{27 e^3}-\frac{65 b^3 n^3 x^2}{216 e}-\frac{2}{27} b^3 n^3 x^3 \log (e x+1)+\frac{8}{81} b^3 n^3 x^3","-\frac{2 b^2 n^2 \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{2 b^2 n^2 \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)}{e^3}+\frac{b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2}{e^3}+\frac{2 b^3 n^3 \text{PolyLog}(2,-e x)}{9 e^3}+\frac{2 b^3 n^3 \text{PolyLog}(3,-e x)}{3 e^3}+\frac{2 b^3 n^3 \text{PolyLog}(4,-e x)}{e^3}-\frac{2 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)}{9 e^2}+\frac{2 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}+\frac{19 b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{36 e}+\frac{2}{9} b^2 n^2 x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{2}{9} b^2 n^2 x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{8 a b^2 n^2 x}{3 e^2}+\frac{4 b n x \left(a+b \log \left(c x^n\right)\right)^2}{3 e^2}-\frac{b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{3 e^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{3 e^2}+\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{3 e^3}-\frac{5 b n x^2 \left(a+b \log \left(c x^n\right)\right)^2}{12 e}-\frac{1}{3} b n x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^3}{6 e}+\frac{1}{3} x^3 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3+\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{9} x^3 \left(a+b \log \left(c x^n\right)\right)^3-\frac{8 b^3 n^2 x \log \left(c x^n\right)}{3 e^2}+\frac{80 b^3 n^3 x}{27 e^2}-\frac{2 b^3 n^3 \log (e x+1)}{27 e^3}-\frac{65 b^3 n^3 x^2}{216 e}-\frac{2}{27} b^3 n^3 x^3 \log (e x+1)+\frac{8}{81} b^3 n^3 x^3",1,"(-8*a*b^2*n^2*x)/(3*e^2) + (80*b^3*n^3*x)/(27*e^2) - (65*b^3*n^3*x^2)/(216*e) + (8*b^3*n^3*x^3)/81 - (8*b^3*n^2*x*Log[c*x^n])/(3*e^2) - (2*b^2*n^2*x*(a + b*Log[c*x^n]))/(9*e^2) + (19*b^2*n^2*x^2*(a + b*Log[c*x^n]))/(36*e) - (2*b^2*n^2*x^3*(a + b*Log[c*x^n]))/9 + (4*b*n*x*(a + b*Log[c*x^n])^2)/(3*e^2) - (5*b*n*x^2*(a + b*Log[c*x^n])^2)/(12*e) + (2*b*n*x^3*(a + b*Log[c*x^n])^2)/9 - (x*(a + b*Log[c*x^n])^3)/(3*e^2) + (x^2*(a + b*Log[c*x^n])^3)/(6*e) - (x^3*(a + b*Log[c*x^n])^3)/9 - (2*b^3*n^3*Log[1 + e*x])/(27*e^3) - (2*b^3*n^3*x^3*Log[1 + e*x])/27 + (2*b^2*n^2*(a + b*Log[c*x^n])*Log[1 + e*x])/(9*e^3) + (2*b^2*n^2*x^3*(a + b*Log[c*x^n])*Log[1 + e*x])/9 - (b*n*(a + b*Log[c*x^n])^2*Log[1 + e*x])/(3*e^3) - (b*n*x^3*(a + b*Log[c*x^n])^2*Log[1 + e*x])/3 + ((a + b*Log[c*x^n])^3*Log[1 + e*x])/(3*e^3) + (x^3*(a + b*Log[c*x^n])^3*Log[1 + e*x])/3 + (2*b^3*n^3*PolyLog[2, -(e*x)])/(9*e^3) - (2*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)])/(3*e^3) + (b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(e*x)])/e^3 + (2*b^3*n^3*PolyLog[3, -(e*x)])/(3*e^3) - (2*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(e*x)])/e^3 + (2*b^3*n^3*PolyLog[4, -(e*x)])/e^3","A",26,12,22,0.5455,1,"{2395, 43, 2377, 2296, 2295, 2305, 2304, 2374, 2383, 6589, 2376, 2391}"
19,1,530,0,0.4932779,"\int x \left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x) \, dx","Int[x*(a + b*Log[c*x^n])^3*Log[1 + e*x],x]","\frac{3 b^2 n^2 \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{3 b^2 n^2 \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{3 b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}-\frac{3 b^3 n^3 \text{PolyLog}(2,-e x)}{4 e^2}-\frac{3 b^3 n^3 \text{PolyLog}(3,-e x)}{2 e^2}-\frac{3 b^3 n^3 \text{PolyLog}(4,-e x)}{e^2}-\frac{3 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}+\frac{3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)}{4 e}+\frac{3}{4} b^2 n^2 x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{9}{8} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{9 a b^2 n^2 x}{2 e}+\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{2 e^2}-\frac{9 b n x \left(a+b \log \left(c x^n\right)\right)^2}{4 e}-\frac{3}{4} b n x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{2 e}+\frac{1}{2} x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{4} x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{9 b^3 n^2 x \log \left(c x^n\right)}{2 e}+\frac{3 b^3 n^3 \log (e x+1)}{8 e^2}-\frac{3}{8} b^3 n^3 x^2 \log (e x+1)-\frac{45 b^3 n^3 x}{8 e}+\frac{3}{4} b^3 n^3 x^2","\frac{3 b^2 n^2 \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{3 b^2 n^2 \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{3 b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}-\frac{3 b^3 n^3 \text{PolyLog}(2,-e x)}{4 e^2}-\frac{3 b^3 n^3 \text{PolyLog}(3,-e x)}{2 e^2}-\frac{3 b^3 n^3 \text{PolyLog}(4,-e x)}{e^2}-\frac{3 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}+\frac{3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)}{4 e}+\frac{3}{4} b^2 n^2 x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{9}{8} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{9 a b^2 n^2 x}{2 e}+\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{2 e^2}-\frac{9 b n x \left(a+b \log \left(c x^n\right)\right)^2}{4 e}-\frac{3}{4} b n x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2+\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{2 e}+\frac{1}{2} x^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{4} x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{9 b^3 n^2 x \log \left(c x^n\right)}{2 e}+\frac{3 b^3 n^3 \log (e x+1)}{8 e^2}-\frac{3}{8} b^3 n^3 x^2 \log (e x+1)-\frac{45 b^3 n^3 x}{8 e}+\frac{3}{4} b^3 n^3 x^2",1,"(9*a*b^2*n^2*x)/(2*e) - (45*b^3*n^3*x)/(8*e) + (3*b^3*n^3*x^2)/4 + (9*b^3*n^2*x*Log[c*x^n])/(2*e) + (3*b^2*n^2*x*(a + b*Log[c*x^n]))/(4*e) - (9*b^2*n^2*x^2*(a + b*Log[c*x^n]))/8 - (9*b*n*x*(a + b*Log[c*x^n])^2)/(4*e) + (3*b*n*x^2*(a + b*Log[c*x^n])^2)/4 + (x*(a + b*Log[c*x^n])^3)/(2*e) - (x^2*(a + b*Log[c*x^n])^3)/4 + (3*b^3*n^3*Log[1 + e*x])/(8*e^2) - (3*b^3*n^3*x^2*Log[1 + e*x])/8 - (3*b^2*n^2*(a + b*Log[c*x^n])*Log[1 + e*x])/(4*e^2) + (3*b^2*n^2*x^2*(a + b*Log[c*x^n])*Log[1 + e*x])/4 + (3*b*n*(a + b*Log[c*x^n])^2*Log[1 + e*x])/(4*e^2) - (3*b*n*x^2*(a + b*Log[c*x^n])^2*Log[1 + e*x])/4 - ((a + b*Log[c*x^n])^3*Log[1 + e*x])/(2*e^2) + (x^2*(a + b*Log[c*x^n])^3*Log[1 + e*x])/2 - (3*b^3*n^3*PolyLog[2, -(e*x)])/(4*e^2) + (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)])/(2*e^2) - (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(e*x)])/(2*e^2) - (3*b^3*n^3*PolyLog[3, -(e*x)])/(2*e^2) + (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(e*x)])/e^2 - (3*b^3*n^3*PolyLog[4, -(e*x)])/e^2","A",23,12,20,0.6000,1,"{2395, 43, 2377, 2296, 2295, 2305, 2304, 2374, 2383, 6589, 2376, 2391}"
20,1,327,0,0.7629961,"\int \left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x) \, dx","Int[(a + b*Log[c*x^n])^3*Log[1 + e*x],x]","-\frac{6 b^2 n^2 \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{6 b^2 n^2 \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{3 b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2}{e}+\frac{6 b^3 n^3 \text{PolyLog}(2,-e x)}{e}+\frac{6 b^3 n^3 \text{PolyLog}(3,-e x)}{e}+\frac{6 b^3 n^3 \text{PolyLog}(4,-e x)}{e}+\frac{6 b^2 n^2 (e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{e}-6 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)-12 a b^2 n^2 x-\frac{3 b n (e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{e}+\frac{(e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{e}+6 b n x \left(a+b \log \left(c x^n\right)\right)^2-x \left(a+b \log \left(c x^n\right)\right)^3-12 b^3 n^2 x \log \left(c x^n\right)-\frac{6 b^3 n^3 (e x+1) \log (e x+1)}{e}+24 b^3 n^3 x","-\frac{6 b^2 n^2 \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{6 b^2 n^2 \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{3 b n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2}{e}+\frac{6 b^3 n^3 \text{PolyLog}(2,-e x)}{e}+\frac{6 b^3 n^3 \text{PolyLog}(3,-e x)}{e}+\frac{6 b^3 n^3 \text{PolyLog}(4,-e x)}{e}+\frac{6 b^2 n^2 (e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{e}-6 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)-12 a b^2 n^2 x-\frac{3 b n (e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{e}+\frac{(e x+1) \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{e}+6 b n x \left(a+b \log \left(c x^n\right)\right)^2-x \left(a+b \log \left(c x^n\right)\right)^3-12 b^3 n^2 x \log \left(c x^n\right)-\frac{6 b^3 n^3 (e x+1) \log (e x+1)}{e}+24 b^3 n^3 x",1,"-12*a*b^2*n^2*x + 24*b^3*n^3*x - 12*b^3*n^2*x*Log[c*x^n] - 6*b^2*n^2*x*(a + b*Log[c*x^n]) + 6*b*n*x*(a + b*Log[c*x^n])^2 - x*(a + b*Log[c*x^n])^3 - (6*b^3*n^3*(1 + e*x)*Log[1 + e*x])/e + (6*b^2*n^2*(1 + e*x)*(a + b*Log[c*x^n])*Log[1 + e*x])/e - (3*b*n*(1 + e*x)*(a + b*Log[c*x^n])^2*Log[1 + e*x])/e + ((1 + e*x)*(a + b*Log[c*x^n])^3*Log[1 + e*x])/e + (6*b^3*n^3*PolyLog[2, -(e*x)])/e - (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)])/e + (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(e*x)])/e + (6*b^3*n^3*PolyLog[3, -(e*x)])/e - (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(e*x)])/e + (6*b^3*n^3*PolyLog[4, -(e*x)])/e","A",24,16,19,0.8421,1,"{2389, 2295, 2370, 2296, 2346, 2302, 30, 6742, 2301, 2411, 43, 2351, 2315, 2374, 6589, 2383}"
21,1,81,0,0.0984286,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x)}{x} \, dx","Int[((a + b*Log[c*x^n])^3*Log[1 + e*x])/x,x]","-6 b^2 n^2 \text{PolyLog}(4,-e x) \left(a+b \log \left(c x^n\right)\right)+3 b n \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)^2-\text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^3+6 b^3 n^3 \text{PolyLog}(5,-e x)","-6 b^2 n^2 \text{PolyLog}(4,-e x) \left(a+b \log \left(c x^n\right)\right)+3 b n \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)^2-\text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^3+6 b^3 n^3 \text{PolyLog}(5,-e x)",1,"-((a + b*Log[c*x^n])^3*PolyLog[2, -(e*x)]) + 3*b*n*(a + b*Log[c*x^n])^2*PolyLog[3, -(e*x)] - 6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[4, -(e*x)] + 6*b^3*n^3*PolyLog[5, -(e*x)]","A",4,3,22,0.1364,1,"{2374, 2383, 6589}"
22,1,360,0,0.6013014,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x)}{x^2} \, dx","Int[((a + b*Log[c*x^n])^3*Log[1 + e*x])/x^2,x]","-6 b^2 e n^2 \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)+6 b^2 e n^2 \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)-3 b e n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2-6 b^3 e n^3 \text{PolyLog}(2,-e x)+6 b^3 e n^3 \text{PolyLog}(3,-e x)-6 b^3 e n^3 \text{PolyLog}(4,-e x)-6 b^2 e n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{e \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}+e \left(a+b \log \left(c x^n\right)\right)^3-e \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{x}+3 b e n \left(a+b \log \left(c x^n\right)\right)^2-3 b e n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2-\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{x}+6 b^3 e n^3 \log (x)-6 b^3 e n^3 \log (e x+1)-\frac{6 b^3 n^3 \log (e x+1)}{x}","6 b^2 e n^2 \text{PolyLog}\left(2,-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)+6 b^2 e n^2 \text{PolyLog}\left(3,-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)+3 b e n \text{PolyLog}\left(2,-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)^2+6 b^3 e n^3 \text{PolyLog}\left(2,-\frac{1}{e x}\right)+6 b^3 e n^3 \text{PolyLog}\left(3,-\frac{1}{e x}\right)+6 b^3 e n^3 \text{PolyLog}\left(4,-\frac{1}{e x}\right)-6 b^2 e n^2 \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{x}-3 b e n \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{x}-e \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{x}+6 b^3 e n^3 \log (x)-6 b^3 e n^3 \log (e x+1)-\frac{6 b^3 n^3 \log (e x+1)}{x}",1,"6*b^3*e*n^3*Log[x] + 3*b*e*n*(a + b*Log[c*x^n])^2 + e*(a + b*Log[c*x^n])^3 + (e*(a + b*Log[c*x^n])^4)/(4*b*n) - 6*b^3*e*n^3*Log[1 + e*x] - (6*b^3*n^3*Log[1 + e*x])/x - 6*b^2*e*n^2*(a + b*Log[c*x^n])*Log[1 + e*x] - (6*b^2*n^2*(a + b*Log[c*x^n])*Log[1 + e*x])/x - 3*b*e*n*(a + b*Log[c*x^n])^2*Log[1 + e*x] - (3*b*n*(a + b*Log[c*x^n])^2*Log[1 + e*x])/x - e*(a + b*Log[c*x^n])^3*Log[1 + e*x] - ((a + b*Log[c*x^n])^3*Log[1 + e*x])/x - 6*b^3*e*n^3*PolyLog[2, -(e*x)] - 6*b^2*e*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)] - 3*b*e*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(e*x)] + 6*b^3*e*n^3*PolyLog[3, -(e*x)] + 6*b^2*e*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(e*x)] - 6*b^3*e*n^3*PolyLog[4, -(e*x)]","A",22,15,22,0.6818,1,"{2305, 2304, 2378, 36, 29, 31, 2344, 2301, 2317, 2391, 2302, 30, 2374, 6589, 2383}"
23,1,499,0,0.8201804,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log (1+e x)}{x^3} \, dx","Int[((a + b*Log[c*x^n])^3*Log[1 + e*x])/x^3,x]","\frac{3}{2} b^2 e^2 n^2 \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)-3 b^2 e^2 n^2 \text{PolyLog}(3,-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{2} b e^2 n \text{PolyLog}(2,-e x) \left(a+b \log \left(c x^n\right)\right)^2+\frac{3}{4} b^3 e^2 n^3 \text{PolyLog}(2,-e x)-\frac{3}{2} b^3 e^2 n^3 \text{PolyLog}(3,-e x)+3 b^3 e^2 n^3 \text{PolyLog}(4,-e x)+\frac{3}{4} b^2 e^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}-\frac{21 b^2 e n^2 \left(a+b \log \left(c x^n\right)\right)}{4 x}-\frac{e^2 \left(a+b \log \left(c x^n\right)\right)^4}{8 b n}-\frac{1}{4} e^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{1}{2} e^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{8} b e^2 n \left(a+b \log \left(c x^n\right)\right)^2+\frac{3}{4} b e^2 n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{e \left(a+b \log \left(c x^n\right)\right)^3}{2 x}-\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{9 b e n \left(a+b \log \left(c x^n\right)\right)^2}{4 x}-\frac{3}{8} b^3 e^2 n^3 \log (x)+\frac{3}{8} b^3 e^2 n^3 \log (e x+1)-\frac{3 b^3 n^3 \log (e x+1)}{8 x^2}-\frac{45 b^3 e n^3}{8 x}","-\frac{3}{2} b^2 e^2 n^2 \text{PolyLog}\left(2,-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)-3 b^2 e^2 n^2 \text{PolyLog}\left(3,-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3}{2} b e^2 n \text{PolyLog}\left(2,-\frac{1}{e x}\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{3}{4} b^3 e^2 n^3 \text{PolyLog}\left(2,-\frac{1}{e x}\right)-\frac{3}{2} b^3 e^2 n^3 \text{PolyLog}\left(3,-\frac{1}{e x}\right)-3 b^3 e^2 n^3 \text{PolyLog}\left(4,-\frac{1}{e x}\right)+\frac{3}{4} b^2 e^2 n^2 \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{21 b^2 e n^2 \left(a+b \log \left(c x^n\right)\right)}{4 x}-\frac{3 b^2 n^2 \log (e x+1) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}+\frac{3}{4} b e^2 n \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} e^2 \log \left(\frac{1}{e x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{9 b e n \left(a+b \log \left(c x^n\right)\right)^2}{4 x}-\frac{3 b n \log (e x+1) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{e \left(a+b \log \left(c x^n\right)\right)^3}{2 x}-\frac{\log (e x+1) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{3}{8} b^3 e^2 n^3 \log (x)+\frac{3}{8} b^3 e^2 n^3 \log (e x+1)-\frac{3 b^3 n^3 \log (e x+1)}{8 x^2}-\frac{45 b^3 e n^3}{8 x}",1,"(-45*b^3*e*n^3)/(8*x) - (3*b^3*e^2*n^3*Log[x])/8 - (21*b^2*e*n^2*(a + b*Log[c*x^n]))/(4*x) - (3*b*e^2*n*(a + b*Log[c*x^n])^2)/8 - (9*b*e*n*(a + b*Log[c*x^n])^2)/(4*x) - (e^2*(a + b*Log[c*x^n])^3)/4 - (e*(a + b*Log[c*x^n])^3)/(2*x) - (e^2*(a + b*Log[c*x^n])^4)/(8*b*n) + (3*b^3*e^2*n^3*Log[1 + e*x])/8 - (3*b^3*n^3*Log[1 + e*x])/(8*x^2) + (3*b^2*e^2*n^2*(a + b*Log[c*x^n])*Log[1 + e*x])/4 - (3*b^2*n^2*(a + b*Log[c*x^n])*Log[1 + e*x])/(4*x^2) + (3*b*e^2*n*(a + b*Log[c*x^n])^2*Log[1 + e*x])/4 - (3*b*n*(a + b*Log[c*x^n])^2*Log[1 + e*x])/(4*x^2) + (e^2*(a + b*Log[c*x^n])^3*Log[1 + e*x])/2 - ((a + b*Log[c*x^n])^3*Log[1 + e*x])/(2*x^2) + (3*b^3*e^2*n^3*PolyLog[2, -(e*x)])/4 + (3*b^2*e^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(e*x)])/2 + (3*b*e^2*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(e*x)])/2 - (3*b^3*e^2*n^3*PolyLog[3, -(e*x)])/2 - 3*b^2*e^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(e*x)] + 3*b^3*e^2*n^3*PolyLog[4, -(e*x)]","A",30,14,22,0.6364,1,"{2305, 2304, 2378, 44, 2351, 2301, 2317, 2391, 2353, 2302, 30, 2374, 6589, 2383}"
24,1,180,0,0.1657151,"\int x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Int[x^3*(a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)],x]","-\frac{b n \text{PolyLog}\left(2,-d f x^2\right)}{8 d^2 f^2}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}+\frac{1}{4} x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{4 d f}-\frac{1}{8} x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{b n \log \left(d f x^2+1\right)}{16 d^2 f^2}-\frac{3 b n x^2}{16 d f}-\frac{1}{16} b n x^4 \log \left(d f x^2+1\right)+\frac{1}{16} b n x^4","-\frac{b n \text{PolyLog}\left(2,-d f x^2\right)}{8 d^2 f^2}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}+\frac{1}{4} x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{4 d f}-\frac{1}{8} x^4 \left(a+b \log \left(c x^n\right)\right)+\frac{b n \log \left(d f x^2+1\right)}{16 d^2 f^2}-\frac{3 b n x^2}{16 d f}-\frac{1}{16} b n x^4 \log \left(d f x^2+1\right)+\frac{1}{16} b n x^4",1,"(-3*b*n*x^2)/(16*d*f) + (b*n*x^4)/16 + (x^2*(a + b*Log[c*x^n]))/(4*d*f) - (x^4*(a + b*Log[c*x^n]))/8 + (b*n*Log[1 + d*f*x^2])/(16*d^2*f^2) - (b*n*x^4*Log[1 + d*f*x^2])/16 - ((a + b*Log[c*x^n])*Log[1 + d*f*x^2])/(4*d^2*f^2) + (x^4*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/4 - (b*n*PolyLog[2, -(d*f*x^2)])/(8*d^2*f^2)","A",7,5,26,0.1923,1,"{2454, 2395, 43, 2376, 2391}"
25,1,114,0,0.1765848,"\int x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Int[x*(a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)],x]","\frac{b n \text{PolyLog}\left(2,-d f x^2\right)}{4 d f}+\frac{\left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d f}-\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b n \left(d f x^2+1\right) \log \left(d f x^2+1\right)}{4 d f}+\frac{1}{2} b n x^2","\frac{b n \text{PolyLog}\left(2,-d f x^2\right)}{4 d f}+\frac{\left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d f}-\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b n \left(d f x^2+1\right) \log \left(d f x^2+1\right)}{4 d f}+\frac{1}{2} b n x^2",1,"(b*n*x^2)/2 - (x^2*(a + b*Log[c*x^n]))/2 - (b*n*(1 + d*f*x^2)*Log[1 + d*f*x^2])/(4*d*f) + ((1 + d*f*x^2)*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/(2*d*f) + (b*n*PolyLog[2, -(d*f*x^2)])/(4*d*f)","A",8,9,24,0.3750,1,"{2454, 2389, 2295, 2376, 2475, 2411, 43, 2351, 2315}"
26,1,39,0,0.032042,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)])/x,x]","\frac{1}{4} b n \text{PolyLog}\left(3,-d f x^2\right)-\frac{1}{2} \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)","\frac{1}{4} b n \text{PolyLog}\left(3,-d f x^2\right)-\frac{1}{2} \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)",1,"-((a + b*Log[c*x^n])*PolyLog[2, -(d*f*x^2)])/2 + (b*n*PolyLog[3, -(d*f*x^2)])/4","A",2,2,26,0.07692,1,"{2374, 6589}"
27,1,141,0,0.1277227,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)])/x^3,x]","-\frac{1}{4} b d f n \text{PolyLog}\left(2,-d f x^2\right)+d f \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} d f \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{4} b d f n \log \left(d f x^2+1\right)-\frac{b n \log \left(d f x^2+1\right)}{4 x^2}-\frac{1}{2} b d f n \log ^2(x)+\frac{1}{2} b d f n \log (x)","-\frac{1}{4} b d f n \text{PolyLog}\left(2,-d f x^2\right)+d f \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} d f \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{4} b d f n \log \left(d f x^2+1\right)-\frac{b n \log \left(d f x^2+1\right)}{4 x^2}-\frac{1}{2} b d f n \log ^2(x)+\frac{1}{2} b d f n \log (x)",1,"(b*d*f*n*Log[x])/2 - (b*d*f*n*Log[x]^2)/2 + d*f*Log[x]*(a + b*Log[c*x^n]) - (b*d*f*n*Log[1 + d*f*x^2])/4 - (b*n*Log[1 + d*f*x^2])/(4*x^2) - (d*f*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/2 - ((a + b*Log[c*x^n])*Log[1 + d*f*x^2])/(2*x^2) - (b*d*f*n*PolyLog[2, -(d*f*x^2)])/4","A",9,8,26,0.3077,1,"{2454, 2395, 36, 29, 31, 2376, 2301, 2391}"
28,1,241,0,0.1793491,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Int[x^2*(a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)],x]","\frac{i b n \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)}{3 d^{3/2} f^{3/2}}-\frac{i b n \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)}{3 d^{3/2} f^{3/2}}-\frac{2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^{3/2} f^{3/2}}+\frac{1}{3} x^3 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2 x \left(a+b \log \left(c x^n\right)\right)}{3 d f}-\frac{2}{9} x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{2 b n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{9 d^{3/2} f^{3/2}}-\frac{1}{9} b n x^3 \log \left(d f x^2+1\right)-\frac{8 b n x}{9 d f}+\frac{4}{27} b n x^3","\frac{i b n \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)}{3 d^{3/2} f^{3/2}}-\frac{i b n \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)}{3 d^{3/2} f^{3/2}}-\frac{2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^{3/2} f^{3/2}}+\frac{1}{3} x^3 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2 x \left(a+b \log \left(c x^n\right)\right)}{3 d f}-\frac{2}{9} x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{2 b n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{9 d^{3/2} f^{3/2}}-\frac{1}{9} b n x^3 \log \left(d f x^2+1\right)-\frac{8 b n x}{9 d f}+\frac{4}{27} b n x^3",1,"(-8*b*n*x)/(9*d*f) + (4*b*n*x^3)/27 + (2*b*n*ArcTan[Sqrt[d]*Sqrt[f]*x])/(9*d^(3/2)*f^(3/2)) + (2*x*(a + b*Log[c*x^n]))/(3*d*f) - (2*x^3*(a + b*Log[c*x^n]))/9 - (2*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a + b*Log[c*x^n]))/(3*d^(3/2)*f^(3/2)) - (b*n*x^3*Log[1 + d*f*x^2])/9 + (x^3*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/3 + ((I/3)*b*n*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x])/(d^(3/2)*f^(3/2)) - ((I/3)*b*n*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])/(d^(3/2)*f^(3/2))","A",9,7,26,0.2692,1,"{2455, 302, 205, 2376, 4848, 2391, 203}"
29,1,182,0,0.1065018,"\int \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Int[(a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)],x]","-\frac{i b n \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+\frac{i b n \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+x \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d} \sqrt{f}}-2 x \left(a+b \log \left(c x^n\right)\right)-b n x \log \left(d f x^2+1\right)-\frac{2 b n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+4 b n x","-\frac{i b n \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+\frac{i b n \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+x \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{d} \sqrt{f}}-2 x \left(a+b \log \left(c x^n\right)\right)-b n x \log \left(d f x^2+1\right)-\frac{2 b n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+4 b n x",1,"4*b*n*x - (2*b*n*ArcTan[Sqrt[d]*Sqrt[f]*x])/(Sqrt[d]*Sqrt[f]) - 2*x*(a + b*Log[c*x^n]) + (2*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a + b*Log[c*x^n]))/(Sqrt[d]*Sqrt[f]) - b*n*x*Log[1 + d*f*x^2] + x*(a + b*Log[c*x^n])*Log[1 + d*f*x^2] - (I*b*n*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x])/(Sqrt[d]*Sqrt[f]) + (I*b*n*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])/(Sqrt[d]*Sqrt[f])","A",8,7,23,0.3043,1,"{2448, 321, 205, 2370, 4848, 2391, 203}"
30,1,169,0,0.1189545,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)])/x^2,x]","-i b \sqrt{d} \sqrt{f} n \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)+i b \sqrt{d} \sqrt{f} n \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}+2 \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b n \log \left(d f x^2+1\right)}{x}+2 b \sqrt{d} \sqrt{f} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)","-i b \sqrt{d} \sqrt{f} n \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)+i b \sqrt{d} \sqrt{f} n \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}+2 \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b n \log \left(d f x^2+1\right)}{x}+2 b \sqrt{d} \sqrt{f} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)",1,"2*b*Sqrt[d]*Sqrt[f]*n*ArcTan[Sqrt[d]*Sqrt[f]*x] + 2*Sqrt[d]*Sqrt[f]*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a + b*Log[c*x^n]) - (b*n*Log[1 + d*f*x^2])/x - ((a + b*Log[c*x^n])*Log[1 + d*f*x^2])/x - I*b*Sqrt[d]*Sqrt[f]*n*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + I*b*Sqrt[d]*Sqrt[f]*n*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]","A",7,6,26,0.2308,1,"{2455, 205, 2376, 4848, 2391, 203}"
31,1,211,0,0.1399324,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^4} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^2)])/x^4,x]","\frac{1}{3} i b d^{3/2} f^{3/2} n \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)-\frac{1}{3} i b d^{3/2} f^{3/2} n \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)-\frac{2}{3} d^{3/2} f^{3/2} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 d f \left(a+b \log \left(c x^n\right)\right)}{3 x}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{2}{9} b d^{3/2} f^{3/2} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)-\frac{b n \log \left(d f x^2+1\right)}{9 x^3}-\frac{8 b d f n}{9 x}","\frac{1}{3} i b d^{3/2} f^{3/2} n \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)-\frac{1}{3} i b d^{3/2} f^{3/2} n \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)-\frac{2}{3} d^{3/2} f^{3/2} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 d f \left(a+b \log \left(c x^n\right)\right)}{3 x}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{2}{9} b d^{3/2} f^{3/2} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)-\frac{b n \log \left(d f x^2+1\right)}{9 x^3}-\frac{8 b d f n}{9 x}",1,"(-8*b*d*f*n)/(9*x) - (2*b*d^(3/2)*f^(3/2)*n*ArcTan[Sqrt[d]*Sqrt[f]*x])/9 - (2*d*f*(a + b*Log[c*x^n]))/(3*x) - (2*d^(3/2)*f^(3/2)*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a + b*Log[c*x^n]))/3 - (b*n*Log[1 + d*f*x^2])/(9*x^3) - ((a + b*Log[c*x^n])*Log[1 + d*f*x^2])/(3*x^3) + (I/3)*b*d^(3/2)*f^(3/2)*n*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - (I/3)*b*d^(3/2)*f^(3/2)*n*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x]","A",8,7,26,0.2692,1,"{2455, 325, 205, 2376, 4848, 2391, 203}"
32,1,367,0,0.364539,"\int x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Int[x^3*(a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)],x]","-\frac{b n \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}+\frac{b^2 n^2 \text{PolyLog}\left(2,-d f x^2\right)}{16 d^2 f^2}+\frac{b^2 n^2 \text{PolyLog}\left(3,-d f x^2\right)}{8 d^2 f^2}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 d^2 f^2}+\frac{b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{8 d^2 f^2}+\frac{1}{4} x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{8} b n x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{4 d f}-\frac{3 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{8 d f}-\frac{1}{8} x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{8} b n x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{b^2 n^2 \log \left(d f x^2+1\right)}{32 d^2 f^2}+\frac{7 b^2 n^2 x^2}{32 d f}+\frac{1}{32} b^2 n^2 x^4 \log \left(d f x^2+1\right)-\frac{3}{64} b^2 n^2 x^4","-\frac{b n \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}+\frac{b^2 n^2 \text{PolyLog}\left(2,-d f x^2\right)}{16 d^2 f^2}+\frac{b^2 n^2 \text{PolyLog}\left(3,-d f x^2\right)}{8 d^2 f^2}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 d^2 f^2}+\frac{b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{8 d^2 f^2}+\frac{1}{4} x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{8} b n x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{4 d f}-\frac{3 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{8 d f}-\frac{1}{8} x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{8} b n x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{b^2 n^2 \log \left(d f x^2+1\right)}{32 d^2 f^2}+\frac{7 b^2 n^2 x^2}{32 d f}+\frac{1}{32} b^2 n^2 x^4 \log \left(d f x^2+1\right)-\frac{3}{64} b^2 n^2 x^4",1,"(7*b^2*n^2*x^2)/(32*d*f) - (3*b^2*n^2*x^4)/64 - (3*b*n*x^2*(a + b*Log[c*x^n]))/(8*d*f) + (b*n*x^4*(a + b*Log[c*x^n]))/8 + (x^2*(a + b*Log[c*x^n])^2)/(4*d*f) - (x^4*(a + b*Log[c*x^n])^2)/8 - (b^2*n^2*Log[1 + d*f*x^2])/(32*d^2*f^2) + (b^2*n^2*x^4*Log[1 + d*f*x^2])/32 + (b*n*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/(8*d^2*f^2) - (b*n*x^4*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/8 - ((a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/(4*d^2*f^2) + (x^4*(a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/4 + (b^2*n^2*PolyLog[2, -(d*f*x^2)])/(16*d^2*f^2) - (b*n*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*x^2)])/(4*d^2*f^2) + (b^2*n^2*PolyLog[3, -(d*f*x^2)])/(8*d^2*f^2)","A",13,9,28,0.3214,1,"{2454, 2395, 43, 2377, 2304, 2374, 6589, 2376, 2391}"
33,1,241,0,0.5053065,"\int x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Int[x*(a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)],x]","\frac{b n \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{2 d f}-\frac{b^2 n^2 \text{PolyLog}\left(2,-d f x^2\right)}{4 d f}-\frac{b^2 n^2 \text{PolyLog}\left(3,-d f x^2\right)}{4 d f}-\frac{b n \left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d f}+\frac{\left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 d f}+b n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{b^2 n^2 \left(d f x^2+1\right) \log \left(d f x^2+1\right)}{4 d f}-\frac{3}{4} b^2 n^2 x^2","\frac{b n \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{2 d f}-\frac{b^2 n^2 \text{PolyLog}\left(2,-d f x^2\right)}{4 d f}-\frac{b^2 n^2 \text{PolyLog}\left(3,-d f x^2\right)}{4 d f}-\frac{b n \left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d f}+\frac{\left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 d f}+b n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{b^2 n^2 \left(d f x^2+1\right) \log \left(d f x^2+1\right)}{4 d f}-\frac{3}{4} b^2 n^2 x^2",1,"(-3*b^2*n^2*x^2)/4 + b*n*x^2*(a + b*Log[c*x^n]) - (x^2*(a + b*Log[c*x^n])^2)/2 + (b^2*n^2*(1 + d*f*x^2)*Log[1 + d*f*x^2])/(4*d*f) - (b*n*(1 + d*f*x^2)*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/(2*d*f) + ((1 + d*f*x^2)*(a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/(2*d*f) - (b^2*n^2*PolyLog[2, -(d*f*x^2)])/(4*d*f) + (b*n*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*x^2)])/(2*d*f) - (b^2*n^2*PolyLog[3, -(d*f*x^2)])/(4*d*f)","A",15,16,26,0.6154,1,"{2454, 2389, 2295, 2377, 2304, 14, 2351, 2301, 6742, 2374, 6589, 2376, 2475, 2411, 43, 2315}"
34,1,70,0,0.066647,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)])/x,x]","\frac{1}{2} b n \text{PolyLog}\left(3,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{4} b^2 n^2 \text{PolyLog}\left(4,-d f x^2\right)","\frac{1}{2} b n \text{PolyLog}\left(3,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{4} b^2 n^2 \text{PolyLog}\left(4,-d f x^2\right)",1,"-((a + b*Log[c*x^n])^2*PolyLog[2, -(d*f*x^2)])/2 + (b*n*(a + b*Log[c*x^n])*PolyLog[3, -(d*f*x^2)])/2 - (b^2*n^2*PolyLog[4, -(d*f*x^2)])/4","A",3,3,28,0.1071,1,"{2374, 2383, 6589}"
35,1,257,0,0.338479,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)])/x^3,x]","\frac{1}{2} b d f n \text{PolyLog}\left(2,-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} b^2 d f n^2 \text{PolyLog}\left(2,-\frac{1}{d f x^2}\right)+\frac{1}{4} b^2 d f n^2 \text{PolyLog}\left(3,-\frac{1}{d f x^2}\right)-\frac{1}{2} b d f n \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{2} d f \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{1}{4} b^2 d f n^2 \log \left(d f x^2+1\right)-\frac{b^2 n^2 \log \left(d f x^2+1\right)}{4 x^2}+\frac{1}{2} b^2 d f n^2 \log (x)","\frac{1}{2} b d f n \text{PolyLog}\left(2,-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} b^2 d f n^2 \text{PolyLog}\left(2,-\frac{1}{d f x^2}\right)+\frac{1}{4} b^2 d f n^2 \text{PolyLog}\left(3,-\frac{1}{d f x^2}\right)-\frac{1}{2} b d f n \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{2} d f \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{1}{4} b^2 d f n^2 \log \left(d f x^2+1\right)-\frac{b^2 n^2 \log \left(d f x^2+1\right)}{4 x^2}+\frac{1}{2} b^2 d f n^2 \log (x)",1,"(b^2*d*f*n^2*Log[x])/2 - (b*d*f*n*Log[1 + 1/(d*f*x^2)]*(a + b*Log[c*x^n]))/2 - (d*f*Log[1 + 1/(d*f*x^2)]*(a + b*Log[c*x^n])^2)/2 - (b^2*d*f*n^2*Log[1 + d*f*x^2])/4 - (b^2*n^2*Log[1 + d*f*x^2])/(4*x^2) - (b*n*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/(2*x^2) - ((a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/(2*x^2) + (b^2*d*f*n^2*PolyLog[2, -(1/(d*f*x^2))])/4 + (b*d*f*n*(a + b*Log[c*x^n])*PolyLog[2, -(1/(d*f*x^2))])/2 + (b^2*d*f*n^2*PolyLog[3, -(1/(d*f*x^2))])/4","A",11,11,28,0.3929,1,"{2305, 2304, 2378, 266, 36, 29, 31, 2345, 2391, 2374, 6589}"
36,1,612,0,1.03388,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Int[x^2*(a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)],x]","\frac{2 b n \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-d)^{3/2} f^{3/2}}-\frac{2 b n \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-d)^{3/2} f^{3/2}}-\frac{2 i b^2 n^2 \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)}{9 d^{3/2} f^{3/2}}+\frac{2 i b^2 n^2 \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)}{9 d^{3/2} f^{3/2}}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right)}{3 (-d)^{3/2} f^{3/2}}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right)}{3 (-d)^{3/2} f^{3/2}}+\frac{4 b n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{9 d^{3/2} f^{3/2}}-\frac{\log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-d)^{3/2} f^{3/2}}+\frac{\log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-d)^{3/2} f^{3/2}}+\frac{1}{3} x^3 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2 x \left(a+b \log \left(c x^n\right)\right)^2}{3 d f}-\frac{2}{9} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{8}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{16 a b n x}{9 d f}-\frac{16 b^2 n x \log \left(c x^n\right)}{9 d f}-\frac{4 b^2 n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{27 d^{3/2} f^{3/2}}+\frac{2}{27} b^2 n^2 x^3 \log \left(d f x^2+1\right)+\frac{52 b^2 n^2 x}{27 d f}-\frac{4}{27} b^2 n^2 x^3","\frac{2 b n \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-d)^{3/2} f^{3/2}}-\frac{2 b n \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-d)^{3/2} f^{3/2}}-\frac{2 i b^2 n^2 \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)}{9 d^{3/2} f^{3/2}}+\frac{2 i b^2 n^2 \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)}{9 d^{3/2} f^{3/2}}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right)}{3 (-d)^{3/2} f^{3/2}}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right)}{3 (-d)^{3/2} f^{3/2}}+\frac{4 b n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{9 d^{3/2} f^{3/2}}-\frac{\log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-d)^{3/2} f^{3/2}}+\frac{\log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-d)^{3/2} f^{3/2}}+\frac{1}{3} x^3 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2 x \left(a+b \log \left(c x^n\right)\right)^2}{3 d f}-\frac{2}{9} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{8}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{16 a b n x}{9 d f}-\frac{16 b^2 n x \log \left(c x^n\right)}{9 d f}-\frac{4 b^2 n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{27 d^{3/2} f^{3/2}}+\frac{2}{27} b^2 n^2 x^3 \log \left(d f x^2+1\right)+\frac{52 b^2 n^2 x}{27 d f}-\frac{4}{27} b^2 n^2 x^3",1,"(-16*a*b*n*x)/(9*d*f) + (52*b^2*n^2*x)/(27*d*f) - (4*b^2*n^2*x^3)/27 - (4*b^2*n^2*ArcTan[Sqrt[d]*Sqrt[f]*x])/(27*d^(3/2)*f^(3/2)) - (16*b^2*n*x*Log[c*x^n])/(9*d*f) + (8*b*n*x^3*(a + b*Log[c*x^n]))/27 + (4*b*n*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a + b*Log[c*x^n]))/(9*d^(3/2)*f^(3/2)) + (2*x*(a + b*Log[c*x^n])^2)/(3*d*f) - (2*x^3*(a + b*Log[c*x^n])^2)/9 - ((a + b*Log[c*x^n])^2*Log[1 - Sqrt[-d]*Sqrt[f]*x])/(3*(-d)^(3/2)*f^(3/2)) + ((a + b*Log[c*x^n])^2*Log[1 + Sqrt[-d]*Sqrt[f]*x])/(3*(-d)^(3/2)*f^(3/2)) + (2*b^2*n^2*x^3*Log[1 + d*f*x^2])/27 - (2*b*n*x^3*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/9 + (x^3*(a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/3 + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -(Sqrt[-d]*Sqrt[f]*x)])/(3*(-d)^(3/2)*f^(3/2)) - (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, Sqrt[-d]*Sqrt[f]*x])/(3*(-d)^(3/2)*f^(3/2)) - (((2*I)/9)*b^2*n^2*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x])/(d^(3/2)*f^(3/2)) + (((2*I)/9)*b^2*n^2*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])/(d^(3/2)*f^(3/2)) - (2*b^2*n^2*PolyLog[3, -(Sqrt[-d]*Sqrt[f]*x)])/(3*(-d)^(3/2)*f^(3/2)) + (2*b^2*n^2*PolyLog[3, Sqrt[-d]*Sqrt[f]*x])/(3*(-d)^(3/2)*f^(3/2))","A",30,17,28,0.6071,1,"{2305, 2304, 2378, 302, 203, 2351, 2295, 2324, 12, 4848, 2391, 2353, 2296, 2330, 2317, 2374, 6589}"
37,1,519,0,0.8011198,"\int \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Int[(a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)],x]","\frac{2 b n \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d} \sqrt{f}}-\frac{2 b n \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d} \sqrt{f}}+\frac{2 i b^2 n^2 \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}-\frac{2 i b^2 n^2 \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right)}{\sqrt{-d} \sqrt{f}}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right)}{\sqrt{-d} \sqrt{f}}-\frac{\log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-d} \sqrt{f}}+\frac{\log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-d} \sqrt{f}}+x \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2-2 x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \log \left(d f x^2+1\right)-\frac{4 b n (a-b n) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+4 a b n x+4 b n x (a-b n)-2 b^2 n x \log \left(c x^n\right) \log \left(d f x^2+1\right)-\frac{4 b^2 n \log \left(c x^n\right) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+8 b^2 n x \log \left(c x^n\right)+2 b^2 n^2 x \log \left(d f x^2+1\right)-8 b^2 n^2 x","\frac{2 b n \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d} \sqrt{f}}-\frac{2 b n \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-d} \sqrt{f}}+\frac{2 i b^2 n^2 \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}-\frac{2 i b^2 n^2 \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}-\frac{2 b^2 n^2 \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right)}{\sqrt{-d} \sqrt{f}}+\frac{2 b^2 n^2 \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right)}{\sqrt{-d} \sqrt{f}}-\frac{\log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-d} \sqrt{f}}+\frac{\log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-d} \sqrt{f}}+x \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2-2 x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \log \left(d f x^2+1\right)-\frac{4 b n (a-b n) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+4 a b n x+4 b n x (a-b n)-2 b^2 n x \log \left(c x^n\right) \log \left(d f x^2+1\right)-\frac{4 b^2 n \log \left(c x^n\right) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)}{\sqrt{d} \sqrt{f}}+8 b^2 n x \log \left(c x^n\right)+2 b^2 n^2 x \log \left(d f x^2+1\right)-8 b^2 n^2 x",1,"4*a*b*n*x - 8*b^2*n^2*x + 4*b*n*(a - b*n)*x - (4*b*n*(a - b*n)*ArcTan[Sqrt[d]*Sqrt[f]*x])/(Sqrt[d]*Sqrt[f]) + 8*b^2*n*x*Log[c*x^n] - (4*b^2*n*ArcTan[Sqrt[d]*Sqrt[f]*x]*Log[c*x^n])/(Sqrt[d]*Sqrt[f]) - 2*x*(a + b*Log[c*x^n])^2 - ((a + b*Log[c*x^n])^2*Log[1 - Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f]) + ((a + b*Log[c*x^n])^2*Log[1 + Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f]) - 2*a*b*n*x*Log[1 + d*f*x^2] + 2*b^2*n^2*x*Log[1 + d*f*x^2] - 2*b^2*n*x*Log[c*x^n]*Log[1 + d*f*x^2] + x*(a + b*Log[c*x^n])^2*Log[1 + d*f*x^2] + (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -(Sqrt[-d]*Sqrt[f]*x)])/(Sqrt[-d]*Sqrt[f]) - (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f]) + ((2*I)*b^2*n^2*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x])/(Sqrt[d]*Sqrt[f]) - ((2*I)*b^2*n^2*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])/(Sqrt[d]*Sqrt[f]) - (2*b^2*n^2*PolyLog[3, -(Sqrt[-d]*Sqrt[f]*x)])/(Sqrt[-d]*Sqrt[f]) + (2*b^2*n^2*PolyLog[3, Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f])","A",26,16,25,0.6400,1,"{2296, 2295, 2371, 6, 321, 203, 2351, 2324, 12, 4848, 2391, 2353, 2330, 2317, 2374, 6589}"
38,1,459,0,0.5556456,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)])/x^2,x]","-2 b \sqrt{-d} \sqrt{f} n \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+2 b \sqrt{-d} \sqrt{f} n \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-2 i b^2 \sqrt{d} \sqrt{f} n^2 \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)+2 i b^2 \sqrt{d} \sqrt{f} n^2 \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)+2 b^2 \sqrt{-d} \sqrt{f} n^2 \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right)-2 b^2 \sqrt{-d} \sqrt{f} n^2 \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right)-\frac{2 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}+\sqrt{-d} \sqrt{f} \log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2-\sqrt{-d} \sqrt{f} \log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}+4 b \sqrt{d} \sqrt{f} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b^2 n^2 \log \left(d f x^2+1\right)}{x}+4 b^2 \sqrt{d} \sqrt{f} n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)","-2 b \sqrt{-d} \sqrt{f} n \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+2 b \sqrt{-d} \sqrt{f} n \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-2 i b^2 \sqrt{d} \sqrt{f} n^2 \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)+2 i b^2 \sqrt{d} \sqrt{f} n^2 \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)+2 b^2 \sqrt{-d} \sqrt{f} n^2 \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right)-2 b^2 \sqrt{-d} \sqrt{f} n^2 \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right)-\frac{2 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}+\sqrt{-d} \sqrt{f} \log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2-\sqrt{-d} \sqrt{f} \log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}+4 b \sqrt{d} \sqrt{f} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)-\frac{2 b^2 n^2 \log \left(d f x^2+1\right)}{x}+4 b^2 \sqrt{d} \sqrt{f} n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)",1,"4*b^2*Sqrt[d]*Sqrt[f]*n^2*ArcTan[Sqrt[d]*Sqrt[f]*x] + 4*b*Sqrt[d]*Sqrt[f]*n*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a + b*Log[c*x^n]) + Sqrt[-d]*Sqrt[f]*(a + b*Log[c*x^n])^2*Log[1 - Sqrt[-d]*Sqrt[f]*x] - Sqrt[-d]*Sqrt[f]*(a + b*Log[c*x^n])^2*Log[1 + Sqrt[-d]*Sqrt[f]*x] - (2*b^2*n^2*Log[1 + d*f*x^2])/x - (2*b*n*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/x - ((a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/x - 2*b*Sqrt[-d]*Sqrt[f]*n*(a + b*Log[c*x^n])*PolyLog[2, -(Sqrt[-d]*Sqrt[f]*x)] + 2*b*Sqrt[-d]*Sqrt[f]*n*(a + b*Log[c*x^n])*PolyLog[2, Sqrt[-d]*Sqrt[f]*x] - (2*I)*b^2*Sqrt[d]*Sqrt[f]*n^2*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + (2*I)*b^2*Sqrt[d]*Sqrt[f]*n^2*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + 2*b^2*Sqrt[-d]*Sqrt[f]*n^2*PolyLog[3, -(Sqrt[-d]*Sqrt[f]*x)] - 2*b^2*Sqrt[-d]*Sqrt[f]*n^2*PolyLog[3, Sqrt[-d]*Sqrt[f]*x]","A",16,12,28,0.4286,1,"{2305, 2304, 2378, 203, 2324, 12, 4848, 2391, 2330, 2317, 2374, 6589}"
39,1,543,0,0.86583,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^4} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^2)])/x^4,x]","-\frac{2}{3} b (-d)^{3/2} f^{3/2} n \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2}{3} b (-d)^{3/2} f^{3/2} n \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2}{9} i b^2 d^{3/2} f^{3/2} n^2 \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)-\frac{2}{9} i b^2 d^{3/2} f^{3/2} n^2 \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)+\frac{2}{3} b^2 (-d)^{3/2} f^{3/2} n^2 \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right)-\frac{2}{3} b^2 (-d)^{3/2} f^{3/2} n^2 \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right)-\frac{4}{9} b d^{3/2} f^{3/2} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} (-d)^{3/2} f^{3/2} \log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{3} (-d)^{3/2} f^{3/2} \log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{16 b d f n \left(a+b \log \left(c x^n\right)\right)}{9 x}-\frac{2 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 x^3}-\frac{2 d f \left(a+b \log \left(c x^n\right)\right)^2}{3 x}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 x^3}-\frac{4}{27} b^2 d^{3/2} f^{3/2} n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)-\frac{2 b^2 n^2 \log \left(d f x^2+1\right)}{27 x^3}-\frac{52 b^2 d f n^2}{27 x}","-\frac{2}{3} b (-d)^{3/2} f^{3/2} n \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2}{3} b (-d)^{3/2} f^{3/2} n \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+\frac{2}{9} i b^2 d^{3/2} f^{3/2} n^2 \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right)-\frac{2}{9} i b^2 d^{3/2} f^{3/2} n^2 \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right)+\frac{2}{3} b^2 (-d)^{3/2} f^{3/2} n^2 \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right)-\frac{2}{3} b^2 (-d)^{3/2} f^{3/2} n^2 \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right)-\frac{4}{9} b d^{3/2} f^{3/2} n \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} (-d)^{3/2} f^{3/2} \log \left(1-\sqrt{-d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{3} (-d)^{3/2} f^{3/2} \log \left(\sqrt{-d} \sqrt{f} x+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{16 b d f n \left(a+b \log \left(c x^n\right)\right)}{9 x}-\frac{2 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 x^3}-\frac{2 d f \left(a+b \log \left(c x^n\right)\right)^2}{3 x}-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 x^3}-\frac{4}{27} b^2 d^{3/2} f^{3/2} n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right)-\frac{2 b^2 n^2 \log \left(d f x^2+1\right)}{27 x^3}-\frac{52 b^2 d f n^2}{27 x}",1,"(-52*b^2*d*f*n^2)/(27*x) - (4*b^2*d^(3/2)*f^(3/2)*n^2*ArcTan[Sqrt[d]*Sqrt[f]*x])/27 - (16*b*d*f*n*(a + b*Log[c*x^n]))/(9*x) - (4*b*d^(3/2)*f^(3/2)*n*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a + b*Log[c*x^n]))/9 - (2*d*f*(a + b*Log[c*x^n])^2)/(3*x) + ((-d)^(3/2)*f^(3/2)*(a + b*Log[c*x^n])^2*Log[1 - Sqrt[-d]*Sqrt[f]*x])/3 - ((-d)^(3/2)*f^(3/2)*(a + b*Log[c*x^n])^2*Log[1 + Sqrt[-d]*Sqrt[f]*x])/3 - (2*b^2*n^2*Log[1 + d*f*x^2])/(27*x^3) - (2*b*n*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/(9*x^3) - ((a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/(3*x^3) - (2*b*(-d)^(3/2)*f^(3/2)*n*(a + b*Log[c*x^n])*PolyLog[2, -(Sqrt[-d]*Sqrt[f]*x)])/3 + (2*b*(-d)^(3/2)*f^(3/2)*n*(a + b*Log[c*x^n])*PolyLog[2, Sqrt[-d]*Sqrt[f]*x])/3 + ((2*I)/9)*b^2*d^(3/2)*f^(3/2)*n^2*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] - ((2*I)/9)*b^2*d^(3/2)*f^(3/2)*n^2*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + (2*b^2*(-d)^(3/2)*f^(3/2)*n^2*PolyLog[3, -(Sqrt[-d]*Sqrt[f]*x)])/3 - (2*b^2*(-d)^(3/2)*f^(3/2)*n^2*PolyLog[3, Sqrt[-d]*Sqrt[f]*x])/3","A",24,15,28,0.5357,1,"{2305, 2304, 2378, 325, 203, 2351, 2324, 12, 4848, 2391, 2353, 2330, 2317, 2374, 6589}"
40,1,591,0,0.7343129,"\int x^3 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Int[x^3*(a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)],x]","\frac{3 b^2 n^2 \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{16 d^2 f^2}+\frac{3 b^2 n^2 \text{PolyLog}\left(3,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{8 d^2 f^2}-\frac{3 b n \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2}{8 d^2 f^2}-\frac{3 b^3 n^3 \text{PolyLog}\left(2,-d f x^2\right)}{64 d^2 f^2}-\frac{3 b^3 n^3 \text{PolyLog}\left(3,-d f x^2\right)}{32 d^2 f^2}-\frac{3 b^3 n^3 \text{PolyLog}\left(4,-d f x^2\right)}{16 d^2 f^2}-\frac{3 b^2 n^2 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{32 d^2 f^2}+\frac{3}{32} b^2 n^2 x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{21 b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{32 d f}-\frac{9}{64} b^2 n^2 x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{4 d^2 f^2}+\frac{3 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{16 d^2 f^2}+\frac{1}{4} x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{16} b n x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^3}{4 d f}-\frac{9 b n x^2 \left(a+b \log \left(c x^n\right)\right)^2}{16 d f}-\frac{1}{8} x^4 \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{16} b n x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{3 b^3 n^3 \log \left(d f x^2+1\right)}{128 d^2 f^2}-\frac{45 b^3 n^3 x^2}{128 d f}-\frac{3}{128} b^3 n^3 x^4 \log \left(d f x^2+1\right)+\frac{3}{64} b^3 n^3 x^4","\frac{3 b^2 n^2 \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{16 d^2 f^2}+\frac{3 b^2 n^2 \text{PolyLog}\left(3,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{8 d^2 f^2}-\frac{3 b n \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2}{8 d^2 f^2}-\frac{3 b^3 n^3 \text{PolyLog}\left(2,-d f x^2\right)}{64 d^2 f^2}-\frac{3 b^3 n^3 \text{PolyLog}\left(3,-d f x^2\right)}{32 d^2 f^2}-\frac{3 b^3 n^3 \text{PolyLog}\left(4,-d f x^2\right)}{16 d^2 f^2}-\frac{3 b^2 n^2 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{32 d^2 f^2}+\frac{3}{32} b^2 n^2 x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{21 b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)}{32 d f}-\frac{9}{64} b^2 n^2 x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{4 d^2 f^2}+\frac{3 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{16 d^2 f^2}+\frac{1}{4} x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{16} b n x^4 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^3}{4 d f}-\frac{9 b n x^2 \left(a+b \log \left(c x^n\right)\right)^2}{16 d f}-\frac{1}{8} x^4 \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{16} b n x^4 \left(a+b \log \left(c x^n\right)\right)^2+\frac{3 b^3 n^3 \log \left(d f x^2+1\right)}{128 d^2 f^2}-\frac{45 b^3 n^3 x^2}{128 d f}-\frac{3}{128} b^3 n^3 x^4 \log \left(d f x^2+1\right)+\frac{3}{64} b^3 n^3 x^4",1,"(-45*b^3*n^3*x^2)/(128*d*f) + (3*b^3*n^3*x^4)/64 + (21*b^2*n^2*x^2*(a + b*Log[c*x^n]))/(32*d*f) - (9*b^2*n^2*x^4*(a + b*Log[c*x^n]))/64 - (9*b*n*x^2*(a + b*Log[c*x^n])^2)/(16*d*f) + (3*b*n*x^4*(a + b*Log[c*x^n])^2)/16 + (x^2*(a + b*Log[c*x^n])^3)/(4*d*f) - (x^4*(a + b*Log[c*x^n])^3)/8 + (3*b^3*n^3*Log[1 + d*f*x^2])/(128*d^2*f^2) - (3*b^3*n^3*x^4*Log[1 + d*f*x^2])/128 - (3*b^2*n^2*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/(32*d^2*f^2) + (3*b^2*n^2*x^4*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/32 + (3*b*n*(a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/(16*d^2*f^2) - (3*b*n*x^4*(a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/16 - ((a + b*Log[c*x^n])^3*Log[1 + d*f*x^2])/(4*d^2*f^2) + (x^4*(a + b*Log[c*x^n])^3*Log[1 + d*f*x^2])/4 - (3*b^3*n^3*PolyLog[2, -(d*f*x^2)])/(64*d^2*f^2) + (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*x^2)])/(16*d^2*f^2) - (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(d*f*x^2)])/(8*d^2*f^2) - (3*b^3*n^3*PolyLog[3, -(d*f*x^2)])/(32*d^2*f^2) + (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(d*f*x^2)])/(8*d^2*f^2) - (3*b^3*n^3*PolyLog[4, -(d*f*x^2)])/(16*d^2*f^2)","A",22,11,28,0.3929,1,"{2454, 2395, 43, 2377, 2305, 2304, 2374, 2383, 6589, 2376, 2391}"
41,1,411,0,1.042208,"\int x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Int[x*(a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)],x]","-\frac{3 b^2 n^2 \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 d f}-\frac{3 b^2 n^2 \text{PolyLog}\left(3,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 d f}+\frac{3 b n \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 d f}+\frac{3 b^3 n^3 \text{PolyLog}\left(2,-d f x^2\right)}{8 d f}+\frac{3 b^3 n^3 \text{PolyLog}\left(3,-d f x^2\right)}{8 d f}+\frac{3 b^3 n^3 \text{PolyLog}\left(4,-d f x^2\right)}{8 d f}+\frac{3 b^2 n^2 \left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 d f}-\frac{9}{4} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{3 b n \left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 d f}+\frac{\left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 d f}+\frac{3}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^3-\frac{3 b^3 n^3 \left(d f x^2+1\right) \log \left(d f x^2+1\right)}{8 d f}+\frac{3}{2} b^3 n^3 x^2","-\frac{3 b^2 n^2 \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 d f}-\frac{3 b^2 n^2 \text{PolyLog}\left(3,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 d f}+\frac{3 b n \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 d f}+\frac{3 b^3 n^3 \text{PolyLog}\left(2,-d f x^2\right)}{8 d f}+\frac{3 b^3 n^3 \text{PolyLog}\left(3,-d f x^2\right)}{8 d f}+\frac{3 b^3 n^3 \text{PolyLog}\left(4,-d f x^2\right)}{8 d f}+\frac{3 b^2 n^2 \left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 d f}-\frac{9}{4} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{3 b n \left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 d f}+\frac{\left(d f x^2+1\right) \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 d f}+\frac{3}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^3-\frac{3 b^3 n^3 \left(d f x^2+1\right) \log \left(d f x^2+1\right)}{8 d f}+\frac{3}{2} b^3 n^3 x^2",1,"(3*b^3*n^3*x^2)/2 - (9*b^2*n^2*x^2*(a + b*Log[c*x^n]))/4 + (3*b*n*x^2*(a + b*Log[c*x^n])^2)/2 - (x^2*(a + b*Log[c*x^n])^3)/2 - (3*b^3*n^3*(1 + d*f*x^2)*Log[1 + d*f*x^2])/(8*d*f) + (3*b^2*n^2*(1 + d*f*x^2)*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/(4*d*f) - (3*b*n*(1 + d*f*x^2)*(a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/(4*d*f) + ((1 + d*f*x^2)*(a + b*Log[c*x^n])^3*Log[1 + d*f*x^2])/(2*d*f) + (3*b^3*n^3*PolyLog[2, -(d*f*x^2)])/(8*d*f) - (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*x^2)])/(4*d*f) + (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(d*f*x^2)])/(4*d*f) + (3*b^3*n^3*PolyLog[3, -(d*f*x^2)])/(8*d*f) - (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(d*f*x^2)])/(4*d*f) + (3*b^3*n^3*PolyLog[4, -(d*f*x^2)])/(8*d*f)","A",24,21,26,0.8077,1,"{2454, 2389, 2295, 2377, 2305, 2304, 2353, 2302, 30, 6742, 2374, 2383, 6589, 14, 2351, 2301, 2376, 2475, 2411, 43, 2315}"
42,1,101,0,0.0999935,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)])/x,x]","-\frac{3}{4} b^2 n^2 \text{PolyLog}\left(4,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b n \text{PolyLog}\left(3,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{8} b^3 n^3 \text{PolyLog}\left(5,-d f x^2\right)","-\frac{3}{4} b^2 n^2 \text{PolyLog}\left(4,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b n \text{PolyLog}\left(3,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} \text{PolyLog}\left(2,-d f x^2\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{8} b^3 n^3 \text{PolyLog}\left(5,-d f x^2\right)",1,"-((a + b*Log[c*x^n])^3*PolyLog[2, -(d*f*x^2)])/2 + (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[3, -(d*f*x^2)])/4 - (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[4, -(d*f*x^2)])/4 + (3*b^3*n^3*PolyLog[5, -(d*f*x^2)])/8","A",4,3,28,0.1071,1,"{2374, 2383, 6589}"
43,1,425,0,0.5833947,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)])/x^3,x]","\frac{3}{4} b^2 d f n^2 \text{PolyLog}\left(2,-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b^2 d f n^2 \text{PolyLog}\left(3,-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b d f n \text{PolyLog}\left(2,-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{3}{8} b^3 d f n^3 \text{PolyLog}\left(2,-\frac{1}{d f x^2}\right)+\frac{3}{8} b^3 d f n^3 \text{PolyLog}\left(3,-\frac{1}{d f x^2}\right)+\frac{3}{8} b^3 d f n^3 \text{PolyLog}\left(4,-\frac{1}{d f x^2}\right)-\frac{3}{4} b^2 d f n^2 \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b^2 n^2 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}-\frac{3}{4} b d f n \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{3 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{1}{2} d f \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{3}{8} b^3 d f n^3 \log \left(d f x^2+1\right)-\frac{3 b^3 n^3 \log \left(d f x^2+1\right)}{8 x^2}+\frac{3}{4} b^3 d f n^3 \log (x)","\frac{3}{4} b^2 d f n^2 \text{PolyLog}\left(2,-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b^2 d f n^2 \text{PolyLog}\left(3,-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b d f n \text{PolyLog}\left(2,-\frac{1}{d f x^2}\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{3}{8} b^3 d f n^3 \text{PolyLog}\left(2,-\frac{1}{d f x^2}\right)+\frac{3}{8} b^3 d f n^3 \text{PolyLog}\left(3,-\frac{1}{d f x^2}\right)+\frac{3}{8} b^3 d f n^3 \text{PolyLog}\left(4,-\frac{1}{d f x^2}\right)-\frac{3}{4} b^2 d f n^2 \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{3 b^2 n^2 \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}-\frac{3}{4} b d f n \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{3 b n \log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{1}{2} d f \log \left(\frac{1}{d f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{\log \left(d f x^2+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{3}{8} b^3 d f n^3 \log \left(d f x^2+1\right)-\frac{3 b^3 n^3 \log \left(d f x^2+1\right)}{8 x^2}+\frac{3}{4} b^3 d f n^3 \log (x)",1,"(3*b^3*d*f*n^3*Log[x])/4 - (3*b^2*d*f*n^2*Log[1 + 1/(d*f*x^2)]*(a + b*Log[c*x^n]))/4 - (3*b*d*f*n*Log[1 + 1/(d*f*x^2)]*(a + b*Log[c*x^n])^2)/4 - (d*f*Log[1 + 1/(d*f*x^2)]*(a + b*Log[c*x^n])^3)/2 - (3*b^3*d*f*n^3*Log[1 + d*f*x^2])/8 - (3*b^3*n^3*Log[1 + d*f*x^2])/(8*x^2) - (3*b^2*n^2*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/(4*x^2) - (3*b*n*(a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/(4*x^2) - ((a + b*Log[c*x^n])^3*Log[1 + d*f*x^2])/(2*x^2) + (3*b^3*d*f*n^3*PolyLog[2, -(1/(d*f*x^2))])/8 + (3*b^2*d*f*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(1/(d*f*x^2))])/4 + (3*b*d*f*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(1/(d*f*x^2))])/4 + (3*b^3*d*f*n^3*PolyLog[3, -(1/(d*f*x^2))])/8 + (3*b^2*d*f*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(1/(d*f*x^2))])/4 + (3*b^3*d*f*n^3*PolyLog[4, -(1/(d*f*x^2))])/8","A",15,12,28,0.4286,1,"{2305, 2304, 2378, 266, 36, 29, 31, 2345, 2391, 2374, 6589, 2383}"
44,1,938,0,1.5464082,"\int \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right) \, dx","Int[(a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)],x]","36 n^3 x b^3-36 n^2 x \log \left(c x^n\right) b^3+\frac{12 n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \log \left(c x^n\right) b^3}{\sqrt{d} \sqrt{f}}-6 n^3 x \log \left(d f x^2+1\right) b^3+6 n^2 x \log \left(c x^n\right) \log \left(d f x^2+1\right) b^3-\frac{6 i n^3 \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right) b^3}{\sqrt{d} \sqrt{f}}+\frac{6 i n^3 \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right) b^3}{\sqrt{d} \sqrt{f}}+\frac{6 n^3 \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}-\frac{6 n^3 \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}+\frac{6 n^3 \text{PolyLog}\left(4,-\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}-\frac{6 n^3 \text{PolyLog}\left(4,\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}-24 a n^2 x b^2-12 n^2 (a-b n) x b^2+\frac{12 n^2 (a-b n) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) b^2}{\sqrt{d} \sqrt{f}}+6 a n^2 x \log \left(d f x^2+1\right) b^2-\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}+\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}-\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}+\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}+12 n x \left(a+b \log \left(c x^n\right)\right)^2 b+\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\sqrt{-d} \sqrt{f} x\right) b}{\sqrt{-d} \sqrt{f}}-\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\sqrt{-d} \sqrt{f} x+1\right) b}{\sqrt{-d} \sqrt{f}}-3 n x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d f x^2+1\right) b+\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) b}{\sqrt{-d} \sqrt{f}}-\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) b}{\sqrt{-d} \sqrt{f}}-2 x \left(a+b \log \left(c x^n\right)\right)^3-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\sqrt{-d} \sqrt{f} x\right)}{\sqrt{-d} \sqrt{f}}+\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(\sqrt{-d} \sqrt{f} x+1\right)}{\sqrt{-d} \sqrt{f}}+x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d f x^2+1\right)","36 n^3 x b^3-36 n^2 x \log \left(c x^n\right) b^3+\frac{12 n^2 \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \log \left(c x^n\right) b^3}{\sqrt{d} \sqrt{f}}-6 n^3 x \log \left(d f x^2+1\right) b^3+6 n^2 x \log \left(c x^n\right) \log \left(d f x^2+1\right) b^3-\frac{6 i n^3 \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right) b^3}{\sqrt{d} \sqrt{f}}+\frac{6 i n^3 \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right) b^3}{\sqrt{d} \sqrt{f}}+\frac{6 n^3 \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}-\frac{6 n^3 \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}+\frac{6 n^3 \text{PolyLog}\left(4,-\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}-\frac{6 n^3 \text{PolyLog}\left(4,\sqrt{-d} \sqrt{f} x\right) b^3}{\sqrt{-d} \sqrt{f}}-24 a n^2 x b^2-12 n^2 (a-b n) x b^2+\frac{12 n^2 (a-b n) \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) b^2}{\sqrt{d} \sqrt{f}}+6 a n^2 x \log \left(d f x^2+1\right) b^2-\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}+\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}-\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}+\frac{6 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right) b^2}{\sqrt{-d} \sqrt{f}}+12 n x \left(a+b \log \left(c x^n\right)\right)^2 b+\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\sqrt{-d} \sqrt{f} x\right) b}{\sqrt{-d} \sqrt{f}}-\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\sqrt{-d} \sqrt{f} x+1\right) b}{\sqrt{-d} \sqrt{f}}-3 n x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d f x^2+1\right) b+\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) b}{\sqrt{-d} \sqrt{f}}-\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) b}{\sqrt{-d} \sqrt{f}}-2 x \left(a+b \log \left(c x^n\right)\right)^3-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\sqrt{-d} \sqrt{f} x\right)}{\sqrt{-d} \sqrt{f}}+\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(\sqrt{-d} \sqrt{f} x+1\right)}{\sqrt{-d} \sqrt{f}}+x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d f x^2+1\right)",1,"-24*a*b^2*n^2*x + 36*b^3*n^3*x - 12*b^2*n^2*(a - b*n)*x + (12*b^2*n^2*(a - b*n)*ArcTan[Sqrt[d]*Sqrt[f]*x])/(Sqrt[d]*Sqrt[f]) - 36*b^3*n^2*x*Log[c*x^n] + (12*b^3*n^2*ArcTan[Sqrt[d]*Sqrt[f]*x]*Log[c*x^n])/(Sqrt[d]*Sqrt[f]) + 12*b*n*x*(a + b*Log[c*x^n])^2 - 2*x*(a + b*Log[c*x^n])^3 + (3*b*n*(a + b*Log[c*x^n])^2*Log[1 - Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f]) - ((a + b*Log[c*x^n])^3*Log[1 - Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f]) - (3*b*n*(a + b*Log[c*x^n])^2*Log[1 + Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f]) + ((a + b*Log[c*x^n])^3*Log[1 + Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f]) + 6*a*b^2*n^2*x*Log[1 + d*f*x^2] - 6*b^3*n^3*x*Log[1 + d*f*x^2] + 6*b^3*n^2*x*Log[c*x^n]*Log[1 + d*f*x^2] - 3*b*n*x*(a + b*Log[c*x^n])^2*Log[1 + d*f*x^2] + x*(a + b*Log[c*x^n])^3*Log[1 + d*f*x^2] - (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(Sqrt[-d]*Sqrt[f]*x)])/(Sqrt[-d]*Sqrt[f]) + (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(Sqrt[-d]*Sqrt[f]*x)])/(Sqrt[-d]*Sqrt[f]) + (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f]) - (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f]) - ((6*I)*b^3*n^3*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x])/(Sqrt[d]*Sqrt[f]) + ((6*I)*b^3*n^3*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x])/(Sqrt[d]*Sqrt[f]) + (6*b^3*n^3*PolyLog[3, -(Sqrt[-d]*Sqrt[f]*x)])/(Sqrt[-d]*Sqrt[f]) - (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(Sqrt[-d]*Sqrt[f]*x)])/(Sqrt[-d]*Sqrt[f]) - (6*b^3*n^3*PolyLog[3, Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f]) + (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f]) + (6*b^3*n^3*PolyLog[4, -(Sqrt[-d]*Sqrt[f]*x)])/(Sqrt[-d]*Sqrt[f]) - (6*b^3*n^3*PolyLog[4, Sqrt[-d]*Sqrt[f]*x])/(Sqrt[-d]*Sqrt[f])","A",42,17,25,0.6800,1,"{2296, 2295, 2371, 6, 321, 203, 2351, 2324, 12, 4848, 2391, 2353, 2330, 2317, 2374, 6589, 2383}"
45,1,849,0,1.0403804,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^2\right)\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^2)])/x^2,x]","12 b^3 \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) n^3-\frac{6 b^3 \log \left(d f x^2+1\right) n^3}{x}-6 i b^3 \sqrt{d} \sqrt{f} \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right) n^3+6 i b^3 \sqrt{d} \sqrt{f} \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right) n^3+6 b^3 \sqrt{-d} \sqrt{f} \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right) n^3-6 b^3 \sqrt{-d} \sqrt{f} \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right) n^3-6 b^3 \sqrt{-d} \sqrt{f} \text{PolyLog}\left(4,-\sqrt{-d} \sqrt{f} x\right) n^3+6 b^3 \sqrt{-d} \sqrt{f} \text{PolyLog}\left(4,\sqrt{-d} \sqrt{f} x\right) n^3+12 b^2 \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right) n^2-\frac{6 b^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d f x^2+1\right) n^2}{x}-6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) n^2+6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) n^2+6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right) n^2-6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right) n^2+3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\sqrt{-d} \sqrt{f} x\right) n-3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\sqrt{-d} \sqrt{f} x+1\right) n-\frac{3 b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d f x^2+1\right) n}{x}-3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) n+3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) n+\sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\sqrt{-d} \sqrt{f} x\right)-\sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\sqrt{-d} \sqrt{f} x+1\right)-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d f x^2+1\right)}{x}","12 b^3 \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) n^3-\frac{6 b^3 \log \left(d f x^2+1\right) n^3}{x}-6 i b^3 \sqrt{d} \sqrt{f} \text{PolyLog}\left(2,-i \sqrt{d} \sqrt{f} x\right) n^3+6 i b^3 \sqrt{d} \sqrt{f} \text{PolyLog}\left(2,i \sqrt{d} \sqrt{f} x\right) n^3+6 b^3 \sqrt{-d} \sqrt{f} \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right) n^3-6 b^3 \sqrt{-d} \sqrt{f} \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right) n^3-6 b^3 \sqrt{-d} \sqrt{f} \text{PolyLog}\left(4,-\sqrt{-d} \sqrt{f} x\right) n^3+6 b^3 \sqrt{-d} \sqrt{f} \text{PolyLog}\left(4,\sqrt{-d} \sqrt{f} x\right) n^3+12 b^2 \sqrt{d} \sqrt{f} \tan ^{-1}\left(\sqrt{d} \sqrt{f} x\right) \left(a+b \log \left(c x^n\right)\right) n^2-\frac{6 b^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d f x^2+1\right) n^2}{x}-6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) n^2+6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) n^2+6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\sqrt{-d} \sqrt{f} x\right) n^2-6 b^2 \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\sqrt{-d} \sqrt{f} x\right) n^2+3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\sqrt{-d} \sqrt{f} x\right) n-3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\sqrt{-d} \sqrt{f} x+1\right) n-\frac{3 b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d f x^2+1\right) n}{x}-3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\sqrt{-d} \sqrt{f} x\right) n+3 b \sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\sqrt{-d} \sqrt{f} x\right) n+\sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\sqrt{-d} \sqrt{f} x\right)-\sqrt{-d} \sqrt{f} \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\sqrt{-d} \sqrt{f} x+1\right)-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d f x^2+1\right)}{x}",1,"12*b^3*Sqrt[d]*Sqrt[f]*n^3*ArcTan[Sqrt[d]*Sqrt[f]*x] + 12*b^2*Sqrt[d]*Sqrt[f]*n^2*ArcTan[Sqrt[d]*Sqrt[f]*x]*(a + b*Log[c*x^n]) + 3*b*Sqrt[-d]*Sqrt[f]*n*(a + b*Log[c*x^n])^2*Log[1 - Sqrt[-d]*Sqrt[f]*x] + Sqrt[-d]*Sqrt[f]*(a + b*Log[c*x^n])^3*Log[1 - Sqrt[-d]*Sqrt[f]*x] - 3*b*Sqrt[-d]*Sqrt[f]*n*(a + b*Log[c*x^n])^2*Log[1 + Sqrt[-d]*Sqrt[f]*x] - Sqrt[-d]*Sqrt[f]*(a + b*Log[c*x^n])^3*Log[1 + Sqrt[-d]*Sqrt[f]*x] - (6*b^3*n^3*Log[1 + d*f*x^2])/x - (6*b^2*n^2*(a + b*Log[c*x^n])*Log[1 + d*f*x^2])/x - (3*b*n*(a + b*Log[c*x^n])^2*Log[1 + d*f*x^2])/x - ((a + b*Log[c*x^n])^3*Log[1 + d*f*x^2])/x - 6*b^2*Sqrt[-d]*Sqrt[f]*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(Sqrt[-d]*Sqrt[f]*x)] - 3*b*Sqrt[-d]*Sqrt[f]*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(Sqrt[-d]*Sqrt[f]*x)] + 6*b^2*Sqrt[-d]*Sqrt[f]*n^2*(a + b*Log[c*x^n])*PolyLog[2, Sqrt[-d]*Sqrt[f]*x] + 3*b*Sqrt[-d]*Sqrt[f]*n*(a + b*Log[c*x^n])^2*PolyLog[2, Sqrt[-d]*Sqrt[f]*x] - (6*I)*b^3*Sqrt[d]*Sqrt[f]*n^3*PolyLog[2, (-I)*Sqrt[d]*Sqrt[f]*x] + (6*I)*b^3*Sqrt[d]*Sqrt[f]*n^3*PolyLog[2, I*Sqrt[d]*Sqrt[f]*x] + 6*b^3*Sqrt[-d]*Sqrt[f]*n^3*PolyLog[3, -(Sqrt[-d]*Sqrt[f]*x)] + 6*b^2*Sqrt[-d]*Sqrt[f]*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(Sqrt[-d]*Sqrt[f]*x)] - 6*b^3*Sqrt[-d]*Sqrt[f]*n^3*PolyLog[3, Sqrt[-d]*Sqrt[f]*x] - 6*b^2*Sqrt[-d]*Sqrt[f]*n^2*(a + b*Log[c*x^n])*PolyLog[3, Sqrt[-d]*Sqrt[f]*x] - 6*b^3*Sqrt[-d]*Sqrt[f]*n^3*PolyLog[4, -(Sqrt[-d]*Sqrt[f]*x)] + 6*b^3*Sqrt[-d]*Sqrt[f]*n^3*PolyLog[4, Sqrt[-d]*Sqrt[f]*x]","A",26,13,28,0.4643,1,"{2305, 2304, 2378, 203, 2324, 12, 4848, 2391, 2330, 2317, 2374, 6589, 2383}"
46,1,350,0,0.2765425,"\int x^2 \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]),x]","-\frac{2 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{3 d^6 f^6}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{12 d^2 f^2}+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 d^3 f^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{6 d^4 f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{3 d^5 f^5}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^6 f^6}+\frac{1}{3} x^3 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{15 d f}-\frac{1}{18} x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{5 b n x^2}{72 d^2 f^2}-\frac{b n x^{3/2}}{9 d^3 f^3}+\frac{2 b n x}{9 d^4 f^4}-\frac{7 b n \sqrt{x}}{9 d^5 f^5}+\frac{b n \log \left(d f \sqrt{x}+1\right)}{9 d^6 f^6}-\frac{11 b n x^{5/2}}{225 d f}-\frac{1}{9} b n x^3 \log \left(d f \sqrt{x}+1\right)+\frac{1}{27} b n x^3","-\frac{2 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{3 d^6 f^6}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{12 d^2 f^2}+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 d^3 f^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{6 d^4 f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{3 d^5 f^5}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^6 f^6}+\frac{1}{3} x^3 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{15 d f}-\frac{1}{18} x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{5 b n x^2}{72 d^2 f^2}-\frac{b n x^{3/2}}{9 d^3 f^3}+\frac{2 b n x}{9 d^4 f^4}-\frac{7 b n \sqrt{x}}{9 d^5 f^5}+\frac{b n \log \left(d f \sqrt{x}+1\right)}{9 d^6 f^6}-\frac{11 b n x^{5/2}}{225 d f}-\frac{1}{9} b n x^3 \log \left(d f \sqrt{x}+1\right)+\frac{1}{27} b n x^3",1,"(-7*b*n*Sqrt[x])/(9*d^5*f^5) + (2*b*n*x)/(9*d^4*f^4) - (b*n*x^(3/2))/(9*d^3*f^3) + (5*b*n*x^2)/(72*d^2*f^2) - (11*b*n*x^(5/2))/(225*d*f) + (b*n*x^3)/27 + (b*n*Log[1 + d*f*Sqrt[x]])/(9*d^6*f^6) - (b*n*x^3*Log[1 + d*f*Sqrt[x]])/9 + (Sqrt[x]*(a + b*Log[c*x^n]))/(3*d^5*f^5) - (x*(a + b*Log[c*x^n]))/(6*d^4*f^4) + (x^(3/2)*(a + b*Log[c*x^n]))/(9*d^3*f^3) - (x^2*(a + b*Log[c*x^n]))/(12*d^2*f^2) + (x^(5/2)*(a + b*Log[c*x^n]))/(15*d*f) - (x^3*(a + b*Log[c*x^n]))/18 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(3*d^6*f^6) + (x^3*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/3 - (2*b*n*PolyLog[2, -(d*f*Sqrt[x])])/(3*d^6*f^6)","A",7,5,28,0.1786,1,"{2454, 2395, 43, 2376, 2391}"
47,1,268,0,0.1921554,"\int x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]),x]","-\frac{b n \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{d^4 f^4}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 d^3 f^3}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^4 f^4}+\frac{1}{2} x^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{6 d f}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{3 b n x}{8 d^2 f^2}-\frac{5 b n \sqrt{x}}{4 d^3 f^3}+\frac{b n \log \left(d f \sqrt{x}+1\right)}{4 d^4 f^4}-\frac{7 b n x^{3/2}}{36 d f}-\frac{1}{4} b n x^2 \log \left(d f \sqrt{x}+1\right)+\frac{1}{8} b n x^2","-\frac{b n \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{d^4 f^4}-\frac{x \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 d^3 f^3}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^4 f^4}+\frac{1}{2} x^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{6 d f}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{3 b n x}{8 d^2 f^2}-\frac{5 b n \sqrt{x}}{4 d^3 f^3}+\frac{b n \log \left(d f \sqrt{x}+1\right)}{4 d^4 f^4}-\frac{7 b n x^{3/2}}{36 d f}-\frac{1}{4} b n x^2 \log \left(d f \sqrt{x}+1\right)+\frac{1}{8} b n x^2",1,"(-5*b*n*Sqrt[x])/(4*d^3*f^3) + (3*b*n*x)/(8*d^2*f^2) - (7*b*n*x^(3/2))/(36*d*f) + (b*n*x^2)/8 + (b*n*Log[1 + d*f*Sqrt[x]])/(4*d^4*f^4) - (b*n*x^2*Log[1 + d*f*Sqrt[x]])/4 + (Sqrt[x]*(a + b*Log[c*x^n]))/(2*d^3*f^3) - (x*(a + b*Log[c*x^n]))/(4*d^2*f^2) + (x^(3/2)*(a + b*Log[c*x^n]))/(6*d*f) - (x^2*(a + b*Log[c*x^n]))/8 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(2*d^4*f^4) + (x^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/2 - (b*n*PolyLog[2, -(d*f*Sqrt[x])])/(d^4*f^4)","A",7,5,26,0.1923,1,"{2454, 2395, 43, 2376, 2391}"
48,1,172,0,0.1048734,"\int \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]),x]","-\frac{2 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{d^2 f^2}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{d f}-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)+\frac{b n \log \left(d f \sqrt{x}+1\right)}{d^2 f^2}-\frac{3 b n \sqrt{x}}{d f}-b n x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right)+b n x","-\frac{2 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{d^2 f^2}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{d f}-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)+\frac{b n \log \left(d f \sqrt{x}+1\right)}{d^2 f^2}-\frac{3 b n \sqrt{x}}{d f}-b n x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right)+b n x",1,"(-3*b*n*Sqrt[x])/(d*f) + b*n*x - b*n*x*Log[d*(d^(-1) + f*Sqrt[x])] + (b*n*Log[1 + d*f*Sqrt[x]])/(d^2*f^2) + (Sqrt[x]*(a + b*Log[c*x^n]))/(d*f) - (x*(a + b*Log[c*x^n]))/2 + x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]) - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(d^2*f^2) - (2*b*n*PolyLog[2, -(d*f*Sqrt[x])])/(d^2*f^2)","A",7,5,25,0.2000,1,"{2448, 266, 43, 2370, 2391}"
49,1,39,0,0.0321699,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]))/x,x]","4 b n \text{PolyLog}\left(3,-d f \sqrt{x}\right)-2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)","4 b n \text{PolyLog}\left(3,-d f \sqrt{x}\right)-2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)",1,"-2*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])] + 4*b*n*PolyLog[3, -(d*f*Sqrt[x])]","A",2,2,28,0.07143,1,"{2374, 6589}"
50,1,196,0,0.1511449,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]))/x^2,x]","2 b d^2 f^2 n \text{PolyLog}\left(2,-d f \sqrt{x}\right)+d^2 f^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} d^2 f^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d f \left(a+b \log \left(c x^n\right)\right)}{\sqrt{x}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{1}{4} b d^2 f^2 n \log ^2(x)+b d^2 f^2 n \log \left(d f \sqrt{x}+1\right)-\frac{1}{2} b d^2 f^2 n \log (x)-\frac{3 b d f n}{\sqrt{x}}-\frac{b n \log \left(d f \sqrt{x}+1\right)}{x}","2 b d^2 f^2 n \text{PolyLog}\left(2,-d f \sqrt{x}\right)+d^2 f^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} d^2 f^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d f \left(a+b \log \left(c x^n\right)\right)}{\sqrt{x}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{1}{4} b d^2 f^2 n \log ^2(x)+b d^2 f^2 n \log \left(d f \sqrt{x}+1\right)-\frac{1}{2} b d^2 f^2 n \log (x)-\frac{3 b d f n}{\sqrt{x}}-\frac{b n \log \left(d f \sqrt{x}+1\right)}{x}",1,"(-3*b*d*f*n)/Sqrt[x] + b*d^2*f^2*n*Log[1 + d*f*Sqrt[x]] - (b*n*Log[1 + d*f*Sqrt[x]])/x - (b*d^2*f^2*n*Log[x])/2 + (b*d^2*f^2*n*Log[x]^2)/4 - (d*f*(a + b*Log[c*x^n]))/Sqrt[x] + d^2*f^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]) - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/x - (d^2*f^2*Log[x]*(a + b*Log[c*x^n]))/2 + 2*b*d^2*f^2*n*PolyLog[2, -(d*f*Sqrt[x])]","A",8,6,28,0.2143,1,"{2454, 2395, 44, 2376, 2391, 2301}"
51,1,289,0,0.2046229,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]))/x^3,x]","b d^4 f^4 n \text{PolyLog}\left(2,-d f \sqrt{x}\right)+\frac{1}{2} d^4 f^4 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} d^4 f^4 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d^3 f^3 \left(a+b \log \left(c x^n\right)\right)}{2 \sqrt{x}}+\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)}{4 x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)}{6 x^{3/2}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{5 b d^3 f^3 n}{4 \sqrt{x}}+\frac{3 b d^2 f^2 n}{8 x}+\frac{1}{8} b d^4 f^4 n \log ^2(x)+\frac{1}{4} b d^4 f^4 n \log \left(d f \sqrt{x}+1\right)-\frac{1}{8} b d^4 f^4 n \log (x)-\frac{7 b d f n}{36 x^{3/2}}-\frac{b n \log \left(d f \sqrt{x}+1\right)}{4 x^2}","b d^4 f^4 n \text{PolyLog}\left(2,-d f \sqrt{x}\right)+\frac{1}{2} d^4 f^4 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} d^4 f^4 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d^3 f^3 \left(a+b \log \left(c x^n\right)\right)}{2 \sqrt{x}}+\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)}{4 x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)}{6 x^{3/2}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{5 b d^3 f^3 n}{4 \sqrt{x}}+\frac{3 b d^2 f^2 n}{8 x}+\frac{1}{8} b d^4 f^4 n \log ^2(x)+\frac{1}{4} b d^4 f^4 n \log \left(d f \sqrt{x}+1\right)-\frac{1}{8} b d^4 f^4 n \log (x)-\frac{7 b d f n}{36 x^{3/2}}-\frac{b n \log \left(d f \sqrt{x}+1\right)}{4 x^2}",1,"(-7*b*d*f*n)/(36*x^(3/2)) + (3*b*d^2*f^2*n)/(8*x) - (5*b*d^3*f^3*n)/(4*Sqrt[x]) + (b*d^4*f^4*n*Log[1 + d*f*Sqrt[x]])/4 - (b*n*Log[1 + d*f*Sqrt[x]])/(4*x^2) - (b*d^4*f^4*n*Log[x])/8 + (b*d^4*f^4*n*Log[x]^2)/8 - (d*f*(a + b*Log[c*x^n]))/(6*x^(3/2)) + (d^2*f^2*(a + b*Log[c*x^n]))/(4*x) - (d^3*f^3*(a + b*Log[c*x^n]))/(2*Sqrt[x]) + (d^4*f^4*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/2 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(2*x^2) - (d^4*f^4*Log[x]*(a + b*Log[c*x^n]))/4 + b*d^4*f^4*n*PolyLog[2, -(d*f*Sqrt[x])]","A",8,6,28,0.2143,1,"{2454, 2395, 44, 2376, 2391, 2301}"
52,1,372,0,0.2518792,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]))/x^4,x]","\frac{2}{3} b d^6 f^6 n \text{PolyLog}\left(2,-d f \sqrt{x}\right)+\frac{1}{3} d^6 f^6 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{6} d^6 f^6 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d^5 f^5 \left(a+b \log \left(c x^n\right)\right)}{3 \sqrt{x}}+\frac{d^4 f^4 \left(a+b \log \left(c x^n\right)\right)}{6 x}-\frac{d^3 f^3 \left(a+b \log \left(c x^n\right)\right)}{9 x^{3/2}}+\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)}{12 x^2}-\frac{d f \left(a+b \log \left(c x^n\right)\right)}{15 x^{5/2}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{b d^3 f^3 n}{9 x^{3/2}}+\frac{5 b d^2 f^2 n}{72 x^2}-\frac{7 b d^5 f^5 n}{9 \sqrt{x}}+\frac{2 b d^4 f^4 n}{9 x}+\frac{1}{12} b d^6 f^6 n \log ^2(x)+\frac{1}{9} b d^6 f^6 n \log \left(d f \sqrt{x}+1\right)-\frac{1}{18} b d^6 f^6 n \log (x)-\frac{11 b d f n}{225 x^{5/2}}-\frac{b n \log \left(d f \sqrt{x}+1\right)}{9 x^3}","\frac{2}{3} b d^6 f^6 n \text{PolyLog}\left(2,-d f \sqrt{x}\right)+\frac{1}{3} d^6 f^6 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{6} d^6 f^6 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d^5 f^5 \left(a+b \log \left(c x^n\right)\right)}{3 \sqrt{x}}+\frac{d^4 f^4 \left(a+b \log \left(c x^n\right)\right)}{6 x}-\frac{d^3 f^3 \left(a+b \log \left(c x^n\right)\right)}{9 x^{3/2}}+\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)}{12 x^2}-\frac{d f \left(a+b \log \left(c x^n\right)\right)}{15 x^{5/2}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{3 x^3}-\frac{b d^3 f^3 n}{9 x^{3/2}}+\frac{5 b d^2 f^2 n}{72 x^2}-\frac{7 b d^5 f^5 n}{9 \sqrt{x}}+\frac{2 b d^4 f^4 n}{9 x}+\frac{1}{12} b d^6 f^6 n \log ^2(x)+\frac{1}{9} b d^6 f^6 n \log \left(d f \sqrt{x}+1\right)-\frac{1}{18} b d^6 f^6 n \log (x)-\frac{11 b d f n}{225 x^{5/2}}-\frac{b n \log \left(d f \sqrt{x}+1\right)}{9 x^3}",1,"(-11*b*d*f*n)/(225*x^(5/2)) + (5*b*d^2*f^2*n)/(72*x^2) - (b*d^3*f^3*n)/(9*x^(3/2)) + (2*b*d^4*f^4*n)/(9*x) - (7*b*d^5*f^5*n)/(9*Sqrt[x]) + (b*d^6*f^6*n*Log[1 + d*f*Sqrt[x]])/9 - (b*n*Log[1 + d*f*Sqrt[x]])/(9*x^3) - (b*d^6*f^6*n*Log[x])/18 + (b*d^6*f^6*n*Log[x]^2)/12 - (d*f*(a + b*Log[c*x^n]))/(15*x^(5/2)) + (d^2*f^2*(a + b*Log[c*x^n]))/(12*x^2) - (d^3*f^3*(a + b*Log[c*x^n]))/(9*x^(3/2)) + (d^4*f^4*(a + b*Log[c*x^n]))/(6*x) - (d^5*f^5*(a + b*Log[c*x^n]))/(3*Sqrt[x]) + (d^6*f^6*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/3 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(3*x^3) - (d^6*f^6*Log[x]*(a + b*Log[c*x^n]))/6 + (2*b*d^6*f^6*n*PolyLog[2, -(d*f*Sqrt[x])])/3","A",8,6,28,0.2143,1,"{2454, 2395, 44, 2376, 2391, 2301}"
53,1,708,0,0.6382866,"\int x^2 \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[x^2*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","-\frac{4 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^6 f^6}+\frac{4 b^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{9 d^6 f^6}+\frac{8 b^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right)}{3 d^6 f^6}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{12 d^2 f^2}+\frac{5 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{36 d^2 f^2}+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{9 d^3 f^3}-\frac{2 b n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 d^3 f^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{6 d^4 f^4}+\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{9 d^4 f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{3 d^5 f^5}-\frac{14 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{9 d^5 f^5}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 d^6 f^6}+\frac{2 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 d^6 f^6}+\frac{1}{3} x^3 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^{5/2} \left(a+b \log \left(c x^n\right)\right)^2}{15 d f}-\frac{22 b n x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{225 d f}-\frac{1}{18} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{2}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{a b n x}{3 d^4 f^4}+\frac{b^2 n x \log \left(c x^n\right)}{3 d^4 f^4}-\frac{19 b^2 n^2 x^2}{216 d^2 f^2}+\frac{14 b^2 n^2 x^{3/2}}{81 d^3 f^3}-\frac{13 b^2 n^2 x}{27 d^4 f^4}+\frac{86 b^2 n^2 \sqrt{x}}{27 d^5 f^5}-\frac{2 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{27 d^6 f^6}+\frac{182 b^2 n^2 x^{5/2}}{3375 d f}+\frac{2}{27} b^2 n^2 x^3 \log \left(d f \sqrt{x}+1\right)-\frac{1}{27} b^2 n^2 x^3","-\frac{4 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 d^6 f^6}+\frac{4 b^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{9 d^6 f^6}+\frac{8 b^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right)}{3 d^6 f^6}-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)^2}{12 d^2 f^2}+\frac{5 b n x^2 \left(a+b \log \left(c x^n\right)\right)}{36 d^2 f^2}+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{9 d^3 f^3}-\frac{2 b n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 d^3 f^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{6 d^4 f^4}+\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{9 d^4 f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{3 d^5 f^5}-\frac{14 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{9 d^5 f^5}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 d^6 f^6}+\frac{2 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 d^6 f^6}+\frac{1}{3} x^3 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^{5/2} \left(a+b \log \left(c x^n\right)\right)^2}{15 d f}-\frac{22 b n x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{225 d f}-\frac{1}{18} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{2}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{a b n x}{3 d^4 f^4}+\frac{b^2 n x \log \left(c x^n\right)}{3 d^4 f^4}-\frac{19 b^2 n^2 x^2}{216 d^2 f^2}+\frac{14 b^2 n^2 x^{3/2}}{81 d^3 f^3}-\frac{13 b^2 n^2 x}{27 d^4 f^4}+\frac{86 b^2 n^2 \sqrt{x}}{27 d^5 f^5}-\frac{2 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{27 d^6 f^6}+\frac{182 b^2 n^2 x^{5/2}}{3375 d f}+\frac{2}{27} b^2 n^2 x^3 \log \left(d f \sqrt{x}+1\right)-\frac{1}{27} b^2 n^2 x^3",1,"(86*b^2*n^2*Sqrt[x])/(27*d^5*f^5) + (a*b*n*x)/(3*d^4*f^4) - (13*b^2*n^2*x)/(27*d^4*f^4) + (14*b^2*n^2*x^(3/2))/(81*d^3*f^3) - (19*b^2*n^2*x^2)/(216*d^2*f^2) + (182*b^2*n^2*x^(5/2))/(3375*d*f) - (b^2*n^2*x^3)/27 - (2*b^2*n^2*Log[1 + d*f*Sqrt[x]])/(27*d^6*f^6) + (2*b^2*n^2*x^3*Log[1 + d*f*Sqrt[x]])/27 + (b^2*n*x*Log[c*x^n])/(3*d^4*f^4) - (14*b*n*Sqrt[x]*(a + b*Log[c*x^n]))/(9*d^5*f^5) + (b*n*x*(a + b*Log[c*x^n]))/(9*d^4*f^4) - (2*b*n*x^(3/2)*(a + b*Log[c*x^n]))/(9*d^3*f^3) + (5*b*n*x^2*(a + b*Log[c*x^n]))/(36*d^2*f^2) - (22*b*n*x^(5/2)*(a + b*Log[c*x^n]))/(225*d*f) + (2*b*n*x^3*(a + b*Log[c*x^n]))/27 + (2*b*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(9*d^6*f^6) - (2*b*n*x^3*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/9 + (Sqrt[x]*(a + b*Log[c*x^n])^2)/(3*d^5*f^5) - (x*(a + b*Log[c*x^n])^2)/(6*d^4*f^4) + (x^(3/2)*(a + b*Log[c*x^n])^2)/(9*d^3*f^3) - (x^2*(a + b*Log[c*x^n])^2)/(12*d^2*f^2) + (x^(5/2)*(a + b*Log[c*x^n])^2)/(15*d*f) - (x^3*(a + b*Log[c*x^n])^2)/18 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/(3*d^6*f^6) + (x^3*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/3 + (4*b^2*n^2*PolyLog[2, -(d*f*Sqrt[x])])/(9*d^6*f^6) - (4*b*n*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])])/(3*d^6*f^6) + (8*b^2*n^2*PolyLog[3, -(d*f*Sqrt[x])])/(3*d^6*f^6)","A",18,10,30,0.3333,1,"{2454, 2395, 43, 2377, 2295, 2304, 2374, 6589, 2376, 2391}"
54,1,557,0,0.4645177,"\int x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","-\frac{2 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4 f^4}+\frac{b^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{d^4 f^4}+\frac{4 b^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right)}{d^4 f^4}+\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}+\frac{b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^4 f^4}-\frac{5 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 d^3 f^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{4 d^2 f^2}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 d^4 f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{2 d^3 f^3}-\frac{7 b n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{18 d f}-\frac{1}{2} b n x^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{6 d f}+\frac{1}{2} x^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{a b n x}{2 d^2 f^2}+\frac{b^2 n x \log \left(c x^n\right)}{2 d^2 f^2}-\frac{7 b^2 n^2 x}{8 d^2 f^2}+\frac{21 b^2 n^2 \sqrt{x}}{4 d^3 f^3}-\frac{b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{4 d^4 f^4}+\frac{37 b^2 n^2 x^{3/2}}{108 d f}+\frac{1}{4} b^2 n^2 x^2 \log \left(d f \sqrt{x}+1\right)-\frac{3}{16} b^2 n^2 x^2","-\frac{2 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^4 f^4}+\frac{b^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{d^4 f^4}+\frac{4 b^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right)}{d^4 f^4}+\frac{b n x \left(a+b \log \left(c x^n\right)\right)}{4 d^2 f^2}+\frac{b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 d^4 f^4}-\frac{5 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 d^3 f^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^2}{4 d^2 f^2}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 d^4 f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{2 d^3 f^3}-\frac{7 b n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{18 d f}-\frac{1}{2} b n x^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{6 d f}+\frac{1}{2} x^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{a b n x}{2 d^2 f^2}+\frac{b^2 n x \log \left(c x^n\right)}{2 d^2 f^2}-\frac{7 b^2 n^2 x}{8 d^2 f^2}+\frac{21 b^2 n^2 \sqrt{x}}{4 d^3 f^3}-\frac{b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{4 d^4 f^4}+\frac{37 b^2 n^2 x^{3/2}}{108 d f}+\frac{1}{4} b^2 n^2 x^2 \log \left(d f \sqrt{x}+1\right)-\frac{3}{16} b^2 n^2 x^2",1,"(21*b^2*n^2*Sqrt[x])/(4*d^3*f^3) + (a*b*n*x)/(2*d^2*f^2) - (7*b^2*n^2*x)/(8*d^2*f^2) + (37*b^2*n^2*x^(3/2))/(108*d*f) - (3*b^2*n^2*x^2)/16 - (b^2*n^2*Log[1 + d*f*Sqrt[x]])/(4*d^4*f^4) + (b^2*n^2*x^2*Log[1 + d*f*Sqrt[x]])/4 + (b^2*n*x*Log[c*x^n])/(2*d^2*f^2) - (5*b*n*Sqrt[x]*(a + b*Log[c*x^n]))/(2*d^3*f^3) + (b*n*x*(a + b*Log[c*x^n]))/(4*d^2*f^2) - (7*b*n*x^(3/2)*(a + b*Log[c*x^n]))/(18*d*f) + (b*n*x^2*(a + b*Log[c*x^n]))/4 + (b*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(2*d^4*f^4) - (b*n*x^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/2 + (Sqrt[x]*(a + b*Log[c*x^n])^2)/(2*d^3*f^3) - (x*(a + b*Log[c*x^n])^2)/(4*d^2*f^2) + (x^(3/2)*(a + b*Log[c*x^n])^2)/(6*d*f) - (x^2*(a + b*Log[c*x^n])^2)/8 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/(2*d^4*f^4) + (x^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/2 + (b^2*n^2*PolyLog[2, -(d*f*Sqrt[x])])/(d^4*f^4) - (2*b*n*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])])/(d^4*f^4) + (4*b^2*n^2*PolyLog[3, -(d*f*Sqrt[x])])/(d^4*f^4)","A",16,10,28,0.3571,1,"{2454, 2395, 43, 2377, 2295, 2304, 2374, 6589, 2376, 2391}"
55,1,374,0,0.2688208,"\int \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","-\frac{4 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+\frac{4 b^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{d^2 f^2}+\frac{8 b^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right)}{d^2 f^2}+\frac{2 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2 f^2}-2 b n x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{d f}+x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{d f}+b n x \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^2+a b n x+b^2 n x \log \left(c x^n\right)-\frac{2 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{d^2 f^2}+\frac{14 b^2 n^2 \sqrt{x}}{d f}+2 b^2 n^2 x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right)-3 b^2 n^2 x","-\frac{4 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+\frac{4 b^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{d^2 f^2}+\frac{8 b^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right)}{d^2 f^2}+\frac{2 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2 f^2}-2 b n x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{d f}+x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{d f}+b n x \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^2+a b n x+b^2 n x \log \left(c x^n\right)-\frac{2 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{d^2 f^2}+\frac{14 b^2 n^2 \sqrt{x}}{d f}+2 b^2 n^2 x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right)-3 b^2 n^2 x",1,"(14*b^2*n^2*Sqrt[x])/(d*f) + a*b*n*x - 3*b^2*n^2*x + 2*b^2*n^2*x*Log[d*(d^(-1) + f*Sqrt[x])] - (2*b^2*n^2*Log[1 + d*f*Sqrt[x]])/(d^2*f^2) + b^2*n*x*Log[c*x^n] - (6*b*n*Sqrt[x]*(a + b*Log[c*x^n]))/(d*f) + b*n*x*(a + b*Log[c*x^n]) - 2*b*n*x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]) + (2*b*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(d^2*f^2) + (Sqrt[x]*(a + b*Log[c*x^n])^2)/(d*f) - (x*(a + b*Log[c*x^n])^2)/2 + x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/(d^2*f^2) + (4*b^2*n^2*PolyLog[2, -(d*f*Sqrt[x])])/(d^2*f^2) - (4*b*n*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])])/(d^2*f^2) + (8*b^2*n^2*PolyLog[3, -(d*f*Sqrt[x])])/(d^2*f^2)","A",14,9,27,0.3333,1,"{2448, 266, 43, 2370, 2295, 2304, 2391, 2374, 6589}"
56,1,70,0,0.0670089,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Int[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x,x]","8 b n \text{PolyLog}\left(3,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)-2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2-16 b^2 n^2 \text{PolyLog}\left(4,-d f \sqrt{x}\right)","8 b n \text{PolyLog}\left(3,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)-2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2-16 b^2 n^2 \text{PolyLog}\left(4,-d f \sqrt{x}\right)",1,"-2*(a + b*Log[c*x^n])^2*PolyLog[2, -(d*f*Sqrt[x])] + 8*b*n*(a + b*Log[c*x^n])*PolyLog[3, -(d*f*Sqrt[x])] - 16*b^2*n^2*PolyLog[4, -(d*f*Sqrt[x])]","A",3,3,30,0.1000,1,"{2374, 2383, 6589}"
57,1,389,0,0.4088888,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x^2} \, dx","Int[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x^2,x]","4 b d^2 f^2 n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)+4 b^2 d^2 f^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right)-8 b^2 d^2 f^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right)-\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^3}{6 b n}+d^2 f^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+2 b d^2 f^2 n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-b d^2 f^2 n \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{x}}-\frac{2 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{6 b d f n \left(a+b \log \left(c x^n\right)\right)}{\sqrt{x}}+\frac{1}{2} b^2 d^2 f^2 n^2 \log ^2(x)+2 b^2 d^2 f^2 n^2 \log \left(d f \sqrt{x}+1\right)-b^2 d^2 f^2 n^2 \log (x)-\frac{14 b^2 d f n^2}{\sqrt{x}}-\frac{2 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{x}","4 b d^2 f^2 n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)+4 b^2 d^2 f^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right)-8 b^2 d^2 f^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right)-\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^3}{6 b n}+d^2 f^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+2 b d^2 f^2 n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-b d^2 f^2 n \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{x}}-\frac{2 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{6 b d f n \left(a+b \log \left(c x^n\right)\right)}{\sqrt{x}}+\frac{1}{2} b^2 d^2 f^2 n^2 \log ^2(x)+2 b^2 d^2 f^2 n^2 \log \left(d f \sqrt{x}+1\right)-b^2 d^2 f^2 n^2 \log (x)-\frac{14 b^2 d f n^2}{\sqrt{x}}-\frac{2 b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{x}",1,"(-14*b^2*d*f*n^2)/Sqrt[x] + 2*b^2*d^2*f^2*n^2*Log[1 + d*f*Sqrt[x]] - (2*b^2*n^2*Log[1 + d*f*Sqrt[x]])/x - b^2*d^2*f^2*n^2*Log[x] + (b^2*d^2*f^2*n^2*Log[x]^2)/2 - (6*b*d*f*n*(a + b*Log[c*x^n]))/Sqrt[x] + 2*b*d^2*f^2*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]) - (2*b*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/x - b*d^2*f^2*n*Log[x]*(a + b*Log[c*x^n]) - (d*f*(a + b*Log[c*x^n])^2)/Sqrt[x] + d^2*f^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/x - (d^2*f^2*(a + b*Log[c*x^n])^3)/(6*b*n) + 4*b^2*d^2*f^2*n^2*PolyLog[2, -(d*f*Sqrt[x])] + 4*b*d^2*f^2*n*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])] - 8*b^2*d^2*f^2*n^2*PolyLog[3, -(d*f*Sqrt[x])]","A",17,14,30,0.4667,1,"{2454, 2395, 44, 2377, 2304, 2376, 2391, 2301, 2374, 6589, 2366, 12, 2302, 30}"
58,1,555,0,0.5502144,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x^3} \, dx","Int[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x^3,x]","2 b d^4 f^4 n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)+b^2 d^4 f^4 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right)-4 b^2 d^4 f^4 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right)-\frac{d^4 f^4 \left(a+b \log \left(c x^n\right)\right)^3}{12 b n}+\frac{1}{2} d^4 f^4 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b d^4 f^4 n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b d^4 f^4 n \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d^3 f^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 \sqrt{x}}-\frac{5 b d^3 f^3 n \left(a+b \log \left(c x^n\right)\right)}{2 \sqrt{x}}+\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^2}{4 x}+\frac{3 b d^2 f^2 n \left(a+b \log \left(c x^n\right)\right)}{4 x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)^2}{6 x^{3/2}}-\frac{7 b d f n \left(a+b \log \left(c x^n\right)\right)}{18 x^{3/2}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{21 b^2 d^3 f^3 n^2}{4 \sqrt{x}}+\frac{7 b^2 d^2 f^2 n^2}{8 x}+\frac{1}{8} b^2 d^4 f^4 n^2 \log ^2(x)+\frac{1}{4} b^2 d^4 f^4 n^2 \log \left(d f \sqrt{x}+1\right)-\frac{1}{8} b^2 d^4 f^4 n^2 \log (x)-\frac{37 b^2 d f n^2}{108 x^{3/2}}-\frac{b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{4 x^2}","2 b d^4 f^4 n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)+b^2 d^4 f^4 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right)-4 b^2 d^4 f^4 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right)-\frac{d^4 f^4 \left(a+b \log \left(c x^n\right)\right)^3}{12 b n}+\frac{1}{2} d^4 f^4 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b d^4 f^4 n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b d^4 f^4 n \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{d^3 f^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 \sqrt{x}}-\frac{5 b d^3 f^3 n \left(a+b \log \left(c x^n\right)\right)}{2 \sqrt{x}}+\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^2}{4 x}+\frac{3 b d^2 f^2 n \left(a+b \log \left(c x^n\right)\right)}{4 x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)^2}{6 x^{3/2}}-\frac{7 b d f n \left(a+b \log \left(c x^n\right)\right)}{18 x^{3/2}}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{21 b^2 d^3 f^3 n^2}{4 \sqrt{x}}+\frac{7 b^2 d^2 f^2 n^2}{8 x}+\frac{1}{8} b^2 d^4 f^4 n^2 \log ^2(x)+\frac{1}{4} b^2 d^4 f^4 n^2 \log \left(d f \sqrt{x}+1\right)-\frac{1}{8} b^2 d^4 f^4 n^2 \log (x)-\frac{37 b^2 d f n^2}{108 x^{3/2}}-\frac{b^2 n^2 \log \left(d f \sqrt{x}+1\right)}{4 x^2}",1,"(-37*b^2*d*f*n^2)/(108*x^(3/2)) + (7*b^2*d^2*f^2*n^2)/(8*x) - (21*b^2*d^3*f^3*n^2)/(4*Sqrt[x]) + (b^2*d^4*f^4*n^2*Log[1 + d*f*Sqrt[x]])/4 - (b^2*n^2*Log[1 + d*f*Sqrt[x]])/(4*x^2) - (b^2*d^4*f^4*n^2*Log[x])/8 + (b^2*d^4*f^4*n^2*Log[x]^2)/8 - (7*b*d*f*n*(a + b*Log[c*x^n]))/(18*x^(3/2)) + (3*b*d^2*f^2*n*(a + b*Log[c*x^n]))/(4*x) - (5*b*d^3*f^3*n*(a + b*Log[c*x^n]))/(2*Sqrt[x]) + (b*d^4*f^4*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/2 - (b*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(2*x^2) - (b*d^4*f^4*n*Log[x]*(a + b*Log[c*x^n]))/4 - (d*f*(a + b*Log[c*x^n])^2)/(6*x^(3/2)) + (d^2*f^2*(a + b*Log[c*x^n])^2)/(4*x) - (d^3*f^3*(a + b*Log[c*x^n])^2)/(2*Sqrt[x]) + (d^4*f^4*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/2 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/(2*x^2) - (d^4*f^4*(a + b*Log[c*x^n])^3)/(12*b*n) + b^2*d^4*f^4*n^2*PolyLog[2, -(d*f*Sqrt[x])] + 2*b*d^4*f^4*n*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])] - 4*b^2*d^4*f^4*n^2*PolyLog[3, -(d*f*Sqrt[x])]","A",19,14,30,0.4667,1,"{2454, 2395, 44, 2377, 2304, 2376, 2391, 2301, 2374, 6589, 2366, 12, 2302, 30}"
59,1,858,0,0.9353426,"\int x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Int[x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^3,x]","\frac{3}{8} n^3 x^2 b^3-\frac{175 n^3 x^{3/2} b^3}{216 d f}+\frac{45 n^3 x b^3}{16 d^2 f^2}+\frac{3 n^3 \log \left(d \sqrt{x} f+1\right) b^3}{8 d^4 f^4}-\frac{3}{8} n^3 x^2 \log \left(d \sqrt{x} f+1\right) b^3-\frac{9 n^2 x \log \left(c x^n\right) b^3}{4 d^2 f^2}-\frac{3 n^3 \text{PolyLog}\left(2,-d f \sqrt{x}\right) b^3}{2 d^4 f^4}-\frac{6 n^3 \text{PolyLog}\left(3,-d f \sqrt{x}\right) b^3}{d^4 f^4}-\frac{24 n^3 \text{PolyLog}\left(4,-d f \sqrt{x}\right) b^3}{d^4 f^4}-\frac{255 n^3 \sqrt{x} b^3}{8 d^3 f^3}-\frac{9 a n^2 x b^2}{4 d^2 f^2}-\frac{9}{16} n^2 x^2 \left(a+b \log \left(c x^n\right)\right) b^2+\frac{37 n^2 x^{3/2} \left(a+b \log \left(c x^n\right)\right) b^2}{36 d f}-\frac{3 n^2 x \left(a+b \log \left(c x^n\right)\right) b^2}{8 d^2 f^2}-\frac{3 n^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right) b^2}{4 d^4 f^4}+\frac{3}{4} n^2 x^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right) b^2+\frac{63 n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right) b^2}{4 d^3 f^3}+\frac{3 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-d f \sqrt{x}\right) b^2}{d^4 f^4}+\frac{12 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-d f \sqrt{x}\right) b^2}{d^4 f^4}+\frac{3}{8} n x^2 \left(a+b \log \left(c x^n\right)\right)^2 b-\frac{7 n x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2 b}{12 d f}+\frac{9 n x \left(a+b \log \left(c x^n\right)\right)^2 b}{8 d^2 f^2}-\frac{3}{4} n x^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2 b+\frac{3 n \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2 b}{4 d^4 f^4}-\frac{15 n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2 b}{4 d^3 f^3}-\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) b}{d^4 f^4}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^3}{6 d f}-\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{4 d^2 f^2}+\frac{1}{2} x^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{\log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 d^4 f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3}{2 d^3 f^3}","\frac{3}{8} n^3 x^2 b^3-\frac{175 n^3 x^{3/2} b^3}{216 d f}+\frac{45 n^3 x b^3}{16 d^2 f^2}+\frac{3 n^3 \log \left(d \sqrt{x} f+1\right) b^3}{8 d^4 f^4}-\frac{3}{8} n^3 x^2 \log \left(d \sqrt{x} f+1\right) b^3-\frac{9 n^2 x \log \left(c x^n\right) b^3}{4 d^2 f^2}-\frac{3 n^3 \text{PolyLog}\left(2,-d f \sqrt{x}\right) b^3}{2 d^4 f^4}-\frac{6 n^3 \text{PolyLog}\left(3,-d f \sqrt{x}\right) b^3}{d^4 f^4}-\frac{24 n^3 \text{PolyLog}\left(4,-d f \sqrt{x}\right) b^3}{d^4 f^4}-\frac{255 n^3 \sqrt{x} b^3}{8 d^3 f^3}-\frac{9 a n^2 x b^2}{4 d^2 f^2}-\frac{9}{16} n^2 x^2 \left(a+b \log \left(c x^n\right)\right) b^2+\frac{37 n^2 x^{3/2} \left(a+b \log \left(c x^n\right)\right) b^2}{36 d f}-\frac{3 n^2 x \left(a+b \log \left(c x^n\right)\right) b^2}{8 d^2 f^2}-\frac{3 n^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right) b^2}{4 d^4 f^4}+\frac{3}{4} n^2 x^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right) b^2+\frac{63 n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right) b^2}{4 d^3 f^3}+\frac{3 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-d f \sqrt{x}\right) b^2}{d^4 f^4}+\frac{12 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-d f \sqrt{x}\right) b^2}{d^4 f^4}+\frac{3}{8} n x^2 \left(a+b \log \left(c x^n\right)\right)^2 b-\frac{7 n x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2 b}{12 d f}+\frac{9 n x \left(a+b \log \left(c x^n\right)\right)^2 b}{8 d^2 f^2}-\frac{3}{4} n x^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2 b+\frac{3 n \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2 b}{4 d^4 f^4}-\frac{15 n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2 b}{4 d^3 f^3}-\frac{3 n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) b}{d^4 f^4}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^3}{6 d f}-\frac{x \left(a+b \log \left(c x^n\right)\right)^3}{4 d^2 f^2}+\frac{1}{2} x^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3-\frac{\log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 d^4 f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3}{2 d^3 f^3}",1,"(-255*b^3*n^3*Sqrt[x])/(8*d^3*f^3) - (9*a*b^2*n^2*x)/(4*d^2*f^2) + (45*b^3*n^3*x)/(16*d^2*f^2) - (175*b^3*n^3*x^(3/2))/(216*d*f) + (3*b^3*n^3*x^2)/8 + (3*b^3*n^3*Log[1 + d*f*Sqrt[x]])/(8*d^4*f^4) - (3*b^3*n^3*x^2*Log[1 + d*f*Sqrt[x]])/8 - (9*b^3*n^2*x*Log[c*x^n])/(4*d^2*f^2) + (63*b^2*n^2*Sqrt[x]*(a + b*Log[c*x^n]))/(4*d^3*f^3) - (3*b^2*n^2*x*(a + b*Log[c*x^n]))/(8*d^2*f^2) + (37*b^2*n^2*x^(3/2)*(a + b*Log[c*x^n]))/(36*d*f) - (9*b^2*n^2*x^2*(a + b*Log[c*x^n]))/16 - (3*b^2*n^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(4*d^4*f^4) + (3*b^2*n^2*x^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/4 - (15*b*n*Sqrt[x]*(a + b*Log[c*x^n])^2)/(4*d^3*f^3) + (9*b*n*x*(a + b*Log[c*x^n])^2)/(8*d^2*f^2) - (7*b*n*x^(3/2)*(a + b*Log[c*x^n])^2)/(12*d*f) + (3*b*n*x^2*(a + b*Log[c*x^n])^2)/8 + (3*b*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/(4*d^4*f^4) - (3*b*n*x^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/4 + (Sqrt[x]*(a + b*Log[c*x^n])^3)/(2*d^3*f^3) - (x*(a + b*Log[c*x^n])^3)/(4*d^2*f^2) + (x^(3/2)*(a + b*Log[c*x^n])^3)/(6*d*f) - (x^2*(a + b*Log[c*x^n])^3)/8 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^3)/(2*d^4*f^4) + (x^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^3)/2 - (3*b^3*n^3*PolyLog[2, -(d*f*Sqrt[x])])/(2*d^4*f^4) + (3*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])])/(d^4*f^4) - (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(d*f*Sqrt[x])])/(d^4*f^4) - (6*b^3*n^3*PolyLog[3, -(d*f*Sqrt[x])])/(d^4*f^4) + (12*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(d*f*Sqrt[x])])/(d^4*f^4) - (24*b^3*n^3*PolyLog[4, -(d*f*Sqrt[x])])/(d^4*f^4)","A",30,13,28,0.4643,1,"{2454, 2395, 43, 2377, 2296, 2295, 2305, 2304, 2374, 2383, 6589, 2376, 2391}"
60,1,604,0,0.5199948,"\int \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Int[Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^3,x]","\frac{12 b^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+\frac{24 b^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}-\frac{6 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2 f^2}-\frac{12 b^3 n^3 \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{d^2 f^2}-\frac{24 b^3 n^3 \text{PolyLog}\left(3,-d f \sqrt{x}\right)}{d^2 f^2}-\frac{48 b^3 n^3 \text{PolyLog}\left(4,-d f \sqrt{x}\right)}{d^2 f^2}-\frac{6 b^2 n^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+6 b^2 n^2 x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)+\frac{42 b^2 n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{d f}-3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)-6 a b^2 n^2 x+\frac{3 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2 f^2}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{d^2 f^2}-3 b n x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{9 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{d f}+x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3}{d f}+3 b n x \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^3-6 b^3 n^2 x \log \left(c x^n\right)+\frac{6 b^3 n^3 \log \left(d f \sqrt{x}+1\right)}{d^2 f^2}-\frac{90 b^3 n^3 \sqrt{x}}{d f}-6 b^3 n^3 x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right)+12 b^3 n^3 x","\frac{12 b^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+\frac{24 b^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}-\frac{6 b n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2 f^2}-\frac{12 b^3 n^3 \text{PolyLog}\left(2,-d f \sqrt{x}\right)}{d^2 f^2}-\frac{24 b^3 n^3 \text{PolyLog}\left(3,-d f \sqrt{x}\right)}{d^2 f^2}-\frac{48 b^3 n^3 \text{PolyLog}\left(4,-d f \sqrt{x}\right)}{d^2 f^2}-\frac{6 b^2 n^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{d^2 f^2}+6 b^2 n^2 x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)+\frac{42 b^2 n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{d f}-3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)-6 a b^2 n^2 x+\frac{3 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{d^2 f^2}-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{d^2 f^2}-3 b n x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{9 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{d f}+x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3}{d f}+3 b n x \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^3-6 b^3 n^2 x \log \left(c x^n\right)+\frac{6 b^3 n^3 \log \left(d f \sqrt{x}+1\right)}{d^2 f^2}-\frac{90 b^3 n^3 \sqrt{x}}{d f}-6 b^3 n^3 x \log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right)+12 b^3 n^3 x",1,"(-90*b^3*n^3*Sqrt[x])/(d*f) - 6*a*b^2*n^2*x + 12*b^3*n^3*x - 6*b^3*n^3*x*Log[d*(d^(-1) + f*Sqrt[x])] + (6*b^3*n^3*Log[1 + d*f*Sqrt[x]])/(d^2*f^2) - 6*b^3*n^2*x*Log[c*x^n] + (42*b^2*n^2*Sqrt[x]*(a + b*Log[c*x^n]))/(d*f) - 3*b^2*n^2*x*(a + b*Log[c*x^n]) + 6*b^2*n^2*x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n]) - (6*b^2*n^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(d^2*f^2) - (9*b*n*Sqrt[x]*(a + b*Log[c*x^n])^2)/(d*f) + 3*b*n*x*(a + b*Log[c*x^n])^2 - 3*b*n*x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^2 + (3*b*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/(d^2*f^2) + (Sqrt[x]*(a + b*Log[c*x^n])^3)/(d*f) - (x*(a + b*Log[c*x^n])^3)/2 + x*Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^3 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^3)/(d^2*f^2) - (12*b^3*n^3*PolyLog[2, -(d*f*Sqrt[x])])/(d^2*f^2) + (12*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])])/(d^2*f^2) - (6*b*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(d*f*Sqrt[x])])/(d^2*f^2) - (24*b^3*n^3*PolyLog[3, -(d*f*Sqrt[x])])/(d^2*f^2) + (24*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(d*f*Sqrt[x])])/(d^2*f^2) - (48*b^3*n^3*PolyLog[4, -(d*f*Sqrt[x])])/(d^2*f^2)","A",24,12,27,0.4444,1,"{2448, 266, 43, 2370, 2296, 2295, 2305, 2304, 2391, 2374, 6589, 2383}"
61,1,101,0,0.0992244,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x} \, dx","Int[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x,x]","-48 b^2 n^2 \text{PolyLog}\left(4,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)+12 b n \text{PolyLog}\left(3,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2-2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^3+96 b^3 n^3 \text{PolyLog}\left(5,-d f \sqrt{x}\right)","-48 b^2 n^2 \text{PolyLog}\left(4,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)+12 b n \text{PolyLog}\left(3,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2-2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^3+96 b^3 n^3 \text{PolyLog}\left(5,-d f \sqrt{x}\right)",1,"-2*(a + b*Log[c*x^n])^3*PolyLog[2, -(d*f*Sqrt[x])] + 12*b*n*(a + b*Log[c*x^n])^2*PolyLog[3, -(d*f*Sqrt[x])] - 48*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[4, -(d*f*Sqrt[x])] + 96*b^3*n^3*PolyLog[5, -(d*f*Sqrt[x])]","A",4,3,30,0.1000,1,"{2374, 2383, 6589}"
62,1,610,0,0.7783954,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x^2} \, dx","Int[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x^2,x]","12 b^2 d^2 f^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)-24 b^2 d^2 f^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)+6 b d^2 f^2 n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2+12 b^3 d^2 f^2 n^3 \text{PolyLog}\left(2,-d f \sqrt{x}\right)-24 b^3 d^2 f^2 n^3 \text{PolyLog}\left(3,-d f \sqrt{x}\right)+48 b^3 d^2 f^2 n^3 \text{PolyLog}\left(4,-d f \sqrt{x}\right)+6 b^2 d^2 f^2 n^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-3 b^2 d^2 f^2 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b^2 n^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{42 b^2 d f n^2 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{x}}-\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^4}{8 b n}-\frac{1}{2} d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^3+d^2 f^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3+3 b d^2 f^2 n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)^3}{\sqrt{x}}-\frac{3 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{9 b d f n \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{x}}+\frac{3}{2} b^3 d^2 f^2 n^3 \log ^2(x)+6 b^3 d^2 f^2 n^3 \log \left(d f \sqrt{x}+1\right)-3 b^3 d^2 f^2 n^3 \log (x)-\frac{90 b^3 d f n^3}{\sqrt{x}}-\frac{6 b^3 n^3 \log \left(d f \sqrt{x}+1\right)}{x}","12 b^2 d^2 f^2 n^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)-24 b^2 d^2 f^2 n^2 \text{PolyLog}\left(3,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)+6 b d^2 f^2 n \text{PolyLog}\left(2,-d f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)^2+12 b^3 d^2 f^2 n^3 \text{PolyLog}\left(2,-d f \sqrt{x}\right)-24 b^3 d^2 f^2 n^3 \text{PolyLog}\left(3,-d f \sqrt{x}\right)+48 b^3 d^2 f^2 n^3 \text{PolyLog}\left(4,-d f \sqrt{x}\right)+6 b^2 d^2 f^2 n^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)-3 b^2 d^2 f^2 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b^2 n^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{42 b^2 d f n^2 \left(a+b \log \left(c x^n\right)\right)}{\sqrt{x}}-\frac{d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^4}{8 b n}-\frac{1}{2} d^2 f^2 \left(a+b \log \left(c x^n\right)\right)^3+d^2 f^2 \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3+3 b d^2 f^2 n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{\log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{x}-\frac{d f \left(a+b \log \left(c x^n\right)\right)^3}{\sqrt{x}}-\frac{3 b n \log \left(d f \sqrt{x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{9 b d f n \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{x}}+\frac{3}{2} b^3 d^2 f^2 n^3 \log ^2(x)+6 b^3 d^2 f^2 n^3 \log \left(d f \sqrt{x}+1\right)-3 b^3 d^2 f^2 n^3 \log (x)-\frac{90 b^3 d f n^3}{\sqrt{x}}-\frac{6 b^3 n^3 \log \left(d f \sqrt{x}+1\right)}{x}",1,"(-90*b^3*d*f*n^3)/Sqrt[x] + 6*b^3*d^2*f^2*n^3*Log[1 + d*f*Sqrt[x]] - (6*b^3*n^3*Log[1 + d*f*Sqrt[x]])/x - 3*b^3*d^2*f^2*n^3*Log[x] + (3*b^3*d^2*f^2*n^3*Log[x]^2)/2 - (42*b^2*d*f*n^2*(a + b*Log[c*x^n]))/Sqrt[x] + 6*b^2*d^2*f^2*n^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]) - (6*b^2*n^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/x - 3*b^2*d^2*f^2*n^2*Log[x]*(a + b*Log[c*x^n]) - (9*b*d*f*n*(a + b*Log[c*x^n])^2)/Sqrt[x] + 3*b*d^2*f^2*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2 - (3*b*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/x - (d^2*f^2*(a + b*Log[c*x^n])^3)/2 - (d*f*(a + b*Log[c*x^n])^3)/Sqrt[x] + d^2*f^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^3 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^3)/x - (d^2*f^2*(a + b*Log[c*x^n])^4)/(8*b*n) + 12*b^3*d^2*f^2*n^3*PolyLog[2, -(d*f*Sqrt[x])] + 12*b^2*d^2*f^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])] + 6*b*d^2*f^2*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(d*f*Sqrt[x])] - 24*b^3*d^2*f^2*n^3*PolyLog[3, -(d*f*Sqrt[x])] - 24*b^2*d^2*f^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(d*f*Sqrt[x])] + 48*b^3*d^2*f^2*n^3*PolyLog[4, -(d*f*Sqrt[x])]","A",28,16,30,0.5333,1,"{2454, 2395, 44, 2377, 2305, 2304, 2376, 2391, 2301, 2374, 6589, 2366, 12, 2302, 30, 2383}"
63,1,849,0,1.1439879,"\int \frac{\log \left(d \left(\frac{1}{d}+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x^3} \, dx","Int[(Log[d*(d^(-1) + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x^3,x]","-\frac{d^4 \left(a+b \log \left(c x^n\right)\right)^4 f^4}{16 b n}-\frac{1}{8} d^4 \left(a+b \log \left(c x^n\right)\right)^3 f^4+\frac{1}{2} d^4 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3 f^4+\frac{3}{16} b^3 d^4 n^3 \log ^2(x) f^4+\frac{3}{4} b d^4 n \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2 f^4+\frac{3}{8} b^3 d^4 n^3 \log \left(d \sqrt{x} f+1\right) f^4-\frac{3}{16} b^3 d^4 n^3 \log (x) f^4+\frac{3}{4} b^2 d^4 n^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right) f^4-\frac{3}{8} b^2 d^4 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right) f^4+\frac{3}{2} b^3 d^4 n^3 \text{PolyLog}\left(2,-d f \sqrt{x}\right) f^4+3 b d^4 n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) f^4+3 b^2 d^4 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-d f \sqrt{x}\right) f^4-6 b^3 d^4 n^3 \text{PolyLog}\left(3,-d f \sqrt{x}\right) f^4-12 b^2 d^4 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-d f \sqrt{x}\right) f^4+24 b^3 d^4 n^3 \text{PolyLog}\left(4,-d f \sqrt{x}\right) f^4-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)^3 f^3}{2 \sqrt{x}}-\frac{15 b d^3 n \left(a+b \log \left(c x^n\right)\right)^2 f^3}{4 \sqrt{x}}-\frac{63 b^2 d^3 n^2 \left(a+b \log \left(c x^n\right)\right) f^3}{4 \sqrt{x}}-\frac{255 b^3 d^3 n^3 f^3}{8 \sqrt{x}}+\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^3 f^2}{4 x}+\frac{9 b d^2 n \left(a+b \log \left(c x^n\right)\right)^2 f^2}{8 x}+\frac{21 b^2 d^2 n^2 \left(a+b \log \left(c x^n\right)\right) f^2}{8 x}+\frac{45 b^3 d^2 n^3 f^2}{16 x}-\frac{d \left(a+b \log \left(c x^n\right)\right)^3 f}{6 x^{3/2}}-\frac{7 b d n \left(a+b \log \left(c x^n\right)\right)^2 f}{12 x^{3/2}}-\frac{37 b^2 d n^2 \left(a+b \log \left(c x^n\right)\right) f}{36 x^{3/2}}-\frac{175 b^3 d n^3 f}{216 x^{3/2}}-\frac{\log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{3 b n \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{3 b^3 n^3 \log \left(d \sqrt{x} f+1\right)}{8 x^2}-\frac{3 b^2 n^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}","-\frac{d^4 \left(a+b \log \left(c x^n\right)\right)^4 f^4}{16 b n}-\frac{1}{8} d^4 \left(a+b \log \left(c x^n\right)\right)^3 f^4+\frac{1}{2} d^4 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3 f^4+\frac{3}{16} b^3 d^4 n^3 \log ^2(x) f^4+\frac{3}{4} b d^4 n \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2 f^4+\frac{3}{8} b^3 d^4 n^3 \log \left(d \sqrt{x} f+1\right) f^4-\frac{3}{16} b^3 d^4 n^3 \log (x) f^4+\frac{3}{4} b^2 d^4 n^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right) f^4-\frac{3}{8} b^2 d^4 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right) f^4+\frac{3}{2} b^3 d^4 n^3 \text{PolyLog}\left(2,-d f \sqrt{x}\right) f^4+3 b d^4 n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-d f \sqrt{x}\right) f^4+3 b^2 d^4 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-d f \sqrt{x}\right) f^4-6 b^3 d^4 n^3 \text{PolyLog}\left(3,-d f \sqrt{x}\right) f^4-12 b^2 d^4 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-d f \sqrt{x}\right) f^4+24 b^3 d^4 n^3 \text{PolyLog}\left(4,-d f \sqrt{x}\right) f^4-\frac{d^3 \left(a+b \log \left(c x^n\right)\right)^3 f^3}{2 \sqrt{x}}-\frac{15 b d^3 n \left(a+b \log \left(c x^n\right)\right)^2 f^3}{4 \sqrt{x}}-\frac{63 b^2 d^3 n^2 \left(a+b \log \left(c x^n\right)\right) f^3}{4 \sqrt{x}}-\frac{255 b^3 d^3 n^3 f^3}{8 \sqrt{x}}+\frac{d^2 \left(a+b \log \left(c x^n\right)\right)^3 f^2}{4 x}+\frac{9 b d^2 n \left(a+b \log \left(c x^n\right)\right)^2 f^2}{8 x}+\frac{21 b^2 d^2 n^2 \left(a+b \log \left(c x^n\right)\right) f^2}{8 x}+\frac{45 b^3 d^2 n^3 f^2}{16 x}-\frac{d \left(a+b \log \left(c x^n\right)\right)^3 f}{6 x^{3/2}}-\frac{7 b d n \left(a+b \log \left(c x^n\right)\right)^2 f}{12 x^{3/2}}-\frac{37 b^2 d n^2 \left(a+b \log \left(c x^n\right)\right) f}{36 x^{3/2}}-\frac{175 b^3 d n^3 f}{216 x^{3/2}}-\frac{\log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{3 b n \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{3 b^3 n^3 \log \left(d \sqrt{x} f+1\right)}{8 x^2}-\frac{3 b^2 n^2 \log \left(d \sqrt{x} f+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}",1,"(-175*b^3*d*f*n^3)/(216*x^(3/2)) + (45*b^3*d^2*f^2*n^3)/(16*x) - (255*b^3*d^3*f^3*n^3)/(8*Sqrt[x]) + (3*b^3*d^4*f^4*n^3*Log[1 + d*f*Sqrt[x]])/8 - (3*b^3*n^3*Log[1 + d*f*Sqrt[x]])/(8*x^2) - (3*b^3*d^4*f^4*n^3*Log[x])/16 + (3*b^3*d^4*f^4*n^3*Log[x]^2)/16 - (37*b^2*d*f*n^2*(a + b*Log[c*x^n]))/(36*x^(3/2)) + (21*b^2*d^2*f^2*n^2*(a + b*Log[c*x^n]))/(8*x) - (63*b^2*d^3*f^3*n^2*(a + b*Log[c*x^n]))/(4*Sqrt[x]) + (3*b^2*d^4*f^4*n^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/4 - (3*b^2*n^2*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n]))/(4*x^2) - (3*b^2*d^4*f^4*n^2*Log[x]*(a + b*Log[c*x^n]))/8 - (7*b*d*f*n*(a + b*Log[c*x^n])^2)/(12*x^(3/2)) + (9*b*d^2*f^2*n*(a + b*Log[c*x^n])^2)/(8*x) - (15*b*d^3*f^3*n*(a + b*Log[c*x^n])^2)/(4*Sqrt[x]) + (3*b*d^4*f^4*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/4 - (3*b*n*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^2)/(4*x^2) - (d^4*f^4*(a + b*Log[c*x^n])^3)/8 - (d*f*(a + b*Log[c*x^n])^3)/(6*x^(3/2)) + (d^2*f^2*(a + b*Log[c*x^n])^3)/(4*x) - (d^3*f^3*(a + b*Log[c*x^n])^3)/(2*Sqrt[x]) + (d^4*f^4*Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^3)/2 - (Log[1 + d*f*Sqrt[x]]*(a + b*Log[c*x^n])^3)/(2*x^2) - (d^4*f^4*(a + b*Log[c*x^n])^4)/(16*b*n) + (3*b^3*d^4*f^4*n^3*PolyLog[2, -(d*f*Sqrt[x])])/2 + 3*b^2*d^4*f^4*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(d*f*Sqrt[x])] + 3*b*d^4*f^4*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(d*f*Sqrt[x])] - 6*b^3*d^4*f^4*n^3*PolyLog[3, -(d*f*Sqrt[x])] - 12*b^2*d^4*f^4*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(d*f*Sqrt[x])] + 24*b^3*d^4*f^4*n^3*PolyLog[4, -(d*f*Sqrt[x])]","A",34,16,30,0.5333,1,"{2454, 2395, 44, 2377, 2305, 2304, 2376, 2391, 2301, 2374, 6589, 2366, 12, 2302, 30, 2383}"
64,1,137,0,0.144183,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^4 \log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^4*Log[d*(d^(-1) + f*x^m)])/x,x]","\frac{24 b^3 n^3 \text{PolyLog}\left(5,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m^4}-\frac{12 b^2 n^2 \text{PolyLog}\left(4,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^2}{m^3}+\frac{4 b n \text{PolyLog}\left(3,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^3}{m^2}-\frac{\text{PolyLog}\left(2,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^4}{m}-\frac{24 b^4 n^4 \text{PolyLog}\left(6,-d f x^m\right)}{m^5}","\frac{24 b^3 n^3 \text{PolyLog}\left(5,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m^4}-\frac{12 b^2 n^2 \text{PolyLog}\left(4,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^2}{m^3}+\frac{4 b n \text{PolyLog}\left(3,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^3}{m^2}-\frac{\text{PolyLog}\left(2,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^4}{m}-\frac{24 b^4 n^4 \text{PolyLog}\left(6,-d f x^m\right)}{m^5}",1,"-(((a + b*Log[c*x^n])^4*PolyLog[2, -(d*f*x^m)])/m) + (4*b*n*(a + b*Log[c*x^n])^3*PolyLog[3, -(d*f*x^m)])/m^2 - (12*b^2*n^2*(a + b*Log[c*x^n])^2*PolyLog[4, -(d*f*x^m)])/m^3 + (24*b^3*n^3*(a + b*Log[c*x^n])*PolyLog[5, -(d*f*x^m)])/m^4 - (24*b^4*n^4*PolyLog[6, -(d*f*x^m)])/m^5","A",5,3,28,0.1071,1,"{2374, 2383, 6589}"
65,1,105,0,0.1137732,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(d^(-1) + f*x^m)])/x,x]","-\frac{6 b^2 n^2 \text{PolyLog}\left(4,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m^3}+\frac{3 b n \text{PolyLog}\left(3,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^2}{m^2}-\frac{\text{PolyLog}\left(2,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^3}{m}+\frac{6 b^3 n^3 \text{PolyLog}\left(5,-d f x^m\right)}{m^4}","-\frac{6 b^2 n^2 \text{PolyLog}\left(4,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m^3}+\frac{3 b n \text{PolyLog}\left(3,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^2}{m^2}-\frac{\text{PolyLog}\left(2,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^3}{m}+\frac{6 b^3 n^3 \text{PolyLog}\left(5,-d f x^m\right)}{m^4}",1,"-(((a + b*Log[c*x^n])^3*PolyLog[2, -(d*f*x^m)])/m) + (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[3, -(d*f*x^m)])/m^2 - (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[4, -(d*f*x^m)])/m^3 + (6*b^3*n^3*PolyLog[5, -(d*f*x^m)])/m^4","A",4,3,28,0.1071,1,"{2374, 2383, 6589}"
66,1,73,0,0.0712155,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(d^(-1) + f*x^m)])/x,x]","\frac{2 b n \text{PolyLog}\left(3,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m^2}-\frac{\text{PolyLog}\left(2,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^2}{m}-\frac{2 b^2 n^2 \text{PolyLog}\left(4,-d f x^m\right)}{m^3}","\frac{2 b n \text{PolyLog}\left(3,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m^2}-\frac{\text{PolyLog}\left(2,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)^2}{m}-\frac{2 b^2 n^2 \text{PolyLog}\left(4,-d f x^m\right)}{m^3}",1,"-(((a + b*Log[c*x^n])^2*PolyLog[2, -(d*f*x^m)])/m) + (2*b*n*(a + b*Log[c*x^n])*PolyLog[3, -(d*f*x^m)])/m^2 - (2*b^2*n^2*PolyLog[4, -(d*f*x^m)])/m^3","A",3,3,28,0.1071,1,"{2374, 2383, 6589}"
67,1,40,0,0.0482115,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(d^(-1) + f*x^m)])/x,x]","\frac{b n \text{PolyLog}\left(3,-d f x^m\right)}{m^2}-\frac{\text{PolyLog}\left(2,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m}","\frac{b n \text{PolyLog}\left(3,-d f x^m\right)}{m^2}-\frac{\text{PolyLog}\left(2,-d f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{m}",1,"-(((a + b*Log[c*x^n])*PolyLog[2, -(d*f*x^m)])/m) + (b*n*PolyLog[3, -(d*f*x^m)])/m^2","A",2,2,26,0.07692,1,"{2374, 6589}"
68,0,0,0,0.0400239,"\int \frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Log[d*(d^(-1) + f*x^m)]/(x*(a + b*Log[c*x^n])),x]","\int \frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Defer[Int][Log[d*(d^(-1) + f*x^m)]/(x*(a + b*Log[c*x^n])), x]","A",0,0,0,0,-1,"{}"
69,0,0,0,0.0423874,"\int \frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Int[Log[d*(d^(-1) + f*x^m)]/(x*(a + b*Log[c*x^n])^2),x]","\int \frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","\text{Int}\left(\frac{\log \left(d \left(\frac{1}{d}+f x^m\right)\right)}{x \left(a+b \log \left(c x^n\right)\right)^2},x\right)",0,"Defer[Int][Log[d*(d^(-1) + f*x^m)]/(x*(a + b*Log[c*x^n])^2), x]","A",0,0,0,0,-1,"{}"
70,1,283,0,0.2062617,"\int x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right) \, dx","Int[x^3*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m],x]","\frac{b e^4 m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{4 f^4}+\frac{1}{4} x^4 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)-\frac{e^4 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{4 f^4}+\frac{e^3 m x \left(a+b \log \left(c x^n\right)\right)}{4 f^3}-\frac{e^2 m x^2 \left(a+b \log \left(c x^n\right)\right)}{8 f^2}+\frac{e m x^3 \left(a+b \log \left(c x^n\right)\right)}{12 f}-\frac{1}{16} m x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b n x^4 \log \left(d (e+f x)^m\right)+\frac{3 b e^2 m n x^2}{32 f^2}-\frac{5 b e^3 m n x}{16 f^3}+\frac{b e^4 m n \log (e+f x)}{16 f^4}+\frac{b e^4 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{4 f^4}-\frac{7 b e m n x^3}{144 f}+\frac{1}{32} b m n x^4","\frac{b e^4 m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{4 f^4}+\frac{1}{4} x^4 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)-\frac{e^4 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{4 f^4}+\frac{e^3 m x \left(a+b \log \left(c x^n\right)\right)}{4 f^3}-\frac{e^2 m x^2 \left(a+b \log \left(c x^n\right)\right)}{8 f^2}+\frac{e m x^3 \left(a+b \log \left(c x^n\right)\right)}{12 f}-\frac{1}{16} m x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b n x^4 \log \left(d (e+f x)^m\right)+\frac{3 b e^2 m n x^2}{32 f^2}-\frac{5 b e^3 m n x}{16 f^3}+\frac{b e^4 m n \log (e+f x)}{16 f^4}+\frac{b e^4 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{4 f^4}-\frac{7 b e m n x^3}{144 f}+\frac{1}{32} b m n x^4",1,"(-5*b*e^3*m*n*x)/(16*f^3) + (3*b*e^2*m*n*x^2)/(32*f^2) - (7*b*e*m*n*x^3)/(144*f) + (b*m*n*x^4)/32 + (e^3*m*x*(a + b*Log[c*x^n]))/(4*f^3) - (e^2*m*x^2*(a + b*Log[c*x^n]))/(8*f^2) + (e*m*x^3*(a + b*Log[c*x^n]))/(12*f) - (m*x^4*(a + b*Log[c*x^n]))/16 + (b*e^4*m*n*Log[e + f*x])/(16*f^4) + (b*e^4*m*n*Log[-((f*x)/e)]*Log[e + f*x])/(4*f^4) - (e^4*m*(a + b*Log[c*x^n])*Log[e + f*x])/(4*f^4) - (b*n*x^4*Log[d*(e + f*x)^m])/16 + (x^4*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/4 + (b*e^4*m*n*PolyLog[2, 1 + (f*x)/e])/(4*f^4)","A",7,5,24,0.2083,1,"{2395, 43, 2376, 2394, 2315}"
71,1,243,0,0.1662345,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right) \, dx","Int[x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m],x]","-\frac{b e^3 m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{3 f^3}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)+\frac{e^3 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{3 f^3}-\frac{e^2 m x \left(a+b \log \left(c x^n\right)\right)}{3 f^2}+\frac{e m x^2 \left(a+b \log \left(c x^n\right)\right)}{6 f}-\frac{1}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b n x^3 \log \left(d (e+f x)^m\right)+\frac{4 b e^2 m n x}{9 f^2}-\frac{b e^3 m n \log (e+f x)}{9 f^3}-\frac{b e^3 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{3 f^3}-\frac{5 b e m n x^2}{36 f}+\frac{2}{27} b m n x^3","-\frac{b e^3 m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{3 f^3}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)+\frac{e^3 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{3 f^3}-\frac{e^2 m x \left(a+b \log \left(c x^n\right)\right)}{3 f^2}+\frac{e m x^2 \left(a+b \log \left(c x^n\right)\right)}{6 f}-\frac{1}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b n x^3 \log \left(d (e+f x)^m\right)+\frac{4 b e^2 m n x}{9 f^2}-\frac{b e^3 m n \log (e+f x)}{9 f^3}-\frac{b e^3 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{3 f^3}-\frac{5 b e m n x^2}{36 f}+\frac{2}{27} b m n x^3",1,"(4*b*e^2*m*n*x)/(9*f^2) - (5*b*e*m*n*x^2)/(36*f) + (2*b*m*n*x^3)/27 - (e^2*m*x*(a + b*Log[c*x^n]))/(3*f^2) + (e*m*x^2*(a + b*Log[c*x^n]))/(6*f) - (m*x^3*(a + b*Log[c*x^n]))/9 - (b*e^3*m*n*Log[e + f*x])/(9*f^3) - (b*e^3*m*n*Log[-((f*x)/e)]*Log[e + f*x])/(3*f^3) + (e^3*m*(a + b*Log[c*x^n])*Log[e + f*x])/(3*f^3) - (b*n*x^3*Log[d*(e + f*x)^m])/9 + (x^3*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/3 - (b*e^3*m*n*PolyLog[2, 1 + (f*x)/e])/(3*f^3)","A",7,5,24,0.2083,1,"{2395, 43, 2376, 2394, 2315}"
72,1,203,0,0.1261773,"\int x \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right) \, dx","Int[x*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m],x]","\frac{b e^2 m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{2 f^2}+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)-\frac{e^2 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{2 f^2}+\frac{e m x \left(a+b \log \left(c x^n\right)\right)}{2 f}-\frac{1}{4} m x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b n x^2 \log \left(d (e+f x)^m\right)+\frac{b e^2 m n \log (e+f x)}{4 f^2}+\frac{b e^2 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{2 f^2}-\frac{3 b e m n x}{4 f}+\frac{1}{4} b m n x^2","\frac{b e^2 m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{2 f^2}+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)-\frac{e^2 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{2 f^2}+\frac{e m x \left(a+b \log \left(c x^n\right)\right)}{2 f}-\frac{1}{4} m x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b n x^2 \log \left(d (e+f x)^m\right)+\frac{b e^2 m n \log (e+f x)}{4 f^2}+\frac{b e^2 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{2 f^2}-\frac{3 b e m n x}{4 f}+\frac{1}{4} b m n x^2",1,"(-3*b*e*m*n*x)/(4*f) + (b*m*n*x^2)/4 + (e*m*x*(a + b*Log[c*x^n]))/(2*f) - (m*x^2*(a + b*Log[c*x^n]))/4 + (b*e^2*m*n*Log[e + f*x])/(4*f^2) + (b*e^2*m*n*Log[-((f*x)/e)]*Log[e + f*x])/(2*f^2) - (e^2*m*(a + b*Log[c*x^n])*Log[e + f*x])/(2*f^2) - (b*n*x^2*Log[d*(e + f*x)^m])/4 + (x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/2 + (b*e^2*m*n*PolyLog[2, 1 + (f*x)/e])/(2*f^2)","A",7,5,22,0.2273,1,"{2395, 43, 2376, 2394, 2315}"
73,1,117,0,0.1450036,"\int \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right) \, dx","Int[(a + b*Log[c*x^n])*Log[d*(e + f*x)^m],x]","-\frac{b e m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{f}+\frac{(e+f x) \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{f}-m x \left(a+b \log \left(c x^n\right)\right)-\frac{b n (e+f x) \log \left(d (e+f x)^m\right)}{f}-\frac{b e n \log \left(-\frac{f x}{e}\right) \log \left(d (e+f x)^m\right)}{f}+2 b m n x","-\frac{b e m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{f}+\frac{(e+f x) \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{f}-m x \left(a+b \log \left(c x^n\right)\right)-\frac{b n (e+f x) \log \left(d (e+f x)^m\right)}{f}-\frac{b e n \log \left(-\frac{f x}{e}\right) \log \left(d (e+f x)^m\right)}{f}+2 b m n x",1,"2*b*m*n*x - m*x*(a + b*Log[c*x^n]) - (b*n*(e + f*x)*Log[d*(e + f*x)^m])/f - (b*e*n*Log[-((f*x)/e)]*Log[d*(e + f*x)^m])/f + ((e + f*x)*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/f - (b*e*m*n*PolyLog[2, 1 + (f*x)/e])/f","A",8,8,21,0.3810,1,"{2389, 2295, 2370, 2411, 43, 2351, 2317, 2391}"
74,1,100,0,0.0927204,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/x,x]","-m \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)+b m n \text{PolyLog}\left(3,-\frac{f x}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{2 b n}-\frac{m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}","-m \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)+b m n \text{PolyLog}\left(3,-\frac{f x}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{2 b n}-\frac{m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}",1,"((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/(2*b*n) - (m*(a + b*Log[c*x^n])^2*Log[1 + (f*x)/e])/(2*b*n) - m*(a + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)] + b*m*n*PolyLog[3, -((f*x)/e)]","A",4,4,24,0.1667,1,"{2375, 2317, 2374, 6589}"
75,1,164,0,0.1175224,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/x^2,x]","\frac{b f m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{e}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x}+\frac{f m \log (x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{f m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{b n \log \left(d (e+f x)^m\right)}{x}-\frac{b f m n \log ^2(x)}{2 e}+\frac{b f m n \log (x)}{e}-\frac{b f m n \log (e+f x)}{e}+\frac{b f m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{e}","\frac{b f m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{e}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x}+\frac{f m \log (x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{f m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{b n \log \left(d (e+f x)^m\right)}{x}-\frac{b f m n \log ^2(x)}{2 e}+\frac{b f m n \log (x)}{e}-\frac{b f m n \log (e+f x)}{e}+\frac{b f m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{e}",1,"(b*f*m*n*Log[x])/e - (b*f*m*n*Log[x]^2)/(2*e) + (f*m*Log[x]*(a + b*Log[c*x^n]))/e - (b*f*m*n*Log[e + f*x])/e + (b*f*m*n*Log[-((f*x)/e)]*Log[e + f*x])/e - (f*m*(a + b*Log[c*x^n])*Log[e + f*x])/e - (b*n*Log[d*(e + f*x)^m])/x - ((a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/x + (b*f*m*n*PolyLog[2, 1 + (f*x)/e])/e","A",9,8,24,0.3333,1,"{2395, 36, 29, 31, 2376, 2301, 2394, 2315}"
76,1,234,0,0.1626719,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/x^3,x]","-\frac{b f^2 m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{2 e^2}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{2 x^2}-\frac{f^2 m \log (x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{f^2 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)}{2 e x}-\frac{b n \log \left(d (e+f x)^m\right)}{4 x^2}+\frac{b f^2 m n \log ^2(x)}{4 e^2}-\frac{b f^2 m n \log (x)}{4 e^2}+\frac{b f^2 m n \log (e+f x)}{4 e^2}-\frac{b f^2 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{2 e^2}-\frac{3 b f m n}{4 e x}","-\frac{b f^2 m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{2 e^2}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{2 x^2}-\frac{f^2 m \log (x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{f^2 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)}{2 e x}-\frac{b n \log \left(d (e+f x)^m\right)}{4 x^2}+\frac{b f^2 m n \log ^2(x)}{4 e^2}-\frac{b f^2 m n \log (x)}{4 e^2}+\frac{b f^2 m n \log (e+f x)}{4 e^2}-\frac{b f^2 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{2 e^2}-\frac{3 b f m n}{4 e x}",1,"(-3*b*f*m*n)/(4*e*x) - (b*f^2*m*n*Log[x])/(4*e^2) + (b*f^2*m*n*Log[x]^2)/(4*e^2) - (f*m*(a + b*Log[c*x^n]))/(2*e*x) - (f^2*m*Log[x]*(a + b*Log[c*x^n]))/(2*e^2) + (b*f^2*m*n*Log[e + f*x])/(4*e^2) - (b*f^2*m*n*Log[-((f*x)/e)]*Log[e + f*x])/(2*e^2) + (f^2*m*(a + b*Log[c*x^n])*Log[e + f*x])/(2*e^2) - (b*n*Log[d*(e + f*x)^m])/(4*x^2) - ((a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/(2*x^2) - (b*f^2*m*n*PolyLog[2, 1 + (f*x)/e])/(2*e^2)","A",8,6,24,0.2500,1,"{2395, 44, 2376, 2301, 2394, 2315}"
77,1,274,0,0.1839557,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x^4} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/x^4,x]","\frac{b f^3 m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{3 e^3}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{3 x^3}+\frac{f^3 m \log (x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{f^3 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)}{3 e^2 x}-\frac{f m \left(a+b \log \left(c x^n\right)\right)}{6 e x^2}-\frac{b n \log \left(d (e+f x)^m\right)}{9 x^3}+\frac{4 b f^2 m n}{9 e^2 x}-\frac{b f^3 m n \log ^2(x)}{6 e^3}+\frac{b f^3 m n \log (x)}{9 e^3}-\frac{b f^3 m n \log (e+f x)}{9 e^3}+\frac{b f^3 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{3 e^3}-\frac{5 b f m n}{36 e x^2}","\frac{b f^3 m n \text{PolyLog}\left(2,\frac{f x}{e}+1\right)}{3 e^3}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{3 x^3}+\frac{f^3 m \log (x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{f^3 m \log (e+f x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)}{3 e^2 x}-\frac{f m \left(a+b \log \left(c x^n\right)\right)}{6 e x^2}-\frac{b n \log \left(d (e+f x)^m\right)}{9 x^3}+\frac{4 b f^2 m n}{9 e^2 x}-\frac{b f^3 m n \log ^2(x)}{6 e^3}+\frac{b f^3 m n \log (x)}{9 e^3}-\frac{b f^3 m n \log (e+f x)}{9 e^3}+\frac{b f^3 m n \log \left(-\frac{f x}{e}\right) \log (e+f x)}{3 e^3}-\frac{5 b f m n}{36 e x^2}",1,"(-5*b*f*m*n)/(36*e*x^2) + (4*b*f^2*m*n)/(9*e^2*x) + (b*f^3*m*n*Log[x])/(9*e^3) - (b*f^3*m*n*Log[x]^2)/(6*e^3) - (f*m*(a + b*Log[c*x^n]))/(6*e*x^2) + (f^2*m*(a + b*Log[c*x^n]))/(3*e^2*x) + (f^3*m*Log[x]*(a + b*Log[c*x^n]))/(3*e^3) - (b*f^3*m*n*Log[e + f*x])/(9*e^3) + (b*f^3*m*n*Log[-((f*x)/e)]*Log[e + f*x])/(3*e^3) - (f^3*m*(a + b*Log[c*x^n])*Log[e + f*x])/(3*e^3) - (b*n*Log[d*(e + f*x)^m])/(9*x^3) - ((a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/(3*x^3) + (b*f^3*m*n*PolyLog[2, 1 + (f*x)/e])/(3*e^3)","A",8,6,24,0.2500,1,"{2395, 44, 2376, 2301, 2394, 2315}"
78,1,452,0,0.6834521,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right) \, dx","Int[x^2*(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m],x]","\frac{2 b e^3 m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^3}-\frac{2 b^2 e^3 m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{9 f^3}-\frac{2 b^2 e^3 m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{3 f^3}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)-\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)+\frac{e^3 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^3}-\frac{2 b e^3 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 f^3}-\frac{e^2 m x \left(a+b \log \left(c x^n\right)\right)^2}{3 f^2}+\frac{e m x^2 \left(a+b \log \left(c x^n\right)\right)^2}{6 f}-\frac{5 b e m n x^2 \left(a+b \log \left(c x^n\right)\right)}{18 f}-\frac{1}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{4}{27} b m n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{8 a b e^2 m n x}{9 f^2}+\frac{8 b^2 e^2 m n x \log \left(c x^n\right)}{9 f^2}+\frac{2}{27} b^2 n^2 x^3 \log \left(d (e+f x)^m\right)-\frac{26 b^2 e^2 m n^2 x}{27 f^2}+\frac{2 b^2 e^3 m n^2 \log (e+f x)}{27 f^3}+\frac{19 b^2 e m n^2 x^2}{108 f}-\frac{2}{27} b^2 m n^2 x^3","\frac{2 b e^3 m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^3}-\frac{2 b^2 e^3 m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{9 f^3}-\frac{2 b^2 e^3 m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{3 f^3}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)-\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)+\frac{e^3 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^3}-\frac{2 b e^3 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 f^3}-\frac{e^2 m x \left(a+b \log \left(c x^n\right)\right)^2}{3 f^2}+\frac{e m x^2 \left(a+b \log \left(c x^n\right)\right)^2}{6 f}-\frac{5 b e m n x^2 \left(a+b \log \left(c x^n\right)\right)}{18 f}-\frac{1}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{4}{27} b m n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{8 a b e^2 m n x}{9 f^2}+\frac{8 b^2 e^2 m n x \log \left(c x^n\right)}{9 f^2}+\frac{2}{27} b^2 n^2 x^3 \log \left(d (e+f x)^m\right)-\frac{26 b^2 e^2 m n^2 x}{27 f^2}+\frac{2 b^2 e^3 m n^2 \log (e+f x)}{27 f^3}+\frac{19 b^2 e m n^2 x^2}{108 f}-\frac{2}{27} b^2 m n^2 x^3",1,"(8*a*b*e^2*m*n*x)/(9*f^2) - (26*b^2*e^2*m*n^2*x)/(27*f^2) + (19*b^2*e*m*n^2*x^2)/(108*f) - (2*b^2*m*n^2*x^3)/27 + (8*b^2*e^2*m*n*x*Log[c*x^n])/(9*f^2) - (5*b*e*m*n*x^2*(a + b*Log[c*x^n]))/(18*f) + (4*b*m*n*x^3*(a + b*Log[c*x^n]))/27 - (e^2*m*x*(a + b*Log[c*x^n])^2)/(3*f^2) + (e*m*x^2*(a + b*Log[c*x^n])^2)/(6*f) - (m*x^3*(a + b*Log[c*x^n])^2)/9 + (2*b^2*e^3*m*n^2*Log[e + f*x])/(27*f^3) + (2*b^2*n^2*x^3*Log[d*(e + f*x)^m])/27 - (2*b*n*x^3*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/9 + (x^3*(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/3 - (2*b*e^3*m*n*(a + b*Log[c*x^n])*Log[1 + (f*x)/e])/(9*f^3) + (e^3*m*(a + b*Log[c*x^n])^2*Log[1 + (f*x)/e])/(3*f^3) - (2*b^2*e^3*m*n^2*PolyLog[2, -((f*x)/e)])/(9*f^3) + (2*b*e^3*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)])/(3*f^3) - (2*b^2*e^3*m*n^2*PolyLog[3, -((f*x)/e)])/(3*f^3)","A",24,12,26,0.4615,1,"{2305, 2304, 2378, 43, 2351, 2295, 2317, 2391, 2353, 2296, 2374, 6589}"
79,1,373,0,0.5312055,"\int x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right) \, dx","Int[x*(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m],x]","-\frac{b e^2 m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{b^2 e^2 m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{2 f^2}+\frac{b^2 e^2 m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{f^2}-\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)+\frac{b e^2 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^2}-\frac{e^2 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f^2}+\frac{e m x \left(a+b \log \left(c x^n\right)\right)^2}{2 f}+\frac{1}{2} b m n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} m x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{3 a b e m n x}{2 f}-\frac{3 b^2 e m n x \log \left(c x^n\right)}{2 f}+\frac{1}{4} b^2 n^2 x^2 \log \left(d (e+f x)^m\right)-\frac{b^2 e^2 m n^2 \log (e+f x)}{4 f^2}+\frac{7 b^2 e m n^2 x}{4 f}-\frac{3}{8} b^2 m n^2 x^2","-\frac{b e^2 m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{b^2 e^2 m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{2 f^2}+\frac{b^2 e^2 m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{f^2}-\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)+\frac{b e^2 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^2}-\frac{e^2 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f^2}+\frac{e m x \left(a+b \log \left(c x^n\right)\right)^2}{2 f}+\frac{1}{2} b m n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} m x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{3 a b e m n x}{2 f}-\frac{3 b^2 e m n x \log \left(c x^n\right)}{2 f}+\frac{1}{4} b^2 n^2 x^2 \log \left(d (e+f x)^m\right)-\frac{b^2 e^2 m n^2 \log (e+f x)}{4 f^2}+\frac{7 b^2 e m n^2 x}{4 f}-\frac{3}{8} b^2 m n^2 x^2",1,"(-3*a*b*e*m*n*x)/(2*f) + (7*b^2*e*m*n^2*x)/(4*f) - (3*b^2*m*n^2*x^2)/8 - (3*b^2*e*m*n*x*Log[c*x^n])/(2*f) + (b*m*n*x^2*(a + b*Log[c*x^n]))/2 + (e*m*x*(a + b*Log[c*x^n])^2)/(2*f) - (m*x^2*(a + b*Log[c*x^n])^2)/4 - (b^2*e^2*m*n^2*Log[e + f*x])/(4*f^2) + (b^2*n^2*x^2*Log[d*(e + f*x)^m])/4 - (b*n*x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/2 + (x^2*(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/2 + (b*e^2*m*n*(a + b*Log[c*x^n])*Log[1 + (f*x)/e])/(2*f^2) - (e^2*m*(a + b*Log[c*x^n])^2*Log[1 + (f*x)/e])/(2*f^2) + (b^2*e^2*m*n^2*PolyLog[2, -((f*x)/e)])/(2*f^2) - (b*e^2*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)])/f^2 + (b^2*e^2*m*n^2*PolyLog[3, -((f*x)/e)])/f^2","A",21,12,24,0.5000,1,"{2305, 2304, 2378, 43, 2351, 2295, 2317, 2391, 2353, 2296, 2374, 6589}"
80,1,288,0,0.3521496,"\int \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right) \, dx","Int[(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m],x]","\frac{2 b e m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f}-\frac{2 b^2 e m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{f}-\frac{2 b^2 e m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{f}+x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)+\frac{e m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f}-m x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \log \left(d (e+f x)^m\right)-\frac{2 b e m n (a-b n) \log (e+f x)}{f}+2 a b m n x+2 b m n x (a-b n)-2 b^2 n x \log \left(c x^n\right) \log \left(d (e+f x)^m\right)-\frac{2 b^2 e m n \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)}{f}+4 b^2 m n x \log \left(c x^n\right)+2 b^2 n^2 x \log \left(d (e+f x)^m\right)-4 b^2 m n^2 x","\frac{2 b e m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f}-\frac{2 b^2 e m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{f}-\frac{2 b^2 e m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{f}+x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)+\frac{e m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f}-m x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \log \left(d (e+f x)^m\right)-\frac{2 b e m n (a-b n) \log (e+f x)}{f}+2 a b m n x+2 b m n x (a-b n)-2 b^2 n x \log \left(c x^n\right) \log \left(d (e+f x)^m\right)-\frac{2 b^2 e m n \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)}{f}+4 b^2 m n x \log \left(c x^n\right)+2 b^2 n^2 x \log \left(d (e+f x)^m\right)-4 b^2 m n^2 x",1,"2*a*b*m*n*x - 4*b^2*m*n^2*x + 2*b*m*n*(a - b*n)*x + 4*b^2*m*n*x*Log[c*x^n] - m*x*(a + b*Log[c*x^n])^2 - (2*b*e*m*n*(a - b*n)*Log[e + f*x])/f - 2*a*b*n*x*Log[d*(e + f*x)^m] + 2*b^2*n^2*x*Log[d*(e + f*x)^m] - 2*b^2*n*x*Log[c*x^n]*Log[d*(e + f*x)^m] + x*(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m] - (2*b^2*e*m*n*Log[c*x^n]*Log[1 + (f*x)/e])/f + (e*m*(a + b*Log[c*x^n])^2*Log[1 + (f*x)/e])/f - (2*b^2*e*m*n^2*PolyLog[2, -((f*x)/e)])/f + (2*b*e*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)])/f - (2*b^2*e*m*n^2*PolyLog[3, -((f*x)/e)])/f","A",18,11,23,0.4783,1,"{2296, 2295, 2371, 6, 43, 2351, 2317, 2391, 2353, 2374, 6589}"
81,1,131,0,0.141113,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/x,x]","-m \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+2 b m n \text{PolyLog}\left(3,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)-2 b^2 m n^2 \text{PolyLog}\left(4,-\frac{f x}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{3 b n}-\frac{m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}","-m \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+2 b m n \text{PolyLog}\left(3,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)-2 b^2 m n^2 \text{PolyLog}\left(4,-\frac{f x}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{3 b n}-\frac{m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}",1,"((a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m])/(3*b*n) - (m*(a + b*Log[c*x^n])^3*Log[1 + (f*x)/e])/(3*b*n) - m*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*x)/e)] + 2*b*m*n*(a + b*Log[c*x^n])*PolyLog[3, -((f*x)/e)] - 2*b^2*m*n^2*PolyLog[4, -((f*x)/e)]","A",5,5,26,0.1923,1,"{2375, 2317, 2374, 2383, 6589}"
82,1,283,0,0.3988132,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/x^2,x]","-\frac{2 b f m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{2 b^2 f m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{e}+\frac{2 b^2 f m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{e}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x}+\frac{f m \left(a+b \log \left(c x^n\right)\right)^3}{3 b e n}+\frac{f m \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{f m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{2 b f m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{2 b^2 n^2 \log \left(d (e+f x)^m\right)}{x}+\frac{2 b^2 f m n^2 \log (x)}{e}-\frac{2 b^2 f m n^2 \log (e+f x)}{e}","\frac{2 b f m n \text{PolyLog}\left(2,-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{2 b^2 f m n^2 \text{PolyLog}\left(2,-\frac{e}{f x}\right)}{e}+\frac{2 b^2 f m n^2 \text{PolyLog}\left(3,-\frac{e}{f x}\right)}{e}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x}-\frac{2 b f m n \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{f m \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{2 b^2 n^2 \log \left(d (e+f x)^m\right)}{x}+\frac{2 b^2 f m n^2 \log (x)}{e}-\frac{2 b^2 f m n^2 \log (e+f x)}{e}",1,"(2*b^2*f*m*n^2*Log[x])/e + (f*m*(a + b*Log[c*x^n])^2)/e + (f*m*(a + b*Log[c*x^n])^3)/(3*b*e*n) - (2*b^2*f*m*n^2*Log[e + f*x])/e - (2*b^2*n^2*Log[d*(e + f*x)^m])/x - (2*b*n*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/x - ((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/x - (2*b*f*m*n*(a + b*Log[c*x^n])*Log[1 + (f*x)/e])/e - (f*m*(a + b*Log[c*x^n])^2*Log[1 + (f*x)/e])/e - (2*b^2*f*m*n^2*PolyLog[2, -((f*x)/e)])/e - (2*b*f*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)])/e + (2*b^2*f*m*n^2*PolyLog[3, -((f*x)/e)])/e","A",15,14,26,0.5385,1,"{2305, 2304, 2378, 36, 29, 31, 2344, 2301, 2317, 2391, 2302, 30, 2374, 6589}"
83,1,385,0,0.5862474,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/x^3,x]","\frac{b f^2 m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{b^2 f^2 m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{2 e^2}-\frac{b^2 f^2 m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{e^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{2 x^2}-\frac{b n \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{2 x^2}-\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)^3}{6 b e^2 n}-\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2}+\frac{f^2 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}+\frac{b f^2 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^2}{2 e x}-\frac{3 b f m n \left(a+b \log \left(c x^n\right)\right)}{2 e x}-\frac{b^2 n^2 \log \left(d (e+f x)^m\right)}{4 x^2}-\frac{b^2 f^2 m n^2 \log (x)}{4 e^2}+\frac{b^2 f^2 m n^2 \log (e+f x)}{4 e^2}-\frac{7 b^2 f m n^2}{4 e x}","-\frac{b f^2 m n \text{PolyLog}\left(2,-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{b^2 f^2 m n^2 \text{PolyLog}\left(2,-\frac{e}{f x}\right)}{2 e^2}-\frac{b^2 f^2 m n^2 \text{PolyLog}\left(3,-\frac{e}{f x}\right)}{e^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{2 x^2}-\frac{b n \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{2 x^2}+\frac{f^2 m \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}+\frac{b f^2 m n \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^2}{2 e x}-\frac{3 b f m n \left(a+b \log \left(c x^n\right)\right)}{2 e x}-\frac{b^2 n^2 \log \left(d (e+f x)^m\right)}{4 x^2}-\frac{b^2 f^2 m n^2 \log (x)}{4 e^2}+\frac{b^2 f^2 m n^2 \log (e+f x)}{4 e^2}-\frac{7 b^2 f m n^2}{4 e x}",1,"(-7*b^2*f*m*n^2)/(4*e*x) - (b^2*f^2*m*n^2*Log[x])/(4*e^2) - (3*b*f*m*n*(a + b*Log[c*x^n]))/(2*e*x) - (f^2*m*(a + b*Log[c*x^n])^2)/(4*e^2) - (f*m*(a + b*Log[c*x^n])^2)/(2*e*x) - (f^2*m*(a + b*Log[c*x^n])^3)/(6*b*e^2*n) + (b^2*f^2*m*n^2*Log[e + f*x])/(4*e^2) - (b^2*n^2*Log[d*(e + f*x)^m])/(4*x^2) - (b*n*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/(2*x^2) - ((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/(2*x^2) + (b*f^2*m*n*(a + b*Log[c*x^n])*Log[1 + (f*x)/e])/(2*e^2) + (f^2*m*(a + b*Log[c*x^n])^2*Log[1 + (f*x)/e])/(2*e^2) + (b^2*f^2*m*n^2*PolyLog[2, -((f*x)/e)])/(2*e^2) + (b*f^2*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)])/e^2 - (b^2*f^2*m*n^2*PolyLog[3, -((f*x)/e)])/e^2","A",19,13,26,0.5000,1,"{2305, 2304, 2378, 44, 2351, 2301, 2317, 2391, 2353, 2302, 30, 2374, 6589}"
84,1,462,0,0.7242223,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x^4} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/x^4,x]","-\frac{2 b f^3 m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}-\frac{2 b^2 f^3 m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{9 e^3}+\frac{2 b^2 f^3 m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{3 e^3}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{3 x^3}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{9 x^3}+\frac{f^3 m \left(a+b \log \left(c x^n\right)\right)^3}{9 b e^3 n}+\frac{f^3 m \left(a+b \log \left(c x^n\right)\right)^2}{9 e^3}-\frac{f^3 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 e^3}-\frac{2 b f^3 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}+\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)^2}{3 e^2 x}+\frac{8 b f^2 m n \left(a+b \log \left(c x^n\right)\right)}{9 e^2 x}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^2}{6 e x^2}-\frac{5 b f m n \left(a+b \log \left(c x^n\right)\right)}{18 e x^2}-\frac{2 b^2 n^2 \log \left(d (e+f x)^m\right)}{27 x^3}+\frac{26 b^2 f^2 m n^2}{27 e^2 x}+\frac{2 b^2 f^3 m n^2 \log (x)}{27 e^3}-\frac{2 b^2 f^3 m n^2 \log (e+f x)}{27 e^3}-\frac{19 b^2 f m n^2}{108 e x^2}","\frac{2 b f^3 m n \text{PolyLog}\left(2,-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{2 b^2 f^3 m n^2 \text{PolyLog}\left(2,-\frac{e}{f x}\right)}{9 e^3}+\frac{2 b^2 f^3 m n^2 \text{PolyLog}\left(3,-\frac{e}{f x}\right)}{3 e^3}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{3 x^3}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{9 x^3}-\frac{f^3 m \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 e^3}-\frac{2 b f^3 m n \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}+\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)^2}{3 e^2 x}+\frac{8 b f^2 m n \left(a+b \log \left(c x^n\right)\right)}{9 e^2 x}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^2}{6 e x^2}-\frac{5 b f m n \left(a+b \log \left(c x^n\right)\right)}{18 e x^2}-\frac{2 b^2 n^2 \log \left(d (e+f x)^m\right)}{27 x^3}+\frac{26 b^2 f^2 m n^2}{27 e^2 x}+\frac{2 b^2 f^3 m n^2 \log (x)}{27 e^3}-\frac{2 b^2 f^3 m n^2 \log (e+f x)}{27 e^3}-\frac{19 b^2 f m n^2}{108 e x^2}",1,"(-19*b^2*f*m*n^2)/(108*e*x^2) + (26*b^2*f^2*m*n^2)/(27*e^2*x) + (2*b^2*f^3*m*n^2*Log[x])/(27*e^3) - (5*b*f*m*n*(a + b*Log[c*x^n]))/(18*e*x^2) + (8*b*f^2*m*n*(a + b*Log[c*x^n]))/(9*e^2*x) + (f^3*m*(a + b*Log[c*x^n])^2)/(9*e^3) - (f*m*(a + b*Log[c*x^n])^2)/(6*e*x^2) + (f^2*m*(a + b*Log[c*x^n])^2)/(3*e^2*x) + (f^3*m*(a + b*Log[c*x^n])^3)/(9*b*e^3*n) - (2*b^2*f^3*m*n^2*Log[e + f*x])/(27*e^3) - (2*b^2*n^2*Log[d*(e + f*x)^m])/(27*x^3) - (2*b*n*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/(9*x^3) - ((a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/(3*x^3) - (2*b*f^3*m*n*(a + b*Log[c*x^n])*Log[1 + (f*x)/e])/(9*e^3) - (f^3*m*(a + b*Log[c*x^n])^2*Log[1 + (f*x)/e])/(3*e^3) - (2*b^2*f^3*m*n^2*PolyLog[2, -((f*x)/e)])/(9*e^3) - (2*b*f^3*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)])/(3*e^3) + (2*b^2*f^3*m*n^2*PolyLog[3, -((f*x)/e)])/(3*e^3)","A",22,13,26,0.5000,1,"{2305, 2304, 2378, 44, 2351, 2301, 2317, 2391, 2353, 2302, 30, 2374, 6589}"
85,1,603,0,0.9744419,"\int x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right) \, dx","Int[x*(a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m],x]","\frac{3 b^2 e^2 m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^2}+\frac{3 b^2 e^2 m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}-\frac{3 b e^2 m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f^2}-\frac{3 b^3 e^2 m n^3 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{4 f^2}-\frac{3 b^3 e^2 m n^3 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{2 f^2}-\frac{3 b^3 e^2 m n^3 \text{PolyLog}\left(4,-\frac{f x}{e}\right)}{f^2}+\frac{3}{4} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)-\frac{3 b^2 e^2 m n^2 \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 f^2}-\frac{9}{8} b^2 m n^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{21 a b^2 e m n^2 x}{4 f}-\frac{3}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)+\frac{3 b e^2 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 f^2}-\frac{e^2 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 f^2}-\frac{9 b e m n x \left(a+b \log \left(c x^n\right)\right)^2}{4 f}+\frac{e m x \left(a+b \log \left(c x^n\right)\right)^3}{2 f}+\frac{3}{4} b m n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{4} m x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{21 b^3 e m n^2 x \log \left(c x^n\right)}{4 f}-\frac{3}{8} b^3 n^3 x^2 \log \left(d (e+f x)^m\right)+\frac{3 b^3 e^2 m n^3 \log (e+f x)}{8 f^2}-\frac{45 b^3 e m n^3 x}{8 f}+\frac{3}{4} b^3 m n^3 x^2","\frac{3 b^2 e^2 m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^2}+\frac{3 b^2 e^2 m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}-\frac{3 b e^2 m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f^2}-\frac{3 b^3 e^2 m n^3 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{4 f^2}-\frac{3 b^3 e^2 m n^3 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{2 f^2}-\frac{3 b^3 e^2 m n^3 \text{PolyLog}\left(4,-\frac{f x}{e}\right)}{f^2}+\frac{3}{4} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)-\frac{3 b^2 e^2 m n^2 \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 f^2}-\frac{9}{8} b^2 m n^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{21 a b^2 e m n^2 x}{4 f}-\frac{3}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)+\frac{3 b e^2 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 f^2}-\frac{e^2 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 f^2}-\frac{9 b e m n x \left(a+b \log \left(c x^n\right)\right)^2}{4 f}+\frac{e m x \left(a+b \log \left(c x^n\right)\right)^3}{2 f}+\frac{3}{4} b m n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{4} m x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{21 b^3 e m n^2 x \log \left(c x^n\right)}{4 f}-\frac{3}{8} b^3 n^3 x^2 \log \left(d (e+f x)^m\right)+\frac{3 b^3 e^2 m n^3 \log (e+f x)}{8 f^2}-\frac{45 b^3 e m n^3 x}{8 f}+\frac{3}{4} b^3 m n^3 x^2",1,"(21*a*b^2*e*m*n^2*x)/(4*f) - (45*b^3*e*m*n^3*x)/(8*f) + (3*b^3*m*n^3*x^2)/4 + (21*b^3*e*m*n^2*x*Log[c*x^n])/(4*f) - (9*b^2*m*n^2*x^2*(a + b*Log[c*x^n]))/8 - (9*b*e*m*n*x*(a + b*Log[c*x^n])^2)/(4*f) + (3*b*m*n*x^2*(a + b*Log[c*x^n])^2)/4 + (e*m*x*(a + b*Log[c*x^n])^3)/(2*f) - (m*x^2*(a + b*Log[c*x^n])^3)/4 + (3*b^3*e^2*m*n^3*Log[e + f*x])/(8*f^2) - (3*b^3*n^3*x^2*Log[d*(e + f*x)^m])/8 + (3*b^2*n^2*x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/4 - (3*b*n*x^2*(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/4 + (x^2*(a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m])/2 - (3*b^2*e^2*m*n^2*(a + b*Log[c*x^n])*Log[1 + (f*x)/e])/(4*f^2) + (3*b*e^2*m*n*(a + b*Log[c*x^n])^2*Log[1 + (f*x)/e])/(4*f^2) - (e^2*m*(a + b*Log[c*x^n])^3*Log[1 + (f*x)/e])/(2*f^2) - (3*b^3*e^2*m*n^3*PolyLog[2, -((f*x)/e)])/(4*f^2) + (3*b^2*e^2*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)])/(2*f^2) - (3*b*e^2*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*x)/e)])/(2*f^2) - (3*b^3*e^2*m*n^3*PolyLog[3, -((f*x)/e)])/(2*f^2) + (3*b^2*e^2*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((f*x)/e)])/f^2 - (3*b^3*e^2*m*n^3*PolyLog[4, -((f*x)/e)])/f^2","A",34,13,24,0.5417,1,"{2305, 2304, 2378, 43, 2351, 2295, 2317, 2391, 2353, 2296, 2374, 6589, 2383}"
86,1,473,0,0.6522716,"\int \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right) \, dx","Int[(a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m],x]","-\frac{6 b^2 e m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f}-\frac{6 b^2 e m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f}+\frac{3 b e m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{f}+\frac{6 b^3 e m n^3 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{f}+\frac{6 b^3 e m n^3 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{f}+\frac{6 b^3 e m n^3 \text{PolyLog}\left(4,-\frac{f x}{e}\right)}{f}+6 a b^2 n^2 x \log \left(d (e+f x)^m\right)+\frac{6 b^2 e m n^2 (a-b n) \log (e+f x)}{f}-12 a b^2 m n^2 x-6 b^2 m n^2 x (a-b n)-3 b n x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)+x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)-\frac{3 b e m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f}+\frac{e m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{f}+6 b m n x \left(a+b \log \left(c x^n\right)\right)^2-m x \left(a+b \log \left(c x^n\right)\right)^3+6 b^3 n^2 x \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+\frac{6 b^3 e m n^2 \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)}{f}-18 b^3 m n^2 x \log \left(c x^n\right)-6 b^3 n^3 x \log \left(d (e+f x)^m\right)+18 b^3 m n^3 x","-\frac{6 b^2 e m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f}-\frac{6 b^2 e m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f}+\frac{3 b e m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{f}+\frac{6 b^3 e m n^3 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{f}+\frac{6 b^3 e m n^3 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{f}+\frac{6 b^3 e m n^3 \text{PolyLog}\left(4,-\frac{f x}{e}\right)}{f}+6 a b^2 n^2 x \log \left(d (e+f x)^m\right)+\frac{6 b^2 e m n^2 (a-b n) \log (e+f x)}{f}-12 a b^2 m n^2 x-6 b^2 m n^2 x (a-b n)-3 b n x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)+x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)-\frac{3 b e m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f}+\frac{e m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{f}+6 b m n x \left(a+b \log \left(c x^n\right)\right)^2-m x \left(a+b \log \left(c x^n\right)\right)^3+6 b^3 n^2 x \log \left(c x^n\right) \log \left(d (e+f x)^m\right)+\frac{6 b^3 e m n^2 \log \left(c x^n\right) \log \left(\frac{f x}{e}+1\right)}{f}-18 b^3 m n^2 x \log \left(c x^n\right)-6 b^3 n^3 x \log \left(d (e+f x)^m\right)+18 b^3 m n^3 x",1,"-12*a*b^2*m*n^2*x + 18*b^3*m*n^3*x - 6*b^2*m*n^2*(a - b*n)*x - 18*b^3*m*n^2*x*Log[c*x^n] + 6*b*m*n*x*(a + b*Log[c*x^n])^2 - m*x*(a + b*Log[c*x^n])^3 + (6*b^2*e*m*n^2*(a - b*n)*Log[e + f*x])/f + 6*a*b^2*n^2*x*Log[d*(e + f*x)^m] - 6*b^3*n^3*x*Log[d*(e + f*x)^m] + 6*b^3*n^2*x*Log[c*x^n]*Log[d*(e + f*x)^m] - 3*b*n*x*(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m] + x*(a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m] + (6*b^3*e*m*n^2*Log[c*x^n]*Log[1 + (f*x)/e])/f - (3*b*e*m*n*(a + b*Log[c*x^n])^2*Log[1 + (f*x)/e])/f + (e*m*(a + b*Log[c*x^n])^3*Log[1 + (f*x)/e])/f + (6*b^3*e*m*n^3*PolyLog[2, -((f*x)/e)])/f - (6*b^2*e*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)])/f + (3*b*e*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*x)/e)])/f + (6*b^3*e*m*n^3*PolyLog[3, -((f*x)/e)])/f - (6*b^2*e*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((f*x)/e)])/f + (6*b^3*e*m*n^3*PolyLog[4, -((f*x)/e)])/f","A",28,12,23,0.5217,1,"{2296, 2295, 2371, 6, 43, 2351, 2317, 2391, 2353, 2374, 6589, 2383}"
87,1,161,0,0.1898153,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m])/x,x]","-6 b^2 m n^2 \text{PolyLog}\left(4,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)-m \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3+3 b m n \text{PolyLog}\left(3,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+6 b^3 m n^3 \text{PolyLog}\left(5,-\frac{f x}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^4 \log \left(d (e+f x)^m\right)}{4 b n}-\frac{m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}","-6 b^2 m n^2 \text{PolyLog}\left(4,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)-m \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3+3 b m n \text{PolyLog}\left(3,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+6 b^3 m n^3 \text{PolyLog}\left(5,-\frac{f x}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^4 \log \left(d (e+f x)^m\right)}{4 b n}-\frac{m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}",1,"((a + b*Log[c*x^n])^4*Log[d*(e + f*x)^m])/(4*b*n) - (m*(a + b*Log[c*x^n])^4*Log[1 + (f*x)/e])/(4*b*n) - m*(a + b*Log[c*x^n])^3*PolyLog[2, -((f*x)/e)] + 3*b*m*n*(a + b*Log[c*x^n])^2*PolyLog[3, -((f*x)/e)] - 6*b^2*m*n^2*(a + b*Log[c*x^n])*PolyLog[4, -((f*x)/e)] + 6*b^3*m*n^3*PolyLog[5, -((f*x)/e)]","A",6,5,26,0.1923,1,"{2375, 2317, 2374, 2383, 6589}"
88,1,459,0,0.6958429,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m])/x^2,x]","-\frac{6 b^2 f m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{6 b^2 f m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{3 b f m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{6 b^3 f m n^3 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{e}+\frac{6 b^3 f m n^3 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{e}-\frac{6 b^3 f m n^3 \text{PolyLog}\left(4,-\frac{f x}{e}\right)}{e}-\frac{6 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x}-\frac{6 b^2 f m n^2 \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{x}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x}+\frac{f m \left(a+b \log \left(c x^n\right)\right)^4}{4 b e n}+\frac{f m \left(a+b \log \left(c x^n\right)\right)^3}{e}-\frac{f m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{e}+\frac{3 b f m n \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{3 b f m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{6 b^3 n^3 \log \left(d (e+f x)^m\right)}{x}+\frac{6 b^3 f m n^3 \log (x)}{e}-\frac{6 b^3 f m n^3 \log (e+f x)}{e}","\frac{6 b^2 f m n^2 \text{PolyLog}\left(2,-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{6 b^2 f m n^2 \text{PolyLog}\left(3,-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{e}+\frac{3 b f m n \text{PolyLog}\left(2,-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)^2}{e}+\frac{6 b^3 f m n^3 \text{PolyLog}\left(2,-\frac{e}{f x}\right)}{e}+\frac{6 b^3 f m n^3 \text{PolyLog}\left(3,-\frac{e}{f x}\right)}{e}+\frac{6 b^3 f m n^3 \text{PolyLog}\left(4,-\frac{e}{f x}\right)}{e}-\frac{6 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{x}-\frac{6 b^2 f m n^2 \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{x}-\frac{3 b f m n \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e}-\frac{f m \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{e}-\frac{6 b^3 n^3 \log \left(d (e+f x)^m\right)}{x}+\frac{6 b^3 f m n^3 \log (x)}{e}-\frac{6 b^3 f m n^3 \log (e+f x)}{e}",1,"(6*b^3*f*m*n^3*Log[x])/e + (3*b*f*m*n*(a + b*Log[c*x^n])^2)/e + (f*m*(a + b*Log[c*x^n])^3)/e + (f*m*(a + b*Log[c*x^n])^4)/(4*b*e*n) - (6*b^3*f*m*n^3*Log[e + f*x])/e - (6*b^3*n^3*Log[d*(e + f*x)^m])/x - (6*b^2*n^2*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/x - (3*b*n*(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/x - ((a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m])/x - (6*b^2*f*m*n^2*(a + b*Log[c*x^n])*Log[1 + (f*x)/e])/e - (3*b*f*m*n*(a + b*Log[c*x^n])^2*Log[1 + (f*x)/e])/e - (f*m*(a + b*Log[c*x^n])^3*Log[1 + (f*x)/e])/e - (6*b^3*f*m*n^3*PolyLog[2, -((f*x)/e)])/e - (6*b^2*f*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)])/e - (3*b*f*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*x)/e)])/e + (6*b^3*f*m*n^3*PolyLog[3, -((f*x)/e)])/e + (6*b^2*f*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((f*x)/e)])/e - (6*b^3*f*m*n^3*PolyLog[4, -((f*x)/e)])/e","A",22,15,26,0.5769,1,"{2305, 2304, 2378, 36, 29, 31, 2344, 2301, 2317, 2391, 2302, 30, 2374, 6589, 2383}"
89,1,614,0,1.0146792,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m])/x^3,x]","\frac{3 b^2 f^2 m n^2 \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{3 b^2 f^2 m n^2 \text{PolyLog}\left(3,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{3 b f^2 m n \text{PolyLog}\left(2,-\frac{f x}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}+\frac{3 b^3 f^2 m n^3 \text{PolyLog}\left(2,-\frac{f x}{e}\right)}{4 e^2}-\frac{3 b^3 f^2 m n^3 \text{PolyLog}\left(3,-\frac{f x}{e}\right)}{2 e^2}+\frac{3 b^3 f^2 m n^3 \text{PolyLog}\left(4,-\frac{f x}{e}\right)}{e^2}-\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{4 x^2}+\frac{3 b^2 f^2 m n^2 \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}-\frac{21 b^2 f m n^2 \left(a+b \log \left(c x^n\right)\right)}{4 e x}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{2 x^2}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{4 x^2}-\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)^4}{8 b e^2 n}-\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)^3}{4 e^2}+\frac{f^2 m \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 e^2}-\frac{3 b f^2 m n \left(a+b \log \left(c x^n\right)\right)^2}{8 e^2}+\frac{3 b f^2 m n \log \left(\frac{f x}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^3}{2 e x}-\frac{9 b f m n \left(a+b \log \left(c x^n\right)\right)^2}{4 e x}-\frac{3 b^3 n^3 \log \left(d (e+f x)^m\right)}{8 x^2}-\frac{3 b^3 f^2 m n^3 \log (x)}{8 e^2}+\frac{3 b^3 f^2 m n^3 \log (e+f x)}{8 e^2}-\frac{45 b^3 f m n^3}{8 e x}","-\frac{3 b^2 f^2 m n^2 \text{PolyLog}\left(2,-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{3 b^2 f^2 m n^2 \text{PolyLog}\left(3,-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{3 b f^2 m n \text{PolyLog}\left(2,-\frac{e}{f x}\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^2}-\frac{3 b^3 f^2 m n^3 \text{PolyLog}\left(2,-\frac{e}{f x}\right)}{4 e^2}-\frac{3 b^3 f^2 m n^3 \text{PolyLog}\left(3,-\frac{e}{f x}\right)}{2 e^2}-\frac{3 b^3 f^2 m n^3 \text{PolyLog}\left(4,-\frac{e}{f x}\right)}{e^2}-\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d (e+f x)^m\right)}{4 x^2}+\frac{3 b^2 f^2 m n^2 \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}-\frac{21 b^2 f m n^2 \left(a+b \log \left(c x^n\right)\right)}{4 e x}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d (e+f x)^m\right)}{4 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d (e+f x)^m\right)}{2 x^2}+\frac{3 b f^2 m n \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2}+\frac{f^2 m \log \left(\frac{e}{f x}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 e^2}-\frac{9 b f m n \left(a+b \log \left(c x^n\right)\right)^2}{4 e x}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^3}{2 e x}-\frac{3 b^3 n^3 \log \left(d (e+f x)^m\right)}{8 x^2}-\frac{3 b^3 f^2 m n^3 \log (x)}{8 e^2}+\frac{3 b^3 f^2 m n^3 \log (e+f x)}{8 e^2}-\frac{45 b^3 f m n^3}{8 e x}",1,"(-45*b^3*f*m*n^3)/(8*e*x) - (3*b^3*f^2*m*n^3*Log[x])/(8*e^2) - (21*b^2*f*m*n^2*(a + b*Log[c*x^n]))/(4*e*x) - (3*b*f^2*m*n*(a + b*Log[c*x^n])^2)/(8*e^2) - (9*b*f*m*n*(a + b*Log[c*x^n])^2)/(4*e*x) - (f^2*m*(a + b*Log[c*x^n])^3)/(4*e^2) - (f*m*(a + b*Log[c*x^n])^3)/(2*e*x) - (f^2*m*(a + b*Log[c*x^n])^4)/(8*b*e^2*n) + (3*b^3*f^2*m*n^3*Log[e + f*x])/(8*e^2) - (3*b^3*n^3*Log[d*(e + f*x)^m])/(8*x^2) - (3*b^2*n^2*(a + b*Log[c*x^n])*Log[d*(e + f*x)^m])/(4*x^2) - (3*b*n*(a + b*Log[c*x^n])^2*Log[d*(e + f*x)^m])/(4*x^2) - ((a + b*Log[c*x^n])^3*Log[d*(e + f*x)^m])/(2*x^2) + (3*b^2*f^2*m*n^2*(a + b*Log[c*x^n])*Log[1 + (f*x)/e])/(4*e^2) + (3*b*f^2*m*n*(a + b*Log[c*x^n])^2*Log[1 + (f*x)/e])/(4*e^2) + (f^2*m*(a + b*Log[c*x^n])^3*Log[1 + (f*x)/e])/(2*e^2) + (3*b^3*f^2*m*n^3*PolyLog[2, -((f*x)/e)])/(4*e^2) + (3*b^2*f^2*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((f*x)/e)])/(2*e^2) + (3*b*f^2*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*x)/e)])/(2*e^2) - (3*b^3*f^2*m*n^3*PolyLog[3, -((f*x)/e)])/(2*e^2) - (3*b^2*f^2*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((f*x)/e)])/e^2 + (3*b^3*f^2*m*n^3*PolyLog[4, -((f*x)/e)])/e^2","A",30,14,26,0.5385,1,"{2305, 2304, 2378, 44, 2351, 2301, 2317, 2391, 2353, 2302, 30, 2374, 6589, 2383}"
90,1,221,0,0.2235331,"\int x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right) \, dx","Int[x^3*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m],x]","\frac{b e^2 m n \text{PolyLog}\left(2,\frac{f x^2}{e}+1\right)}{8 f^2}+\frac{1}{4} x^4 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)-\frac{e^2 m \log \left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 f^2}+\frac{e m x^2 \left(a+b \log \left(c x^n\right)\right)}{4 f}-\frac{1}{8} m x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b n x^4 \log \left(d \left(e+f x^2\right)^m\right)+\frac{b e^2 m n \log \left(e+f x^2\right)}{16 f^2}+\frac{b e^2 m n \log \left(-\frac{f x^2}{e}\right) \log \left(e+f x^2\right)}{8 f^2}-\frac{3 b e m n x^2}{16 f}+\frac{1}{16} b m n x^4","\frac{b e^2 m n \text{PolyLog}\left(2,\frac{f x^2}{e}+1\right)}{8 f^2}+\frac{1}{4} x^4 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)-\frac{e^2 m \log \left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 f^2}+\frac{e m x^2 \left(a+b \log \left(c x^n\right)\right)}{4 f}-\frac{1}{8} m x^4 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{16} b n x^4 \log \left(d \left(e+f x^2\right)^m\right)+\frac{b e^2 m n \log \left(e+f x^2\right)}{16 f^2}+\frac{b e^2 m n \log \left(-\frac{f x^2}{e}\right) \log \left(e+f x^2\right)}{8 f^2}-\frac{3 b e m n x^2}{16 f}+\frac{1}{16} b m n x^4",1,"(-3*b*e*m*n*x^2)/(16*f) + (b*m*n*x^4)/16 + (e*m*x^2*(a + b*Log[c*x^n]))/(4*f) - (m*x^4*(a + b*Log[c*x^n]))/8 + (b*e^2*m*n*Log[e + f*x^2])/(16*f^2) + (b*e^2*m*n*Log[-((f*x^2)/e)]*Log[e + f*x^2])/(8*f^2) - (e^2*m*(a + b*Log[c*x^n])*Log[e + f*x^2])/(4*f^2) - (b*n*x^4*Log[d*(e + f*x^2)^m])/16 + (x^4*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/4 + (b*e^2*m*n*PolyLog[2, 1 + (f*x^2)/e])/(8*f^2)","A",9,6,26,0.2308,1,"{2454, 2395, 43, 2376, 2394, 2315}"
91,1,148,0,0.2175733,"\int x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right) \, dx","Int[x*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m],x]","-\frac{b e m n \text{PolyLog}\left(2,\frac{f x^2}{e}+1\right)}{4 f}+\frac{\left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{2 f}-\frac{1}{2} m x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b n \left(e+f x^2\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 f}-\frac{b e n \log \left(-\frac{f x^2}{e}\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 f}+\frac{1}{2} b m n x^2","-\frac{b e m n \text{PolyLog}\left(2,\frac{f x^2}{e}+1\right)}{4 f}+\frac{\left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{2 f}-\frac{1}{2} m x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{b n \left(e+f x^2\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 f}-\frac{b e n \log \left(-\frac{f x^2}{e}\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 f}+\frac{1}{2} b m n x^2",1,"(b*m*n*x^2)/2 - (m*x^2*(a + b*Log[c*x^n]))/2 - (b*n*(e + f*x^2)*Log[d*(e + f*x^2)^m])/(4*f) - (b*e*n*Log[-((f*x^2)/e)]*Log[d*(e + f*x^2)^m])/(4*f) + ((e + f*x^2)*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/(2*f) - (b*e*m*n*PolyLog[2, 1 + (f*x^2)/e])/(4*f)","A",9,10,24,0.4167,1,"{2454, 2389, 2295, 2376, 2475, 2411, 43, 2351, 2317, 2391}"
92,1,113,0,0.1259808,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x,x]","-\frac{1}{2} m \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} b m n \text{PolyLog}\left(3,-\frac{f x^2}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{2 b n}-\frac{m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}","-\frac{1}{2} m \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{4} b m n \text{PolyLog}\left(3,-\frac{f x^2}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{2 b n}-\frac{m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}",1,"((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/(2*b*n) - (m*(a + b*Log[c*x^n])^2*Log[1 + (f*x^2)/e])/(2*b*n) - (m*(a + b*Log[c*x^n])*PolyLog[2, -((f*x^2)/e)])/2 + (b*m*n*PolyLog[3, -((f*x^2)/e)])/4","A",4,4,26,0.1538,1,"{2375, 2337, 2374, 6589}"
93,1,195,0,0.1815676,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x^3,x]","\frac{b f m n \text{PolyLog}\left(2,\frac{f x^2}{e}+1\right)}{4 e}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}+\frac{f m \log (x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{f m \log \left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}-\frac{b f m n \log \left(e+f x^2\right)}{4 e}+\frac{b f m n \log \left(-\frac{f x^2}{e}\right) \log \left(e+f x^2\right)}{4 e}-\frac{b f m n \log ^2(x)}{2 e}+\frac{b f m n \log (x)}{2 e}","\frac{b f m n \text{PolyLog}\left(2,\frac{f x^2}{e}+1\right)}{4 e}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}+\frac{f m \log (x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{f m \log \left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}-\frac{b f m n \log \left(e+f x^2\right)}{4 e}+\frac{b f m n \log \left(-\frac{f x^2}{e}\right) \log \left(e+f x^2\right)}{4 e}-\frac{b f m n \log ^2(x)}{2 e}+\frac{b f m n \log (x)}{2 e}",1,"(b*f*m*n*Log[x])/(2*e) - (b*f*m*n*Log[x]^2)/(2*e) + (f*m*Log[x]*(a + b*Log[c*x^n]))/e - (b*f*m*n*Log[e + f*x^2])/(4*e) + (b*f*m*n*Log[-((f*x^2)/e)]*Log[e + f*x^2])/(4*e) - (f*m*(a + b*Log[c*x^n])*Log[e + f*x^2])/(2*e) - (b*n*Log[d*(e + f*x^2)^m])/(4*x^2) - ((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/(2*x^2) + (b*f*m*n*PolyLog[2, 1 + (f*x^2)/e])/(4*e)","A",11,9,26,0.3462,1,"{2454, 2395, 36, 29, 31, 2376, 2301, 2394, 2315}"
94,1,248,0,0.226004,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x^5} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x^5,x]","-\frac{b f^2 m n \text{PolyLog}\left(2,\frac{f x^2}{e}+1\right)}{8 e^2}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 x^4}-\frac{f^2 m \log (x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{f^2 m \log \left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)}{4 e x^2}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{16 x^4}+\frac{b f^2 m n \log \left(e+f x^2\right)}{16 e^2}-\frac{b f^2 m n \log \left(-\frac{f x^2}{e}\right) \log \left(e+f x^2\right)}{8 e^2}+\frac{b f^2 m n \log ^2(x)}{4 e^2}-\frac{b f^2 m n \log (x)}{8 e^2}-\frac{3 b f m n}{16 e x^2}","-\frac{b f^2 m n \text{PolyLog}\left(2,\frac{f x^2}{e}+1\right)}{8 e^2}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 x^4}-\frac{f^2 m \log (x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}+\frac{f^2 m \log \left(e+f x^2\right) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)}{4 e x^2}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{16 x^4}+\frac{b f^2 m n \log \left(e+f x^2\right)}{16 e^2}-\frac{b f^2 m n \log \left(-\frac{f x^2}{e}\right) \log \left(e+f x^2\right)}{8 e^2}+\frac{b f^2 m n \log ^2(x)}{4 e^2}-\frac{b f^2 m n \log (x)}{8 e^2}-\frac{3 b f m n}{16 e x^2}",1,"(-3*b*f*m*n)/(16*e*x^2) - (b*f^2*m*n*Log[x])/(8*e^2) + (b*f^2*m*n*Log[x]^2)/(4*e^2) - (f*m*(a + b*Log[c*x^n]))/(4*e*x^2) - (f^2*m*Log[x]*(a + b*Log[c*x^n]))/(2*e^2) + (b*f^2*m*n*Log[e + f*x^2])/(16*e^2) - (b*f^2*m*n*Log[-((f*x^2)/e)]*Log[e + f*x^2])/(8*e^2) + (f^2*m*(a + b*Log[c*x^n])*Log[e + f*x^2])/(4*e^2) - (b*n*Log[d*(e + f*x^2)^m])/(16*x^4) - ((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/(4*x^4) - (b*f^2*m*n*PolyLog[2, 1 + (f*x^2)/e])/(8*e^2)","A",10,7,26,0.2692,1,"{2454, 2395, 44, 2376, 2301, 2394, 2315}"
95,1,251,0,0.1845833,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right) \, dx","Int[x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m],x]","\frac{i b e^{3/2} m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 f^{3/2}}-\frac{i b e^{3/2} m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 f^{3/2}}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)-\frac{2 e^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^{3/2}}+\frac{2 e m x \left(a+b \log \left(c x^n\right)\right)}{3 f}-\frac{2}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b n x^3 \log \left(d \left(e+f x^2\right)^m\right)+\frac{2 b e^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{9 f^{3/2}}-\frac{8 b e m n x}{9 f}+\frac{4}{27} b m n x^3","\frac{i b e^{3/2} m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 f^{3/2}}-\frac{i b e^{3/2} m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 f^{3/2}}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)-\frac{2 e^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^{3/2}}+\frac{2 e m x \left(a+b \log \left(c x^n\right)\right)}{3 f}-\frac{2}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b n x^3 \log \left(d \left(e+f x^2\right)^m\right)+\frac{2 b e^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{9 f^{3/2}}-\frac{8 b e m n x}{9 f}+\frac{4}{27} b m n x^3",1,"(-8*b*e*m*n*x)/(9*f) + (4*b*m*n*x^3)/27 + (2*b*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/(9*f^(3/2)) + (2*e*m*x*(a + b*Log[c*x^n]))/(3*f) - (2*m*x^3*(a + b*Log[c*x^n]))/9 - (2*e^(3/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*x^n]))/(3*f^(3/2)) - (b*n*x^3*Log[d*(e + f*x^2)^m])/9 + (x^3*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/3 + ((I/3)*b*e^(3/2)*m*n*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/f^(3/2) - ((I/3)*b*e^(3/2)*m*n*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/f^(3/2)","A",9,6,26,0.2308,1,"{2455, 302, 205, 2376, 4848, 2391}"
96,1,194,0,0.1157239,"\int \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right) \, dx","Int[(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m],x]","-\frac{i b \sqrt{e} m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+\frac{i b \sqrt{e} m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)+\frac{2 \sqrt{e} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{f}}-2 m x \left(a+b \log \left(c x^n\right)\right)-b n x \log \left(d \left(e+f x^2\right)^m\right)-\frac{2 b \sqrt{e} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+4 b m n x","-\frac{i b \sqrt{e} m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+\frac{i b \sqrt{e} m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)+\frac{2 \sqrt{e} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{f}}-2 m x \left(a+b \log \left(c x^n\right)\right)-b n x \log \left(d \left(e+f x^2\right)^m\right)-\frac{2 b \sqrt{e} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+4 b m n x",1,"4*b*m*n*x - (2*b*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/Sqrt[f] - 2*m*x*(a + b*Log[c*x^n]) + (2*Sqrt[e]*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*x^n]))/Sqrt[f] - b*n*x*Log[d*(e + f*x^2)^m] + x*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m] - (I*b*Sqrt[e]*m*n*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/Sqrt[f] + (I*b*Sqrt[e]*m*n*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/Sqrt[f]","A",8,6,23,0.2609,1,"{2448, 321, 205, 2370, 4848, 2391}"
97,1,179,0,0.1328495,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x^2,x]","-\frac{i b \sqrt{f} m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}+\frac{i b \sqrt{f} m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x}+\frac{2 \sqrt{f} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e}}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{x}+\frac{2 b \sqrt{f} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}","-\frac{i b \sqrt{f} m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}+\frac{i b \sqrt{f} m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x}+\frac{2 \sqrt{f} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e}}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{x}+\frac{2 b \sqrt{f} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}",1,"(2*b*Sqrt[f]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/Sqrt[e] + (2*Sqrt[f]*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*x^n]))/Sqrt[e] - (b*n*Log[d*(e + f*x^2)^m])/x - ((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x - (I*b*Sqrt[f]*m*n*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/Sqrt[e] + (I*b*Sqrt[f]*m*n*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/Sqrt[e]","A",7,5,26,0.1923,1,"{2455, 205, 2376, 4848, 2391}"
98,1,227,0,0.1627257,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x^4} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x^4,x]","\frac{i b f^{3/2} m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 e^{3/2}}-\frac{i b f^{3/2} m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 e^{3/2}}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{3 x^3}-\frac{2 f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^{3/2}}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)}{3 e x}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{9 x^3}-\frac{2 b f^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{9 e^{3/2}}-\frac{8 b f m n}{9 e x}","\frac{i b f^{3/2} m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 e^{3/2}}-\frac{i b f^{3/2} m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{3 e^{3/2}}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{3 x^3}-\frac{2 f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^{3/2}}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)}{3 e x}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{9 x^3}-\frac{2 b f^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{9 e^{3/2}}-\frac{8 b f m n}{9 e x}",1,"(-8*b*f*m*n)/(9*e*x) - (2*b*f^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/(9*e^(3/2)) - (2*f*m*(a + b*Log[c*x^n]))/(3*e*x) - (2*f^(3/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*x^n]))/(3*e^(3/2)) - (b*n*Log[d*(e + f*x^2)^m])/(9*x^3) - ((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/(3*x^3) + ((I/3)*b*f^(3/2)*m*n*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/e^(3/2) - ((I/3)*b*f^(3/2)*m*n*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/e^(3/2)","A",8,6,26,0.2308,1,"{2455, 325, 205, 2376, 4848, 2391}"
99,1,267,0,0.1890249,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x^6} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x^6,x]","-\frac{i b f^{5/2} m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{5 e^{5/2}}+\frac{i b f^{5/2} m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{5 e^{5/2}}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{5 x^5}+\frac{2 f^2 m \left(a+b \log \left(c x^n\right)\right)}{5 e^2 x}+\frac{2 f^{5/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{5 e^{5/2}}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)}{15 e x^3}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{25 x^5}+\frac{12 b f^2 m n}{25 e^2 x}+\frac{2 b f^{5/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{25 e^{5/2}}-\frac{16 b f m n}{225 e x^3}","-\frac{i b f^{5/2} m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{5 e^{5/2}}+\frac{i b f^{5/2} m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{5 e^{5/2}}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{5 x^5}+\frac{2 f^2 m \left(a+b \log \left(c x^n\right)\right)}{5 e^2 x}+\frac{2 f^{5/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{5 e^{5/2}}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)}{15 e x^3}-\frac{b n \log \left(d \left(e+f x^2\right)^m\right)}{25 x^5}+\frac{12 b f^2 m n}{25 e^2 x}+\frac{2 b f^{5/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{25 e^{5/2}}-\frac{16 b f m n}{225 e x^3}",1,"(-16*b*f*m*n)/(225*e*x^3) + (12*b*f^2*m*n)/(25*e^2*x) + (2*b*f^(5/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/(25*e^(5/2)) - (2*f*m*(a + b*Log[c*x^n]))/(15*e*x^3) + (2*f^2*m*(a + b*Log[c*x^n]))/(5*e^2*x) + (2*f^(5/2)*m*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*x^n]))/(5*e^(5/2)) - (b*n*Log[d*(e + f*x^2)^m])/(25*x^5) - ((a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/(5*x^5) - ((I/5)*b*f^(5/2)*m*n*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/e^(5/2) + ((I/5)*b*f^(5/2)*m*n*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/e^(5/2)","A",9,6,26,0.2308,1,"{2455, 325, 205, 2376, 4848, 2391}"
100,1,310,0,0.536124,"\int x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Int[x*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m],x]","\frac{b e m n \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f}-\frac{b^2 e m n^2 \text{PolyLog}\left(2,-\frac{f x^2}{e}\right)}{4 f}-\frac{b^2 e m n^2 \text{PolyLog}\left(3,-\frac{f x^2}{e}\right)}{4 f}-\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)-\frac{b e m n \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 f}+\frac{e m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f}+b m n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} m x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{4} b^2 n^2 x^2 \log \left(d \left(e+f x^2\right)^m\right)+\frac{b^2 e m n^2 \log \left(e+f x^2\right)}{4 f}-\frac{3}{4} b^2 m n^2 x^2","\frac{b e m n \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f}-\frac{b^2 e m n^2 \text{PolyLog}\left(2,-\frac{f x^2}{e}\right)}{4 f}-\frac{b^2 e m n^2 \text{PolyLog}\left(3,-\frac{f x^2}{e}\right)}{4 f}-\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)-\frac{b e m n \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 f}+\frac{e m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f}+b m n x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} m x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{4} b^2 n^2 x^2 \log \left(d \left(e+f x^2\right)^m\right)+\frac{b^2 e m n^2 \log \left(e+f x^2\right)}{4 f}-\frac{3}{4} b^2 m n^2 x^2",1,"(-3*b^2*m*n^2*x^2)/4 + b*m*n*x^2*(a + b*Log[c*x^n]) - (m*x^2*(a + b*Log[c*x^n])^2)/2 + (b^2*e*m*n^2*Log[e + f*x^2])/(4*f) + (b^2*n^2*x^2*Log[d*(e + f*x^2)^m])/4 - (b*n*x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/2 + (x^2*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/2 - (b*e*m*n*(a + b*Log[c*x^n])*Log[1 + (f*x^2)/e])/(2*f) + (e*m*(a + b*Log[c*x^n])^2*Log[1 + (f*x^2)/e])/(2*f) - (b^2*e*m*n^2*PolyLog[2, -((f*x^2)/e)])/(4*f) + (b*e*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*x^2)/e)])/(2*f) - (b^2*e*m*n^2*PolyLog[3, -((f*x^2)/e)])/(4*f)","A",17,11,26,0.4231,1,"{2305, 2304, 2378, 266, 43, 2351, 2337, 2391, 2353, 2374, 6589}"
101,1,147,0,0.1750812,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x,x]","-\frac{1}{2} m \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b m n \text{PolyLog}\left(3,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b^2 m n^2 \text{PolyLog}\left(4,-\frac{f x^2}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{3 b n}-\frac{m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}","-\frac{1}{2} m \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{2} b m n \text{PolyLog}\left(3,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b^2 m n^2 \text{PolyLog}\left(4,-\frac{f x^2}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{3 b n}-\frac{m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}",1,"((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/(3*b*n) - (m*(a + b*Log[c*x^n])^3*Log[1 + (f*x^2)/e])/(3*b*n) - (m*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*x^2)/e)])/2 + (b*m*n*(a + b*Log[c*x^n])*PolyLog[3, -((f*x^2)/e)])/2 - (b^2*m*n^2*PolyLog[4, -((f*x^2)/e)])/4","A",5,5,28,0.1786,1,"{2375, 2337, 2374, 2383, 6589}"
102,1,276,0,0.3300234,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x^3,x]","\frac{b f m n \text{PolyLog}\left(2,-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e}+\frac{b^2 f m n^2 \text{PolyLog}\left(2,-\frac{e}{f x^2}\right)}{4 e}+\frac{b^2 f m n^2 \text{PolyLog}\left(3,-\frac{e}{f x^2}\right)}{4 e}-\frac{b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}-\frac{b f m n \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{f m \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e}-\frac{b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}-\frac{b^2 f m n^2 \log \left(e+f x^2\right)}{4 e}+\frac{b^2 f m n^2 \log (x)}{2 e}","\frac{b f m n \text{PolyLog}\left(2,-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e}+\frac{b^2 f m n^2 \text{PolyLog}\left(2,-\frac{e}{f x^2}\right)}{4 e}+\frac{b^2 f m n^2 \text{PolyLog}\left(3,-\frac{e}{f x^2}\right)}{4 e}-\frac{b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}-\frac{b f m n \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)}{2 e}-\frac{f m \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e}-\frac{b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}-\frac{b^2 f m n^2 \log \left(e+f x^2\right)}{4 e}+\frac{b^2 f m n^2 \log (x)}{2 e}",1,"(b^2*f*m*n^2*Log[x])/(2*e) - (b*f*m*n*Log[1 + e/(f*x^2)]*(a + b*Log[c*x^n]))/(2*e) - (f*m*Log[1 + e/(f*x^2)]*(a + b*Log[c*x^n])^2)/(2*e) - (b^2*f*m*n^2*Log[e + f*x^2])/(4*e) - (b^2*n^2*Log[d*(e + f*x^2)^m])/(4*x^2) - (b*n*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/(2*x^2) - ((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/(2*x^2) + (b^2*f*m*n^2*PolyLog[2, -(e/(f*x^2))])/(4*e) + (b*f*m*n*(a + b*Log[c*x^n])*PolyLog[2, -(e/(f*x^2))])/(2*e) + (b^2*f*m*n^2*PolyLog[3, -(e/(f*x^2))])/(4*e)","A",11,11,28,0.3929,1,"{2305, 2304, 2378, 266, 36, 29, 31, 2345, 2391, 2374, 6589}"
103,1,408,0,0.6719959,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x^5} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x^5,x]","\frac{b f^2 m n \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}+\frac{b^2 f^2 m n^2 \text{PolyLog}\left(2,-\frac{f x^2}{e}\right)}{16 e^2}-\frac{b^2 f^2 m n^2 \text{PolyLog}\left(3,-\frac{f x^2}{e}\right)}{8 e^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{4 x^4}-\frac{b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{8 x^4}-\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)^3}{6 b e^2 n}-\frac{f^2 m \left(a+b \log \left(c x^n\right)\right)^2}{8 e^2}+\frac{f^2 m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2}+\frac{b f^2 m n \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{8 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^2}{4 e x^2}-\frac{3 b f m n \left(a+b \log \left(c x^n\right)\right)}{8 e x^2}-\frac{b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{32 x^4}+\frac{b^2 f^2 m n^2 \log \left(e+f x^2\right)}{32 e^2}-\frac{b^2 f^2 m n^2 \log (x)}{16 e^2}-\frac{7 b^2 f m n^2}{32 e x^2}","-\frac{b f^2 m n \text{PolyLog}\left(2,-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}-\frac{b^2 f^2 m n^2 \text{PolyLog}\left(2,-\frac{e}{f x^2}\right)}{16 e^2}-\frac{b^2 f^2 m n^2 \text{PolyLog}\left(3,-\frac{e}{f x^2}\right)}{8 e^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{4 x^4}-\frac{b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{8 x^4}+\frac{f^2 m \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2}+\frac{b f^2 m n \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)}{8 e^2}-\frac{f m \left(a+b \log \left(c x^n\right)\right)^2}{4 e x^2}-\frac{3 b f m n \left(a+b \log \left(c x^n\right)\right)}{8 e x^2}-\frac{b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{32 x^4}+\frac{b^2 f^2 m n^2 \log \left(e+f x^2\right)}{32 e^2}-\frac{b^2 f^2 m n^2 \log (x)}{16 e^2}-\frac{7 b^2 f m n^2}{32 e x^2}",1,"(-7*b^2*f*m*n^2)/(32*e*x^2) - (b^2*f^2*m*n^2*Log[x])/(16*e^2) - (3*b*f*m*n*(a + b*Log[c*x^n]))/(8*e*x^2) - (f^2*m*(a + b*Log[c*x^n])^2)/(8*e^2) - (f*m*(a + b*Log[c*x^n])^2)/(4*e*x^2) - (f^2*m*(a + b*Log[c*x^n])^3)/(6*b*e^2*n) + (b^2*f^2*m*n^2*Log[e + f*x^2])/(32*e^2) - (b^2*n^2*Log[d*(e + f*x^2)^m])/(32*x^4) - (b*n*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/(8*x^4) - ((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/(4*x^4) + (b*f^2*m*n*(a + b*Log[c*x^n])*Log[1 + (f*x^2)/e])/(8*e^2) + (f^2*m*(a + b*Log[c*x^n])^2*Log[1 + (f*x^2)/e])/(4*e^2) + (b^2*f^2*m*n^2*PolyLog[2, -((f*x^2)/e)])/(16*e^2) + (b*f^2*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*x^2)/e)])/(4*e^2) - (b^2*f^2*m*n^2*PolyLog[3, -((f*x^2)/e)])/(8*e^2)","A",20,14,28,0.5000,1,"{2305, 2304, 2378, 266, 44, 2351, 2301, 2337, 2391, 2353, 2302, 30, 2374, 6589}"
104,1,630,0,1.0653286,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Int[x^2*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m],x]","\frac{2 b (-e)^{3/2} m n \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^{3/2}}-\frac{2 b (-e)^{3/2} m n \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^{3/2}}-\frac{2 i b^2 e^{3/2} m n^2 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 f^{3/2}}+\frac{2 i b^2 e^{3/2} m n^2 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 f^{3/2}}-\frac{2 b^2 (-e)^{3/2} m n^2 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 f^{3/2}}+\frac{2 b^2 (-e)^{3/2} m n^2 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 f^{3/2}}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)-\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)+\frac{4 b e^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{9 f^{3/2}}-\frac{(-e)^{3/2} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^{3/2}}+\frac{(-e)^{3/2} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^{3/2}}+\frac{2 e m x \left(a+b \log \left(c x^n\right)\right)^2}{3 f}-\frac{2}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{8}{27} b m n x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{16 a b e m n x}{9 f}-\frac{16 b^2 e m n x \log \left(c x^n\right)}{9 f}+\frac{2}{27} b^2 n^2 x^3 \log \left(d \left(e+f x^2\right)^m\right)-\frac{4 b^2 e^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{27 f^{3/2}}+\frac{52 b^2 e m n^2 x}{27 f}-\frac{4}{27} b^2 m n^2 x^3","\frac{2 b (-e)^{3/2} m n \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^{3/2}}-\frac{2 b (-e)^{3/2} m n \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^{3/2}}-\frac{2 i b^2 e^{3/2} m n^2 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 f^{3/2}}+\frac{2 i b^2 e^{3/2} m n^2 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 f^{3/2}}-\frac{2 b^2 (-e)^{3/2} m n^2 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 f^{3/2}}+\frac{2 b^2 (-e)^{3/2} m n^2 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 f^{3/2}}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)-\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)+\frac{4 b e^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{9 f^{3/2}}-\frac{(-e)^{3/2} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^{3/2}}+\frac{(-e)^{3/2} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^{3/2}}+\frac{2 e m x \left(a+b \log \left(c x^n\right)\right)^2}{3 f}-\frac{2}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{8}{27} b m n x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{16 a b e m n x}{9 f}-\frac{16 b^2 e m n x \log \left(c x^n\right)}{9 f}+\frac{2}{27} b^2 n^2 x^3 \log \left(d \left(e+f x^2\right)^m\right)-\frac{4 b^2 e^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{27 f^{3/2}}+\frac{52 b^2 e m n^2 x}{27 f}-\frac{4}{27} b^2 m n^2 x^3",1,"(-16*a*b*e*m*n*x)/(9*f) + (52*b^2*e*m*n^2*x)/(27*f) - (4*b^2*m*n^2*x^3)/27 - (4*b^2*e^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/(27*f^(3/2)) - (16*b^2*e*m*n*x*Log[c*x^n])/(9*f) + (8*b*m*n*x^3*(a + b*Log[c*x^n]))/27 + (4*b*e^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*x^n]))/(9*f^(3/2)) + (2*e*m*x*(a + b*Log[c*x^n])^2)/(3*f) - (2*m*x^3*(a + b*Log[c*x^n])^2)/9 - ((-e)^(3/2)*m*(a + b*Log[c*x^n])^2*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/(3*f^(3/2)) + ((-e)^(3/2)*m*(a + b*Log[c*x^n])^2*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/(3*f^(3/2)) + (2*b^2*n^2*x^3*Log[d*(e + f*x^2)^m])/27 - (2*b*n*x^3*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/9 + (x^3*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/3 + (2*b*(-e)^(3/2)*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/(3*f^(3/2)) - (2*b*(-e)^(3/2)*m*n*(a + b*Log[c*x^n])*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/(3*f^(3/2)) - (((2*I)/9)*b^2*e^(3/2)*m*n^2*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/f^(3/2) + (((2*I)/9)*b^2*e^(3/2)*m*n^2*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/f^(3/2) - (2*b^2*(-e)^(3/2)*m*n^2*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/(3*f^(3/2)) + (2*b^2*(-e)^(3/2)*m*n^2*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/(3*f^(3/2))","A",30,17,28,0.6071,1,"{2305, 2304, 2378, 302, 205, 2351, 2295, 2324, 12, 4848, 2391, 2353, 2296, 2330, 2317, 2374, 6589}"
105,1,546,0,0.8062115,"\int \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Int[(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m],x]","\frac{2 b \sqrt{-e} m n \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{f}}-\frac{2 b \sqrt{-e} m n \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{f}}+\frac{2 i b^2 \sqrt{e} m n^2 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}-\frac{2 i b^2 \sqrt{e} m n^2 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}-\frac{2 b^2 \sqrt{-e} m n^2 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{f}}+\frac{2 b^2 \sqrt{-e} m n^2 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{f}}+x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)-\frac{\sqrt{-e} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{f}}+\frac{\sqrt{-e} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{f}}-2 m x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \log \left(d \left(e+f x^2\right)^m\right)-\frac{4 b \sqrt{e} m n (a-b n) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+4 a b m n x+4 b m n x (a-b n)-2 b^2 n x \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)-\frac{4 b^2 \sqrt{e} m n \log \left(c x^n\right) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+8 b^2 m n x \log \left(c x^n\right)+2 b^2 n^2 x \log \left(d \left(e+f x^2\right)^m\right)-8 b^2 m n^2 x","\frac{2 b \sqrt{-e} m n \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{f}}-\frac{2 b \sqrt{-e} m n \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{f}}+\frac{2 i b^2 \sqrt{e} m n^2 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}-\frac{2 i b^2 \sqrt{e} m n^2 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}-\frac{2 b^2 \sqrt{-e} m n^2 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{f}}+\frac{2 b^2 \sqrt{-e} m n^2 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{f}}+x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)-\frac{\sqrt{-e} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{f}}+\frac{\sqrt{-e} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{f}}-2 m x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \log \left(d \left(e+f x^2\right)^m\right)-\frac{4 b \sqrt{e} m n (a-b n) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+4 a b m n x+4 b m n x (a-b n)-2 b^2 n x \log \left(c x^n\right) \log \left(d \left(e+f x^2\right)^m\right)-\frac{4 b^2 \sqrt{e} m n \log \left(c x^n\right) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{f}}+8 b^2 m n x \log \left(c x^n\right)+2 b^2 n^2 x \log \left(d \left(e+f x^2\right)^m\right)-8 b^2 m n^2 x",1,"4*a*b*m*n*x - 8*b^2*m*n^2*x + 4*b*m*n*(a - b*n)*x - (4*b*Sqrt[e]*m*n*(a - b*n)*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/Sqrt[f] + 8*b^2*m*n*x*Log[c*x^n] - (4*b^2*Sqrt[e]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n])/Sqrt[f] - 2*m*x*(a + b*Log[c*x^n])^2 - (Sqrt[-e]*m*(a + b*Log[c*x^n])^2*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f] + (Sqrt[-e]*m*(a + b*Log[c*x^n])^2*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f] - 2*a*b*n*x*Log[d*(e + f*x^2)^m] + 2*b^2*n^2*x*Log[d*(e + f*x^2)^m] - 2*b^2*n*x*Log[c*x^n]*Log[d*(e + f*x^2)^m] + x*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m] + (2*b*Sqrt[-e]*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[f] - (2*b*Sqrt[-e]*m*n*(a + b*Log[c*x^n])*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f] + ((2*I)*b^2*Sqrt[e]*m*n^2*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/Sqrt[f] - ((2*I)*b^2*Sqrt[e]*m*n^2*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/Sqrt[f] - (2*b^2*Sqrt[-e]*m*n^2*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[f] + (2*b^2*Sqrt[-e]*m*n^2*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f]","A",26,16,25,0.6400,1,"{2296, 2295, 2371, 6, 321, 205, 2351, 2324, 12, 4848, 2391, 2353, 2330, 2317, 2374, 6589}"
106,1,478,0,0.5153914,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x^2,x]","-\frac{2 b \sqrt{f} m n \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-e}}+\frac{2 b \sqrt{f} m n \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-e}}-\frac{2 i b^2 \sqrt{f} m n^2 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}+\frac{2 i b^2 \sqrt{f} m n^2 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}+\frac{2 b^2 \sqrt{f} m n^2 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{-e}}-\frac{2 b^2 \sqrt{f} m n^2 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{-e}}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x}+\frac{\sqrt{f} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-e}}-\frac{\sqrt{f} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-e}}+\frac{4 b \sqrt{f} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e}}-\frac{2 b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{x}+\frac{4 b^2 \sqrt{f} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}","-\frac{2 b \sqrt{f} m n \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-e}}+\frac{2 b \sqrt{f} m n \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{-e}}-\frac{2 i b^2 \sqrt{f} m n^2 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}+\frac{2 i b^2 \sqrt{f} m n^2 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}+\frac{2 b^2 \sqrt{f} m n^2 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{-e}}-\frac{2 b^2 \sqrt{f} m n^2 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{-e}}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x}+\frac{\sqrt{f} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-e}}-\frac{\sqrt{f} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{\sqrt{-e}}+\frac{4 b \sqrt{f} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{\sqrt{e}}-\frac{2 b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{x}+\frac{4 b^2 \sqrt{f} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{\sqrt{e}}",1,"(4*b^2*Sqrt[f]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/Sqrt[e] + (4*b*Sqrt[f]*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*x^n]))/Sqrt[e] + (Sqrt[f]*m*(a + b*Log[c*x^n])^2*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e] - (Sqrt[f]*m*(a + b*Log[c*x^n])^2*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e] - (2*b^2*n^2*Log[d*(e + f*x^2)^m])/x - (2*b*n*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x - ((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x - (2*b*Sqrt[f]*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[-e] + (2*b*Sqrt[f]*m*n*(a + b*Log[c*x^n])*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e] - ((2*I)*b^2*Sqrt[f]*m*n^2*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/Sqrt[e] + ((2*I)*b^2*Sqrt[f]*m*n^2*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/Sqrt[e] + (2*b^2*Sqrt[f]*m*n^2*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[-e] - (2*b^2*Sqrt[f]*m*n^2*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e]","A",16,12,28,0.4286,1,"{2305, 2304, 2378, 205, 2324, 12, 4848, 2391, 2330, 2317, 2374, 6589}"
107,1,571,0,0.9310518,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{x^4} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x^4,x]","-\frac{2 b f^{3/2} m n \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-e)^{3/2}}+\frac{2 b f^{3/2} m n \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-e)^{3/2}}+\frac{2 i b^2 f^{3/2} m n^2 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 e^{3/2}}-\frac{2 i b^2 f^{3/2} m n^2 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 e^{3/2}}+\frac{2 b^2 f^{3/2} m n^2 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 (-e)^{3/2}}-\frac{2 b^2 f^{3/2} m n^2 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 (-e)^{3/2}}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{9 x^3}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{3 x^3}-\frac{4 b f^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{9 e^{3/2}}+\frac{f^{3/2} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-e)^{3/2}}-\frac{f^{3/2} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-e)^{3/2}}-\frac{16 b f m n \left(a+b \log \left(c x^n\right)\right)}{9 e x}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)^2}{3 e x}-\frac{2 b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{27 x^3}-\frac{4 b^2 f^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{27 e^{3/2}}-\frac{52 b^2 f m n^2}{27 e x}","-\frac{2 b f^{3/2} m n \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-e)^{3/2}}+\frac{2 b f^{3/2} m n \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)}{3 (-e)^{3/2}}+\frac{2 i b^2 f^{3/2} m n^2 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 e^{3/2}}-\frac{2 i b^2 f^{3/2} m n^2 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{9 e^{3/2}}+\frac{2 b^2 f^{3/2} m n^2 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 (-e)^{3/2}}-\frac{2 b^2 f^{3/2} m n^2 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 (-e)^{3/2}}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{9 x^3}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{3 x^3}-\frac{4 b f^{3/2} m n \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right)}{9 e^{3/2}}+\frac{f^{3/2} m \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-e)^{3/2}}-\frac{f^{3/2} m \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 (-e)^{3/2}}-\frac{16 b f m n \left(a+b \log \left(c x^n\right)\right)}{9 e x}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)^2}{3 e x}-\frac{2 b^2 n^2 \log \left(d \left(e+f x^2\right)^m\right)}{27 x^3}-\frac{4 b^2 f^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right)}{27 e^{3/2}}-\frac{52 b^2 f m n^2}{27 e x}",1,"(-52*b^2*f*m*n^2)/(27*e*x) - (4*b^2*f^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/(27*e^(3/2)) - (16*b*f*m*n*(a + b*Log[c*x^n]))/(9*e*x) - (4*b*f^(3/2)*m*n*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*x^n]))/(9*e^(3/2)) - (2*f*m*(a + b*Log[c*x^n])^2)/(3*e*x) + (f^(3/2)*m*(a + b*Log[c*x^n])^2*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/(3*(-e)^(3/2)) - (f^(3/2)*m*(a + b*Log[c*x^n])^2*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/(3*(-e)^(3/2)) - (2*b^2*n^2*Log[d*(e + f*x^2)^m])/(27*x^3) - (2*b*n*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/(9*x^3) - ((a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/(3*x^3) - (2*b*f^(3/2)*m*n*(a + b*Log[c*x^n])*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/(3*(-e)^(3/2)) + (2*b*f^(3/2)*m*n*(a + b*Log[c*x^n])*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/(3*(-e)^(3/2)) + (((2*I)/9)*b^2*f^(3/2)*m*n^2*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/e^(3/2) - (((2*I)/9)*b^2*f^(3/2)*m*n^2*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/e^(3/2) + (2*b^2*f^(3/2)*m*n^2*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/(3*(-e)^(3/2)) - (2*b^2*f^(3/2)*m*n^2*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/(3*(-e)^(3/2))","A",24,15,28,0.5357,1,"{2305, 2304, 2378, 325, 205, 2351, 2324, 12, 4848, 2391, 2353, 2330, 2317, 2374, 6589}"
108,1,514,0,0.9244663,"\int x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Int[x*(a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m],x]","-\frac{3 b^2 e m n^2 \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{4 f}-\frac{3 b^2 e m n^2 \text{PolyLog}\left(3,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{4 f}+\frac{3 b e m n \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 f}+\frac{3 b^3 e m n^3 \text{PolyLog}\left(2,-\frac{f x^2}{e}\right)}{8 f}+\frac{3 b^3 e m n^3 \text{PolyLog}\left(3,-\frac{f x^2}{e}\right)}{8 f}+\frac{3 b^3 e m n^3 \text{PolyLog}\left(4,-\frac{f x^2}{e}\right)}{8 f}+\frac{3}{4} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)+\frac{3 b^2 e m n^2 \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 f}-\frac{9}{4} b^2 m n^2 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{3}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)-\frac{3 b e m n \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 f}+\frac{e m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 f}+\frac{3}{2} b m n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} m x^2 \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{8} b^3 n^3 x^2 \log \left(d \left(e+f x^2\right)^m\right)-\frac{3 b^3 e m n^3 \log \left(e+f x^2\right)}{8 f}+\frac{3}{2} b^3 m n^3 x^2","-\frac{3 b^2 e m n^2 \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{4 f}-\frac{3 b^2 e m n^2 \text{PolyLog}\left(3,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{4 f}+\frac{3 b e m n \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 f}+\frac{3 b^3 e m n^3 \text{PolyLog}\left(2,-\frac{f x^2}{e}\right)}{8 f}+\frac{3 b^3 e m n^3 \text{PolyLog}\left(3,-\frac{f x^2}{e}\right)}{8 f}+\frac{3 b^3 e m n^3 \text{PolyLog}\left(4,-\frac{f x^2}{e}\right)}{8 f}+\frac{3}{4} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)+\frac{3 b^2 e m n^2 \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 f}-\frac{9}{4} b^2 m n^2 x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{3}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)-\frac{3 b e m n \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 f}+\frac{e m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 f}+\frac{3}{2} b m n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} m x^2 \left(a+b \log \left(c x^n\right)\right)^3-\frac{3}{8} b^3 n^3 x^2 \log \left(d \left(e+f x^2\right)^m\right)-\frac{3 b^3 e m n^3 \log \left(e+f x^2\right)}{8 f}+\frac{3}{2} b^3 m n^3 x^2",1,"(3*b^3*m*n^3*x^2)/2 - (9*b^2*m*n^2*x^2*(a + b*Log[c*x^n]))/4 + (3*b*m*n*x^2*(a + b*Log[c*x^n])^2)/2 - (m*x^2*(a + b*Log[c*x^n])^3)/2 - (3*b^3*e*m*n^3*Log[e + f*x^2])/(8*f) - (3*b^3*n^3*x^2*Log[d*(e + f*x^2)^m])/8 + (3*b^2*n^2*x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/4 - (3*b*n*x^2*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/4 + (x^2*(a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/2 + (3*b^2*e*m*n^2*(a + b*Log[c*x^n])*Log[1 + (f*x^2)/e])/(4*f) - (3*b*e*m*n*(a + b*Log[c*x^n])^2*Log[1 + (f*x^2)/e])/(4*f) + (e*m*(a + b*Log[c*x^n])^3*Log[1 + (f*x^2)/e])/(2*f) + (3*b^3*e*m*n^3*PolyLog[2, -((f*x^2)/e)])/(8*f) - (3*b^2*e*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((f*x^2)/e)])/(4*f) + (3*b*e*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*x^2)/e)])/(4*f) + (3*b^3*e*m*n^3*PolyLog[3, -((f*x^2)/e)])/(8*f) - (3*b^2*e*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((f*x^2)/e)])/(4*f) + (3*b^3*e*m*n^3*PolyLog[4, -((f*x^2)/e)])/(8*f)","A",26,12,26,0.4615,1,"{2305, 2304, 2378, 266, 43, 2351, 2337, 2391, 2353, 2374, 6589, 2383}"
109,1,181,0,0.2145284,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/x,x]","-\frac{3}{4} b^2 m n^2 \text{PolyLog}\left(4,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} m \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{4} b m n \text{PolyLog}\left(3,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{3}{8} b^3 m n^3 \text{PolyLog}\left(5,-\frac{f x^2}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^4 \log \left(d \left(e+f x^2\right)^m\right)}{4 b n}-\frac{m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}","-\frac{3}{4} b^2 m n^2 \text{PolyLog}\left(4,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} m \text{PolyLog}\left(2,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{4} b m n \text{PolyLog}\left(3,-\frac{f x^2}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{3}{8} b^3 m n^3 \text{PolyLog}\left(5,-\frac{f x^2}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^4 \log \left(d \left(e+f x^2\right)^m\right)}{4 b n}-\frac{m \log \left(\frac{f x^2}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}",1,"((a + b*Log[c*x^n])^4*Log[d*(e + f*x^2)^m])/(4*b*n) - (m*(a + b*Log[c*x^n])^4*Log[1 + (f*x^2)/e])/(4*b*n) - (m*(a + b*Log[c*x^n])^3*PolyLog[2, -((f*x^2)/e)])/2 + (3*b*m*n*(a + b*Log[c*x^n])^2*PolyLog[3, -((f*x^2)/e)])/4 - (3*b^2*m*n^2*(a + b*Log[c*x^n])*PolyLog[4, -((f*x^2)/e)])/4 + (3*b^3*m*n^3*PolyLog[5, -((f*x^2)/e)])/8","A",6,5,28,0.1786,1,"{2375, 2337, 2374, 2383, 6589}"
110,1,451,0,0.5694808,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/x^3,x]","\frac{3 b^2 f m n^2 \text{PolyLog}\left(2,-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)}{4 e}+\frac{3 b^2 f m n^2 \text{PolyLog}\left(3,-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)}{4 e}+\frac{3 b f m n \text{PolyLog}\left(2,-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e}+\frac{3 b^3 f m n^3 \text{PolyLog}\left(2,-\frac{e}{f x^2}\right)}{8 e}+\frac{3 b^3 f m n^3 \text{PolyLog}\left(3,-\frac{e}{f x^2}\right)}{8 e}+\frac{3 b^3 f m n^3 \text{PolyLog}\left(4,-\frac{e}{f x^2}\right)}{8 e}-\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}-\frac{3 b^2 f m n^2 \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 e}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}-\frac{3 b f m n \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e}-\frac{f m \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 e}-\frac{3 b^3 n^3 \log \left(d \left(e+f x^2\right)^m\right)}{8 x^2}-\frac{3 b^3 f m n^3 \log \left(e+f x^2\right)}{8 e}+\frac{3 b^3 f m n^3 \log (x)}{4 e}","\frac{3 b^2 f m n^2 \text{PolyLog}\left(2,-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)}{4 e}+\frac{3 b^2 f m n^2 \text{PolyLog}\left(3,-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)}{4 e}+\frac{3 b f m n \text{PolyLog}\left(2,-\frac{e}{f x^2}\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e}+\frac{3 b^3 f m n^3 \text{PolyLog}\left(2,-\frac{e}{f x^2}\right)}{8 e}+\frac{3 b^3 f m n^3 \text{PolyLog}\left(3,-\frac{e}{f x^2}\right)}{8 e}+\frac{3 b^3 f m n^3 \text{PolyLog}\left(4,-\frac{e}{f x^2}\right)}{8 e}-\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}-\frac{3 b^2 f m n^2 \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)}{4 e}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^2\right)^m\right)}{4 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{2 x^2}-\frac{3 b f m n \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 e}-\frac{f m \log \left(\frac{e}{f x^2}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 e}-\frac{3 b^3 n^3 \log \left(d \left(e+f x^2\right)^m\right)}{8 x^2}-\frac{3 b^3 f m n^3 \log \left(e+f x^2\right)}{8 e}+\frac{3 b^3 f m n^3 \log (x)}{4 e}",1,"(3*b^3*f*m*n^3*Log[x])/(4*e) - (3*b^2*f*m*n^2*Log[1 + e/(f*x^2)]*(a + b*Log[c*x^n]))/(4*e) - (3*b*f*m*n*Log[1 + e/(f*x^2)]*(a + b*Log[c*x^n])^2)/(4*e) - (f*m*Log[1 + e/(f*x^2)]*(a + b*Log[c*x^n])^3)/(2*e) - (3*b^3*f*m*n^3*Log[e + f*x^2])/(8*e) - (3*b^3*n^3*Log[d*(e + f*x^2)^m])/(8*x^2) - (3*b^2*n^2*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/(4*x^2) - (3*b*n*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/(4*x^2) - ((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/(2*x^2) + (3*b^3*f*m*n^3*PolyLog[2, -(e/(f*x^2))])/(8*e) + (3*b^2*f*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, -(e/(f*x^2))])/(4*e) + (3*b*f*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, -(e/(f*x^2))])/(4*e) + (3*b^3*f*m*n^3*PolyLog[3, -(e/(f*x^2))])/(8*e) + (3*b^2*f*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, -(e/(f*x^2))])/(4*e) + (3*b^3*f*m*n^3*PolyLog[4, -(e/(f*x^2))])/(8*e)","A",15,12,28,0.4286,1,"{2305, 2304, 2378, 266, 36, 29, 31, 2345, 2391, 2374, 6589, 2383}"
111,1,1092,0,1.8072298,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Int[x^2*(a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m],x]","\frac{16}{81} m n^3 x^3 b^3-\frac{160 e m n^3 x b^3}{27 f}+\frac{4 e^{3/2} m n^3 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) b^3}{27 f^{3/2}}+\frac{52 e m n^2 x \log \left(c x^n\right) b^3}{9 f}-\frac{2}{27} n^3 x^3 \log \left(d \left(f x^2+e\right)^m\right) b^3+\frac{2 i e^{3/2} m n^3 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{9 f^{3/2}}-\frac{2 i e^{3/2} m n^3 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{9 f^{3/2}}+\frac{2 (-e)^{3/2} m n^3 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{3 f^{3/2}}-\frac{2 (-e)^{3/2} m n^3 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{3 f^{3/2}}+\frac{2 (-e)^{3/2} m n^3 \text{PolyLog}\left(4,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{f^{3/2}}-\frac{2 (-e)^{3/2} m n^3 \text{PolyLog}\left(4,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{f^{3/2}}+\frac{52 a e m n^2 x b^2}{9 f}-\frac{4}{9} m n^2 x^3 \left(a+b \log \left(c x^n\right)\right) b^2-\frac{4 e^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right) b^2}{9 f^{3/2}}+\frac{2}{9} n^2 x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(f x^2+e\right)^m\right) b^2-\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{3 f^{3/2}}+\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{3 f^{3/2}}-\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{f^{3/2}}+\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{f^{3/2}}+\frac{4}{9} m n x^3 \left(a+b \log \left(c x^n\right)\right)^2 b-\frac{8 e m n x \left(a+b \log \left(c x^n\right)\right)^2 b}{3 f}+\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{3 f^{3/2}}-\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) b}{3 f^{3/2}}-\frac{1}{3} n x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) b+\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{f^{3/2}}-\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{f^{3/2}}-\frac{2}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)^3+\frac{2 e m x \left(a+b \log \left(c x^n\right)\right)^3}{3 f}-\frac{(-e)^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 f^{3/2}}+\frac{(-e)^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{3 f^{3/2}}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)","\frac{16}{81} m n^3 x^3 b^3-\frac{160 e m n^3 x b^3}{27 f}+\frac{4 e^{3/2} m n^3 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) b^3}{27 f^{3/2}}+\frac{52 e m n^2 x \log \left(c x^n\right) b^3}{9 f}-\frac{2}{27} n^3 x^3 \log \left(d \left(f x^2+e\right)^m\right) b^3+\frac{2 i e^{3/2} m n^3 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{9 f^{3/2}}-\frac{2 i e^{3/2} m n^3 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{9 f^{3/2}}+\frac{2 (-e)^{3/2} m n^3 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{3 f^{3/2}}-\frac{2 (-e)^{3/2} m n^3 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{3 f^{3/2}}+\frac{2 (-e)^{3/2} m n^3 \text{PolyLog}\left(4,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{f^{3/2}}-\frac{2 (-e)^{3/2} m n^3 \text{PolyLog}\left(4,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{f^{3/2}}+\frac{52 a e m n^2 x b^2}{9 f}-\frac{4}{9} m n^2 x^3 \left(a+b \log \left(c x^n\right)\right) b^2-\frac{4 e^{3/2} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right) b^2}{9 f^{3/2}}+\frac{2}{9} n^2 x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(f x^2+e\right)^m\right) b^2-\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{3 f^{3/2}}+\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{3 f^{3/2}}-\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{f^{3/2}}+\frac{2 (-e)^{3/2} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{f^{3/2}}+\frac{4}{9} m n x^3 \left(a+b \log \left(c x^n\right)\right)^2 b-\frac{8 e m n x \left(a+b \log \left(c x^n\right)\right)^2 b}{3 f}+\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{3 f^{3/2}}-\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) b}{3 f^{3/2}}-\frac{1}{3} n x^3 \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) b+\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{f^{3/2}}-\frac{(-e)^{3/2} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{f^{3/2}}-\frac{2}{9} m x^3 \left(a+b \log \left(c x^n\right)\right)^3+\frac{2 e m x \left(a+b \log \left(c x^n\right)\right)^3}{3 f}-\frac{(-e)^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 f^{3/2}}+\frac{(-e)^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{3 f^{3/2}}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)",1,"(52*a*b^2*e*m*n^2*x)/(9*f) - (160*b^3*e*m*n^3*x)/(27*f) + (16*b^3*m*n^3*x^3)/81 + (4*b^3*e^(3/2)*m*n^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/(27*f^(3/2)) + (52*b^3*e*m*n^2*x*Log[c*x^n])/(9*f) - (4*b^2*m*n^2*x^3*(a + b*Log[c*x^n]))/9 - (4*b^2*e^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*x^n]))/(9*f^(3/2)) - (8*b*e*m*n*x*(a + b*Log[c*x^n])^2)/(3*f) + (4*b*m*n*x^3*(a + b*Log[c*x^n])^2)/9 + (2*e*m*x*(a + b*Log[c*x^n])^3)/(3*f) - (2*m*x^3*(a + b*Log[c*x^n])^3)/9 + (b*(-e)^(3/2)*m*n*(a + b*Log[c*x^n])^2*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/(3*f^(3/2)) - ((-e)^(3/2)*m*(a + b*Log[c*x^n])^3*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/(3*f^(3/2)) - (b*(-e)^(3/2)*m*n*(a + b*Log[c*x^n])^2*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/(3*f^(3/2)) + ((-e)^(3/2)*m*(a + b*Log[c*x^n])^3*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/(3*f^(3/2)) - (2*b^3*n^3*x^3*Log[d*(e + f*x^2)^m])/27 + (2*b^2*n^2*x^3*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/9 - (b*n*x^3*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/3 + (x^3*(a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/3 - (2*b^2*(-e)^(3/2)*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/(3*f^(3/2)) + (b*(-e)^(3/2)*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/f^(3/2) + (2*b^2*(-e)^(3/2)*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/(3*f^(3/2)) - (b*(-e)^(3/2)*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/f^(3/2) + (((2*I)/9)*b^3*e^(3/2)*m*n^3*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/f^(3/2) - (((2*I)/9)*b^3*e^(3/2)*m*n^3*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/f^(3/2) + (2*b^3*(-e)^(3/2)*m*n^3*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/(3*f^(3/2)) - (2*b^2*(-e)^(3/2)*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/f^(3/2) - (2*b^3*(-e)^(3/2)*m*n^3*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/(3*f^(3/2)) + (2*b^2*(-e)^(3/2)*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/f^(3/2) + (2*b^3*(-e)^(3/2)*m*n^3*PolyLog[4, -((Sqrt[f]*x)/Sqrt[-e])])/f^(3/2) - (2*b^3*(-e)^(3/2)*m*n^3*PolyLog[4, (Sqrt[f]*x)/Sqrt[-e]])/f^(3/2)","A",49,18,28,0.6429,1,"{2305, 2304, 2378, 302, 205, 2351, 2295, 2324, 12, 4848, 2391, 2353, 2296, 2330, 2317, 2374, 6589, 2383}"
112,1,977,0,1.4989507,"\int \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right) \, dx","Int[(a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m],x]","36 m n^3 x b^3-36 m n^2 x \log \left(c x^n\right) b^3+\frac{12 \sqrt{e} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log \left(c x^n\right) b^3}{\sqrt{f}}-6 n^3 x \log \left(d \left(f x^2+e\right)^m\right) b^3+6 n^2 x \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) b^3-\frac{6 i \sqrt{e} m n^3 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{\sqrt{f}}+\frac{6 i \sqrt{e} m n^3 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^3 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}-\frac{6 \sqrt{-e} m n^3 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^3 \text{PolyLog}\left(4,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}-\frac{6 \sqrt{-e} m n^3 \text{PolyLog}\left(4,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}-24 a m n^2 x b^2-12 m n^2 (a-b n) x b^2+\frac{12 \sqrt{e} m n^2 (a-b n) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) b^2}{\sqrt{f}}+6 a n^2 x \log \left(d \left(f x^2+e\right)^m\right) b^2-\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}-\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}+12 m n x \left(a+b \log \left(c x^n\right)\right)^2 b+\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{\sqrt{f}}-\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) b}{\sqrt{f}}-3 n x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) b+\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{\sqrt{f}}-\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{\sqrt{f}}-2 m x \left(a+b \log \left(c x^n\right)\right)^3-\frac{\sqrt{-e} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{f}}+\frac{\sqrt{-e} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{\sqrt{f}}+x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)","36 m n^3 x b^3-36 m n^2 x \log \left(c x^n\right) b^3+\frac{12 \sqrt{e} m n^2 \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \log \left(c x^n\right) b^3}{\sqrt{f}}-6 n^3 x \log \left(d \left(f x^2+e\right)^m\right) b^3+6 n^2 x \log \left(c x^n\right) \log \left(d \left(f x^2+e\right)^m\right) b^3-\frac{6 i \sqrt{e} m n^3 \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{\sqrt{f}}+\frac{6 i \sqrt{e} m n^3 \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right) b^3}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^3 \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}-\frac{6 \sqrt{-e} m n^3 \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^3 \text{PolyLog}\left(4,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}-\frac{6 \sqrt{-e} m n^3 \text{PolyLog}\left(4,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^3}{\sqrt{f}}-24 a m n^2 x b^2-12 m n^2 (a-b n) x b^2+\frac{12 \sqrt{e} m n^2 (a-b n) \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) b^2}{\sqrt{f}}+6 a n^2 x \log \left(d \left(f x^2+e\right)^m\right) b^2-\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}-\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}+\frac{6 \sqrt{-e} m n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b^2}{\sqrt{f}}+12 m n x \left(a+b \log \left(c x^n\right)\right)^2 b+\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{\sqrt{f}}-\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) b}{\sqrt{f}}-3 n x \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) b+\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{\sqrt{f}}-\frac{3 \sqrt{-e} m n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) b}{\sqrt{f}}-2 m x \left(a+b \log \left(c x^n\right)\right)^3-\frac{\sqrt{-e} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{f}}+\frac{\sqrt{-e} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{\sqrt{f}}+x \left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)",1,"-24*a*b^2*m*n^2*x + 36*b^3*m*n^3*x - 12*b^2*m*n^2*(a - b*n)*x + (12*b^2*Sqrt[e]*m*n^2*(a - b*n)*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/Sqrt[f] - 36*b^3*m*n^2*x*Log[c*x^n] + (12*b^3*Sqrt[e]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*Log[c*x^n])/Sqrt[f] + 12*b*m*n*x*(a + b*Log[c*x^n])^2 - 2*m*x*(a + b*Log[c*x^n])^3 + (3*b*Sqrt[-e]*m*n*(a + b*Log[c*x^n])^2*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f] - (Sqrt[-e]*m*(a + b*Log[c*x^n])^3*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f] - (3*b*Sqrt[-e]*m*n*(a + b*Log[c*x^n])^2*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f] + (Sqrt[-e]*m*(a + b*Log[c*x^n])^3*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f] + 6*a*b^2*n^2*x*Log[d*(e + f*x^2)^m] - 6*b^3*n^3*x*Log[d*(e + f*x^2)^m] + 6*b^3*n^2*x*Log[c*x^n]*Log[d*(e + f*x^2)^m] - 3*b*n*x*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m] + x*(a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m] - (6*b^2*Sqrt[-e]*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[f] + (3*b*Sqrt[-e]*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[f] + (6*b^2*Sqrt[-e]*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f] - (3*b*Sqrt[-e]*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f] - ((6*I)*b^3*Sqrt[e]*m*n^3*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/Sqrt[f] + ((6*I)*b^3*Sqrt[e]*m*n^3*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/Sqrt[f] + (6*b^3*Sqrt[-e]*m*n^3*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[f] - (6*b^2*Sqrt[-e]*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[f] - (6*b^3*Sqrt[-e]*m*n^3*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f] + (6*b^2*Sqrt[-e]*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f] + (6*b^3*Sqrt[-e]*m*n^3*PolyLog[4, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[f] - (6*b^3*Sqrt[-e]*m*n^3*PolyLog[4, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[f]","A",42,17,25,0.6800,1,"{2296, 2295, 2371, 6, 321, 205, 2351, 2324, 12, 4848, 2391, 2353, 2330, 2317, 2374, 6589, 2383}"
113,1,879,0,1.1058652,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/x^2,x]","\frac{12 b^3 \sqrt{f} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) n^3}{\sqrt{e}}-\frac{6 b^3 \log \left(d \left(f x^2+e\right)^m\right) n^3}{x}-\frac{6 i b^3 \sqrt{f} m \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{\sqrt{e}}+\frac{6 i b^3 \sqrt{f} m \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{\sqrt{e}}+\frac{6 b^3 \sqrt{f} m \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}-\frac{6 b^3 \sqrt{f} m \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}-\frac{6 b^3 \sqrt{f} m \text{PolyLog}\left(4,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}+\frac{6 b^3 \sqrt{f} m \text{PolyLog}\left(4,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}+\frac{12 b^2 \sqrt{f} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right) n^2}{\sqrt{e}}-\frac{6 b^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(f x^2+e\right)^m\right) n^2}{x}-\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}+\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}+\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}-\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}+\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{\sqrt{-e}}-\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) n}{\sqrt{-e}}-\frac{3 b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) n}{x}-\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{\sqrt{-e}}+\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{\sqrt{-e}}+\frac{\sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{-e}}-\frac{\sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{\sqrt{-e}}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)}{x}","\frac{12 b^3 \sqrt{f} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) n^3}{\sqrt{e}}-\frac{6 b^3 \log \left(d \left(f x^2+e\right)^m\right) n^3}{x}-\frac{6 i b^3 \sqrt{f} m \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{\sqrt{e}}+\frac{6 i b^3 \sqrt{f} m \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{\sqrt{e}}+\frac{6 b^3 \sqrt{f} m \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}-\frac{6 b^3 \sqrt{f} m \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}-\frac{6 b^3 \sqrt{f} m \text{PolyLog}\left(4,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}+\frac{6 b^3 \sqrt{f} m \text{PolyLog}\left(4,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{\sqrt{-e}}+\frac{12 b^2 \sqrt{f} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right) n^2}{\sqrt{e}}-\frac{6 b^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(f x^2+e\right)^m\right) n^2}{x}-\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}+\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}+\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}-\frac{6 b^2 \sqrt{f} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{\sqrt{-e}}+\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{\sqrt{-e}}-\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) n}{\sqrt{-e}}-\frac{3 b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) n}{x}-\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{\sqrt{-e}}+\frac{3 b \sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{\sqrt{-e}}+\frac{\sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{\sqrt{-e}}-\frac{\sqrt{f} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{\sqrt{-e}}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)}{x}",1,"(12*b^3*Sqrt[f]*m*n^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/Sqrt[e] + (12*b^2*Sqrt[f]*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*x^n]))/Sqrt[e] + (3*b*Sqrt[f]*m*n*(a + b*Log[c*x^n])^2*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e] + (Sqrt[f]*m*(a + b*Log[c*x^n])^3*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e] - (3*b*Sqrt[f]*m*n*(a + b*Log[c*x^n])^2*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e] - (Sqrt[f]*m*(a + b*Log[c*x^n])^3*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e] - (6*b^3*n^3*Log[d*(e + f*x^2)^m])/x - (6*b^2*n^2*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/x - (3*b*n*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/x - ((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/x - (6*b^2*Sqrt[f]*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[-e] - (3*b*Sqrt[f]*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[-e] + (6*b^2*Sqrt[f]*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e] + (3*b*Sqrt[f]*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e] - ((6*I)*b^3*Sqrt[f]*m*n^3*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/Sqrt[e] + ((6*I)*b^3*Sqrt[f]*m*n^3*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/Sqrt[e] + (6*b^3*Sqrt[f]*m*n^3*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[-e] + (6*b^2*Sqrt[f]*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[-e] - (6*b^3*Sqrt[f]*m*n^3*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e] - (6*b^2*Sqrt[f]*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e] - (6*b^3*Sqrt[f]*m*n^3*PolyLog[4, -((Sqrt[f]*x)/Sqrt[-e])])/Sqrt[-e] + (6*b^3*Sqrt[f]*m*n^3*PolyLog[4, (Sqrt[f]*x)/Sqrt[-e]])/Sqrt[-e]","A",26,13,28,0.4643,1,"{2305, 2304, 2378, 205, 2324, 12, 4848, 2391, 2330, 2317, 2374, 6589, 2383}"
114,1,1007,0,1.7020816,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^2\right)^m\right)}{x^4} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/x^4,x]","-\frac{4 b^3 f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) n^3}{27 e^{3/2}}-\frac{2 b^3 \log \left(d \left(f x^2+e\right)^m\right) n^3}{27 x^3}+\frac{2 i b^3 f^{3/2} m \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{9 e^{3/2}}-\frac{2 i b^3 f^{3/2} m \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{9 e^{3/2}}+\frac{2 b^3 f^{3/2} m \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{3 (-e)^{3/2}}-\frac{2 b^3 f^{3/2} m \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{3 (-e)^{3/2}}-\frac{2 b^3 f^{3/2} m \text{PolyLog}\left(4,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{(-e)^{3/2}}+\frac{2 b^3 f^{3/2} m \text{PolyLog}\left(4,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{(-e)^{3/2}}-\frac{160 b^3 f m n^3}{27 e x}-\frac{4 b^2 f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right) n^2}{9 e^{3/2}}-\frac{52 b^2 f m \left(a+b \log \left(c x^n\right)\right) n^2}{9 e x}-\frac{2 b^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(f x^2+e\right)^m\right) n^2}{9 x^3}-\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{3 (-e)^{3/2}}+\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{3 (-e)^{3/2}}+\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{(-e)^{3/2}}-\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{(-e)^{3/2}}-\frac{8 b f m \left(a+b \log \left(c x^n\right)\right)^2 n}{3 e x}+\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{3 (-e)^{3/2}}-\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) n}{3 (-e)^{3/2}}-\frac{b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) n}{3 x^3}-\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{(-e)^{3/2}}+\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{(-e)^{3/2}}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)^3}{3 e x}+\frac{f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 (-e)^{3/2}}-\frac{f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{3 (-e)^{3/2}}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)}{3 x^3}","-\frac{4 b^3 f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) n^3}{27 e^{3/2}}-\frac{2 b^3 \log \left(d \left(f x^2+e\right)^m\right) n^3}{27 x^3}+\frac{2 i b^3 f^{3/2} m \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{9 e^{3/2}}-\frac{2 i b^3 f^{3/2} m \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right) n^3}{9 e^{3/2}}+\frac{2 b^3 f^{3/2} m \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{3 (-e)^{3/2}}-\frac{2 b^3 f^{3/2} m \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{3 (-e)^{3/2}}-\frac{2 b^3 f^{3/2} m \text{PolyLog}\left(4,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{(-e)^{3/2}}+\frac{2 b^3 f^{3/2} m \text{PolyLog}\left(4,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^3}{(-e)^{3/2}}-\frac{160 b^3 f m n^3}{27 e x}-\frac{4 b^2 f^{3/2} m \tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c x^n\right)\right) n^2}{9 e^{3/2}}-\frac{52 b^2 f m \left(a+b \log \left(c x^n\right)\right) n^2}{9 e x}-\frac{2 b^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(f x^2+e\right)^m\right) n^2}{9 x^3}-\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{3 (-e)^{3/2}}+\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{3 (-e)^{3/2}}+\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{(-e)^{3/2}}-\frac{2 b^2 f^{3/2} m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n^2}{(-e)^{3/2}}-\frac{8 b f m \left(a+b \log \left(c x^n\right)\right)^2 n}{3 e x}+\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{3 (-e)^{3/2}}-\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right) n}{3 (-e)^{3/2}}-\frac{b \left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(f x^2+e\right)^m\right) n}{3 x^3}-\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{(-e)^{3/2}}+\frac{b f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,\frac{\sqrt{f} x}{\sqrt{-e}}\right) n}{(-e)^{3/2}}-\frac{2 f m \left(a+b \log \left(c x^n\right)\right)^3}{3 e x}+\frac{f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(1-\frac{\sqrt{f} x}{\sqrt{-e}}\right)}{3 (-e)^{3/2}}-\frac{f^{3/2} m \left(a+b \log \left(c x^n\right)\right)^3 \log \left(\frac{\sqrt{f} x}{\sqrt{-e}}+1\right)}{3 (-e)^{3/2}}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(f x^2+e\right)^m\right)}{3 x^3}",1,"(-160*b^3*f*m*n^3)/(27*e*x) - (4*b^3*f^(3/2)*m*n^3*ArcTan[(Sqrt[f]*x)/Sqrt[e]])/(27*e^(3/2)) - (52*b^2*f*m*n^2*(a + b*Log[c*x^n]))/(9*e*x) - (4*b^2*f^(3/2)*m*n^2*ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*x^n]))/(9*e^(3/2)) - (8*b*f*m*n*(a + b*Log[c*x^n])^2)/(3*e*x) - (2*f*m*(a + b*Log[c*x^n])^3)/(3*e*x) + (b*f^(3/2)*m*n*(a + b*Log[c*x^n])^2*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/(3*(-e)^(3/2)) + (f^(3/2)*m*(a + b*Log[c*x^n])^3*Log[1 - (Sqrt[f]*x)/Sqrt[-e]])/(3*(-e)^(3/2)) - (b*f^(3/2)*m*n*(a + b*Log[c*x^n])^2*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/(3*(-e)^(3/2)) - (f^(3/2)*m*(a + b*Log[c*x^n])^3*Log[1 + (Sqrt[f]*x)/Sqrt[-e]])/(3*(-e)^(3/2)) - (2*b^3*n^3*Log[d*(e + f*x^2)^m])/(27*x^3) - (2*b^2*n^2*(a + b*Log[c*x^n])*Log[d*(e + f*x^2)^m])/(9*x^3) - (b*n*(a + b*Log[c*x^n])^2*Log[d*(e + f*x^2)^m])/(3*x^3) - ((a + b*Log[c*x^n])^3*Log[d*(e + f*x^2)^m])/(3*x^3) - (2*b^2*f^(3/2)*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/(3*(-e)^(3/2)) - (b*f^(3/2)*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((Sqrt[f]*x)/Sqrt[-e])])/(-e)^(3/2) + (2*b^2*f^(3/2)*m*n^2*(a + b*Log[c*x^n])*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/(3*(-e)^(3/2)) + (b*f^(3/2)*m*n*(a + b*Log[c*x^n])^2*PolyLog[2, (Sqrt[f]*x)/Sqrt[-e]])/(-e)^(3/2) + (((2*I)/9)*b^3*f^(3/2)*m*n^3*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/e^(3/2) - (((2*I)/9)*b^3*f^(3/2)*m*n^3*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/e^(3/2) + (2*b^3*f^(3/2)*m*n^3*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/(3*(-e)^(3/2)) + (2*b^2*f^(3/2)*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((Sqrt[f]*x)/Sqrt[-e])])/(-e)^(3/2) - (2*b^3*f^(3/2)*m*n^3*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/(3*(-e)^(3/2)) - (2*b^2*f^(3/2)*m*n^2*(a + b*Log[c*x^n])*PolyLog[3, (Sqrt[f]*x)/Sqrt[-e]])/(-e)^(3/2) - (2*b^3*f^(3/2)*m*n^3*PolyLog[4, -((Sqrt[f]*x)/Sqrt[-e])])/(-e)^(3/2) + (2*b^3*f^(3/2)*m*n^3*PolyLog[4, (Sqrt[f]*x)/Sqrt[-e]])/(-e)^(3/2)","A",39,16,28,0.5714,1,"{2305, 2304, 2378, 325, 205, 2351, 2324, 12, 4848, 2391, 2353, 2330, 2317, 2374, 6589, 2383}"
115,1,403,0,0.3446354,"\int x^2 \log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^2*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]),x]","\frac{2 b e^6 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{3 f^6}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{e^6 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^6}+\frac{e^5 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{3 f^5}-\frac{e^4 k x \left(a+b \log \left(c x^n\right)\right)}{6 f^4}+\frac{e^3 k x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 f^3}-\frac{e^2 k x^2 \left(a+b \log \left(c x^n\right)\right)}{12 f^2}+\frac{e k x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{15 f}-\frac{1}{18} k x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b n x^3 \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{b e^3 k n x^{3/2}}{9 f^3}+\frac{5 b e^2 k n x^2}{72 f^2}-\frac{7 b e^5 k n \sqrt{x}}{9 f^5}+\frac{2 b e^4 k n x}{9 f^4}+\frac{b e^6 k n \log \left(e+f \sqrt{x}\right)}{9 f^6}+\frac{2 b e^6 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 f^6}-\frac{11 b e k n x^{5/2}}{225 f}+\frac{1}{27} b k n x^3","\frac{2 b e^6 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{3 f^6}+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{e^6 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^6}+\frac{e^5 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{3 f^5}-\frac{e^4 k x \left(a+b \log \left(c x^n\right)\right)}{6 f^4}+\frac{e^3 k x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 f^3}-\frac{e^2 k x^2 \left(a+b \log \left(c x^n\right)\right)}{12 f^2}+\frac{e k x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{15 f}-\frac{1}{18} k x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{9} b n x^3 \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{b e^3 k n x^{3/2}}{9 f^3}+\frac{5 b e^2 k n x^2}{72 f^2}-\frac{7 b e^5 k n \sqrt{x}}{9 f^5}+\frac{2 b e^4 k n x}{9 f^4}+\frac{b e^6 k n \log \left(e+f \sqrt{x}\right)}{9 f^6}+\frac{2 b e^6 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 f^6}-\frac{11 b e k n x^{5/2}}{225 f}+\frac{1}{27} b k n x^3",1,"(-7*b*e^5*k*n*Sqrt[x])/(9*f^5) + (2*b*e^4*k*n*x)/(9*f^4) - (b*e^3*k*n*x^(3/2))/(9*f^3) + (5*b*e^2*k*n*x^2)/(72*f^2) - (11*b*e*k*n*x^(5/2))/(225*f) + (b*k*n*x^3)/27 + (b*e^6*k*n*Log[e + f*Sqrt[x]])/(9*f^6) - (b*n*x^3*Log[d*(e + f*Sqrt[x])^k])/9 + (2*b*e^6*k*n*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/(3*f^6) + (e^5*k*Sqrt[x]*(a + b*Log[c*x^n]))/(3*f^5) - (e^4*k*x*(a + b*Log[c*x^n]))/(6*f^4) + (e^3*k*x^(3/2)*(a + b*Log[c*x^n]))/(9*f^3) - (e^2*k*x^2*(a + b*Log[c*x^n]))/(12*f^2) + (e*k*x^(5/2)*(a + b*Log[c*x^n]))/(15*f) - (k*x^3*(a + b*Log[c*x^n]))/18 - (e^6*k*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(3*f^6) + (x^3*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/3 + (2*b*e^6*k*n*PolyLog[2, 1 + (f*Sqrt[x])/e])/(3*f^6)","A",9,6,28,0.2143,1,"{2454, 2395, 43, 2376, 2394, 2315}"
116,1,313,0,0.2443328,"\int x \log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]),x]","\frac{b e^4 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{f^4}+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{e^4 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^4}+\frac{e^3 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 f^3}-\frac{e^2 k x \left(a+b \log \left(c x^n\right)\right)}{4 f^2}+\frac{e k x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{6 f}-\frac{1}{8} k x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b n x^2 \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{5 b e^3 k n \sqrt{x}}{4 f^3}+\frac{3 b e^2 k n x}{8 f^2}+\frac{b e^4 k n \log \left(e+f \sqrt{x}\right)}{4 f^4}+\frac{b e^4 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^4}-\frac{7 b e k n x^{3/2}}{36 f}+\frac{1}{8} b k n x^2","\frac{b e^4 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{f^4}+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{e^4 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^4}+\frac{e^3 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 f^3}-\frac{e^2 k x \left(a+b \log \left(c x^n\right)\right)}{4 f^2}+\frac{e k x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{6 f}-\frac{1}{8} k x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} b n x^2 \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{5 b e^3 k n \sqrt{x}}{4 f^3}+\frac{3 b e^2 k n x}{8 f^2}+\frac{b e^4 k n \log \left(e+f \sqrt{x}\right)}{4 f^4}+\frac{b e^4 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^4}-\frac{7 b e k n x^{3/2}}{36 f}+\frac{1}{8} b k n x^2",1,"(-5*b*e^3*k*n*Sqrt[x])/(4*f^3) + (3*b*e^2*k*n*x)/(8*f^2) - (7*b*e*k*n*x^(3/2))/(36*f) + (b*k*n*x^2)/8 + (b*e^4*k*n*Log[e + f*Sqrt[x]])/(4*f^4) - (b*n*x^2*Log[d*(e + f*Sqrt[x])^k])/4 + (b*e^4*k*n*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/f^4 + (e^3*k*Sqrt[x]*(a + b*Log[c*x^n]))/(2*f^3) - (e^2*k*x*(a + b*Log[c*x^n]))/(4*f^2) + (e*k*x^(3/2)*(a + b*Log[c*x^n]))/(6*f) - (k*x^2*(a + b*Log[c*x^n]))/8 - (e^4*k*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(2*f^4) + (x^2*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/2 + (b*e^4*k*n*PolyLog[2, 1 + (f*Sqrt[x])/e])/f^4","A",9,6,26,0.2308,1,"{2454, 2395, 43, 2376, 2394, 2315}"
117,1,209,0,0.1495647,"\int \log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]),x]","\frac{2 b e^2 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{f^2}+x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{e^2 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{e k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{f}-\frac{1}{2} k x \left(a+b \log \left(c x^n\right)\right)-b n x \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{b e^2 k n \log \left(e+f \sqrt{x}\right)}{f^2}+\frac{2 b e^2 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^2}-\frac{3 b e k n \sqrt{x}}{f}+b k n x","\frac{2 b e^2 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{f^2}+x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)-\frac{e^2 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{e k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{f}-\frac{1}{2} k x \left(a+b \log \left(c x^n\right)\right)-b n x \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{b e^2 k n \log \left(e+f \sqrt{x}\right)}{f^2}+\frac{2 b e^2 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^2}-\frac{3 b e k n \sqrt{x}}{f}+b k n x",1,"(-3*b*e*k*n*Sqrt[x])/f + b*k*n*x + (b*e^2*k*n*Log[e + f*Sqrt[x]])/f^2 - b*n*x*Log[d*(e + f*Sqrt[x])^k] + (2*b*e^2*k*n*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/f^2 + (e*k*Sqrt[x]*(a + b*Log[c*x^n]))/f - (k*x*(a + b*Log[c*x^n]))/2 - (e^2*k*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/f^2 + x*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]) + (2*b*e^2*k*n*PolyLog[2, 1 + (f*Sqrt[x])/e])/f^2","A",9,7,25,0.2800,1,"{2448, 266, 43, 2370, 2454, 2394, 2315}"
118,1,117,0,0.1461337,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x} \, dx","Int[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x,x]","-2 k \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)+4 b k n \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{2 b n}-\frac{k \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}","-2 k \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)+4 b k n \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)+\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{2 b n}-\frac{k \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}",1,"(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n])^2)/(2*b*n) - (k*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^2)/(2*b*n) - 2*k*(a + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)] + 4*b*k*n*PolyLog[3, -((f*Sqrt[x])/e)]","A",4,4,28,0.1429,1,"{2375, 2337, 2374, 6589}"
119,1,248,0,0.2100725,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^2} \, dx","Int[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^2,x]","-\frac{2 b f^2 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e^2}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{x}+\frac{f^2 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{f^2 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{x}}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{x}+\frac{b f^2 k n \log ^2(x)}{4 e^2}+\frac{b f^2 k n \log \left(e+f \sqrt{x}\right)}{e^2}-\frac{2 b f^2 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{b f^2 k n \log (x)}{2 e^2}-\frac{3 b f k n}{e \sqrt{x}}","-\frac{2 b f^2 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e^2}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{x}+\frac{f^2 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{f^2 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{2 e^2}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{x}}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{x}+\frac{b f^2 k n \log ^2(x)}{4 e^2}+\frac{b f^2 k n \log \left(e+f \sqrt{x}\right)}{e^2}-\frac{2 b f^2 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{b f^2 k n \log (x)}{2 e^2}-\frac{3 b f k n}{e \sqrt{x}}",1,"(-3*b*f*k*n)/(e*Sqrt[x]) + (b*f^2*k*n*Log[e + f*Sqrt[x]])/e^2 - (b*n*Log[d*(e + f*Sqrt[x])^k])/x - (2*b*f^2*k*n*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/e^2 - (b*f^2*k*n*Log[x])/(2*e^2) + (b*f^2*k*n*Log[x]^2)/(4*e^2) - (f*k*(a + b*Log[c*x^n]))/(e*Sqrt[x]) + (f^2*k*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/e^2 - (Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x - (f^2*k*Log[x]*(a + b*Log[c*x^n]))/(2*e^2) - (2*b*f^2*k*n*PolyLog[2, 1 + (f*Sqrt[x])/e])/e^2","A",10,7,28,0.2500,1,"{2454, 2395, 44, 2376, 2394, 2315, 2301}"
120,1,346,0,0.2797927,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^3} \, dx","Int[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^3,x]","-\frac{b f^4 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e^4}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{2 x^2}+\frac{f^4 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}-\frac{f^4 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{4 e^4}-\frac{f^3 k \left(a+b \log \left(c x^n\right)\right)}{2 e^3 \sqrt{x}}+\frac{f^2 k \left(a+b \log \left(c x^n\right)\right)}{4 e^2 x}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{6 e x^{3/2}}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{4 x^2}-\frac{5 b f^3 k n}{4 e^3 \sqrt{x}}+\frac{3 b f^2 k n}{8 e^2 x}+\frac{b f^4 k n \log ^2(x)}{8 e^4}+\frac{b f^4 k n \log \left(e+f \sqrt{x}\right)}{4 e^4}-\frac{b f^4 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^4}-\frac{b f^4 k n \log (x)}{8 e^4}-\frac{7 b f k n}{36 e x^{3/2}}","-\frac{b f^4 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e^4}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{2 x^2}+\frac{f^4 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}-\frac{f^4 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{4 e^4}-\frac{f^3 k \left(a+b \log \left(c x^n\right)\right)}{2 e^3 \sqrt{x}}+\frac{f^2 k \left(a+b \log \left(c x^n\right)\right)}{4 e^2 x}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{6 e x^{3/2}}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{4 x^2}-\frac{5 b f^3 k n}{4 e^3 \sqrt{x}}+\frac{3 b f^2 k n}{8 e^2 x}+\frac{b f^4 k n \log ^2(x)}{8 e^4}+\frac{b f^4 k n \log \left(e+f \sqrt{x}\right)}{4 e^4}-\frac{b f^4 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^4}-\frac{b f^4 k n \log (x)}{8 e^4}-\frac{7 b f k n}{36 e x^{3/2}}",1,"(-7*b*f*k*n)/(36*e*x^(3/2)) + (3*b*f^2*k*n)/(8*e^2*x) - (5*b*f^3*k*n)/(4*e^3*Sqrt[x]) + (b*f^4*k*n*Log[e + f*Sqrt[x]])/(4*e^4) - (b*n*Log[d*(e + f*Sqrt[x])^k])/(4*x^2) - (b*f^4*k*n*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/e^4 - (b*f^4*k*n*Log[x])/(8*e^4) + (b*f^4*k*n*Log[x]^2)/(8*e^4) - (f*k*(a + b*Log[c*x^n]))/(6*e*x^(3/2)) + (f^2*k*(a + b*Log[c*x^n]))/(4*e^2*x) - (f^3*k*(a + b*Log[c*x^n]))/(2*e^3*Sqrt[x]) + (f^4*k*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(2*e^4) - (Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/(2*x^2) - (f^4*k*Log[x]*(a + b*Log[c*x^n]))/(4*e^4) - (b*f^4*k*n*PolyLog[2, 1 + (f*Sqrt[x])/e])/e^4","A",10,7,28,0.2500,1,"{2454, 2395, 44, 2376, 2394, 2315, 2301}"
121,1,434,0,0.34986,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^4} \, dx","Int[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^4,x]","-\frac{2 b f^6 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{3 e^6}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{3 x^3}+\frac{f^6 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^6}-\frac{f^6 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{6 e^6}-\frac{f^5 k \left(a+b \log \left(c x^n\right)\right)}{3 e^5 \sqrt{x}}+\frac{f^4 k \left(a+b \log \left(c x^n\right)\right)}{6 e^4 x}-\frac{f^3 k \left(a+b \log \left(c x^n\right)\right)}{9 e^3 x^{3/2}}+\frac{f^2 k \left(a+b \log \left(c x^n\right)\right)}{12 e^2 x^2}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{15 e x^{5/2}}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{9 x^3}-\frac{b f^3 k n}{9 e^3 x^{3/2}}+\frac{5 b f^2 k n}{72 e^2 x^2}-\frac{7 b f^5 k n}{9 e^5 \sqrt{x}}+\frac{2 b f^4 k n}{9 e^4 x}+\frac{b f^6 k n \log ^2(x)}{12 e^6}+\frac{b f^6 k n \log \left(e+f \sqrt{x}\right)}{9 e^6}-\frac{2 b f^6 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 e^6}-\frac{b f^6 k n \log (x)}{18 e^6}-\frac{11 b f k n}{225 e x^{5/2}}","-\frac{2 b f^6 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{3 e^6}-\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{3 x^3}+\frac{f^6 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^6}-\frac{f^6 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{6 e^6}-\frac{f^5 k \left(a+b \log \left(c x^n\right)\right)}{3 e^5 \sqrt{x}}+\frac{f^4 k \left(a+b \log \left(c x^n\right)\right)}{6 e^4 x}-\frac{f^3 k \left(a+b \log \left(c x^n\right)\right)}{9 e^3 x^{3/2}}+\frac{f^2 k \left(a+b \log \left(c x^n\right)\right)}{12 e^2 x^2}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{15 e x^{5/2}}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{9 x^3}-\frac{b f^3 k n}{9 e^3 x^{3/2}}+\frac{5 b f^2 k n}{72 e^2 x^2}-\frac{7 b f^5 k n}{9 e^5 \sqrt{x}}+\frac{2 b f^4 k n}{9 e^4 x}+\frac{b f^6 k n \log ^2(x)}{12 e^6}+\frac{b f^6 k n \log \left(e+f \sqrt{x}\right)}{9 e^6}-\frac{2 b f^6 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 e^6}-\frac{b f^6 k n \log (x)}{18 e^6}-\frac{11 b f k n}{225 e x^{5/2}}",1,"(-11*b*f*k*n)/(225*e*x^(5/2)) + (5*b*f^2*k*n)/(72*e^2*x^2) - (b*f^3*k*n)/(9*e^3*x^(3/2)) + (2*b*f^4*k*n)/(9*e^4*x) - (7*b*f^5*k*n)/(9*e^5*Sqrt[x]) + (b*f^6*k*n*Log[e + f*Sqrt[x]])/(9*e^6) - (b*n*Log[d*(e + f*Sqrt[x])^k])/(9*x^3) - (2*b*f^6*k*n*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/(3*e^6) - (b*f^6*k*n*Log[x])/(18*e^6) + (b*f^6*k*n*Log[x]^2)/(12*e^6) - (f*k*(a + b*Log[c*x^n]))/(15*e*x^(5/2)) + (f^2*k*(a + b*Log[c*x^n]))/(12*e^2*x^2) - (f^3*k*(a + b*Log[c*x^n]))/(9*e^3*x^(3/2)) + (f^4*k*(a + b*Log[c*x^n]))/(6*e^4*x) - (f^5*k*(a + b*Log[c*x^n]))/(3*e^5*Sqrt[x]) + (f^6*k*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(3*e^6) - (Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/(3*x^3) - (f^6*k*Log[x]*(a + b*Log[c*x^n]))/(6*e^6) - (2*b*f^6*k*n*PolyLog[2, 1 + (f*Sqrt[x])/e])/(3*e^6)","A",10,7,28,0.2500,1,"{2454, 2395, 44, 2376, 2394, 2315, 2301}"
122,1,750,0,0.8462061,"\int x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[x^2*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","-\frac{4 b e^6 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^6}-\frac{4 b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{9 f^6}+\frac{8 b^2 e^6 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{3 f^6}+\frac{1}{3} x^3 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{e^6 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^6}+\frac{2 b e^6 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{9 f^6}+\frac{e^5 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{3 f^5}-\frac{14 b e^5 n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{9 f^5}-\frac{e^4 x \left(a+b \log \left(c x^n\right)\right)^2}{6 f^4}+\frac{b e^4 n x \left(a+b \log \left(c x^n\right)\right)}{9 f^4}+\frac{e^3 x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{9 f^3}-\frac{2 b e^3 n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 f^3}-\frac{e^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2}{12 f^2}+\frac{5 b e^2 n x^2 \left(a+b \log \left(c x^n\right)\right)}{36 f^2}+\frac{e x^{5/2} \left(a+b \log \left(c x^n\right)\right)^2}{15 f}-\frac{22 b e n x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{225 f}-\frac{1}{18} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{2}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{a b e^4 n x}{3 f^4}+\frac{b^2 e^4 n x \log \left(c x^n\right)}{3 f^4}+\frac{2}{27} b^2 n^2 x^3 \log \left(d \left(e+f \sqrt{x}\right)\right)+\frac{14 b^2 e^3 n^2 x^{3/2}}{81 f^3}-\frac{19 b^2 e^2 n^2 x^2}{216 f^2}+\frac{86 b^2 e^5 n^2 \sqrt{x}}{27 f^5}-\frac{13 b^2 e^4 n^2 x}{27 f^4}-\frac{2 b^2 e^6 n^2 \log \left(e+f \sqrt{x}\right)}{27 f^6}-\frac{4 b^2 e^6 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{9 f^6}+\frac{182 b^2 e n^2 x^{5/2}}{3375 f}-\frac{1}{27} b^2 n^2 x^3","-\frac{4 b e^6 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^6}-\frac{4 b^2 e^6 n^2 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{9 f^6}+\frac{8 b^2 e^6 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{3 f^6}+\frac{1}{3} x^3 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{2}{9} b n x^3 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{e^6 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{3 f^6}+\frac{2 b e^6 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{9 f^6}+\frac{e^5 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{3 f^5}-\frac{14 b e^5 n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{9 f^5}-\frac{e^4 x \left(a+b \log \left(c x^n\right)\right)^2}{6 f^4}+\frac{b e^4 n x \left(a+b \log \left(c x^n\right)\right)}{9 f^4}+\frac{e^3 x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{9 f^3}-\frac{2 b e^3 n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{9 f^3}-\frac{e^2 x^2 \left(a+b \log \left(c x^n\right)\right)^2}{12 f^2}+\frac{5 b e^2 n x^2 \left(a+b \log \left(c x^n\right)\right)}{36 f^2}+\frac{e x^{5/2} \left(a+b \log \left(c x^n\right)\right)^2}{15 f}-\frac{22 b e n x^{5/2} \left(a+b \log \left(c x^n\right)\right)}{225 f}-\frac{1}{18} x^3 \left(a+b \log \left(c x^n\right)\right)^2+\frac{2}{27} b n x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{a b e^4 n x}{3 f^4}+\frac{b^2 e^4 n x \log \left(c x^n\right)}{3 f^4}+\frac{2}{27} b^2 n^2 x^3 \log \left(d \left(e+f \sqrt{x}\right)\right)+\frac{14 b^2 e^3 n^2 x^{3/2}}{81 f^3}-\frac{19 b^2 e^2 n^2 x^2}{216 f^2}+\frac{86 b^2 e^5 n^2 \sqrt{x}}{27 f^5}-\frac{13 b^2 e^4 n^2 x}{27 f^4}-\frac{2 b^2 e^6 n^2 \log \left(e+f \sqrt{x}\right)}{27 f^6}-\frac{4 b^2 e^6 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{9 f^6}+\frac{182 b^2 e n^2 x^{5/2}}{3375 f}-\frac{1}{27} b^2 n^2 x^3",1,"(86*b^2*e^5*n^2*Sqrt[x])/(27*f^5) + (a*b*e^4*n*x)/(3*f^4) - (13*b^2*e^4*n^2*x)/(27*f^4) + (14*b^2*e^3*n^2*x^(3/2))/(81*f^3) - (19*b^2*e^2*n^2*x^2)/(216*f^2) + (182*b^2*e*n^2*x^(5/2))/(3375*f) - (b^2*n^2*x^3)/27 - (2*b^2*e^6*n^2*Log[e + f*Sqrt[x]])/(27*f^6) + (2*b^2*n^2*x^3*Log[d*(e + f*Sqrt[x])])/27 - (4*b^2*e^6*n^2*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/(9*f^6) + (b^2*e^4*n*x*Log[c*x^n])/(3*f^4) - (14*b*e^5*n*Sqrt[x]*(a + b*Log[c*x^n]))/(9*f^5) + (b*e^4*n*x*(a + b*Log[c*x^n]))/(9*f^4) - (2*b*e^3*n*x^(3/2)*(a + b*Log[c*x^n]))/(9*f^3) + (5*b*e^2*n*x^2*(a + b*Log[c*x^n]))/(36*f^2) - (22*b*e*n*x^(5/2)*(a + b*Log[c*x^n]))/(225*f) + (2*b*n*x^3*(a + b*Log[c*x^n]))/27 + (2*b*e^6*n*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(9*f^6) - (2*b*n*x^3*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n]))/9 + (e^5*Sqrt[x]*(a + b*Log[c*x^n])^2)/(3*f^5) - (e^4*x*(a + b*Log[c*x^n])^2)/(6*f^4) + (e^3*x^(3/2)*(a + b*Log[c*x^n])^2)/(9*f^3) - (e^2*x^2*(a + b*Log[c*x^n])^2)/(12*f^2) + (e*x^(5/2)*(a + b*Log[c*x^n])^2)/(15*f) - (x^3*(a + b*Log[c*x^n])^2)/18 + (x^3*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/3 - (e^6*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^2)/(3*f^6) - (4*b^2*e^6*n^2*PolyLog[2, 1 + (f*Sqrt[x])/e])/(9*f^6) - (4*b*e^6*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)])/(3*f^6) + (8*b^2*e^6*n^2*PolyLog[3, -((f*Sqrt[x])/e)])/(3*f^6)","A",22,13,28,0.4643,1,"{2454, 2395, 43, 2377, 2295, 2304, 2375, 2337, 2374, 6589, 2376, 2394, 2315}"
123,1,598,0,0.6562444,"\int x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[x*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","-\frac{2 b e^4 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^4}-\frac{b^2 e^4 n^2 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{f^4}+\frac{4 b^2 e^4 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{f^4}+\frac{1}{2} x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} b n x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{e^4 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f^4}+\frac{b e^4 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^4}+\frac{e^3 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{2 f^3}-\frac{5 b e^3 n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 f^3}-\frac{e^2 x \left(a+b \log \left(c x^n\right)\right)^2}{4 f^2}+\frac{b e^2 n x \left(a+b \log \left(c x^n\right)\right)}{4 f^2}+\frac{e x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{6 f}-\frac{7 b e n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{18 f}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{a b e^2 n x}{2 f^2}+\frac{b^2 e^2 n x \log \left(c x^n\right)}{2 f^2}+\frac{1}{4} b^2 n^2 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)+\frac{21 b^2 e^3 n^2 \sqrt{x}}{4 f^3}-\frac{7 b^2 e^2 n^2 x}{8 f^2}-\frac{b^2 e^4 n^2 \log \left(e+f \sqrt{x}\right)}{4 f^4}-\frac{b^2 e^4 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^4}+\frac{37 b^2 e n^2 x^{3/2}}{108 f}-\frac{3}{16} b^2 n^2 x^2","-\frac{2 b e^4 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^4}-\frac{b^2 e^4 n^2 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{f^4}+\frac{4 b^2 e^4 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{f^4}+\frac{1}{2} x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} b n x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{e^4 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 f^4}+\frac{b e^4 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^4}+\frac{e^3 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{2 f^3}-\frac{5 b e^3 n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{2 f^3}-\frac{e^2 x \left(a+b \log \left(c x^n\right)\right)^2}{4 f^2}+\frac{b e^2 n x \left(a+b \log \left(c x^n\right)\right)}{4 f^2}+\frac{e x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2}{6 f}-\frac{7 b e n x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{18 f}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^2+\frac{1}{4} b n x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{a b e^2 n x}{2 f^2}+\frac{b^2 e^2 n x \log \left(c x^n\right)}{2 f^2}+\frac{1}{4} b^2 n^2 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)+\frac{21 b^2 e^3 n^2 \sqrt{x}}{4 f^3}-\frac{7 b^2 e^2 n^2 x}{8 f^2}-\frac{b^2 e^4 n^2 \log \left(e+f \sqrt{x}\right)}{4 f^4}-\frac{b^2 e^4 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^4}+\frac{37 b^2 e n^2 x^{3/2}}{108 f}-\frac{3}{16} b^2 n^2 x^2",1,"(21*b^2*e^3*n^2*Sqrt[x])/(4*f^3) + (a*b*e^2*n*x)/(2*f^2) - (7*b^2*e^2*n^2*x)/(8*f^2) + (37*b^2*e*n^2*x^(3/2))/(108*f) - (3*b^2*n^2*x^2)/16 - (b^2*e^4*n^2*Log[e + f*Sqrt[x]])/(4*f^4) + (b^2*n^2*x^2*Log[d*(e + f*Sqrt[x])])/4 - (b^2*e^4*n^2*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/f^4 + (b^2*e^2*n*x*Log[c*x^n])/(2*f^2) - (5*b*e^3*n*Sqrt[x]*(a + b*Log[c*x^n]))/(2*f^3) + (b*e^2*n*x*(a + b*Log[c*x^n]))/(4*f^2) - (7*b*e*n*x^(3/2)*(a + b*Log[c*x^n]))/(18*f) + (b*n*x^2*(a + b*Log[c*x^n]))/4 + (b*e^4*n*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(2*f^4) - (b*n*x^2*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n]))/2 + (e^3*Sqrt[x]*(a + b*Log[c*x^n])^2)/(2*f^3) - (e^2*x*(a + b*Log[c*x^n])^2)/(4*f^2) + (e*x^(3/2)*(a + b*Log[c*x^n])^2)/(6*f) - (x^2*(a + b*Log[c*x^n])^2)/8 + (x^2*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/2 - (e^4*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^2)/(2*f^4) - (b^2*e^4*n^2*PolyLog[2, 1 + (f*Sqrt[x])/e])/f^4 - (2*b*e^4*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)])/f^4 + (4*b^2*e^4*n^2*PolyLog[3, -((f*Sqrt[x])/e)])/f^4","A",20,13,26,0.5000,1,"{2454, 2395, 43, 2377, 2295, 2304, 2375, 2337, 2374, 6589, 2376, 2394, 2315}"
124,1,405,0,0.4412009,"\int \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2 \, dx","Int[Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2,x]","-\frac{4 b e^2 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}-\frac{4 b^2 e^2 n^2 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{f^2}+\frac{8 b^2 e^2 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{f^2}-2 b n x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)+x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{2 b e^2 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}-\frac{e^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f^2}-\frac{6 b e n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{f}+\frac{e \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{f}+b n x \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^2+a b n x+b^2 n x \log \left(c x^n\right)+2 b^2 n^2 x \log \left(d \left(e+f \sqrt{x}\right)\right)-\frac{2 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right)}{f^2}-\frac{4 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^2}+\frac{14 b^2 e n^2 \sqrt{x}}{f}-3 b^2 n^2 x","-\frac{4 b e^2 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}-\frac{4 b^2 e^2 n^2 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{f^2}+\frac{8 b^2 e^2 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{f^2}-2 b n x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)+x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2+\frac{2 b e^2 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}-\frac{e^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f^2}-\frac{6 b e n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{f}+\frac{e \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{f}+b n x \left(a+b \log \left(c x^n\right)\right)-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^2+a b n x+b^2 n x \log \left(c x^n\right)+2 b^2 n^2 x \log \left(d \left(e+f \sqrt{x}\right)\right)-\frac{2 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right)}{f^2}-\frac{4 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^2}+\frac{14 b^2 e n^2 \sqrt{x}}{f}-3 b^2 n^2 x",1,"(14*b^2*e*n^2*Sqrt[x])/f + a*b*n*x - 3*b^2*n^2*x - (2*b^2*e^2*n^2*Log[e + f*Sqrt[x]])/f^2 + 2*b^2*n^2*x*Log[d*(e + f*Sqrt[x])] - (4*b^2*e^2*n^2*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/f^2 + b^2*n*x*Log[c*x^n] - (6*b*e*n*Sqrt[x]*(a + b*Log[c*x^n]))/f + b*n*x*(a + b*Log[c*x^n]) + (2*b*e^2*n*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/f^2 - 2*b*n*x*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n]) + (e*Sqrt[x]*(a + b*Log[c*x^n])^2)/f - (x*(a + b*Log[c*x^n])^2)/2 + x*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2 - (e^2*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^2)/f^2 - (4*b^2*e^2*n^2*PolyLog[2, 1 + (f*Sqrt[x])/e])/f^2 - (4*b*e^2*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)])/f^2 + (8*b^2*e^2*n^2*PolyLog[3, -((f*Sqrt[x])/e)])/f^2","A",18,13,25,0.5200,1,"{2448, 266, 43, 2370, 2295, 2304, 2375, 2337, 2374, 6589, 2454, 2394, 2315}"
125,1,145,0,0.1937132,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x} \, dx","Int[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x,x]","-2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+8 b n \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)-16 b^2 n^2 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right)+\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-\frac{\log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}","-2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+8 b n \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)-16 b^2 n^2 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right)+\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}-\frac{\log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}",1,"(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/(3*b*n) - (Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^3)/(3*b*n) - 2*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*Sqrt[x])/e)] + 8*b*n*(a + b*Log[c*x^n])*PolyLog[3, -((f*Sqrt[x])/e)] - 16*b^2*n^2*PolyLog[4, -((f*Sqrt[x])/e)]","A",5,5,28,0.1786,1,"{2375, 2337, 2374, 2383, 6589}"
126,1,441,0,0.6325565,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x^2} \, dx","Int[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x^2,x]","\frac{4 b f^2 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{4 b^2 f^2 n^2 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e^2}-\frac{8 b^2 f^2 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{2 b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^3}{6 b e^2 n}+\frac{f^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^2}+\frac{2 b f^2 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{b f^2 n \log (x) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{f \left(a+b \log \left(c x^n\right)\right)^2}{e \sqrt{x}}-\frac{6 b f n \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{x}}-\frac{2 b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right)}{x}+\frac{b^2 f^2 n^2 \log ^2(x)}{2 e^2}+\frac{2 b^2 f^2 n^2 \log \left(e+f \sqrt{x}\right)}{e^2}-\frac{4 b^2 f^2 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{b^2 f^2 n^2 \log (x)}{e^2}-\frac{14 b^2 f n^2}{e \sqrt{x}}","\frac{4 b f^2 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{4 b^2 f^2 n^2 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e^2}-\frac{8 b^2 f^2 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{2 b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^3}{6 b e^2 n}+\frac{f^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^2}+\frac{2 b f^2 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{b f^2 n \log (x) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{f \left(a+b \log \left(c x^n\right)\right)^2}{e \sqrt{x}}-\frac{6 b f n \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{x}}-\frac{2 b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right)}{x}+\frac{b^2 f^2 n^2 \log ^2(x)}{2 e^2}+\frac{2 b^2 f^2 n^2 \log \left(e+f \sqrt{x}\right)}{e^2}-\frac{4 b^2 f^2 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{b^2 f^2 n^2 \log (x)}{e^2}-\frac{14 b^2 f n^2}{e \sqrt{x}}",1,"(-14*b^2*f*n^2)/(e*Sqrt[x]) + (2*b^2*f^2*n^2*Log[e + f*Sqrt[x]])/e^2 - (2*b^2*n^2*Log[d*(e + f*Sqrt[x])])/x - (4*b^2*f^2*n^2*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/e^2 - (b^2*f^2*n^2*Log[x])/e^2 + (b^2*f^2*n^2*Log[x]^2)/(2*e^2) - (6*b*f*n*(a + b*Log[c*x^n]))/(e*Sqrt[x]) + (2*b*f^2*n*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/e^2 - (2*b*n*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n]))/x - (b*f^2*n*Log[x]*(a + b*Log[c*x^n]))/e^2 - (f*(a + b*Log[c*x^n])^2)/(e*Sqrt[x]) - (Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x + (f^2*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^2)/e^2 - (f^2*(a + b*Log[c*x^n])^3)/(6*b*e^2*n) - (4*b^2*f^2*n^2*PolyLog[2, 1 + (f*Sqrt[x])/e])/e^2 + (4*b*f^2*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)])/e^2 - (8*b^2*f^2*n^2*PolyLog[3, -((f*Sqrt[x])/e)])/e^2","A",21,17,28,0.6071,1,"{2454, 2395, 44, 2377, 2304, 2375, 2337, 2374, 6589, 2376, 2394, 2315, 2301, 2366, 12, 2302, 30}"
127,1,608,0,0.783712,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x^3} \, dx","Int[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x^3,x]","\frac{2 b f^4 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{b^2 f^4 n^2 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e^4}-\frac{4 b^2 f^4 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{e^4}-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{f^4 \left(a+b \log \left(c x^n\right)\right)^3}{12 b e^4 n}+\frac{f^4 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^4}+\frac{b f^4 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}-\frac{b f^4 n \log (x) \left(a+b \log \left(c x^n\right)\right)}{4 e^4}-\frac{f^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^3 \sqrt{x}}-\frac{5 b f^3 n \left(a+b \log \left(c x^n\right)\right)}{2 e^3 \sqrt{x}}+\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2 x}+\frac{3 b f^2 n \left(a+b \log \left(c x^n\right)\right)}{4 e^2 x}-\frac{f \left(a+b \log \left(c x^n\right)\right)^2}{6 e x^{3/2}}-\frac{7 b f n \left(a+b \log \left(c x^n\right)\right)}{18 e x^{3/2}}-\frac{b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right)}{4 x^2}-\frac{21 b^2 f^3 n^2}{4 e^3 \sqrt{x}}+\frac{7 b^2 f^2 n^2}{8 e^2 x}+\frac{b^2 f^4 n^2 \log ^2(x)}{8 e^4}+\frac{b^2 f^4 n^2 \log \left(e+f \sqrt{x}\right)}{4 e^4}-\frac{b^2 f^4 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^4}-\frac{b^2 f^4 n^2 \log (x)}{8 e^4}-\frac{37 b^2 f n^2}{108 e x^{3/2}}","\frac{2 b f^4 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^4}-\frac{b^2 f^4 n^2 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e^4}-\frac{4 b^2 f^4 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{e^4}-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 x^2}-\frac{b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{f^4 \left(a+b \log \left(c x^n\right)\right)^3}{12 b e^4 n}+\frac{f^4 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 e^4}+\frac{b f^4 n \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^4}-\frac{b f^4 n \log (x) \left(a+b \log \left(c x^n\right)\right)}{4 e^4}-\frac{f^3 \left(a+b \log \left(c x^n\right)\right)^2}{2 e^3 \sqrt{x}}-\frac{5 b f^3 n \left(a+b \log \left(c x^n\right)\right)}{2 e^3 \sqrt{x}}+\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^2}{4 e^2 x}+\frac{3 b f^2 n \left(a+b \log \left(c x^n\right)\right)}{4 e^2 x}-\frac{f \left(a+b \log \left(c x^n\right)\right)^2}{6 e x^{3/2}}-\frac{7 b f n \left(a+b \log \left(c x^n\right)\right)}{18 e x^{3/2}}-\frac{b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right)}{4 x^2}-\frac{21 b^2 f^3 n^2}{4 e^3 \sqrt{x}}+\frac{7 b^2 f^2 n^2}{8 e^2 x}+\frac{b^2 f^4 n^2 \log ^2(x)}{8 e^4}+\frac{b^2 f^4 n^2 \log \left(e+f \sqrt{x}\right)}{4 e^4}-\frac{b^2 f^4 n^2 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^4}-\frac{b^2 f^4 n^2 \log (x)}{8 e^4}-\frac{37 b^2 f n^2}{108 e x^{3/2}}",1,"(-37*b^2*f*n^2)/(108*e*x^(3/2)) + (7*b^2*f^2*n^2)/(8*e^2*x) - (21*b^2*f^3*n^2)/(4*e^3*Sqrt[x]) + (b^2*f^4*n^2*Log[e + f*Sqrt[x]])/(4*e^4) - (b^2*n^2*Log[d*(e + f*Sqrt[x])])/(4*x^2) - (b^2*f^4*n^2*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/e^4 - (b^2*f^4*n^2*Log[x])/(8*e^4) + (b^2*f^4*n^2*Log[x]^2)/(8*e^4) - (7*b*f*n*(a + b*Log[c*x^n]))/(18*e*x^(3/2)) + (3*b*f^2*n*(a + b*Log[c*x^n]))/(4*e^2*x) - (5*b*f^3*n*(a + b*Log[c*x^n]))/(2*e^3*Sqrt[x]) + (b*f^4*n*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(2*e^4) - (b*n*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n]))/(2*x^2) - (b*f^4*n*Log[x]*(a + b*Log[c*x^n]))/(4*e^4) - (f*(a + b*Log[c*x^n])^2)/(6*e*x^(3/2)) + (f^2*(a + b*Log[c*x^n])^2)/(4*e^2*x) - (f^3*(a + b*Log[c*x^n])^2)/(2*e^3*Sqrt[x]) - (Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/(2*x^2) + (f^4*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^2)/(2*e^4) - (f^4*(a + b*Log[c*x^n])^3)/(12*b*e^4*n) - (b^2*f^4*n^2*PolyLog[2, 1 + (f*Sqrt[x])/e])/e^4 + (2*b*f^4*n*(a + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)])/e^4 - (4*b^2*f^4*n^2*PolyLog[3, -((f*Sqrt[x])/e)])/e^4","A",23,17,28,0.6071,1,"{2454, 2395, 44, 2377, 2304, 2375, 2337, 2374, 6589, 2376, 2394, 2315, 2301, 2366, 12, 2302, 30}"
128,1,907,0,1.3087134,"\int x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Int[x*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3,x]","-\frac{\log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3 e^4}{2 f^4}+\frac{3 b n \log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2 e^4}{4 f^4}+\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) e^4}{8 f^4}+\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right) e^4}{2 f^4}-\frac{3 b^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right) e^4}{4 f^4}+\frac{3 b^3 n^3 \text{PolyLog}\left(2,\frac{\sqrt{x} f}{e}+1\right) e^4}{2 f^4}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}+\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}-\frac{6 b^3 n^3 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}+\frac{12 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}-\frac{24 b^3 n^3 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3 e^3}{2 f^3}-\frac{15 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2 e^3}{4 f^3}+\frac{63 b^2 n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right) e^3}{4 f^3}-\frac{255 b^3 n^3 \sqrt{x} e^3}{8 f^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^3 e^2}{4 f^2}+\frac{9 b n x \left(a+b \log \left(c x^n\right)\right)^2 e^2}{8 f^2}+\frac{45 b^3 n^3 x e^2}{16 f^2}-\frac{9 a b^2 n^2 x e^2}{4 f^2}-\frac{9 b^3 n^2 x \log \left(c x^n\right) e^2}{4 f^2}-\frac{3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right) e^2}{8 f^2}+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^3 e}{6 f}-\frac{7 b n x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2 e}{12 f}-\frac{175 b^3 n^3 x^{3/2} e}{216 f}+\frac{37 b^2 n^2 x^{3/2} \left(a+b \log \left(c x^n\right)\right) e}{36 f}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{1}{2} x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{8} b^3 n^3 x^2+\frac{3}{8} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{3}{4} b n x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{3}{8} b^3 n^3 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)-\frac{9}{16} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b^2 n^2 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)","-\frac{\log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3 e^4}{2 f^4}+\frac{3 b n \log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2 e^4}{4 f^4}+\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) e^4}{8 f^4}+\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right) e^4}{2 f^4}-\frac{3 b^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right) e^4}{4 f^4}+\frac{3 b^3 n^3 \text{PolyLog}\left(2,\frac{\sqrt{x} f}{e}+1\right) e^4}{2 f^4}-\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}+\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}-\frac{6 b^3 n^3 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}+\frac{12 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}-\frac{24 b^3 n^3 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right) e^4}{f^4}+\frac{\sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3 e^3}{2 f^3}-\frac{15 b n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2 e^3}{4 f^3}+\frac{63 b^2 n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right) e^3}{4 f^3}-\frac{255 b^3 n^3 \sqrt{x} e^3}{8 f^3}-\frac{x \left(a+b \log \left(c x^n\right)\right)^3 e^2}{4 f^2}+\frac{9 b n x \left(a+b \log \left(c x^n\right)\right)^2 e^2}{8 f^2}+\frac{45 b^3 n^3 x e^2}{16 f^2}-\frac{9 a b^2 n^2 x e^2}{4 f^2}-\frac{9 b^3 n^2 x \log \left(c x^n\right) e^2}{4 f^2}-\frac{3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right) e^2}{8 f^2}+\frac{x^{3/2} \left(a+b \log \left(c x^n\right)\right)^3 e}{6 f}-\frac{7 b n x^{3/2} \left(a+b \log \left(c x^n\right)\right)^2 e}{12 f}-\frac{175 b^3 n^3 x^{3/2} e}{216 f}+\frac{37 b^2 n^2 x^{3/2} \left(a+b \log \left(c x^n\right)\right) e}{36 f}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)^3+\frac{1}{2} x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3}{8} b^3 n^3 x^2+\frac{3}{8} b n x^2 \left(a+b \log \left(c x^n\right)\right)^2-\frac{3}{4} b n x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2-\frac{3}{8} b^3 n^3 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right)-\frac{9}{16} b^2 n^2 x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{3}{4} b^2 n^2 x^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)",1,"(-255*b^3*e^3*n^3*Sqrt[x])/(8*f^3) - (9*a*b^2*e^2*n^2*x)/(4*f^2) + (45*b^3*e^2*n^3*x)/(16*f^2) - (175*b^3*e*n^3*x^(3/2))/(216*f) + (3*b^3*n^3*x^2)/8 + (3*b^3*e^4*n^3*Log[e + f*Sqrt[x]])/(8*f^4) - (3*b^3*n^3*x^2*Log[d*(e + f*Sqrt[x])])/8 + (3*b^3*e^4*n^3*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/(2*f^4) - (9*b^3*e^2*n^2*x*Log[c*x^n])/(4*f^2) + (63*b^2*e^3*n^2*Sqrt[x]*(a + b*Log[c*x^n]))/(4*f^3) - (3*b^2*e^2*n^2*x*(a + b*Log[c*x^n]))/(8*f^2) + (37*b^2*e*n^2*x^(3/2)*(a + b*Log[c*x^n]))/(36*f) - (9*b^2*n^2*x^2*(a + b*Log[c*x^n]))/16 - (3*b^2*e^4*n^2*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(4*f^4) + (3*b^2*n^2*x^2*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n]))/4 - (15*b*e^3*n*Sqrt[x]*(a + b*Log[c*x^n])^2)/(4*f^3) + (9*b*e^2*n*x*(a + b*Log[c*x^n])^2)/(8*f^2) - (7*b*e*n*x^(3/2)*(a + b*Log[c*x^n])^2)/(12*f) + (3*b*n*x^2*(a + b*Log[c*x^n])^2)/8 - (3*b*n*x^2*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/4 + (3*b*e^4*n*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^2)/(4*f^4) + (e^3*Sqrt[x]*(a + b*Log[c*x^n])^3)/(2*f^3) - (e^2*x*(a + b*Log[c*x^n])^3)/(4*f^2) + (e*x^(3/2)*(a + b*Log[c*x^n])^3)/(6*f) - (x^2*(a + b*Log[c*x^n])^3)/8 + (x^2*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/2 - (e^4*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^3)/(2*f^4) + (3*b^3*e^4*n^3*PolyLog[2, 1 + (f*Sqrt[x])/e])/(2*f^4) + (3*b^2*e^4*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)])/f^4 - (3*b*e^4*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*Sqrt[x])/e)])/f^4 - (6*b^3*e^4*n^3*PolyLog[3, -((f*Sqrt[x])/e)])/f^4 + (12*b^2*e^4*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((f*Sqrt[x])/e)])/f^4 - (24*b^3*e^4*n^3*PolyLog[4, -((f*Sqrt[x])/e)])/f^4","A",36,16,26,0.6154,1,"{2454, 2395, 43, 2377, 2296, 2295, 2305, 2304, 2375, 2337, 2374, 2383, 6589, 2376, 2394, 2315}"
129,1,639,0,0.8555466,"\int \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3 \, dx","Int[Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3,x]","\frac{12 b^2 e^2 n^2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{24 b^2 e^2 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}-\frac{6 b e^2 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{f^2}+\frac{12 b^3 e^2 n^3 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{f^2}-\frac{24 b^3 e^2 n^3 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{f^2}-\frac{48 b^3 e^2 n^3 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right)}{f^2}+6 b^2 n^2 x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{42 b^2 e n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{f}-3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)-6 a b^2 n^2 x-3 b n x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2+x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3 b e^2 n \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f^2}-\frac{e^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{f^2}-\frac{9 b e n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{f}+\frac{e \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3}{f}+3 b n x \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^3-6 b^3 n^2 x \log \left(c x^n\right)-6 b^3 n^3 x \log \left(d \left(e+f \sqrt{x}\right)\right)+\frac{6 b^3 e^2 n^3 \log \left(e+f \sqrt{x}\right)}{f^2}+\frac{12 b^3 e^2 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^2}-\frac{90 b^3 e n^3 \sqrt{x}}{f}+12 b^3 n^3 x","\frac{12 b^2 e^2 n^2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{24 b^2 e^2 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}-\frac{6 b e^2 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{f^2}+\frac{12 b^3 e^2 n^3 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{f^2}-\frac{24 b^3 e^2 n^3 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{f^2}-\frac{48 b^3 e^2 n^3 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right)}{f^2}+6 b^2 n^2 x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)-\frac{6 b^2 e^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{f^2}+\frac{42 b^2 e n^2 \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{f}-3 b^2 n^2 x \left(a+b \log \left(c x^n\right)\right)-6 a b^2 n^2 x-3 b n x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2+x \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3+\frac{3 b e^2 n \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{f^2}-\frac{e^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{f^2}-\frac{9 b e n \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^2}{f}+\frac{e \sqrt{x} \left(a+b \log \left(c x^n\right)\right)^3}{f}+3 b n x \left(a+b \log \left(c x^n\right)\right)^2-\frac{1}{2} x \left(a+b \log \left(c x^n\right)\right)^3-6 b^3 n^2 x \log \left(c x^n\right)-6 b^3 n^3 x \log \left(d \left(e+f \sqrt{x}\right)\right)+\frac{6 b^3 e^2 n^3 \log \left(e+f \sqrt{x}\right)}{f^2}+\frac{12 b^3 e^2 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{f^2}-\frac{90 b^3 e n^3 \sqrt{x}}{f}+12 b^3 n^3 x",1,"(-90*b^3*e*n^3*Sqrt[x])/f - 6*a*b^2*n^2*x + 12*b^3*n^3*x + (6*b^3*e^2*n^3*Log[e + f*Sqrt[x]])/f^2 - 6*b^3*n^3*x*Log[d*(e + f*Sqrt[x])] + (12*b^3*e^2*n^3*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/f^2 - 6*b^3*n^2*x*Log[c*x^n] + (42*b^2*e*n^2*Sqrt[x]*(a + b*Log[c*x^n]))/f - 3*b^2*n^2*x*(a + b*Log[c*x^n]) - (6*b^2*e^2*n^2*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/f^2 + 6*b^2*n^2*x*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n]) - (9*b*e*n*Sqrt[x]*(a + b*Log[c*x^n])^2)/f + 3*b*n*x*(a + b*Log[c*x^n])^2 - 3*b*n*x*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2 + (3*b*e^2*n*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^2)/f^2 + (e*Sqrt[x]*(a + b*Log[c*x^n])^3)/f - (x*(a + b*Log[c*x^n])^3)/2 + x*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3 - (e^2*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^3)/f^2 + (12*b^3*e^2*n^3*PolyLog[2, 1 + (f*Sqrt[x])/e])/f^2 + (12*b^2*e^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)])/f^2 - (6*b*e^2*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*Sqrt[x])/e)])/f^2 - (24*b^3*e^2*n^3*PolyLog[3, -((f*Sqrt[x])/e)])/f^2 + (24*b^2*e^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((f*Sqrt[x])/e)])/f^2 - (48*b^3*e^2*n^3*PolyLog[4, -((f*Sqrt[x])/e)])/f^2","A",30,16,25,0.6400,1,"{2448, 266, 43, 2370, 2296, 2295, 2305, 2304, 2375, 2337, 2374, 2383, 6589, 2454, 2394, 2315}"
130,1,178,0,0.2316095,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x} \, dx","Int[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x,x]","-48 b^2 n^2 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)-2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3+12 b n \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+96 b^3 n^3 \text{PolyLog}\left(5,-\frac{f \sqrt{x}}{e}\right)+\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}-\frac{\log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}","-48 b^2 n^2 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)-2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3+12 b n \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2+96 b^3 n^3 \text{PolyLog}\left(5,-\frac{f \sqrt{x}}{e}\right)+\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}-\frac{\log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}",1,"(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^4)/(4*b*n) - (Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^4)/(4*b*n) - 2*(a + b*Log[c*x^n])^3*PolyLog[2, -((f*Sqrt[x])/e)] + 12*b*n*(a + b*Log[c*x^n])^2*PolyLog[3, -((f*Sqrt[x])/e)] - 48*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[4, -((f*Sqrt[x])/e)] + 96*b^3*n^3*PolyLog[5, -((f*Sqrt[x])/e)]","A",6,5,28,0.1786,1,"{2375, 2337, 2374, 2383, 6589}"
131,1,673,0,1.1815527,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x^2} \, dx","Int[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x^2,x]","\frac{12 b^2 f^2 n^2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{24 b^2 f^2 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{6 b f^2 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^2}-\frac{12 b^3 f^2 n^3 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e^2}-\frac{24 b^3 f^2 n^3 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{e^2}+\frac{48 b^3 f^2 n^3 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{6 b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{6 b^2 f^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{3 b^2 f^2 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{42 b^2 f n^2 \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{x}}-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x}-\frac{3 b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^4}{8 b e^2 n}-\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^3}{2 e^2}+\frac{f^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{e^2}+\frac{3 b f^2 n \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^2}-\frac{f \left(a+b \log \left(c x^n\right)\right)^3}{e \sqrt{x}}-\frac{9 b f n \left(a+b \log \left(c x^n\right)\right)^2}{e \sqrt{x}}-\frac{6 b^3 n^3 \log \left(d \left(e+f \sqrt{x}\right)\right)}{x}+\frac{3 b^3 f^2 n^3 \log ^2(x)}{2 e^2}+\frac{6 b^3 f^2 n^3 \log \left(e+f \sqrt{x}\right)}{e^2}-\frac{12 b^3 f^2 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{3 b^3 f^2 n^3 \log (x)}{e^2}-\frac{90 b^3 f n^3}{e \sqrt{x}}","\frac{12 b^2 f^2 n^2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{24 b^2 f^2 n^2 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}+\frac{6 b f^2 n \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^2}-\frac{12 b^3 f^2 n^3 \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e^2}-\frac{24 b^3 f^2 n^3 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right)}{e^2}+\frac{48 b^3 f^2 n^3 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{6 b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{x}+\frac{6 b^2 f^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{3 b^2 f^2 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right)}{e^2}-\frac{42 b^2 f n^2 \left(a+b \log \left(c x^n\right)\right)}{e \sqrt{x}}-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x}-\frac{3 b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{x}-\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^4}{8 b e^2 n}-\frac{f^2 \left(a+b \log \left(c x^n\right)\right)^3}{2 e^2}+\frac{f^2 \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{e^2}+\frac{3 b f^2 n \log \left(\frac{f \sqrt{x}}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{e^2}-\frac{f \left(a+b \log \left(c x^n\right)\right)^3}{e \sqrt{x}}-\frac{9 b f n \left(a+b \log \left(c x^n\right)\right)^2}{e \sqrt{x}}-\frac{6 b^3 n^3 \log \left(d \left(e+f \sqrt{x}\right)\right)}{x}+\frac{3 b^3 f^2 n^3 \log ^2(x)}{2 e^2}+\frac{6 b^3 f^2 n^3 \log \left(e+f \sqrt{x}\right)}{e^2}-\frac{12 b^3 f^2 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e^2}-\frac{3 b^3 f^2 n^3 \log (x)}{e^2}-\frac{90 b^3 f n^3}{e \sqrt{x}}",1,"(-90*b^3*f*n^3)/(e*Sqrt[x]) + (6*b^3*f^2*n^3*Log[e + f*Sqrt[x]])/e^2 - (6*b^3*n^3*Log[d*(e + f*Sqrt[x])])/x - (12*b^3*f^2*n^3*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/e^2 - (3*b^3*f^2*n^3*Log[x])/e^2 + (3*b^3*f^2*n^3*Log[x]^2)/(2*e^2) - (42*b^2*f*n^2*(a + b*Log[c*x^n]))/(e*Sqrt[x]) + (6*b^2*f^2*n^2*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/e^2 - (6*b^2*n^2*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n]))/x - (3*b^2*f^2*n^2*Log[x]*(a + b*Log[c*x^n]))/e^2 - (9*b*f*n*(a + b*Log[c*x^n])^2)/(e*Sqrt[x]) - (3*b*n*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/x + (3*b*f^2*n*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^2)/e^2 - (f^2*(a + b*Log[c*x^n])^3)/(2*e^2) - (f*(a + b*Log[c*x^n])^3)/(e*Sqrt[x]) - (Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x + (f^2*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^3)/e^2 - (f^2*(a + b*Log[c*x^n])^4)/(8*b*e^2*n) - (12*b^3*f^2*n^3*PolyLog[2, 1 + (f*Sqrt[x])/e])/e^2 + (12*b^2*f^2*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)])/e^2 + (6*b*f^2*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*Sqrt[x])/e)])/e^2 - (24*b^3*f^2*n^3*PolyLog[3, -((f*Sqrt[x])/e)])/e^2 - (24*b^2*f^2*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((f*Sqrt[x])/e)])/e^2 + (48*b^3*f^2*n^3*PolyLog[4, -((f*Sqrt[x])/e)])/e^2","A",34,19,28,0.6786,1,"{2454, 2395, 44, 2377, 2305, 2304, 2375, 2337, 2374, 2383, 6589, 2376, 2394, 2315, 2301, 2366, 12, 2302, 30}"
132,1,914,0,1.5204238,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{x^3} \, dx","Int[(Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/x^3,x]","-\frac{\left(a+b \log \left(c x^n\right)\right)^4 f^4}{16 b e^4 n}+\frac{\log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3 f^4}{2 e^4}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 f^4}{8 e^4}+\frac{3 b^3 n^3 \log ^2(x) f^4}{16 e^4}+\frac{3 b n \log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2 f^4}{4 e^4}+\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) f^4}{8 e^4}-\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right) f^4}{2 e^4}-\frac{3 b^3 n^3 \log (x) f^4}{16 e^4}+\frac{3 b^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right) f^4}{4 e^4}-\frac{3 b^2 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right) f^4}{8 e^4}-\frac{3 b^3 n^3 \text{PolyLog}\left(2,\frac{\sqrt{x} f}{e}+1\right) f^4}{2 e^4}+\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}+\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}-\frac{6 b^3 n^3 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}-\frac{12 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}+\frac{24 b^3 n^3 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 f^3}{2 e^3 \sqrt{x}}-\frac{15 b n \left(a+b \log \left(c x^n\right)\right)^2 f^3}{4 e^3 \sqrt{x}}-\frac{63 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) f^3}{4 e^3 \sqrt{x}}-\frac{255 b^3 n^3 f^3}{8 e^3 \sqrt{x}}+\frac{\left(a+b \log \left(c x^n\right)\right)^3 f^2}{4 e^2 x}+\frac{9 b n \left(a+b \log \left(c x^n\right)\right)^2 f^2}{8 e^2 x}+\frac{21 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) f^2}{8 e^2 x}+\frac{45 b^3 n^3 f^2}{16 e^2 x}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 f}{6 e x^{3/2}}-\frac{7 b n \left(a+b \log \left(c x^n\right)\right)^2 f}{12 e x^{3/2}}-\frac{37 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) f}{36 e x^{3/2}}-\frac{175 b^3 n^3 f}{216 e x^{3/2}}-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{3 b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{3 b^3 n^3 \log \left(d \left(e+f \sqrt{x}\right)\right)}{8 x^2}-\frac{3 b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}","-\frac{\left(a+b \log \left(c x^n\right)\right)^4 f^4}{16 b e^4 n}+\frac{\log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3 f^4}{2 e^4}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 f^4}{8 e^4}+\frac{3 b^3 n^3 \log ^2(x) f^4}{16 e^4}+\frac{3 b n \log \left(\frac{\sqrt{x} f}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2 f^4}{4 e^4}+\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) f^4}{8 e^4}-\frac{3 b^3 n^3 \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right) f^4}{2 e^4}-\frac{3 b^3 n^3 \log (x) f^4}{16 e^4}+\frac{3 b^2 n^2 \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right) f^4}{4 e^4}-\frac{3 b^2 n^2 \log (x) \left(a+b \log \left(c x^n\right)\right) f^4}{8 e^4}-\frac{3 b^3 n^3 \text{PolyLog}\left(2,\frac{\sqrt{x} f}{e}+1\right) f^4}{2 e^4}+\frac{3 b n \left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}+\frac{3 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}-\frac{6 b^3 n^3 \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}-\frac{12 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}+\frac{24 b^3 n^3 \text{PolyLog}\left(4,-\frac{f \sqrt{x}}{e}\right) f^4}{e^4}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 f^3}{2 e^3 \sqrt{x}}-\frac{15 b n \left(a+b \log \left(c x^n\right)\right)^2 f^3}{4 e^3 \sqrt{x}}-\frac{63 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) f^3}{4 e^3 \sqrt{x}}-\frac{255 b^3 n^3 f^3}{8 e^3 \sqrt{x}}+\frac{\left(a+b \log \left(c x^n\right)\right)^3 f^2}{4 e^2 x}+\frac{9 b n \left(a+b \log \left(c x^n\right)\right)^2 f^2}{8 e^2 x}+\frac{21 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) f^2}{8 e^2 x}+\frac{45 b^3 n^3 f^2}{16 e^2 x}-\frac{\left(a+b \log \left(c x^n\right)\right)^3 f}{6 e x^{3/2}}-\frac{7 b n \left(a+b \log \left(c x^n\right)\right)^2 f}{12 e x^{3/2}}-\frac{37 b^2 n^2 \left(a+b \log \left(c x^n\right)\right) f}{36 e x^{3/2}}-\frac{175 b^3 n^3 f}{216 e x^{3/2}}-\frac{\log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^3}{2 x^2}-\frac{3 b n \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)^2}{4 x^2}-\frac{3 b^3 n^3 \log \left(d \left(e+f \sqrt{x}\right)\right)}{8 x^2}-\frac{3 b^2 n^2 \log \left(d \left(e+f \sqrt{x}\right)\right) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}",1,"(-175*b^3*f*n^3)/(216*e*x^(3/2)) + (45*b^3*f^2*n^3)/(16*e^2*x) - (255*b^3*f^3*n^3)/(8*e^3*Sqrt[x]) + (3*b^3*f^4*n^3*Log[e + f*Sqrt[x]])/(8*e^4) - (3*b^3*n^3*Log[d*(e + f*Sqrt[x])])/(8*x^2) - (3*b^3*f^4*n^3*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/(2*e^4) - (3*b^3*f^4*n^3*Log[x])/(16*e^4) + (3*b^3*f^4*n^3*Log[x]^2)/(16*e^4) - (37*b^2*f*n^2*(a + b*Log[c*x^n]))/(36*e*x^(3/2)) + (21*b^2*f^2*n^2*(a + b*Log[c*x^n]))/(8*e^2*x) - (63*b^2*f^3*n^2*(a + b*Log[c*x^n]))/(4*e^3*Sqrt[x]) + (3*b^2*f^4*n^2*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(4*e^4) - (3*b^2*n^2*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n]))/(4*x^2) - (3*b^2*f^4*n^2*Log[x]*(a + b*Log[c*x^n]))/(8*e^4) - (7*b*f*n*(a + b*Log[c*x^n])^2)/(12*e*x^(3/2)) + (9*b*f^2*n*(a + b*Log[c*x^n])^2)/(8*e^2*x) - (15*b*f^3*n*(a + b*Log[c*x^n])^2)/(4*e^3*Sqrt[x]) - (3*b*n*Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^2)/(4*x^2) + (3*b*f^4*n*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^2)/(4*e^4) - (f^4*(a + b*Log[c*x^n])^3)/(8*e^4) - (f*(a + b*Log[c*x^n])^3)/(6*e*x^(3/2)) + (f^2*(a + b*Log[c*x^n])^3)/(4*e^2*x) - (f^3*(a + b*Log[c*x^n])^3)/(2*e^3*Sqrt[x]) - (Log[d*(e + f*Sqrt[x])]*(a + b*Log[c*x^n])^3)/(2*x^2) + (f^4*Log[1 + (f*Sqrt[x])/e]*(a + b*Log[c*x^n])^3)/(2*e^4) - (f^4*(a + b*Log[c*x^n])^4)/(16*b*e^4*n) - (3*b^3*f^4*n^3*PolyLog[2, 1 + (f*Sqrt[x])/e])/(2*e^4) + (3*b^2*f^4*n^2*(a + b*Log[c*x^n])*PolyLog[2, -((f*Sqrt[x])/e)])/e^4 + (3*b*f^4*n*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*Sqrt[x])/e)])/e^4 - (6*b^3*f^4*n^3*PolyLog[3, -((f*Sqrt[x])/e)])/e^4 - (12*b^2*f^4*n^2*(a + b*Log[c*x^n])*PolyLog[3, -((f*Sqrt[x])/e)])/e^4 + (24*b^3*f^4*n^3*PolyLog[4, -((f*Sqrt[x])/e)])/e^4","A",40,19,28,0.6786,1,"{2454, 2395, 44, 2377, 2305, 2304, 2375, 2337, 2374, 2383, 6589, 2376, 2394, 2315, 2301, 2366, 12, 2302, 30}"
133,1,367,0,0.2980579,"\int x^{3/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[x^(3/2)*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]),x]","-\frac{4 b e^5 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{5 f^5}+\frac{2}{5} x^{5/2} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{2 e^5 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{5 f^5}-\frac{2 e^4 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{5 f^4}+\frac{e^3 k x \left(a+b \log \left(c x^n\right)\right)}{5 f^3}-\frac{2 e^2 k x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{15 f^2}+\frac{e k x^2 \left(a+b \log \left(c x^n\right)\right)}{10 f}-\frac{2}{25} k x^{5/2} \left(a+b \log \left(c x^n\right)\right)-\frac{4}{25} b n x^{5/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{32 b e^2 k n x^{3/2}}{225 f^2}+\frac{24 b e^4 k n \sqrt{x}}{25 f^4}-\frac{7 b e^3 k n x}{25 f^3}-\frac{4 b e^5 k n \log \left(e+f \sqrt{x}\right)}{25 f^5}-\frac{4 b e^5 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{5 f^5}-\frac{9 b e k n x^2}{100 f}+\frac{8}{125} b k n x^{5/2}","-\frac{4 b e^5 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{5 f^5}+\frac{2}{5} x^{5/2} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{2 e^5 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{5 f^5}-\frac{2 e^4 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{5 f^4}+\frac{e^3 k x \left(a+b \log \left(c x^n\right)\right)}{5 f^3}-\frac{2 e^2 k x^{3/2} \left(a+b \log \left(c x^n\right)\right)}{15 f^2}+\frac{e k x^2 \left(a+b \log \left(c x^n\right)\right)}{10 f}-\frac{2}{25} k x^{5/2} \left(a+b \log \left(c x^n\right)\right)-\frac{4}{25} b n x^{5/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{32 b e^2 k n x^{3/2}}{225 f^2}+\frac{24 b e^4 k n \sqrt{x}}{25 f^4}-\frac{7 b e^3 k n x}{25 f^3}-\frac{4 b e^5 k n \log \left(e+f \sqrt{x}\right)}{25 f^5}-\frac{4 b e^5 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{5 f^5}-\frac{9 b e k n x^2}{100 f}+\frac{8}{125} b k n x^{5/2}",1,"(24*b*e^4*k*n*Sqrt[x])/(25*f^4) - (7*b*e^3*k*n*x)/(25*f^3) + (32*b*e^2*k*n*x^(3/2))/(225*f^2) - (9*b*e*k*n*x^2)/(100*f) + (8*b*k*n*x^(5/2))/125 - (4*b*e^5*k*n*Log[e + f*Sqrt[x]])/(25*f^5) - (4*b*n*x^(5/2)*Log[d*(e + f*Sqrt[x])^k])/25 - (4*b*e^5*k*n*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/(5*f^5) - (2*e^4*k*Sqrt[x]*(a + b*Log[c*x^n]))/(5*f^4) + (e^3*k*x*(a + b*Log[c*x^n]))/(5*f^3) - (2*e^2*k*x^(3/2)*(a + b*Log[c*x^n]))/(15*f^2) + (e*k*x^2*(a + b*Log[c*x^n]))/(10*f) - (2*k*x^(5/2)*(a + b*Log[c*x^n]))/25 + (2*e^5*k*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(5*f^5) + (2*x^(5/2)*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/5 - (4*b*e^5*k*n*PolyLog[2, 1 + (f*Sqrt[x])/e])/(5*f^5)","A",9,6,30,0.2000,1,"{2454, 2395, 43, 2376, 2394, 2315}"
134,1,283,0,0.2282111,"\int \sqrt{x} \log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right) \, dx","Int[Sqrt[x]*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]),x]","-\frac{4 b e^3 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{3 f^3}+\frac{2}{3} x^{3/2} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{2 e^3 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^3}-\frac{2 e^2 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{3 f^2}+\frac{e k x \left(a+b \log \left(c x^n\right)\right)}{3 f}-\frac{2}{9} k x^{3/2} \left(a+b \log \left(c x^n\right)\right)-\frac{4}{9} b n x^{3/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{16 b e^2 k n \sqrt{x}}{9 f^2}-\frac{4 b e^3 k n \log \left(e+f \sqrt{x}\right)}{9 f^3}-\frac{4 b e^3 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 f^3}-\frac{5 b e k n x}{9 f}+\frac{8}{27} b k n x^{3/2}","-\frac{4 b e^3 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{3 f^3}+\frac{2}{3} x^{3/2} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{2 e^3 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^3}-\frac{2 e^2 k \sqrt{x} \left(a+b \log \left(c x^n\right)\right)}{3 f^2}+\frac{e k x \left(a+b \log \left(c x^n\right)\right)}{3 f}-\frac{2}{9} k x^{3/2} \left(a+b \log \left(c x^n\right)\right)-\frac{4}{9} b n x^{3/2} \log \left(d \left(e+f \sqrt{x}\right)^k\right)+\frac{16 b e^2 k n \sqrt{x}}{9 f^2}-\frac{4 b e^3 k n \log \left(e+f \sqrt{x}\right)}{9 f^3}-\frac{4 b e^3 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 f^3}-\frac{5 b e k n x}{9 f}+\frac{8}{27} b k n x^{3/2}",1,"(16*b*e^2*k*n*Sqrt[x])/(9*f^2) - (5*b*e*k*n*x)/(9*f) + (8*b*k*n*x^(3/2))/27 - (4*b*e^3*k*n*Log[e + f*Sqrt[x]])/(9*f^3) - (4*b*n*x^(3/2)*Log[d*(e + f*Sqrt[x])^k])/9 - (4*b*e^3*k*n*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/(3*f^3) - (2*e^2*k*Sqrt[x]*(a + b*Log[c*x^n]))/(3*f^2) + (e*k*x*(a + b*Log[c*x^n]))/(3*f) - (2*k*x^(3/2)*(a + b*Log[c*x^n]))/9 + (2*e^3*k*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(3*f^3) + (2*x^(3/2)*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/3 - (4*b*e^3*k*n*PolyLog[2, 1 + (f*Sqrt[x])/e])/(3*f^3)","A",9,6,30,0.2000,1,"{2454, 2395, 43, 2376, 2394, 2315}"
135,1,199,0,0.1703076,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^{3/2}} \, dx","Int[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^(3/2),x]","\frac{4 b f k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e}-\frac{2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{\sqrt{x}}+\frac{f k \log (x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{2 f k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{4 b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{\sqrt{x}}-\frac{b f k n \log ^2(x)}{2 e}+\frac{2 b f k n \log (x)}{e}-\frac{4 b f k n \log \left(e+f \sqrt{x}\right)}{e}+\frac{4 b f k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e}","\frac{4 b f k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{e}-\frac{2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{\sqrt{x}}+\frac{f k \log (x) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{2 f k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{e}-\frac{4 b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{\sqrt{x}}-\frac{b f k n \log ^2(x)}{2 e}+\frac{2 b f k n \log (x)}{e}-\frac{4 b f k n \log \left(e+f \sqrt{x}\right)}{e}+\frac{4 b f k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{e}",1,"(-4*b*f*k*n*Log[e + f*Sqrt[x]])/e - (4*b*n*Log[d*(e + f*Sqrt[x])^k])/Sqrt[x] + (4*b*f*k*n*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/e + (2*b*f*k*n*Log[x])/e - (b*f*k*n*Log[x]^2)/(2*e) - (2*f*k*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/e - (2*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/Sqrt[x] + (f*k*Log[x]*(a + b*Log[c*x^n]))/e + (4*b*f*k*n*PolyLog[2, 1 + (f*Sqrt[x])/e])/e","A",11,9,30,0.3000,1,"{2454, 2395, 36, 29, 31, 2376, 2394, 2315, 2301}"
136,1,310,0,0.2419804,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^{5/2}} \, dx","Int[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^(5/2),x]","\frac{4 b f^3 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{3 e^3}-\frac{2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{3 x^{3/2}}-\frac{2 f^3 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{f^3 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{2 f^2 k \left(a+b \log \left(c x^n\right)\right)}{3 e^2 \sqrt{x}}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{3 e x}-\frac{4 b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{9 x^{3/2}}+\frac{16 b f^2 k n}{9 e^2 \sqrt{x}}-\frac{b f^3 k n \log ^2(x)}{6 e^3}-\frac{4 b f^3 k n \log \left(e+f \sqrt{x}\right)}{9 e^3}+\frac{4 b f^3 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 e^3}+\frac{2 b f^3 k n \log (x)}{9 e^3}-\frac{5 b f k n}{9 e x}","\frac{4 b f^3 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{3 e^3}-\frac{2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{3 x^{3/2}}-\frac{2 f^3 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{f^3 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{3 e^3}+\frac{2 f^2 k \left(a+b \log \left(c x^n\right)\right)}{3 e^2 \sqrt{x}}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{3 e x}-\frac{4 b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{9 x^{3/2}}+\frac{16 b f^2 k n}{9 e^2 \sqrt{x}}-\frac{b f^3 k n \log ^2(x)}{6 e^3}-\frac{4 b f^3 k n \log \left(e+f \sqrt{x}\right)}{9 e^3}+\frac{4 b f^3 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{3 e^3}+\frac{2 b f^3 k n \log (x)}{9 e^3}-\frac{5 b f k n}{9 e x}",1,"(-5*b*f*k*n)/(9*e*x) + (16*b*f^2*k*n)/(9*e^2*Sqrt[x]) - (4*b*f^3*k*n*Log[e + f*Sqrt[x]])/(9*e^3) - (4*b*n*Log[d*(e + f*Sqrt[x])^k])/(9*x^(3/2)) + (4*b*f^3*k*n*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/(3*e^3) + (2*b*f^3*k*n*Log[x])/(9*e^3) - (b*f^3*k*n*Log[x]^2)/(6*e^3) - (f*k*(a + b*Log[c*x^n]))/(3*e*x) + (2*f^2*k*(a + b*Log[c*x^n]))/(3*e^2*Sqrt[x]) - (2*f^3*k*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(3*e^3) - (2*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/(3*x^(3/2)) + (f^3*k*Log[x]*(a + b*Log[c*x^n]))/(3*e^3) + (4*b*f^3*k*n*PolyLog[2, 1 + (f*Sqrt[x])/e])/(3*e^3)","A",10,7,30,0.2333,1,"{2454, 2395, 44, 2376, 2394, 2315, 2301}"
137,1,394,0,0.3047404,"\int \frac{\log \left(d \left(e+f \sqrt{x}\right)^k\right) \left(a+b \log \left(c x^n\right)\right)}{x^{7/2}} \, dx","Int[(Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/x^(7/2),x]","\frac{4 b f^5 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{5 e^5}-\frac{2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{5 x^{5/2}}-\frac{2 f^5 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{5 e^5}+\frac{f^5 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{5 e^5}+\frac{2 f^4 k \left(a+b \log \left(c x^n\right)\right)}{5 e^4 \sqrt{x}}-\frac{f^3 k \left(a+b \log \left(c x^n\right)\right)}{5 e^3 x}+\frac{2 f^2 k \left(a+b \log \left(c x^n\right)\right)}{15 e^2 x^{3/2}}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{10 e x^2}-\frac{4 b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{25 x^{5/2}}+\frac{32 b f^2 k n}{225 e^2 x^{3/2}}+\frac{24 b f^4 k n}{25 e^4 \sqrt{x}}-\frac{7 b f^3 k n}{25 e^3 x}-\frac{b f^5 k n \log ^2(x)}{10 e^5}-\frac{4 b f^5 k n \log \left(e+f \sqrt{x}\right)}{25 e^5}+\frac{4 b f^5 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{5 e^5}+\frac{2 b f^5 k n \log (x)}{25 e^5}-\frac{9 b f k n}{100 e x^2}","\frac{4 b f^5 k n \text{PolyLog}\left(2,\frac{f \sqrt{x}}{e}+1\right)}{5 e^5}-\frac{2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{5 x^{5/2}}-\frac{2 f^5 k \log \left(e+f \sqrt{x}\right) \left(a+b \log \left(c x^n\right)\right)}{5 e^5}+\frac{f^5 k \log (x) \left(a+b \log \left(c x^n\right)\right)}{5 e^5}+\frac{2 f^4 k \left(a+b \log \left(c x^n\right)\right)}{5 e^4 \sqrt{x}}-\frac{f^3 k \left(a+b \log \left(c x^n\right)\right)}{5 e^3 x}+\frac{2 f^2 k \left(a+b \log \left(c x^n\right)\right)}{15 e^2 x^{3/2}}-\frac{f k \left(a+b \log \left(c x^n\right)\right)}{10 e x^2}-\frac{4 b n \log \left(d \left(e+f \sqrt{x}\right)^k\right)}{25 x^{5/2}}+\frac{32 b f^2 k n}{225 e^2 x^{3/2}}+\frac{24 b f^4 k n}{25 e^4 \sqrt{x}}-\frac{7 b f^3 k n}{25 e^3 x}-\frac{b f^5 k n \log ^2(x)}{10 e^5}-\frac{4 b f^5 k n \log \left(e+f \sqrt{x}\right)}{25 e^5}+\frac{4 b f^5 k n \log \left(e+f \sqrt{x}\right) \log \left(-\frac{f \sqrt{x}}{e}\right)}{5 e^5}+\frac{2 b f^5 k n \log (x)}{25 e^5}-\frac{9 b f k n}{100 e x^2}",1,"(-9*b*f*k*n)/(100*e*x^2) + (32*b*f^2*k*n)/(225*e^2*x^(3/2)) - (7*b*f^3*k*n)/(25*e^3*x) + (24*b*f^4*k*n)/(25*e^4*Sqrt[x]) - (4*b*f^5*k*n*Log[e + f*Sqrt[x]])/(25*e^5) - (4*b*n*Log[d*(e + f*Sqrt[x])^k])/(25*x^(5/2)) + (4*b*f^5*k*n*Log[e + f*Sqrt[x]]*Log[-((f*Sqrt[x])/e)])/(5*e^5) + (2*b*f^5*k*n*Log[x])/(25*e^5) - (b*f^5*k*n*Log[x]^2)/(10*e^5) - (f*k*(a + b*Log[c*x^n]))/(10*e*x^2) + (2*f^2*k*(a + b*Log[c*x^n]))/(15*e^2*x^(3/2)) - (f^3*k*(a + b*Log[c*x^n]))/(5*e^3*x) + (2*f^4*k*(a + b*Log[c*x^n]))/(5*e^4*Sqrt[x]) - (2*f^5*k*Log[e + f*Sqrt[x]]*(a + b*Log[c*x^n]))/(5*e^5) - (2*Log[d*(e + f*Sqrt[x])^k]*(a + b*Log[c*x^n]))/(5*x^(5/2)) + (f^5*k*Log[x]*(a + b*Log[c*x^n]))/(5*e^5) + (4*b*f^5*k*n*PolyLog[2, 1 + (f*Sqrt[x])/e])/(5*e^5)","A",10,7,30,0.2333,1,"{2454, 2395, 44, 2376, 2394, 2315, 2301}"
138,0,0,0,0.0204296,"\int (g x)^q \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Int[(g*x)^q*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\int (g x)^q \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","\text{Int}\left((g x)^q \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right),x\right)",0,"Defer[Int][(g*x)^q*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k], x]","A",0,0,0,0,-1,"{}"
139,1,185,0,0.2987331,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^m\right)^r\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^3*Log[d*(e + f*x^m)^r])/x,x]","-\frac{6 b^2 n^2 r \text{PolyLog}\left(4,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m^3}+\frac{3 b n r \text{PolyLog}\left(3,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{m^2}-\frac{r \text{PolyLog}\left(2,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3}{m}+\frac{6 b^3 n^3 r \text{PolyLog}\left(5,-\frac{f x^m}{e}\right)}{m^4}+\frac{\left(a+b \log \left(c x^n\right)\right)^4 \log \left(d \left(e+f x^m\right)^r\right)}{4 b n}-\frac{r \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}","-\frac{6 b^2 n^2 r \text{PolyLog}\left(4,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m^3}+\frac{3 b n r \text{PolyLog}\left(3,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{m^2}-\frac{r \text{PolyLog}\left(2,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)^3}{m}+\frac{6 b^3 n^3 r \text{PolyLog}\left(5,-\frac{f x^m}{e}\right)}{m^4}+\frac{\left(a+b \log \left(c x^n\right)\right)^4 \log \left(d \left(e+f x^m\right)^r\right)}{4 b n}-\frac{r \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^4}{4 b n}",1,"((a + b*Log[c*x^n])^4*Log[d*(e + f*x^m)^r])/(4*b*n) - (r*(a + b*Log[c*x^n])^4*Log[1 + (f*x^m)/e])/(4*b*n) - (r*(a + b*Log[c*x^n])^3*PolyLog[2, -((f*x^m)/e)])/m + (3*b*n*r*(a + b*Log[c*x^n])^2*PolyLog[3, -((f*x^m)/e)])/m^2 - (6*b^2*n^2*r*(a + b*Log[c*x^n])*PolyLog[4, -((f*x^m)/e)])/m^3 + (6*b^3*n^3*r*PolyLog[5, -((f*x^m)/e)])/m^4","A",6,5,28,0.1786,1,"{2375, 2337, 2374, 2383, 6589}"
140,1,150,0,0.2488439,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^m\right)^r\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^2*Log[d*(e + f*x^m)^r])/x,x]","\frac{2 b n r \text{PolyLog}\left(3,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m^2}-\frac{r \text{PolyLog}\left(2,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{m}-\frac{2 b^2 n^2 r \text{PolyLog}\left(4,-\frac{f x^m}{e}\right)}{m^3}+\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^m\right)^r\right)}{3 b n}-\frac{r \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}","\frac{2 b n r \text{PolyLog}\left(3,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m^2}-\frac{r \text{PolyLog}\left(2,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)^2}{m}-\frac{2 b^2 n^2 r \text{PolyLog}\left(4,-\frac{f x^m}{e}\right)}{m^3}+\frac{\left(a+b \log \left(c x^n\right)\right)^3 \log \left(d \left(e+f x^m\right)^r\right)}{3 b n}-\frac{r \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^3}{3 b n}",1,"((a + b*Log[c*x^n])^3*Log[d*(e + f*x^m)^r])/(3*b*n) - (r*(a + b*Log[c*x^n])^3*Log[1 + (f*x^m)/e])/(3*b*n) - (r*(a + b*Log[c*x^n])^2*PolyLog[2, -((f*x^m)/e)])/m + (2*b*n*r*(a + b*Log[c*x^n])*PolyLog[3, -((f*x^m)/e)])/m^2 - (2*b^2*n^2*r*PolyLog[4, -((f*x^m)/e)])/m^3","A",5,5,28,0.1786,1,"{2375, 2337, 2374, 2383, 6589}"
141,1,114,0,0.1934293,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^r\right)}{x} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^r])/x,x]","-\frac{r \text{PolyLog}\left(2,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m}+\frac{b n r \text{PolyLog}\left(3,-\frac{f x^m}{e}\right)}{m^2}+\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^m\right)^r\right)}{2 b n}-\frac{r \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}","-\frac{r \text{PolyLog}\left(2,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m}+\frac{b n r \text{PolyLog}\left(3,-\frac{f x^m}{e}\right)}{m^2}+\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^m\right)^r\right)}{2 b n}-\frac{r \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}",1,"((a + b*Log[c*x^n])^2*Log[d*(e + f*x^m)^r])/(2*b*n) - (r*(a + b*Log[c*x^n])^2*Log[1 + (f*x^m)/e])/(2*b*n) - (r*(a + b*Log[c*x^n])*PolyLog[2, -((f*x^m)/e)])/m + (b*n*r*PolyLog[3, -((f*x^m)/e)])/m^2","A",4,4,26,0.1538,1,"{2375, 2337, 2374, 6589}"
142,0,0,0,0.0340532,"\int \frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[Log[d*(e + f*x^m)^r]/(x*(a + b*Log[c*x^n])),x]","\int \frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Defer[Int][Log[d*(e + f*x^m)^r]/(x*(a + b*Log[c*x^n])), x]","A",0,0,0,0,-1,"{}"
143,0,0,0,0.0337653,"\int \frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Int[Log[d*(e + f*x^m)^r]/(x*(a + b*Log[c*x^n])^2),x]","\int \frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","\text{Int}\left(\frac{\log \left(d \left(e+f x^m\right)^r\right)}{x \left(a+b \log \left(c x^n\right)\right)^2},x\right)",0,"Defer[Int][Log[d*(e + f*x^m)^r]/(x*(a + b*Log[c*x^n])^2), x]","A",0,0,0,0,-1,"{}"
144,0,0,0,0.0194123,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Int[x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\int x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","\text{Int}\left(x^2 \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right),x\right)",0,"Defer[Int][x^2*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k], x]","A",0,0,0,0,-1,"{}"
145,0,0,0,0.0114566,"\int x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Int[x*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\int x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","\text{Int}\left(x \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right),x\right)",0,"Defer[Int][x*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k], x]","A",0,0,0,0,-1,"{}"
146,0,0,0,0.0050263,"\int \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Int[(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\int \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","\text{Int}\left(\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right),x\right)",0,"Defer[Int][(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k], x]","A",0,0,0,0,-1,"{}"
147,1,114,0,0.187817,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/x,x]","-\frac{k \text{PolyLog}\left(2,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m}+\frac{b k n \text{PolyLog}\left(3,-\frac{f x^m}{e}\right)}{m^2}+\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^m\right)^k\right)}{2 b n}-\frac{k \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}","-\frac{k \text{PolyLog}\left(2,-\frac{f x^m}{e}\right) \left(a+b \log \left(c x^n\right)\right)}{m}+\frac{b k n \text{PolyLog}\left(3,-\frac{f x^m}{e}\right)}{m^2}+\frac{\left(a+b \log \left(c x^n\right)\right)^2 \log \left(d \left(e+f x^m\right)^k\right)}{2 b n}-\frac{k \log \left(\frac{f x^m}{e}+1\right) \left(a+b \log \left(c x^n\right)\right)^2}{2 b n}",1,"((a + b*Log[c*x^n])^2*Log[d*(e + f*x^m)^k])/(2*b*n) - (k*(a + b*Log[c*x^n])^2*Log[1 + (f*x^m)/e])/(2*b*n) - (k*(a + b*Log[c*x^n])*PolyLog[2, -((f*x^m)/e)])/m + (b*k*n*PolyLog[3, -((f*x^m)/e)])/m^2","A",4,4,26,0.1538,1,"{2375, 2337, 2374, 6589}"
148,0,0,0,0.0195598,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/x^2,x]","\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x^2} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x^2},x\right)",0,"Defer[Int][((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/x^2, x]","A",0,0,0,0,-1,"{}"
149,0,0,0,0.0193067,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/x^3,x]","\int \frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x^3} \, dx","\text{Int}\left(\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{x^3},x\right)",0,"Defer[Int][((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/x^3, x]","A",0,0,0,0,-1,"{}"
150,1,433,0,0.6025271,"\int (g x)^{-1+3 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Int[(g*x)^(-1 + 3*m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","-\frac{b e^3 k n x^{-3 m} (g x)^{3 m} \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{3 f^3 g m^2}+\frac{(g x)^{3 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{3 g m}+\frac{e^3 k x^{-3 m} (g x)^{3 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^3 g m}-\frac{e^2 k x^{-2 m} (g x)^{3 m} \left(a+b \log \left(c x^n\right)\right)}{3 f^2 g m}+\frac{e k x^{-m} (g x)^{3 m} \left(a+b \log \left(c x^n\right)\right)}{6 f g m}-\frac{k (g x)^{3 m} \left(a+b \log \left(c x^n\right)\right)}{9 g m}-\frac{b n (g x)^{3 m} \log \left(d \left(e+f x^m\right)^k\right)}{9 g m^2}+\frac{4 b e^2 k n x^{-2 m} (g x)^{3 m}}{9 f^2 g m^2}-\frac{b e^3 k n x^{-3 m} (g x)^{3 m} \log \left(e+f x^m\right)}{9 f^3 g m^2}-\frac{b e^3 k n x^{-3 m} (g x)^{3 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{3 f^3 g m^2}-\frac{5 b e k n x^{-m} (g x)^{3 m}}{36 f g m^2}+\frac{2 b k n (g x)^{3 m}}{27 g m^2}","-\frac{b e^3 k n x^{-3 m} (g x)^{3 m} \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{3 f^3 g m^2}+\frac{(g x)^{3 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{3 g m}+\frac{e^3 k x^{-3 m} (g x)^{3 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{3 f^3 g m}-\frac{e^2 k x^{-2 m} (g x)^{3 m} \left(a+b \log \left(c x^n\right)\right)}{3 f^2 g m}+\frac{e k x^{-m} (g x)^{3 m} \left(a+b \log \left(c x^n\right)\right)}{6 f g m}-\frac{k (g x)^{3 m} \left(a+b \log \left(c x^n\right)\right)}{9 g m}-\frac{b n (g x)^{3 m} \log \left(d \left(e+f x^m\right)^k\right)}{9 g m^2}+\frac{4 b e^2 k n x^{-2 m} (g x)^{3 m}}{9 f^2 g m^2}-\frac{b e^3 k n x^{-3 m} (g x)^{3 m} \log \left(e+f x^m\right)}{9 f^3 g m^2}-\frac{b e^3 k n x^{-3 m} (g x)^{3 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{3 f^3 g m^2}-\frac{5 b e k n x^{-m} (g x)^{3 m}}{36 f g m^2}+\frac{2 b k n (g x)^{3 m}}{27 g m^2}",1,"(2*b*k*n*(g*x)^(3*m))/(27*g*m^2) + (4*b*e^2*k*n*(g*x)^(3*m))/(9*f^2*g*m^2*x^(2*m)) - (5*b*e*k*n*(g*x)^(3*m))/(36*f*g*m^2*x^m) - (k*(g*x)^(3*m)*(a + b*Log[c*x^n]))/(9*g*m) - (e^2*k*(g*x)^(3*m)*(a + b*Log[c*x^n]))/(3*f^2*g*m*x^(2*m)) + (e*k*(g*x)^(3*m)*(a + b*Log[c*x^n]))/(6*f*g*m*x^m) - (b*e^3*k*n*(g*x)^(3*m)*Log[e + f*x^m])/(9*f^3*g*m^2*x^(3*m)) - (b*e^3*k*n*(g*x)^(3*m)*Log[-((f*x^m)/e)]*Log[e + f*x^m])/(3*f^3*g*m^2*x^(3*m)) + (e^3*k*(g*x)^(3*m)*(a + b*Log[c*x^n])*Log[e + f*x^m])/(3*f^3*g*m*x^(3*m)) - (b*n*(g*x)^(3*m)*Log[d*(e + f*x^m)^k])/(9*g*m^2) + ((g*x)^(3*m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/(3*g*m) - (b*e^3*k*n*(g*x)^(3*m)*PolyLog[2, 1 + (f*x^m)/e])/(3*f^3*g*m^2*x^(3*m))","A",18,12,32,0.3750,1,"{2455, 20, 266, 43, 2376, 16, 32, 30, 19, 2454, 2394, 2315}"
151,1,363,0,0.4177496,"\int (g x)^{-1+2 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Int[(g*x)^(-1 + 2*m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\frac{b e^2 k n x^{-2 m} (g x)^{2 m} \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{2 f^2 g m^2}+\frac{(g x)^{2 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{2 g m}-\frac{e^2 k x^{-2 m} (g x)^{2 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^2 g m}+\frac{e k x^{-m} (g x)^{2 m} \left(a+b \log \left(c x^n\right)\right)}{2 f g m}-\frac{k (g x)^{2 m} \left(a+b \log \left(c x^n\right)\right)}{4 g m}-\frac{b n (g x)^{2 m} \log \left(d \left(e+f x^m\right)^k\right)}{4 g m^2}+\frac{b e^2 k n x^{-2 m} (g x)^{2 m} \log \left(e+f x^m\right)}{4 f^2 g m^2}+\frac{b e^2 k n x^{-2 m} (g x)^{2 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{2 f^2 g m^2}-\frac{3 b e k n x^{-m} (g x)^{2 m}}{4 f g m^2}+\frac{b k n (g x)^{2 m}}{4 g m^2}","\frac{b e^2 k n x^{-2 m} (g x)^{2 m} \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{2 f^2 g m^2}+\frac{(g x)^{2 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{2 g m}-\frac{e^2 k x^{-2 m} (g x)^{2 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{2 f^2 g m}+\frac{e k x^{-m} (g x)^{2 m} \left(a+b \log \left(c x^n\right)\right)}{2 f g m}-\frac{k (g x)^{2 m} \left(a+b \log \left(c x^n\right)\right)}{4 g m}-\frac{b n (g x)^{2 m} \log \left(d \left(e+f x^m\right)^k\right)}{4 g m^2}+\frac{b e^2 k n x^{-2 m} (g x)^{2 m} \log \left(e+f x^m\right)}{4 f^2 g m^2}+\frac{b e^2 k n x^{-2 m} (g x)^{2 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{2 f^2 g m^2}-\frac{3 b e k n x^{-m} (g x)^{2 m}}{4 f g m^2}+\frac{b k n (g x)^{2 m}}{4 g m^2}",1,"(b*k*n*(g*x)^(2*m))/(4*g*m^2) - (3*b*e*k*n*(g*x)^(2*m))/(4*f*g*m^2*x^m) - (k*(g*x)^(2*m)*(a + b*Log[c*x^n]))/(4*g*m) + (e*k*(g*x)^(2*m)*(a + b*Log[c*x^n]))/(2*f*g*m*x^m) + (b*e^2*k*n*(g*x)^(2*m)*Log[e + f*x^m])/(4*f^2*g*m^2*x^(2*m)) + (b*e^2*k*n*(g*x)^(2*m)*Log[-((f*x^m)/e)]*Log[e + f*x^m])/(2*f^2*g*m^2*x^(2*m)) - (e^2*k*(g*x)^(2*m)*(a + b*Log[c*x^n])*Log[e + f*x^m])/(2*f^2*g*m*x^(2*m)) - (b*n*(g*x)^(2*m)*Log[d*(e + f*x^m)^k])/(4*g*m^2) + ((g*x)^(2*m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/(2*g*m) + (b*e^2*k*n*(g*x)^(2*m)*PolyLog[2, 1 + (f*x^m)/e])/(2*f^2*g*m^2*x^(2*m))","A",16,12,32,0.3750,1,"{2455, 20, 266, 43, 2376, 16, 32, 30, 19, 2454, 2394, 2315}"
152,1,255,0,0.2452524,"\int (g x)^{-1+m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Int[(g*x)^(-1 + m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","-\frac{b e k n x^{-m} (g x)^m \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{f g m^2}+\frac{(g x)^m \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{g m}+\frac{e k x^{-m} (g x)^m \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{f g m}-\frac{k (g x)^m \left(a+b \log \left(c x^n\right)\right)}{g m}-\frac{b n (g x)^m \log \left(d \left(e+f x^m\right)^k\right)}{g m^2}-\frac{b e k n x^{-m} (g x)^m \log \left(e+f x^m\right)}{f g m^2}-\frac{b e k n x^{-m} (g x)^m \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{f g m^2}+\frac{2 b k n (g x)^m}{g m^2}","-\frac{b e k n x^{-m} (g x)^m \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{f g m^2}+\frac{(g x)^m \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{g m}+\frac{e k x^{-m} (g x)^m \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{f g m}-\frac{k (g x)^m \left(a+b \log \left(c x^n\right)\right)}{g m}-\frac{b n (g x)^m \log \left(d \left(e+f x^m\right)^k\right)}{g m^2}-\frac{b e k n x^{-m} (g x)^m \log \left(e+f x^m\right)}{f g m^2}-\frac{b e k n x^{-m} (g x)^m \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{f g m^2}+\frac{2 b k n (g x)^m}{g m^2}",1,"(2*b*k*n*(g*x)^m)/(g*m^2) - (k*(g*x)^m*(a + b*Log[c*x^n]))/(g*m) - (b*e*k*n*(g*x)^m*Log[e + f*x^m])/(f*g*m^2*x^m) - (b*e*k*n*(g*x)^m*Log[-((f*x^m)/e)]*Log[e + f*x^m])/(f*g*m^2*x^m) + (e*k*(g*x)^m*(a + b*Log[c*x^n])*Log[e + f*x^m])/(f*g*m*x^m) - (b*n*(g*x)^m*Log[d*(e + f*x^m)^k])/(g*m^2) + ((g*x)^m*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/(g*m) - (b*e*k*n*(g*x)^m*PolyLog[2, 1 + (f*x^m)/e])/(f*g*m^2*x^m)","A",14,11,30,0.3667,1,"{2455, 20, 266, 43, 2376, 16, 32, 19, 2454, 2394, 2315}"
153,1,304,0,0.305099,"\int (g x)^{-1-m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Int[(g*x)^(-1 - m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\frac{b f k n x^m (g x)^{-m} \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{e g m^2}-\frac{(g x)^{-m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{g m}+\frac{f k x^m \log (x) (g x)^{-m} \left(a+b \log \left(c x^n\right)\right)}{e g}-\frac{f k x^m (g x)^{-m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{e g m}-\frac{b n (g x)^{-m} \log \left(d \left(e+f x^m\right)^k\right)}{g m^2}-\frac{b f k n x^m (g x)^{-m} \log \left(e+f x^m\right)}{e g m^2}+\frac{b f k n x^m (g x)^{-m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{e g m^2}-\frac{b f k n x^m \log ^2(x) (g x)^{-m}}{2 e g}+\frac{b f k n x^m \log (x) (g x)^{-m}}{e g m}","\frac{b f k n x^m (g x)^{-m} \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{e g m^2}-\frac{(g x)^{-m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{g m}+\frac{f k x^m \log (x) (g x)^{-m} \left(a+b \log \left(c x^n\right)\right)}{e g}-\frac{f k x^m (g x)^{-m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{e g m}-\frac{b n (g x)^{-m} \log \left(d \left(e+f x^m\right)^k\right)}{g m^2}-\frac{b f k n x^m (g x)^{-m} \log \left(e+f x^m\right)}{e g m^2}+\frac{b f k n x^m (g x)^{-m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{e g m^2}-\frac{b f k n x^m \log ^2(x) (g x)^{-m}}{2 e g}+\frac{b f k n x^m \log (x) (g x)^{-m}}{e g m}",1,"(b*f*k*n*x^m*Log[x])/(e*g*m*(g*x)^m) - (b*f*k*n*x^m*Log[x]^2)/(2*e*g*(g*x)^m) + (f*k*x^m*Log[x]*(a + b*Log[c*x^n]))/(e*g*(g*x)^m) - (b*f*k*n*x^m*Log[e + f*x^m])/(e*g*m^2*(g*x)^m) + (b*f*k*n*x^m*Log[-((f*x^m)/e)]*Log[e + f*x^m])/(e*g*m^2*(g*x)^m) - (f*k*x^m*(a + b*Log[c*x^n])*Log[e + f*x^m])/(e*g*m*(g*x)^m) - (b*n*Log[d*(e + f*x^m)^k])/(g*m^2*(g*x)^m) - ((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/(g*m*(g*x)^m) + (b*f*k*n*x^m*PolyLog[2, 1 + (f*x^m)/e])/(e*g*m^2*(g*x)^m)","A",15,12,32,0.3750,1,"{2455, 19, 266, 36, 29, 31, 2376, 2301, 2454, 2394, 2315, 16}"
154,1,414,0,0.5212059,"\int (g x)^{-1-2 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Int[(g*x)^(-1 - 2*m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","-\frac{b f^2 k n x^{2 m} (g x)^{-2 m} \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{2 e^2 g m^2}-\frac{(g x)^{-2 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{2 g m}-\frac{f^2 k x^{2 m} \log (x) (g x)^{-2 m} \left(a+b \log \left(c x^n\right)\right)}{2 e^2 g}+\frac{f^2 k x^{2 m} (g x)^{-2 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2 g m}-\frac{f k x^m (g x)^{-2 m} \left(a+b \log \left(c x^n\right)\right)}{2 e g m}-\frac{b n (g x)^{-2 m} \log \left(d \left(e+f x^m\right)^k\right)}{4 g m^2}+\frac{b f^2 k n x^{2 m} (g x)^{-2 m} \log \left(e+f x^m\right)}{4 e^2 g m^2}-\frac{b f^2 k n x^{2 m} (g x)^{-2 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{2 e^2 g m^2}+\frac{b f^2 k n x^{2 m} \log ^2(x) (g x)^{-2 m}}{4 e^2 g}-\frac{b f^2 k n x^{2 m} \log (x) (g x)^{-2 m}}{4 e^2 g m}-\frac{3 b f k n x^m (g x)^{-2 m}}{4 e g m^2}","-\frac{b f^2 k n x^{2 m} (g x)^{-2 m} \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{2 e^2 g m^2}-\frac{(g x)^{-2 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{2 g m}-\frac{f^2 k x^{2 m} \log (x) (g x)^{-2 m} \left(a+b \log \left(c x^n\right)\right)}{2 e^2 g}+\frac{f^2 k x^{2 m} (g x)^{-2 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{2 e^2 g m}-\frac{f k x^m (g x)^{-2 m} \left(a+b \log \left(c x^n\right)\right)}{2 e g m}-\frac{b n (g x)^{-2 m} \log \left(d \left(e+f x^m\right)^k\right)}{4 g m^2}+\frac{b f^2 k n x^{2 m} (g x)^{-2 m} \log \left(e+f x^m\right)}{4 e^2 g m^2}-\frac{b f^2 k n x^{2 m} (g x)^{-2 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{2 e^2 g m^2}+\frac{b f^2 k n x^{2 m} \log ^2(x) (g x)^{-2 m}}{4 e^2 g}-\frac{b f^2 k n x^{2 m} \log (x) (g x)^{-2 m}}{4 e^2 g m}-\frac{3 b f k n x^m (g x)^{-2 m}}{4 e g m^2}",1,"(-3*b*f*k*n*x^m)/(4*e*g*m^2*(g*x)^(2*m)) - (b*f^2*k*n*x^(2*m)*Log[x])/(4*e^2*g*m*(g*x)^(2*m)) + (b*f^2*k*n*x^(2*m)*Log[x]^2)/(4*e^2*g*(g*x)^(2*m)) - (f*k*x^m*(a + b*Log[c*x^n]))/(2*e*g*m*(g*x)^(2*m)) - (f^2*k*x^(2*m)*Log[x]*(a + b*Log[c*x^n]))/(2*e^2*g*(g*x)^(2*m)) + (b*f^2*k*n*x^(2*m)*Log[e + f*x^m])/(4*e^2*g*m^2*(g*x)^(2*m)) - (b*f^2*k*n*x^(2*m)*Log[-((f*x^m)/e)]*Log[e + f*x^m])/(2*e^2*g*m^2*(g*x)^(2*m)) + (f^2*k*x^(2*m)*(a + b*Log[c*x^n])*Log[e + f*x^m])/(2*e^2*g*m*(g*x)^(2*m)) - (b*n*Log[d*(e + f*x^m)^k])/(4*g*m^2*(g*x)^(2*m)) - ((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/(2*g*m*(g*x)^(2*m)) - (b*f^2*k*n*x^(2*m)*PolyLog[2, 1 + (f*x^m)/e])/(2*e^2*g*m^2*(g*x)^(2*m))","A",16,12,32,0.3750,1,"{2455, 20, 266, 44, 2376, 30, 19, 2301, 2454, 2394, 2315, 16}"
155,1,484,0,0.7009728,"\int (g x)^{-1-3 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right) \, dx","Int[(g*x)^(-1 - 3*m)*(a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k],x]","\frac{b f^3 k n x^{3 m} (g x)^{-3 m} \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{3 e^3 g m^2}-\frac{(g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{3 g m}+\frac{f^2 k x^{2 m} (g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right)}{3 e^2 g m}+\frac{f^3 k x^{3 m} \log (x) (g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right)}{3 e^3 g}-\frac{f^3 k x^{3 m} (g x)^{-3 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^3 g m}-\frac{f k x^m (g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right)}{6 e g m}-\frac{b n (g x)^{-3 m} \log \left(d \left(e+f x^m\right)^k\right)}{9 g m^2}+\frac{4 b f^2 k n x^{2 m} (g x)^{-3 m}}{9 e^2 g m^2}-\frac{b f^3 k n x^{3 m} (g x)^{-3 m} \log \left(e+f x^m\right)}{9 e^3 g m^2}+\frac{b f^3 k n x^{3 m} (g x)^{-3 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{3 e^3 g m^2}-\frac{b f^3 k n x^{3 m} \log ^2(x) (g x)^{-3 m}}{6 e^3 g}+\frac{b f^3 k n x^{3 m} \log (x) (g x)^{-3 m}}{9 e^3 g m}-\frac{5 b f k n x^m (g x)^{-3 m}}{36 e g m^2}","\frac{b f^3 k n x^{3 m} (g x)^{-3 m} \text{PolyLog}\left(2,\frac{f x^m}{e}+1\right)}{3 e^3 g m^2}-\frac{(g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right) \log \left(d \left(e+f x^m\right)^k\right)}{3 g m}+\frac{f^2 k x^{2 m} (g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right)}{3 e^2 g m}+\frac{f^3 k x^{3 m} \log (x) (g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right)}{3 e^3 g}-\frac{f^3 k x^{3 m} (g x)^{-3 m} \log \left(e+f x^m\right) \left(a+b \log \left(c x^n\right)\right)}{3 e^3 g m}-\frac{f k x^m (g x)^{-3 m} \left(a+b \log \left(c x^n\right)\right)}{6 e g m}-\frac{b n (g x)^{-3 m} \log \left(d \left(e+f x^m\right)^k\right)}{9 g m^2}+\frac{4 b f^2 k n x^{2 m} (g x)^{-3 m}}{9 e^2 g m^2}-\frac{b f^3 k n x^{3 m} (g x)^{-3 m} \log \left(e+f x^m\right)}{9 e^3 g m^2}+\frac{b f^3 k n x^{3 m} (g x)^{-3 m} \log \left(-\frac{f x^m}{e}\right) \log \left(e+f x^m\right)}{3 e^3 g m^2}-\frac{b f^3 k n x^{3 m} \log ^2(x) (g x)^{-3 m}}{6 e^3 g}+\frac{b f^3 k n x^{3 m} \log (x) (g x)^{-3 m}}{9 e^3 g m}-\frac{5 b f k n x^m (g x)^{-3 m}}{36 e g m^2}",1,"(-5*b*f*k*n*x^m)/(36*e*g*m^2*(g*x)^(3*m)) + (4*b*f^2*k*n*x^(2*m))/(9*e^2*g*m^2*(g*x)^(3*m)) + (b*f^3*k*n*x^(3*m)*Log[x])/(9*e^3*g*m*(g*x)^(3*m)) - (b*f^3*k*n*x^(3*m)*Log[x]^2)/(6*e^3*g*(g*x)^(3*m)) - (f*k*x^m*(a + b*Log[c*x^n]))/(6*e*g*m*(g*x)^(3*m)) + (f^2*k*x^(2*m)*(a + b*Log[c*x^n]))/(3*e^2*g*m*(g*x)^(3*m)) + (f^3*k*x^(3*m)*Log[x]*(a + b*Log[c*x^n]))/(3*e^3*g*(g*x)^(3*m)) - (b*f^3*k*n*x^(3*m)*Log[e + f*x^m])/(9*e^3*g*m^2*(g*x)^(3*m)) + (b*f^3*k*n*x^(3*m)*Log[-((f*x^m)/e)]*Log[e + f*x^m])/(3*e^3*g*m^2*(g*x)^(3*m)) - (f^3*k*x^(3*m)*(a + b*Log[c*x^n])*Log[e + f*x^m])/(3*e^3*g*m*(g*x)^(3*m)) - (b*n*Log[d*(e + f*x^m)^k])/(9*g*m^2*(g*x)^(3*m)) - ((a + b*Log[c*x^n])*Log[d*(e + f*x^m)^k])/(3*g*m*(g*x)^(3*m)) + (b*f^3*k*n*x^(3*m)*PolyLog[2, 1 + (f*x^m)/e])/(3*e^3*g*m^2*(g*x)^(3*m))","A",18,12,32,0.3750,1,"{2455, 20, 266, 44, 2376, 30, 19, 2301, 2454, 2394, 2315, 16}"
156,1,84,0,0.0748924,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right) \, dx","Int[x^2*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]),x]","\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{1}{27} e r x^3 \left(3 a+3 b \log \left(c x^n\right)-b n\right)-\frac{1}{9} b n x^3 \left(d+e \log \left(f x^r\right)\right)+\frac{1}{27} b e n r x^3","\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{1}{27} e r x^3 \left(3 a+3 b \log \left(c x^n\right)-b n\right)-\frac{1}{9} b n x^3 \left(d+e \log \left(f x^r\right)\right)+\frac{1}{27} b e n r x^3",1,"(b*e*n*r*x^3)/27 - (e*r*x^3*(3*a - b*n + 3*b*Log[c*x^n]))/27 - (b*n*x^3*(d + e*Log[f*x^r]))/9 + (x^3*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/3","A",3,3,24,0.1250,1,"{2304, 2366, 12}"
157,1,84,0,0.0518652,"\int x \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right) \, dx","Int[x*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]),x]","\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{1}{8} e r x^2 \left(2 a+2 b \log \left(c x^n\right)-b n\right)-\frac{1}{4} b n x^2 \left(d+e \log \left(f x^r\right)\right)+\frac{1}{8} b e n r x^2","\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{1}{8} e r x^2 \left(2 a+2 b \log \left(c x^n\right)-b n\right)-\frac{1}{4} b n x^2 \left(d+e \log \left(f x^r\right)\right)+\frac{1}{8} b e n r x^2",1,"(b*e*n*r*x^2)/8 - (e*r*x^2*(2*a - b*n + 2*b*Log[c*x^n]))/8 - (b*n*x^2*(d + e*Log[f*x^r]))/4 + (x^2*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/2","A",3,3,22,0.1364,1,"{2304, 2366, 12}"
158,1,77,0,0.0355213,"\int \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right) \, dx","Int[(a + b*Log[c*x^n])*(d + e*Log[f*x^r]),x]","-e r x (a-b n)+a x \left(d+e \log \left(f x^r\right)\right)+b x \log \left(c x^n\right) \left(d+e \log \left(f x^r\right)\right)-b e r x \log \left(c x^n\right)-b n x \left(d+e \log \left(f x^r\right)\right)+b e n r x","-e r x (a-b n)+a x \left(d+e \log \left(f x^r\right)\right)+b x \log \left(c x^n\right) \left(d+e \log \left(f x^r\right)\right)-b e r x \log \left(c x^n\right)-b n x \left(d+e \log \left(f x^r\right)\right)+b e n r x",1,"b*e*n*r*x - e*(a - b*n)*r*x - b*e*r*x*Log[c*x^n] + a*x*(d + e*Log[f*x^r]) - b*n*x*(d + e*Log[f*x^r]) + b*x*Log[c*x^n]*(d + e*Log[f*x^r])","A",3,2,21,0.09524,1,"{2295, 2361}"
159,1,57,0,0.0717311,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x} \, dx","Int[((a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/x,x]","\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{2 b n}-\frac{e r \left(a+b \log \left(c x^n\right)\right)^3}{6 b^2 n^2}","\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{2 b n}-\frac{e r \left(a+b \log \left(c x^n\right)\right)^3}{6 b^2 n^2}",1,"-(e*r*(a + b*Log[c*x^n])^3)/(6*b^2*n^2) + ((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/(2*b*n)","A",4,5,24,0.2083,1,"{2301, 2366, 12, 2302, 30}"
160,1,72,0,0.0707982,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/x^2,x]","-\frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{e r \left(a+b \log \left(c x^n\right)+b n\right)}{x}-\frac{b n \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{b e n r}{x}","-\frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{e r \left(a+b \log \left(c x^n\right)+b n\right)}{x}-\frac{b n \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{b e n r}{x}",1,"-((b*e*n*r)/x) - (e*r*(a + b*n + b*Log[c*x^n]))/x - (b*n*(d + e*Log[f*x^r]))/x - ((a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/x","A",2,2,24,0.08333,1,"{2304, 2366}"
161,1,83,0,0.0726216,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/x^3,x]","-\frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{2 x^2}-\frac{e r \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{8 x^2}-\frac{b n \left(d+e \log \left(f x^r\right)\right)}{4 x^2}-\frac{b e n r}{8 x^2}","-\frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{2 x^2}-\frac{e r \left(2 a+2 b \log \left(c x^n\right)+b n\right)}{8 x^2}-\frac{b n \left(d+e \log \left(f x^r\right)\right)}{4 x^2}-\frac{b e n r}{8 x^2}",1,"-(b*e*n*r)/(8*x^2) - (e*r*(2*a + b*n + 2*b*Log[c*x^n]))/(8*x^2) - (b*n*(d + e*Log[f*x^r]))/(4*x^2) - ((a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/(2*x^2)","A",3,3,24,0.1250,1,"{2304, 2366, 12}"
162,1,83,0,0.0744238,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x^4} \, dx","Int[((a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/x^4,x]","-\frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{3 x^3}-\frac{e r \left(3 a+3 b \log \left(c x^n\right)+b n\right)}{27 x^3}-\frac{b n \left(d+e \log \left(f x^r\right)\right)}{9 x^3}-\frac{b e n r}{27 x^3}","-\frac{\left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{3 x^3}-\frac{e r \left(3 a+3 b \log \left(c x^n\right)+b n\right)}{27 x^3}-\frac{b n \left(d+e \log \left(f x^r\right)\right)}{9 x^3}-\frac{b e n r}{27 x^3}",1,"-(b*e*n*r)/(27*x^3) - (e*r*(3*a + b*n + 3*b*Log[c*x^n]))/(27*x^3) - (b*n*(d + e*Log[f*x^r]))/(9*x^3) - ((a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/(3*x^3)","A",3,3,24,0.1250,1,"{2304, 2366, 12}"
163,1,207,0,0.2027597,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right) \, dx","Int[x^2*(a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]),x]","-\frac{1}{81} e r x^3 \left(9 a^2-6 a b n+2 b^2 n^2\right)+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)-\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{2}{27} b e r x^3 (3 a-b n) \log \left(c x^n\right)+\frac{2}{81} b e n r x^3 (3 a-b n)-\frac{1}{9} b^2 e r x^3 \log ^2\left(c x^n\right)+\frac{2}{27} b^2 e n r x^3 \log \left(c x^n\right)+\frac{2}{27} b^2 n^2 x^3 \left(d+e \log \left(f x^r\right)\right)-\frac{2}{81} b^2 e n^2 r x^3","-\frac{1}{81} e r x^3 \left(9 a^2-6 a b n+2 b^2 n^2\right)+\frac{1}{3} x^3 \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)-\frac{2}{9} b n x^3 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{2}{27} b e r x^3 (3 a-b n) \log \left(c x^n\right)+\frac{2}{81} b e n r x^3 (3 a-b n)-\frac{1}{9} b^2 e r x^3 \log ^2\left(c x^n\right)+\frac{2}{27} b^2 e n r x^3 \log \left(c x^n\right)+\frac{2}{27} b^2 n^2 x^3 \left(d+e \log \left(f x^r\right)\right)-\frac{2}{81} b^2 e n^2 r x^3",1,"(-2*b^2*e*n^2*r*x^3)/81 + (2*b*e*n*(3*a - b*n)*r*x^3)/81 - (e*(9*a^2 - 6*a*b*n + 2*b^2*n^2)*r*x^3)/81 + (2*b^2*e*n*r*x^3*Log[c*x^n])/27 - (2*b*e*(3*a - b*n)*r*x^3*Log[c*x^n])/27 - (b^2*e*r*x^3*Log[c*x^n]^2)/9 + (2*b^2*n^2*x^3*(d + e*Log[f*x^r]))/27 - (2*b*n*x^3*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/9 + (x^3*(a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/3","A",7,5,26,0.1923,1,"{2305, 2304, 2366, 12, 14}"
164,1,206,0,0.1656446,"\int x \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right) \, dx","Int[x*(a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]),x]","-\frac{1}{8} e r x^2 \left(2 a^2-2 a b n+b^2 n^2\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)-\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{1}{4} b e r x^2 (2 a-b n) \log \left(c x^n\right)+\frac{1}{8} b e n r x^2 (2 a-b n)-\frac{1}{4} b^2 e r x^2 \log ^2\left(c x^n\right)+\frac{1}{4} b^2 e n r x^2 \log \left(c x^n\right)+\frac{1}{4} b^2 n^2 x^2 \left(d+e \log \left(f x^r\right)\right)-\frac{1}{8} b^2 e n^2 r x^2","-\frac{1}{8} e r x^2 \left(2 a^2-2 a b n+b^2 n^2\right)+\frac{1}{2} x^2 \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)-\frac{1}{2} b n x^2 \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)-\frac{1}{4} b e r x^2 (2 a-b n) \log \left(c x^n\right)+\frac{1}{8} b e n r x^2 (2 a-b n)-\frac{1}{4} b^2 e r x^2 \log ^2\left(c x^n\right)+\frac{1}{4} b^2 e n r x^2 \log \left(c x^n\right)+\frac{1}{4} b^2 n^2 x^2 \left(d+e \log \left(f x^r\right)\right)-\frac{1}{8} b^2 e n^2 r x^2",1,"-(b^2*e*n^2*r*x^2)/8 + (b*e*n*(2*a - b*n)*r*x^2)/8 - (e*(2*a^2 - 2*a*b*n + b^2*n^2)*r*x^2)/8 + (b^2*e*n*r*x^2*Log[c*x^n])/4 - (b*e*(2*a - b*n)*r*x^2*Log[c*x^n])/4 - (b^2*e*r*x^2*Log[c*x^n]^2)/4 + (b^2*n^2*x^2*(d + e*Log[f*x^r]))/4 - (b*n*x^2*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/2 + (x^2*(a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/2","A",7,5,24,0.2083,1,"{2305, 2304, 2366, 12, 14}"
165,1,147,0,0.0881252,"\int \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right) \, dx","Int[(a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]),x]","x \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)-e r x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \left(d+e \log \left(f x^r\right)\right)+2 a b e n r x+2 b e n r x (a-b n)-2 b^2 n x \log \left(c x^n\right) \left(d+e \log \left(f x^r\right)\right)+4 b^2 e n r x \log \left(c x^n\right)+2 b^2 n^2 x \left(d+e \log \left(f x^r\right)\right)-4 b^2 e n^2 r x","x \left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)-e r x \left(a+b \log \left(c x^n\right)\right)^2-2 a b n x \left(d+e \log \left(f x^r\right)\right)+2 a b e n r x+2 b e n r x (a-b n)-2 b^2 n x \log \left(c x^n\right) \left(d+e \log \left(f x^r\right)\right)+4 b^2 e n r x \log \left(c x^n\right)+2 b^2 n^2 x \left(d+e \log \left(f x^r\right)\right)-4 b^2 e n^2 r x",1,"2*a*b*e*n*r*x - 4*b^2*e*n^2*r*x + 2*b*e*n*(a - b*n)*r*x + 4*b^2*e*n*r*x*Log[c*x^n] - e*r*x*(a + b*Log[c*x^n])^2 - 2*a*b*n*x*(d + e*Log[f*x^r]) + 2*b^2*n^2*x*(d + e*Log[f*x^r]) - 2*b^2*n*x*Log[c*x^n]*(d + e*Log[f*x^r]) + x*(a + b*Log[c*x^n])^2*(d + e*Log[f*x^r])","A",6,3,23,0.1304,1,"{2296, 2295, 2361}"
166,1,57,0,0.095202,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/x,x]","\frac{\left(a+b \log \left(c x^n\right)\right)^3 \left(d+e \log \left(f x^r\right)\right)}{3 b n}-\frac{e r \left(a+b \log \left(c x^n\right)\right)^4}{12 b^2 n^2}","\frac{\left(a+b \log \left(c x^n\right)\right)^3 \left(d+e \log \left(f x^r\right)\right)}{3 b n}-\frac{e r \left(a+b \log \left(c x^n\right)\right)^4}{12 b^2 n^2}",1,"-(e*r*(a + b*Log[c*x^n])^4)/(12*b^2*n^2) + ((a + b*Log[c*x^n])^3*(d + e*Log[f*x^r]))/(3*b*n)","A",4,4,26,0.1538,1,"{2302, 30, 2366, 12}"
167,1,181,0,0.1927188,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/x^2,x]","-\frac{e r \left(a^2+2 a b n+2 b^2 n^2\right)}{x}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{2 b e r (a+b n) \log \left(c x^n\right)}{x}-\frac{2 b e n r (a+b n)}{x}-\frac{b^2 e r \log ^2\left(c x^n\right)}{x}-\frac{2 b^2 e n r \log \left(c x^n\right)}{x}-\frac{2 b^2 n^2 \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{2 b^2 e n^2 r}{x}","-\frac{e r \left(a^2+2 a b n+2 b^2 n^2\right)}{x}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{2 b e r (a+b n) \log \left(c x^n\right)}{x}-\frac{2 b e n r (a+b n)}{x}-\frac{b^2 e r \log ^2\left(c x^n\right)}{x}-\frac{2 b^2 e n r \log \left(c x^n\right)}{x}-\frac{2 b^2 n^2 \left(d+e \log \left(f x^r\right)\right)}{x}-\frac{2 b^2 e n^2 r}{x}",1,"(-2*b^2*e*n^2*r)/x - (2*b*e*n*(a + b*n)*r)/x - (e*(a^2 + 2*a*b*n + 2*b^2*n^2)*r)/x - (2*b^2*e*n*r*Log[c*x^n])/x - (2*b*e*(a + b*n)*r*Log[c*x^n])/x - (b^2*e*r*Log[c*x^n]^2)/x - (2*b^2*n^2*(d + e*Log[f*x^r]))/x - (2*b*n*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/x - ((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/x","A",6,4,26,0.1538,1,"{2305, 2304, 2366, 14}"
168,1,204,0,0.2059041,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/x^3,x]","-\frac{e r \left(2 a^2+2 a b n+b^2 n^2\right)}{8 x^2}-\frac{b n \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{2 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{2 x^2}-\frac{b e r (2 a+b n) \log \left(c x^n\right)}{4 x^2}-\frac{b e n r (2 a+b n)}{8 x^2}-\frac{b^2 e r \log ^2\left(c x^n\right)}{4 x^2}-\frac{b^2 e n r \log \left(c x^n\right)}{4 x^2}-\frac{b^2 n^2 \left(d+e \log \left(f x^r\right)\right)}{4 x^2}-\frac{b^2 e n^2 r}{8 x^2}","-\frac{e r \left(2 a^2+2 a b n+b^2 n^2\right)}{8 x^2}-\frac{b n \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{2 x^2}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{2 x^2}-\frac{b e r (2 a+b n) \log \left(c x^n\right)}{4 x^2}-\frac{b e n r (2 a+b n)}{8 x^2}-\frac{b^2 e r \log ^2\left(c x^n\right)}{4 x^2}-\frac{b^2 e n r \log \left(c x^n\right)}{4 x^2}-\frac{b^2 n^2 \left(d+e \log \left(f x^r\right)\right)}{4 x^2}-\frac{b^2 e n^2 r}{8 x^2}",1,"-(b^2*e*n^2*r)/(8*x^2) - (b*e*n*(2*a + b*n)*r)/(8*x^2) - (e*(2*a^2 + 2*a*b*n + b^2*n^2)*r)/(8*x^2) - (b^2*e*n*r*Log[c*x^n])/(4*x^2) - (b*e*(2*a + b*n)*r*Log[c*x^n])/(4*x^2) - (b^2*e*r*Log[c*x^n]^2)/(4*x^2) - (b^2*n^2*(d + e*Log[f*x^r]))/(4*x^2) - (b*n*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/(2*x^2) - ((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/(2*x^2)","A",7,5,26,0.1923,1,"{2305, 2304, 2366, 12, 14}"
169,1,205,0,0.2113571,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{x^4} \, dx","Int[((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/x^4,x]","-\frac{e r \left(9 a^2+6 a b n+2 b^2 n^2\right)}{81 x^3}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{9 x^3}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{3 x^3}-\frac{2 b e r (3 a+b n) \log \left(c x^n\right)}{27 x^3}-\frac{2 b e n r (3 a+b n)}{81 x^3}-\frac{b^2 e r \log ^2\left(c x^n\right)}{9 x^3}-\frac{2 b^2 e n r \log \left(c x^n\right)}{27 x^3}-\frac{2 b^2 n^2 \left(d+e \log \left(f x^r\right)\right)}{27 x^3}-\frac{2 b^2 e n^2 r}{81 x^3}","-\frac{e r \left(9 a^2+6 a b n+2 b^2 n^2\right)}{81 x^3}-\frac{2 b n \left(a+b \log \left(c x^n\right)\right) \left(d+e \log \left(f x^r\right)\right)}{9 x^3}-\frac{\left(a+b \log \left(c x^n\right)\right)^2 \left(d+e \log \left(f x^r\right)\right)}{3 x^3}-\frac{2 b e r (3 a+b n) \log \left(c x^n\right)}{27 x^3}-\frac{2 b e n r (3 a+b n)}{81 x^3}-\frac{b^2 e r \log ^2\left(c x^n\right)}{9 x^3}-\frac{2 b^2 e n r \log \left(c x^n\right)}{27 x^3}-\frac{2 b^2 n^2 \left(d+e \log \left(f x^r\right)\right)}{27 x^3}-\frac{2 b^2 e n^2 r}{81 x^3}",1,"(-2*b^2*e*n^2*r)/(81*x^3) - (2*b*e*n*(3*a + b*n)*r)/(81*x^3) - (e*(9*a^2 + 6*a*b*n + 2*b^2*n^2)*r)/(81*x^3) - (2*b^2*e*n*r*Log[c*x^n])/(27*x^3) - (2*b*e*(3*a + b*n)*r*Log[c*x^n])/(27*x^3) - (b^2*e*r*Log[c*x^n]^2)/(9*x^3) - (2*b^2*n^2*(d + e*Log[f*x^r]))/(27*x^3) - (2*b*n*(a + b*Log[c*x^n])*(d + e*Log[f*x^r]))/(9*x^3) - ((a + b*Log[c*x^n])^2*(d + e*Log[f*x^r]))/(3*x^3)","A",7,5,26,0.1923,1,"{2305, 2304, 2366, 12, 14}"
170,1,141,0,0.1799741,"\int \frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{d+e \log \left(f x^m\right)} \, dx","Int[(x^2*(a + b*Log[c*x^n]))/(d + e*Log[f*x^m]),x]","\frac{x^3 e^{-\frac{3 d}{e m}} \left(f x^m\right)^{-3/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(\frac{3 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e m}-\frac{b n x^3 e^{-\frac{3 d}{e m}} \left(f x^m\right)^{-3/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(\frac{3 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e^2 m^2}+\frac{b n x^3}{3 e m}","\frac{x^3 e^{-\frac{3 d}{e m}} \left(f x^m\right)^{-3/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(\frac{3 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e m}-\frac{b n x^3 e^{-\frac{3 d}{e m}} \left(f x^m\right)^{-3/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(\frac{3 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e^2 m^2}+\frac{b n x^3}{3 e m}",1,"(b*n*x^3)/(3*e*m) - (b*n*x^3*ExpIntegralEi[(3*(d + e*Log[f*x^m]))/(e*m)]*(d + e*Log[f*x^m]))/(e^2*E^((3*d)/(e*m))*m^2*(f*x^m)^(3/m)) + (x^3*ExpIntegralEi[(3*(d + e*Log[f*x^m]))/(e*m)]*(a + b*Log[c*x^n]))/(e*E^((3*d)/(e*m))*m*(f*x^m)^(3/m))","A",6,6,26,0.2308,1,"{2310, 2178, 2366, 12, 15, 6482}"
171,1,141,0,0.1539977,"\int \frac{x \left(a+b \log \left(c x^n\right)\right)}{d+e \log \left(f x^m\right)} \, dx","Int[(x*(a + b*Log[c*x^n]))/(d + e*Log[f*x^m]),x]","\frac{x^2 e^{-\frac{2 d}{e m}} \left(f x^m\right)^{-2/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e m}-\frac{b n x^2 e^{-\frac{2 d}{e m}} \left(f x^m\right)^{-2/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e^2 m^2}+\frac{b n x^2}{2 e m}","\frac{x^2 e^{-\frac{2 d}{e m}} \left(f x^m\right)^{-2/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e m}-\frac{b n x^2 e^{-\frac{2 d}{e m}} \left(f x^m\right)^{-2/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e^2 m^2}+\frac{b n x^2}{2 e m}",1,"(b*n*x^2)/(2*e*m) - (b*n*x^2*ExpIntegralEi[(2*(d + e*Log[f*x^m]))/(e*m)]*(d + e*Log[f*x^m]))/(e^2*E^((2*d)/(e*m))*m^2*(f*x^m)^(2/m)) + (x^2*ExpIntegralEi[(2*(d + e*Log[f*x^m]))/(e*m)]*(a + b*Log[c*x^n]))/(e*E^((2*d)/(e*m))*m*(f*x^m)^(2/m))","A",6,6,24,0.2500,1,"{2310, 2178, 2366, 12, 15, 6482}"
172,1,130,0,0.1220351,"\int \frac{a+b \log \left(c x^n\right)}{d+e \log \left(f x^m\right)} \, dx","Int[(a + b*Log[c*x^n])/(d + e*Log[f*x^m]),x]","\frac{x e^{-\frac{d}{e m}} \left(f x^m\right)^{-1/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e m}-\frac{b n x e^{-\frac{d}{e m}} \left(f x^m\right)^{-1/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e^2 m^2}+\frac{b n x}{e m}","\frac{x e^{-\frac{d}{e m}} \left(f x^m\right)^{-1/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e m}-\frac{b n x e^{-\frac{d}{e m}} \left(f x^m\right)^{-1/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e^2 m^2}+\frac{b n x}{e m}",1,"(b*n*x)/(e*m) - (b*n*x*ExpIntegralEi[(d + e*Log[f*x^m])/(e*m)]*(d + e*Log[f*x^m]))/(e^2*E^(d/(e*m))*m^2*(f*x^m)^m^(-1)) + (x*ExpIntegralEi[(d + e*Log[f*x^m])/(e*m)]*(a + b*Log[c*x^n]))/(e*E^(d/(e*m))*m*(f*x^m)^m^(-1))","A",6,6,23,0.2609,1,"{2300, 2178, 2361, 12, 15, 6482}"
173,1,71,0,0.1061626,"\int \frac{a+b \log \left(c x^n\right)}{x \left(d+e \log \left(f x^m\right)\right)} \, dx","Int[(a + b*Log[c*x^n])/(x*(d + e*Log[f*x^m])),x]","\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d+e \log \left(f x^m\right)\right)}{e m}-\frac{b n \left(d+e \log \left(f x^m\right)\right) \log \left(d+e \log \left(f x^m\right)\right)}{e^2 m^2}+\frac{b n \log (x)}{e m}","\frac{\left(a+b \log \left(c x^n\right)\right) \log \left(d+e \log \left(f x^m\right)\right)}{e m}-\frac{b n \left(d+e \log \left(f x^m\right)\right) \log \left(d+e \log \left(f x^m\right)\right)}{e^2 m^2}+\frac{b n \log (x)}{e m}",1,"(b*n*Log[x])/(e*m) - (b*n*(d + e*Log[f*x^m])*Log[d + e*Log[f*x^m]])/(e^2*m^2) + ((a + b*Log[c*x^n])*Log[d + e*Log[f*x^m]])/(e*m)","A",5,6,26,0.2308,1,"{2302, 29, 2366, 12, 2389, 2295}"
174,1,133,0,0.1716257,"\int \frac{a+b \log \left(c x^n\right)}{x^2 \left(d+e \log \left(f x^m\right)\right)} \, dx","Int[(a + b*Log[c*x^n])/(x^2*(d + e*Log[f*x^m])),x]","\frac{e^{\frac{d}{e m}} \left(f x^m\right)^{\frac{1}{m}} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(-\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e m x}-\frac{b n e^{\frac{d}{e m}} \left(f x^m\right)^{\frac{1}{m}} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(-\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e^2 m^2 x}-\frac{b n}{e m x}","\frac{e^{\frac{d}{e m}} \left(f x^m\right)^{\frac{1}{m}} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(-\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e m x}-\frac{b n e^{\frac{d}{e m}} \left(f x^m\right)^{\frac{1}{m}} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(-\frac{d+e \log \left(f x^m\right)}{e m}\right)}{e^2 m^2 x}-\frac{b n}{e m x}",1,"-((b*n)/(e*m*x)) - (b*E^(d/(e*m))*n*(f*x^m)^m^(-1)*ExpIntegralEi[-((d + e*Log[f*x^m])/(e*m))]*(d + e*Log[f*x^m]))/(e^2*m^2*x) + (E^(d/(e*m))*(f*x^m)^m^(-1)*ExpIntegralEi[-((d + e*Log[f*x^m])/(e*m))]*(a + b*Log[c*x^n]))/(e*m*x)","A",6,6,26,0.2308,1,"{2310, 2178, 2366, 12, 15, 6482}"
175,1,141,0,0.1690695,"\int \frac{a+b \log \left(c x^n\right)}{x^3 \left(d+e \log \left(f x^m\right)\right)} \, dx","Int[(a + b*Log[c*x^n])/(x^3*(d + e*Log[f*x^m])),x]","\frac{e^{\frac{2 d}{e m}} \left(f x^m\right)^{2/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(-\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e m x^2}-\frac{b n e^{\frac{2 d}{e m}} \left(f x^m\right)^{2/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(-\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e^2 m^2 x^2}-\frac{b n}{2 e m x^2}","\frac{e^{\frac{2 d}{e m}} \left(f x^m\right)^{2/m} \left(a+b \log \left(c x^n\right)\right) \text{Ei}\left(-\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e m x^2}-\frac{b n e^{\frac{2 d}{e m}} \left(f x^m\right)^{2/m} \left(d+e \log \left(f x^m\right)\right) \text{Ei}\left(-\frac{2 \left(d+e \log \left(f x^m\right)\right)}{e m}\right)}{e^2 m^2 x^2}-\frac{b n}{2 e m x^2}",1,"-(b*n)/(2*e*m*x^2) - (b*E^((2*d)/(e*m))*n*(f*x^m)^(2/m)*ExpIntegralEi[(-2*(d + e*Log[f*x^m]))/(e*m)]*(d + e*Log[f*x^m]))/(e^2*m^2*x^2) + (E^((2*d)/(e*m))*(f*x^m)^(2/m)*ExpIntegralEi[(-2*(d + e*Log[f*x^m]))/(e*m)]*(a + b*Log[c*x^n]))/(e*m*x^2)","A",6,6,26,0.2308,1,"{2310, 2178, 2366, 12, 15, 6482}"
176,1,135,0,0.1384858,"\int \frac{a+b \log \left(c x^n\right)}{\left(d+e \log \left(c x^n\right)\right)^2} \, dx","Int[(a + b*Log[c*x^n])/(d + e*Log[c*x^n])^2,x]","-\frac{x \left(c x^n\right)^{-1/n} e^{-\frac{d}{e n}} (b d-a e) \text{Ei}\left(\frac{d+e \log \left(c x^n\right)}{e n}\right)}{e^3 n^2}+\frac{x (b d-a e)}{e^2 n \left(e \log \left(c x^n\right)+d\right)}+\frac{b x \left(c x^n\right)^{-1/n} e^{-\frac{d}{e n}} \text{Ei}\left(\frac{d+e \log \left(c x^n\right)}{e n}\right)}{e^2 n}","\frac{x \left(c x^n\right)^{-1/n} e^{-\frac{d}{e n}} (a e-b d+b e n) \text{Ei}\left(\frac{d+e \log \left(c x^n\right)}{e n}\right)}{e^3 n^2}+\frac{x (b d-a e)}{e^2 n \left(e \log \left(c x^n\right)+d\right)}",1,"-(((b*d - a*e)*x*ExpIntegralEi[(d + e*Log[c*x^n])/(e*n)])/(e^3*E^(d/(e*n))*n^2*(c*x^n)^n^(-1))) + (b*x*ExpIntegralEi[(d + e*Log[c*x^n])/(e*n)])/(e^2*E^(d/(e*n))*n*(c*x^n)^n^(-1)) + ((b*d - a*e)*x)/(e^2*n*(d + e*Log[c*x^n]))","A",7,4,23,0.1739,1,"{2360, 2297, 2300, 2178}"
177,1,29,0,0.0531439,"\int \frac{a+b \log \left(c x^n\right)}{x \log (x)} \, dx","Int[(a + b*Log[c*x^n])/(x*Log[x]),x]","\log (\log (x)) \left(a+b \log \left(c x^n\right)\right)+b n \log (x)-b n \log (\log (x)) \log (x)","\log (\log (x)) \left(a+b \log \left(c x^n\right)\right)+b n \log (x)-b n \log (\log (x)) \log (x)",1,"b*n*Log[x] - b*n*Log[x]*Log[Log[x]] + (a + b*Log[c*x^n])*Log[Log[x]]","A",2,4,18,0.2222,1,"{2302, 29, 2366, 2521}"
178,1,347,0,0.3581708,"\int (g x)^m \left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right) \, dx","Int[(g*x)^m*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]),x]","\frac{(g x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{g (m+1)}-\frac{e r x (g x)^m e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,-\frac{a (m+1)}{b n}-\frac{(m+1) \log \left(c x^n\right)}{n}\right)}{(m+1)^2}-\frac{e r x (g x)^m e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a (m+1)}{b n}-\frac{(m+1) \log \left(c x^n\right)}{n}\right)}{b (m+1) n}","\frac{(g x)^{m+1} e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{g (m+1)}-\frac{e r x (g x)^m e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,-\frac{a (m+1)}{b n}-\frac{(m+1) \log \left(c x^n\right)}{n}\right)}{(m+1)^2}-\frac{e r x (g x)^m e^{-\frac{a (m+1)}{b n}} \left(c x^n\right)^{-\frac{m+1}{n}} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{(m+1) \left(a+b \log \left(c x^n\right)\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a (m+1)}{b n}-\frac{(m+1) \log \left(c x^n\right)}{n}\right)}{b (m+1) n}",1,"-((e*r*x*(g*x)^m*Gamma[2 + p, -((a*(1 + m))/(b*n)) - ((1 + m)*Log[c*x^n])/n]*(a + b*Log[c*x^n])^p)/(E^((a*(1 + m))/(b*n))*(1 + m)^2*(c*x^n)^((1 + m)/n)*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p)) - (e*r*x*(g*x)^m*Gamma[1 + p, -((a*(1 + m))/(b*n)) - ((1 + m)*Log[c*x^n])/n]*(a + b*Log[c*x^n])^(1 + p))/(b*E^((a*(1 + m))/(b*n))*(1 + m)*n*(c*x^n)^((1 + m)/n)*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p) + ((g*x)^(1 + m)*Gamma[1 + p, -(((1 + m)*(a + b*Log[c*x^n]))/(b*n))]*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/(E^((a*(1 + m))/(b*n))*g*(1 + m)*(c*x^n)^((1 + m)/n)*(-(((1 + m)*(a + b*Log[c*x^n]))/(b*n)))^p)","A",8,7,28,0.2500,1,"{2310, 2181, 2366, 12, 15, 19, 6557}"
179,1,298,0,0.2450492,"\int x^2 \left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right) \, dx","Int[x^2*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]),x]","3^{-p-1} x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)+e \left(-3^{-p-2}\right) r x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,-\frac{3 a}{b n}-\frac{3 \log \left(c x^n\right)}{n}\right)-\frac{e 3^{-p-1} r x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{3 a}{b n}-\frac{3 \log \left(c x^n\right)}{n}\right)}{b n}","3^{-p-1} x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)+e \left(-3^{-p-2}\right) r x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,-\frac{3 a}{b n}-\frac{3 \log \left(c x^n\right)}{n}\right)-\frac{e 3^{-p-1} r x^3 e^{-\frac{3 a}{b n}} \left(c x^n\right)^{-3/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{3 a}{b n}-\frac{3 \log \left(c x^n\right)}{n}\right)}{b n}",1,"-((3^(-2 - p)*e*r*x^3*Gamma[2 + p, (-3*a)/(b*n) - (3*Log[c*x^n])/n]*(a + b*Log[c*x^n])^p)/(E^((3*a)/(b*n))*(c*x^n)^(3/n)*(-((a + b*Log[c*x^n])/(b*n)))^p)) - (3^(-1 - p)*e*r*x^3*Gamma[1 + p, (-3*a)/(b*n) - (3*Log[c*x^n])/n]*(a + b*Log[c*x^n])^(1 + p))/(b*E^((3*a)/(b*n))*n*(c*x^n)^(3/n)*(-((a + b*Log[c*x^n])/(b*n)))^p) + (3^(-1 - p)*x^3*Gamma[1 + p, (-3*(a + b*Log[c*x^n]))/(b*n)]*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/(E^((3*a)/(b*n))*(c*x^n)^(3/n)*(-((a + b*Log[c*x^n])/(b*n)))^p)","A",7,7,26,0.2692,1,"{2310, 2181, 2366, 12, 15, 19, 6557}"
180,1,298,0,0.2199951,"\int x \left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right) \, dx","Int[x*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]),x]","2^{-p-1} x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)+e \left(-2^{-p-2}\right) r x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,-\frac{2 a}{b n}-\frac{2 \log \left(c x^n\right)}{n}\right)-\frac{e 2^{-p-1} r x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 a}{b n}-\frac{2 \log \left(c x^n\right)}{n}\right)}{b n}","2^{-p-1} x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)+e \left(-2^{-p-2}\right) r x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,-\frac{2 a}{b n}-\frac{2 \log \left(c x^n\right)}{n}\right)-\frac{e 2^{-p-1} r x^2 e^{-\frac{2 a}{b n}} \left(c x^n\right)^{-2/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 a}{b n}-\frac{2 \log \left(c x^n\right)}{n}\right)}{b n}",1,"-((2^(-2 - p)*e*r*x^2*Gamma[2 + p, (-2*a)/(b*n) - (2*Log[c*x^n])/n]*(a + b*Log[c*x^n])^p)/(E^((2*a)/(b*n))*(c*x^n)^(2/n)*(-((a + b*Log[c*x^n])/(b*n)))^p)) - (2^(-1 - p)*e*r*x^2*Gamma[1 + p, (-2*a)/(b*n) - (2*Log[c*x^n])/n]*(a + b*Log[c*x^n])^(1 + p))/(b*E^((2*a)/(b*n))*n*(c*x^n)^(2/n)*(-((a + b*Log[c*x^n])/(b*n)))^p) + (2^(-1 - p)*x^2*Gamma[1 + p, (-2*(a + b*Log[c*x^n]))/(b*n)]*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/(E^((2*a)/(b*n))*(c*x^n)^(2/n)*(-((a + b*Log[c*x^n])/(b*n)))^p)","A",7,7,24,0.2917,1,"{2310, 2181, 2366, 12, 15, 19, 6557}"
181,1,271,0,0.1661887,"\int \left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right) \, dx","Int[(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]),x]","x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c x^n\right)}{b n}\right)-e r x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,-\frac{a}{b n}-\frac{\log \left(c x^n\right)}{n}\right)-\frac{e r x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a}{b n}-\frac{\log \left(c x^n\right)}{n}\right)}{b n}","x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c x^n\right)}{b n}\right)-e r x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(a+b \log \left(c x^n\right)\right)^p \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,-\frac{a}{b n}-\frac{\log \left(c x^n\right)}{n}\right)-\frac{e r x e^{-\frac{a}{b n}} \left(c x^n\right)^{-1/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(-\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a}{b n}-\frac{\log \left(c x^n\right)}{n}\right)}{b n}",1,"-((e*r*x*Gamma[2 + p, -(a/(b*n)) - Log[c*x^n]/n]*(a + b*Log[c*x^n])^p)/(E^(a/(b*n))*(c*x^n)^n^(-1)*(-((a + b*Log[c*x^n])/(b*n)))^p)) - (e*r*x*Gamma[1 + p, -(a/(b*n)) - Log[c*x^n]/n]*(a + b*Log[c*x^n])^(1 + p))/(b*E^(a/(b*n))*n*(c*x^n)^n^(-1)*(-((a + b*Log[c*x^n])/(b*n)))^p) + (x*Gamma[1 + p, -((a + b*Log[c*x^n])/(b*n))]*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/(E^(a/(b*n))*(c*x^n)^n^(-1)*(-((a + b*Log[c*x^n])/(b*n)))^p)","A",7,7,23,0.3043,1,"{2300, 2181, 2361, 12, 15, 19, 6557}"
182,1,71,0,0.1552526,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/x,x]","\frac{\left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^{p+1}}{b n (p+1)}-\frac{e r \left(a+b \log \left(c x^n\right)\right)^{p+2}}{b^2 n^2 (p+1) (p+2)}","\frac{\left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^{p+1}}{b n (p+1)}-\frac{e r \left(a+b \log \left(c x^n\right)\right)^{p+2}}{b^2 n^2 (p+1) (p+2)}",1,"-((e*r*(a + b*Log[c*x^n])^(2 + p))/(b^2*n^2*(1 + p)*(2 + p))) + ((a + b*Log[c*x^n])^(1 + p)*(d + e*Log[f*x^r]))/(b*n*(1 + p))","A",4,4,26,0.1538,1,"{2302, 30, 2366, 12}"
183,1,260,0,0.2266113,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right)}{x^2} \, dx","Int[((a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/x^2,x]","-\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{a+b \log \left(c x^n\right)}{b n}\right)}{x}-\frac{e r e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,\frac{a}{b n}+\frac{\log \left(c x^n\right)}{n}\right)}{x}+\frac{e r e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{a}{b n}+\frac{\log \left(c x^n\right)}{n}\right)}{b n x}","-\frac{e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{a+b \log \left(c x^n\right)}{b n}\right)}{x}-\frac{e r e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,\frac{a}{b n}+\frac{\log \left(c x^n\right)}{n}\right)}{x}+\frac{e r e^{\frac{a}{b n}} \left(c x^n\right)^{\frac{1}{n}} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{a}{b n}+\frac{\log \left(c x^n\right)}{n}\right)}{b n x}",1,"-((e*E^(a/(b*n))*r*(c*x^n)^n^(-1)*Gamma[2 + p, a/(b*n) + Log[c*x^n]/n]*(a + b*Log[c*x^n])^p)/(x*((a + b*Log[c*x^n])/(b*n))^p)) + (e*E^(a/(b*n))*r*(c*x^n)^n^(-1)*Gamma[1 + p, a/(b*n) + Log[c*x^n]/n]*(a + b*Log[c*x^n])^(1 + p))/(b*n*x*((a + b*Log[c*x^n])/(b*n))^p) - (E^(a/(b*n))*(c*x^n)^n^(-1)*Gamma[1 + p, (a + b*Log[c*x^n])/(b*n)]*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/(x*((a + b*Log[c*x^n])/(b*n))^p)","A",7,7,26,0.2692,1,"{2310, 2181, 2366, 12, 15, 19, 6557}"
184,1,295,0,0.2343542,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right)}{x^3} \, dx","Int[((a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/x^3,x]","-\frac{2^{-p-1} e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{x^2}-\frac{e 2^{-p-2} r e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,\frac{2 a}{b n}+\frac{2 \log \left(c x^n\right)}{n}\right)}{x^2}+\frac{e 2^{-p-1} r e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{2 a}{b n}+\frac{2 \log \left(c x^n\right)}{n}\right)}{b n x^2}","-\frac{2^{-p-1} e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{2 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{x^2}-\frac{e 2^{-p-2} r e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,\frac{2 a}{b n}+\frac{2 \log \left(c x^n\right)}{n}\right)}{x^2}+\frac{e 2^{-p-1} r e^{\frac{2 a}{b n}} \left(c x^n\right)^{2/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{2 a}{b n}+\frac{2 \log \left(c x^n\right)}{n}\right)}{b n x^2}",1,"-((2^(-2 - p)*e*E^((2*a)/(b*n))*r*(c*x^n)^(2/n)*Gamma[2 + p, (2*a)/(b*n) + (2*Log[c*x^n])/n]*(a + b*Log[c*x^n])^p)/(x^2*((a + b*Log[c*x^n])/(b*n))^p)) + (2^(-1 - p)*e*E^((2*a)/(b*n))*r*(c*x^n)^(2/n)*Gamma[1 + p, (2*a)/(b*n) + (2*Log[c*x^n])/n]*(a + b*Log[c*x^n])^(1 + p))/(b*n*x^2*((a + b*Log[c*x^n])/(b*n))^p) - (2^(-1 - p)*E^((2*a)/(b*n))*(c*x^n)^(2/n)*Gamma[1 + p, (2*(a + b*Log[c*x^n]))/(b*n)]*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/(x^2*((a + b*Log[c*x^n])/(b*n))^p)","A",7,7,26,0.2692,1,"{2310, 2181, 2366, 12, 15, 19, 6557}"
185,1,295,0,0.2404441,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \left(d+e \log \left(f x^r\right)\right)}{x^4} \, dx","Int[((a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/x^4,x]","-\frac{3^{-p-1} e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{x^3}-\frac{e 3^{-p-2} r e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,\frac{3 a}{b n}+\frac{3 \log \left(c x^n\right)}{n}\right)}{x^3}+\frac{e 3^{-p-1} r e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{3 a}{b n}+\frac{3 \log \left(c x^n\right)}{n}\right)}{b n x^3}","-\frac{3^{-p-1} e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(d+e \log \left(f x^r\right)\right) \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{3 \left(a+b \log \left(c x^n\right)\right)}{b n}\right)}{x^3}-\frac{e 3^{-p-2} r e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(a+b \log \left(c x^n\right)\right)^p \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+2,\frac{3 a}{b n}+\frac{3 \log \left(c x^n\right)}{n}\right)}{x^3}+\frac{e 3^{-p-1} r e^{\frac{3 a}{b n}} \left(c x^n\right)^{3/n} \left(a+b \log \left(c x^n\right)\right)^{p+1} \left(\frac{a+b \log \left(c x^n\right)}{b n}\right)^{-p} \text{Gamma}\left(p+1,\frac{3 a}{b n}+\frac{3 \log \left(c x^n\right)}{n}\right)}{b n x^3}",1,"-((3^(-2 - p)*e*E^((3*a)/(b*n))*r*(c*x^n)^(3/n)*Gamma[2 + p, (3*a)/(b*n) + (3*Log[c*x^n])/n]*(a + b*Log[c*x^n])^p)/(x^3*((a + b*Log[c*x^n])/(b*n))^p)) + (3^(-1 - p)*e*E^((3*a)/(b*n))*r*(c*x^n)^(3/n)*Gamma[1 + p, (3*a)/(b*n) + (3*Log[c*x^n])/n]*(a + b*Log[c*x^n])^(1 + p))/(b*n*x^3*((a + b*Log[c*x^n])/(b*n))^p) - (3^(-1 - p)*E^((3*a)/(b*n))*(c*x^n)^(3/n)*Gamma[1 + p, (3*(a + b*Log[c*x^n]))/(b*n)]*(a + b*Log[c*x^n])^p*(d + e*Log[f*x^r]))/(x^3*((a + b*Log[c*x^n])/(b*n))^p)","A",7,7,26,0.2692,1,"{2310, 2181, 2366, 12, 15, 19, 6557}"
186,1,246,0,0.2332455,"\int \left(d+e x^2\right) \sin ^{-1}(a x) \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcSin[a*x]*Log[c*x^n],x]","\frac{\sqrt{1-a^2 x^2} \left(3 a^2 d+e\right) \log \left(c x^n\right)}{3 a^3}-\frac{e \left(1-a^2 x^2\right)^{3/2} \log \left(c x^n\right)}{9 a^3}-\frac{n \sqrt{1-a^2 x^2} \left(3 a^2 d+e\right)}{3 a^3}+\frac{n \left(3 a^2 d+e\right) \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{3 a^3}-\frac{d n \sqrt{1-a^2 x^2}}{a}+\frac{2 e n \left(1-a^2 x^2\right)^{3/2}}{27 a^3}-\frac{e n \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{9 a^3}+d x \sin ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \sin ^{-1}(a x) \log \left(c x^n\right)-d n x \sin ^{-1}(a x)-\frac{1}{9} e n x^3 \sin ^{-1}(a x)","\frac{\sqrt{1-a^2 x^2} \left(3 a^2 d+e\right) \log \left(c x^n\right)}{3 a^3}-\frac{e \left(1-a^2 x^2\right)^{3/2} \log \left(c x^n\right)}{9 a^3}-\frac{n \sqrt{1-a^2 x^2} \left(3 a^2 d+e\right)}{3 a^3}+\frac{n \left(3 a^2 d+e\right) \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{3 a^3}-\frac{d n \sqrt{1-a^2 x^2}}{a}+\frac{2 e n \left(1-a^2 x^2\right)^{3/2}}{27 a^3}-\frac{e n \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{9 a^3}+d x \sin ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \sin ^{-1}(a x) \log \left(c x^n\right)-d n x \sin ^{-1}(a x)-\frac{1}{9} e n x^3 \sin ^{-1}(a x)",1,"-((d*n*Sqrt[1 - a^2*x^2])/a) - ((3*a^2*d + e)*n*Sqrt[1 - a^2*x^2])/(3*a^3) + (2*e*n*(1 - a^2*x^2)^(3/2))/(27*a^3) - d*n*x*ArcSin[a*x] - (e*n*x^3*ArcSin[a*x])/9 - (e*n*ArcTanh[Sqrt[1 - a^2*x^2]])/(9*a^3) + ((3*a^2*d + e)*n*ArcTanh[Sqrt[1 - a^2*x^2]])/(3*a^3) + ((3*a^2*d + e)*Sqrt[1 - a^2*x^2]*Log[c*x^n])/(3*a^3) - (e*(1 - a^2*x^2)^(3/2)*Log[c*x^n])/(9*a^3) + d*x*ArcSin[a*x]*Log[c*x^n] + (e*x^3*ArcSin[a*x]*Log[c*x^n])/3","A",17,11,18,0.6111,1,"{4665, 444, 43, 2387, 266, 50, 63, 208, 4619, 261, 4627}"
187,1,245,0,0.2273441,"\int \left(d+e x^2\right) \cos ^{-1}(a x) \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcCos[a*x]*Log[c*x^n],x]","-\frac{\sqrt{1-a^2 x^2} \left(3 a^2 d+e\right) \log \left(c x^n\right)}{3 a^3}+\frac{e \left(1-a^2 x^2\right)^{3/2} \log \left(c x^n\right)}{9 a^3}+\frac{n \sqrt{1-a^2 x^2} \left(3 a^2 d+e\right)}{3 a^3}-\frac{n \left(3 a^2 d+e\right) \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{3 a^3}+\frac{d n \sqrt{1-a^2 x^2}}{a}-\frac{2 e n \left(1-a^2 x^2\right)^{3/2}}{27 a^3}+\frac{e n \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{9 a^3}+d x \cos ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \cos ^{-1}(a x) \log \left(c x^n\right)-d n x \cos ^{-1}(a x)-\frac{1}{9} e n x^3 \cos ^{-1}(a x)","-\frac{\sqrt{1-a^2 x^2} \left(3 a^2 d+e\right) \log \left(c x^n\right)}{3 a^3}+\frac{e \left(1-a^2 x^2\right)^{3/2} \log \left(c x^n\right)}{9 a^3}+\frac{n \sqrt{1-a^2 x^2} \left(3 a^2 d+e\right)}{3 a^3}-\frac{n \left(3 a^2 d+e\right) \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{3 a^3}+\frac{d n \sqrt{1-a^2 x^2}}{a}-\frac{2 e n \left(1-a^2 x^2\right)^{3/2}}{27 a^3}+\frac{e n \tanh ^{-1}\left(\sqrt{1-a^2 x^2}\right)}{9 a^3}+d x \cos ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \cos ^{-1}(a x) \log \left(c x^n\right)-d n x \cos ^{-1}(a x)-\frac{1}{9} e n x^3 \cos ^{-1}(a x)",1,"(d*n*Sqrt[1 - a^2*x^2])/a + ((3*a^2*d + e)*n*Sqrt[1 - a^2*x^2])/(3*a^3) - (2*e*n*(1 - a^2*x^2)^(3/2))/(27*a^3) - d*n*x*ArcCos[a*x] - (e*n*x^3*ArcCos[a*x])/9 + (e*n*ArcTanh[Sqrt[1 - a^2*x^2]])/(9*a^3) - ((3*a^2*d + e)*n*ArcTanh[Sqrt[1 - a^2*x^2]])/(3*a^3) - ((3*a^2*d + e)*Sqrt[1 - a^2*x^2]*Log[c*x^n])/(3*a^3) + (e*(1 - a^2*x^2)^(3/2)*Log[c*x^n])/(9*a^3) + d*x*ArcCos[a*x]*Log[c*x^n] + (e*x^3*ArcCos[a*x]*Log[c*x^n])/3","A",17,11,18,0.6111,1,"{4666, 444, 43, 2387, 266, 50, 63, 208, 4620, 261, 4628}"
188,1,182,0,0.1644465,"\int \left(d+e x^2\right) \tan ^{-1}(a x) \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcTan[a*x]*Log[c*x^n],x]","-\frac{n \left(3 a^2 d-e\right) \text{PolyLog}\left(2,-a^2 x^2\right)}{12 a^3}-\frac{\left(3 a^2 d-e\right) \log \left(a^2 x^2+1\right) \log \left(c x^n\right)}{6 a^3}+\frac{d n \log \left(a^2 x^2+1\right)}{2 a}-\frac{e n \log \left(a^2 x^2+1\right)}{18 a^3}+d x \tan ^{-1}(a x) \log \left(c x^n\right)-\frac{e x^2 \log \left(c x^n\right)}{6 a}+\frac{1}{3} e x^3 \tan ^{-1}(a x) \log \left(c x^n\right)-d n x \tan ^{-1}(a x)+\frac{5 e n x^2}{36 a}-\frac{1}{9} e n x^3 \tan ^{-1}(a x)","-\frac{n \left(3 a^2 d-e\right) \text{PolyLog}\left(2,-a^2 x^2\right)}{12 a^3}-\frac{\left(3 a^2 d-e\right) \log \left(a^2 x^2+1\right) \log \left(c x^n\right)}{6 a^3}+\frac{d n \log \left(a^2 x^2+1\right)}{2 a}-\frac{e n \log \left(a^2 x^2+1\right)}{18 a^3}+d x \tan ^{-1}(a x) \log \left(c x^n\right)-\frac{e x^2 \log \left(c x^n\right)}{6 a}+\frac{1}{3} e x^3 \tan ^{-1}(a x) \log \left(c x^n\right)-d n x \tan ^{-1}(a x)+\frac{5 e n x^2}{36 a}-\frac{1}{9} e n x^3 \tan ^{-1}(a x)",1,"(5*e*n*x^2)/(36*a) - d*n*x*ArcTan[a*x] - (e*n*x^3*ArcTan[a*x])/9 - (e*x^2*Log[c*x^n])/(6*a) + d*x*ArcTan[a*x]*Log[c*x^n] + (e*x^3*ArcTan[a*x]*Log[c*x^n])/3 + (d*n*Log[1 + a^2*x^2])/(2*a) - (e*n*Log[1 + a^2*x^2])/(18*a^3) - ((3*a^2*d - e)*Log[c*x^n]*Log[1 + a^2*x^2])/(6*a^3) - ((3*a^2*d - e)*n*PolyLog[2, -(a^2*x^2)])/(12*a^3)","A",9,10,18,0.5556,1,"{4912, 1593, 444, 43, 2388, 4846, 260, 4852, 266, 2391}"
189,1,182,0,0.1478883,"\int \left(d+e x^2\right) \cot ^{-1}(a x) \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcCot[a*x]*Log[c*x^n],x]","\frac{n \left(3 a^2 d-e\right) \text{PolyLog}\left(2,-a^2 x^2\right)}{12 a^3}+\frac{\left(3 a^2 d-e\right) \log \left(a^2 x^2+1\right) \log \left(c x^n\right)}{6 a^3}-\frac{d n \log \left(a^2 x^2+1\right)}{2 a}+\frac{e n \log \left(a^2 x^2+1\right)}{18 a^3}+d x \cot ^{-1}(a x) \log \left(c x^n\right)+\frac{e x^2 \log \left(c x^n\right)}{6 a}+\frac{1}{3} e x^3 \cot ^{-1}(a x) \log \left(c x^n\right)-d n x \cot ^{-1}(a x)-\frac{5 e n x^2}{36 a}-\frac{1}{9} e n x^3 \cot ^{-1}(a x)","\frac{n \left(3 a^2 d-e\right) \text{PolyLog}\left(2,-a^2 x^2\right)}{12 a^3}+\frac{\left(3 a^2 d-e\right) \log \left(a^2 x^2+1\right) \log \left(c x^n\right)}{6 a^3}-\frac{d n \log \left(a^2 x^2+1\right)}{2 a}+\frac{e n \log \left(a^2 x^2+1\right)}{18 a^3}+d x \cot ^{-1}(a x) \log \left(c x^n\right)+\frac{e x^2 \log \left(c x^n\right)}{6 a}+\frac{1}{3} e x^3 \cot ^{-1}(a x) \log \left(c x^n\right)-d n x \cot ^{-1}(a x)-\frac{5 e n x^2}{36 a}-\frac{1}{9} e n x^3 \cot ^{-1}(a x)",1,"(-5*e*n*x^2)/(36*a) - d*n*x*ArcCot[a*x] - (e*n*x^3*ArcCot[a*x])/9 + (e*x^2*Log[c*x^n])/(6*a) + d*x*ArcCot[a*x]*Log[c*x^n] + (e*x^3*ArcCot[a*x]*Log[c*x^n])/3 - (d*n*Log[1 + a^2*x^2])/(2*a) + (e*n*Log[1 + a^2*x^2])/(18*a^3) + ((3*a^2*d - e)*Log[c*x^n]*Log[1 + a^2*x^2])/(6*a^3) + ((3*a^2*d - e)*n*PolyLog[2, -(a^2*x^2)])/(12*a^3)","A",9,10,18,0.5556,1,"{4913, 1593, 444, 43, 2388, 4847, 260, 4853, 266, 2391}"
190,1,244,0,0.2185696,"\int \left(d+e x^2\right) \sinh ^{-1}(a x) \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcSinh[a*x]*Log[c*x^n],x]","-\frac{\sqrt{a^2 x^2+1} \left(3 a^2 d-e\right) \log \left(c x^n\right)}{3 a^3}-\frac{e \left(a^2 x^2+1\right)^{3/2} \log \left(c x^n\right)}{9 a^3}+\frac{n \sqrt{a^2 x^2+1} \left(3 a^2 d-e\right)}{3 a^3}-\frac{n \left(3 a^2 d-e\right) \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)}{3 a^3}+\frac{d n \sqrt{a^2 x^2+1}}{a}+\frac{2 e n \left(a^2 x^2+1\right)^{3/2}}{27 a^3}-\frac{e n \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)}{9 a^3}+d x \sinh ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \sinh ^{-1}(a x) \log \left(c x^n\right)-d n x \sinh ^{-1}(a x)-\frac{1}{9} e n x^3 \sinh ^{-1}(a x)","-\frac{\sqrt{a^2 x^2+1} \left(3 a^2 d-e\right) \log \left(c x^n\right)}{3 a^3}-\frac{e \left(a^2 x^2+1\right)^{3/2} \log \left(c x^n\right)}{9 a^3}+\frac{n \sqrt{a^2 x^2+1} \left(3 a^2 d-e\right)}{3 a^3}-\frac{n \left(3 a^2 d-e\right) \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)}{3 a^3}+\frac{d n \sqrt{a^2 x^2+1}}{a}+\frac{2 e n \left(a^2 x^2+1\right)^{3/2}}{27 a^3}-\frac{e n \tanh ^{-1}\left(\sqrt{a^2 x^2+1}\right)}{9 a^3}+d x \sinh ^{-1}(a x) \log \left(c x^n\right)+\frac{1}{3} e x^3 \sinh ^{-1}(a x) \log \left(c x^n\right)-d n x \sinh ^{-1}(a x)-\frac{1}{9} e n x^3 \sinh ^{-1}(a x)",1,"(d*n*Sqrt[1 + a^2*x^2])/a + ((3*a^2*d - e)*n*Sqrt[1 + a^2*x^2])/(3*a^3) + (2*e*n*(1 + a^2*x^2)^(3/2))/(27*a^3) - d*n*x*ArcSinh[a*x] - (e*n*x^3*ArcSinh[a*x])/9 - ((3*a^2*d - e)*n*ArcTanh[Sqrt[1 + a^2*x^2]])/(3*a^3) - (e*n*ArcTanh[Sqrt[1 + a^2*x^2]])/(9*a^3) - ((3*a^2*d - e)*Sqrt[1 + a^2*x^2]*Log[c*x^n])/(3*a^3) - (e*(1 + a^2*x^2)^(3/2)*Log[c*x^n])/(9*a^3) + d*x*ArcSinh[a*x]*Log[c*x^n] + (e*x^3*ArcSinh[a*x]*Log[c*x^n])/3","A",17,11,18,0.6111,1,"{5704, 444, 43, 2387, 266, 50, 63, 208, 5653, 261, 5661}"
191,1,312,0,0.2103023,"\int \left(d+e x^2\right) \cosh ^{-1}(a x) \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcCosh[a*x]*Log[c*x^n],x]","-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 d+2 e\right) \log \left(c x^n\right)}{9 a^3}+\frac{n \sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 d+2 e\right)}{9 a^3}-\frac{n \left(9 a^2 d+2 e\right) \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)}{9 a^3}+\frac{e n (a x-1)^{3/2} (a x+1)^{3/2}}{27 a^3}+\frac{2 e n \sqrt{a x-1} \sqrt{a x+1}}{27 a^3}+d x \cosh ^{-1}(a x) \log \left(c x^n\right)-\frac{e x^2 \sqrt{a x-1} \sqrt{a x+1} \log \left(c x^n\right)}{9 a}+\frac{1}{3} e x^3 \cosh ^{-1}(a x) \log \left(c x^n\right)+\frac{d n \sqrt{a x-1} \sqrt{a x+1}}{a}-d n x \cosh ^{-1}(a x)+\frac{e n x^2 \sqrt{a x-1} \sqrt{a x+1}}{27 a}-\frac{1}{9} e n x^3 \cosh ^{-1}(a x)","-\frac{\sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 d+2 e\right) \log \left(c x^n\right)}{9 a^3}+\frac{n \sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 d+2 e\right)}{9 a^3}-\frac{n \left(9 a^2 d+2 e\right) \tan ^{-1}\left(\sqrt{a x-1} \sqrt{a x+1}\right)}{9 a^3}+\frac{e n (a x-1)^{3/2} (a x+1)^{3/2}}{27 a^3}+\frac{2 e n \sqrt{a x-1} \sqrt{a x+1}}{27 a^3}+d x \cosh ^{-1}(a x) \log \left(c x^n\right)-\frac{e x^2 \sqrt{a x-1} \sqrt{a x+1} \log \left(c x^n\right)}{9 a}+\frac{1}{3} e x^3 \cosh ^{-1}(a x) \log \left(c x^n\right)+\frac{d n \sqrt{a x-1} \sqrt{a x+1}}{a}-d n x \cosh ^{-1}(a x)+\frac{e n x^2 \sqrt{a x-1} \sqrt{a x+1}}{27 a}-\frac{1}{9} e n x^3 \cosh ^{-1}(a x)",1,"(d*n*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/a + (2*e*n*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(27*a^3) + ((9*a^2*d + 2*e)*n*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(9*a^3) + (e*n*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x])/(27*a) + (e*n*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2))/(27*a^3) - d*n*x*ArcCosh[a*x] - (e*n*x^3*ArcCosh[a*x])/9 - ((9*a^2*d + 2*e)*n*ArcTan[Sqrt[-1 + a*x]*Sqrt[1 + a*x]])/(9*a^3) - ((9*a^2*d + 2*e)*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Log[c*x^n])/(9*a^3) - (e*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*Log[c*x^n])/(9*a) + d*x*ArcCosh[a*x]*Log[c*x^n] + (e*x^3*ArcCosh[a*x]*Log[c*x^n])/3","A",12,11,18,0.6111,1,"{5705, 460, 74, 2387, 101, 92, 205, 5654, 5662, 100, 12}"
192,1,180,0,0.1624286,"\int \left(d+e x^2\right) \tanh ^{-1}(a x) \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcTanh[a*x]*Log[c*x^n],x]","\frac{n \left(3 a^2 d+e\right) \text{PolyLog}\left(2,a^2 x^2\right)}{12 a^3}+\frac{\left(3 a^2 d+e\right) \log \left(1-a^2 x^2\right) \log \left(c x^n\right)}{6 a^3}-\frac{d n \log \left(1-a^2 x^2\right)}{2 a}-\frac{e n \log \left(1-a^2 x^2\right)}{18 a^3}+d x \tanh ^{-1}(a x) \log \left(c x^n\right)+\frac{e x^2 \log \left(c x^n\right)}{6 a}+\frac{1}{3} e x^3 \tanh ^{-1}(a x) \log \left(c x^n\right)-d n x \tanh ^{-1}(a x)-\frac{5 e n x^2}{36 a}-\frac{1}{9} e n x^3 \tanh ^{-1}(a x)","\frac{n \left(3 a^2 d+e\right) \text{PolyLog}\left(2,a^2 x^2\right)}{12 a^3}+\frac{\left(3 a^2 d+e\right) \log \left(1-a^2 x^2\right) \log \left(c x^n\right)}{6 a^3}-\frac{d n \log \left(1-a^2 x^2\right)}{2 a}-\frac{e n \log \left(1-a^2 x^2\right)}{18 a^3}+d x \tanh ^{-1}(a x) \log \left(c x^n\right)+\frac{e x^2 \log \left(c x^n\right)}{6 a}+\frac{1}{3} e x^3 \tanh ^{-1}(a x) \log \left(c x^n\right)-d n x \tanh ^{-1}(a x)-\frac{5 e n x^2}{36 a}-\frac{1}{9} e n x^3 \tanh ^{-1}(a x)",1,"(-5*e*n*x^2)/(36*a) - d*n*x*ArcTanh[a*x] - (e*n*x^3*ArcTanh[a*x])/9 + (e*x^2*Log[c*x^n])/(6*a) + d*x*ArcTanh[a*x]*Log[c*x^n] + (e*x^3*ArcTanh[a*x]*Log[c*x^n])/3 - (d*n*Log[1 - a^2*x^2])/(2*a) - (e*n*Log[1 - a^2*x^2])/(18*a^3) + ((3*a^2*d + e)*Log[c*x^n]*Log[1 - a^2*x^2])/(6*a^3) + ((3*a^2*d + e)*n*PolyLog[2, a^2*x^2])/(12*a^3)","A",9,10,18,0.5556,1,"{5976, 1593, 444, 43, 2388, 5910, 260, 5916, 266, 2391}"
193,1,180,0,0.1561828,"\int \left(d+e x^2\right) \coth ^{-1}(a x) \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcCoth[a*x]*Log[c*x^n],x]","\frac{n \left(3 a^2 d+e\right) \text{PolyLog}\left(2,a^2 x^2\right)}{12 a^3}+\frac{\left(3 a^2 d+e\right) \log \left(1-a^2 x^2\right) \log \left(c x^n\right)}{6 a^3}-\frac{d n \log \left(1-a^2 x^2\right)}{2 a}-\frac{e n \log \left(1-a^2 x^2\right)}{18 a^3}+d x \coth ^{-1}(a x) \log \left(c x^n\right)+\frac{e x^2 \log \left(c x^n\right)}{6 a}+\frac{1}{3} e x^3 \coth ^{-1}(a x) \log \left(c x^n\right)-d n x \coth ^{-1}(a x)-\frac{5 e n x^2}{36 a}-\frac{1}{9} e n x^3 \coth ^{-1}(a x)","\frac{n \left(3 a^2 d+e\right) \text{PolyLog}\left(2,a^2 x^2\right)}{12 a^3}+\frac{\left(3 a^2 d+e\right) \log \left(1-a^2 x^2\right) \log \left(c x^n\right)}{6 a^3}-\frac{d n \log \left(1-a^2 x^2\right)}{2 a}-\frac{e n \log \left(1-a^2 x^2\right)}{18 a^3}+d x \coth ^{-1}(a x) \log \left(c x^n\right)+\frac{e x^2 \log \left(c x^n\right)}{6 a}+\frac{1}{3} e x^3 \coth ^{-1}(a x) \log \left(c x^n\right)-d n x \coth ^{-1}(a x)-\frac{5 e n x^2}{36 a}-\frac{1}{9} e n x^3 \coth ^{-1}(a x)",1,"(-5*e*n*x^2)/(36*a) - d*n*x*ArcCoth[a*x] - (e*n*x^3*ArcCoth[a*x])/9 + (e*x^2*Log[c*x^n])/(6*a) + d*x*ArcCoth[a*x]*Log[c*x^n] + (e*x^3*ArcCoth[a*x]*Log[c*x^n])/3 - (d*n*Log[1 - a^2*x^2])/(2*a) - (e*n*Log[1 - a^2*x^2])/(18*a^3) + ((3*a^2*d + e)*Log[c*x^n]*Log[1 - a^2*x^2])/(6*a^3) + ((3*a^2*d + e)*n*PolyLog[2, a^2*x^2])/(12*a^3)","A",9,10,18,0.5556,1,"{5977, 1593, 444, 43, 2388, 5911, 260, 5917, 266, 2391}"
194,1,482,0,0.7344418,"\int \left(d+e x^2\right) \sin ^{-1}(a x)^2 \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcSin[a*x]^2*Log[c*x^n],x]","-\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)}{9 a^3}+\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)}{9 a^3}+\frac{2 d \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)}{a}-\frac{4 e x \log \left(c x^n\right)}{9 a^2}+\frac{2 e x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)}{9 a}+\frac{4 e \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}-\frac{2 n \sqrt{1-a^2 x^2} \left(9 a^2 d+2 e\right) \sin ^{-1}(a x)}{9 a^3}+\frac{4}{9} n x \left(\frac{2 e}{a^2}+9 d\right)+\frac{4 n \left(9 a^2 d+2 e\right) \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{9 a^3}-\frac{2 d n \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{a}-\frac{2 e n x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a}+\frac{2 e n \left(1-a^2 x^2\right)^{3/2} \sin ^{-1}(a x)}{27 a^3}-\frac{4 e n \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a^3}+\frac{2 e n x}{27 a^2}+d x \sin ^{-1}(a x)^2 \log \left(c x^n\right)+\frac{1}{3} e x^3 \sin ^{-1}(a x)^2 \log \left(c x^n\right)-d n x \sin ^{-1}(a x)^2-\frac{1}{9} e n x^3 \sin ^{-1}(a x)^2-2 d x \log \left(c x^n\right)-\frac{2}{27} e x^3 \log \left(c x^n\right)+2 d n x+\frac{2}{27} e n x^3","-\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,-e^{i \sin ^{-1}(a x)}\right)}{9 a^3}+\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,e^{i \sin ^{-1}(a x)}\right)}{9 a^3}+\frac{2 d \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)}{a}-\frac{4 e x \log \left(c x^n\right)}{9 a^2}+\frac{2 e x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)}{9 a}+\frac{4 e \sqrt{1-a^2 x^2} \sin ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}-\frac{2 n \sqrt{1-a^2 x^2} \left(9 a^2 d+2 e\right) \sin ^{-1}(a x)}{9 a^3}+\frac{4}{9} n x \left(\frac{2 e}{a^2}+9 d\right)+\frac{4 n \left(9 a^2 d+2 e\right) \sin ^{-1}(a x) \tanh ^{-1}\left(e^{i \sin ^{-1}(a x)}\right)}{9 a^3}-\frac{2 d n \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{a}-\frac{2 e n x^2 \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a}+\frac{2 e n \left(1-a^2 x^2\right)^{3/2} \sin ^{-1}(a x)}{27 a^3}-\frac{4 e n \sqrt{1-a^2 x^2} \sin ^{-1}(a x)}{27 a^3}+\frac{2 e n x}{27 a^2}+d x \sin ^{-1}(a x)^2 \log \left(c x^n\right)+\frac{1}{3} e x^3 \sin ^{-1}(a x)^2 \log \left(c x^n\right)-d n x \sin ^{-1}(a x)^2-\frac{1}{9} e n x^3 \sin ^{-1}(a x)^2-2 d x \log \left(c x^n\right)-\frac{2}{27} e x^3 \log \left(c x^n\right)+2 d n x+\frac{2}{27} e n x^3",1,"2*d*n*x + (2*e*n*x)/(27*a^2) + (4*(9*d + (2*e)/a^2)*n*x)/9 + (2*e*n*x^3)/27 - (2*d*n*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/a - (4*e*n*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(27*a^3) - (2*(9*a^2*d + 2*e)*n*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(9*a^3) - (2*e*n*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x])/(27*a) + (2*e*n*(1 - a^2*x^2)^(3/2)*ArcSin[a*x])/(27*a^3) - d*n*x*ArcSin[a*x]^2 - (e*n*x^3*ArcSin[a*x]^2)/9 + (4*(9*a^2*d + 2*e)*n*ArcSin[a*x]*ArcTanh[E^(I*ArcSin[a*x])])/(9*a^3) - 2*d*x*Log[c*x^n] - (4*e*x*Log[c*x^n])/(9*a^2) - (2*e*x^3*Log[c*x^n])/27 + (2*d*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*Log[c*x^n])/a + (4*e*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*Log[c*x^n])/(9*a^3) + (2*e*x^2*Sqrt[1 - a^2*x^2]*ArcSin[a*x]*Log[c*x^n])/(9*a) + d*x*ArcSin[a*x]^2*Log[c*x^n] + (e*x^3*ArcSin[a*x]^2*Log[c*x^n])/3 - (((2*I)/9)*(9*a^2*d + 2*e)*n*PolyLog[2, -E^(I*ArcSin[a*x])])/a^3 + (((2*I)/9)*(9*a^2*d + 2*e)*n*PolyLog[2, E^(I*ArcSin[a*x])])/a^3","A",21,14,20,0.7000,1,"{4667, 4619, 4677, 8, 4627, 4707, 30, 2387, 6, 4697, 4709, 4183, 2279, 2391}"
195,1,490,0,0.7023396,"\int \left(d+e x^2\right) \cos ^{-1}(a x)^2 \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcCos[a*x]^2*Log[c*x^n],x]","-\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)}{9 a^3}+\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)}{9 a^3}-\frac{2 d \sqrt{1-a^2 x^2} \cos ^{-1}(a x) \log \left(c x^n\right)}{a}-\frac{4 e x \log \left(c x^n\right)}{9 a^2}-\frac{2 e x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x) \log \left(c x^n\right)}{9 a}-\frac{4 e \sqrt{1-a^2 x^2} \cos ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}+\frac{2 n \sqrt{1-a^2 x^2} \left(9 a^2 d+2 e\right) \cos ^{-1}(a x)}{9 a^3}+\frac{4}{9} n x \left(\frac{2 e}{a^2}+9 d\right)+\frac{4 i n \left(9 a^2 d+2 e\right) \cos ^{-1}(a x) \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)}{9 a^3}+\frac{2 d n \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{a}+\frac{2 e n x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{27 a}-\frac{2 e n \left(1-a^2 x^2\right)^{3/2} \cos ^{-1}(a x)}{27 a^3}+\frac{4 e n \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{27 a^3}+\frac{2 e n x}{27 a^2}+d x \cos ^{-1}(a x)^2 \log \left(c x^n\right)+\frac{1}{3} e x^3 \cos ^{-1}(a x)^2 \log \left(c x^n\right)-d n x \cos ^{-1}(a x)^2-\frac{1}{9} e n x^3 \cos ^{-1}(a x)^2-2 d x \log \left(c x^n\right)-\frac{2}{27} e x^3 \log \left(c x^n\right)+2 d n x+\frac{2}{27} e n x^3","-\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,-i e^{i \cos ^{-1}(a x)}\right)}{9 a^3}+\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,i e^{i \cos ^{-1}(a x)}\right)}{9 a^3}-\frac{2 d \sqrt{1-a^2 x^2} \cos ^{-1}(a x) \log \left(c x^n\right)}{a}-\frac{4 e x \log \left(c x^n\right)}{9 a^2}-\frac{2 e x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x) \log \left(c x^n\right)}{9 a}-\frac{4 e \sqrt{1-a^2 x^2} \cos ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}+\frac{2 n \sqrt{1-a^2 x^2} \left(9 a^2 d+2 e\right) \cos ^{-1}(a x)}{9 a^3}+\frac{4}{9} n x \left(\frac{2 e}{a^2}+9 d\right)+\frac{4 i n \left(9 a^2 d+2 e\right) \cos ^{-1}(a x) \tan ^{-1}\left(e^{i \cos ^{-1}(a x)}\right)}{9 a^3}+\frac{2 d n \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{a}+\frac{2 e n x^2 \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{27 a}-\frac{2 e n \left(1-a^2 x^2\right)^{3/2} \cos ^{-1}(a x)}{27 a^3}+\frac{4 e n \sqrt{1-a^2 x^2} \cos ^{-1}(a x)}{27 a^3}+\frac{2 e n x}{27 a^2}+d x \cos ^{-1}(a x)^2 \log \left(c x^n\right)+\frac{1}{3} e x^3 \cos ^{-1}(a x)^2 \log \left(c x^n\right)-d n x \cos ^{-1}(a x)^2-\frac{1}{9} e n x^3 \cos ^{-1}(a x)^2-2 d x \log \left(c x^n\right)-\frac{2}{27} e x^3 \log \left(c x^n\right)+2 d n x+\frac{2}{27} e n x^3",1,"2*d*n*x + (2*e*n*x)/(27*a^2) + (4*(9*d + (2*e)/a^2)*n*x)/9 + (2*e*n*x^3)/27 + (2*d*n*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/a + (4*e*n*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(27*a^3) + (2*(9*a^2*d + 2*e)*n*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(9*a^3) + (2*e*n*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x])/(27*a) - (2*e*n*(1 - a^2*x^2)^(3/2)*ArcCos[a*x])/(27*a^3) - d*n*x*ArcCos[a*x]^2 - (e*n*x^3*ArcCos[a*x]^2)/9 + (((4*I)/9)*(9*a^2*d + 2*e)*n*ArcCos[a*x]*ArcTan[E^(I*ArcCos[a*x])])/a^3 - 2*d*x*Log[c*x^n] - (4*e*x*Log[c*x^n])/(9*a^2) - (2*e*x^3*Log[c*x^n])/27 - (2*d*Sqrt[1 - a^2*x^2]*ArcCos[a*x]*Log[c*x^n])/a - (4*e*Sqrt[1 - a^2*x^2]*ArcCos[a*x]*Log[c*x^n])/(9*a^3) - (2*e*x^2*Sqrt[1 - a^2*x^2]*ArcCos[a*x]*Log[c*x^n])/(9*a) + d*x*ArcCos[a*x]^2*Log[c*x^n] + (e*x^3*ArcCos[a*x]^2*Log[c*x^n])/3 - (((2*I)/9)*(9*a^2*d + 2*e)*n*PolyLog[2, (-I)*E^(I*ArcCos[a*x])])/a^3 + (((2*I)/9)*(9*a^2*d + 2*e)*n*PolyLog[2, I*E^(I*ArcCos[a*x])])/a^3","A",21,14,20,0.7000,1,"{4668, 4620, 4678, 8, 4628, 4708, 30, 2387, 6, 4698, 4710, 4181, 2279, 2391}"
196,1,458,0,0.7020169,"\int \left(d+e x^2\right) \sinh ^{-1}(a x)^2 \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcSinh[a*x]^2*Log[c*x^n],x]","-\frac{2 n \left(9 a^2 d-2 e\right) \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)}{9 a^3}+\frac{2 n \left(9 a^2 d-2 e\right) \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)}{9 a^3}-\frac{2 d \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \log \left(c x^n\right)}{a}-\frac{4 e x \log \left(c x^n\right)}{9 a^2}-\frac{2 e x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \log \left(c x^n\right)}{9 a}+\frac{4 e \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}+\frac{2 n \sqrt{a^2 x^2+1} \left(9 a^2 d-2 e\right) \sinh ^{-1}(a x)}{9 a^3}-\frac{4}{9} n x \left(9 d-\frac{2 e}{a^2}\right)-\frac{4 n \left(9 a^2 d-2 e\right) \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{9 a^3}+\frac{2 d n \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a}+\frac{2 e n x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a}+\frac{2 e n \left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)}{27 a^3}-\frac{4 e n \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a^3}+\frac{2 e n x}{27 a^2}+d x \sinh ^{-1}(a x)^2 \log \left(c x^n\right)+\frac{1}{3} e x^3 \sinh ^{-1}(a x)^2 \log \left(c x^n\right)-d n x \sinh ^{-1}(a x)^2-\frac{1}{9} e n x^3 \sinh ^{-1}(a x)^2+2 d x \log \left(c x^n\right)+\frac{2}{27} e x^3 \log \left(c x^n\right)-2 d n x-\frac{2}{27} e n x^3","-\frac{2 n \left(9 a^2 d-2 e\right) \text{PolyLog}\left(2,-e^{\sinh ^{-1}(a x)}\right)}{9 a^3}+\frac{2 n \left(9 a^2 d-2 e\right) \text{PolyLog}\left(2,e^{\sinh ^{-1}(a x)}\right)}{9 a^3}-\frac{2 d \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \log \left(c x^n\right)}{a}-\frac{4 e x \log \left(c x^n\right)}{9 a^2}-\frac{2 e x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \log \left(c x^n\right)}{9 a}+\frac{4 e \sqrt{a^2 x^2+1} \sinh ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}+\frac{2 n \sqrt{a^2 x^2+1} \left(9 a^2 d-2 e\right) \sinh ^{-1}(a x)}{9 a^3}-\frac{4}{9} n x \left(9 d-\frac{2 e}{a^2}\right)-\frac{4 n \left(9 a^2 d-2 e\right) \sinh ^{-1}(a x) \tanh ^{-1}\left(e^{\sinh ^{-1}(a x)}\right)}{9 a^3}+\frac{2 d n \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{a}+\frac{2 e n x^2 \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a}+\frac{2 e n \left(a^2 x^2+1\right)^{3/2} \sinh ^{-1}(a x)}{27 a^3}-\frac{4 e n \sqrt{a^2 x^2+1} \sinh ^{-1}(a x)}{27 a^3}+\frac{2 e n x}{27 a^2}+d x \sinh ^{-1}(a x)^2 \log \left(c x^n\right)+\frac{1}{3} e x^3 \sinh ^{-1}(a x)^2 \log \left(c x^n\right)-d n x \sinh ^{-1}(a x)^2-\frac{1}{9} e n x^3 \sinh ^{-1}(a x)^2+2 d x \log \left(c x^n\right)+\frac{2}{27} e x^3 \log \left(c x^n\right)-2 d n x-\frac{2}{27} e n x^3",1,"-2*d*n*x + (2*e*n*x)/(27*a^2) - (4*(9*d - (2*e)/a^2)*n*x)/9 - (2*e*n*x^3)/27 + (2*d*n*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/a + (2*(9*a^2*d - 2*e)*n*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(9*a^3) - (4*e*n*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(27*a^3) + (2*e*n*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x])/(27*a) + (2*e*n*(1 + a^2*x^2)^(3/2)*ArcSinh[a*x])/(27*a^3) - d*n*x*ArcSinh[a*x]^2 - (e*n*x^3*ArcSinh[a*x]^2)/9 - (4*(9*a^2*d - 2*e)*n*ArcSinh[a*x]*ArcTanh[E^ArcSinh[a*x]])/(9*a^3) + 2*d*x*Log[c*x^n] - (4*e*x*Log[c*x^n])/(9*a^2) + (2*e*x^3*Log[c*x^n])/27 - (2*d*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]*Log[c*x^n])/a + (4*e*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]*Log[c*x^n])/(9*a^3) - (2*e*x^2*Sqrt[1 + a^2*x^2]*ArcSinh[a*x]*Log[c*x^n])/(9*a) + d*x*ArcSinh[a*x]^2*Log[c*x^n] + (e*x^3*ArcSinh[a*x]^2*Log[c*x^n])/3 - (2*(9*a^2*d - 2*e)*n*PolyLog[2, -E^ArcSinh[a*x]])/(9*a^3) + (2*(9*a^2*d - 2*e)*n*PolyLog[2, E^ArcSinh[a*x]])/(9*a^3)","A",21,14,20,0.7000,1,"{5706, 5653, 5717, 8, 5661, 5758, 30, 2387, 6, 5742, 5760, 4182, 2279, 2391}"
197,1,508,0,1.5460642,"\int \left(d+e x^2\right) \cosh ^{-1}(a x)^2 \log \left(c x^n\right) \, dx","Int[(d + e*x^2)*ArcCosh[a*x]^2*Log[c*x^n],x]","\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{9 a^3}-\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{9 a^3}+\frac{4 e x \log \left(c x^n\right)}{9 a^2}-\frac{4 e \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}-\frac{4}{9} n x \left(\frac{2 e}{a^2}+9 d\right)+\frac{2 n \sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 d+2 e\right) \cosh ^{-1}(a x)}{9 a^3}-\frac{4 n \left(9 a^2 d+2 e\right) \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{9 a^3}-\frac{2 e n x}{27 a^2}+\frac{2 e n (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)}{27 a^3}+\frac{4 e n \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a^3}+d x \cosh ^{-1}(a x)^2 \log \left(c x^n\right)-\frac{2 d \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(c x^n\right)}{a}+\frac{1}{3} e x^3 \cosh ^{-1}(a x)^2 \log \left(c x^n\right)-\frac{2 e x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(c x^n\right)}{9 a}-d n x \cosh ^{-1}(a x)^2+\frac{2 d n \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{a}-\frac{1}{9} e n x^3 \cosh ^{-1}(a x)^2+\frac{2 e n x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a}+2 d x \log \left(c x^n\right)+\frac{2}{27} e x^3 \log \left(c x^n\right)-2 d n x-\frac{2}{27} e n x^3","\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,-i e^{\cosh ^{-1}(a x)}\right)}{9 a^3}-\frac{2 i n \left(9 a^2 d+2 e\right) \text{PolyLog}\left(2,i e^{\cosh ^{-1}(a x)}\right)}{9 a^3}+\frac{4 e x \log \left(c x^n\right)}{9 a^2}-\frac{4 e \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(c x^n\right)}{9 a^3}-\frac{4}{9} n x \left(\frac{2 e}{a^2}+9 d\right)+\frac{2 n \sqrt{a x-1} \sqrt{a x+1} \left(9 a^2 d+2 e\right) \cosh ^{-1}(a x)}{9 a^3}-\frac{4 n \left(9 a^2 d+2 e\right) \cosh ^{-1}(a x) \tan ^{-1}\left(e^{\cosh ^{-1}(a x)}\right)}{9 a^3}-\frac{2 e n x}{27 a^2}+\frac{2 e n (a x-1)^{3/2} (a x+1)^{3/2} \cosh ^{-1}(a x)}{27 a^3}+\frac{4 e n \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a^3}+d x \cosh ^{-1}(a x)^2 \log \left(c x^n\right)-\frac{2 d \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(c x^n\right)}{a}+\frac{1}{3} e x^3 \cosh ^{-1}(a x)^2 \log \left(c x^n\right)-\frac{2 e x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x) \log \left(c x^n\right)}{9 a}-d n x \cosh ^{-1}(a x)^2+\frac{2 d n \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{a}-\frac{1}{9} e n x^3 \cosh ^{-1}(a x)^2+\frac{2 e n x^2 \sqrt{a x-1} \sqrt{a x+1} \cosh ^{-1}(a x)}{27 a}+2 d x \log \left(c x^n\right)+\frac{2}{27} e x^3 \log \left(c x^n\right)-2 d n x-\frac{2}{27} e n x^3",1,"-2*d*n*x - (2*e*n*x)/(27*a^2) - (4*(9*d + (2*e)/a^2)*n*x)/9 - (2*e*n*x^3)/27 + (2*d*n*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/a + (4*e*n*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(27*a^3) + (2*(9*a^2*d + 2*e)*n*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(9*a^3) + (2*e*n*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x])/(27*a) + (2*e*n*(-1 + a*x)^(3/2)*(1 + a*x)^(3/2)*ArcCosh[a*x])/(27*a^3) - d*n*x*ArcCosh[a*x]^2 - (e*n*x^3*ArcCosh[a*x]^2)/9 - (4*(9*a^2*d + 2*e)*n*ArcCosh[a*x]*ArcTan[E^ArcCosh[a*x]])/(9*a^3) + 2*d*x*Log[c*x^n] + (4*e*x*Log[c*x^n])/(9*a^2) + (2*e*x^3*Log[c*x^n])/27 - (2*d*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*Log[c*x^n])/a - (4*e*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*Log[c*x^n])/(9*a^3) - (2*e*x^2*Sqrt[-1 + a*x]*Sqrt[1 + a*x]*ArcCosh[a*x]*Log[c*x^n])/(9*a) + d*x*ArcCosh[a*x]^2*Log[c*x^n] + (e*x^3*ArcCosh[a*x]^2*Log[c*x^n])/3 + (((2*I)/9)*(9*a^2*d + 2*e)*n*PolyLog[2, (-I)*E^ArcCosh[a*x]])/a^3 - (((2*I)/9)*(9*a^2*d + 2*e)*n*PolyLog[2, I*E^ArcCosh[a*x]])/a^3","A",21,14,20,0.7000,1,"{5707, 5654, 5718, 8, 5662, 5759, 30, 2387, 6, 5743, 5761, 4180, 2279, 2391}"
198,0,0,0,0.0331453,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \text{PolyLog}\left(k,e x^q\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^p*PolyLog[k, e*x^q])/x,x]","\int \frac{\left(a+b \log \left(c x^n\right)\right)^p \text{PolyLog}\left(k,e x^q\right)}{x} \, dx","\text{Int}\left(\frac{\text{PolyLog}\left(k,e x^q\right) \left(a+b \log \left(c x^n\right)\right)^p}{x},x\right)",0,"Defer[Int][((a + b*Log[c*x^n])^p*PolyLog[k, e*x^q])/x, x]","A",0,0,0,0,-1,"{}"
199,1,104,0,0.1120947,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^3 \text{PolyLog}\left(k,e x^q\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^3*PolyLog[k, e*x^q])/x,x]","\frac{6 b^2 n^2 \text{PolyLog}\left(k+3,e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{q^3}-\frac{3 b n \text{PolyLog}\left(k+2,e x^q\right) \left(a+b \log \left(c x^n\right)\right)^2}{q^2}+\frac{\text{PolyLog}\left(k+1,e x^q\right) \left(a+b \log \left(c x^n\right)\right)^3}{q}-\frac{6 b^3 n^3 \text{PolyLog}\left(k+4,e x^q\right)}{q^4}","\frac{6 b^2 n^2 \text{PolyLog}\left(k+3,e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{q^3}-\frac{3 b n \text{PolyLog}\left(k+2,e x^q\right) \left(a+b \log \left(c x^n\right)\right)^2}{q^2}+\frac{\text{PolyLog}\left(k+1,e x^q\right) \left(a+b \log \left(c x^n\right)\right)^3}{q}-\frac{6 b^3 n^3 \text{PolyLog}\left(k+4,e x^q\right)}{q^4}",1,"((a + b*Log[c*x^n])^3*PolyLog[1 + k, e*x^q])/q - (3*b*n*(a + b*Log[c*x^n])^2*PolyLog[2 + k, e*x^q])/q^2 + (6*b^2*n^2*(a + b*Log[c*x^n])*PolyLog[3 + k, e*x^q])/q^3 - (6*b^3*n^3*PolyLog[4 + k, e*x^q])/q^4","A",4,2,23,0.08696,1,"{2383, 6589}"
200,1,72,0,0.0693812,"\int \frac{\left(a+b \log \left(c x^n\right)\right)^2 \text{PolyLog}\left(k,e x^q\right)}{x} \, dx","Int[((a + b*Log[c*x^n])^2*PolyLog[k, e*x^q])/x,x]","-\frac{2 b n \text{PolyLog}\left(k+2,e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{q^2}+\frac{\text{PolyLog}\left(k+1,e x^q\right) \left(a+b \log \left(c x^n\right)\right)^2}{q}+\frac{2 b^2 n^2 \text{PolyLog}\left(k+3,e x^q\right)}{q^3}","-\frac{2 b n \text{PolyLog}\left(k+2,e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{q^2}+\frac{\text{PolyLog}\left(k+1,e x^q\right) \left(a+b \log \left(c x^n\right)\right)^2}{q}+\frac{2 b^2 n^2 \text{PolyLog}\left(k+3,e x^q\right)}{q^3}",1,"((a + b*Log[c*x^n])^2*PolyLog[1 + k, e*x^q])/q - (2*b*n*(a + b*Log[c*x^n])*PolyLog[2 + k, e*x^q])/q^2 + (2*b^2*n^2*PolyLog[3 + k, e*x^q])/q^3","A",3,2,23,0.08696,1,"{2383, 6589}"
201,1,40,0,0.0331271,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(k,e x^q\right)}{x} \, dx","Int[((a + b*Log[c*x^n])*PolyLog[k, e*x^q])/x,x]","\frac{\text{PolyLog}\left(k+1,e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{q}-\frac{b n \text{PolyLog}\left(k+2,e x^q\right)}{q^2}","\frac{\text{PolyLog}\left(k+1,e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{q}-\frac{b n \text{PolyLog}\left(k+2,e x^q\right)}{q^2}",1,"((a + b*Log[c*x^n])*PolyLog[1 + k, e*x^q])/q - (b*n*PolyLog[2 + k, e*x^q])/q^2","A",2,2,21,0.09524,1,"{2383, 6589}"
202,0,0,0,0.0320926,"\int \frac{\text{PolyLog}\left(k,e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","Int[PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])),x]","\int \frac{\text{PolyLog}\left(k,e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)} \, dx","\text{Int}\left(\frac{\text{PolyLog}\left(k,e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)},x\right)",0,"Defer[Int][PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])), x]","A",0,0,0,0,-1,"{}"
203,0,0,0,0.070842,"\int \frac{\text{PolyLog}\left(k,e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","Int[PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])^2),x]","\int \frac{\text{PolyLog}\left(k,e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)^2} \, dx","\frac{q \text{Int}\left(\frac{\text{PolyLog}\left(k-1,e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)},x\right)}{b n}-\frac{\text{PolyLog}\left(k,e x^q\right)}{b n \left(a+b \log \left(c x^n\right)\right)}",0,"-(PolyLog[k, e*x^q]/(b*n*(a + b*Log[c*x^n]))) + (q*Defer[Int][PolyLog[-1 + k, e*x^q]/(x*(a + b*Log[c*x^n])), x])/(b*n)","A",0,0,0,0,-1,"{}"
204,0,0,0,0.1115339,"\int \frac{\text{PolyLog}\left(k,e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)^3} \, dx","Int[PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])^3),x]","\int \frac{\text{PolyLog}\left(k,e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)^3} \, dx","\frac{q^2 \text{Int}\left(\frac{\text{PolyLog}\left(k-2,e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)},x\right)}{2 b^2 n^2}-\frac{q \text{PolyLog}\left(k-1,e x^q\right)}{2 b^2 n^2 \left(a+b \log \left(c x^n\right)\right)}-\frac{\text{PolyLog}\left(k,e x^q\right)}{2 b n \left(a+b \log \left(c x^n\right)\right)^2}",0,"-(q*PolyLog[-1 + k, e*x^q])/(2*b^2*n^2*(a + b*Log[c*x^n])) - PolyLog[k, e*x^q]/(2*b*n*(a + b*Log[c*x^n])^2) + (q^2*Defer[Int][PolyLog[-2 + k, e*x^q]/(x*(a + b*Log[c*x^n])), x])/(2*b^2*n^2)","A",0,0,0,0,-1,"{}"
205,1,20,0,0.0238397,"\int \frac{\log (x) \text{PolyLog}(n,a x)}{x} \, dx","Int[(Log[x]*PolyLog[n, a*x])/x,x]","\log (x) \text{PolyLog}(n+1,a x)-\text{PolyLog}(n+2,a x)","\log (x) \text{PolyLog}(n+1,a x)-\text{PolyLog}(n+2,a x)",1,"Log[x]*PolyLog[1 + n, a*x] - PolyLog[2 + n, a*x]","A",2,2,11,0.1818,1,"{2383, 6589}"
206,1,33,0,0.0443116,"\int \frac{\log ^2(x) \text{PolyLog}(n,a x)}{x} \, dx","Int[(Log[x]^2*PolyLog[n, a*x])/x,x]","2 \text{PolyLog}(n+3,a x)+\log ^2(x) \text{PolyLog}(n+1,a x)-2 \log (x) \text{PolyLog}(n+2,a x)","2 \text{PolyLog}(n+3,a x)+\log ^2(x) \text{PolyLog}(n+1,a x)-2 \log (x) \text{PolyLog}(n+2,a x)",1,"Log[x]^2*PolyLog[1 + n, a*x] - 2*Log[x]*PolyLog[2 + n, a*x] + 2*PolyLog[3 + n, a*x]","A",3,2,13,0.1538,1,"{2383, 6589}"
207,1,26,0,0.1098635,"\int \left(\frac{q \text{PolyLog}\left(-1+k,e x^q\right)}{b n x \left(a+b \log \left(c x^n\right)\right)}-\frac{\text{PolyLog}\left(k,e x^q\right)}{x \left(a+b \log \left(c x^n\right)\right)^2}\right) \, dx","Int[(q*PolyLog[-1 + k, e*x^q])/(b*n*x*(a + b*Log[c*x^n])) - PolyLog[k, e*x^q]/(x*(a + b*Log[c*x^n])^2),x]","\frac{\text{PolyLog}\left(k,e x^q\right)}{b n \left(a+b \log \left(c x^n\right)\right)}","\frac{\text{PolyLog}\left(k,e x^q\right)}{b n \left(a+b \log \left(c x^n\right)\right)}",1,"PolyLog[k, e*x^q]/(b*n*(a + b*Log[c*x^n]))","A",2,1,57,0.01754,1,"{2384}"
208,1,217,0,0.1809585,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(2,e x) \, dx","Int[x^2*(a + b*Log[c*x^n])*PolyLog[2, e*x],x]","\frac{1}{3} x^3 \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{PolyLog}(2,e x)}{9 e^3}-\frac{1}{9} b n x^3 \text{PolyLog}(2,e x)-\frac{x \left(a+b \log \left(c x^n\right)\right)}{9 e^2}-\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}+\frac{1}{9} x^3 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{18 e}-\frac{1}{27} x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{5 b n x}{27 e^2}+\frac{2 b n \log (1-e x)}{27 e^3}+\frac{7 b n x^2}{108 e}-\frac{2}{27} b n x^3 \log (1-e x)+\frac{1}{27} b n x^3","\frac{1}{3} x^3 \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{PolyLog}(2,e x)}{9 e^3}-\frac{1}{9} b n x^3 \text{PolyLog}(2,e x)-\frac{x \left(a+b \log \left(c x^n\right)\right)}{9 e^2}-\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{9 e^3}+\frac{1}{9} x^3 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{18 e}-\frac{1}{27} x^3 \left(a+b \log \left(c x^n\right)\right)+\frac{5 b n x}{27 e^2}+\frac{2 b n \log (1-e x)}{27 e^3}+\frac{7 b n x^2}{108 e}-\frac{2}{27} b n x^3 \log (1-e x)+\frac{1}{27} b n x^3",1,"(5*b*n*x)/(27*e^2) + (7*b*n*x^2)/(108*e) + (b*n*x^3)/27 - (x*(a + b*Log[c*x^n]))/(9*e^2) - (x^2*(a + b*Log[c*x^n]))/(18*e) - (x^3*(a + b*Log[c*x^n]))/27 + (2*b*n*Log[1 - e*x])/(27*e^3) - (2*b*n*x^3*Log[1 - e*x])/27 - ((a + b*Log[c*x^n])*Log[1 - e*x])/(9*e^3) + (x^3*(a + b*Log[c*x^n])*Log[1 - e*x])/9 - (b*n*PolyLog[2, e*x])/(9*e^3) - (b*n*x^3*PolyLog[2, e*x])/9 + (x^3*(a + b*Log[c*x^n])*PolyLog[2, e*x])/3","A",10,5,19,0.2632,1,"{2385, 2395, 43, 2376, 2391}"
209,1,185,0,0.1315463,"\int x \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(2,e x) \, dx","Int[x*(a + b*Log[c*x^n])*PolyLog[2, e*x],x]","\frac{1}{2} x^2 \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{PolyLog}(2,e x)}{4 e^2}-\frac{1}{4} b n x^2 \text{PolyLog}(2,e x)-\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}+\frac{1}{4} x^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{x \left(a+b \log \left(c x^n\right)\right)}{4 e}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{b n \log (1-e x)}{4 e^2}-\frac{1}{4} b n x^2 \log (1-e x)+\frac{b n x}{2 e}+\frac{3}{16} b n x^2","\frac{1}{2} x^2 \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)-\frac{b n \text{PolyLog}(2,e x)}{4 e^2}-\frac{1}{4} b n x^2 \text{PolyLog}(2,e x)-\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{4 e^2}+\frac{1}{4} x^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{x \left(a+b \log \left(c x^n\right)\right)}{4 e}-\frac{1}{8} x^2 \left(a+b \log \left(c x^n\right)\right)+\frac{b n \log (1-e x)}{4 e^2}-\frac{1}{4} b n x^2 \log (1-e x)+\frac{b n x}{2 e}+\frac{3}{16} b n x^2",1,"(b*n*x)/(2*e) + (3*b*n*x^2)/16 - (x*(a + b*Log[c*x^n]))/(4*e) - (x^2*(a + b*Log[c*x^n]))/8 + (b*n*Log[1 - e*x])/(4*e^2) - (b*n*x^2*Log[1 - e*x])/4 - ((a + b*Log[c*x^n])*Log[1 - e*x])/(4*e^2) + (x^2*(a + b*Log[c*x^n])*Log[1 - e*x])/4 - (b*n*PolyLog[2, e*x])/(4*e^2) - (b*n*x^2*PolyLog[2, e*x])/4 + (x^2*(a + b*Log[c*x^n])*PolyLog[2, e*x])/2","A",10,5,17,0.2941,1,"{2385, 2395, 43, 2376, 2391}"
210,1,106,0,0.114032,"\int \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(2,e x) \, dx","Int[(a + b*Log[c*x^n])*PolyLog[2, e*x],x]","x \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)-b n x \text{PolyLog}(2,e x)-\frac{b n \text{PolyLog}(2,e x)}{e}-\frac{(1-e x) \log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{e}-x \left(a+b \log \left(c x^n\right)\right)+\frac{2 b n (1-e x) \log (1-e x)}{e}+3 b n x","x \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)-b n x \text{PolyLog}(2,e x)-\frac{b n \text{PolyLog}(2,e x)}{e}-\frac{(1-e x) \log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{e}-x \left(a+b \log \left(c x^n\right)\right)+\frac{2 b n (1-e x) \log (1-e x)}{e}+3 b n x",1,"3*b*n*x - x*(a + b*Log[c*x^n]) + (2*b*n*(1 - e*x)*Log[1 - e*x])/e - ((1 - e*x)*(a + b*Log[c*x^n])*Log[1 - e*x])/e - (b*n*PolyLog[2, e*x])/e - b*n*x*PolyLog[2, e*x] + x*(a + b*Log[c*x^n])*PolyLog[2, e*x]","A",10,8,16,0.5000,1,"{2381, 2389, 2295, 2370, 2411, 43, 2351, 2315}"
211,1,26,0,0.0293442,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(2,e x)}{x} \, dx","Int[((a + b*Log[c*x^n])*PolyLog[2, e*x])/x,x]","\text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)-b n \text{PolyLog}(4,e x)","\text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)-b n \text{PolyLog}(4,e x)",1,"(a + b*Log[c*x^n])*PolyLog[3, e*x] - b*n*PolyLog[4, e*x]","A",2,2,19,0.1053,1,"{2383, 6589}"
212,1,142,0,0.1136849,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(2,e x)}{x^2} \, dx","Int[((a + b*Log[c*x^n])*PolyLog[2, e*x])/x^2,x]","-\frac{\text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)}{x}-b e n \text{PolyLog}(2,e x)-\frac{b n \text{PolyLog}(2,e x)}{x}+e \log (x) \left(a+b \log \left(c x^n\right)\right)-e \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{1}{2} b e n \log ^2(x)+2 b e n \log (x)-2 b e n \log (1-e x)+\frac{2 b n \log (1-e x)}{x}","-\frac{\text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)}{x}-b e n \text{PolyLog}(2,e x)-\frac{b n \text{PolyLog}(2,e x)}{x}+e \log (x) \left(a+b \log \left(c x^n\right)\right)-e \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{1}{2} b e n \log ^2(x)+2 b e n \log (x)-2 b e n \log (1-e x)+\frac{2 b n \log (1-e x)}{x}",1,"2*b*e*n*Log[x] - (b*e*n*Log[x]^2)/2 + e*Log[x]*(a + b*Log[c*x^n]) - 2*b*e*n*Log[1 - e*x] + (2*b*n*Log[1 - e*x])/x - e*(a + b*Log[c*x^n])*Log[1 - e*x] + ((a + b*Log[c*x^n])*Log[1 - e*x])/x - b*e*n*PolyLog[2, e*x] - (b*n*PolyLog[2, e*x])/x - ((a + b*Log[c*x^n])*PolyLog[2, e*x])/x","A",13,8,19,0.4211,1,"{2385, 2395, 36, 29, 31, 2376, 2301, 2391}"
213,1,202,0,0.1572902,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(2,e x)}{x^3} \, dx","Int[((a + b*Log[c*x^n])*PolyLog[2, e*x])/x^3,x]","-\frac{\text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{4} b e^2 n \text{PolyLog}(2,e x)-\frac{b n \text{PolyLog}(2,e x)}{4 x^2}+\frac{1}{4} e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} e^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{e \left(a+b \log \left(c x^n\right)\right)}{4 x}+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}-\frac{1}{8} b e^2 n \log ^2(x)+\frac{1}{4} b e^2 n \log (x)-\frac{1}{4} b e^2 n \log (1-e x)+\frac{b n \log (1-e x)}{4 x^2}-\frac{b e n}{2 x}","-\frac{\text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{4} b e^2 n \text{PolyLog}(2,e x)-\frac{b n \text{PolyLog}(2,e x)}{4 x^2}+\frac{1}{4} e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{4} e^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{e \left(a+b \log \left(c x^n\right)\right)}{4 x}+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}-\frac{1}{8} b e^2 n \log ^2(x)+\frac{1}{4} b e^2 n \log (x)-\frac{1}{4} b e^2 n \log (1-e x)+\frac{b n \log (1-e x)}{4 x^2}-\frac{b e n}{2 x}",1,"-(b*e*n)/(2*x) + (b*e^2*n*Log[x])/4 - (b*e^2*n*Log[x]^2)/8 - (e*(a + b*Log[c*x^n]))/(4*x) + (e^2*Log[x]*(a + b*Log[c*x^n]))/4 - (b*e^2*n*Log[1 - e*x])/4 + (b*n*Log[1 - e*x])/(4*x^2) - (e^2*(a + b*Log[c*x^n])*Log[1 - e*x])/4 + ((a + b*Log[c*x^n])*Log[1 - e*x])/(4*x^2) - (b*e^2*n*PolyLog[2, e*x])/4 - (b*n*PolyLog[2, e*x])/(4*x^2) - ((a + b*Log[c*x^n])*PolyLog[2, e*x])/(2*x^2)","A",11,6,19,0.3158,1,"{2385, 2395, 44, 2376, 2301, 2391}"
214,1,253,0,0.2543565,"\int x^2 \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(3,e x) \, dx","Int[x^2*(a + b*Log[c*x^n])*PolyLog[3, e*x],x]","-\frac{1}{9} x^3 \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} x^3 \text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)+\frac{b n \text{PolyLog}(2,e x)}{27 e^3}+\frac{2}{27} b n x^3 \text{PolyLog}(2,e x)-\frac{1}{9} b n x^3 \text{PolyLog}(3,e x)+\frac{x \left(a+b \log \left(c x^n\right)\right)}{27 e^2}+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{27 e^3}-\frac{1}{27} x^3 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{54 e}+\frac{1}{81} x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{2 b n x}{27 e^2}-\frac{b n \log (1-e x)}{27 e^3}-\frac{b n x^2}{36 e}+\frac{1}{27} b n x^3 \log (1-e x)-\frac{4}{243} b n x^3","-\frac{1}{9} x^3 \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{3} x^3 \text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)+\frac{b n \text{PolyLog}(2,e x)}{27 e^3}+\frac{2}{27} b n x^3 \text{PolyLog}(2,e x)-\frac{1}{9} b n x^3 \text{PolyLog}(3,e x)+\frac{x \left(a+b \log \left(c x^n\right)\right)}{27 e^2}+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{27 e^3}-\frac{1}{27} x^3 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{x^2 \left(a+b \log \left(c x^n\right)\right)}{54 e}+\frac{1}{81} x^3 \left(a+b \log \left(c x^n\right)\right)-\frac{2 b n x}{27 e^2}-\frac{b n \log (1-e x)}{27 e^3}-\frac{b n x^2}{36 e}+\frac{1}{27} b n x^3 \log (1-e x)-\frac{4}{243} b n x^3",1,"(-2*b*n*x)/(27*e^2) - (b*n*x^2)/(36*e) - (4*b*n*x^3)/243 + (x*(a + b*Log[c*x^n]))/(27*e^2) + (x^2*(a + b*Log[c*x^n]))/(54*e) + (x^3*(a + b*Log[c*x^n]))/81 - (b*n*Log[1 - e*x])/(27*e^3) + (b*n*x^3*Log[1 - e*x])/27 + ((a + b*Log[c*x^n])*Log[1 - e*x])/(27*e^3) - (x^3*(a + b*Log[c*x^n])*Log[1 - e*x])/27 + (b*n*PolyLog[2, e*x])/(27*e^3) + (2*b*n*x^3*PolyLog[2, e*x])/27 - (x^3*(a + b*Log[c*x^n])*PolyLog[2, e*x])/9 - (b*n*x^3*PolyLog[3, e*x])/9 + (x^3*(a + b*Log[c*x^n])*PolyLog[3, e*x])/3","A",15,6,19,0.3158,1,"{2385, 2395, 43, 2376, 2391, 6591}"
215,1,221,0,0.1896055,"\int x \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(3,e x) \, dx","Int[x*(a + b*Log[c*x^n])*PolyLog[3, e*x],x]","-\frac{1}{4} x^2 \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} x^2 \text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)+\frac{b n \text{PolyLog}(2,e x)}{8 e^2}+\frac{1}{4} b n x^2 \text{PolyLog}(2,e x)-\frac{1}{4} b n x^2 \text{PolyLog}(3,e x)+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{8 e^2}-\frac{1}{8} x^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{x \left(a+b \log \left(c x^n\right)\right)}{8 e}+\frac{1}{16} x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{3 b n \log (1-e x)}{16 e^2}+\frac{3}{16} b n x^2 \log (1-e x)-\frac{5 b n x}{16 e}-\frac{1}{8} b n x^2","-\frac{1}{4} x^2 \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)+\frac{1}{2} x^2 \text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)+\frac{b n \text{PolyLog}(2,e x)}{8 e^2}+\frac{1}{4} b n x^2 \text{PolyLog}(2,e x)-\frac{1}{4} b n x^2 \text{PolyLog}(3,e x)+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{8 e^2}-\frac{1}{8} x^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{x \left(a+b \log \left(c x^n\right)\right)}{8 e}+\frac{1}{16} x^2 \left(a+b \log \left(c x^n\right)\right)-\frac{3 b n \log (1-e x)}{16 e^2}+\frac{3}{16} b n x^2 \log (1-e x)-\frac{5 b n x}{16 e}-\frac{1}{8} b n x^2",1,"(-5*b*n*x)/(16*e) - (b*n*x^2)/8 + (x*(a + b*Log[c*x^n]))/(8*e) + (x^2*(a + b*Log[c*x^n]))/16 - (3*b*n*Log[1 - e*x])/(16*e^2) + (3*b*n*x^2*Log[1 - e*x])/16 + ((a + b*Log[c*x^n])*Log[1 - e*x])/(8*e^2) - (x^2*(a + b*Log[c*x^n])*Log[1 - e*x])/8 + (b*n*PolyLog[2, e*x])/(8*e^2) + (b*n*x^2*PolyLog[2, e*x])/4 - (x^2*(a + b*Log[c*x^n])*PolyLog[2, e*x])/4 - (b*n*x^2*PolyLog[3, e*x])/4 + (x^2*(a + b*Log[c*x^n])*PolyLog[3, e*x])/2","A",15,6,17,0.3529,1,"{2385, 2395, 43, 2376, 2391, 6591}"
216,1,131,0,0.1273967,"\int \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(3,e x) \, dx","Int[(a + b*Log[c*x^n])*PolyLog[3, e*x],x]","-x \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)+x \text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)+2 b n x \text{PolyLog}(2,e x)-b n x \text{PolyLog}(3,e x)+\frac{b n \text{PolyLog}(2,e x)}{e}+\frac{(1-e x) \log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{e}+x \left(a+b \log \left(c x^n\right)\right)-\frac{3 b n (1-e x) \log (1-e x)}{e}-4 b n x","-x \text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)+x \text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)+2 b n x \text{PolyLog}(2,e x)-b n x \text{PolyLog}(3,e x)+\frac{b n \text{PolyLog}(2,e x)}{e}+\frac{(1-e x) \log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{e}+x \left(a+b \log \left(c x^n\right)\right)-\frac{3 b n (1-e x) \log (1-e x)}{e}-4 b n x",1,"-4*b*n*x + x*(a + b*Log[c*x^n]) - (3*b*n*(1 - e*x)*Log[1 - e*x])/e + ((1 - e*x)*(a + b*Log[c*x^n])*Log[1 - e*x])/e + (b*n*PolyLog[2, e*x])/e + 2*b*n*x*PolyLog[2, e*x] - x*(a + b*Log[c*x^n])*PolyLog[2, e*x] - b*n*x*PolyLog[3, e*x] + x*(a + b*Log[c*x^n])*PolyLog[3, e*x]","A",14,9,16,0.5625,1,"{2381, 2389, 2295, 2370, 2411, 43, 2351, 2315, 6586}"
217,1,26,0,0.0282443,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(3,e x)}{x} \, dx","Int[((a + b*Log[c*x^n])*PolyLog[3, e*x])/x,x]","\text{PolyLog}(4,e x) \left(a+b \log \left(c x^n\right)\right)-b n \text{PolyLog}(5,e x)","\text{PolyLog}(4,e x) \left(a+b \log \left(c x^n\right)\right)-b n \text{PolyLog}(5,e x)",1,"(a + b*Log[c*x^n])*PolyLog[4, e*x] - b*n*PolyLog[5, e*x]","A",2,2,19,0.1053,1,"{2383, 6589}"
218,1,174,0,0.1556634,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(3,e x)}{x^2} \, dx","Int[((a + b*Log[c*x^n])*PolyLog[3, e*x])/x^2,x]","-\frac{\text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{\text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)}{x}-b e n \text{PolyLog}(2,e x)-\frac{2 b n \text{PolyLog}(2,e x)}{x}-\frac{b n \text{PolyLog}(3,e x)}{x}+e \log (x) \left(a+b \log \left(c x^n\right)\right)-e \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{1}{2} b e n \log ^2(x)+3 b e n \log (x)-3 b e n \log (1-e x)+\frac{3 b n \log (1-e x)}{x}","-\frac{\text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{\text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)}{x}-b e n \text{PolyLog}(2,e x)-\frac{2 b n \text{PolyLog}(2,e x)}{x}-\frac{b n \text{PolyLog}(3,e x)}{x}+e \log (x) \left(a+b \log \left(c x^n\right)\right)-e \log (1-e x) \left(a+b \log \left(c x^n\right)\right)+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{x}-\frac{1}{2} b e n \log ^2(x)+3 b e n \log (x)-3 b e n \log (1-e x)+\frac{3 b n \log (1-e x)}{x}",1,"3*b*e*n*Log[x] - (b*e*n*Log[x]^2)/2 + e*Log[x]*(a + b*Log[c*x^n]) - 3*b*e*n*Log[1 - e*x] + (3*b*n*Log[1 - e*x])/x - e*(a + b*Log[c*x^n])*Log[1 - e*x] + ((a + b*Log[c*x^n])*Log[1 - e*x])/x - b*e*n*PolyLog[2, e*x] - (2*b*n*PolyLog[2, e*x])/x - ((a + b*Log[c*x^n])*PolyLog[2, e*x])/x - (b*n*PolyLog[3, e*x])/x - ((a + b*Log[c*x^n])*PolyLog[3, e*x])/x","A",19,9,19,0.4737,1,"{2385, 2395, 36, 29, 31, 2376, 2301, 2391, 6591}"
219,1,238,0,0.2176867,"\int \frac{\left(a+b \log \left(c x^n\right)\right) \text{PolyLog}(3,e x)}{x^3} \, dx","Int[((a + b*Log[c*x^n])*PolyLog[3, e*x])/x^3,x]","-\frac{\text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}-\frac{\text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{8} b e^2 n \text{PolyLog}(2,e x)-\frac{b n \text{PolyLog}(2,e x)}{4 x^2}-\frac{b n \text{PolyLog}(3,e x)}{4 x^2}+\frac{1}{8} e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{8} e^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{e \left(a+b \log \left(c x^n\right)\right)}{8 x}+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{8 x^2}-\frac{1}{16} b e^2 n \log ^2(x)+\frac{3}{16} b e^2 n \log (x)-\frac{3}{16} b e^2 n \log (1-e x)+\frac{3 b n \log (1-e x)}{16 x^2}-\frac{5 b e n}{16 x}","-\frac{\text{PolyLog}(2,e x) \left(a+b \log \left(c x^n\right)\right)}{4 x^2}-\frac{\text{PolyLog}(3,e x) \left(a+b \log \left(c x^n\right)\right)}{2 x^2}-\frac{1}{8} b e^2 n \text{PolyLog}(2,e x)-\frac{b n \text{PolyLog}(2,e x)}{4 x^2}-\frac{b n \text{PolyLog}(3,e x)}{4 x^2}+\frac{1}{8} e^2 \log (x) \left(a+b \log \left(c x^n\right)\right)-\frac{1}{8} e^2 \log (1-e x) \left(a+b \log \left(c x^n\right)\right)-\frac{e \left(a+b \log \left(c x^n\right)\right)}{8 x}+\frac{\log (1-e x) \left(a+b \log \left(c x^n\right)\right)}{8 x^2}-\frac{1}{16} b e^2 n \log ^2(x)+\frac{3}{16} b e^2 n \log (x)-\frac{3}{16} b e^2 n \log (1-e x)+\frac{3 b n \log (1-e x)}{16 x^2}-\frac{5 b e n}{16 x}",1,"(-5*b*e*n)/(16*x) + (3*b*e^2*n*Log[x])/16 - (b*e^2*n*Log[x]^2)/16 - (e*(a + b*Log[c*x^n]))/(8*x) + (e^2*Log[x]*(a + b*Log[c*x^n]))/8 - (3*b*e^2*n*Log[1 - e*x])/16 + (3*b*n*Log[1 - e*x])/(16*x^2) - (e^2*(a + b*Log[c*x^n])*Log[1 - e*x])/8 + ((a + b*Log[c*x^n])*Log[1 - e*x])/(8*x^2) - (b*e^2*n*PolyLog[2, e*x])/8 - (b*n*PolyLog[2, e*x])/(4*x^2) - ((a + b*Log[c*x^n])*PolyLog[2, e*x])/(4*x^2) - (b*n*PolyLog[3, e*x])/(4*x^2) - ((a + b*Log[c*x^n])*PolyLog[3, e*x])/(2*x^2)","A",16,7,19,0.3684,1,"{2385, 2395, 44, 2376, 2301, 2391, 6591}"
220,0,0,0,0.0215918,"\int -(d x)^m \left(a+b \log \left(c x^n\right)\right) \log \left(1-e x^q\right) \, dx","Int[-((d*x)^m*(a + b*Log[c*x^n])*Log[1 - e*x^q]),x]","\int -(d x)^m \left(a+b \log \left(c x^n\right)\right) \log \left(1-e x^q\right) \, dx","-\text{Int}\left((d x)^m \log \left(1-e x^q\right) \left(a+b \log \left(c x^n\right)\right),x\right)",0,"-Defer[Int][(d*x)^m*(a + b*Log[c*x^n])*Log[1 - e*x^q], x]","A",0,0,0,0,-1,"{}"
221,0,0,0,0.1036052,"\int (d x)^m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,e x^q\right) \, dx","Int[(d*x)^m*(a + b*Log[c*x^n])*PolyLog[2, e*x^q],x]","\int (d x)^m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(2,e x^q\right) \, dx","\frac{q \text{Int}\left((d x)^m \log \left(1-e x^q\right) \left(a+b \log \left(c x^n\right)\right),x\right)}{m+1}+\frac{(d x)^{m+1} \text{PolyLog}\left(2,e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{d (m+1)}-\frac{b n (d x)^{m+1} \text{PolyLog}\left(2,e x^q\right)}{d (m+1)^2}-\frac{b e n q^2 x^{q+1} (d x)^m \, _2F_1\left(1,\frac{m+q+1}{q};\frac{m+2 q+1}{q};e x^q\right)}{(m+1)^3 (m+q+1)}-\frac{b n q (d x)^{m+1} \log \left(1-e x^q\right)}{d (m+1)^3}",0,"-((b*e*n*q^2*x^(1 + q)*(d*x)^m*Hypergeometric2F1[1, (1 + m + q)/q, (1 + m + 2*q)/q, e*x^q])/((1 + m)^3*(1 + m + q))) - (b*n*q*(d*x)^(1 + m)*Log[1 - e*x^q])/(d*(1 + m)^3) - (b*n*(d*x)^(1 + m)*PolyLog[2, e*x^q])/(d*(1 + m)^2) + ((d*x)^(1 + m)*(a + b*Log[c*x^n])*PolyLog[2, e*x^q])/(d*(1 + m)) + (q*Defer[Int][(d*x)^m*(a + b*Log[c*x^n])*Log[1 - e*x^q], x])/(1 + m)","A",0,0,0,0,-1,"{}"
222,0,0,0,0.2165041,"\int (d x)^m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,e x^q\right) \, dx","Int[(d*x)^m*(a + b*Log[c*x^n])*PolyLog[3, e*x^q],x]","\int (d x)^m \left(a+b \log \left(c x^n\right)\right) \text{PolyLog}\left(3,e x^q\right) \, dx","-\frac{q^2 \text{Int}\left((d x)^m \log \left(1-e x^q\right) \left(a+b \log \left(c x^n\right)\right),x\right)}{(m+1)^2}-\frac{q (d x)^{m+1} \text{PolyLog}\left(2,e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{d (m+1)^2}+\frac{(d x)^{m+1} \text{PolyLog}\left(3,e x^q\right) \left(a+b \log \left(c x^n\right)\right)}{d (m+1)}+\frac{2 b n q (d x)^{m+1} \text{PolyLog}\left(2,e x^q\right)}{d (m+1)^3}-\frac{b n (d x)^{m+1} \text{PolyLog}\left(3,e x^q\right)}{d (m+1)^2}+\frac{2 b e n q^3 x^{q+1} (d x)^m \, _2F_1\left(1,\frac{m+q+1}{q};\frac{m+2 q+1}{q};e x^q\right)}{(m+1)^4 (m+q+1)}+\frac{2 b n q^2 (d x)^{m+1} \log \left(1-e x^q\right)}{d (m+1)^4}",0,"(2*b*e*n*q^3*x^(1 + q)*(d*x)^m*Hypergeometric2F1[1, (1 + m + q)/q, (1 + m + 2*q)/q, e*x^q])/((1 + m)^4*(1 + m + q)) + (2*b*n*q^2*(d*x)^(1 + m)*Log[1 - e*x^q])/(d*(1 + m)^4) + (2*b*n*q*(d*x)^(1 + m)*PolyLog[2, e*x^q])/(d*(1 + m)^3) - (q*(d*x)^(1 + m)*(a + b*Log[c*x^n])*PolyLog[2, e*x^q])/(d*(1 + m)^2) - (b*n*(d*x)^(1 + m)*PolyLog[3, e*x^q])/(d*(1 + m)^2) + ((d*x)^(1 + m)*(a + b*Log[c*x^n])*PolyLog[3, e*x^q])/(d*(1 + m)) - (q^2*Defer[Int][(d*x)^m*(a + b*Log[c*x^n])*Log[1 - e*x^q], x])/(1 + m)^2","A",0,0,0,0,-1,"{}"
223,1,27,0,0.0310341,"\int x^2 \log \left(c \left(b x^n\right)^p\right) \, dx","Int[x^2*Log[c*(b*x^n)^p],x]","\frac{1}{3} x^3 \log \left(c \left(b x^n\right)^p\right)-\frac{1}{9} n p x^3","\frac{1}{3} x^3 \log \left(c \left(b x^n\right)^p\right)-\frac{1}{9} n p x^3",1,"-(n*p*x^3)/9 + (x^3*Log[c*(b*x^n)^p])/3","A",2,2,14,0.1429,1,"{2304, 2445}"
224,1,27,0,0.016509,"\int x \log \left(c \left(b x^n\right)^p\right) \, dx","Int[x*Log[c*(b*x^n)^p],x]","\frac{1}{2} x^2 \log \left(c \left(b x^n\right)^p\right)-\frac{1}{4} n p x^2","\frac{1}{2} x^2 \log \left(c \left(b x^n\right)^p\right)-\frac{1}{4} n p x^2",1,"-(n*p*x^2)/4 + (x^2*Log[c*(b*x^n)^p])/2","A",2,2,12,0.1667,1,"{2304, 2445}"
225,1,18,0,0.0070388,"\int \log \left(c \left(b x^n\right)^p\right) \, dx","Int[Log[c*(b*x^n)^p],x]","x \log \left(c \left(b x^n\right)^p\right)-n p x","x \log \left(c \left(b x^n\right)^p\right)-n p x",1,"-(n*p*x) + x*Log[c*(b*x^n)^p]","A",2,2,10,0.2000,1,"{2295, 2445}"
226,1,22,0,0.0299711,"\int \frac{\log \left(c \left(b x^n\right)^p\right)}{x} \, dx","Int[Log[c*(b*x^n)^p]/x,x]","\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{2 n p}","\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{2 n p}",1,"Log[c*(b*x^n)^p]^2/(2*n*p)","A",2,2,14,0.1429,1,"{2301, 2445}"
227,1,23,0,0.0311087,"\int \frac{\log \left(c \left(b x^n\right)^p\right)}{x^2} \, dx","Int[Log[c*(b*x^n)^p]/x^2,x]","-\frac{\log \left(c \left(b x^n\right)^p\right)}{x}-\frac{n p}{x}","-\frac{\log \left(c \left(b x^n\right)^p\right)}{x}-\frac{n p}{x}",1,"-((n*p)/x) - Log[c*(b*x^n)^p]/x","A",2,2,14,0.1429,1,"{2304, 2445}"
228,1,27,0,0.0291405,"\int \frac{\log \left(c \left(b x^n\right)^p\right)}{x^3} \, dx","Int[Log[c*(b*x^n)^p]/x^3,x]","-\frac{\log \left(c \left(b x^n\right)^p\right)}{2 x^2}-\frac{n p}{4 x^2}","-\frac{\log \left(c \left(b x^n\right)^p\right)}{2 x^2}-\frac{n p}{4 x^2}",1,"-(n*p)/(4*x^2) - Log[c*(b*x^n)^p]/(2*x^2)","A",2,2,14,0.1429,1,"{2304, 2445}"
229,1,27,0,0.0296407,"\int \frac{\log \left(c \left(b x^n\right)^p\right)}{x^4} \, dx","Int[Log[c*(b*x^n)^p]/x^4,x]","-\frac{\log \left(c \left(b x^n\right)^p\right)}{3 x^3}-\frac{n p}{9 x^3}","-\frac{\log \left(c \left(b x^n\right)^p\right)}{3 x^3}-\frac{n p}{9 x^3}",1,"-(n*p)/(9*x^3) - Log[c*(b*x^n)^p]/(3*x^3)","A",2,2,14,0.1429,1,"{2304, 2445}"
230,1,52,0,0.0708018,"\int x^2 \log ^2\left(c \left(b x^n\right)^p\right) \, dx","Int[x^2*Log[c*(b*x^n)^p]^2,x]","\frac{1}{3} x^3 \log ^2\left(c \left(b x^n\right)^p\right)-\frac{2}{9} n p x^3 \log \left(c \left(b x^n\right)^p\right)+\frac{2}{27} n^2 p^2 x^3","\frac{1}{3} x^3 \log ^2\left(c \left(b x^n\right)^p\right)-\frac{2}{9} n p x^3 \log \left(c \left(b x^n\right)^p\right)+\frac{2}{27} n^2 p^2 x^3",1,"(2*n^2*p^2*x^3)/27 - (2*n*p*x^3*Log[c*(b*x^n)^p])/9 + (x^3*Log[c*(b*x^n)^p]^2)/3","A",3,3,16,0.1875,1,"{2305, 2304, 2445}"
231,1,52,0,0.0446348,"\int x \log ^2\left(c \left(b x^n\right)^p\right) \, dx","Int[x*Log[c*(b*x^n)^p]^2,x]","\frac{1}{2} x^2 \log ^2\left(c \left(b x^n\right)^p\right)-\frac{1}{2} n p x^2 \log \left(c \left(b x^n\right)^p\right)+\frac{1}{4} n^2 p^2 x^2","\frac{1}{2} x^2 \log ^2\left(c \left(b x^n\right)^p\right)-\frac{1}{2} n p x^2 \log \left(c \left(b x^n\right)^p\right)+\frac{1}{4} n^2 p^2 x^2",1,"(n^2*p^2*x^2)/4 - (n*p*x^2*Log[c*(b*x^n)^p])/2 + (x^2*Log[c*(b*x^n)^p]^2)/2","A",3,3,14,0.2143,1,"{2305, 2304, 2445}"
232,1,39,0,0.0220322,"\int \log ^2\left(c \left(b x^n\right)^p\right) \, dx","Int[Log[c*(b*x^n)^p]^2,x]","x \log ^2\left(c \left(b x^n\right)^p\right)-2 n p x \log \left(c \left(b x^n\right)^p\right)+2 n^2 p^2 x","x \log ^2\left(c \left(b x^n\right)^p\right)-2 n p x \log \left(c \left(b x^n\right)^p\right)+2 n^2 p^2 x",1,"2*n^2*p^2*x - 2*n*p*x*Log[c*(b*x^n)^p] + x*Log[c*(b*x^n)^p]^2","A",3,3,12,0.2500,1,"{2296, 2295, 2445}"
233,1,22,0,0.0496139,"\int \frac{\log ^2\left(c \left(b x^n\right)^p\right)}{x} \, dx","Int[Log[c*(b*x^n)^p]^2/x,x]","\frac{\log ^3\left(c \left(b x^n\right)^p\right)}{3 n p}","\frac{\log ^3\left(c \left(b x^n\right)^p\right)}{3 n p}",1,"Log[c*(b*x^n)^p]^3/(3*n*p)","A",3,3,16,0.1875,1,"{2302, 30, 2445}"
234,1,46,0,0.0701019,"\int \frac{\log ^2\left(c \left(b x^n\right)^p\right)}{x^2} \, dx","Int[Log[c*(b*x^n)^p]^2/x^2,x]","-\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{x}-\frac{2 n p \log \left(c \left(b x^n\right)^p\right)}{x}-\frac{2 n^2 p^2}{x}","-\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{x}-\frac{2 n p \log \left(c \left(b x^n\right)^p\right)}{x}-\frac{2 n^2 p^2}{x}",1,"(-2*n^2*p^2)/x - (2*n*p*Log[c*(b*x^n)^p])/x - Log[c*(b*x^n)^p]^2/x","A",3,3,16,0.1875,1,"{2305, 2304, 2445}"
235,1,52,0,0.0696167,"\int \frac{\log ^2\left(c \left(b x^n\right)^p\right)}{x^3} \, dx","Int[Log[c*(b*x^n)^p]^2/x^3,x]","-\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{2 x^2}-\frac{n p \log \left(c \left(b x^n\right)^p\right)}{2 x^2}-\frac{n^2 p^2}{4 x^2}","-\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{2 x^2}-\frac{n p \log \left(c \left(b x^n\right)^p\right)}{2 x^2}-\frac{n^2 p^2}{4 x^2}",1,"-(n^2*p^2)/(4*x^2) - (n*p*Log[c*(b*x^n)^p])/(2*x^2) - Log[c*(b*x^n)^p]^2/(2*x^2)","A",3,3,16,0.1875,1,"{2305, 2304, 2445}"
236,1,52,0,0.0702828,"\int \frac{\log ^2\left(c \left(b x^n\right)^p\right)}{x^4} \, dx","Int[Log[c*(b*x^n)^p]^2/x^4,x]","-\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{3 x^3}-\frac{2 n p \log \left(c \left(b x^n\right)^p\right)}{9 x^3}-\frac{2 n^2 p^2}{27 x^3}","-\frac{\log ^2\left(c \left(b x^n\right)^p\right)}{3 x^3}-\frac{2 n p \log \left(c \left(b x^n\right)^p\right)}{9 x^3}-\frac{2 n^2 p^2}{27 x^3}",1,"(-2*n^2*p^2)/(27*x^3) - (2*n*p*Log[c*(b*x^n)^p])/(9*x^3) - Log[c*(b*x^n)^p]^2/(3*x^3)","A",3,3,16,0.1875,1,"{2305, 2304, 2445}"
237,1,135,0,0.2208543,"\int (e x)^q \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^3 \, dx","Int[(e*x)^q*(a + b*Log[c*(d*x^m)^n])^3,x]","\frac{6 b^2 m^2 n^2 (e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{e (q+1)^3}+\frac{(e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^3}{e (q+1)}-\frac{3 b m n (e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2}{e (q+1)^2}-\frac{6 b^3 m^3 n^3 (e x)^{q+1}}{e (q+1)^4}","\frac{6 b^2 m^2 n^2 (e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{e (q+1)^3}+\frac{(e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^3}{e (q+1)}-\frac{3 b m n (e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2}{e (q+1)^2}-\frac{6 b^3 m^3 n^3 (e x)^{q+1}}{e (q+1)^4}",1,"(-6*b^3*m^3*n^3*(e*x)^(1 + q))/(e*(1 + q)^4) + (6*b^2*m^2*n^2*(e*x)^(1 + q)*(a + b*Log[c*(d*x^m)^n]))/(e*(1 + q)^3) - (3*b*m*n*(e*x)^(1 + q)*(a + b*Log[c*(d*x^m)^n])^2)/(e*(1 + q)^2) + ((e*x)^(1 + q)*(a + b*Log[c*(d*x^m)^n])^3)/(e*(1 + q))","A",4,3,22,0.1364,1,"{2305, 2304, 2445}"
238,1,93,0,0.1262682,"\int (e x)^q \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2 \, dx","Int[(e*x)^q*(a + b*Log[c*(d*x^m)^n])^2,x]","\frac{(e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2}{e (q+1)}-\frac{2 b m n (e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{e (q+1)^2}+\frac{2 b^2 m^2 n^2 (e x)^{q+1}}{e (q+1)^3}","\frac{(e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2}{e (q+1)}-\frac{2 b m n (e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{e (q+1)^2}+\frac{2 b^2 m^2 n^2 (e x)^{q+1}}{e (q+1)^3}",1,"(2*b^2*m^2*n^2*(e*x)^(1 + q))/(e*(1 + q)^3) - (2*b*m*n*(e*x)^(1 + q)*(a + b*Log[c*(d*x^m)^n]))/(e*(1 + q)^2) + ((e*x)^(1 + q)*(a + b*Log[c*(d*x^m)^n])^2)/(e*(1 + q))","A",3,3,22,0.1364,1,"{2305, 2304, 2445}"
239,1,51,0,0.0457418,"\int (e x)^q \left(a+b \log \left(c \left(d x^m\right)^n\right)\right) \, dx","Int[(e*x)^q*(a + b*Log[c*(d*x^m)^n]),x]","\frac{(e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{e (q+1)}-\frac{b m n (e x)^{q+1}}{e (q+1)^2}","\frac{(e x)^{q+1} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{e (q+1)}-\frac{b m n (e x)^{q+1}}{e (q+1)^2}",1,"-((b*m*n*(e*x)^(1 + q))/(e*(1 + q)^2)) + ((e*x)^(1 + q)*(a + b*Log[c*(d*x^m)^n]))/(e*(1 + q))","A",2,2,20,0.1000,1,"{2304, 2445}"
240,1,86,0,0.1842672,"\int \frac{(e x)^q}{a+b \log \left(c \left(d x^m\right)^n\right)} \, dx","Int[(e*x)^q/(a + b*Log[c*(d*x^m)^n]),x]","\frac{(e x)^{q+1} e^{-\frac{a (q+1)}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{q+1}{m n}} \text{Ei}\left(\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{b e m n}","\frac{(e x)^{q+1} e^{-\frac{a (q+1)}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{q+1}{m n}} \text{Ei}\left(\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{b e m n}",1,"((e*x)^(1 + q)*ExpIntegralEi[((1 + q)*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)])/(b*e*E^((a*(1 + q))/(b*m*n))*m*n*(c*(d*x^m)^n)^((1 + q)/(m*n)))","A",3,3,22,0.1364,1,"{2310, 2178, 2445}"
241,1,127,0,0.2418098,"\int \frac{(e x)^q}{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^2} \, dx","Int[(e*x)^q/(a + b*Log[c*(d*x^m)^n])^2,x]","\frac{(q+1) (e x)^{q+1} e^{-\frac{a (q+1)}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{q+1}{m n}} \text{Ei}\left(\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{b^2 e m^2 n^2}-\frac{(e x)^{q+1}}{b e m n \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}","\frac{(q+1) (e x)^{q+1} e^{-\frac{a (q+1)}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{q+1}{m n}} \text{Ei}\left(\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{b^2 e m^2 n^2}-\frac{(e x)^{q+1}}{b e m n \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}",1,"((1 + q)*(e*x)^(1 + q)*ExpIntegralEi[((1 + q)*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)])/(b^2*e*E^((a*(1 + q))/(b*m*n))*m^2*n^2*(c*(d*x^m)^n)^((1 + q)/(m*n))) - (e*x)^(1 + q)/(b*e*m*n*(a + b*Log[c*(d*x^m)^n]))","A",4,4,22,0.1818,1,"{2306, 2310, 2178, 2445}"
242,1,134,0,0.1901156,"\int (e x)^q \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \, dx","Int[(e*x)^q*(a + b*Log[c*(d*x^m)^n])^p,x]","\frac{(e x)^{q+1} e^{-\frac{a (q+1)}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{q+1}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{e (q+1)}","\frac{(e x)^{q+1} e^{-\frac{a (q+1)}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{q+1}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{(q+1) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{e (q+1)}",1,"((e*x)^(1 + q)*Gamma[1 + p, -(((1 + q)*(a + b*Log[c*(d*x^m)^n]))/(b*m*n))]*(a + b*Log[c*(d*x^m)^n])^p)/(e*E^((a*(1 + q))/(b*m*n))*(1 + q)*(c*(d*x^m)^n)^((1 + q)/(m*n))*(-(((1 + q)*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)))^p)","A",3,3,22,0.1364,1,"{2310, 2181, 2445}"
243,1,117,0,0.1679436,"\int x^2 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \, dx","Int[x^2*(a + b*Log[c*(d*x^m)^n])^p,x]","3^{-p-1} x^3 e^{-\frac{3 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{3}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{3 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)","3^{-p-1} x^3 e^{-\frac{3 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{3}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{3 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)",1,"(3^(-1 - p)*x^3*Gamma[1 + p, (-3*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)]*(a + b*Log[c*(d*x^m)^n])^p)/(E^((3*a)/(b*m*n))*(c*(d*x^m)^n)^(3/(m*n))*(-((a + b*Log[c*(d*x^m)^n])/(b*m*n)))^p)","A",3,3,20,0.1500,1,"{2310, 2181, 2445}"
244,1,117,0,0.1334192,"\int x \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \, dx","Int[x*(a + b*Log[c*(d*x^m)^n])^p,x]","2^{-p-1} x^2 e^{-\frac{2 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{2}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)","2^{-p-1} x^2 e^{-\frac{2 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{2}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{2 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)",1,"(2^(-1 - p)*x^2*Gamma[1 + p, (-2*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)]*(a + b*Log[c*(d*x^m)^n])^p)/(E^((2*a)/(b*m*n))*(c*(d*x^m)^n)^(2/(m*n))*(-((a + b*Log[c*(d*x^m)^n])/(b*m*n)))^p)","A",3,3,18,0.1667,1,"{2310, 2181, 2445}"
245,1,108,0,0.09875,"\int \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \, dx","Int[(a + b*Log[c*(d*x^m)^n])^p,x]","x e^{-\frac{a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{1}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)","x e^{-\frac{a}{b m n}} \left(c \left(d x^m\right)^n\right)^{-\frac{1}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,-\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)",1,"(x*Gamma[1 + p, -((a + b*Log[c*(d*x^m)^n])/(b*m*n))]*(a + b*Log[c*(d*x^m)^n])^p)/(E^(a/(b*m*n))*(c*(d*x^m)^n)^(1/(m*n))*(-((a + b*Log[c*(d*x^m)^n])/(b*m*n)))^p)","A",3,3,16,0.1875,1,"{2300, 2181, 2445}"
246,1,33,0,0.0939415,"\int \frac{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p}{x} \, dx","Int[(a + b*Log[c*(d*x^m)^n])^p/x,x]","\frac{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^{p+1}}{b m n (p+1)}","\frac{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^{p+1}}{b m n (p+1)}",1,"(a + b*Log[c*(d*x^m)^n])^(1 + p)/(b*m*n*(1 + p))","A",3,3,20,0.1500,1,"{2302, 30, 2445}"
247,1,107,0,0.1595485,"\int \frac{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p}{x^2} \, dx","Int[(a + b*Log[c*(d*x^m)^n])^p/x^2,x]","-\frac{e^{\frac{a}{b m n}} \left(c \left(d x^m\right)^n\right)^{\frac{1}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)}{x}","-\frac{e^{\frac{a}{b m n}} \left(c \left(d x^m\right)^n\right)^{\frac{1}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)}{x}",1,"-((E^(a/(b*m*n))*(c*(d*x^m)^n)^(1/(m*n))*Gamma[1 + p, (a + b*Log[c*(d*x^m)^n])/(b*m*n)]*(a + b*Log[c*(d*x^m)^n])^p)/(x*((a + b*Log[c*(d*x^m)^n])/(b*m*n))^p))","A",3,3,20,0.1500,1,"{2310, 2181, 2445}"
248,1,117,0,0.1632997,"\int \frac{\left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p}{x^3} \, dx","Int[(a + b*Log[c*(d*x^m)^n])^p/x^3,x]","-\frac{2^{-p-1} e^{\frac{2 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{\frac{2}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,\frac{2 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{x^2}","-\frac{2^{-p-1} e^{\frac{2 a}{b m n}} \left(c \left(d x^m\right)^n\right)^{\frac{2}{m n}} \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)^p \left(\frac{a+b \log \left(c \left(d x^m\right)^n\right)}{b m n}\right)^{-p} \text{Gamma}\left(p+1,\frac{2 \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{b m n}\right)}{x^2}",1,"-((2^(-1 - p)*E^((2*a)/(b*m*n))*(c*(d*x^m)^n)^(2/(m*n))*Gamma[1 + p, (2*(a + b*Log[c*(d*x^m)^n]))/(b*m*n)]*(a + b*Log[c*(d*x^m)^n])^p)/(x^2*((a + b*Log[c*(d*x^m)^n])/(b*m*n))^p))","A",3,3,20,0.1500,1,"{2310, 2181, 2445}"
249,1,111,0,0.1615183,"\int \frac{a+b \log \left(c \left(d x^m\right)^n\right)}{e+f x^2} \, dx","Int[(a + b*Log[c*(d*x^m)^n])/(e + f*x^2),x]","-\frac{i b m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{2 \sqrt{e} \sqrt{f}}+\frac{i b m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{2 \sqrt{e} \sqrt{f}}+\frac{\tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{\sqrt{e} \sqrt{f}}","-\frac{i b m n \text{PolyLog}\left(2,-\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{2 \sqrt{e} \sqrt{f}}+\frac{i b m n \text{PolyLog}\left(2,\frac{i \sqrt{f} x}{\sqrt{e}}\right)}{2 \sqrt{e} \sqrt{f}}+\frac{\tan ^{-1}\left(\frac{\sqrt{f} x}{\sqrt{e}}\right) \left(a+b \log \left(c \left(d x^m\right)^n\right)\right)}{\sqrt{e} \sqrt{f}}",1,"(ArcTan[(Sqrt[f]*x)/Sqrt[e]]*(a + b*Log[c*(d*x^m)^n]))/(Sqrt[e]*Sqrt[f]) - ((I/2)*b*m*n*PolyLog[2, ((-I)*Sqrt[f]*x)/Sqrt[e]])/(Sqrt[e]*Sqrt[f]) + ((I/2)*b*m*n*PolyLog[2, (I*Sqrt[f]*x)/Sqrt[e]])/(Sqrt[e]*Sqrt[f])","A",6,6,24,0.2500,1,"{205, 2324, 12, 4848, 2391, 2445}"